Peterson's SAT Prep Guide

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PETERSON’S®
®

SAT Prep Guide:
The Ultimate Guide to
Mastering the SAT®

About Peterson’s®
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TABLE OF CONTENTS
PART IV: WRITING STRATEGIES FOR THE
SAT® EXAM

Introduction to Peterson’s SAT   ® Prep Guide	������������������vii
The Peterson’s Suite of SAT  ® Products	�������������������������xi

PART I: BASICS FACTS ABOUT THE SAT®

1

4

ALL ABOUT THE SAT®

How the SAT ® Is Used for College Admissions	�����������4
When to Take the SAT ® (and SAT Subject Tests™)	������4
How Your Scores Are Reported	����������������������������������������5
How Often to Take the SAT ®	���������������������������������������������5
Registering for the SAT ®	�����������������������������������������������������5
Get to Know the Current SAT ® Exam Format	��������������7
Get to Know the SAT ® Question Types	��������������������������8
Evidence-Based Reading Test Section	��������������������������8
Writing and Language Test Section	�������������������������������14
Math Test Sections	���������������������������������������������������������������17
Grid-Ins	�������������������������������������������������������������������������������������20
SAT ® Essay (Optional)	����������������������������������������������������������24
The SAT ® Answer Sheet	������������������������������������������������������24
How the SAT ® Is Scored	������������������������������������������������������25
Strategies for SAT ® Success	�����������������������������������������������26
Make an SAT ® Study Plan	���������������������������������������������������27
Measuring Your Progress	���������������������������������������������������28
Simulate Test-Taking Conditions	�������������������������������������29
The Night Before and Day of the Exam	�������������������������31
Top 10 Strategies to Raise Your Score	����������������������������32
Summing It Up	����������������������������������������������������������������������33

5

PART II: THE DIAGNOSTIC TEST

2

THE DIAGNOSTIC TEST

Introduction to the Diagnostic Test	�������������������������������37
Answer Sheets	�����������������������������������������������������������������������39
Section 1: Reading Test	�������������������������������������������������������45
Section 2: Writing and Language Test	���������������������������57
Section 3: Math Test—No Calculator	�����������������������������69
Section 4: Math Test—Calculator	������������������������������������77
Essay	������������������������������������������������������������������������������������������93
Answer Keys and Explanations	����������������������������������������97
Computing Your Scores	������������������������������������������������������120

6

3

A Closer Look at the Evidence-Based
Reading Test	���������������������������������������������������������������������������129
Basic Steps for Answering Evidence-Based
Reading Questions	���������������������������������������������������������������130
Tips for Taking the Reading Test	��������������������������������������136
Strategies for Answering Specific Question Types	���138
Exercise: Evidence-Based Reading Test	������������������������139
Summing It Up	����������������������������������������������������������������������150

A Closer Look at the Writing and Language Test	������155
The Three Most Common Multiple-Choice
Editing Questions	�����������������������������������������������������������������156
Expression of Ideas Questions: Words In Context	�����157
Expression of Ideas Questions: Adding or
Deleting Text	��������������������������������������������������������������������������158
Expression of Ideas Questions:
Reordering Sentences	���������������������������������������������������������159
Expression of Ideas Questions: Combining
Sentencesand Using Transitional Words and
Phrases Correctly	������������������������������������������������������������������160
Graphic Organizer Questions	�������������������������������������������160
Exercise: Writing and Language Test	�����������������������������162
Summing It Up	����������������������������������������������������������������������171

ENGLISH LANGUAGE CONVENTIONS

Sentence Formation	������������������������������������������������������������174
Verb Tense, Mood, and Voice	��������������������������������������������181
Conventions of Usage	���������������������������������������������������������184
Agreement	������������������������������������������������������������������������������188
Frequently Confused Words	���������������������������������������������192
Conventions of Punctuation	���������������������������������������������225
Summing It Up	����������������������������������������������������������������������240

PART V: ESSAY WRITING STRATEGIES
FOR THE SAT®
THE SAT® ESSAY

A Closer Look at the Essay Question	������������������������������244
Pacing Your Writing	��������������������������������������������������������������244
Prewriting	��������������������������������������������������������������������������������244
Writing the Introduction	����������������������������������������������������246
Developing Your Ideas	��������������������������������������������������������248
Writing the Conclusion	�������������������������������������������������������250
The Scoring Rubric for the SAT® Essay	���������������������������252
Exercise: Practicing Your Essay Skills	������������������������������253
Additional Essay Writing Practice	�����������������������������������259
Summing It Up	����������������������������������������������������������������������262

PART III: READING STRATEGIES
FOR THE SAT®
EVIDENCE-BASED READING
TEST STRATEGIES

WRITING AND LANGUAGE
TEST STRATEGIES

7

PART VI: MATH STRATEGIES FOR
THE SAT®
MULTIPLE-CHOICE MATH

Why Multiple-Choice Math Is Easier	������������������������������267
Question Format	�������������������������������������������������������������������268
Solving Multiple-Choice Math Questions	��������������������269
Know When to Use Your Calculator	��������������������������������270
Learn the Most Important Multiple-Choice
Math Tips	���������������������������������������������������������������������������������271
Exercises: Multiple-Choice Math	�������������������������������������284
Summing It Up	����������������������������������������������������������������������296

8
9

GRID-IN STRATEGIES

Why Grid-Ins Are Easier Than You Think	�����������������������297
How to Record Your Answers	�������������������������������������������298
Guessing on Grid-Ins Can’t Hurt You	�����������������������������302
Exercises: Grid-Ins	�����������������������������������������������������������������303
Summing It Up	����������������������������������������������������������������������317

12

Functions	���������������������������������������������������������������������������������473
Exercises: Functions	�������������������������������������������������������������479
Integer and Rational Exponents	��������������������������������������482
Exercises: Integer and Rational Exponents	������������������485
Solving Complex Equations	����������������������������������������������488
Exercises: Solving Complex Equations	��������������������������492
Linear, Quadratic, and Exponential Functions	�����������496
Exercises: Linear, Quadratic, and
Exponential Functions	��������������������������������������������������������505
Summing It Up	����������������������������������������������������������������������511

NUMBERS AND OPERATIONS

Operations with Fractions	�������������������������������������������������320
Tests for Divisibility	��������������������������������������������������������������320
Exercises: Operations with Fractions	�����������������������������323
Word Problems Involving Fractions	�������������������������������325
Exercises: Word Problems Involving Fractions	�����������327
Complex Numbers	���������������������������������������������������������������333
Exercises: Complex Numbers	�������������������������������������������336
Direct and Inverse Variation	����������������������������������������������341
Exercises: Direct and Inverse Variation	��������������������������343
Finding Percents	�������������������������������������������������������������������347
Exercises: Finding Percents	�����������������������������������������������353
Percent Word Problems	������������������������������������������������������356
Exercises: Percent Word Problems	����������������������������������360
Summing It Up	����������������������������������������������������������������������365

13

10 BASIC ALGEBRA

Signed Numbers	�������������������������������������������������������������������367
Exercises: Signed Numbers	�����������������������������������������������368
Linear Equations	�������������������������������������������������������������������372
Simultaneous Equations	����������������������������������������������������380
Exercises: Simultaneous Equations	��������������������������������387
Exponents	�������������������������������������������������������������������������������392
Exercises: Exponents	�����������������������������������������������������������394
Quadratic Equations	������������������������������������������������������������397
Exercises: Quadratic Equations	����������������������������������������400
Literal Equations	�������������������������������������������������������������������403
Exercises: Literal Equations	�����������������������������������������������404
Roots and Radicals	���������������������������������������������������������������407
Exercises: Roots and Radicals	�������������������������������������������410
Monomials and Polynomials	��������������������������������������������413
Exercises: Monomials and Polynomials	������������������������416
Problem Solving in Algebra	����������������������������������������������419
Exercises: Problem Solving in Algebra	��������������������������424
Inequalities	�����������������������������������������������������������������������������427
Exercises: Inequalities	���������������������������������������������������������431
Summing It Up	����������������������������������������������������������������������434

11

GEOMETRY

Geometric Notation	������������������������������������������������������������435
Angle Measurement	����������������������������������������������������������437
Intersecting Lines	�����������������������������������������������������������������439
Area	��������������������������������������������������������������������������������������������441
Circles	����������������������������������������������������������������������������������������442
Volume	�������������������������������������������������������������������������������������445
Triangles	�����������������������������������������������������������������������������������447
Parallel Lines	���������������������������������������������������������������������������453
Coordinate Geometry	���������������������������������������������������������454
Exercises: Geometry	������������������������������������������������������������462
Summing It Up	����������������������������������������������������������������������472

FUNCTIONS AND INTERMEDIATE
ALGEBRA

DATA ANALYSIS, STATISTICS,
AND PROBABILITY

Averages	����������������������������������������������������������������������������������513
Weighted Average	����������������������������������������������������������������516
Exercises: Averages	��������������������������������������������������������������517
Probability	�������������������������������������������������������������������������������523
Exercises: Probability	�����������������������������������������������������������526
Data Interpretation	��������������������������������������������������������������532
Exercises: Date Interpretation	������������������������������������������538
Statistics	�����������������������������������������������������������������������������������545
Exercises: Statistics	���������������������������������������������������������������552
Summing It Up	����������������������������������������������������������������������558

PART VII: PRACTICE TESTS FOR
THE SAT® EXAM

14

SAT® PRACTICE TESTS

Introduction to the Practice Tests	�����������������������������������561
Practice Test 1	�������������������������������������������������������������������������563
Practice Test 1—Answer Keys and Explanations	�������619
Computing Your Scores	������������������������������������������������������643
Practice Test 2	�������������������������������������������������������������������������651
Practice Test 2—Answer Keys and Explanations	�������709
Computing Your Scores	������������������������������������������������������734
Practice Test 3	�������������������������������������������������������������������������741
Practice Test 3—Answer Keys and Explanations	�������801
Computing Your Scores	������������������������������������������������������827
Practice Test 4	�������������������������������������������������������������������������835
Practice Test 4—Answer Keys and Explanations	�������897
Computing Your Scores	������������������������������������������������������922
Practice Test 5	�������������������������������������������������������������������������929
Practice Test 5—Answer Keys and Explanations	�������987
Computing Your Scores	������������������������������������������������������1013

PART VIII: APPENDIX
Parents’ Guide to College Admission Testing	�������������1023

INTRODUCTION TO PETERSON’S SAT   ® PREP GUIDE
Whether you have three long months or just four short weeks to prepare for the exam, Peterson’s® SAT® Prep Guide can help you
develop a study plan that caters to your individual needs and personal timetable. These step-by-step plans are easy to follow and
remarkably effective. No matter which plan you select, begin by taking a diagnostic practice test.

The Diagnostic Practice Test and Process
The diagnostic practice test does more than give you testing experience. Easy-to-use diagnostic tables help you track your performance, identify your strengths, and pinpoint areas for improvement. At the end of the diagnostic testing process, you will know
which question formats are giving you the most difficulty. You will also know which topics to review in depth and which ones you
can spend less time on, whether they are algebra or geometry, literary analysis, or reading charts and graphs. By understanding your
testing profile, you can immediately address your weak areas by working through the relevant review chapters, learning the important
test-taking tips, and completing the additional practice exercises.

Five Full Practice Tests in This Book
When you have completed your formal review, take the practice tests to sharpen your skills further. Even if you understand the
redesigned SAT® perfectly, you still need to practice applying the methods you have learned in Peterson’s® SAT® Prep Guide. Take the
practice tests under simulated test conditions. Find a quiet place where you won’t be interrupted, set a timer for the required time
for each section, and work through each test as though it were test day. This will help you to get used to the time limits and to learn
to pace yourself. If you don’t have time to take full-length practice tests, Peterson’s® SAT® Prep Guide explains how to use timing drills
to take shorter sections of the exams to combat your weaknesses, work on your pacing, and increase your level of confidence.

Comprehensive Answer Explanations
At the end of each practice session, read all the answers and explanations, even for the questions that you answered correctly. There
are comprehensive explanations for every one of the book’s 1,600+ questions! By reading the answer explanations, you can learn
from your mistakes.
You’ll also find that Peterson’s® SAT® Prep Guide discusses all of the “big picture issues” other books ignore. For example, it addresses
questions such as:

• How is the SAT® really used for college admission?
• When should you take the test?

Peterson's SAT® Prep Guide

  vii

• How many times should you plan to take the SAT® exam?
• Do all SAT® exam sscores “count” in college admissions?
By addressing these questions, Peterson’s® SAT® Prep Guide debunks prevailing myths and helps you put the SAT® into its proper
perspective. It also serves as your “college guidance counselor,” giving you the expert advice you need to apply to college. And when
you think about it, that’s our number-one goal here. Our objective is to help you dramatically raise your scores so that you can
maximize the likelihood of getting into the college of your choice.

How This Book Is Organized
Peterson’s SAT® Prep Guide is divided into eight parts to facilitate your study.

• Part I explains everything you need to know about the SAT® exam and provides an overview with examples of the different
question types you’ll find on the actual test.

• Part II offers a diagnostic test to help you identify your areas of strength and those areas where you need to spend more time in
your review sessions.

• Part III explores the Evidence-Based Reading Test section and offers expert strategies for answering each type of question.
• Part IV goes into detail about the different types of questions you’ll see on the Writing and Language Test section of the SAT®
exam. You’ll also find a helpful review of Standard English Conventions.

• Part V describes the optional Essay part of the SAT® exam and provides strategies for developing a well-supported and coherent
response to the essay prompt in this section.

• Part VI offers a thorough review of all math topics you’ll see on the Math Test–No Calculator and Math Test–Calculator sections.
You’ll find helpful information on multiple-choice and grid-in math strategies, plus helpful reviews of numbers and operations,
basic algebra, geometry, functions and intermediate algebra, and data analysis, statistics, and probability.

• Part VII has five more tests that provide you with practice for the SAT® exam so you can simulate taking the test under timed
conditions. Each of the practice tests has detailed answer explanations plus instructions on how to determine your scores for
the Evidence-Based Reading and Writing portion and the two Math sections. You’ll also be able to calculate your subscores in
the categories of Expression of Ideas, Standard English Conventions, Words in Context, Command of Evidence, Heart of Algebra,
Problem Solving and Data Analysis, and Passport to Advanced Math as well as the cross-test scores for the Analysis in History/
Social Studies and Analysis in Science questions.

• Part VIII is the Appendix: Parents’ Guide to College Admission Testing, offering great information for parents in creating a plan to
help their teen prepare for college-admissions tests. It discusses the various roles parents play, how to approach teens on this
subject matter, and how to work with the guidance counselor. It also provides great tips on how to help teens improve their
time management—essential when preparing for standardized tests like the SAT® exam.

  viii

www.petersons.com

Special Study Features
You will find four kinds of special study features scattered throughout the book. Each study feature highlights specific types of
information:
Tips point out valuable information you need to know when taking the SAT® exam. Tips provide quick and
simple hints for selecting the correct answers for the most common SAT® question types.
Alerts identify potential pitfalls in the testing format or question types that can cause common mistakes in
selecting answers.
NOTES:

Notes address information about the test structure itself.

Cautions provide warnings, such as common grammatical errors or possible errors in computation or formulas
that can result in choosing incorrect answers.

How to Use This Book
It’s understandable that all of the information you’ll be reading about the SAT® exam might seem a little overwhelming. But even if
you are feeling confused by everything the exam requires, take some comfort in the knowledge that you are holding a great resource
to help you do well on test day. This book’s job is not to make you a genius; its job is to make sure you are prepared to take the SAT®
exam. If you become a genius in the process, consider that a bonus.
The following four steps will help you get the most out of using this guide:

Step 1: First Things First—Get to Know the Exam
You will get the most out of Peterson’s SAT® Prep Guide by using this book as it is organized. You may want to skip Chapter 1: All About
the SAT® because you’re anxious to get right to the lessons, since that’s where the real preparation begins, but Chapter 1 is very useful
for giving you a picture of the exam’s content as a whole.
ALERT: If you skip Chapter 1, you won’t learn about when and how many times you should take the SAT®; how to register
for the SAT®; how the SAT® is scored and how scores are reported; strategies for SAT® success; the SAT® test format and
question types, including a first look at kinds of questions on the Evidence-Based Reading Test, the Writing and Language
Test, and the Math Tests (Calculator and No Calculator); and much more!

Step 2: The Diagnostic Test Is Your Friend—Don’t Skip It!
Once you’ve learned the essential information about the SAT® in general, you will need to take the first step toward getting your
scores where you want them to be by taking the diagnostic test. The diagnostic test is a full-length practice test that you take before
you start studying or reviewing any subject material.
Understandably, taking a long diagnostic test may not seem the ideal way to get started on your test-preparation path. However,
the point of a diagnostic test is to give you an idea of what your strengths and weaknesses are before you dive into your SAT® preparation. By taking the diagnostic test and analyzing your answers, you may discover that you retained more information from your
English classes than you realized. You might also learn that you aren’t quite the math expert you thought you were. Or maybe you

Peterson's SAT® Prep Guide

  ix

will find that most of your math skills are really strong, but you need some help when it comes to quadratic equations.
Getting a clear idea of your strengths and weaknesses will help you know which chapters of this book really demand
your focus. The diagnostic test will help you get that clear idea.

Step 3: Build Your Skills—Practice, Practice, Practice!
After evaluating your diagnostic test results, you should
know the skills on which you need to focus. By diligently
studying the information presented, you will become
familiar with not only the question types that will appear
on the SAT®, but also the language of the exam to help
you be prepared for how the test will be worded.

Familiarizing yourself with the way certain questions
are worded on the SAT® may help you figure out the
kind of question you are answering, which may help
you select the best answer.

Throughout each review chapter (Chapters 3–13), you will find numerous practice questions, which will help familiarize
you with the language and presentation of the SAT® exam. The exercises and quizzes in these review chapters are a
great way to practice, and the thorough answer explanations will help you understand why an answer is right—or more
importantly why an answer is wrong. This can hopefully keep you from making a similar mistake again when you take
the real test.

Step 4: See What You Have Learned—Test Yourself Again
Near the end of the book, in Part VII, you will have the opportunity to take five complete SAT® practice tests. With each
practice test, you should see an improvement in your score since taking the diagnostic test.
You should take these tests under the same circumstances you will encounter on test day. That means completing each
test section in the exact same time that will be allotted for the actual test:

• Reading Test: 65 minutes
• Writing and Language Test: 35 minutes
• Math Test—No Calculator: 25 minutes
• Math Test—Calculator: 55 minutes
• Essay: 50 minutes

If you begin using this book to prepare for the SAT® well in
advance of test day, you might want to hold off taking the
last practice test until a few days before taking the actual SAT®
to re-familiarize yourself with the test’s format and content.

  x

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THE PETERSON’S SUITE OF SAT® PRODUCTS
In addition to Peterson’s SAT® Prep Guide, Peterson’s has an array of cutting-edge SAT® preparation resources designed to give you the
best test preparation possible. Our online course and interactive practice tests can be used alone or combined with other Peterson’s
SAT®-focused products to help you succeed and get the test scores you want. Take a few minutes to discover what’s available in
Peterson’s suite of SAT® products or visit our website at www.petersons.com/sat.

Peterson’s SAT® Prep Guide
Peterson’s SAT® Prep Guide features content and strategies that will help you master the SAT®. It contains a full-length diagnostic test
and access to eight full-length practice tests—five within the book and three online. The expert subject review and skill-specific
exercises in Peterson’s SAT® Prep Guide can help familiarize you with the unique content, structure, and format of the test. Test-taking
tips and advice guide you smoothly from your first day of test preparation to test day.
In addition, taking online practice tests is ideal because you get immediate feedback and automated scoring. Peterson’s SAT® Prep
Guide gives you access to three full-length online SAT® practice tests, with detailed feedback to help you understand the concepts
presented. The content in these three practice tests was created by the test-prep experts at Peterson’s to help you boost your test-prep
confidence so you can score high on test day. You can access these three practice tests at www.petersons.com/sat.

Peterson’s Practice Tests for the SAT®
Looking for even more online test practice? You can find it with Peterson’s Practice Tests for the SAT®. This test-prep tool provides three
full-length tests with immediate feedback and explanations for each question. Your purchase allows you 90-day access to these tests,
which feature the Essay Self-Score option—you can compare your essay to samples provided to give you an idea of how your essay
will be evaluated based on official scoring guidelines. Equipped with on-the-spot feedback and sample essays for comparison, you
can be confident that you’re getting the guidance you need to improve your score in all sections of the SAT®.

Peterson’s SAT® Online Course
Peterson’s SAT® Online Course is a comprehensive test prep course that is customized for you. In addition to practice tests, the online
course allows access to supplemental content, including additional subject-specific strategies and lessons, tips, and college search
options tailored to your projected test scores and interests.
Here’s how the course works:
1.
2.
3.
4.

An initial diagnostic pretest determines your strengths and weaknesses.
Based on your diagnostic test results, interactive lessons teach you the subject areas you need to learn.
Quizzes after each lesson gauge how well you have learned the materials just taught.
Full-length practice tests allow you to apply all the skills you’ve learned and monitor your progress.

Peterson’s SAT® Online Course gives you the opportunity to solidify your understanding and build your confidence about any concept
you may encounter on the SAT®—no matter how close it is to test day!

Interested in going the extra mile and using additional online practice tests or the online course? Take advantage of
customer-friendly discounts available only to customers who purchase Peterson’s SAT® Prep Guide. For more information and to
obtain your 20% discount on Peterson’s online courses, go to www.petersons.com/sat and enter the code: SAT2017.

Peterson's SAT® Prep Guide

  xi

Give Us Your Feedback
• Peterson’s publishes a full line of books—test prep, career preparation, education exploration, and financial aid. Peterson’s
publications can be found at high school guidance offices, college libraries and career centers, and your local bookstore and
library. Peterson’s books are also available online at www.petersonsbooks.com.

• We welcome any comments or suggestions you may have about this publication. Your feedback will help us make educational
dreams possible for you—and others like you.

Good
Luck!

  xii

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Now that you know why Peterson’s SAT® Prep Guide is an essential resource to prepare you to take a very important
test, it’s time to make the most of this powerful preparation tool. Turn the page and find out everything you need
to know about the SAT®!

part i : basic facts
about the sat ®
Chapter 1: All About the SAT

®

Chapter 1:

All About The SAT®
OVERVIEW
How the SAT® Is Used for College Admissions
When to Take the SAT® (and SAT Subject Tests™)
How Your Scores Are Reported
How Often to Take the SAT®
Registering for the SAT®
Get to Know the Current SAT® Exam Format
Get to Know the SAT® Question Types
Evidence-Based Reading Test Section
Writing and Language Test Section
Math Test Sections
SAT® Essay (Optional)

3

The SAT® Answer Sheet

Chapter 1

How the SAT® Is Scored

All About
the SAT®

Strategies for SAT® Success
Make an SAT® Study Plan
Measuring Your Progress
Simulate Test-Taking Conditions
The Night Before and Day of the Exam
Summing It Up

Peterson’s SAT® Prep Guide 2017

HOW THE SAT ® IS USED FOR COLLEGE ADMISSIONS
The explicitly stated purpose of the SAT® exam is to predict how students will perform academically as first-year college students.
But the more practical purpose of the test is to help college admissions officers make acceptance decisions. When you think
about it, admissions officers have a difficult job, particularly when they are asked to compare the academic records of students
from different high schools in different parts of the country taking different classes. It’s not easy to figure out how one student’s
grade point average (GPA) in New Mexico correlates with that of another student in Florida. Even though admissions officers
can do a good deal of detective work to fairly evaluate candidates, they benefit a great deal from the SAT®. The SAT® provides a
single, standardized means of comparison. After all, virtually every student takes the SAT®, and the SAT® is the same for everyone.
It doesn’t matter whether you hail from Maine, Maryland, or Montana.
So the SAT® is an important test. But it is not the be-all, end-all. Keep it in perspective! It is only one of several important pieces
of the college admissions puzzle. Other factors that weigh heavily into the admissions process include GPA, difficulty of course
load, level of extracurricular involvement, and the strength of the college application itself.

WHEN TO TAKE THE SAT ® (AND SAT SUBJECT TESTS™)
When you decide which schools you’re going to apply to, find out if they require the SAT®. Most do! Your next step is to determine
when they need your SAT® scores. Write that date down. That’s the one you really don’t want to miss.
You do have some leeway in choosing your test date. The SAT® is typically offered on one Saturday morning in October, November,
December, January, March (or April, alternating), May, and June. Check the exact dates to see which ones meet your deadlines.
Tests are offered on a Sunday, usually the day after each Saturday test date, for students who cannot take the test on Saturday
due to religious observance.

4
Chapter 1
All About
the SAT®

What if you don’t know which schools you want to apply to? Don’t panic! Even if you take the exam in December or January of
your senior year, you’ll probably have plenty of time to send your scores to most schools.
When you plan to take the SAT®, there is something even more important than the application deadlines of particular schools.
You need to select a test date that works best with your schedule. Ideally, you should allow yourself at least two to three months
to use this book to prepare. Many students like to take the test in March of their junior year. That way, they take the SAT® several
months before final exams, the prom, and end-of-the-year distractions. Taking the test in March also gives students early feedback
as to how they are scoring. If they are dissatisfied with their scores, there is ample opportunity to take the test again in the spring
or following fall. But your schedule might not easily accommodate a March testing. Maybe you’re involved in a winter sport or
school play that will take too much time away from studying. Maybe you have a family reunion planned over spring break in
March. Or maybe you simply prefer to prepare during a different time of year. If that’s the case, just pick another date.
If the schools you’ve decided on also require SAT Subject Tests™, here’s one good piece of advice: Try to take SAT Subject
Tests™ immediately after you finish the subject(s) in school. For most of you, this means taking the SAT Subject Tests™ in June.
By taking the exam then, you’ll save an awful lot of review work. Remember this, too: You have to register for the SAT Subject
Tests™ separately, and you can’t take the Subject Tests on the same day as the SAT®. So check the dates, think ahead, and plan
it out. It’s worth it in the end.
Are you starting to prepare a little later than you had planned? Don’t get upset;
it happens. Using the accelerated plan, you should be able to cover most of the
material within a month. You probably won’t have much time to practice, but you’ll
get the most important facts about the test and be able to take a few sample exams.

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HOW YOUR SCORES ARE REPORTED
After you have taken the SAT®, College Board scores your test and creates a score report. We will discuss in detail how the SAT®
is scored later in this chapter. You and your high school receive score reports from each SAT® and SAT Subject Test™ that you
decide to take.
At the time of registration, you can pick four colleges or universities to receive your score report. College Board will send your
scores to these four schools for free. Within nine days of taking the test, you can change your school selection. If you want to
send more than four reports or change your mind more than nine days after your test date, you will have to pay to do so.
If you decide to take the SAT®, or any SAT Subject Test™, more than once, you have the option to decide which scores to send
to the schools you’ve picked—scores from one, several, or all test dates.
You may only designate the test date or dates for your score reports; you cannot designate individual test sections. In other
words, if you take the SAT® exam in October, December, and March, you cannot pick the Evidence-Based Reading and Writing
section score from October, Math score from December, and Essay score from March and ask to have those results sent to the
schools of your choice. You can only choose whether to send your complete results from one, two, or all three test dates.
If you choose not to take advantage of this option, all of your scores will be sent to the schools you’ve selected. However, no
score reports will ever be sent without your specific consent. You and your counselor will receive e-mail reminders, asking which
scores you want to send. You can find more information about this and how colleges and universities use your score reports on
the website https://sat.collegeboard.org/register/sat-score-choice.

HOW OFTEN TO TAKE THE SAT ®
Different colleges evaluate the exam in different ways. Some take your highest math, evidence-based reading and writing, and
essay scores, even if they were earned on different test days. So if you nailed the math portion in March, the evidence-based
reading and writing section in October, and the essay in December, the colleges will combine those scores to maximize your
overall score. However, many other colleges won’t do that. Some pay most attention to your highest combined score from a
single day. Many others will average all of your scores or lend equal weight to all of them.

5
Chapter 1
All About
the SAT®

So what does this mean? It means that you should only take the SAT® when you are truly prepared. There is nothing wrong with
taking the SAT® two or three times, as long as you are confident that your scores will improve substantially each time. Let’s say
that you scored an 1100 on your first SAT®. If you would have been thrilled to have hit 1120, it’s probably not worth taking the
test again. Most colleges look at SAT® scores in ranges and will not hold 20 points against you. They understand that scoring an
1100 means that you were only one or two questions away from 1120. But if you scored an 1100 and expected to score closer
to 1200 or 1300 based on practice testing, then you should probably retake the exam. In other words, it is of little value to take
the SAT® multiple times if you expect to earn roughly the same score. But it is worthwhile if you expect to score significantly
higher on a second or third try. For more advice about this, see your high school guidance counselor.

REGISTERING FOR THE SAT ®
You should register for the SAT® at least six weeks before your testing date. That way you will avoid late registration fees
and increase your chances of taking the exam at your first-choice testing center. You can register through the mail by completing the SAT® registration form found inside The SAT® and SAT Subject TestsTM Student Registration Booklet, which can be
found in your guidance counselor’s office or online (printable PDF) at https://collegereadiness.collegeboard.org/pdf/
sat-registration-booklet-students.pdf. Registering online is probably the quickest and easiest method, and you will receive

Peterson’s SAT® Prep Guide 2017

immediate registration confirmation. You will need to pay by credit card, and you will need to upload a photo with your
registration. The photo you provide will become part of your Admission Ticket on test day. For more information, visit
https://sat.collegeboard.org/register.

Photo ID
The photo you provide (either uploaded with your online registration or mailed in with the printed registration) becomes
part of your Admission Ticket on test day.
Photos must be properly focused with a full-face view. The photo must be clearly identifiable as you, and it must match your
appearance on test day. IMPORTANT: If you are not easily recognizable in your photo, you will not be admitted to the test
center.
Choose a photo that:

•
•
•
•

Shows only you—no other people in the shot
Shows a head-and-shoulders view, with the entire face, both eyes, and hair clearly visible
Is properly focused and has no dark spots or shadows
Shows a head covering only if it is worn for religious purposes

Visit https://sat.collegeboard.org/register/photo-requirements for more information about the required photo ID.
In addition, you are responsible for bringing an acceptable form of identification.
Some acceptable examples include:

6
Chapter 1
All About
the SAT®

•
•
•
•
•
•
•

State-issued driver’s license
State-issued nondriver ID
School identification card
Passport (required in India, Ghana, Nepal, Nigeria, and Pakistan)
Government-issued ID
School ID Form* prepared by your school
Talent Identification Program ID/Authorization to Test Form (grades 7 and 8 only); photo not required

* Your school can prepare an ID form for you. This form must include a recognizable photo, and the school seal must overlap the photo. Sign
the ID form in the presence of your counselor or principal. You will be asked to sign the ID form again at the test center. This form must be
dated and is good only for one year.

ALERT: You must provide a photo when you sign up for the SAT®. The photo will be part of your Admission Ticket, and it will
be checked against your photo ID on test day.

Registration Fees
At the time of this book’s printing, the fee for the SAT® (no essay) is $45. If you are planning to take the SAT® with the Essay section,
you will need to pay $57. To determine if you are eligible for a fee waiver, visit https://collegereadiness.collegeboard.org/sat/
register/fees/fee-waivers.

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GET TO KNOW THE CURRENT SAT ® EXAM FORMAT
The SAT® consists of sections on math, evidence-based reading and writing, and an optional essay. The sections are timed to
range from 25 to 65 minutes. The whole test takes 3 hours, plus 50 minutes for the optional essay. Don’t worry. There are breaks.
The following chart gives you an idea of what to expect. The test sections appear in the following order: Reading Test, Writing
and Language Test, Math Test—No Calculator, Math Test—Calculator, and the Essay.

Format of the SAT® Test
Evidence-Based Reading and Writing
Evidence-Based Reading questions based on:

• Passages in U.S. and world literature, history/social
•
•
•

studies, and science
Paired passages
Lower and higher text complexities
Words in context, command of evidence, and analysis

Score 200–800
Time—Total: 100 Minutes

• Reading Test (65 minutes)
• Writing and Language Test (35 minutes)
Question Types

• Multiple-choice with 4 answer choices

Writing and Language questions based on:

• Passages in careers, history/social studies, humanities,
•
•

and science
Argument, informative/explanatory, and nonfiction
narrative passages
Words in context, grammar, expression of ideas,
and analysis

Math

7

Score 200–800

Real-world problems solved using:

•
•
•
•
•
•

Algebra
Problem solving and data analysis
Advanced math
Area and volume calculations
Lines, triangles, and circles using theorems
Trigonometric functions

Time—Total: 80 Minutes

• Math Test—No Calculator (25 minutes)
• Math Test—Calculator (55 minutes)
Question Types

Chapter 1
All About
the SAT®

• Multiple-choice with 4 answer choices
• Student-produced responses (grid-ins)

Optional Essay
What’s involved:

• Read an argument-type passage written for a
•

general audience
Analyze the passage in terms of how the writer uses
evidence, reasoning, and stylistic elements to build
an argument to persuade his or her audience

Time—Total: 50 minutes
Question Type

• One prompt that emphasizes analyzing the
argument presented in the passage
Score: 3–12 (Reading: 1–4 scale, Analysis: 1–4 scale,
Writing: 1–4 scale)

Peterson’s SAT® Prep Guide 2017

GET TO KNOW THE SAT ® QUESTION TYPES
The question types in the SAT® don’t cover a wide variety of topics. They are very limited—no science, no world languages, no
social studies. You’ll find only questions testing reading comprehension, writing skills, and math skills—skills that you’ve been
working on since kindergarten.
Most of the questions are multiple choice. That’s good, because it means the correct answer is right there on the page for you.
You just have to find it—easier said than done sometimes, but true. Only the math grid-ins and the essay are student-produced
answers. For the grid-ins, you’ll need to do the calculations and then fill in circles on the answer sheet to show your answers.
(More about the answer circles later in this chapter.) The following pages provide you with a closer look at the question types
and question formats that you will find in each section of the SAT®.

On the SAT®, all questions count the same. You won’t get more points for answering a
really difficult question than you will get for answering a very simple one. Remember
that when you’re moving through the test. The more time you spend wrestling with the
answer to one “stumper,” the less time you have to whip through several easier questions.

EVIDENCE-BASED READING TEST SECTION

8
Chapter 1
All About
the SAT®

The reading section tests your knowledge of words in context, command of evidence in the passages, and your analysis of the
passage, including graphics. All the questions are multiple choice. The questions in the Evidence-Based Reading section are all
passage-based. All passages are from previously published sources and cover topics in U.S. and world literature, history/social
studies, and science.

Words in Context
Just as the name implies, words-in-context questions assess your ability to determine the meaning of words or phrases in the
context of an extended passage. If you do not recognize the meaning of the word, its meaning may be determined by context.
Your job is to read the passage and the question, and then analyze the answer choices to figure out which one makes the most
sense based on the words around it. That means you must look for clues in the passage.
Here is an excerpt from a passage on the opah fish. There are three sample words-in-context questions. Read the passage excerpt
and try to answer each question on your own before you read the answer explanations on the next page.

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The silvery fish, roughly the size of a large automobile

Nicholas Wegner of NOAA Fisheries’ Southwest Fisheries Science
Center in La Jolla, California, is lead author of a new paper on the
opah, or moonfish. He and his coauthor, biologist Owyn Snodgrass,
discovered that the opah has the unusual ability to keep its body
warm, even in the cold depths of the ocean. An excerpt on their
findings follows.

tire, is known from oceans around the world and dwells
hundreds of feet beneath the surface in chilly, dimly lit
waters. . . .
10

Courtesy: NOAA Fisheries

Fish that typically inhabit such cold depths tend to be
slow and sluggish, conserving energy by ambushing prey
instead of chasing it. But the opah’s constant flapping of its

Warm Blood Makes Opah an Agile Predator

fins heats its body, speeding its metabolism, movement and

New research by NOAA Fisheries has revealed the opah, or
moonfish, as the first fully warm-blooded fish that circulates
heated blood throughout its body much like mammals and

reaction times, scientists report today in the journal
15 Science. . . .

Line birds, giving it a competitive advantage in the cold ocean

“Before this discovery, I was under the impression

5 depths.

this was a slow-moving fish, like most other fish in cold
environments,” Wegner said. “But because it can warm its
body, it turns out to be a very active predator that chases
20 down agile prey like squid and can migrate long distances.”

Questions:
1. As used in the first paragraph, “competitive advantage” refers to
A.

a way to seek out a mate.

B.

an ability to outperform rivals.

C.

an aptitude for keeping itself moving.

D.

a capacity to conceal itself from predators.

9
Chapter 1
All About
the SAT®

2. As it is used in paragraph 3, “ambushing” most nearly means
A.

pursuing for long distances.

B.

moving slowly at first.

C.

hiding and then attacking.

D.

weakening and then killing.

3. As it is used in paragraph 4, “agile” most nearly means
A.

nimble.

B.

inactive.

C.

strong.

D.

clever.

Peterson’s SAT® Prep Guide 2017

Answer Explanations:
1. Clues to the meaning of the phrase don’t appear until the fourth paragraph: “I was under the impression . . . like
most other fish in cold environments” and “But . . . it turns out to be a very active predator.” Here, you’re told that the
opah is unlike other fish in that it can swim faster and farther and catch more prey. Choices A, C, and D are specific
traits that might help the fish in its environment. But choice B is the only one that makes sense in the context of the
passage. The correct answer is choice B.
2. The biggest clue to the meaning of ambushing is “instead of chasing it.” Because you know that the fish don’t chase
their prey, you can exclude choice A. Choices B and D don’t make sense in the context of the sentence because neither
is a method for capturing prey, as chasing is. Choice C, however, makes sense when you consider the context clue.
The correct answer is choice C.
3. The clue “very active predator” is your clue that agile must mean that the squid provides a challenge for the opah.
This eliminates choice B. Choice D can also be eliminated because the context emphasizes physical, not mental,
abilities. Likewise, you can eliminate choice C because the level of activity, not strength, is the focus. Choice A fits
the context, as it suggests that the squid is able to move quickly and easily. The correct answer is choice A.

In SAT® evidence-based reading questions, the answers will always be
directly stated or implied in the passage.

10
Chapter 1
All About
the SAT®

Command of Evidence
The evidence-based reading and writing sections of the SAT® require you to interpret information or ideas in a passage and then
use evidence to support your conclusion. This element of the Reading Test, which makes up 20 percent of the questions, works
like this: You answer a multiple-choice question in which you analyze a portion of the passage or pair of passages. You then answer
a second question requiring you to cite the best evidence in the text for the answer.
The passages include literary texts from U.S. and world literature, as well as nonfiction texts in science and history/social studies.
In some cases, related passages are paired and require you to make connections between the texts.
The following is an example of how these “command of evidence” questions work. The passage is a continuation of the NOAA
article cited previously, “Warm Blood Makes Opah an Agile Predator.”

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Questions 1–2 refer to the following passage.

“There has never been anything like this seen in a fish’s
gills before,” Wegner said. “This is a cool innovation by these

Gills Show Unusual Design

animals that gives them a competitive edge. The concept
of counter-current heat exchange was invented in fish long

Courtesy: NOAA Fisheries

20 before we thought of it.”

Wegner realized the opah was unusual when a coauthor
The researchers collected temperature data from opah

of the study, biologist Owyn Snodgrass, collected a sample

caught during surveys off the West Coast, finding that

of its gill tissue. Wegner recognized an unusual design:

their body temperatures were regularly warmer than the

Line Blood vessels that carry warm blood into the fish’s gills wind

surrounding water. They also attached temperature monitors

5 around those carrying cold blood back to the body core

after absorbing oxygen from water.

25 to opah as they tracked the fish on dives to several hundred

feet and found that their body temperatures remained
The design is known in engineering as “counter-current

steady even as the water temperature dropped sharply. The

heat exchange.” In opah it means that warm blood leaving

20 fish had an average muscle temperature about 5 degrees

the body core helps heat up cold blood returning from the
10 respiratory surface of the gills, where it absorbs oxygen.

C above the surrounding water while swimming about 150
30 to 1,000 feet below the surface, the researchers found. . . .

Resembling a car radiator, it’s a natural adaptation that
conserves heat. The unique location of the heat exchange

A few other fish . . . warm certain parts of their bodies . . .

within the gills allows nearly the fish’s entire body to

boosting their swimming performance. But internal organs,

maintain an elevated temperature, known as endothermy,

including their hearts, cool off quickly and begin to slow
down when they dive into cold depths, forcing them to

15 even in the chilly depths.

11

35 return to shallower depths to warm up.

Chapter 1
All About
the SAT®

Questions:
1. The author discusses the adaptations of some fish in the last paragraph mainly to show that
A.

opah swim faster because they are able to keep themselves warm.

B.

some fish maintain a body temperature warmer than the sea water.

C.

biologists have found evidence that some fish are warm-blooded.

D.

opah have a distinctive design that keeps them warm at greater depths.

2. Which choice provides the best evidence for the answer to the previous question?
A.

Lines 12–15 (“The unique . . . chilly depths.”)

B.

Lines 18–20 (“The concept . . . of it.”)

C.

Lines 21–24 (“The researchers . . . surrounding water.”)

D.

Lines 27–30 (“The 20 fish . . . researchers found.”)

Peterson’s SAT® Prep Guide 2017

Answer Explanations:
1. In the first question, the author’s intention is to contrast the warming ability of other fish with the warming ability of
the opah. Though the passage does note that some fish maintain a body temperature warmer than seawater for a
short period, this is not the reason the author includes details about other fish. Thus, choice B is not correct. Choices
A and C are incorrect because neither idea is noted in the text. The correct answer is choice D.
2. The second question asks you to determine which of four segments of the passage provides the best evidence to
support your answer to the first question. Choices B, C, and D do not provide textual support for the contrast the
author makes in the last paragraph. The correct answer is choice A.

Analysis and Graphics
Two passages in the SAT® Reading Test include a graphic. Your job is to analyze the passage and interpret the information in the
graphic as it relates to the passage. Questions based on the graphic are multiple choice. Here is a sample reading passage with
an accompanying graphic, in this case a map, and a question that requires your analysis.
From “About John Snow,” by Professor Paul Fine, London School of Hygiene & Tropical Medicine and The John Snow Society.
John Snow (1813–1858)
John Snow is an iconic figure in epidemiology and public

12

Line

health, best known for his work on cholera, for a famous map,

interested in the physiology of respiration in recognition of

and for organizing the removal of a pump handle in Soho.

the major problem of asphyxia of the newborn.

Less well-known are his important contributions to

5 anesthesia and to epidemiological methods, and his

Chapter 1
All About
the SAT®

set up general practice in Soho. Early in his career he became

These interests led him to be invited to witness one of the
25 first applications of ether anesthesia in the UK in December

engagement in public debates of the time. The breadth and

1846. He immediately recognized the importance of ambient

depth of Snow’s activities provide a model for population

temperature and within one month published tables of

researchers concerned not only with sound method but also

the vapor pressure of ether. This initiated an important line

with bringing their results to public benefit.

of research on instruments for administering anesthetics
30 and led to his becoming the most prominent authority on

10

Indeed, though epidemiology is often described as the
study of health-related aspects of populations, its methods

anesthesia in the UK. He administered chloroform to Queen
Victoria at the birth of Prince Leopold in 1853.

are applicable to studies of virtually anything in populations,
and disciplines which now acknowledge the methods and
terminology of epidemiology range from education to crime
15 science and economics.

The second great cholera epidemic arrived in London
in 1848, and many attributed its cause to an atmospheric
35 “effluence” or “miasma.” Snow’s firsthand experience of the

disease in 1832, combined with studies of respiration, led
Snow was born in York on 15 March 1813, one of eight
children in a family of modest means. He apprenticed with
a surgeon-apothecary in Newcastle from 1827 to 1833, and
there witnessed the first epidemic of cholera in the UK. He
20 then moved to London, qualified as physician in 1843 and

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him to question miasma theories and to publish the first
edition of On the Mode of Communication of Cholera in 1849,
in which he proposed that cholera was attributable to a
40 self-replicating agent which was excreted in the cholera

evacuations and inadvertently ingested, often, but not

Though the epidemic was already in decline by that date,

necessarily, through the medium of water.

the rapidity of his action, the logic of the analysis, and the
60 pragmatism of the response has made this a classic event

When cholera returned in 1853, Snow recognized an

in the history of public health, well known to students and

ideal opportunity to test his hypothesis by comparing

practitioners the world over. The combination of these

45 cholera mortality rates in populations of south London

studies provided overwhelming evidence for an infectious

supplied by water drawn from sewage-contaminated versus

agent, known now as Vibrio cholerae.

uncontaminated regions of the Thames. He personally carried
out a cohort study to make this comparison, recognizing the
need to confirm the water source of each case and to assure
50 comparability of the populations concerned. On 30 August

65

Snow described this work in the second edition of On the
Mode of Communication of Cholera. He then expanded his
public health interests by becoming involved in debates over

1854 while involved in these studies, a dramatic cholera

legislation concerning nuisance industries in London, while

epidemic began near his home in Soho, leading to more than

maintaining his research and practice in anesthesia until his

550 deaths within two weeks. Analysis of the addresses of

70 death in 1858.

the cholera deaths and interviews of residents of the area
55 led him to suspect that water from a pump on Broad Street

was responsible—and he prevailed upon the local council to
remove the handle of the pump on 8 September 1854.

The 200th anniversary of Snow’s birth provides an
occasion to celebrate his achievements, to consider their
original context, to discuss their place in contemporary
epidemiology, and consider their likely future, not only as
75 the armamentarium of public health, but as a framework of

method for science and society.

13
Chapter 1
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Peterson’s SAT® Prep Guide 2017

Question:
On John Snow’s map, deaths from the 1854 cholera epidemic are represented by stacks of black lines. Based on the
image and the passage, what can we assume about Blenheim Street (shown magnified in the upper-left side of the
map)?
A.

No one lived there.

B.

Broad Street did not supply their water.

C.

Its residents were as affected as the rest of the neighborhood.

D.

Relatives came to stay there to avoid the cholera outbreak.

Answer Explanation:
The passage explains that Snow determined that the pump on Broad Street supplied contaminated water to nearby
residents. You can infer that people living on streets containing stacks of bars used the Broad Street pump. Based on
the map, then, people on Blenheim Street likely did not use the Broad Street pump. The correct answer is choice B.

WRITING AND LANGUAGE TEST SECTION
The SAT® Writing and Language Test consists of multiple-choice questions based on passages. The multiple-choice questions test
how well you understand and use Standard Written English, as well as recognize words in context and command of evidence in
the passages. Analysis of the passages and graphics is also included.

14
Chapter 1
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the SAT®

Standard Written English and Words in Context
The Standard Written English questions require you to act as an editor and revise text so that it conforms to the standard rules for
punctuation, sentence structure, and usage. In most instances, you will be given a multiparagraph passage that includes several
errors. The most common question format asks you to choose the best alternative to a potential error, identified as an underlined
portion of the passage. Here is a sample question that concerns sentence structure:
Question:

Scientists conducted a series of experiments with

1

chimpanzees in the 1 Democratic Republic of the

Which choice most effectively combines the sentences
at the underlined portion?

Congo. The results were astounding. The conclusion, that

A.

Democratic Republic of the Congo, and the
results were astounding.

B.

Democratic Republic of the Congo, the results
were astounding.

C.

Democratic Republic of the Congo: the results
were astounding.

D.

Democratic Republic of the Congo, but the results
were astounding.

chimpanzees would eventually learn to cook if provided an
oven, could help explain how and when early humans began
to cook their food.

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Answer Explanation:
Choice B creates a comma splice, which is a form of a run-on sentence, so that’s not correct. Likewise, the colon in
choice C is not correct, as the clause it introduces does not really explain the first part of the sentence. Introducing
but in choice D changes the meaning of the sentences by setting up a contrasting scenario. Only choice A maintains
the two sentences’ meanings and combines them without confusion. The correct answer is choice A.
The words-in-context questions on the test measure your ability to choose appropriate words based on the context of the passage.
These questions are multiple choice and include the option to keep the word that is used.
Question:

There is a debate about whether early humans had

2

the mental capacity to cook. Though it may not seem
sophisticated, cooking requires planning, an ability to
2 interrupt gratification, and the complicated use of tools.

A.

NO CHANGE

B.

apprehend

C.

delay

D.

restrain

Answer Explanation:
Here, you must choose the word that makes the most sense in the context. The words interrupt, apprehend, and restrain
don’t convey what is meant here—to hold off. Only delay, choice C, conveys that sense. The correct answer is choice C.

Command of Evidence

15
Chapter 1

To answer the Command of Evidence questions in the Writing and Language Test section, you need to carefully read the passage
in question. Here is an example of this type of question. The excerpt comes from the passage “About John Snow”.

All About
the SAT®

Question:

The second great cholera epidemic arrived in London in

3

1848, and many attributed its cause to an atmospheric

Which choice best summarizes the main idea of the
paragraph?

“effluence” or “miasma.” Snow’s firsthand experience of the

A.

In 1848, many people were incorrect to blame
atmospheric miasma for the spread of cholera.

B.

John Snow’s study, On the Mode of Communication
of Cholera, was read by scholars worldwide.

C.

John Snow was curious, and he never took
anything at face value.

D.

Snow’s questioning of the miasma theory and
theories on water contamination changed the
conversation of disease circulation.

disease in 1832, combined with studies of respiration, led
him to question miasma theories and to publish the first
edition of On the Mode of Communication of Cholera in 1849,
in which he proposed that cholera was attributable to a
self-replicating agent which was excreted in the cholera
evacuations and inadvertently ingested, often, but not
necessarily, through the medium of water. 3

Peterson’s SAT® Prep Guide 2017

Answer Explanation:
The question asks you to determine which sentence best summarizes the main idea of the paragraph. Choices A, B,
and C all contain ideas that are important in the paragraph. But choice D contains the crux of the paragraph: that Snow
questioned the prevailing wisdom and then proposed his own theory about how cholera was transmitted. The correct
answer is choice D.

Analysis and Graphics
One or two of the passages in the Writing and Language Test section include graphics. You will be asked to determine how the
passage needs to be revised based on the information in the graphic. Here is an excerpt from another paragraph in “About John
Snow” and a sample question to help illustrate this concept.
Question:

Snow’s mapping of the outbreak showed few surprising
results. Little Pulteney Street is a case in point. The street
is blocks from Broad Street and closer to two other water
pumps. Among residents of the street, there 4 were no
cases of cholera reported during the outbreak.

16
Chapter 1
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the SAT®

www.petersons.com

4

Which choice completes the sentence using accurate data
based on the map?
A.

NO CHANGE

B.

was one new case of cholera

C.

were fewer than ten new cases of cholera

D.

were more than twenty new cases of cholera

Answer Explanation:
Here, you are being asked to interpret the information in the passage based on the map. If you look closely at the area
in question, Little Pulteney Street, you’ll see that there are about six bars, and we can infer that each bar represents a
case of cholera. The correct answer is choice C.

MATH TEST SECTIONS
The questions in the math sections (Math Test—No Calculator and Math Test—Calculator) address concepts, skills, and practices
that are most useful for students after they graduate from high school. There are two question formats for math questions: multiple-choice and grid-ins (student-produced responses).

A four-function, battery-powered, scientific or graphing calculator is allowed for
the Math Test—Calculator section of the SAT®. You may not use the following:
handheld mini-computers, laptop computers, pocket organizers, calculators
that print or “talk,” or calculators with letters on the keyboard.

Multiple-Choice Math
SAT® multiple-choice math questions look like all the other standard multiple-choice math questions you’ve ever seen. A problem
is given in algebra, problem solving, data analysis, advanced math, or additional topics, and four choices are presented from
which you must choose the correct answer. The major concepts that you might need in order to solve math problems are given
in the test section. You don’t need to worry about memorizing these facts, but you do need to know when to use each one.
The directions are similar to the following:

DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
V = lwh

h

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w

Chapter 1
All About
the SAT®

Triangle:

w

Rectangular
Solid:

17

x

x

Special Right Triangles

a2 + b2 = c2
Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

Peterson’s SAT® Prep Guide 2017

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted (is permitted for the Math Test—Calculator section).
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real
number.

Here are some sample multiple-choice math questions. Try them yourself before looking at the solutions that are given.
Example:
Michele is at the airport renting a car that costs $39.95 per day plus tax. A tax of 7% is applied to the rental rate, and
an additional one-time untaxed fee of $5.00 is charged by the airport where she picks up the car. Which of the
following represents Michele’s total charge c(x), in dollars, for renting a car for x days?
A.

c(x) = (39.95 + 0.07x) + 5

B.

c(x) = 1.07(39.95x) + 5

C.

c(x) = 1.07(39.95x + 5)

D.

c(x) = 1.07(39.95 + 5)x

Solution:

18
Chapter 1

The total cost, c(x), can be found by multiplying any daily charges by the number of days, x, and then adding any
one-time charges. The daily charges include the $39.95 daily rate and the 7% tax. This can be computed by:
$39.95 + 0.07($39.95) = 1($39.95) + 0.07($39.95) = 1.07($39.95)

All About
the SAT®

Multiply the daily charge by x and add the one-time charge of $5 to obtain the function rule:
c(x) = 1.07(39.95)x + 5
The correct answer is choice B.

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Example:
The graph of y = (3x + 9)(x – 5) is a parabola in the xy-plane. In which of the following equivalent equations do the
x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?
A.

y = 3x2 – 6x – 45

B.

y = 3x(x – 2) – 45

C.

y = 3(x – 1)2 + (– 48)

D.

y = (x + 3)(3x – 15)

Solution:
The equation y = (3x + 9)(x – 5) can be written in vertex form y = a(x – h)2 + k, where the vertex of the parabola is
(h, k). To put the equation in vertex form, first multiply the factors, then complete the square. The correct answer is
choice C.
Example:
The same final exam is given to two separate groups of students taking the same class. The students who took the
exam on the first floor had a mean score of 84. The students who took the exam on the second floor had a mean
score of 78. Which of the following represents the mean score x of both groups of students?
A.

x = 81

B.

x < 81

C.

x > 81

D.

78 < x < 84

19
Chapter 1
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the SAT®

Solution:
Many students will select choice A as the answer because 81 is the mean of 78 and 84, but there is no information
about the size of the two groups that are being averaged. If the groups were equal in size, choice A would be correct. If
there were more students on the second floor, then choice B would be the correct answer. Similarly, if there were more
students on the first floor, then choice C would be correct. Since we don’t know which floor has more students taking
the exam or if the number of students is equal, we can only say that choice D is true. The correct answer is choice D.

Peterson’s SAT® Prep Guide 2017

GRID-INS
Unlike multiple-choice math, the grid-in section of the SAT® does not give you the answers. You have to compute the answer and
then fill in your answer in the circles on your answer sheet. You may use the Reference Information table that appeared earlier
in this chapter for these problems also.
On the SAT®, each set of grid-in questions starts with directions that look approximately like this:

DIRECTIONS: For these questions, solve the problem and enter your answer in the grid, as described below, on the
answer sheet.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
7
1
5. Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
		
If 3

20

1
is entered into the grid as
2

, it will be interpreted as

1
31
, not 3 .
2
2

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.

Chapter 1
All About
the SAT®

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7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

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1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

3

3

4

4

4

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4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

21

.

0

0

0

0

0

0

0

0

0

1

1

1

1

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6

Chapter 1
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the SAT®

6

Once you understand the following six rules, you can concentrate on just solving the math problems in this section.
1. Write your answer in the boxes at the top of the grid.
2. Mark the corresponding circles, one per column.
3. Start in any column.
4. Work with decimals or fractions.
5. Express mixed numbers as decimals or improper fractions.
6. If more than one answer is possible, grid any one.

Peterson’s SAT® Prep Guide 2017

NOTE: Don’t use a comma in a number larger than 999. Just fill in the four digits and the corresponding circles.
You only have circles for numbers, decimal points, and fraction slashes; there aren’t any for commas.

Now let’s look at these rules in more detail:
1.

Write your answer in the boxes at the top of the grid. Technically, this isn’t required by the SAT®. Realistically, it gives you
something to follow as you fill in the circles. Do it—it will help you.

2.

Make sure to mark the circles that correspond to the answer you entered in the boxes, one per column. The machine that
scores the test can only read the circles, so if you don’t fill them in, you won’t get credit. Just entering your answer in the
boxes is not enough!

3.

You can start entering your answer in any column, if space permits. Unused columns should be left blank; don’t put in zeroes.
Here are some examples of these kinds of problems:

Examples:
Use the grids provided to try the following grid-in quesions.
1.

The circumference of a circle is 20π. If the area of a sector of the circle with a central angle of
3p
is aπ, what is the value of a?
2

22

2.

There are 70 students in a school who participate in the music program. If 35% of the students participate in the music
program, how many students are in the school?

3.

What is one possible solution to the equation

Chapter 1

1.

2.

All About
the SAT®

www.petersons.com

1
3
+
= −4 ?
x x −1

/
.

/
.

.

0

0

0

0

1

1

1

2

2

3

3

4
5

4
5

3.
/
.

/
.

.

/
.

/
.

0

0

0

0

.

0

0

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0

1

1

1

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1

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9

Solutions:
1. C = 2pr = 20 p
r = 10
3
3
A = pr 2 = p(10 ) 2 = 75p = ap
4
4
a = 75
2.

35 70
=
100 x
35 x = 7, 000
x = 200

3.

1
3
+
= −4
x x −1
x − 1+ 3 x = −4 x ( x − 1)
4 x − 1 = −4 x 2 +4 x
0 = −4 x 2 +1
0 = ( −2 x + 1)(2 x + 1)
x = ±0.5
Only 0.5 or

1
(1/2) can be entered in the grid because, as the directions stated, no answer requires a minus sign.
2

1.

2.
/
.

/
.

3.

.

/
.

/
.

OR
/
.

.

/
.

.

.

/
.

/
.

.
0

23

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Chapter 1

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All About
the SAT®

4
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You will learn more about grid-ins in Chapter 8: “Grid-In Strategies.”

Peterson’s SAT® Prep Guide 2017

SAT ® ESSAY (OPTIONAL)
For the essay, you will be given a previously published passage that examines ideas in the sciences and arts, as well as in civic,
cultural, and political life. The passages are written for a broad-based audience, and prior knowledge of the topic is not expected.
Your task in writing the essay is to read and comprehend the text sufficiently to write a thoughtful analysis of the passage.
Though the passage contents may vary from test to test, the prompt will not change. You will be asked to explain how the author
of the passage builds an argument to persuade an audience. The prompt will likely look something like this:

As you read the following passage, consider how the author uses the following:

• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power to
the ideas expressed.
Your response will be evaluated based on your comprehension of the text, as well as on the quality of your analysis and writing.
This means that you must show thoughtful understanding of the source text and appropriate use of textual evidence to support
your arguments. You will also be expected to organize your ideas in a coherent way and to express them clearly, using the conventions of Standard Written English. The essay does not elicit your opinion or ask you to use your imagination to write creatively.
Instead, your response should depend entirely on the source text to support your analysis. You can learn more about the optional
Essay in Chapter 6: “The SAT® Essay.”

24
Chapter 1
All About
the SAT®

THE SAT ® ANSWER SHEET
On the day of the test when you are given your test booklet, you’ll also be given a separate answer sheet. For each multiple-choice
question, you’ll see a corresponding set of answer circles. The circles are labeled A, B, C, and D. Remember the following about
the answer sheet:

• Answer sheets are read by machines—and machines can’t think. That means it’s up to you to make sure you’re in the right place
on the answer sheet every time you record an answer. The machine won’t know that you really meant to answer Question 25
when you marked the space for Question 26.

• If you skip a question, list the number on your scratch paper. Don’t mark the answer sheet in any way as a reminder. Any stray
marks may affect how the machine scores your answer sheet.

• Always check to see that the answer space you have filled in corresponds to the question you are answering.
• Be sure to fill in the answer circles completely so that there can be no mistake about which answers you chose.
These seem like simple things, but you’d be surprised how many students fail to do them, especially keeping track of answer
lines if they skip a question.

Make sure you’re in the right place! Always check to see that the answer space you
fill in corresponds to the question you are answering.

As you just read in the “Grid-Ins” section of this chapter, grid-inresponses are only for questions you will see in the math sections.
You’ll still be filling in circles, but they will look a little different from the multiple-choice circles. Again, here’s a sample of the
special grid you will use.

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/
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/
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boxes to write your numerical answer
fraction lines—use one at most per answer
decimal points—use one at most per answer

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At the top of the grid, you’ll write in the numerical answer. The slashes that appear in the second row are used for answers with
fractions. If you need one of these fraction lines in your answer, darken one of the circles. The circles with the dots are for answers
with decimal points—use these circles just as you do the fraction line circles. In the lower part of the grid, fill in the numbered
circles that correspond to the numbers in your answer.
Here are some examples. Note that for grid-in responses, answers can begin on the left or the right.

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25
Chapter 1
All About
the SAT®

HOW THE SAT ® IS SCORED
OK, you’ve filled in all your answer circles and perhaps written an essay. The 3 hours (and 50 minutes if you are taking the optional
essay portion) are up (not a minute too soon), and you’ve turned in your answer sheet and your essay sheet. What next? Off your
answers go to the machines at College Board and to the high school and college teachers who have been trained to read and
score the essays. The machines can scan the bubble sheets in seconds and calculate a score for most of your test. If you are taking
the optional essay portion, two readers will score it based on three criteria: reading, analysis, and writing. Their scores will be
combined and reported separately from the main portion of the SAT®.

Peterson’s SAT® Prep Guide 2017

In scoring the multiple-choice and grid-in sections of the SAT®, the machines give one point for each correct answer. Incorrect
answers have no effect on your score. Each reader of your essay uses a rubric against which he or she reads your essay. Each reader
then gives your essay a score from 1 to 4. The two scores will be combined to give you an essay subscore.
The result of these calculations for each part of the SAT®—Math and Evidence-Based Reading and Writing—is your raw score.
This is then converted to a scaled score between 400 and 1600. Your essay will be given a score ranging between 6 and 24, and
it will be reported separately. These scores will be reported to you and to the colleges you have chosen.
Remember, if you take the SAT® more than once, you can choose whether the schools you are applying to receive the scores
from each test date or just some of them.

NOTE: Because the SAT® can vary in format, scaled scores allow the test-maker to account for differences from
one version of the SAT® to another. Using scaled scores ensures that a score of 500 on one SAT® is equivalent to
500 on another.

STRATEGIES FOR SAT ® SUCCESS
What makes some people better test-takers than others? The secret isn’t just knowing the subject; it’s knowing specific test-taking
strategies that can add up to extra points. This means psyching out the test, knowing how the test-makers think and what they’re
looking for, and using this knowledge to your advantage. Smart test-takers know how to use pacing and guessing to add points
to their score.

Pace Yourself

26
Chapter 1

Suppose there are 20 questions in one of the math sections and they need to be answered in 25 minutes. That means that you
have 1 minute and 15 seconds to answer each question. But smart test-takers know that’s not the best way to use their time. If
you use less than a minute to answer the easier questions, you’ll have extra time to answer the more difficult ones. That’s why
learning to pace yourself is so important.

All About
the SAT®

ALERT: Don’t spin your wheels by spending too much time on any one question. Give it some thought, take your best shot,
and move along.

Question Sets in Math Usually Go from Easiest to Most Difficult—You Should, Too
A question set is one set of similar questions within the larger math and evidence-based reading and writing sections. In the
math sections, SAT® questions follow the pattern of easiest to hardest. Work your way through the easier questions as quickly as
you can. That way you’ll have more time for the more difficult ones.
But two words of caution: First, what may be easy to the test-writer may not be to you. Don’t panic if Question 3 seems hard. Try
to work through it, but don’t spend too much time on it if it’s a topic such as factoring that has just never been easy for you to
understand. Second, work quickly but carefully. Don’t work so fast that you make a silly mistake and lose a point that you should
have gained.

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You Can Set Your Own Speed Limit
All right, how will you know what your speed limit is? Use the practice tests to check your timing and see how it affects your
answers. If you’ve answered most of the questions in the time limit but have a lot of incorrect answers, you’d better slow down.
On the other hand, if you are very accurate in your answers but aren’t answering every question in a section, you can probably
pick up the pace a bit.

It’s Smart to Keep Moving
It’s hard to let go, but sometimes you have to. Don’t spend too much time on any one question before you’ve tried all the questions in a section. There may be questions later on in the test that you can answer easily, and you don’t want to lose points just
because you didn’t get to them.

The Easy Choice Isn’t Always Best
Are you at the end of a math section? Remember, that’s where you’ll usually find the hardest questions, which means that the
answers are more complex. Look carefully at the choices and really think about what the question is asking.

You Don’t Have to Read the Directions
What? Yes, you read it correctly the first time—you don’t have to read the directions. By the time you actually sit down to take the
SAT®, you’ve read this book, you’ve taken all the practice tests you could find, and you’ve read enough SAT® directions to fill a library.
So when the exam clock starts ticking, don’t waste time rereading directions you already know. Instead, go directly to Question 1.

27

You’re Going to Need a Watch
If you’re going to pace yourself, you need to keep track of the time—and what if there is no clock in your room or if the only clock
is out of your line of vision? That’s why it’s a good idea to bring a watch to the test. A word of warning: Don’t use a watch alarm
or your watch will end up on the proctor’s desk.

Chapter 1
All About
the SAT®

MAKE AN SAT ® STUDY PLAN
As with almost any form of learning, preparing for the SAT® is an investment of time. The more you have, the better your chances
of boosting your score significantly. Next, we’ll walk you through two different study plans, each tailored to a specific amount of
preparation time. Choose the plan that fits your circumstances and adapt it to your needs.
Regardless of how much time you have before the actual exam, your first step should be to take the Diagnostic Test in Part II of
this book. After you score it, compute your category percentages to assess your relative strengths and weaknesses. Hang on to
the scoring sheet so you know where to get started.

The Complete Plan
If you have three or more months to prepare, you should congratulate yourself! This will give you sufficient time to familiarize
yourself with the test, learn critical strategies, review grammar and math fundamentals, practice writing, and take full-length tests.

Peterson’s SAT® Prep Guide 2017

You’ll get the most out of your SAT® preparation if you:

•
•
•
•
•
•

Reread this chapter to ensure that you understand the format, structure, and scoring of the SAT®.
Take the Diagnostic Test and identify your areas that need improvement.
Read each and every strategy and review chapter.
Work through all the examples, exercises, and practice exams.
Read all the answer explanations.
Focus on the chapters where your scores show you need to improve.

The Accelerated Plan
If you have one month or less to prepare for the SAT® or if you cannot devote a lot of time to studying for any other reason, follow
the accelerated plan. You’ll get the most out of this plan if you:

• Reread this chapter to ensure that you understand the format, structure, and scoring of the SAT®.
• Take the Diagnostic Test and identify your areas that need improvement.
• Focus on the chapters that cover material that is most problematic for you and work through all the examples and
exercises in these chapters.

• Work through as many practice exams as you can.
• Read all the answer explanations.

28

NOTE: You may be wondering how you can possibly wade through all this information in time for the test. Don’t be
discouraged! We wrote this book knowing that some of you would be on very condensed schedules. The information
in this section will help you construct a study plan that works for you—one that will help you boost your score no
matter how limited your time may be. Remember, though, that practice and targeted study are essential elements
of that score boosting, so invest as much time as possible in your SAT® preparation.

Chapter 1
All About
the SAT®

MEASURING YOUR PROGRESS
It does seem as if you’re on a treadmill sometimes, doesn’t it? Question after question after question—are you really getting
anywhere? Is all of this studying really working?
The way to find out is to monitor your progress throughout the preparation period, whether it’s three months or four weeks. By
taking a diagnostic examination at the beginning, you’ll establish your skill baseline, and you’ll be able to craft the study plan
that’s right for you. Then, you can either start to read the entire book (if you are using the complete plan) or go directly to the
chapters that address your weaknesses (if you are using the accelerated plan). At the end of each chapter, complete the exercises
and compare your percentages to your original diagnostic percentages. How have you improved? Where do you still need work?
Even if you haven’t reached your ultimate performance goal, are you at least applying new test-taking methods?

Here’s an important point: You don’t have to go through the book in order. You might want to start with
the topic that you find most difficult, such as functions or grammar, or the question type that you’re
most unsure about, such as grid-ins. Then move to the next most difficult and so on down the line,
saving the easiest topics or question types until the end. If you use the accelerated plan, you should
definitely take this approach.

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SIMULATE TEST-TAKING CONDITIONS
The five full-length practice exams in Chapter 14 can help you prepare for the experience of taking a timed, standardized test.
Taking these tests will improve your familiarity with the SAT®, reduce your number of careless errors, and increase your overall
level of confidence. To make sure that you get the most out of this practice, you should do everything in your power to simulate
actual test-taking conditions.

Find a Block of Time
Because the SAT® is administered in one long block of time, the best way to simulate test-taking conditions is to take an entire
practice exam in one sitting. This means that you should set aside 3½–4 hours of consecutive time.
If you find it difficult to find approximately 4 quiet hours at home, maybe take the test in the library. If you decide to take a test
at home, take precautions. Let your friends know you are taking a practice test, put your phone in another room, and convince
siblings to stay out of your room. Easier said than done, right? Although infrequent interruptions won’t completely invalidate
your testing experience, you should try to avoid them.

Work at a Desk and Wear a Watch
Don’t take a practice test while you are lounging on your bed. After all, the SAT® proctors won’t let you take the test lying down!
Clear off sufficient space on a desk or table to work comfortably. Wear a watch to properly administer the sections under timed
conditions. Or use a timer. The time for each section is marked on the section, so check the beginning of each section and set
your timer or your watch for that amount of time.
You are not allowed to explore other sections on the test while you are supposed to be working on a particular one. So when you
take your practice tests, don’t look ahead or back. Take the full time to complete each section.

29
Chapter 1

If you’re worried that you won’t be able to resist the temptation to check the answer keys
during the practice tests, cover them up before you take a test. Don’t allow yourself to become
dependent upon a sneak look now and then. You won’t have answer keys available on test
day, and the main purpose of the practice tests is to prepare you for the real experience.

All About
the SAT®

Practice on a Weekend Morning
Since the SAT® is typically administered at 8:30 a.m. on Saturday (or Sunday for religious observers), why not take the practice test
at the exact same time on a weekend morning? You should be most energetic in the morning anyway. If you are not a morning
person, now is a good time to become one since that’s when you’ll have to take the actual SAT®! When you take the practice test,
allow yourself two breaks. Give yourself a 5-minute break after Section 2: Writing and Language Test to run to the bathroom, eat
a snack, and re-sharpen your pencils. You can take another 5-minute break after Section 4: Math Test—Calculator.
Remember that your goal is to take these practice tests in as true an environment as possible so that you’re prepared to take the
real SAT®. You will be accustomed to sitting for a long period of time, but you will get two breaks. This knowledge will make you
considerably less anxious on test day.

Peterson’s SAT® Prep Guide 2017

The following table puts all of the SAT® section times in a one-stop format, so you can refer to it often when planning your SAT®
study time.

Section

Number of Questions

Time Allowed

Reading

52

65 minutes

Writing and Language

44

35 minutes

Math Test—No Calculator

20

25 minutes

Math Test—Calculator

38

55 minutes

Essay

--

50 minutes

One Third of the Way Through Your Study
When you are approximately one third of the way through your plan of study—this can be after ten days or a month—it’s time
to take one of the practice tests. When you have finished scoring and reading the answer explanations, compare your scores with
your original diagnostic scores. Hopefully, you’re doing better. But if you’re not, don’t panic. At this point in test preparation, it’s
not unusual to score about the same as you did at the beginning.
What’s more important than what you scored is how you took the practice test. Did you really use the test-taking strategies to
which you’ve been introduced? If you didn’t, go back to the strategy chapters and either reread them, if you are doing the complete plan, or at least reread the summaries, if you are on the accelerated plan. Then continue your review. Read more review
chapters and complete the exercises.

30
Chapter 1
All About
the SAT®

Two Thirds of the Way Through Your Study
After you have worked through most of the review chapters (under the complete plan) or all of the material relating to your
areas of weakness (under the accelerated plan), it’s time to take another practice test. By now, you should be seeing some real
improvement in your scores. If you are still having trouble with certain topics, review the problematic material again.

The Home Stretch
For the most part, the last phase of study should involve less learning and more practice. Take more practice tests! By now, you
probably understand how to take the exam. What you need is more practice taking the test under simulated test-day conditions
to work on your pacing and test-taking strategies.
When you take additional practice exams, be sure to do so in a near-test environment. Keep analyzing your scores to ensure that
all of this practice is working. Determine which areas need additional work. If you skipped over any of the review chapters in this
book, go back and use the exercises to improve your skills.

The Final Week
One last word of advice: No matter which study plan you select, you should probably take one full, timed practice SAT® the week
before you take the actual SAT®. This will get you ready for the big day. But don’t take the practice test the day before the real
exam. That’s a time when you should be relaxing, not cramming.

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THE NIGHT BEFORE AND DAY OF THE EXAM
If you follow the guidelines in this book, you will be extremely well prepared. You will know the format inside and out; you will
know how to approach every type of question; you will have worked hard to strengthen your weak areas; and you will have taken
multiple practice tests under simulated testing conditions. The last 24 hours before the SAT® exam is not the time to cram—it’s
actually the time to relax. Remember that the SAT® is primarily a test of how you think, not what you know. So last-minute
cramming can be more confusing than illuminating.
In the morning, take a shower to wake up and then eat a sensible breakfast. If you are a person who usually eats breakfast, you
should probably eat your customary meal. If you don’t usually eat breakfast, don’t gorge yourself on test day, because it will be
a shock to your system. Eat something light (like a granola bar and a piece of fruit) and pack that snack.

Test Day Checklist
On the night before the big day, find a diversion to keep yourself from obsessing about the SAT®. Maybe stay home
and watch some of your favorite television shows. Or go out to an early movie. Do whatever is best for you. Just
make sure you get plenty of sleep.
You should also lay out the following items before you go to bed:
Test ticket
A cceptable photo ID
S harp pencils with erasers

NOTE: Make sure you allow enough time to arrive at the
test site at least 15 minutes before the 8 a.m. arrival time.
You don’t want to raise your level of anxiety by having to
rush to get there.

P ermissible calculator
S nack and bottle of water
A  sweater or sweatshirt in case of cooler test center conditions (optional)

31
Chapter 1
All About
the SAT®

Peterson’s SAT® Prep Guide 2017

TOP 10 STRATEGIES TO RAISE YOUR SCORE
When it comes to taking the SAT®, some test-taking skills will do you more good than others. There are concepts you can learn
and techniques you can follow that will help you do your best. Here’s our pick for the top 10 strategies to raise your score:

32
Chapter 1
All About
the SAT®

1.

Create a study plan and follow it. The right SAT® study plan will help you get the most out of this book in whatever time
you have.

2.

Don’t get stuck on any one question. Since you have a specific amount of time to answer questions, you can’t afford to
spend too much time on any one problem.

3.

Learn the directions in advance. If you already know the directions, you won’t have to waste your time reading them. You’ll
be able to jump right in and start answering questions as soon as the testing clock begins.

4.

If you choose to take the essay portion of the test, it’s important to develop your ideas and express them clearly, using
examples to back them up. Your essay doesn’t have to be grammatically perfect, but it does have to be focused and organized, and it should explain how the author develops his or her argument.

5.

For the Writing and Language Test multiple-choice questions, think about the simplest, clearest way to express an idea.
If an answer choice sounds awkward or overly complicated, chances are good that it’s wrong.

6.

For relevant words in context, be sure to read the sentences around the word carefully. The SAT® is no longer testing obscure
words but instead is focusing on defining words in the context of a passage.

7.

For Evidence-Based Reading Test questions, first skim the passage to see what it’s about. Look for the main ideas, and then
tackle the questions that direct you straight to the answer by referring you to a specific line in the passage. Then work on
the detailed questions that require a closer reading of the passage.

8.

For the math multiple-choice questions, it can help if you know how to approach the problems. If you’re stuck, try substituting numbers for variables. You can also try plugging in numbers from the answer choices. Start with one of the middle
numbers. That way, if it doesn’t work, you can strategically choose one that’s higher or lower.

9.

For the math grid-ins, you determine the answer and fill it into a grid. Be sure to make your best guess, even if you’re
not sure.

10. Finally, relax the night before the test. Don’t cram. Studying at the last minute will only stress you out. Go to a movie or
hang out with a friend—anything to get your mind off the test!

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SUMMING IT UP
• Learning the question types is the best way to prepare for the SAT® exam. Knowing the test format and question types will
relieve test anxiety, because you’ll know exactly what to expect on test day.
1.	Evidence-Based Reading and Writing: The answer to every question will be either directly stated or implied in the
passage.
2.	Standard Written English: These question sets test your ability to spot and correct grammatical errors, usage problems,
and wordiness. You will also be expected to answer questions to improve the development and organization of a particular paragraph or the passage as a whole.
3. Multiple-Choice Math: A set of reference formulas is given at the beginning of each math section, so you don’t have
to worry about forgetting an important formula.
4. Grid-ins: You have to calculate the answer and then fill in circles on the grids provided on the answer sheet. Only the
circles count, so fill in each one correctly.
5. Essay (Optional): You will have 50 minutes to write your essay, which tests reading, analysis, and writing skills. You will
be asked to produce a written analysis of a provided source text. You will need to explain how the author has effectively
built an argument to persuade his or her audience. The readers are trained to evaluate the essays as first drafts, not
polished final products.

• When you take a full practice examination, try to simulate test-taking conditions:
ºº You’ll need to set aside approximately 4 quiet hours.
ºº Work at a desk and wear a watch.
ºº Cover the answers before you start the test.
ºº Whenever possible, take the full practice tests on weekend mornings.

• You may use a calculator on the SAT®, but only in one math section. For some questions, you will need to decide if the
calculator will help you or slow you down.

33

• Every SAT® exam question is worth 1 point, whether it is an easy question or a difficult one. So nail the easier questions—and
Chapter 1

quickly accumulate points.

• Fill in the answer circles cleanly and completely, or you won’t get credit for your answers.
• Random guessing will have little effect on your score, but educated guessing can boost your score.

All About
the SAT®

• Pace yourself and move through the test relatively quickly.
• Relax the evening before the SAT®, but also be sure you’re prepared.
ºº Assemble the supplies you will need for the test.
ºº Pick out what you’ll wear and remember to layer your clothes.
ºº Be sure your calculator has fresh batteries.

• On the morning of the exam, eat breakfast, pack your snack, and leave for the test site in plenty of time to get there at least
15 minutes before the start time.

Peterson’s SAT® Prep Guide 2017

ONLINE
PREP

Want to Know More?

Access more practice questions, valuable lessons, helpful tips, and expert strategies from the following introductory lessons about
the SAT® in Peterson’s SAT® Online Course:

• About the SAT®
• Demystifying the SAT®
• Scoring
To purchase and access the course, go to www.petersons.com/sat.

34
Chapter 1
All About
the SAT®

www.petersons.com

part ii: the diagnostic test

Chapter 2: The Diagnostic Test

Chapter 2:
The Diagnostic Test
OVERVIEW
Introduction to the Diagnostic Test
Answer Sheets
Section 1: Reading Test
Section 2: Writing and Language Test
Section 3: Math Test—No Calculator
Section 4: Math Test—Calculator
Section 5: Essay
Answer Keys and Explanations
Computing Your Scores

INTRODUCTION TO THE DIAGNOSTIC TEST
Before you begin preparing for the SAT® exam, it’s important to know your strengths and the areas where you need improvement.
If you find the questions easy for the Reading Test, for example, it would be a mistake to dedicate hours practicing them. Taking the
Diagnostic Test in this chapter and then working out your scores will help you determine how you should apportion your study time.

Chapter 2
The
Diagnostic
Test

Preparing To Take the Diagnostic Test
If possible, take the test in one sitting. Give yourself at least 4 hours to complete the Diagnostic Test. The actual test is 3 hours and
45 minutes, and you’ll be allowed to take three short breaks—you may even want to have some healthy snacks nearby for a quick
break you’ll want to take. Simulating the test this way will give you an idea of how long the sections are and how it feels to take the
entire test. You will also get a sense of how long you can spend on each question in each section, so you can begin to work out a
pacing schedule for yourself.
First, assemble all the things you will need to take the test. These include:

•
•
•
•

37

No. 2 pencils, at least three
A calculator with fresh batteries
A timer
The answer sheets and the lined paper for the essay—provided on the following pages

Set a timer for the time specified for each section, which is noted at the top of the first page of each test section. Stick to that time,
so you are simulating the real test. At this point, it’s as important to know how many questions you can answer in the time allotted
as it is to answer questions correctly. Good luck!

Peterson’s SAT® Prep Guide 2017

Diagnostic Test—Answer Sheet
Section 1: Reading Test
1.

12.

23.

33.

43.

2.

13.

24.

34.

44.

3.

14.

25.

35.

45.

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15.

26.

36.

46.

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37.

47.

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48.

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49.

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30.

40.

50.

9.

20.

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41.

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10.

21.

32.

42.

52.

11.

22.

Section 2: Writing and Language Test
1.

10.

19.

28.

37.

2.

11.

20.

29.

38.

3.

12.

21.

30.

39.

4.

13.

22.

31.

40.

5.

14.

23.

32.

41.

6.

15.

24.

33.

42.

7.

16.

25.

34.

43.

8.

17.

26.

35.

44.

9.

18.

27.

36.

Section 3: Math Test—No Calculator
1.

4.

7.

10.

13.

2.

5.

8.

11.

14.

3.

6.

9.

12.

15.

Peterson's SAT® Prep Guide 2017

  39

Diagnostic Test—Answer Sheet
Section 3: Math Test—No Calculator
16.

17.

18.

19.

20.

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Diagnostic Test—Answer Sheet
Section 5: Essay
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Diagnostic Test—Answer Sheet

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Diagnostic Test—Answer Sheet

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Diagnostic Test—Answer Sheet

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Diagnostic Test
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

John James Audubon (1785–1851) is known primarily for his bird
studies, but as this passage from Ornithological Biography shows,
he wrote about the behavior of other animals as well.

35

Black Bear

Line
5

10

15

20

25

30

		 The Black Bear (Ursus americanus), however clumsy
in appearance, is active, vigilant, and persevering;
possesses great strength, courage, and address; and
undergoes with little injury the greatest fatigues and
hardships in avoiding the pursuit of the hunter. Like the
Deer, it changes its haunts with the seasons, and for the
same reason, namely, the desire of obtaining suitable
food, or of retiring to the more inaccessible parts, where
it can pass the time in security, unobserved by man,
the most dangerous of its enemies. During the spring
months, it searches for food in the low rich alluvial lands
that border the rivers, or by the margins of such inland
lakes as, on account of their small size, are called by us
ponds. There it procures abundance of succulent roots,
and of the tender juicy stems of plants, on which it chiefly
feeds at that season. During the summer heat, it enters
the gloomy swamps, passes much of its time wallowing
in the mud, like a hog, and contents itself with crayfish,
roots, and nettles, now and then, when hard pressed
by hunger, seizing on a young pig, or perhaps a sow, or
even a calf. As soon as the different kinds of berries which
grow on the mountain begin to ripen, the Bears betake
themselves to the high grounds, followed by their cubs.
In such retired parts of the country where there are no
hilly grounds, it pays visits to the maize fields, which
it ravages for a while. After this, the various species of
nuts, acorns, grapes, and other forest fruits, that form
what in the western country is called mast, attract its
attention. The Bear is then seen rambling singly through
the woods to gather this harvest, not forgetting to rob

40

45

50

55

60

every Bee tree it meets with, Bears being, as you well
know, expert at this operation. You also know that they
are good climbers, and may have been told, or at least
may now be told, that the Black Bear now and then
houses itself in the hollow trunks of the larger trees for
weeks together, when it is said to suck its paws. You
are probably not aware of a habit in which it indulges,
and which, being curious, must be interesting to you.
At one season, the Black Bear may be seen examining
the lower part of the trunk of a tree for several minutes
with much attention, at the same time looking around,
and snuffing the air, to assure itself that no enemy is
near. It then raises itself on its hind legs, approaches
the trunk, embraces it with its forelegs, and scratches
the bark with its teeth and claws for several minutes
in continuance. Its jaws clash against each other, until
a mass of foam runs down both sides of the mouth.
After this it continues its rambles. In various portions
of our country, many of our woodsmen and hunters
who have seen the Bear performing the singular operation just described, imagine that it does so for the
purpose of leaving behind an indication of its size and
power. They measure the height at which the scratches
are made, and in this manner, can, in fact, form an
estimate of the magnitude of the individual. My own
opinion, however, is different. It seems to me that the
Bear scratches on the trees, not for the purpose of
showing its size or its strength, but merely for that of
sharpening its teeth and claws, to enable it better to
encounter a rival of its own species during the amatory
season. The Wild Boar of Europe clashes its tusks and
scrapes the earth with its feet, and the Deer rubs its
antlers against the lower part of the stems of young
trees or bushes, for the same purpose.

Diagnostic Test — reading

Questions 1–10 are based on the following passage.

CONTINUE
Peterson's SAT® Prep Guide 2017

  45

Diagnostic Test
1

2

3

4

5

  46

As used in line 3, “address” refers to
A.

habitat.

B.

anxiety.

C.

skill.

D.

direction.

What is the most likely reason that Audubon wrote about
the black bear?
A.

He wanted to provide more information about
another animal to his readers.

B.

He was fascinated by mammals.

C.

He wanted to prove he had interests other than
birds.

D.

He wanted to show the commonalities in
behavioral patterns of bears and birds.

Which of the following quotes from the text provides
evidence to support the idea that certain dissimilar forest
mammals share some of the same traits?

6

7

8

Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 16–17 (“During . . . swamps”)

B.

Lines 17–18 (“passes . . . mud”)

C.

Lines 19–20 (“now and . . . hunger”)

D.

Lines 20–21 (“seizing on . . . calf.”)

According to Audubon, how are the claws of the black bear
like the tusks of the wild boar?
A.

Both are parts of the body that warn other animals
that they are predators.

B.

Both animals use these parts of their bodies to
forage for crayfish and roots.

C.

Both animals use these body parts to defend
themselves from human predators.

D.

Both are parts of the body that the animal sharpens
to better compete for a mate.

The fact that Audubon calls man the bear’s “most dangerous” enemy (line 10) indicates that he
A.

is a hunter himself.

A.

Lines 5–6 (“Like . . . seasons”)

B.

has some sympathy for hunted bears.

B.

Line 14 (“it procures . . . roots”)

C.

does not believe that bears are dangerous.

C.

Lines 18–20 (“contents itself . . . pig”)

D.

thinks bears are more dangerous than people.

D.

Lines 30–32 (“not forgetting . . . operation”)

Huntsmen and woodsmen claim that the bear scratches
tree bark with its teeth and claws to
A.

sharpen its teeth.

B.

mark the tree for winter hibernation.

C.

ward off potential predators by showing its size.

D.

mark the tree so that other animals can’t harvest its
nuts and acorns.

9

Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 5–6 (“Like the Deer . . . seasons”)

B.

Lines 6–8 (“for the same . . . food”)

C.

Line 8 (“retiring . . . parts”)

D.

Lines 9–10 (“man, . . . enemies.”)

10 The author indicates that he believes that the reader
A.

knows absolutely nothing about bears.

What is the main rhetorical effect of the author’s description of how black bears behave in swamps, lines 16–21?

B.

already has some knowledge of bears.

C.

needs help overcoming a fear of bears.

A.

To show that the bear is an exceptional predator

D.

believes bears can climb trees as well as apes.

B.

To explain why humans might want to hunt bears

C.

To impress the reader with how varied a bear’s
diet is

D.

To create an image of a bear placidly foraging for
food

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Diagnostic Test
Questions 11–21 are based on the following passage.
Thomas Jefferson wrote in 1787 to his nephew, Peter Carr, a student
at the College of William and Mary.
Paris, August 10, 1787

Line
5

10

15

		 Dear Peter, I have received your two letters of
December 30 and April 18 and am very happy to find by
them, as well as by letters from Mr. Wythe,* that you have
been so fortunate as to attract his notice and good will: I
am sure you will find this to have been one of the more
fortunate events of your life, as I have ever been sensible
it was of mine. I enclose you a sketch of the sciences to
which I would wish you to apply in such order as Mr. Wythe
shall advise: I mention also the books in them worth your
reading, which submit to his correction. Many of these
are among your father’s books, which you should have
brought to you. As I do not recollect those of them not in
his library, you must write to me for them, making out a
catalogue of such as you think you shall have occasion for
in 18 months from the date of your letter, and consulting
Mr. Wythe on the subject. To this sketch I will add a few
particular observations.
		

1. Italian. I fear the learning of this language will

ploughman and a professor. The former will decide it
as well, and often better than the latter, because he has
not been led astray by artificial rules.
*George Wythe, a well-respected scholar, the first American
law professor, and one of the signatories of the Declaration of
Independence, became an important teacher and mentor to
Thomas Jefferson.

11 What is the best description of Mr. Wythe and his relationship to the Jefferson family?
A.

Teacher

B.

Cousin

C.

Family friend

D.

Public servant

12 What is the purpose of Jefferson’s letter to his nephew?
A.

To advise him about his education

B.

To advise him about leading a moral life

C.

To make sure he will learn a second language

D.

To keep in touch with his family while abroad

20 confound your French and Spanish. Being all of them

degenerated dialects of the Latin, they are apt to mix in
conversation. I have never seen a person speaking the
three languages who did not mix them. It is a delightful
language, but late events having rendered the Spanish
25 more useful, lay it aside to prosecute that.
		 2. Spanish. Bestow great attention on this, and
endeavor to acquire an accurate knowledge of it. Our
future connections with Spain and Spanish America will
render that language a valuable acquisition. The ancient
30 history of a great part of America too is written in that
language. I send you a dictionary.
		 3. Moral philosophy. I think it lost time to attend
lectures in this branch. He who made us would have been
a pitiful bungler if he had made the rules of our moral
35 conduct a matter of science. For one man of science, there
are thousands who are not. What would have become of
them? Man was destined for society. His morality therefore
was to be formed to this object. He was endowed with a
sense of right and wrong merely relative to this. This sense
40 is as much a part of his nature as the sense of hearing,
seeing, feeling; it is the true foundation of morality. . . .The
moral sense, or conscience, is as much a part of man as
his leg or arm. It is given to all human beings in a stronger
or weaker degree, as force of members is given them
45 in a greater or less degree. . . . State a moral case to a

13 What does Jefferson suggest his reader do about studying
the Italian language?
A.

Ignore it to pursue Spanish instead

B.

Ignore it to study French instead

C.

Use it as a building block to studying Spanish

D.

Use it in conversation with Spanish people

14 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 19–20 (“I fear . . . Spanish.”)

B.

Lines 20–22 (“Being all . . . conversation.”)

C.

Lines 22–23 (“I have . . . mix them.”)

D.

Lines 23–25 (“It is a . . . prosecute that.”)

CONTINUE
Peterson's SAT® Prep Guide 2017

  47

Diagnostic Test
15 In lines 42–43, Jefferson compares conscience to a physical
limb of the body to show

18 Jefferson tells his nephew to lay Italian aside because it is
A.

a degenerated dialect.

A.

that it is natural and present in all human beings.

B.

not necessary since he already knows French.

B.

how easily we take it for granted.

C.

not useful to be multilingual.

C.

that without it, humans are powerless.

D.

too easy to get it mixed up with Spanish.

D.

how mental and physical states are integrated.

16 Based on the passage, what country does Jefferson think
will most closely align with the newly independent colonies in the future?
A.

England

B.

France

C.

Italy

D.

Spain

19 Which of the following best summarizes Jefferson’s overall
view of morality?
A.

Morality is a science that can be taught by professors
and scholars.

B.

Moral philosophy is self-taught.

C.

A sense of morality is part of human nature.

D.

Humans are moral beings who need rules to guide
their behavior.

17 By “lost time” (line 32), Jefferson means
A.

wasted time.

B.

the past.

C.

missing time.

D.

youth.
Three Generations of the Jefferson Family
Peter Jefferson (b: 1708; d: 1757) - [spouse] Jane Randolph (b: 1721; d: 1776)
[children: 10]

Thomas (1743 - 1826) - [spouse] Martha Wales (1748 - 1782) Martha (1746 - 1811) - [spouse] Dabney Carr (1743 - 1773)
[children: 6]

[children: 6]

(others died before reaching adulthood)

Martha (b: 1772; d: 1836)

Mary (b: 1778; d: 1782)

20 Based on information in the family tree, Peter may have
relied on advice from his uncle Thomas because Peter

21 Which of the following best describes the tone of Jefferson’s letter to his nephew?

considered Thomas to be a better parental figure
than his father was.

A.

Invested and warm

B.

Anxious and worried

B.

did not receive reliable advice from his own mother.

C.

Objective and matter-of-fact

C.

did not have a father, and his mother was busy with
her 5 other children.

D.

Distant and preoccupied

D.

wanted the best education so he could help take
care of his 5 siblings.

A.

  48

Peter (b: 1770; d: 1815)

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Diagnostic Test
Questions 22–32 are based on the following passage
and supplementary material.
This excerpt is from the article “New Link in the Food Chain? Marine
Plastic Pollution and Seafood Safety,” by Nate Seltenrich. It has been
reproduced from the journal Environmental Health Perspectives.
		 World plastics production has experienced almost
constant growth for more than half a century, rising from
approximately 1.9 tons in 1950 to approximately 330
Line million tons in 2013. The World Bank estimates that 1.4
5 billion tons of trash are generated globally each year,
10% of it plastic. The International Maritime Organization
has banned the dumping of plastic waste (and most
other garbage) at sea. However, an unknown portion of
the plastic produced each year escapes into the envi10 ronment—instead of being landfilled, incinerated, or
recycled—and at least some of it eventually makes its way
to sea.
		 Plastics that reach the ocean will gradually break
down into ever-smaller pieces due to sunlight exposure,
15 oxidation, and the physical action of waves, currents, and
grazing by fish and birds. So-called microplastics—variably
defined in the scientific literature and popular press as
smaller than 1 or 5 mm in diameter—are understood to
be the most abundant type of plastic in the ocean. The 5
20 Gyres’ authors* found microplastics almost everywhere
they sampled, from near-shore environments to the open
ocean, in varying concentrations, and they estimated
that particles 4.75 mm or smaller—about the size of a
lentil—made up roughly 90% of the total plastic pieces
25 they collected.
		 But the degradation of larger pieces of plastic is not
the only way microplastics end up in the ocean. Nurdles—
the plastic pellets used as a feedstock for producing
plastic goods—can spill from ships or land-based sources,
30 and “microbeads” used as scrubbing agents in personal
care products such as skin cleansers, toothpastes, and
shampoos, can escape water-treatment facilities and pass
into water-sheds with treated water. (In June 2014, Illinois
became the first US state to ban the manufacture and
35 sale of products containing microbeads, which have been
documented in the Great Lakes and Chicago’s North Shore
Channel.)
		 Marine organisms throughout the food chain
commonly consume plastics of various sizes. The tiniest
40 microplastics are small enough to be mistaken for food by
zooplankton, allowing them to enter the food chain at very
low trophic levels. Some larger predators are thought to
confuse nurdles (which typically measure less than 5 mm
in diameter) with fish eggs or other food sources.

45 		

Once plastics have been consumed, laboratory tests
show that chemical additives and adsorbed pollutants and
metals on their surface can desorb (leach out) and transfer
into the guts and tissues of marine organisms. . . .
		

Research has shown that harmful and persistent

50 substances can both bioaccumulate (or increase in

concentration as exposures persist) and biomagnify (or
increase in concentration at higher trophic levels) within
organisms as they assume some of the chemical burden
of their prey or environment. Yet again, no research has yet
55 demonstrated the bioaccumulation of sorbed pollutants
in the environment.
		 Three key questions remain to be determined. To
what extent do plastics transfer pollutants and additives to
organisms upon ingestion? What contribution are plastics
60 making to the contaminant burden in organisms above
and beyond their exposures through water, sediments, and
food? And, finally, what proportion of humans’ exposure
to plastic ingredients and environmental pollutants occurs
through seafood? Researchers are moving carefully in the
65 direction of answers to these questions. . . .
		 New laws . . . could require handling plastics more
responsibly at the end of their useful life through recycling,
proper disposal, and extended producer responsibility.
		

Rolf Halden, director of the Center for Environmental

70 Security at the Biodesign Institute at Arizona State Uni-

versity, advocates for another solution: manufacturing
more sustainable plastics from the start. “We need to
design the next generation of plastics to make them more
biodegradable so that they don’t have a long half-life,
75 they don’t accumulate in the oceans, and they don’t have
the opportunity to collect chemicals long-term,” he says.
“There’s just no way we can shield people from all exposures that could occur. Let’s design safer chemicals and
make the whole problem moot.”
*The 5 Gyres Institute addresses plastic pollution in the ocean.

22 According to the passage, plastic is
A.

wasted more than any other material.

B.

responsible for a massive amount of waste.

C.

not being produced as much as it once was.

D.

the single most dangerous material to the planet.

CONTINUE
Peterson's SAT® Prep Guide 2017

  49

Diagnostic Test
23 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 1–2 (“World . . . century”)

A.

Passing laws to mandate more rigorous recycling

B.

Lines 4–6 (“The World . . . it plastic.”)

B.

Developing plastics that are biodegradable

C.

Lines 6–8 (“The International . . . at sea.”)

C.

Making plastics that are safe to ingest

D.

Lines 8–10 (“However . . . environment”)

D.

Banning the production of new plastic products

24 Which best describes the overall tone of the article?

  50

25 What solution does Rolf Halden support to decrease the
effects of pollution from plastics on humans?

A.

Neutral and scientific

B.

Emotional and persuasive

C.

Personal and human

D.

Subjective and opinionated

www.petersons.com

26 This article was most likely written to
A.

offer a theory about why the environment is in
danger.

B.

inform the public of the problems of plastic in the
ocean.

C.

start a movement to halt all plastic production.

D.

inspire readers to clean up the oceans personally.

Diagnostic Test
27 Which choice provides the best evidence for the answer
to the previous question?

30 Which of the following words would be most helpful in
figuring out the meaning of the word “adsorbed” (line 46)?

A.

Lines 45–48 (“Once plastics . . . organisms . . . ”)

A.

Absolve

B.

Lines 49–51 (“Research . . . biomagnify”)

B.

Adhere

C.

Lines 54–56 (“Yet again . . . environment.”)

C.

Absorb

D.

Line 57 (“Three key . . . determined.”)

D.

Sorbet

28 Which of the following statements could be learned from
the diagram on the previous page about how plastics
disrupt the food chain?
A.

Plastics enter the food chain when small fish eat
small pieces of plastic.

B.

Sunlight breaks down larger pieces of plastic that
have been tossed in the ocean.

C.

Emptying wastewater directly into the ocean is
illegal in many places.

D.

People should only eat a limited amount of seafood
because it may contain unsafe contaminants.

29 Why did Illinois ban the sale of certain personal care
products?
A.

Residues from the products were ending up in the
ocean.

B.

The containers couldn’t be recycled.

C.

The products were determined to be carcinogenic.

D.

The products contained microbeads that were
getting into the water system.

31 One of the questions the author raises in lines 57–65 deals
with
A.

how much plastic waste from the oceans people
might be ingesting.

B.

how sea creatures happen to ingest plastic waste in
the oceans.

C.

what kinds of plastic waste can be found in the
oceans.

D.

why people are so careless about dumping plastic
waste into the oceans.

32 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 57–59 (“To what . . . ingestion?”)

B.

Lines 59–62 (“What contribution . . . food?”)

C.

Lines 62–64 (“And, finally . . . seafood.”)

D.

Line 64–65 (“Researchers . . . questions . . . ”)

CONTINUE
Peterson's SAT® Prep Guide 2017

  51

Diagnostic Test
Questions 33–42 are based on the following passage.
Angel Decora was born Hinookmahiwikilinaka on the Winnebago
Reservation in Nebraska in 1871. She worked as a book illustrator,
particularly on books by and about Native Americans, and lectured
and wrote about Indian art. The story from which this excerpt is
taken, “The Sick Child,” may be autobiographical.
		 It was about sunset when I, a little child, was sent
with a handful of powdered tobacco leaves and red
feathers to make an offering to the spirit who had caused
Line the sickness of my little sister. It had been a long, hard
5 winter, and the snow lay deep on the prairie as far as
the eye could reach. The medicine-woman’s directions
had been that the offering must be laid upon the naked
earth, and that to find it I must face toward the setting
sun.
10 		

I was taught the prayer: “Spirit grandfather, I offer
this to thee. I pray thee restore my little sister to health.”
Full of reverence and a strong faith that I could appease
the anger of the spirit, I started out to plead for the life
of our little one.

15 		

But now where was a spot of earth to be found in
all that white monotony? They had talked of death at
the house. I hoped that my little sister would live, but I
was afraid of nature.

		 I reached a little spring. I looked down to its pebbly
20 bottom, wondering whether I should leave my offering
there, or keep on in search of a spot of earth. If I put my
offering in the water, would it reach the bottom and
touch the earth, or would it float away, as it had always
done when I made my offering to the water spirit?
25 		

Once more I started on in my search of the bare
ground.

		 The surface was crusted in some places, and
walking was easy; in other places I would wade through
a foot or more of snow. Often I paused, thinking to clear
30 the snow away in some place and there lay my offering.
But no, my faith must be in nature, and I must trust to it
to lay bare the earth.
		

It was a hard struggle for so small a child.

		 I went on and on; the reeds were waving their tas35 selled ends in the wind. I stopped and looked at them.
A reed, whirling in the wind, had formed a space round
its stem, making a loose socket. I stood looking into the
opening. The reed must be rooted in the ground, and
the hole must follow the stem to the earth. If I poured
40 my offerings into the hole, surely they must reach the

  52

www.petersons.com

ground; so I said the prayer I had been taught, and
dropped my tobacco and red feathers into the opening
that nature itself had created.
		

No sooner was the sacrifice accomplished than a

45 feeling of doubt and fear thrilled me. What if my offering

should never reach the earth? Would my little sister die?
		 Not till I turned homeward did I realize how cold I
was. When at last I reached the house they took me in
and warmed me, but did not question me, and I said
50 nothing. Everyone was sad, for the little one had grown
worse.
		 The next day the medicine woman said my little
sister was beyond hope; she could not live. Then bitter
remorse was mine, for I thought I had been unfaithful,
55 and therefore my little sister was to be called to the
spirit-land. I was a silent child, and did not utter my
feelings; my remorse was intense.
		 My parents would not listen to what the medicine-woman had said, but clung to hope. As soon as
60 she had gone, they sent for a medicine-man who lived
many miles away.
		 He arrived about dark. He was a large man, with
a sad, gentle face. His presence had always filled me
with awe, and that night it was especially so, for he
65 was coming as a holy man. He entered the room where
the baby lay, and took a seat, hardly noticing any one.
There was silence saving only for the tinkling of the
little tin ornaments on his medicine-bag. He began to
speak: “A soul has departed from this house, gone to the
70 spirit-land. As I came I saw luminous vapor above the
house. It ascended, it grew less, it was gone on its way
to the spirit-land. It was the spirit of the little child who
is sick; she still breathes, but her spirit is beyond our
reach . . .
33 The narrator wants to place her offering correctly because
she
A.

will have to explain her choice to everyone else.

B.

wants to be trusted with similar tasks in the future.

C.

thinks doing so will save her little sister’s life.

D.

is afraid of being punished if she does it incorrectly.

Diagnostic Test
34 The medicine man describes the appearance of the spirit
of the narrator’s sister as
A.

luminous vapor.

B.

a tin ornament.

C.

a baby.

D.

beyond our reach.

35 Why didn’t the girl’s parents send for the medicine man in
the first place?

39 Based on the passage, which choice best describes the
narrator’s relationship with her parents?
A.

The parents seem to treat the narrator as if she
were an adult.

B.

The narrator wishes her parents would give her
more responsibility.

C.

The parents love their youngest child, but not the
narrator.

D.

The narrator receives warmth and validation from
her parents.

A.

He was busy helping another family at the time.

B.

He had to come from a long distance.

C.

They thought the medicine woman would be able
to help their daughter.

A.

A Native American recalls her experience of trying
to save and losing her baby sister.

D.

They preferred a woman to cure their female child.

B.

A Native American child is called upon to make an
offering to the spirits.

C.

A Native American family struggles with illness in
the depths of winter on the Plains.

D.

A Native American family uses their religious beliefs
to try to save their daughter.

36 What evidence from the text shows the girl’s dilemma in
following the medicine woman’s directions?
A.

Lines 7–8 (“the offering . . . naked earth”)

B.

Lines 21–23 (“If I put . . . away”)

C.

Lines 27–29 (“The surface . . . of snow. ”)

D.

Lines 34–35 (“I went on . . . the wind.”)

37 Which title best expresses an important theme of the
passage?

40 What is the central idea in the passage?

41 When the girl says, “bitter remorse was mine” (lines 53–54),
she feels
A.

that she is responsible for her sister’s illness.

B.

badly because she didn’t listen to the medicine
woman.

A.

The Medicine-Man

C.

angry about being given so much responsibility.

B.

Acts of Faith

D.

C.

Native American Culture

guilty because she feels as though she has failed
her sister.

D.

Walking on Snow

38 Which choice provides the best evidence for the answer
to the previous question?

42 Which of the following best describes the meaning of
“thrilled” in line 45?
A.

Inspired

A.

Lines 1–4 (“It was . . . little sister.”)

B.

Refreshed

B.

Lines 12–13 (“Full of . . . spirit”)

C.

Frightened

C.

Lines 44–45 (“No sooner . . . thrilled me.”)

D.

Stimulated

D.

Lines 59–61 (“As soon . . . away.”)

CONTINUE
Peterson's SAT® Prep Guide 2017

  53

Diagnostic Test
Questions 43–52 are based on the following
passages and supplementary material.
Passage 1: Fanny Wright was a reformer, author, and orator, which
were unusual occupations for a woman in the early nineteenth
century.
Passage 2: Young Robert Emmet was condemned to death for
treason after organizing a rebellion against the English in Ireland.
He, too, had achieved fame as an orator, with speeches decrying
tyranny.

35

40

PASSAGE 1
Fanny Wright to a Fourth-of-July Audience
at New Harmony, Indiana (1828)

Line
5

10

15

20

25

		 In continental Europe, of late years, the words patriotism and patriot have been used in a more enlarged
sense than it is usual here to attribute to them, or than
is attached to them in Great Britain. Since the political
struggles of France, Italy, Spain, and Greece, the word
patriotism has been employed, throughout continental
Europe, to express a love of the public good; a preference
for the interests of the many to those of the few; a desire
for the emancipation of the human race from the thrall of
despotism, religious and civil: in short, patriotism there is
used rather to express the interest felt in the human race
in general than that felt for any country, or inhabitants
of a country, in particular. And patriot, in like manner, is
employed to signify a lover of human liberty and human
improvement rather than a mere lover of the country in
which he lives, or the tribe to which he belongs. Used
in this sense, patriotism is a virtue, and a patriot is a
virtuous man. With such an interpretation, a patriot is a
useful member of society capable of enlarging all minds
and bettering all hearts with which he comes in contact;
a useful member of the human family, capable of establishing fundamental principles and of merging his own
interests, those of his associates, and those of his nation
in the interests of the human race. Laurels and statues
are vain things, and mischievous as they are childish; but
could we imagine them of use, on such a patriot alone
could they be with any reason bestowed. . . .

PASSAGE 2
Robert Emmet to the Court That
Condemned Him to Death (1803)

30

  54

		 I am charged with being an emissary of France An
emissary of France! and for what end? It is alleged that
I wish to sell the independence of my country; and for
what end? . . .

www.petersons.com

45

50

		 No; I am no emissary. . . . Sell my country’s independence to France! and for what? Was it a change of masters?
No, but for ambition. Oh, my country! Was it personal
ambition that could influence me? Had it been the soul
of my actions, could I not, by my education and fortune,
by the rank and consideration of my family, have placed
myself amongst the proudest of your oppressors? My
country was my idol! To it I sacrificed every selfish, every
endearing sentiment; and for it I now offer up myself, O
God! No, my lords; I acted as an Irishman, determined
on delivering my country from the yoke of a foreign
and unrelenting tyranny, and the more galling yoke of
a domestic faction, which is its joint partner. . . . It was
the wish of my heart to extricate my country from this
double riveted despotism—I wished to place her independence beyond the reach of any power on earth. I
wished to exalt her to that proud station in the world.
Connection with France was, indeed, intended, but only
as far as mutual interest would sanction or require.
		 Were the French to assume any authority inconsistent with the purest independence, it would be the
signal for their destruction . . .
		

I wished to prove to France and to the world that

55 Irishmen deserved to be assisted . . . I wished to procure

for my country the guarantee which Washington procured for America—to procure an aid, . . . which would
perceive the good, and polish the rough points of our
character . . . These were my objects; not to receive new
60 taskmasters, hilt to expel old tyrants. And it was for these
ends I sought aid from France . . .
		
Let no man dare, when I am dead, to charge me with
dishonor; let no man attaint my memory by believing
that I could have engaged in any cause but that of my
65 country’s liberty and independence . . . The proclamation
of the provisional government speaks for our views;
no inference can be tortured from it to countenance
barbarity or debasement at home, or subjection,
humiliation, or treachery from abroad. I would not have
70 submitted to a foreign oppressor, for the same reason
that I would resist the foreign and domestic oppressor.
In the dignity of freedom, I would have fought upon the
threshold of my country, and its enemy should enter only
by passing over my lifeless corpse. And am I, who lived
75 but for my country, and who have subjected myself to
the dangers of the jealous and watchful oppressor, and
the bondage of the grave, only to give my countrymen
their rights, and my country its independence . . . —no,
God forbid!

Diagnostic Test
43 Which of the following statements from Emmet’s speech
shows that he thinks he is a martyr?

45 Based on the timeline, the historical events of which year
most likely influenced the American concept of patriotism?

A.

Lines 36–38 (“could I not . . . your oppressors”)

A.

1707

B.

Lines 46–47 (“I wished to . . . on earth”)

B.

1776

C.

Lines 54–55 (“I wished to . . . to be assisted”)

C.

1803

D.

Lines 62–63 (“Let no man . . . with dishonor”)

D.

1828

44 Which of the following of Emmet’s statements shows that
he thinks he is a patriot?
A.

Line 32 (“No; . . . emissary”)

B.

Lines 34–35 (“Was it . . . influence me?”)

C.

Lines 54–55 (“I wished . . . assisted”)

D.

Lines 65–66 (“The proclamation . . . for our views”)

Timeline
1707

Acts of Union between Scotland
and England create the Kingdom
of Great Britain

1776–1783

American colonies declare and win
independence

1789

French storm the Bastille (prison),
fight to end French monarchy

1798

Society of United Irishmen rebel
unsuccessfully against British rule

1800

British Parliament passes The Act of
Union, abolishing the Irish parliament

1801

United Kingdom of Great Britain and
Ireland created

1803

United States purchases Louisiana
Territory from France
Robert Emmet leads a rebellion in
Dublin against the union

1803–1815

Napoleonic Wars in Europe
(France vs. European powers)

1808–1833

Spanish wars of independence

1823

France invades Spain to help restore
monarchy

1828

Andrew Jackson elected president of
United States

46 Based on information shown in the timeline, why might
France have turned down Emmet’s request for help?
A.

France was in the midst of trying to restore the
monarchy in Spain.

B.

France was engaged in the drawn-out Napoleonic
Wars.

C.

France had fought its own revolution and didn’t
want to get involved in that of another country.

D.

France was trying to keep the United States from
taking Louisiana.

47 Emmet would not fit Wright’s definition of a patriot
because he
A.

saw no dishonor in his actions.

B.

wanted to free his people.

C.

idolized his own country above all others.

D.

declared the court’s sentence to be unjust.

48 Which one of the following statements is true?
A.

Although years apart, both Wright and Emmet were
advocating to rethink their country’s ideas about
patriotism.

B.

Emmet was focused on freedom and independence
for his own country, while Wright was focused on
freedom and independence for all humankind.

C.

Emmet loved his country more than Wright loved
her country.

D.

Wright didn’t understand tyranny because she lived
in a democracy, while Emmet fought against
tyranny.

CONTINUE
Peterson's SAT® Prep Guide 2017

  55

Diagnostic Test
49 How does the tone of Wright’s speech compare with that
of Emmet’s speech?

51 Which of the following fits Wright’s definition of a patriot?
A.

A person willing to die for their country

A.

Both express anger, although in response to
different causes.

B.

A person who fights for improving the lives of
others

B.

Wright’s expresses a calm plea while Emmet
expresses desperation and anger.

C.

A person who enlists in the armed forces of his
country

C.

Emmet speaks calmly, and Wright speaks
passionately.

D.

A person who loves his country

D.

Both use a tone that prevents their specific
positions from being convincing.

52 When the British government claims that Emmet is an
“emissary” (line 29) of France, they are accusing him of
being

50 Which of the following statements is most analogous to
Emmet’s statement: “In the dignity of freedom, I would
have fought upon the threshold of my country, and its enemy should enter only by passing over my lifeless corpse.”
(lines 72–74)
A.

Never yield to force; never yield to the apparently
overwhelming might of the enemy.

B.

With the enemy at their back, with our bayonets at
their breasts, in the day of their distress, perhaps
the Americans would have submitted . . .

C.

Give me liberty or give me death.

D.

It is sweet and fitting to die for one’s country.

A.

an ambassador.

B.

a spy.

C.

a minister.

D.

a mercenary.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  56

www.petersons.com

Diagnostic Test
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you will
need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you to
consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).

After reading each passage, select the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following passage.

1

While most American cities must adapt to constant growth, Detroit
is undergoing change as a result of depopulation.

Which choice provides the most logical introduction to
the sentence?
A.

NO CHANGE

B.

Civic growth caused by the depression

C.

The improvement in living conditions

D.

The decrease in pollution

manufacturing, and other factors have wreaked havoc on the

A.

NO CHANGE

once prosperous city, driving away its middle class and 2 it

B.

having left behind vast tracts of urban blight.

left behind vast tracts of urban blight.

C.

to leave behind vast tracts of urban blight.

D.

leaving behind vast tracts of urban blight.

A city of 139 square miles, with a long history of growth and
middle-class success, Detroit now faces an unusual, though
not entirely novel, situation for U.S. cities: depopulation. 1
Economic transformations caused by recessions, the loss of

2

Diagnostic Test — writing and language

Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.

CONTINUE
Peterson's SAT® Prep Guide 2017

  57

Diagnostic Test
The statistics 3 are staggering—since 1950, some 60

3

percent of the population has gone elsewhere, leaving the

A.

NO CHANGE

city with 4 20,000 new residents. When the people left,

B.

are staggering since: 1950 some

thousands of businesses went with them.

C.

are staggering since 1950 some

D.

are staggering since; 1950 some

City planners have been responding to the challenge of
depopulation. Over several years, they have studied their

4

urban spaces and used varying and innovative techniques
to 5 confuse the input of some 30,000 of their residents.
Planners have come up with what 6 she calls Detroit
Future City, a vision that takes the long view and is projected
to take some fifty years to implement. Within this plan are
different strands of redevelopment, development, and—most

Which choice provides information that best supports
the claim made by this sentence?
A.

NO CHANGE

B.

100,000 vacant residences or lots

C.

50,000 more middle-class residents

D.

30,000 homeless people

A.

NO CHANGE

B.

belittle

C.

solicit

D.

return

A.

NO CHANGE

B.

they call

C.

he calls

D.

we call

A.

NO CHANGE

B.

In fact,

C.

Nevertheless,

D.

Besides,

5

dramatically—un-development. 7 Similarly, the strategic
plan includes a concept not often seen in U.S. city planning:
downsizing, or what some prefer to call “right sizing.”

6

7

  58

www.petersons.com

Diagnostic Test
[1] One of the boldest suggestions of the plan is a basic

8

conversion of about one third of all Detroit’s urban space. [2]
Making the city more compact, the planners 8

reasoned,

A.

NO CHANGE

B.

insisted

would save money on services and allow them to devote

C.

noted

more resources to a smaller total area. [3] Walking paths,

D.

commented

parks, ponds for rainwater collection and retention (the city’s
sewage system is overburdened), sports fields, meadows,

9

forested areas, campgrounds, and other green space

To improve the flow of this paragraph, sentence 4 should
be placed
A.

where it is now.

B.

before sentence 1.

C.

after sentence 5.

D.

after sentence 6.

for strengthening. [6] The plan also calls for remaining

A.

NO CHANGE

neighborhoods to be 10 transformed but—not by the

B.

transformed—but not by the

traditional models of economic growth. [7] For example, the

C.

transformed but not—by the

city, if organized carefully with viable public transportation

D.

transformed, but not by—the

A.

NO CHANGE

B.

has; namely, healthcare and education; government
and transportation, local businesses

C.

has; namely, healthcare; education; government;
transportation; and local businesses

D.

has; namely, healthcare, education, government,
transportation; and local businesses

initiatives would then gradually transform the shutdown area.
9 [4] The plan contained some creative and bold
suggestions. [5] Controversially, the plan suggests shutting
down services in certain areas to drive current residents
out of them and into neighborhoods being targeted

options, hopes to create jobs right where people live. In
part, the plan is predicated on the idea that within their
own various redevelopment areas, or “natural economic
zones,” people can both live and work in fields that every
city 11 has, namely, healthcare, education, government,

10

11

transportation, and local businesses that meet core needs,
such as grocery stores and eating places. The plan is also
predicated on the idea that the well-planned urban space
generates its own economic success, as well as on the idea
that such areas will eventually draw some outside business
and industry. Debt-ridden Detroit is definitely going to
need the latter. A recent NPR report on Detroit posited that
commercial real estate taxes can make up a substantial 70
percent of the revenue for a city.

CONTINUE
Peterson's SAT® Prep Guide 2017

  59

Diagnostic Test
Questions 12–22 are based on the following passage.

12

In a public square on the Indonesian island of Java, dusk falls.
Families gather; it is a festival day. Children dart around while,
on the edges of the square, vendors 12 hawk snacks and

A.

NO CHANGE

B.

stock

C.

advertise

D.

trade

toys. A large screen, lit from behind, stands prominently in
the square. A twenty-piece percussion orchestra, or gamelan,
prepares to play.

13 At this point, the author is considering deleting the underlined sentence. Should the writer do this?

13 The scene is traditional Java, hundreds of years ago.

A.

Yes, because it inserts an irrelevant opinion.

B.

Yes, because it distracts from the main ideas of the
paragraph.

C.

No, because it provides a transition from the
previous paragraph to this one.

D.

No, because it explains what wayang kulit is.

A.

NO CHANGE

B.

traditions and its origins stretch

C.

traditions, its origins stretch

D.

traditions. Its origins stretch

A.

NO CHANGE

The performance is wayang kulit, or shadow puppetry, one
of the world’s oldest storytelling 14 traditions its origins
stretch back to the ancient spiritual practices of Indonesia’s
original inhabitants, who believed that the spirits of the
ancestors governed the living world. Ceremonial puppet plays

14

addressed the spirits, asking them to help the living.
Over two thousand years ago, islands such as Java, Bali, and
Sumatra saw their first 15 Indian migrants, a nation to which
Indonesia was linked through trade relations. In the centuries
that followed, Indian culture influenced every aspect of
Indonesian life.

15

B.

migrants from India, a nation to which Indonesia

The puppet plays reflected these cultural changes. 16 They

C.

Indian migrants, to which a nation Indonesia

began to depict narratives from Hindu religious texts,

D.

Indian migrants, a nation of people to which
Indonesia

including the Mahabharata, the Ramayana, and the Serat
Menak. Traditional Indonesian stories were blended into Hindu
epics or lost altogether. Later, when Islam began to spread

16 At this point, the writer is considering adding the following sentence.

throughout Indonesia, puppet plays again transformed.

A master of shadow puppetry is called a dalang.
Should the writer make this addition here?

  60

www.petersons.com

A.

Yes, because it provides relevant and new
information about the practice of wayang kulit.

B.

Yes, because it adds an important fact to the
paragraph’s focus on shadow puppetry.

C.

No, because it repeats information that has already
been given.

D.

No, because it distracts from the paragraph’s focus
on cultural changes.

Diagnostic Test
The Islamic religion 17 prohibited the display of gods in

17

human form, so Indonesians adapted their art by making flat,

A.

NO CHANGE

leather puppets that cast shadows on a screen. The puppets

B.

discouraged

18 themselves remain unseen during the performances;

C.

hindered

D.

restricted

shadow puppet tradition. 19 Performances are epic events,

A.

NO CHANGE

lasting all night long from sunset to sunrise with no break at

B.

themselves will remain unseen during the
performances

C.

themselves remained unseen during the
performances

D.

themselves had been remaining unseen during the
performances

A.

NO CHANGE

B.

Performances are epic events, lasting from sunset to
sunrise with no break.

C.

Performances are epic events, lasting all night long
from sunset to sunrise without taking a break.

D.

Performances are epic events, lasting all night.

A.

NO CHANGE

B.

Simultaneously he directs, the gamelan the large,
percussive orchestra which consists of percussive,
instruments some of which are mallets.

C.

Simultaneously, he directs the gamelan—the large
percussive orchestra, which consists of percussive
instruments, some of which are mallets.

D.

Simultaneously, he directs, the gamelan, the large,
percussive orchestra, which consists, of percussive
instruments, some of which, are mallets.

only their shadows were visible. Wayang kulit was born.
Java is particularly well-known for its continuation of the

18

all. They take place in public spaces and are performed on
holidays and at family celebrations. At the center is a large
screen, backlit by a gas or electrical light. Behind this screen
sits the dalang, or shadow master, traditionally a man. He
manipulates the puppets—sometimes more than a hundred
of them in one show—with rods, voicing and singing all of the

19

roles. 20 Simultaneously he directs the gamelan the large
percussive orchestra which consists of percussive instruments
some of which are mallets.

20

CONTINUE
Peterson's SAT® Prep Guide 2017

  61

Diagnostic Test
Each puppet is carefully crafted, a flat figure that is perforated

21

to project a detailed shadow. Artists begin creating a puppet

A.

NO CHANGE

by tracing the outline of a paper model on leather. The leather

B.

to manipulate his parts

figure is painstakingly smoothed and treated before being

C.

to manipulate its parts

passed onto another craftsperson, who paints it. Then, the

D.

to manipulate her parts

These puppets follow an established set of conventions: evil

A.

NO CHANGE

characters have grotesque faces, while noble ones have more

B.

that

C.

than

D.

this

puppet’s moving parts—the arms and hands—are added,
along with the sticks used 21 to manipulate their parts.

22

refined features. They are highly stylized caricatures, rather
22 then realistic figures.

Questions 23–33 are based on the following passage
and supplementary material.
Water issues are hardly unknown to the American Southwest, but
they have recently taken on a new urgency.
23 The arid climate and limited water resources of the
American Southwest 24 has always influenced the peoples

23 Which of the following sentences would make the most
effective introductory sentence to this passage?

of the region. The Anasazi, ancient people of some of the
most inhospitable areas of the Southwest, made a series of
accommodations to 25 they’re hot, arid environment by

A.

Consider a vacation to the American Southwest!

B.

What do you know about the majestic American
Southwest?

C.

The Anasazi are the original people who inhabited
the American Southwest.

D.

There’s a serious problem occurring in the American
Southwest.

A.

NO CHANGE

B.

had always influence

C.

have always influenced

D.

is always influenced

A.

NO CHANGE

B.

their hot, arid environment

C.

there hot, arid environment

D.

its hot, arid environment

means of adaptive agricultural practices, cliff-side residences,
and elaborate catchment systems.

24

25

  62

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Diagnostic Test
Today, the American Southwest, simplistically defined in this
document as encompassing all of Utah, Nevada, New Mexico,

26 Which choice most effectively combines the sentences at
the underlined portion?

Arizona, and California, is the country’s fastest-growing
26 region. It is home to more than 50 million people who
are the source of ever-increasing water demands. Yet, the
region is dependent for its water on just two river systems,
the Colorado and the Rio Grande, of which the former is

region, but it is home

B.

region; home

C.

region it is home

D.

region, home

A.

NO CHANGE

B.

California. However,

C.

California? However,

D.

California, however,

A.

NO CHANGE

27

unequivocally the primary.
The Colorado supplies water to some 38 million users and
irrigates some 300 million acres of farmland, much of it in
27 California! However, the mighty Colorado’s flow was
apportioned almost one hundred years ago to include not just

A.

28

the southwestern United States but also Mexico. It was also
apportioned according to a volume that simply does not exist

B.

hoped

in current years; for example, in the years 2001–2006, river

C.

desired

water that had been 28 projected to flow versus river water

D.

thought

that did flow came up a staggering 34 percent short.
In 2014, the U.S. Department of the Interior warned that the

29 At this point, the writer is considering deleting this
sentence. Should the writer do this?

Colorado River basin area “is in the midst of a fourteen-year

A.

Yes, because it repeats information that has already
been presented in the passage.

B.

Yes, because it blurs the paragraph’s focus by
introducing a new idea.

C.

No, because it illustrates the severity of drought
conditions with a specific example.

D.

No, because it introduces the argument that the
Southwest’s water supply is drying up.

A.

NO CHANGE

B.

Equally dire, and possibly more alarming,

C.

Equally dire and possibly more alarming

D.

Equally dire and, possibly more alarming,

A.

NO CHANGE

B.

For all intentional purposes,

C.

For all intents and purposes,

D.

For all intended purposes,

drought nearly unrivaled in 1,250 years.” 29 It further
noted that the river’s two major reservoirs, Lake Powell and
Lake Mead—the once-massive backup systems for years
in which drought occurs—were, alarmingly, more than 50
percent depleted. 30 Equally dire, and possibly, more
alarming, predictions came out of a recent study, cited in
the Proceedings of the National Academy of Science of the

30

United States, that suggested a 50 percent chance of Lakes
Powell and Mead reaching a level so low that they become
inoperable by the 2020s. 31 For all intensive purposes, the
Southwest’s water supply is drying up.
31

CONTINUE
Peterson's SAT® Prep Guide 2017

  63

Diagnostic Test
32 Compounding the problems of drought, increasing

32

population, and an overly optimistic historical assessment

A.

NO CHANGE

of water resources are problems related to climate change.

B.

Escalating

For example, between 2000 and 2014, the 33 highest air

C.

Inflating

temperatures in much of the Southwest rose as much as 2

D.

Exaggerating

degrees, increasing the negative effects of evapotranspiration,
the evaporation of water from the soil. Finally, climate change
and drought are leading to the greater prevalence and
intensity of fires, including so-called “super fires,” a result,
in part, of the beetle infestations and dying trees that are
weakened by the lack of water.

33 Which choice makes appropriate and effective use of the
data in the accompanying map?
A.

NO CHANGE

B.

lowest air temperatures

C.

hottest water temperature

D.

average air temperatures

Average Temperatures in the Southwestern United States 2000–2014 Versus Long-Term Average

This map shows how the average air temperature from 2000 to 2014 has differed from the long-term average (1895–2014). To provide
more detailed information, each state has been divided into climate divisions, which are zones that share similar climate features.

  64

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Diagnostic Test
Questions 34–44 are based on the following passage.
Women in Film: Troubling Inequalities

34 Which choice most effectively establishes the main topic of
the paragraph?
A.

There are many actresses in Hollywood with
extraordinary talent, but they cannot seem to get the
same roles as men.

B.

Though women land far fewer leading roles than
men, in other categories of filmmaking, they do a little
better.

C.

Women are not adequately represented in Hollywood,
either by the roles they play or by the amount of time
they appear on-screen.

D.

The movie industry needs to pay female actresses
more than their male counterparts, in an effort to
attract new and extraordinary talent.

A.

NO CHANGE

B.

agents

C.

necessities

D.

relationships

A.

NO CHANGE

B.

Women simply can’t expect to play the leading roles
men play or even, in general, while there seems to be
no end of extraordinary acting talent among women
in Hollywood, to be on-screen for as many minutes as
men are in any given film.

C.

Women simply can’t expect to play the leading roles
men play or to be on-screen for as many minutes as
men, and there seems to be no end of extraordinary
acting talent among women in Hollywood in general.

D.

While there seems to be no end of extraordinary
acting talent among women in Hollywood, women
simply can’t expect to play the leading roles men
play or even, in general, to be on-screen for as many
minutes as men are in any given film.

34 In a society in which television and movies have been
well documented as 35 roles of social change, current
data about women in the movies are far from reassuring.
36 Women simply can’t expect to play the leading roles men
play or even, in general, to be on-screen for as many minutes
as men are in any given film, while there seems to be no end
of extraordinary acting talent among women in Hollywood. As
for other categories of filmmaking, at least by Oscar standards,
women seem barely to exist at all.
35

36

CONTINUE
Peterson's SAT® Prep Guide 2017

  65

Diagnostic Test
Indeed, 37 women were the protagonists in only 15

37

percent of the top grossing films of 2013, according to a study

A.

NO CHANGE

conducted at San Diego State University. Other study findings

B.

women were the protagonist

included the fact that when women are on-screen, 38 their

C.

a woman was the protagonists

marriage status is more identifiable than men. Also, males over

D.

the protagonists were a woman

A.

NO CHANGE

B.

their marriage status is more identifiable than of a
man.

C.

their marriage status is more identifiable than that of
men.

D.

their marriage status is more identifiable than men’s
marriage.

age 40 are much more commonly represented on-screen than
women in the same age group.

38

Other inequities have been revealed by Cinemetrics, which
strives to gather objective data on movies, and by other
organizations. 39 For example, in 2013, lead actresses in
full-length films spent 57 minutes on-screen, while lead actors
spent 85 minutes on-screen. Compounding the inequity is
the tendency of the camera to stay on a female actress longer
in a single shot, or stare at 40 them passively, while the

39 Which choice most effectively maintains support for claims
or points in the text?

camera moves more actively when it shows a male character.
In other aspects of films, women 41 are treated even more
outrageously. Since the Oscars began in 1928, only 16 percent
of all nominees have been women. In fact, there were no

A.

NO CHANGE

B.

For example, women direct more documentaries
than narrative films.

C.

For example, the highest paid actress in 2013 made
$33 million dollars.

D.

For example, women buy about half of movie tickets
purchased in the United States.

A.

NO CHANGE

B.

him

C.

her

D.

us

A.

NO CHANGE

B.

are taken advantage of.

C.

are cheated.

D.

fare even worse.

women nominees at all in seven categories of achievement for
the 2014 Oscars. More significantly, Oscar trends do not seem
to be improving over time.
40

41

  66

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Diagnostic Test
Some women, however, have managed to shine despite

42

these inequities. Actress Meryl Streep has been nominated

A.

NO CHANGE

for 19 Oscars as of 2015, easily surpassing both male and

B.

famous

female competitors for the record of most Academy Award

C.

forgotten

nominations. She is 42 confused for her strong, authoritative

D.

lambasted

(2014). Streep has received 43 accolades for such parts, as 15

A.

NO CHANGE

of her 19 Academy Award nominations were in the category of

B.

privileges

C.

recognition

D.

attention

A.

NO CHANGE

B.

character love life

C.

character’s love life

D.

character loves life

roles; she portrayed a powerful—if terrifying—boss in The
Devil Wears Prada (2006) and a formidable leader in The Giver

43

Best Actress in a Leading Role. Even Streep, however, is subject
to the inequities of the film industry: in The Devil Wears Prada
her 44 characters love life was brought to the forefront and

44

depicted as a sacrifice that she, as a woman in power, had to
continually make for the good of her career.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

Peterson's SAT® Prep Guide 2017

  67

Diagnostic Test
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions
TURN TO SECTION 3 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

Diagnostic Test — math — no calculator

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

CONTINUE
Peterson's SAT® Prep Guide 2017

  69

Diagnostic Test
SHOW YOUR WORK HERE

1
6

4

2

–2

0

2

4

6

–2

If the line drawn above is translated 3 units to the left and
6 units down, what is the slope of the new line?

2

  70

A.

−

1
9

B.

−

4
3

C.

−

7
10

D.

–2

Catherine is performing a science experiment on the distance traveled by a snail. She sets the snail on her driveway
and records the time it takes the snail to crawl to the end
of her driveway. She uses the equation D = 0.4t + 12, where
D is the total distance traveled in feet, and t represents the
time in minutes. Which of the following statements best
interprets the meaning of 12 in Catherine’s equation?
A.

It would take the snail 12 minutes to reach the end
of the driveway.

B.

The snail began 12 feet from the beginning of the
driveway.

C.

The snail traveled a total distance of 12 feet.

D.

The snail traveled at a rate of 12 feet per minute.

www.petersons.com

Diagnostic Test
3

If –2x + 5 = 2 – (5 – 2x), what is the value of x?
A.

–2

B.

2

C.

3

D.

5

4

SHOW YOUR WORK HERE

15"
6"

6"

15"
T

The figure shows one square inside another and a rectangle
with diagonal T. The best approximation of the value of T,
in inches, is given by which of the following inequalities?

5

A.

8 40

C.

8 6
+ ≥ 40
m n

D.

8 6
+ > 40
m n

SHOW YOUR WORK HERE

Amy is renting a moving van that charges $19.99 per day,
plus an additional $0.15 per mile. A tax of 7.5% is applied
to both the daily rate and the mileage rate. Which of the
following represents the total charge, y, that Amy will pay
to rent the van for one day and drive it miles?
A.

y = 19.99 + 0.075x + 0.15

B.

y = 1.075(19.99) + 0.15x

C.

y = 1.075(19.99 + 0.15x)

D.

y = 1.075(19.99 + 0.15)x

If nails are bought at 35 cents per dozen and sold at 3 for
1
10 cents, the total profit on 5 dozen is
2
A.

25 cents.

B.

27

C.

1
31 cents.
2

D.

35 cents.

1
cents.
2

A cubic foot of concrete weighs approximately 150 pounds.
How many pounds will a similar block of concrete weigh
if the edges are twice as long?
A.

300 pounds

B.

450 pounds

C.

800 pounds

D.

1,200 pounds

CONTINUE
Peterson's SAT® Prep Guide 2017

  79

Diagnostic Test
9

Which of the following expressions is equivalent to
–2(1 – x)2 + 2(1 – x2)?
A.

–2x

B.

–4x2 + 4x

C.

–4x2 – 4x – 4

D.

0

10 An organization is giving away t-shirts for its 5-kilometer
road race. The cost to produce the t-shirts is defined by the
equation C(x) = 7x + 60, where x is the number of t-shirts
produced. The organization gives away the t-shirts for free
to people who sign up for the race more than one month
in advance and pay the $20 sign-up fee. What is the fewest number of people who must sign up in order for the
organization to profit if the only cost is manufacturing the
t-shirts and the only income is the sign-up fee?
A.

3

B.

5

C.

13

D.

20

11 A small college, which has a population of 2,180 students,
recently held a fundraiser in which each male student
raised $20, and each female student raised $25. Together,
they raised a total of $50,000. If x represents the number of
male students in the college and y represents the number
of female students in the college, which system of equations can be used to represent the scenario?

A.

x + y = 50 , 000
20 x + 25 y = 2,180

B.

x + y = 2,180
20 x + 25 y = 50 , 000

  80

C.

x + y = 2,180
25 x + 20 y = 50 , 000

D.

x + y = 50 , 000
25 x + 20 y = 50 , 000

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SHOW YOUR WORK HERE

Diagnostic Test
12

Which of the following is an expression equivalent to
9 x 3 y 5z 6 ?

SHOW YOUR WORK HERE

3

A.

3y2z3

B.

3xy2z3

C.

9 3 xy 2 z 3

D.

9 3 xy 3 z 2

1

1

5

13
4

2

–4

–2

0

2

4

–2

–4

y = x +1
y = − x2 +1
A system of equations and their graphs are shown above.
Which of the following are solutions to the system?
I. (0, 1)
II. (1, 0)
III. (–1, 0)
IV. (0, –1)

14

A.

I only

B.

II only

C.

I and III only

D.

II and IV only

If

x y
− = 5 , what is the value of 8x – 6y?
3 4

A.

–120

B.

–60

C.

60

D.

120

CONTINUE
Peterson's SAT® Prep Guide 2017

  81

Diagnostic Test
15 At a restaurant, the rates for meals are $7.50 for a lunch
and $12.00 for a dinner. One weekend, the restaurant sold
a total of 241 meals for $2,523.00. Which of the following
systems of equations can be used to determine the number of lunches, x, and the number of dinners, y, that the
restaurant sold?

A.

7.5 x + 12 y = 241
x + y = 2, 523

B.

12 x + 7.5 y = 241
x + y = 2, 523

C.

7.5 x + 12 y = 2, 523
x + y = 241

D.

12 x + 7.5 y = 2, 523
x + y = 241

16
United States Population

Number of people (in millions)

400M

300M

200M

100M

0

1920

1940

1960

1980

2000

Years

The graph shows the relationship between the population
of the United States (in millions) and the year the population
was recorded. Which of the following statements is true
about the data shown on the graph?

  82

A.

There is a weak correlation between the variables.

B.

There is a strong correlation between the variables.

C.

There is no clear correlation between the variables.

D.

There is an exponential correlation between the
variables.

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SHOW YOUR WORK HERE

Diagnostic Test
17

SHOW YOUR WORK HERE

GDP of China

10T

D olla r s in t r illions

8T

6T

4T

2T

0

1970

1980

1990

2000

2010

2020

Years

The graph shows data representing the gross domestic product (GDP), in trillions of dollars, of China from
1970 through 2013. Which of the following function
types would best represent the data?

B.

13
( x − 1970 )
8
y = ln (2015 – x)

C.

y = (x – 1970)3 + 2

D.

y = 1970e0.0003x

A.

y=

18 A college graduate goes to work for x dollars per week.
After several months, the company gives all the employees
a 10% pay cut. A few months later, the company gives all
the employees a 10% raise. Which expression is equal to
the college graduate’s weekly salary resulting from these
changes?
A.

0.90x

B.

0.99x

C.

x

D.

1.01x

CONTINUE
Peterson's SAT® Prep Guide 2017

  83

Diagnostic Test
19 Which of the following systems of inequalities has a solution set that intersects the first quadrant of the xy-plane?

A.

 y ≤ −2 x + 4

 y > −2 x + 2

B.

 x ≤ −2

y ≥ 5

C.

y ≥ x

 y < −3 − x

D.

 y > 5 + 3x

 y ≤ −3 + 3 x

20 Suppose two legs of a right triangle are such that the
length of one is 3 units shorter than the other. If the hypotenuse is 4 units long, what is the length of the longer
leg of the triangle?
A.
B.
C.
D.

3.5 units

(3 + 7 ) units

3 + 23 units
2
3 units

21 What is the original price of an item if it costs $12.60 after
a 10% discount is applied to the selling price?

22

A.

$11.34

B.

$12.48

C.

$13.86

D.

$14.00

1
A recipe for a homemade weed killer calls for 1 gallons of
3
white vinegar and 2 cups of table salt. Miguel made a large
batch of the weed killer and used 7 cups of table salt. If he
followed the recipe correctly, how many gallons of white
vinegar did he use?
A.
B.
C.
D.

  84

4
2
3
1
5
3
6
4

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SHOW YOUR WORK HERE

Diagnostic Test
23

A circle has a circumference that is equal to the perimeter
of a hexagon. The sides of the hexagon are each 22 inches
long. Which of the following is closest to the length of the
radius of the circle?
A.

7

B.

14

C.

21

D.

28

24 If (x – 4) and (x + 2) are factors of f(x), which of the following
graphs could represent the function f(x)?
A.

C.

–4

–2

4

4

2

2

0

2

–4

4

–2

0

–2

–2

–4

–4

2

4

2

4

D.

B.

–4

–2

4

4

2

2

0

2

4

–4

–2

0

–2

–2

–4

–4

CONTINUE
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  85

Diagnostic Test
SHOW YOUR WORK HERE

25

None

1 to 3

4 or more

Group A

8

23

19

Group B

14

21

5

Total

22

44

24

The table above shows data from demographic researchers studying the number of living siblings people have. If
a person is chosen at random from Group A, what is the
probability that the person has no living siblings?
A.

4
25

B.

4
11

C.

7
11

D.

22
25

26 During the Apollo 14 mission, astronaut Alan Shepard hit
a golf ball on the moon. The height of the ball in meters is
modeled by the function f(t) = –0.81t2 + 55t + 0.02, where
t is the time in seconds after the ball was hit. What does
0.02 stand for in this equation?

  86

A.

Acceleration of the ball due to gravity

B.

Vertical velocity of the ball

C.

Horizontal velocity of the ball

D.

Height of the ball before it is hit

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Diagnostic Test
27 If k is a positive constant other than 1, which of the following could be the graph of kx + y = c?
A.

C.

–4

–2

4

4

2

2

0

2

–4

4

–2

0

–2

–2

–4

–4

2

4

2

4

D.

B.

–4

–2

4

4

2

2

0

2

4

–4

–2

0

–2

–2

–4

–4

CONTINUE
Peterson's SAT® Prep Guide 2017

  87

Diagnostic Test
28 The Cyber Corporation buys a new machine for $80,000.
If the machine loses 15% of its value each year, what is its
value after 4 years?
A.

$41,760.50

B.

$42,750.50

C.

$48,000.00

D.

$49,130.00

29 The table below shows the total number of medals won
by the United States in the last six Winter Olympics.

Number of
Medals

Year

12

1994

13

1998

31

2002

25

2006

37

2010

28

2014

How many medals will the United States have to win in the
2018 Olympics in order for the average number of medals
for the years 1994 to 2018 to be one more than the average
number of medals won during the years 1994 to 2014?

30

  88

A.

29

B.

31

C.

32

D.

36

A
6x
is written in the form 3 +
,
x
+2
2x + 4
what is the value of A?
If the expression

A.

–12

B.

–6

C.

6

D.

12

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SHOW YOUR WORK HERE

Diagnostic Test
DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
		

If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

, it will be interpreted as

31
1
, not 3 .
2
2

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

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6

6

6

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9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

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4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

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2

2

2

2

2

3

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3

3

3

3

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3

4

4

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5

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3

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8

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9

9

9

9

9

9

9

6

6

CONTINUE
Peterson's SAT® Prep Guide 2017

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Diagnostic Test
31 If (ax – 1)(2x + b) = 4x2 + 4x – 3, what is the value of a + b?

32 Derek has $50 to spend on organic produce at the local
farmer’s market. A pint of berries costs $4.00, a 1-pound
bag of peaches costs $3.75, and a head of lettuce costs
$1.50. If he buys at least two of each item, what is the
maximum number of pints of berries he could purchase?

33 In a 3-hour examination of 350 questions, there are 50
mathematical problems. If twice as much time should be
allowed for each mathematical problem as for each of the
other questions, how many minutes should be spent on
the mathematical problems?

34 In the 1924–25 season of the National Hockey League
(NHL), the Montreal Canadiens won 57% of their games.
During the 1947–48 season, they won 33% of their games.
If there were twice as many games played in the 1947–48
season as in the1924–25 season, what percentage of the
games did the Montreal Canadiens win in these two seasons of the league? (Do not grid the percentage sign.)

35 A polling company surveys 625 randomly selected registered voters to determine whether a proposed ballot
measure might pass. Of those surveyed, 400 voters were in
favor of the ballot measure. The polling company reports
that the poll results have a conservative margin of error
of 4%. If 9,000 people actually vote, what is the minimum
number of people likely to vote for the ballot measure?

  90

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SHOW YOUR WORK HERE

Diagnostic Test
36 The average weight of a medium-sized bottlenose dolphin
is 400 pounds. If a particular medium-sized bottlenose
dolphin weighs 110% of the average, how many pounds
does the dolphin weigh?

37

SHOW YOUR WORK HERE

3 x + y = −4
x + y = 13
If (x, y) is a solution for the system of equations above, what
is the value of y?

38

−3 x + 2 y = −1
6 x − by = 8
What is the value for b that will make the system above
have no solution?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

Peterson's SAT® Prep Guide 2017

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Diagnostic Test
SECTION 5: ESSAY
50 Minutes—1 Essay

Directions: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

• Evidence, such as facts, statistics, or examples, to support claims
• Reasoning to develop ideas and to connect claims and evidence
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed

Adapted from “Penn State Hack Exposes Theft Risk of Student Personal Data” by Peter Krapp, originally published in The
Conversation on May 20, 2015. Peter Krapp is a professor of film & media studies at University of California, Irvine.
(This passage was edited for length.)
1

Pennsylvania State University’s College of Engineering took its computer network offline on May 15 after disclosing two
cyberattacks. The perpetrators were able to access information on 18,000 students, who are being contacted this week with
the news that their personal identifying information is in hackers’ hands.

2

Three days later, the computer network is back online, with new protections for its users. One of the two attacks is ascribed
by a forensic cybersecurity corporation retained by Penn State to computers apparently based in China.

3

As a researcher who has published on hacking and hacktivism and serves on the board of the UC Irvine data science
initiative, I believe two aspects of this news story deserve particular attention.
Compromising student data

4

Penn State announced last week that the FBI alerted it on November 21, 2014, about an attack with custom malware that
started as early as September 2012.

5

Why did it take so long for Penn State to disclose the breach, despite the fact that the experience of large-scale hacks
in 2013 and 2014 (against Target, Home Depot, and others) clearly demonstrated an urgent need for quick and full
disclosure—both to help the victims and to preserve a modicum of trust?

6

Penn State stated only that any disclosure would have tipped off the perpetrators before their access to the College of
Engineering computers could be cut off. Meanwhile, student data may have been compromised for at least six months,
maybe longer.

7

Another conspicuous problem with public discussion of events like this is, in fact, the lack of distinction often made in the
media between actual appropriation of data (as at Penn State) and mere temporary disabling or defacement of websites
(as happened to Rutgers University last month). That is like being unable to make a difference between a grand theft auto
and keying a car.

8

The question is, what can universities do to limit the risk to their students?

Diagnostic Test — essay

As you read the passage below, consider how Peter Krapp uses the following:

CONTINUE
Peterson's SAT® Prep Guide 2017

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Diagnostic Test
9

The exposure of student data in higher education is not limited to Social Security numbers or email passwords. Information
collected and retained by educational institutions includes full name, address, phone number, credit and debit card
information, workplace information, date of birth, personal interests and of course academic performance and grade
information.

Concern with data practices
Data Storage and Security
Very much

75%

Transparency About Data Use
Very much

80%

Legal Standards & Oversight
Very much

Somewhat

Somewhat

Somewhat

Only a little

Only a little

Only a little

Not at all

Not at all

Not at all

No response

No response

No response

Collection of Location Data
Very much

58%

Collection of Video/Audio Data
Very much

59%

81%

Collection of Telecom Data
Very much

Somewhat

Somewhat

Somewhat

Only a little

Only a little

Only a little

Not at all

Not at all

Not at all

No response

No response

No response

64%

A survey conducted by the Obama administration collected responses from 24,092 individuals on how much they
trusted various institutions to keep their data safe. There was a high level of concern around transparency and legal
standards.

...
10

President Obama only recently called for laws covering data hacking and student privacy. “We’re saying that data collected
on students in the classroom should only be used for educational purposes,” he stated in his speech to the Federal Trade
Commission (FTC) earlier this year.
Data privacy concerns

  94

11

If students’ right to privacy needs to be protected from the specter of foreign intelligence agencies poking around the Penn
State Engineering School, then by the same logic it should be protected also against data-mining by for-profit actors right
here in the US.

12

Until May 2014, Google, for instance, routinely mined its apps for education services for advertising and monetizing
purposes. When Education Week reported that Google was mining student emails, it quickly led not only to lawsuits but also
to landmark legislation. The California Senate Bill 1177 was enacted to prevent educational services from selling student
information or mining it for advertising purposes.

13

Yet, almost a year later, students in California remain just as concerned about their data privacy as before—since the new
state law was watered down to apply only to K–12 and not to higher education. And when it was disclosed earlier this spring
that education publisher Pearson secretly monitored social media to discern references to their content, the legislative
response was one that, according to the Electronic Privacy Information Center (EPIC) in Washington, DC, “fails to uphold
President Obama’s promise that the data collected in an educational context can be used only for educational purposes.”

14

Students in higher education nationwide are still in a position where they cannot opt out of the computer services of their
learning institutions, and so they have no expectation of privacy.

15

Despite President Obama’s promises for safeguarding the privacy of consumers and families, and despite the fact that a
number of technology companies concerned with growing consumer distrust recently signed a pledge to safeguard student
privacy, neither Google nor Apple signed on.

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Diagnostic Test
16

The President’s Council of Advisors on Science and Technology (PCAST) was tasked to examine current and likely future
capabilities of key technologies, both those associated with the collection, analysis, and use of big data and those that can
help to preserve privacy, resulting in a direct recommendation to strengthen US research in privacy-related technologies.

17

And overwhelmingly, respondents to a White House survey recently expressed severe reservations about the collection,
storage, and security and use of private information.

18

Maybe it is time for higher education to heed those signals.
Write an essay in which you explain how Peter Krapp builds an argument to persuade his audience that
the use of college students’ personal information for anything other than educational purposes is a
serious violation of privacy and a major breach of computer security. In your essay, analyze how Peter
Krapp uses one or more of the features listed above (or features of your own choice) to strengthen
the logic and persuasiveness of his argument. Be sure that your analysis focuses on the most relevant
features of the passage. Your essay should not explain whether you agree with the writer’s claims, but
rather explain how he builds an argument to persuade his audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

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  95

Answer Keys and Explanations
Section 1: Reading Test

1. C

12. A

23. B

33. C

43. D

2. A

13. A

24. A

34. A

44. D

3. A

14. D

25. B

35. C

45. B

4. C

15. A

26. B

36. B

46. B

5. D

16. D

27. B

37. B

47. C

6. B

17. A

28. A

38. B

48. B

7. D

18. D

29. D

39. A

49. B

8. B

19. C

30. B

40. A

50. C

9. D

20. C

31. A

41. D

51. B

10. B

21. A

32. C

42. C

52. B

11. A

22. B

READING TEST RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is C. Address appears in the author’s
description of the black bear, including qualities that
the bear possesses. So the context here tells us that
address is not being used to mean direction, choice D,
because one can possess a great sense of direction but
not direction. Habitat, choice A, can also be eliminated
because the correct answer choice should refer to a trait
of the black bear, and one’s habitat is not a personal
trait. Anxiety is a personal trait, but it contradicts the
author’s description of the black bear as possessing
great courage, so choice B can be eliminated. Therefore,
the correct answer is choice C, since skill is a positive
personality trait that would be listed among traits such
as strength and courage.
The correct answer is A. Choice A is correct because
Audubon clearly wanted to inform readers about black
bears even though he was mainly known as a studier of
birds. Had this not been his goal, he would not have
written this particular passage, nor would he address
the reader directly with phrases such as, “You are
probably not aware . . . ” Choice B can be eliminated
because its conclusion is too general; Audubon seems
as though he was likely fascinated by the black bear, but
there is no strong evidence that this man, who mostly
studied birds, was fascinated by all mammals. Choice C

is incorrect because it assumes the reader is more
interested in what Audubon knows than the topic
he is actually discussing, shifting the focus from
bears and placing it onto the author, himself.
Choice D is incorrect because Audubon never
compared the black bear to any species of bird in
the passage.
3.

The correct answer is A. In lines 5–6, the author
compares the bear’s migratory behavior to that of
the deer, so even though the deer and the bear are
very dissimilar mammals, they do share some
significant traits. Choice B is incorrect because the
author is not making a direct comparison here even
if it is likely that other mammals eat roots. Choice C
is incorrect because the comparison between the
bear and the hog ended with the discussion of how
both animals wallow in mud, and it is unlikely a hog
would eat its own species, so the author clearly is
not comparing the bear to a hog when stating that
the bear might eat a young pig. Choice D is
incorrect because the author is not making a
comparison between bees and bears in these lines;
a bee would not rob its own tree.

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Answer Keys and Explanations
4.

5.

6.

7.

8.

  98

The correct answer is C. The author explicitly states
that “many of our woodsmen and hunters who have
seen the Bear performing the singular operation just
described, imagine that it does so for the purpose of
leaving behind an indication of its size and power,”
which supports choice C. Choice A represents
Audubon’s claim, which begins with the phrase “It
seems to me,” not that of the huntsmen and woodsmen.
There’s no indication that the tree will be used for
hibernation, choice B, nor that such behavior is a way of
obtaining food, choice D.
The correct answer is D. The author explains how bears
forage for food by using descriptive phrases that create
a placid, or peaceful, image. The author mentions that
bears may eat livestock, but that is not the main focus,
so choices A and B are incorrect. While the lines in
choice C do show that the bear eats a wide range of
foods, the author’s use of descriptive phrases is
evidence that he is creating an image as opposed to
making a scientific list of what the bear eats.
The correct answer is B. The previous question
indicated that the author was trying to create a placid,
or peaceful, effect with his description of how bears
behave in swamps in lines 17–18, and the words “passes
much of its time” and “wallowing” help achieve that
effect. The wording in lines 16–17 creates a sense of
discomfort by using phrases such as “During the
summer heat” and “gloomy,” so choice A is not the best
answer. Focusing on the bear’s hunger, as choice C does,
or how it seizes prey, as choice D does, does not
contribute to the placid atmosphere the author is trying
to achieve.
The correct answer is D. Audubon explains that the
bear sharpens its claws and the wild boar sharpens its
tusks for the same purpose: to prepare themselves for
competition during the mating season, choice D—not
for defense from human predators, choice C, which are
only mentioned very briefly in the passage. A predator
would not be very effective if it went out of its way to
warn potential prey that it was a predator, so choice A
does not make much sense. The author only mentions
that the black bear forages for crayfish and roots and
does not indicate what the wild boar eats, so choice B is
incorrect.
The correct answer is B. The fact that Audubon calls
man the bear’s “most dangerous” enemy shows that he
has some sympathy for hunted bears, making choice B
the correct answer. Nothing indicates that Audubon
hunts, so choice A is incorrect. He never denies that
bears are dangerous nor does he state that bears are

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more dangerous than people, so choices C and D are
also incorrect.
9.

The correct answer is D. By referring to man as “the
most dangerous of its enemies,” Audubon creates an
image of man as almost villainous in his treatment of
hunted bears, which indicates that he has sympathy for
the creatures. Choice A refers to the bear’s migratory
habits in a neutral way, indicating nothing about the
author’s feelings for the bear. Neither does choice B,
which merely refers to a basic instinct of the bear.
Choice C only indicates how the bear protects itself
from its most dangerous enemies; it does not comment
on those enemies in a way that expresses the author’s
sympathy for bears.

10.

The correct answer is B. The author addresses the
reader directly with such phrases as “as you well know”
and “you also know that” when stating information
about bears. This shows that he believes the reader
already has some knowledge about bears and contradicts the assumption in choice A. While it is entirely
possible that some readers may have a fear of bears,
there is no evidence that the author believes this in the
passage, so choice C is not the best answer. Although
the author assumes that the reader knows that bears
are “good climbers,” he never compares their climbing
abilities to that of apes, so choice D is incorrect.

11.

The correct answer is A. The first paragraph of the
letter indicates that Wythe and Jefferson have an
established relationship and Jefferson believes Wythe
had a positive influence on Jefferson’s education, thus
we can infer that Wythe was a teacher. The letter does
not imply any familial relationship or that Wythe and
Jefferson are friends—choices B and C—rather, it shows
a more formal connection. There is no indication of how
Wythe is employed—choice D. While he could be a
public servant of some kind, that conclusion could not
be drawn from the information provided.

12.

The correct answer is A. Jefferson’s overall concern is
that his nephew should receive a solid education,
choice A. This letter has a greater purpose than merely
staying in touch, choice D. His advice about studying
languages, choice C, is part of the overall advice about
education, and morality is also a part of his course of
study, choice B.

13.

The correct answer is A. Jefferson indicates that
learning Italian might actually make it harder to learn
Spanish, which he views as the more useful language.
This contradicts the conclusion in choice C. Jefferson
only briefly mentions French to indicate that it is a

Answer Keys and Explanations
similar language to Italian and Spanish and never
indicates he believes that it is more important to learn
French than Spanish or Italian, so choice B is incorrect.
Although he mentions that Spanish and Italian are
similar, Jefferson never suggests that they are so similar
that it makes sense to speak Italian to Spanish people,
which eliminates choice D.
14.

15.

The correct answer is D. The word “prosecute” in this
context is used to mean “pursue,” so in lines 23–25,
Jefferson is suggesting that Peter lay Italian aside to
learn Spanish instead. Choices A and B introduce the
problem of learning Italian and Spanish at the same
time, but neither choice suggests how Peter should deal
with this problem. Choice C is incorrect because it
merely indicates Jefferson’s own observations about
people who speak Italian, French, and Spanish.
The correct answer is A. Jefferson compares conscience to a physical limb of the body to show that it is
natural and present in all human beings, choice A.
Choices B, C, and D may be true, but Jefferson only
covers the first point: that morality is as natural as an
arm or leg and is given to all “in a stronger or weaker
degree” (lines 43–44).

16.

The correct answer is D. In advising Peter about
language studies, Jefferson tells him to learn Spanish
(lines 26–29). He predicts that it will be valuable in the
future because of “connections with Spain and Spanish
America,” choice D. He dismisses Italian, choice C, as
unworthy of Peter’s attention and doesn’t discuss
America’s future with France, choice B, or England,
choice A.

17.

The correct answer is A. By “lost time,” Jefferson means
“wasted time,” choice A. In his third point, Jefferson tells
Peter that he shouldn’t bother to study moral philosophy because it is something everyone knows
intuitively, stating that morality “is as much a part of his
nature as the sense of hearing, seeing, feeling.” “Lost
time” could refer to the past, choice B, or mean “missing
time,” choice C, but Jefferson is not discussing the past
or a gap in time in this context. He says nothing about
youth either, so choice D does not make much sense.

18.

The correct answer is D. Jefferson claims that he has
never seen anyone who spoke French, Spanish, and
Italian who didn’t get them confused, choice D. All three
languages are derived from Latin, choice A, as Jefferson
notes (“all of them degenerated dialects of the Latin”),
but that is not the reason he gives to avoid the study of
Italian. Jefferson does think it is necessary to learn a
language other than French, choice B, because he

recommends learning Spanish. Jefferson states that it is
useful to be multilingual, as he advocates the study of
Spanish; he only suggests that one should be careful
when choosing which languages to study, so choice C is
incorrect.
19.

The correct answer is C. Jefferson says morality is
innate, therefore it doesn’t need to be taught. In fact, he
argues, teaching it can have a negative effect of leading
“astray” (lines 47–48).

20.

The correct answer is C. The family tree shows that
Peter’s father died when Peter was only 3 years old, and
that his mother had 5 other children to care for, so
choice C is the best conclusion to reach. The fact that
Peter’s father was already dead when Thomas wrote this
letter eliminates choice A, since a comparison cannot be
fairly made between someone currently living and
someone who is dead. Choice B is too speculative and is
not as logical a conclusion as choice C. Choice D
assumes that Peter was responsible for caring for his 5
siblings, and there is no evidence of this in the family
tree or the passage.

21.

The correct answer is A. The letter shows Jefferson to
be very involved in ensuring that his nephew gets the
best education since it refers to a number of important
study topics and how Peter should approach them.
Expressing that he felt “very happy” to receive letters
from Peter also helps create a warm tone. Although
Jefferson clearly cares for his nephew, he does not seem
particularly worried about the boy since there is no
anxious language in this letter, so choice B can be
eliminated. The letter’s warmth also eliminates choices
C and D since an “objective and matter-of-fact” tone
would be contrary to warmth, as would a “distant and
preoccupied” tone.

22.

The correct answer is B. In the first paragraph, the
author provides a number of statistics that support
choice B. However, the author never compares plastic
waste to other kinds of waste, so choice A cannot be
concluded based on information in this particular
passage. The author writes that “World plastics production has experienced almost constant growth for
more than half a century,” which contradicts choice C.
While the entire passage discusses the impact of plastic
waste on the planet, the author never compares that to
the impact other forms of waste have, so choice D is not
the best answer.

23.

The correct answer is B. Lines 4–6 provide specific
statistics about how plastic accounts for 10 percent of
the 1.4 billion tons of trash the world generates each

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  99

Answer Keys and Explanations
year. By any standards, that is a massive amount of
waste. Choice A indicates that plastic production
continues to grow, but, without specific numbers, there
is no way to use this information to conclude that
plastic is responsible for a massive amount of waste.
That the International Maritime Organization has had to
ban dumping of plastic waste indicates it is a big
enough problem to warrant such action, but choice C is
simply not as specific as choice B is, so it is not the best
answer choice. Choice D also refers to a problem but
fails to supply specific numbers.
24.

The correct answer is A. The overall tone is neutral,
choice A. The author provides facts and data using
scientific terminology and explanations. Nowhere does
he attempt to persuade the reader to a particular view,
choice B, inject a personal story, choice C, or offer his
own opinion, choice D, although he does offer differing
viewpoints on possible solutions.

25.

The correct answer is B. In lines 72–74, Halden’s quote
(“We need to design the next generation of plastics to
make them more biodegradable…”) shows that he
believes science can find a way to make plastics
biodegradable, choice B, which he says will eliminate
the problem. The author states that new laws may help
minimize the problem (“New laws … could require
handling plastics more responsibly at the end of their
useful life through recycling, proper disposal, and
extended producer responsibility”), not Halden, so
choice A is incorrect. The author describes how some
sea creatures have ingested plastic, but Halden never
advocates for the invention of edible plastic in this
passage, so choice C is incorrect. Banning all new plastic
production is an extreme and unrealistic solution that
Halden never suggests, so choice D is incorrect.

26.

27.

  100

The correct answer is B. The article includes scientific
data and explanations of the effects of plastics in the
ocean and waterways, offering information to the public,
choice B. The specific data in this passage contradict the
idea that the author is merely theorizing that the
environment could be in danger, and this conclusion is
too general in any event, so choice A is not the best
answer. Choices C and D are too extreme and unrealistic;
it is unlikely a movement will halt all plastic production,
which is not even something the author advocates, and
cleaning up the oceans is too huge a job for readers to
personally take on. Choice B remains the most logical
and realistic answer.
The correct answer is B. Lines 49–51: “Research has
shown that harmful and persistent substances can both
bioaccumulate … and biomagnify …” indicate that

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plastic pollution in the ocean is a problem by specifying
that they are “harmful.” Choice A merely states what
happens when animals eat plastics without suggesting
that this is or is not a problem, so choice A is not the
best answer. Choice C describes how certain problems
associated with plastic pollution are still unknown, so it
fails to support the previous question’s conclusion that
plastic pollution is a problem. Choice D merely sets up
questions to follow without providing evidence that
plastic pollution in the ocean is a problem.
28.

The correct answer is A. Choice A is the only choice
that refers specifically to the food chain as detailed in
the diagram. Choices B and D may have some bearing
on how plastics impact the ocean, but they don’t
explain the disruption to the food chain. Although the
diagram depicts the emptying of wastewater into the
ocean, it makes no statement about the legality of this
practice, so choice C is incorrect.

29.

The correct answer is D. The author explains that a law
was passed in Illinois to prevent infiltration of these tiny
microbeads into the water system (lines 33–37), choice
D. The microbeads were ending up in the Great Lakes
and Chicago’s waterways. None of the other options are
offered as a reason for the law.

30.

The correct answer is B. Knowing the meaning of
absorb, choice C, does not assist in understanding the
meaning of adsorbed. The words share the same suffix,
but it’s the prefix that makes the word less familiar.
Absolve, choice A, has the same prefix as absorb but
does not help in figuring out the meaning of adsorb.
The “sorb” in “sorbet” (a frozen dessert) has nothing to
do with the word “adsorbed,” so choice D is incorrect.
Adhere, choice B, is when something sticks to something
else; so adsorb must mean when one substance sticks to
another.

31.

The correct answer is A. The author indicates that
there are ways humans may be ingesting plastic waste
in lines 57–65. The author had already discussed how
sea creatures ingest such waste in the previous
paragraphs, so choice B is not the best answer. Choice C
had already been discussed earlier, too. Choice D is
incorrect because the author never theorizes about why
people dump plastic waste into the oceans in this
passage.

32.

The correct answer is C. These lines (“And, finally, what
proportion of humans’ exposure to plastic ingredients
and environmental pollutants occurs through
seafood?”) deal with how much plastic waste from the
oceans people might be ingesting by eating seafood.

Answer Keys and Explanations
Choice A has to do with the transference of plastic
pollutants, not the amount of such pollutants people
are ingesting. Choice B deals with the effects of plastic
pollutants. Choice D is a general statement about the
efforts to answer the questions the author raises.
33.

34.

35.

36.

The correct answer is C. As she places the offering, the
narrator wonders whether or not her sister will die, so it
is logical to conclude that she wants to place her
offering correctly to prevent that from happening. No
one at home asks her about the offering once she
returns, so choices A and D can be eliminated. By
worrying about her sister’s potential death, the narrator
indicates that she has more important things on her
mind than whether or not she’ll be trusted to make
offerings again in the future, so choice B is not the best
answer.
The correct answer is A. In line 70, the medicine man
describes seeing a “luminous vapor above the house,”
and clarifies that “It was the spirit of the little child who
is sick” in line 72. Choice B describes objects that were in
his medicine bag, not the appearance of the sister’s
spirit. The sister was a baby, but the medicine man
never describes her as a baby, so choice C is not the best
answer. In line 73, the medicine man says the “spirit is
beyond our reach,” but this describes the spirit’s
location, not its appearance.
The correct answer is C. The family didn’t send for the
medicine man until the medicine woman had given up
hope, which makes choice C the most logical answer.
What the medicine man had been doing before arriving
at the family’s house is never indicated, so there is no
evidence for choice A. Although we are told that the
medicine man had to travel quite a distance, choice B,
this is not offered as a reason why he was not contacted
in the first place. Although the family did have a
medicine woman attempt to cure their child before
calling the medicine man, the narrator never implies
that the healers’ genders were of any significance.
The correct answer is B. These lines show the girl
having trouble analyzing how nature will affect the
delivery of her offering and unsure if she is making the
right decision. Choice A describes the instructions given
by the medicine woman; it doesn’t explain why they
were difficult to follow. Choice C describes the variance
in the terrain where she was searching for the right
spot, but it does not describe any particular problem.
Choice D describes the narrator’s surroundings without
indicating that they were causing her any particular
problem.

37.

The correct answer is B. The narrator has faith that her
offering will save her sister, and the medicine man has
faith that the girl’s spirit still exists. Choice B emphasizes
the theme of faith in this passage. Choice A is not the
best answer because it places the medicine man at the
center of the story when it is mainly about the narrator’s
faith that her actions will save her sister. Choice C
implies that the passage is mostly concerned with
Native American culture when the rituals in the story
are not as important as how the characters feel about
them. Choice D describes one passing incident in the
passage that says nothing about the story’s overall
theme.

38.

The correct answer is B. Choice B most effectively
indicates the strength of the narrator’s faith by
describing how she believes her offering will save her
sister. Choice A merely describes the offering without
indicating the narrator’s faith that it has any power to
save her sister. Choice C describes a moment in the
story in which the narrator’s faith is shaken, so it
contradicts the conclusion in the previous question.
Choice D mistakes the correct answer to the previous
question.

39.

The correct answer is A. The parents seem oblivious to
the natural emotions of a child. Though they give the
narrator responsibility and take care of her physical
needs (lines 48–49), they don’t seem to offer comfort or
consolation. The narrator is probably given more
responsibility than she wants, which makes choice B
incorrect. The parents naturally focus on the child likely
to die, but there is no indication they prefer the younger
child, so choice C is incorrect. The narrator seems very
alone and her parents display little warmth or affection,
making choice D incorrect.

40.

The correct answer is A. Choice A covers the central
idea of the passage best by including its most important
details: the sister’s death and the narrator’s efforts to
save her. Choice B narrowly focuses on the girl following
the instructions of the medicine woman without
indicating why she was following those instructions.
Choices C and D do not capture the concept of the
narrative and the point of view because they both shift
focus from the narrator to the entire family.

41.

The correct answer is D. The narrator feels remorseful
because she feels as if she failed since her sister dies
despite her own efforts to save the baby. The narrator
may feel responsible for her sister’s death, but there is
no evidence that she has any reason to feel as though
she caused her sister’s illness, so choice A is not the best

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Answer Keys and Explanations
answer. The narrator follows the instructions of the
medicine woman meticulously, so choice B is not the
best conclusion. The narrator may have felt burdened
by the amount of responsibility she took on, but her
remorse is more directly related to her sister’s death, so
choice C is not the best answer.
42.

The correct answer is C. The modern meaning of
“thrilled” is usually “excited,” but in line 45, the author is
talking about fear and doubt. Choices A, B, and D all
have positive connotations that fail to capture the
feelings of heightened fear the narrator was experiencing when she began thinking that her offering had
failed to save her sister’s life.

43.

The correct answer is D. In choice D, Emmet acknowledges his death sentence and declares that he is dying
for a cause. Choice C explains why he asked France for
assistance, and choice B explains that he was fighting
for his country’s independence and freedom from
tyranny. In choice A, he defends his actions by saying
that he could have stood by and done nothing, given
his family’s privileged position, but chose instead to
defend liberty.

44.

The correct answer is D. Choice D shows Emmet’s
pride in his country by saying that his government
speaks for him. In choice A, he merely states that he is
not working for France, but this alone does not prove
that he feels pride in his own country. In choice B, he
theorizes about the different influences that could have
caused him to betray his country. Choice C makes a
statement about how he feels the people in his country
deserve assistance from France, but that alone does not
make a strong case for the author’s patriotism.

45.

46.

  102

The correct answer is B. According to the timeline,
“American colonies declare” independence in 1776, and
the fact that the country needed to define itself outside
of the rule of another country probably caused
America’s view of patriotism to focus more on the
country, itself, rather than a greater concern for all
people. Choice A refers to events that did not concern
America. Choices C and D do refer to events that
concerned America, but neither had as significant an
impact on the country and its views as declaring
independence in 1776 did.
The correct answer is B. Noting the date of Emmet’s
speech in his defense of his actions prior to his execution, choice A is not possible. The Louisiana Purchase
by the United States, choice D, would have given France
more resources to help. However, the Napoleonic Wars
were draining the French treasury, choice B, leaving the

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country overburdened and uninterested in becoming
involved elsewhere. The French Revolution had started
in 1789, triggering the rise of Napoleon, but this was
not directly related to its refusal to aid Emmet.
47.

The correct answer is C. Emmet loved his country and
declared his patriotism toward Ireland as his reason for
his actions, choice C. Wright’s view was more inclusive,
defining it as freeing all people, whatever the country.
Emmet’s primary focus was on his own people, choice B,
not all of humankind. He defended his actions, choice A,
but this action is unrelated to Wright’s concept of a
patriot, as is a court that renders an unjust sentence,
choice D.

48.

The correct answer is B. Although both Emmet and
Wright wanted freedom from tyranny, Emmet’s focus
was on Ireland, and Wright had a broader objective of
freedom and independence for all humankind, choice B.
Choice A is incorrect because only Wright states that her
country’s concept of patriotism needs to be rethought.
Wright was focused on advancing an expansive concept
of patriotism that included other countries, which does
not mean that she did not love her country, so choice C
is not the best answer. Choice D is incorrect because
Wright indicates that she does understand tyranny by
advocating for its opposite: freedom and concern for all
people.

49.

The correct answer is B. Wright’s speech reads as a
sincere yet calm plea for understanding and concern for
all people, while Emmet’s feels more motivated by his
desperation to save himself and his anger regarding the
charges of treason against him, which is clear through
his regular use of exclamations throughout his speech.
Wright does not express anger, so choice A is incorrect.
It is Emmet who is passionate and angry and Wright
who is calm, not the other way around, so choice C is
incorrect. Someone can speak calmly yet sincerely, as
Wright does, or desperately and angrily, as Emmet does,
and still be convincing, so choice D is not the best
answer.

50.

The correct answer is C. All the options refer to patriotism, but choice A is mostly about perseverance and the
importance of freedom. Choice B speculates on how
Americans might react if attacked and suggests submission as one possibility. Choice C sets up the either-or
scenario in which there can only be one of two outcomes:
liberty or death. Emmet’s statement is analogous because
there are only two choices: if the enemy wishes to come
into his homeland (symbolized by the word “threshold”),
he will defend it to the death. Choice D expresses too

Answer Keys and Explanations
much pleasure in the act of fighting for and dying for one’s
country while Emmet’s statements show that he is
motivated more by his belief in the righteousness of
freedom than more romantic ideas about dying for one’s
country.
51.

The correct answer is B. Wright says Americans’ idea of
a patriot is someone who loves his/her country, choice
D, but that idea is too narrow. She explains that
Europeans see patriotism as a more expansive concept
that extends to freedom for all humans. This idea, she
explains, includes working toward the best interests of
all human lives, wherever they are, so that they are free
from despotism. This statement suggests that she
herself holds these ideas, choice B, and wants others to
consider them. Physically fighting for one’s country,
choices A and C, is an example of vanity.

52.

The correct answer is B. Emmet speaks of being
accused of secretly selling his country out to France,
which would be the actions of a spy. In this context, an
emissary is a spy, choice B. The government wouldn’t
accuse someone of being an ambassador, an official
position as a representative, choice A. Similarly, a
minister is an official head of a government department,
which eliminates choice C. Choice D is incorrect
because a mercenary is a paid soldier, and there is
nothing that suggests the government thinks Emmet is
a “hired gun.”

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Answer Keys and Explanations
Section 2: Writing and Language Test
1. A

11. A

21. C

31. C

41. D

2. D

12. A

22. C

32. A

42. B

3. A

13. C

23. D

33. D

43. A

4. B

14. D

24. C

34. C

44. C

5. C

15. B

25. B

35. B

6. B

16. D

26. D

36. D

7. B

17. A

27. B

37. A

8. A

18. C

28. A

38. C

9. B

19. B

29. C

39. A

10. B

20. C

30. B

40. C

WRITING TEST RAW SCORE
(Number of correct answers)

1.

The correct answer is A. Choice A correctly sets up the
sentence’s focus on the various causes of depopulation
and their negative impact. Choices B, C, and D are
incorrect because they present potentially positive
developments.

2.

The correct answer is D. Choice D follows the same
parallel construction as the preceding gerund phrase,
“driving away its middle class.” Choices A, B, and C are
incorrect because they do not demonstrate parallel
construction.

3.

4.

  104

The correct answer is A. Choice A is correct because
the dash is being used to indicate the following
explanation of what is staggering. Choice C is incorrect
because it creates a run-on sentence. Choices B and D
are incorrect because they move the punctuation to the
wrong part of the sentence.
The correct answer is B. Choice B correctly maintains
the sentence’s focus on the effects of depopulation.
Choices A and C are incorrect because they suggest a
growth in residency, which contradicts the main
argument of the passage. Choice D is incorrect because
homelessness is unrelated to the main focus of the
passage, which is Detroit’s depopulation.

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5.

The correct answer is C. Choice C, solicit, correctly
establishes the implied intent of the city planners within
the context of the passage—to solicit, or ask for, the
input of city residents while studying their urban
spaces. Choices A, B, and D do not make sense within
the context of the passage, as all of these terms imply
the opposite of the city planner’s intent.

6.

The correct answer is B. The plural pronoun they is
required here to agree with the plural noun planners, so
they call (choice B) is the correct answer. Choices A and
C are incorrect because they incorrectly use singular
pronouns. Choice D is incorrect because “we call” is
first-person plural, not third-person plural, which is what
is required here.

7.

The correct answer is B. Choice B is correct because “in
fact” properly suggests an elaboration of the previous
sentence. Choice A is incorrect because it suggests the
second sentence is an equal example, rather than an
elaboration of the first. Choice C is incorrect because it
implies the author is drawing a conclusion despite a
contradiction. Choice D is also incorrect because it
implies that the second sentence is a second example
supporting a contrast scenario, which is not the case.

Answer Keys and Explanations
8.

The correct answer is A. In choice A, the sentence
explains the planners’ logic. Choice B implies that there
was resistance to their thinking or that their thinking
was absolute, which is incorrect. Choices C and D do not
denote the careful calculation that the rest of the
sentence implies.

15.

The correct answer is B. Choice B is correct because
the phrase, “a nation to which Indonesia was linked
through trade relations” should refer to the country of
India, not “migrants.” Choices A and D are incorrect
because the modifier is misplaced. Choice C is incorrect
because it is awkward and doesn’t make sense.

9.

The correct answer is B. This sentence would best
serve as a transition between the previous and current
paragraphs. The previous paragraph refers to the city
planner’s strategic plan, and the current paragraph
begins with an example of one of the plan’s boldest
suggestions. A sentence that mentions that the plan
contained bold suggestions, choice B, would work well
here. The other choices would place this notion after
providing examples of the plan’s bold suggestions,
rendering it ineffective and unnecessary.

16.

The correct answer is D. Choice D is correct because
this sentence is tangential to the paragraph’s focus on
the cultural influences of Hindu culture on the
Indonesian way of life. Choice A is incorrect because this
information is not relevant. Choice B is incorrect
because this paragraph is not focused on the actual
practice of shadow puppetry. Choice C is incorrect
because this information has not been presented before
this sentence.

17.

The correct answer is A. Choice A reflects the paragraph’s emphasis that depicting gods in human form
was not allowed under any circumstance. Choices B, C,
and D are incorrect because these words do not suggest
complete proscription the way choice A does.

10.

The correct answer is B. Choice B correctly places the
dash so that it separates the two clauses. Choices A, C,
and D are incorrect because they place the dash in the
wrong place.

11.

The correct answer is A. Choice A is correct because
items in a series should be separated by commas.
Choice B is incorrect because it is unnecessarily wordy
and misuses semicolons. Choice C is incorrect because it
misuses semicolons. Choice D is also incorrect because
it incorrectly mixes a semicolon with commas.

18.

The correct answer is C. Choice C is correct because it
places the verb in the past tense. Choice A is incorrect
because the present tense is an inappropriate shift from
the past tense that the rest of the paragraph uses.
Choices B and D are incorrect because the sentence
requires the simple past tense.

12.

The correct answer is A. Choice A is correct because
“hawk” means to call out and sell, which is what vendors
at festivals do. Choice B is incorrect because, while the
vendors may stock merchandise, the author’s intent
here is to describe how they sell that merchandise.
Similarly, choices C and D are incorrect because the
vendors are selling—not advertising or trading—goods.

19.

13.

The correct answer is C. Choice C correctly suggests
that this sentence provides a transition between the
scene depicted in the first paragraph and the ancient
and modern tradition of puppetry, and the writer
should not delete it. Choice A is incorrect because this
sentence is not an opinion. Choice B is incorrect
because this sentence does not distract from but rather
helps in contextualizing the main ideas of the paragraph. Choice D is incorrect because it is the following
sentence that explains what wayang kulit is.

The correct answer is B. Choice B conveys both the
duration of the events and the lack of interruptions
without being redundant or wordy. Choice A is incorrect
because “all night long” is redundant. Choice C is
incorrect because it is redundant and wordy; while it is
constructed better by omitting “at all,” “all night long
from sunset to sunrise” is still redundant. Choice D is
incorrect because just noting that the performance
lasted all night isn’t as informative as noting that, from
dusk to dawn, the performance had no interruptions.

20.

The correct answer is C. As written, the sentence is a
run-on and needs some added punctuation to reduce
confusion. Choice C fixes the run on by adding the
appropriate commas and an em-dash. Choices B and D
add commas in inappropriate places, creating additional confusion.

21.

The correct answer is C. Choice C is correct because
the pronoun “its” should refer back to the antecedent
“the puppet.” Choice A is incorrect because “their” is
plural and “puppet” is not. Choices B and D are incorrect
because “the puppet” is neither male nor female.

14.

The correct answer is D. Choice D correctly uses end
punctuation to correct this run-on sentence. Choices A,
B, and C are incorrect because they do not employ the
correct punctuation to denote two independent
clauses.

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Answer Keys and Explanations
22.

The correct answer is C. Choice C is correct because
comparisons require “than,” not “then Choice A is
incorrect because “then” is an adverb that refers to time.
Choices B and D are incorrect because they don’t make
sense in the sentence.

23.

The correct answer is D. The intent of this passage is to
bring attention to the serious water issues occurring in
the American Southwest, so choice D would be the
most effective introductory sentence. The passage is not
an enticement to vacation in the American Southwest,
so choice A is incorrect. It is also not focused on
pointing out the majestic aspects of the American
Southwest, so choice B is incorrect. The Anasazi people
are a supporting detail about the American Southwest
in the context of this passage, so choice C is also
incorrect.

24.

25.

26.

  106

The correct answer is C. Choice C is correct because
the sentence subject that includes “arid climate and
limited water resources,” is a compound subject, which
means the verb must also be plural. Choice A is
incorrect because “has” is singular. Choice B is incorrect
because it is the past perfect instead of the present
perfect tense. Choice D is incorrect because it is present
tense and changes the meaning of the sentence.
The correct answer is B. Choice B is correct because
the sentence requires a possessive pronoun in order to
refer back to the Anasazi people. Choice A is incorrect
because “they’re” is a contraction, not a possessive.
Choice C is incorrect because “there” is an adverb, not a
possessive. Choice D is incorrect because “its” is singular
possessive, while the antecedent, “people,” is plural.
The correct answer is D. Choice D combines the
sentences in a way that helps emphasize the connection between the two. Choice A is incorrect because
“but” implies that the two ideas are contradictory.
Choice B is incorrect because it misuses a semicolon to
connect an independent clause and what is now a
dependent clause. Choice C is incorrect because it
creates a run-on sentence.

27.

The correct answer is B. Choice B is correct because
the sentence is a statement, and thus it should end in a
period. Choice A is incorrect because the sentence does
not warrant the excitement or surprise that an exclamation point conveys. Choice C is incorrect because the
sentence is not a question. Choice D is incorrect
because it creates a run-on sentence.

28.

The correct answer is A. Choice A is correct because
the context of the sentence suggests that a scientific

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forecast or prediction about water flow has been made.
Choices B and C are incorrect because they reflect
subjective impulses and do not maintain the neutral
and scientific tone of the passage. Choice D is incorrect
because it is vague and fails to suggest a basis in
research.
29.

The correct answer is C. This sentence adds new and
relevant information by providing an example that
shows the reader how severe the drought really is.
Choice A is incorrect because this information has not
been presented previously in the passage. Choice B is
incorrect because this sentence does not blur the
paragraph’s focus; rather, it is relevant to the paragraph’s
main argument. Choice D is incorrect because this
sentence does not introduce this argument; rather, it
supports the argument.

30.

The correct answer is B. Choice B is correct because
the dependent clause “and possibly more alarming”
must be set off by commas. Choice A is incorrect
because it contains one too many commas. Choice C is
incorrect because it contains no commas. Choice D is
incorrect because the comma should be before “and.”

31.

The correct answer is C. Although it may sound
otherwise, the conventional expression is “for all intents
and purposes,” choice C. Choices A, B, and D are
incorrect.

32.

The correct answer is A. Choice A is correct because
the author’s intent is to suggest that there are other
factors that make the problems of drought worse and
more complicated. Choices B, C, and D are incorrect
because each word emphasizes an increase in severity
rather than an increase in the number of factors
contributing to problems in the area.

33.

The correct answer is D. The accompanying map
measures average air temperatures, so choice D is
correct. The map does not measure the highest or
lowest air temperatures, so choices A and B are
incorrect. It also doesn’t measure water temperature, so
choice C is incorrect.

34.

The correct answer is C. Choice C is correct because
this first paragraph establishes that women do not get
as many leading roles as men nor do they spend as
much time on-screen. Choice A is incorrect because it
does not stress the number of roles nor the amount of
on-screen time. Choice B is incorrect because it does not
cite the amount of on-screen time, alluding to it only
vaguely. Choice D is incorrect because the main idea of
the passage is not a plea to pay female actresses more
than their male counterparts to attract new talent.

Answer Keys and Explanations
35.

The correct answer is B. Choice B is correct because
only “agents” expresses the idea that television and
movies play an active role in causing social change.
Choices A, C, and D are incorrect because they don’t
suggest a causal relationship to social change.

40.

The correct answer is C. Choice C is correct because
the pronoun should refer to the female actress using
“her.” Choice A is incorrect because it is plural. Choice B
is incorrect because it is masculine. Choice D is incorrect
because it is plural and first person.

36.

The correct answer is D. Choice D is correct because
the subordinate clause that begins with “while” is tied to
the central premise of the sentence and needs to be at
the beginning. Choice A is incorrect because at the end
of the sentence, the relationship of the clause to the
central idea is lost. Choices B and C are incorrect
because they obscure the relationship of the clause to
the central idea of the sentence.

41.

The correct answer is D. Choice D maintains the
objective and neutral tone of the passage while noting
unfavorable comparisons. Choices A, B, and C are
incorrect because the tone of each choice is emotionally
charged, which is inconsistent with the objective tone
of the passage.

42.

The correct answer is B. Given the context of the
sentence and paragraph, famous is the most appropriate word choice. Streep is offered as an example of a
woman who has achieved great acclaim as an actress,
despite gender inequalities in the film industry. The
previous sentence mentions her many award nominations, so referring to her fame here makes the most
sense. The other answer choices either don’t make
sense given the context, or we are not given enough
information to determine if they are appropriate
choices, so they are incorrect.

43.

The correct answer is A. Choice A is correct because
“accolades” connotes the achievements, honor, and
respect that the passage goes on to describe. Choice B
is incorrect because the awards were not privileges.
Choices C and D are incorrect because they do not
connote the honor and respect that “accolades” does.

44.

The correct answer is C. The word “characters” should
be the possessive “character’s,” so choice C is correct.
Choice A is incorrect because “characters” is plural
instead of possessive. Choice B is incorrect because
“character” is not possessive. Choice D is incorrect
because it does not convey the appropriate meaning.

37.

The correct answer is A. Choice A is correct because
the noun “women” should agree in number with
“protagonists.” Choice B is incorrect because “protagonists” should be plural. Choice C is incorrect because
“protagonist” should be singular if it is to agree with the
subject. Choice D is incorrect because “a woman” is not
plural.

38.

The correct answer is C. Choice C clarifies that the
comparison is between women’s marital status and the
marital status of men. Choice A is incorrect because it
makes an illogical comparison between women’s
marital status and men in general. Choice B is incorrect
because it uses the singular “man,” meaning that only
one man’s marriage status is being compared. Choice D
is incorrect because it compares women’s marital status
to the grammatically incorrect phrase “men’s marriage.”

39.

The correct answer is A. Choice A supports the
paragraph’s claim that women are underrepresented in
the film industry. Choices B, C, and D are incorrect
because they don’t support the paragraph’s main focus
that women are underrepresented in the film industry.

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Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. B

6. A

10. A

14. A

2. B

7. D

11. C

15. D

3. B

8. C

12. C

16. 80

4. C

9. B

13. D

17. 6

18. 0.55
or 5/9
19. 15
20. 4

5. C

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)
1.

The correct answer is B. The slope of a line can be
determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for
any two points on the line. Using the points indicated,
5 −1
4
= − . Translating the line moves all the
the slope is
3
0−3
points on the line the same distance in the same

5.

(2 x ) 2 + (3 x ) 2 = 13 2
4 x 2 + 9 x 2 = 169
13 x 2 = 169
x 2 = 13

direction, and the image will be a parallel line.
4
Therefore, the slope of the line is − .
3
2.

The correct answer is B. The constant 12 represents the
starting distance on the driveway. In other words,
before the snail even moved, it was already 12 feet from
the beginning of the driveway. Therefore, Catherine
must have placed the snail 12 feet from the start of her
driveway before she began recording the time it took
for the snail to get to the end of her driveway.

3.

The correct answer is B. Solve for x:
−2 x + 5 = 2 − (5 − 2 x )
−2 x + 5 = 2 − 5 + 2 x
−2 x + 5 = −3 + 2 x
Add 2x to bo
oth sides.
5 = −3 + 4 x
Add +3 to both sides.
8 = 4x
Divide by 4.
2= x

4.

The correct answer is C. The right triangle, of which T is
the hypotenuse, has legs that are 6 inches and 9 inches.
Hence,
T 2 = 62 + 92
T 2 = 36 + 81 = 117
T = 117
Therefore, 10 < T < 11.

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The correct answer is C. Let the legs equal 2x and 3x.
By the Pythagorean theorem,

x = 13
The shorter leg measures 2x, or 2 13 .
6.

The correct answer is A. The amount of grain added
each week is 1,000 bushels. Divide 1,000 bushels by 0.8
bushels per cubic foot to obtain 1,250 cubic feet per
week. So, the total amount of grain in the silo is 32,500
(what is already there) plus 1,250w (the amount added
each week times the number of weeks), which must be
less than or equal to the volume of the silo, 45,000 cubic
feet.

7.

The correct answer is D. The vertex of a parabola is
found when the equation is written in the form
y = a(x – h)2 + k. You don’t need to perform any
calculations, because only choice D is written in this
form.

8.

The correct answer is C.
− x 2 + 2 y − (− x − y ) = − x 2 + 2 y + x + y
= − x 2 + x + 3y

Answer Keys and Explanations
9.

The correct answer is B. Since Jorge’s truck is traveling
at an average speed of 55 miles per hour and the truck
gets 6 miles per gallon, the number of gallons of diesel
used each hour can be found by the equation
55 miles 1 gallon 55 . The truck uses 55 gallons of
×
=
6
1 hour
6 miles 6
55
diesel per hour, so it uses
h gallons of diesel in h
6
hours. The truck’s fuel tank has 125 gallons of diesel at

14.

650 − 500 150
=
= 0.3
500
500

the beginning of the trip. Therefore, the function that

Since the population is growing, add the percent of
change, in decimal format, to 1 to get 1.3.
Therefore, the expression representing the population
growth is 500 × 1.3x.

models the number of gallons of diesel remaining in the
tank h hours after the trip begins is d (h) = 125 −
10.

55h
.
6

The correct answer is A.
M
M−N
A(M − N) = M
A=

AM − AN = M
AM − M = AN
M( A − 1) = AN
AN
M=
A −1
11.

12.

The correct answer is C. The down payment is only
made once, and the sum of the down payment plus the
monthly payments is equal to the cost of the sofa.
The correct answer is C. The sum of the values that
satisfy the equation is the sum of the solution
2.5 + 3 = 5.5.
2n 2 − 11n + 15 = 0

(2n − 5) (n − 3) = 0

The correct answer is A. The initial population of the
town is 500. The rate of change between consecutive x
values (1 year, 2 years, 3 years) is not constant. As a
result, the expression cannot be linear, but exponential.
Determine the percent of increase of the population
from the initial population to that of one year:

15.

The correct answer is D. You can see right away that
4 +1
choice A is not correct, because
= 2.5, which is not
2
equivalent to the fraction for all values of x. The three
other answer choices all start with a whole number, so
to find out which of them is correct, rewrite the given
fraction as a mixed number. Since the denominator is
x + 2 and the numerator includes a 4x, rewrite it so that
it is the sum of two fractions where one has a 4(x + 2), or
4x + 8, in the numerator. Then, simplify the expression
until you have a whole number and check the result
against the three answer choices to find the correct one.
4x +1 4x
1
=
+
x +2 x +2 x +2
4x
8
1
8
=
+
+
−
x +2 x +2 x +2 x +2
4 x + 8 1− 8
=
+
x +2 x +2
7
=4−
x +2

2n − 5 = 0 , n − 3 = 0
n = 2.5, n = 3
13.

The correct answer is D. The graph will cross the x-axis
at the point where the function (that is, the y-coordinate) has a value of 0. As a result, the following
equation needs to be solved:
480 − 60t = 0
−60t = −480
t =8
Since t represents the independent variable, the point
is (8, 0).

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Answer Keys and Explanations
16.

The correct answer is 80. If AC = BC, then m–A =
m–B = 50°.
A

50

˚

50

˚

19.

B

The correct answer is 15. To begin,
f(p + 3) = 5(p + 3)+ 12 = 5p + 15 + 12 = 5p + 27.
Similarly, f(p) = 5p + 12. Thus,
f ( p + 3) − f ( p) = 5p + 27 − (5p + 12)
= 5p + 27 − 5p − 12
= 15

80

20.

˚

C

80

The correct answer is 4. Solve for x:
9
16
+
=5
x −2 x +3

˚

16 
 9
+
( x − 2) ( x + 3) = 5 ( x − 2) ( x + 3)
 x − 2 x + 3 

E

9 x + 27 + 16 x − 32 = 5 x 2 + 5 x − 30
D

In ∆ABC, m – ACB = 180° – (m – A + m – B). So,
m – ACB = 80°. Further, m – ACB = m – ECD because
they are vertical angles. Therefore, m – ECD = 80°.
17.

The correct answer is 6. First, solve for x by multiplying
the second equation and adding it to the first one:

5 x − 4 y = 13
2[ x + 2 y = 4 ]
7 x = 21
x =3
Then, substitute x = 3 into the second equation to get
the value of y:
3 + 2y = 4
2y = 1
1
y=
2
x
1
Finally, substitute x = 3 and y =
into
to get the
y
2
value of the ratio:
x 3
= =6
y 1
2
18.

The correct answer is

5
= 0.55 . Solve for b:
9

−9 x + 5 = −9 ( x − b)
−9 x + 5 = −9 x + 9b
5 = 9b
5
=b
9

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0 = 5 x 2 − 20 x − 25
0 = 5( x + 1)( x − 5)
x = −1 or x = 5
To get the sum of the solutions, simply add –1 and 5:
–1 + 5 = 4.

Answer Keys and Explanations
Section 4: Math Test—Calculator

1. C

9. B

17. D

25. A

33. 45

2. D

10. B

18. B

26. D

34. 41

3. D

11. B

19. A

27. D

35. 5400

4. A

12. D

20. C

28. A

36. 440

5. A

13. C

21. D

29. A

37. 21.5

6. C

14. D

22. B

30. B

38. 4

7. B

15. C

23. C

31. 5

8. D

16. B

24. A

32. 9

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is C. 15% of $12.50 is (0.15)($12.50)
= $1.875. So, the discount for every 10 audio singles
purchased is $1.875. Multiply this by 4 to get the savings
when purchasing 40 audio singles: 4($1.875) = $7.50.

2.

The correct answer is D. 20 square yards = 180 square
feet. At $1.30 per square foot, it will cost 180 × $1.30 =
$234.00.

3.

The correct answer is D. Let x represent the score of
one of the two games for which he scored identically.
Then, the score of the third game is x + 20. Since the
average of all six games is 182, solve the following
equation for x:
212 + 181+ 160 + x + x + ( x + 20)
= 182
6
573 + 3 x
= 182
6
573 + 3 x = 1, 092
3 x = 519
x = 173
So, his six scores were 160, 173, 173, 181, 193, and
212. Therefore, the second highest score is 193.

4.

The correct answer is A. The volume of the fish tank is
11(14)(9) = 1,386 cubic inches. The amount needed to
fill the tank is 1,386 ÷ 231 = 6 gallons.

5.

The correct answer is A. The amount of protein in m
cups of milk is 8m grams, and the amount of protein in
n eggs is 6n grams. The problem asks for the amount to
meet or exceed the recommended daily intake, which
sets up a greater-than-or-equal-to scenario.

6.

The correct answer is C. The total charge that Amy will
pay is the daily rate, the mileage rate, and the 7.5% tax
on both. If Amy drove x miles, then the total charge is
(19.99 + 0.15x) + 0.075(19.99 + 0.15x), which can be
rewritten as 1.075(19.99 + 0.15x).

7.

The correct answer is B. 5

1
dozen nails are bought for
2

1
5 dozen × 35 cents per dozen = 192.5 cents. There are
2
1
66 nails in 5 dozen and 66 ÷ 3 = 22 sets sold at 10
2
cents per set, so 22 sets × 10 cents per set = 220 cents.
1
The profit is 220 – 192.5 = 27 cents.
2
8.

The correct answer is D. The weights are proportional
to the volumes, and the volumes vary as the cubes of
their dimensions. If the edges are doubled, the volume
becomes 23 = 8 times as large. Therefore, the weight is
8 × 150 = 1,200 pounds.

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  111

Answer Keys and Explanations
9.

The correct answer is B.

16.

The correct answer is B. The scatterplot shows a strong
correlation between the variables. As the years increase,
the population also increases.

17.

The correct answer is D. The points on the graph
display a pattern of exponential growth, as a curve
could be used to connect them; therefore, an exponential curve would best represent the data.

18.

The correct answer is B. The graduate starts at x dollars
per week. After the pay cut, the graduate receives 90%
of the original salary. The 10% raise adds 9% to the
salary (10% of 90%), so the new salary is 0.99x.

19.

The correct answer is A. The solution set is as follows.
Note that it extends into all quadrants except the third.

−2(1− x ) 2 + 2(1− x 2 ) = −2(1− 2 x + x 2 ) + 2(1− x 2 )
= −2 + 4 x − 2 x 2 + 2 − 2 x 2
= −4 x 2 + 4 x

10.

11.

12.

The correct answer is B. One method to find the
correct answer is to create an inequality. The income
from the sign-up fees for x people is 20x. For the
organization to profit, 20x must be greater than the cost
of x t-shirts Therefore, 20x > 7x + 60 can be used to
model the situation. Solving this inequality yields x >
4.6. Since there can’t be 4.6 people, round the answer
up to 5.
The correct answer is B. The total number of students,
x + y, is equal to 2,180, so the answer must be choice B
or choice C. The male students raised $20 each, and the
female students raised $25 each. Since x represents the
number of male students, then the amount the male
students raised is represented by 20x, and the amount
the female students raised is represented by 25y. The
total amount raised is $50,000, so the sum is 20x + 25y =
50,000. That leaves choice B as the only correct answer.

(

9 x 3 y 5z 6 = 9 x 3 y 5z 6

)

15.

  112

2°
1

2

x

y = –2y+ 4

20.

The correct answer is C. The two intersections of the
graphs of the equations are at the points (0, 1) and
(–1, 0). Substituting 0 for x and 1 for y makes both
equations true.Also, substituting –1 for x and 0 for y
makes both equations true.

The correct answer is C. The legs have lengths x and
x – 3, and the hypotenuse has length 4. Using the
Pythagorean theorem yields:
x 2 + ( x − 3)2 = 4 2
x 2 + x 2 − 6 x + 9 = 16

The correct answer is D. Find the solution to this
problem by using the structure of the given equation.
x y
Multiplying both sides of the equation − = 5 by 24
3 4
will clear fractions from the equation and yield
8x – 6y = 120.
The correct answer is C. If x is the number of lunches
sold and y is the number of dinners sold, then x + y
represents the number of meals sold during the
weekend. The equation 7.5x + 12y represents the total
amount collected in the weekend. Therefore, the correct
system of equations is x + y = 241 and 7.5x + 12y =
2,523.

www.petersons.com

y = –2x+ 4

1
3

1
5
= 9 3 xy 3 z 2

14.

4°

The correct answer is D. The cube root of an expression
1
is equal to that expression raised to the
power, so
3
3

13.

y

2x2 − 6x − 7 = 0
x=

−( −6 ) ± ( −6 )2 − 4(2) i ( −7)
2(2)

x=

6 ± 92 6 ± 2 23 3 + 23
=
=
2
4
4

A length cannot be negative, so the hypotenuse has
length
21.

3 + 23
units.
2

The correct answer is D. If the discount is 10%, then
$12.60 is 90% of $14.00.

Answer Keys and Explanations
22.

The correct answer is B. To solve for the number of
gallons of white vinegar, set up a proportion.

29.

12 + 13 + 31+ 25 + 37 + 28 146
=
6
6
= 24.3
≈ 24

1
3=x
2 7
28
2x =
3
2
4
x =4 =4
6
3

1

23.

24.

25.

26.

27.

28.

The new average will have to be 25, but it will be
spread over 7 Winter Olympics:

The correct answer is C. A hexagon with 22-inch sides
has a perimeter of 6 × 22, or 132 inches.
C = 2pr
132 = 2pr
132 = 2(3.14 )r
132 = 6.28r
21.02 = r
The correct answer is A. Because the function f has
(x – 4) and (x + 2) as factors, the function should have
zeros when x – 4 = 0 and x + 2 = 0. The only graph that
shows a curve that has x-intercepts at –2 and 4 is
choice A.

12 + 13 + 31+ 25 + 37 + 28 + x 146 + x
=
= 25
7
7
146 + x = 175
x = 29
30.

31.

The correct answer is D. If k is a positive constant other
than 1, then the equation kx + y = c can be rewritten as
y = –kx + c. If k is positive, then –k is negative, and it
must be something other than –1. The only graph with
a negative slope other than –1 is answer choice D.
The correct answer is A. If the machine loses 15% of its
value each year, then each year its value is 85% of what
it was the year before. Therefore, we are looking for the
fifth term of a geometric sequence with first term
$80,000 at time zero and common ratio 0.85. Using the
formula a n = a1 × r n −1, we can compute a5 = $80,000 ×
(0.85)4 = $41,760.50.

6x
by
2x + 4
factoring out the greatest common factor (2).
A
3x
3x
= 3+
The result is
. Set
and solve.
x +2
x +2
x +2
A = –6.
The correct answer is B. Simplify the ratio

The correct answer is 5. Expand the left side and then
equate corresponding coefficients:
(ax − 1) ⋅ (2 x + b ) = 4 x 2 + 4 x − 3

The correct answer is A. There are a total of 8 + 23 + 19
= 50 people in Group A. Then, reduce the fraction to
8
4
find that
.
=
50 25
The correct answer is D. When t = 0, the height of the
ball is 0.02 m, so 0.02 represents the height of the ball
before it is hit.

The correct answer is A. To find the current average,
add all of the medals and divide by 6:

2ax 2 − 2 x + abx − b = 4 x 2 + 4 x − 3
2ax 2 + (ab − 2) x − b = 4 x 2 + 4 x − 3
So, 2a = 4, ab – 2 = 4, and –b = –3. So, a = 2 and b = 3.
Therefore, a + b = 5.
32.

The correct answer is 9. Since he must buy at least two
of each item, first determine the cost of buying exactly 2
of each:
2($4.00 + $3.75 + $1.50) = $18.50
Now, subtract that from $50: $50 – $18.50 = $31.50.
Divide this difference by the cost of a pint of berries
($4.00) to get $7.875.
So, Derek would be able to buy at most 7 more pints
of berries. This, together with the 2 pints we accounted for at the start of the solution, gives a maximum of
9 pints of berries that he could purchase.

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Answer Keys and Explanations
33.

The correct answer is 45. Letting m be the time per
regular question, 2m is the time per math problem. The
total time for all the regular questions is 300m, and the
total time for all the math problems is 50(2m). Since the
exam is 3 hours, or 180 minutes, 300m + 100m = 180

37.

3 x + y = −4
−( x + y = 13)

180 9
=
. The time to
400 20
 9 9
. All 50 math
do a math problem is 2   =
 20  10
9
problems can be done in 50   = 45 minutes.
 10 

2 x = −17
x = −8.5

minutes, 400m = 180, and m =

34.

35.

36.

  114

Then solve for x and substitute into one of the equations to solve for y:

The correct answer is 41. The number of games that
the Montreal Canadiens played is not provided, but it is
given that the ratio of the number of games played in
the 1947–48 season to that in the 1924–25 season is 2:1.
Problems like this can be solved by plugging in real
numbers. Let’s say that there were 100 games in the
1924–25 season, so they won 57 of those games. In the
1947–48 season, there were twice as many games, or
200 games, so they won 33% of 200 games, or 66
games. Altogether they won 123 out of 300 games, and
this fraction can be simplified to 41 out of 100, or 41%.
The correct answer is 5400. Of the number of voters
polled, 400 of 625, or 64%, were in favor of the measure.
If the margin of error is 4%, the likely population
proportion will be between 60% and 68%: 60% of 9,000
total voters is (0.6)(9,000) = 5,400.
The correct answer is 440. If the dolphin weighs 110%
of the average, it weighs 10% more than the average
weight of 400 pounds, or 0.10 × 400 = 40 pounds. The
dolphin weighs 400 + 40 = 440 pounds.

www.petersons.com

The correct answer is 21.5. First, combine the
equations by subtracting (x + y = 13) from (3x + y= –4):

−8.5 + y = 13
y = 21.5
38.

The correct answer is 4. To find the value that will
make the system have no solution, you must show that
the two equations are parallel lines. In standard form,
parallel lines are equal on the left side of their equations, but not the right. In standard form, the first
equation would need to be equal to the second on the
left side. Find a factor that you could multiply the first
equation by:
−3 x + 2 y = −1
6 x − by = 8
( −3 x + 2 y = −1)( −2)
6x − 4y = 2
so b = 4
If b = 4, the left side of both equations are equal, but
not the right. Therefore, they are parallel.

Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
The following is an analysis of the passage by Peter Krapp, noting how the writer used evidence, reasoning, and stylistic or persuasive
elements to support his claims, connect the claims and evidence, and add power to the ideas he expressed. Check to see if you
evaluated the passage in a similar way.

1

Pennsylvania State University’s College of Engineering took
its computer network offline on May 15 after disclosing
two cyberattacks. The perpetrators were able to access
information on 18,000 students, who are being contacted
this week with the news that their personal identifying
information is in hackers’ hands.

1

The writer cites a specific example of a computer security
breach and uses facts and statistics to show the seriousness
of the problem.

Three days later, the computer network is back online, with
new protections for its users.
2

One of the two attacks is ascribed by a forensic
cybersecurity corporation retained by Penn State to
computers apparently based in China.

2

By mentioning that the computer hackers appear to be
located in China, the writer underscores the global risks of
the security breach.

3

As a researcher who has published on hacking and
hacktivism and serves on the board of the UC Irvine data
science initiative, I believe two aspects of this news story
deserve particular attention.

3

The writer establishes his credentials to write about and offer
an argument on this topic.

Compromising student data
4

Penn State announced last week that the FBI alerted it on
November 21, 2014, about an attack with custom malware
that started as early as September 2012.

4

The writer uses facts and dates to lay the groundwork for the
point he is about to make.

5

Why did it take so long for Penn State to disclose the breach,
despite the fact that the experience of large-scale hacks in
2013 and 2014 (against Target, Home Depot, and others)
clearly demonstrated an urgent need for quick and full
disclosure—both to help the victims and to preserve a
modicum of trust?

5

The writer poses a rhetorical question to address one
aspect of this story that he earlier said deserves “particular
attention.” His first point is that Penn State took too long to
disclose the security breach. He cites two past breaches to
support his argument about the need for quick disclosure
and uses evocative words (“help the victims and to preserve
a modicum of trust”) to emphasize how important early
disclosure is.

6

Penn State stated only that any disclosure would have
tipped off the perpetrators before their access to the
College of Engineering computers could be cut off.

6

The writer states Penn State’s justification for delaying
disclosure. He uses the word only to imply that Penn State
should have been more forthcoming, thus strengthening
his own position. At the same time, he presents himself as
reasonable because he offers Penn State’s argument before
going on with his own.

7

Meanwhile, student data may have been compromised
for at least six months, maybe longer.

7

The writer shows why, in his opinion, Penn State’s position is
weak.

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Answer Keys and Explanations
8

Another conspicuous problem with public discussion
of events like this is, in fact, the lack of distinction often
made in the media between actual appropriation of
data (as at Penn State) and mere temporary disabling
or defacement of websites (as happened to Rutgers
University last month). That is like being unable to make a
difference between a grand theft auto and keying a car.

8

The writer now addresses the second point that he feels
“deserve[s] particular attention” — The media do not treat
breaches like the one at Penn State seriously, often viewing
them more like nuisance problems. He supports his view that
the media should be able to make a distinction between
serious and non-serious security breaches by juxtaposing a
significant crime (grand theft auto) with a minor infraction
(keying a car).

The question is, what can universities do to limit the risk
to their students?
9

The exposure of student data in higher education is not
limited to Social Security numbers or email passwords.
Information collected and retained by educational
institutions includes full name, address, phone number,
credit and debit card information, workplace information,
date of birth, personal interests and of course academic
performance and grade information.

9

The writer shows how dangerous these kinds of security
breaches are, using specific examples of the kinds of
information that can fall into hackers’ hands.

10

A survey conducted by the Obama administration
collected responses from 24,092 individuals on how
much they trusted various institutions to keep their
data safe. There was a high level of concern around
transparency and legal standards. (https://www.
whitehouse.gov/issues/technology/big-data-review)

10

The writer strengthens his viewpoint by providing statistical
evidence in the form of a survey that reveals how concerned
people are about the safety of their personal data.

11

The writer supports his argument by quoting an authority
no less than the president of the United States. (He also
makes the point that he believes the president’s concern is
overdue, by saying this statement was made “only recently.”)

12

The writer underscores the depth of the problem by pointing
out that there are many entities that might access students’
computer data: not only foreign intelligence agencies (as was
the case with the Penn State breach), but US companies that
mine computer data for profit. The writer argues that just as
foreign breaches have been recognized as serious, so should
domestic for-profit breaches.

13

The writer offers a specific example of a US company mining
personal data for profit to strengthen his case.

The California Senate Bill 1177 was enacted to prevent
educational services from selling student information or
mining it for advertising purposes.

14

The writer underscores the validity of his argument by citing
legislation enacted to address the problem.

15 Yet, almost a year later, students in California remain just
as concerned about their data privacy as before—since
the new state law was watered down to apply only to
K–12 and not to higher education.

15

The writer points out that the final form of the legislation to
protect students’ data does not extend to college students.

...
11

President Obama only recently called for laws covering
data hacking and student privacy. “We’re saying that data
collected on students in the classroom should only be
used for educational purposes,” he stated in his speech to
the Federal Trade Commission (FTC) earlier this year.
Data privacy concerns

12

If students’ right to privacy needs to be protected from
the specter of foreign intelligence agencies poking
around the Penn State Engineering School, then by the
same logic it should be protected also against datamining by for-profit actors right here in the US.

13

Until May 2014, Google, for instance, routinely mined
its apps for education services for advertising and
monetizing purposes. When Education Week reported
that Google was mining student emails, it quickly led not
only to lawsuits but also to landmark legislation.

14

  116

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Answer Keys and Explanations
16

And when it was disclosed earlier this spring that
education publisher Pearson secretly monitored social
media to discern references to their content, the legislative
response was one that, according to the Electronic Privacy
Information Center (EPIC) in Washington, DC, “fails to
uphold President Obama’s promise that the data collected
in an educational context can be used only for educational
purposes.”

16

The writer reinforces his argument that not enough is being
done to protect college students’ personal data by citing
another example of a US company data-mining for profit. He
also quotes an authoritative source to support this claim.

17

Students in higher education nationwide are still in a
position where they cannot opt out of the computer
services of their learning institutions, and so they have no
expectation of privacy.

17

The writer points out a reality that makes and keeps college
students vulnerable: “they cannot opt out of the computer
services of their learning institutions.”

18

Despite President Obama’s promises for safeguarding
the privacy of consumers and families, and despite the
fact that a number of technology companies concerned
with growing consumer distrust recently signed a pledge
to safeguard student privacy, neither Google nor Apple
signed on.

18

The writer underscores college students’ vulnerability by
pointing out that two major companies (Google and Apple)
have refused to sign a pledge to safeguard student privacy.

19 The President’s Council of Advisors on Science and
Technology (PCAST) was tasked to examine current
and likely future capabilities of key technologies, both
those associated with the collection, analysis, and use
of big data and those that can help to preserve privacy,
resulting in a direct recommendation to strengthen US
research in privacy-related technologies.

19

The writer points out that an advisory board to the US
president has recommended strengthening research on the
problem.

20

And overwhelmingly, respondents to a White House
survey recently expressed severe reservations about
the collection, storage, and security and use of private
information.

20

21

Maybe it is time for higher education to heed those
signals.

The writer cites a White House survey that reflected “severe
reservations about the collection, storage, and security and
use of private information.” The survey shows that despite
the measures that have been put in place, the public still
feels their data is at risk.

21

The writer concludes his argument by saying it’s time for
colleges (where people are particularly vulnerable) to pay
attention to—and act on—the information they have, in
order to remedy the situation.

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Answer Keys and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Peter Krapp.

High-Scoring Essay
Peter Krapp builds a well-constructed argument designed to persuade readers that computer hacking is a danger that steals
our most valuable possession—personal information—from our most vulnerable people—students. The article focuses on
personal information about college students stolen from college computer networks. The writer builds his argument brick by
brick. He starts by giving an example of student data stolen from a college by hackers in China, relating his topic to an event
that really happened. The writer quickly establishes himself as an expert in the topic so readers can trust his information.
Krapp asks and answers questions about the theft of data, goes into more depth about the type of information stolen from
college networks, and then briefly touches on the laws, or the lack of laws, to protect students. He points out that data is
stolen from students by not only foreign hackers, but also by American companies. The writer finishes with a call for colleges
to protect student data, clearly stating his purpose.
The theft of 18,000 students’ data from Pennsylvania State University’s College of Engineering is a strong example to start the
article. Naming the college and identifying the large number of students tells the reader immediately that a single incident
affected many people. The location of the hackers shows that protecting the physical location of the data is useless, and it
adds a bit of foreign intrigue.
The second paragraph is a single sentence, but accomplishes two important things. It gives the reader his credentials,
proving that he is qualified to speak as an authority on the topic. It also provides structure for the next section by telling the
reader that the writer will focus on two aspects of the news story.
Krapp reveals the first aspect to be discussed right away—Penn State knew that data was being stolen for six months before
doing anything about it. To emphasize just how astonishing Penn State’s behavior is, Krapp asks the same question that any
reader might ask: Why? He asks the question in words that urge a fast response such as “urgent need” and “help the victims.”
He demonstrates that Penn State’s response is weak by describing the response as “stated only.”
The next paragraph starts with “Another conspicuous problem.” This phrase presents the second aspect he wants to discuss,
which is the media’s lack of understanding about the difference between the major problem of stealing data and the minor
problem of disabling a website for a short period of time. He helps readers to understand the difference by comparing
stealing a car to causing only minor damage to the car.
Krapp follows the reader’s natural thought process by asking the next question: If it’s a problem, how do we fix it? He presents
information in two ways, listing the type of information at risk and displaying bar charts that show the results of a presidential
survey on the public’s perception of data security.
The section title, “Data privacy concerns,” informs readers that Krapp is addressing another concern, the theft of student data
by US companies that want to mine data for profit. He gives two examples that are recognized and used by college students:
Google and Pearson. He points out that students are particularly vulnerable to theft by the corporations that provide the
apps and class materials that students must use for school. The school dictates which apps are to be used, so students “cannot
opt out.” He touches again on the law, but reveals that it doesn’t protect college students. This information reinforces his
arguments that college students are vulnerable to data theft. Presenting the facts this way says that college students are not
only vulnerable, they are betrayed by the universities, US companies, and laws that should protect them.
The argument Krapp has built leads to a solid conclusion that Krapp states in a single, final sentence that is brief but
summarizes the conclusion readers should draw. The brevity of the statement ensures that readers will get the point of the
article and remember it in the future. The information that Krapp presents in examples, lists, survey results and bar charts
provides a solid foundation for the conclusion that becomes obvious to any reader. Protect student data.

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Answer Keys and Explanations
Low-Scoring Essay
Peter Krapp tries to persuade us that students should be allowed to opt out of giving their data to colleges and companies.
This would protect them from having their full name, address, phone number, credit and debit card information, workplace
information, date of birth, personal interests and of course academic performance and grade information stolen by people
like Chinese hackers and companies like Google and Pearson.
Peter Krapp persuades us by giving lots of examples of data being stolen, like Pennsylvania State University’s College of
Engineering, Target, Home Depot, Google, and Pearson. One of the examples includes a chart that shows how much 24,092
individuals trusted various institutions to keep their data safe. Most of them didn’t think their data was safe.
All of this information, charts, and examples that Peter Krapp included in his essay is very convincing. I think we should pass
some laws like Peter Krapp suggested. The laws would keep American companies from stealing our data and punish hackers
from other countries who steal our data.
All college students should try to opt out of giving away all of their private information because we know the colleges won’t
protect it. The colleges actually tell students to use apps that they know companies steal data from. This makes college
students more vulnerable than anyone else to losing their data.
If companies are going to use the data they take from students, they should pay the students for the data. Then, students
might not mind so much if companies take their data because the students would make money from it and college is very
expensive.
When I go to college, I will opt out of giving my data to colleges and companies. My information is important to me and I
don’t want it stolen from me.

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Computing Your Scores
COMPUTING YOUR SCORES
Now that you've completed this diagnostic test, it's time to compute your scores. Simply follow the instructions on the following
pages, and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation
as possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then calculate the total score. It sounds a little confusing, but we’ll take you
through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test.
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for wrong
answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page123. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1. Count the number of correct answers you got on the Section 3: Math Test—No Calculator and the Section 4: Math
Test—Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2. Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—Calculator.
3. Use the Raw Score Conversion Table 1: Section and Test Scores on page 123 and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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Computing Your Scores
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test that focus on linear equations and inequalities.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 1–3, 6, 9, 11, 17, 18
ºº Math Test—Calculator: Questions 5, 6, 10, 11, 14, 15, 19, 27, 29, 37, 38
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
the interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: None
ºº Math Test—Calculator: Questions 1–3, 7, 8, 16–18, 21, 22, 25, 28, 32, 33–36
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability
to progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations,
and interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 7, 8, 10, 12–15, 19, 20
ºº Math Test—Calculator: Questions 9, 12, 13, 24, 26, 30, 31
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Passport to Advanced Math subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 1, 4, 5, 7–9, 12, 13, 16, 17, 19, 20, 23, 26, 28, 29, 32–35, 39, 41–43

• Your Raw Score = the total number of correct answers from all of these questions
• Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 2, 3, 6, 10, 11, 14, 15, 18, 21, 22, 24, 25, 27, 30, 31, 36–38, 40, 44

• Your Raw Score = the total number of correct answers from all of these questions
• Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Standard English Conventions
subscore.

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Computing Your Scores
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 1, 5, 12, 16, 27, 30, 41, 42, 51, 52
ºº Writing and Language Test: Questions 5, 8, 12, 17, 28, 32, 35, 43
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 3, 6, 9, 14, 19, 23, 28, 32, 36, 38, 42, 43, 44
ºº Writing and Language Test: Questions 1, 4, 13, 16, 29, 33, 34, 42
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 2: Subscores on page 124 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 11–21, 43–52
ºº Writing and Language Test: Questions 12, 13, 16, 17, 19, 20
ºº Math Test—No Calculator: Question 14
ºº Math Test—Calculator: Questions 11, 16, 17, 25, 29, 34, 35
Your Raw Score = the total number of correct answers from all of these questions
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 126 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these sections:
• Reading Test: Questions 1–10, 22–32
• Writing and Language Test: Questions 25, 26, 28, 29, 32, 33
• Math Test—No Calculator: Questions 2, 13
• Math Test—Calculator: Questions 4, 5, 8, 22, 26, 36
• Your Raw Score = the total number of correct answers from all of these questions
• Use the Raw Score Conversion Table 3: Cross-Test Scores on page 126 to determine your Analysis in Science cross-test
score.

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Computing Your Scores

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

TOTAL SAT® SCORE
(400–1600)

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Computing Your Scores

  124

Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

2

1

1

2

2

5

2

2

3

2

2

3

3

6

3

3

4

3

2

4

4

7

4

4

5

4

3

5

5

8

5

5

6

5

4

6

6

9

6

6

7

6

5

6

7

10

6

7

8

6

6

7

8

11

7

8

9

7

6

8

8

11

8

8

10

7

7

8

9

12

8

9

11

8

7

9

10

12

9

10

12

8

8

9

10

13

9

10

13

9

8

9

11

13

10

11

14

9

9

10

12

14

11

12

15

10

10

10

13

14

12

13

16

10

10

11

14

15

13

14

17

11

11

12

15

14

15

18

11

12

13

15

15

19

12

13

15

20

12

15

21

13

22

14

23

14

24

15

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Computing Your Scores
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

1

10

11

19

29

27

2

11

12

20

30

27

3

12

13

21

30

28

4

14

14

22

31

29

5

15

15

23

32

30

6

16

16

24

32

30

7

17

17

25

33

31

8

18

18

26

34

32

9

20

19

27

35

33

10

21

20

28

35

33

11

22

20

29

36

34

12

23

21

30

37

35

13

24

22

31

38

36

14

25

23

32

38

37

15

26

24

33

39

38

16

27

24

34

40

39

17

28

25

35

40

40

Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

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Computing Your Scores
Conversion Equation 3: Cross-Test Scores
ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

RAW SCORE

ANALYSIS IN SCIENCE
QUESTIONS

Reading Test

11–21, 43–52

1–10, 22–32

Writing and
Language Test

12, 13, 16, 17, 19, 20

25, 26, 28, 29, 32, 33

Math Test—No
Calculator

14

2, 13

Math
Test—Calculator

11, 16, 17, 25, 29,
34, 35

4, 5, 8, 22, 26, 36

TOTAL

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ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (10–40)

RAW SCORE

part iii: reading
strategies for the sat ®

Chapter 3: Evidence-Based Reading Test Strategies

Chapter 3:
Evidence-Based Reading
Test Strategies
OVERVIEW
A Closer Look at the Evidence-Based Reading Test
Basic Steps for Answering Evidence-Based
Reading Questions
Tips for Taking the Reading Test
Strategies for Answering Specific Question Types
Exercise: Evidence-Based Reading Test
Answer Key and Explanations
Summing It Up

A CLOSER LOOK AT THE EVIDENCE-BASED READING TEST
The SAT® Evidence-Based Reading Test is focused on demonstrating comprehension and reasoning skills through responses to
a variety of reading passages. The passages are chosen to reflect the complexity and reading levels appropriate to college and
career readiness. The questions will require you to analyze the text and use textual evidence to assess meaning and to support
ideas. The emphasis is on using the text to support your answers and on understanding the overall concepts and how they are
developed through the course of the passage.
Passage topics are drawn from U.S. and world literature, historical and social science documents, and scientific writing. There will
be four single passages and one paired passage, with a total of 52 questions. The single passages’ lengths are between 500–750
words; the paired passage has the same word length between the two passages.

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EvidenceBased
Reading Test
Strategies

The reading comprehension questions are designed to assess how well you read and understand information. The questions
don’t test the specifics you have learned in your course work. They are based solely on explicit and implicit information contained
in the passage. At least one passage will be accompanied by an informational graphic from which one or more questions will be
drawn. These questions require you to analyze the data presented in such formats as tables, graphs, and charts.

NOTE: Evidence-based reading questions are not arranged in order of difficulty. The questions
for each passage will generally begin with broader questions about the overall ideas in the
text and will then focus on specific portions of the passage.

Peterson’s SAT® Prep Guide 2017

Question Format
On the SAT® exam, each evidence-based reading passage and question set starts with a direction line that looks like this:

Questions 1–10 are based on the following passage.
OR

Questions 1–10 are based on the following passage[s] and supplementary material.
OR

Questions 1–10 are based on the following two passages.
The direction line is followed by a brief introduction to the text. The introduction describes the origin of the passage. Sometimes,
the introduction will include additional background information.
The questions for each passage are in standard multiple-choice format with four answer choices each. Most often, these questions
ask you to do one of the following:

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Chapter 3
EvidenceBased
Reading Test
Strategies

•
•
•
•
•
•

Determine central themes and ideas as presented in the passage.
Determine the author’s purpose or point of view of the text.
Cite textual evidence to support inferences, conclusions, or arguments.
Cite evidence to illustrate or support interpretations of meaning, mood, or tone of the passage.
Analyze words and phrases in the context of the passage.
Analyze information in an accompanying table, graph, chart, etc.

BASIC STEPS FOR ANSWERING EVIDENCE-BASED READING QUESTIONS
To answer the reading questions, follow these five steps:
1. Read the introduction.
2. Read the questions.
3. Read the passage with the questions in mind.
4. Answer the questions.
5. For any question you’re not sure of, eliminate obviously wrong answers and take your best guess. Answer all the questions.
Let’s look at the five steps in more detail.
1. You don’t want to blow past the introductory paragraph because it can be very helpful to you. It might provide some
important background information about the passage, or it might set the stage so you know what you’re reading about.
2. Read the questions so you know what to look for in the passage. For example, if there’s a question about the theme,
consider that as you read. If there’s a question that references a particular word or phrase, or perhaps a quotation in
the text, look for it as you read the passage.
3. Now read the passage as quickly as you can without getting lost. Don’t fret over details; focus on the larger ideas and
try to follow the sequence, argument, or plot.

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4. Answer the questions that are easiest for you. Then tackle the others in order, referring to the text to find and confirm
answers as time permits.
5. Eliminate answer choices that you know are incorrect and guess at the remaining choices. Remember, there is no
penalty for incorrect answers, so be sure not to leave any answer circles blank.
Now that you’re familiar with how to approach evidence-based reading passages and questions, let’s try a few. Note that in the
SAT® and all of the practice tests in this book, the reading passages will appear in two columns. For instructional purposes, we
have placed the passages full page in this chapter.

NOTE: Never skip the introduction as it is likely to contain some important information about both the passage and the
types of questions that accompany it. The introduction will identify the type of passage being presented, the source or
author of the passage, the era in which the passage was written, or the event that the passage describes. All of this information will help you focus your reading and find the correct answers to the questions.

Sample Reading Passage 1
Questions 1–4 are based on the following passage.
José Martí was a Cuban teacher, organizer, writer, and poet. The lyrics to the popular folksong “Guantanamera” were adapted from
one of Martí’s poems. Although Cuban by birth, he is considered one of the most influential writers in all of Latin America. He died in
the battle for Cuba’s independence from Spain, a cause to which he had devoted much of his life.
The following excerpt comes from an article by Martí that was published in El Partido Liberal (Mexico City), March 5, 1892.
Our America
The prideful villager thinks his hometown contains the whole world, and as long as he can stay on as mayor or
humiliate the rival who stole his sweetheart or watch his nest egg accumulating in its strongbox he believes the universe
to be in good order, unaware of the giants in seven-league boots who can crush him underfoot or the battling comets
Line in the heavens that go through the air devouring the sleeping worlds. … It is the hour of reckoning and of marching in
5 unison, and we must move in lines as compact as the veins of silver that lie at the roots of the Andes. …
Our youth go out into the world wearing Yankee- or French-colored glasses and aspire to rule by guesswork a
country they do not know. … To know is to solve. To know the country and govern it in accordance with that knowledge
is the only way of freeing it from tyranny. The European university must yield to the American university. The history of
America from the Incas to the present must be taught in its smallest detail, even if the Greek Archons go untaught. Our
10 own Greece is preferable to the Greece that is not ours; we need it more. Statesmen who arise from the nation must
replace statesmen who are alien to it. …

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What a vision we were: the chest of an athlete, the hands of a dandy, and the forehead of a child. We were a whole
fancy dress ball, in English trousers, a Parisian waistcoat, a North American overcoat, and a Spanish bullfighter’s hat.
The Indian circled about us, mute, and went to the mountaintop to christen his children. The black, pursued from afar,
15 alone and unknown, sang his heart’s music in the night, between waves and wild beasts. The campesinos, the men of
the land, the creators, rose up in blind indignation against the disdainful city, their own creation. We wore epaulets
and judge’s robes, in countries that came into the world wearing rope sandals and Indian headbands. The wise thing
would have been to pair, with charitable hearts and the audacity of our founders, the Indian headband and the judicial
robe, to undam the Indian, make a place for the able black, and tailor liberty to the bodies of those who rose up and
20 triumphed in its name. … No Yankee or European book could furnish the key to the Hispanoamerican enigma. So the
people tried hatred instead, and our countries amounted to less and less each year. Weary of useless hatred … we are
beginning, almost unknowingly, to try love. The nations arise and salute one another. “What are we like?” they ask, and

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begin telling each other what they are like. … The young men of America are rolling up their sleeves and plunging their
hands into the dough, and making it rise with the leavening of their sweat. They understand that there is too much
25 imitation, and that salvation lies in creating. Create is this generation’s password. Make wine from plantains; it may be
sour, but it is our wine! …
Anyone who promotes and disseminates opposition or hatred among races is committing a sin against humanity. …
To think is to serve. We must not, out of a villager’s antipathy, impute some lethal congenital wickedness to the continent’s
light-skinned nation simply because it does not speak our language or share our view of what home life should be or
30 resemble us in its political failings, which are different from ours, or because it does not think highly of quick-tempered,
swarthy men or look with charity, from its still uncertain eminence, upon those less favored by history who, in heroic
stages, are climbing the road that republics travel. But neither should we seek to conceal the obvious facts of the problem,
which can, for the peace of the centuries, be resolved by timely study and the urgent, wordless union of the continental
soul. For the unanimous hymn is already ringing forth, and the present generation is bearing industrious America along
35 the road sanctioned by our sublime forefathers. From the Rio Bravo to the Straits of Magellan, the Great Cemi,* seated
on a condor’s back, has scattered the seeds of the new America across the romantic nations of the continent and the
suffering islands of the sea!
*Cemi is a deity or ancestral spirit of the Taíno people—one of the indigenous groups of the Caribbean.

1.

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What is the most likely reason Martí wrote this article?
A.

To appeal to fellow Latin Americans to be more like the Europeans

B.

To gain support from fellow Latin Americans to join in a fight against European invaders

C.

To rally support for himself as a leader of a revolution to free his country from tyranny

D.

To encourage fellow Latin Americans to educate themselves about their own mixed heritage

Review the introduction and note that Martí was a teacher, writer, and organizer and that he spent a good part of his life fighting
for Cuban independence. You can infer from that information that he would try to persuade people to educate themselves. Martí
talks about how little his fellow countrymen know of their own heritage and says that they cannot expect to govern themselves
unless they understand their own heritage (lines 6–8). Choice D pinpoints one rationale Martí gives for education. Overall, the
excerpt does not address revolution, nor does Martí present himself as revolutionary. He appeals to pride in one’s heritage. These
ideas are connected, because Martí believes that his fellow Latin Americans can free themselves through education (lines 7–8:
“To know the country and govern it in accordance with that knowledge is the only way of freeing it from tyranny.”). The correct
answer is choice D.
2.

As used in line 12, “vision” refers to
A.

how others perceive the peoples of Latin America.

B.

a picture of a unified culture.

C.

Martí’s ideals about freedom.

D.

the opportunity to create a new beginning.

When a question refers to a specific part of the text, quickly reread the line(s) and the surrounding text. In paragraph 3, Martí
offers a detailed, mocking description of the disparate parts blended to compose the peoples of Latin America. The picture he
paints is of a person comprising various elements of other cultures—none his or her own. This, he says, is how Europeans saw
the people of Latin America. The vision is the image others have of them and how it is misunderstood and even hated by others.
So, the correct answer is choice A.

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3.

Which statement represents Martí’s attitude toward education?
A.

Universal education is of the utmost importance.

B.

Everyone should learn about Latin American history.

C.

Education is necessary for new leadership.

D.

Education should include the study of Greek democracy as a model for freedom.

This question is asking for an overview, so you need to think about the points Martí makes and his overall message. You can
eliminate choices A and B because they are general statements that anyone could make—they are not ideas that are represented
in the passage (though they are related). Choice D is an incorrect interpretation of the text. Choice C is the best answer because
Martí says that education is important for new leaders, and these leaders must be well-versed in the history of Latin America.
People who are educated about their own country and heritage will rise as leaders and take over for “statesmen who are alien to
it” (line 11). The correct answer is choice C.
4.

Which of the following best describes of the overall tone of the article?
A.

Passionate and resolute

B.

Angry and bitter

C.

Scolding and arrogant

D.

Inflammatory and rebellious

This type of question also requires you to think about the point of view and presentation, which determine the tone. Martí tries
to persuade his readers, advising them to wake up to threats from those who don’t understand them or hate them (lines 20–21:
“No Yankee or European book could furnish the key to the Hispanoamerican enigma. So the people tried hatred instead, and
our countries amounted to less and less each year.”). His passion comes through in the use of flowery and emotional language:
“the hour of reckoning and of marching in unison” (lines 4–5); similes: “move in lines as compact as the veins of silver” (line 5);
and metaphors: “sang his heart’s music in the night, between waves and wild beasts” (line 15). He expresses a resolve, not anger
or bitterness: “Make wine from plantains; it may be sour, but it is our wine!” (lines 25–26). Although Martí admonishes his fellow
countrymen for being naïve and for ignoring dangers (line 3): they are “unaware of the giants in seven-league boots who can
crush him underfoot”), he does not take the position of preacher. Rather, he speaks as one of the people (lines 4–5: “It is the
hour of reckoning and of marching in unison, and we must move in lines as compact as the veins of silver that lie at the roots of
the Andes.”). Martí does not use inflammatory language; nor does he call for rebellion, choice D. Rather, he tries to persuade his
fellow Latin Americans to unite in spite of their differences and to defend their lands from foreigners who do not understand
them. The correct answer is choice A.

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Sample Reading Passage 2
Questions 1–4 are based on the following two passages.
The following passages discuss theories of how culture and language spread across Europe and Central Asia to form modern European
and Asian peoples. Two teams of scientists—one based at the University of Copenhagen and one at the University of Adelaide—presented studies about the DNA of ancient Europeans, based on 170 skeletons found in countries from Spain to Russia.
Passage 1 is excerpted from “When modern Eurasia was born,” originally published by the University of Copenhagen on June 10, 2015,
by the Center for GeoGenetics and the Natural History Museum of Denmark.

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PASSAGE 1
When Modern Eurasia Was Born
With this new investigation, the researchers confirm that the changes came about as a result of migrations. The
researchers think that this is interesting also because later developments in the Bronze Age are a continuation of this new
social perception. Things add up because the migrations can also explain the origin of the northern European language
Line families. Both language and genetics have been with us all the way up to the present. Kristian Kristiansen [professor of
5 archaeology at the University of Gothenburg, Sweden] even thinks that it was crucial that events happened during these
few centuries, as crucial as the colonization of the Americas.
One of the main findings from the study is how these migrations resulted in huge changes to the European gene-pool,
in particular conferring a large degree of admixture on the present populations. Genetically speaking, ancient Europeans
from the time post these migrations are much more similar to modern Europeans than those prior to the Bronze Age.
Mobile warrior people

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The re-writing of the genetic map began in the early Bronze Age, about 5,000 years ago. From the steppes in the
Caucasus, the Yamnaya Culture migrated principally westward into North and Central Europe, and to a lesser degree, into
western Siberia. Yamnaya was characterized by a new system of family and property. In northern Europe the Yamnaya
mixed with the Stone Age people who inhabited this region and along the way established the Corded Ware Culture,
which genetically speaking resembles present-day Europeans living north of the Alps today.

15

Later, about 4,000 years ago, the Sintashta Culture evolved in the Caucasus. This culture’s sophisticated new weapons
and chariots were rapidly expanding across Europe. The area east of the Urals and far into Central Asia was colonized
around 3,800 years ago by the Andronovo Culture. The researchers’ investigation shows that this culture had a European
DNA background.
During the last part of the Bronze Age, and at the beginning of the Iron Age, East Asian peoples arrived in Central Asia.

20 Here it is not genetic admixture we see, but rather a replacement of genes. The European genes in the area disappear.

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These new results derive from DNA analyses of skeletons excavated across large areas of Europe and Central Asia, thus
enabling these crucial glimpses into the dynamics of the Bronze Age. In addition to the population movement insights, the
data also held other surprises. For example, contrary to the research team’s expectations, the data revealed that lactose tolerance rose to high frequency in Europeans, in comparison to prior belief that it evolved earlier in time (5,000–7,000 years ago).

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Passage 2 is excerpted from “European invasion: DNA reveals the origins of modern Europeans,” published in March 2015, by Alan
Cooper, a director at the Australian Centre for Ancient DNA at the University of Adelaide, and Wolfgang Haak, a senior research fellow
at the University of Adelaide.
PASSAGE 2
European Invasion: DNA Reveals the Origins of Modern Europeans
25

What we have found is that, in addition to the original European hunter-gatherers and a heavy dose of Near Eastern
farmers, we can now add a third major population: steppe pastoralists. These nomads appear to have “invaded” central
Europe in a previously unknown wave during the early Bronze Age (about 4,500 years ago).
This event saw the introduction of two very significant new technologies to western Europe: domestic horses and
the wheel. It also reveals the mysterious source for the Indo-European languages.

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30

The genetic results have answered a number of contentious and long-standing questions in European history. The
first big issue was whether the first farmers in Europe were hunter-gatherers who had learnt farming techniques from
neighbours in southeast Europe, or did they instead come from the Near East, where farming was invented.
The genetic results are clear: farming was introduced widely across Europe in one or two rapid waves around 8,000
years ago by populations from the Near East—effectively the very first skilled migrants.

35

At first the original hunter-gatherer populations appear to have retreated to the fringes of Europe: to Britain, Scandinavia and Finland. But the genetics show that within a few thousand years they had returned, and significant amounts
of hunter-gatherer genomic DNA was mixed in with the farmers 7,000 to 5,000 years ago across many parts of Europe.
Wheeling across Europe

But there was still a major outstanding mystery. Apart from these two groups, the genomic signals clearly showed
that a third—previously unsuspected—large contribution had been made sometime before the Iron Age, around 2,000
40 years ago. But by whom?
We have finally been able to identify the mystery culprit, using a clever new system invented by our colleagues at
Harvard University.
Instead of sequencing the entire genome from a very small number of well-preserved skeletons, we analysed 400,000
small genetic markers right across the genome. This made it possible to rapidly survey large numbers of skeletons from
45 all across Europe and Eurasia.
This process revealed the solution to the mystery. Our survey showed that skeletons of the Yamnaya culture from
the Russian/Ukrainian grasslands north of the Black Sea, buried in large mounds known as kurgans, turned out to be the
genetic source we were missing.
1.

How do the passages illustrate the contributions of DNA evidence to scientific inquiry?
A.

Both provide examples of how DNA evidence enabled scientists to fill in gaps in their knowledge about human
migrations.

B.

Both describe how DNA analysis is used in scientific investigations.

C.

The passages imply that DNA evidence can solve evolutionary questions.

D.

The passages show how scientists solved the mysteries of DNA evidence.

Chapter 3

Both passages illustrate how DNA has been used to answer questions about human migration patterns—questions that had
been unresolved before the ability to use DNA as evidence for such studies, choice A. Neither passage gives details about the
actual scientific methodology as both are focused on the results. Choices C and D are not correct interpretations of the passages.
The correct answer is choice A.
2.

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Which lines from the text support the idea that migration of human populations can be tracked through DNA testing?
A.

Line 1: (“With this … migrations.”)

B.

Lines 8–9: (“Genetically … the Bronze Age.”)

C.

Lines 26–27: (“These nomads … 4,500 years ago).”)

D.

Lines 28–29: (“This event … Indo-European languages.”)

This type of question requires that you find specific text to support an answer to a question. Although the concept given—that
DNA testing was used to track population migrations—can be found in both passages, you only need to review the specific lines
given in the answer choices to find the correct answer. Review only the options to find the one that that best supports the concept.

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Choices C and D are not directly related to DNA evidence. Choice A confirms the idea of migration, but the text does not refer
to DNA as the process that tracked the migration. Choice B refers to the genetic evidence, another term for DNA, which shows
a similarity between ancient and modern Europeans. This evidence illustrates that scientists have been tracking the migration
patterns. The correct answer is choice B.
3.

What is the best description of the two passages?
A.

They show conflicting claims about the migrations.

B.

They describe different scientific methodologies.

C.

They provide supplementary information.

D.

They are written from a different perspective.

When reading paired passages, compare the passages as you read. This question asks you to compare the information. On your
first reading, you probably noticed that they do not contradict one another, choice A; nor do they show different points of view,
choice D. Both passages describe scientific studies and what scientists were able to learn from them, and both describe using
DNA as the methodology, so you can eliminate choice B. But the second passage adds to the information in the first, making
them supplements, choice C, to one another. The correct answer is choice C.
4.

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Based on information in the two passages, which of the following statements could be made about scientific inquiry?
A.

DNA evidence showed why many Europeans are lactose intolerant.

B.

Research can provide historical information.

C.

Evidence showed that the steppe pastoralists introduced horses and the wheel to Western Europe.

D.

Scientific investigation can provide evidence about human history not obtainable through other means.

Like the preceding question, this one asks you to compare the two passages, except this question looks at a topic not directly
discussed in the passages but one that is implicit within it—the nature of scientific inquiry. So while choices A and C are true,
neither one answers the question. Choice B is also true, but it doesn’t address the nature of scientific investigations; it is simply
a general statement that could apply to many texts. Choice D, however, states a fact about scientific inquiry that can be gleaned
from the text: Both passages describe how scientists were able to use DNA data to answer questions they were unable to address
before the use of DNA testing was available. The correct answer is choice D.

NOTE: The paired passages have the same types of questions as the single passages. Some
of the questions, however, may ask you to synthesize the information presented in the two
passages by noting commonalities or comparing them in some way.

TIPS FOR TAKING THE READING TEST
You will be allotted 65 minutes to answer the 52 questions in the Reading section. That’s a lot of questions in a short period of
time. However, you can use some specific strategies and techniques to move through this portion of the SAT® efficiently. Check
out these strategies for answering the evidence-based reading questions quickly and accurately.

Answer All of the Questions Before You Start the Next Passage
There won’t be time to go back to reread the passages and recheck your answers, so answer every question that you can about
the passage. If you don’t know an answer, skip the question and return to it when you have answered the other questions in

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the passage. Check your time, and if you think you can answer one of the skipped questions with a quick reread of part of the
passage, go ahead. If not, or if you find it is taking too long, just give it your best guess and then move on. Remember, wrong
answers are not held against you, so don’t leave anything blank. Make sure you have answered every question for each passage
before you move on to the next one.

Remember That the Questions Get More Specific
The question order often holds a key to understanding a passage. The SAT® Reading Test organizes the questions from broader
questions about themes, purpose, point of view, and main ideas to more specific questions about explicit and implicit meaning,
specific language, and structure of the text. Review the questions and take note of the information they ask for before reading
the passage. As you read, underline or make notes to highlight text that may answer a question. Remember, answers will be in
the text—either stated or implied.

Paired Passages
For the paired passages, look for the characteristics in each passage that tie them together. Skim the questions so you know
what to look for and underline parts of the text that you may want to refer to. Try to form an overview of the two passages. Ask
yourself why they are paired: what do they have in common; how are they different. In answering the questions for this type of
passage, follow the same strategy: first answer all the questions you are fairly sure about. Then fill in the others based on best
guesses, and, if time allows, review the evidence in the text to support your guess and answer the question accordingly. Make
sure you have answered all the questions, and then go to the next passage.

Don’t Panic When You Read an Unfamiliar Passage
The passages can be unfamiliar. In their attempt to be fair, the test-makers purposely choose a variety of passages. This helps
make sure that each test-taker can demonstrate his or her reading and analysis skills. Remember, you’re not being tested on your
knowledge of the topic but on how well you do the following:

•
•
•
•
•

Understand the author’s assumptions, point of view, and theme

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Determine how the author supports the main ideas in the text

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Determine how the author uses specific language to create mood or tone
Analyze the logical structure of the text
Analyze overall meaning as well as specific words and phrases in context of the passage

Remember That Everything You Need to Know Is Right There in Front of You
The introductory paragraph and the passage have all the information you’ll need to answer the questions. Even if the passage is
about the price of beans in Bulgaria or the genetic makeup of a wombat, don’t worry. It’s all right there on the page.

Start with the Passages That Interest You
A point is a point. It doesn’t matter if the point comes from answering correctly a question about a piece of fiction or a scientific
experiment. If the style and subject matter appeal to you, you will probably go through a passage more quickly and answer the
questions more easily. So before you start, quickly check the topics by skimming the titles and introductions. Start with the topics
that are most familiar or most interesting. Then work your way down to the ones that you think will be hardest. Make a notation
so you know which passages you have completed, and double check that your answers on the answer sheet correspond to the
correct question numbers.

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Highlight Important Information as You Read the Passages
It pays to be an active reader, and making quick notes is a part of this process. Let the questions guide your notations. Based on
the questions, actively use your pencil to look for and bracket the text evidence that addresses questions about the big ideas,
themes, and purpose as you read. Use other markings to indicate places in the text that may provide evidence for other questions,
for example, a specific word or phrase referred to in a question. The questions will be related to the most important information in
the passage. If you’ve highlighted those pieces of information, you’ll be able to find them more easily to help answer the questions.

Don’t Get Bogged Down in the Details
Remember, you don’t have to understand every bit of information. You just have to find the information you need to answer the
questions. Don’t waste your time trying to analyze technical details or information not related to a question.

Don’t Confuse a “True” Answer with a “Correct” Answer
The fact that an answer choice is true doesn’t mean it’s right. What does that mean? It means that a certain answer choice may be
perfectly true—in fact, all of the answer choices may be true. But the right answer must be the correct answer to the question that’s
being asked. Only one of the answer choices will be correct and, therefore, the right choice. Read carefully—and don’t be fooled!

STRATEGIES FOR ANSWERING SPECIFIC QUESTION TYPES
As you learned earlier, each reading question asks you to do one of the following:

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•
•
•
•
•
•

Determine central themes and ideas as presented in the passage.
Determine the author’s purpose or point of view of the text.
Cite textual evidence to support inferences, conclusions, or arguments.
Cite evidence to illustrate or support interpretation of meaning, mood, or tone of the passage.
Analyze words and phrases in the context of the passage.
Analyze quantitative information in an accompanying graphic, such as a table, graph, or chart.

The following tips present strategies for dealing with specific types of SAT® reading questions. You should use these strategies
in combination with the basic steps for approaching the reading test. These strategies don’t take the place of the basic steps but
are extra tools to help you with certain types of questions. These tools work with both single and paired passages on any topic.
1. A broad question about the passage requires you to think about the passage as a whole. Keep this in mind as you read
the passage, noting any references to an overview in the introduction and/or conclusion of the passage.
2. Before you begin, note the subject of the passage and the voice/perspective. These items can often be found in the
introduction. Ask yourself if the author is providing information about a specific topic, making an argument for or
against something, or telling a story. Whether fiction or nonfiction, ask yourself who is telling the story and why.
3. Look for evidence of inferences in the text and evaluate how they support the author’s ideas.
4. As you read, notice the overall tone and mood of the passage and find textual evidence—specific words or phrases—
that contribute to these elements.
5. If a question asks about a specific word, read the surrounding text to verify the context in which the word is used.
6. Examine the graphic illustration specifically in response to the question associated with it. If it asks to apply the illustration to the text, read that portion of the text in conjunction with the graphic illustration.
To help you see how these tips work, read the passage in the exercise on the next page. Then read each tip and try to use it to help
you answer each question before you read the answer explanation. Note, again, that on the real exam and in the practice tests
in this book, reading passages will appear in two columns. For instructional purposes, the following passages appear full page.

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EXERCISE: EVIDENCE-BASED READING TEST
30 Minutes—23 Questions
DIRECTIONS: Each passage or pair of passages below is followed by a number of questions. After reading each passage
or pair, choose the best answer to each question based on what is stated or implied in the passage or passages and in any
accompanying graphics (such as a table or graph).

Questions 1–6 are based on the following passage.
The passage below discusses how Alaska Native cultural practices and heritage are being preserved in the twenty-first century.
(For the full article, please visit http://nps.gov.)
Alaska Native cultural practices continue to be a central force in virtually all villages throughout Alaska. In order to
maintain cultural knowledge and ensure its survival, Alaska Native people need to learn the best methods of recording
and archiving music, dance, and oral history. Along with the expansion of Europeans and Americans into Alaska were
Line accompanying hardships for the indigenous people: epidemic diseases, strong Christian missionary activities, and western
5 educational policies such as English language-only rules. These resulted in decimated populations throughout the entire
territory of Alaska, a decline in indigenous languages, and, in many cases, the abolishment of traditional religion and
associated music and dance repertoires.
Native people are deeply spiritual people; historically, they had a rich ceremonial life that was profoundly expressed
through music and dance—core means by which people communicate their identities and beliefs. With the introduction
10 of Christianity, traditional cultures, including aspects such as music and dance, were not viewed favorably by the missionaries. Sadly, most of the missionaries did not tolerate masked dancing and other forms of religious expressions. Dance,
language, and ceremonial practices either had to be practiced in secret, or were lost.
In the 1960s, during the Native Solidarity Movement, as Alaska Native people became more politically active, their
re-identification with their cultures, languages, music, and dance became a banner of their newfound political and social
15 strength. One of the major outcomes of that movement has been a renaissance in traditional music and dance practices,
resulting in multiple dance festivals and younger people becoming actively involved in their village dance groups. …
The Fifth Annual Kingikmiut Dance Festival featured a large Russian dance group, as well as the Tikigaq Traditional
Dancers of Point Hope and dance groups from Brevig Mission and other villages on the Seward Peninsula. Kingikmiut,
or Wales, was once known as the dance capital of the Seward Peninsula. Captain Henry Trollope visited Wales in 1853–54
20 and wrote “… the place is sort of a capital in these parts and has four dancing houses, which is a very expressive manner
of estimating the extent and population for a place.” (Ray 1975) Because of its strategic location, Kingikmiut flourished.
Before the 1900 and 1917 epidemics, it consisted of two related villages and consolidated into one village once the populations had been decimated by disease. After these terrible epidemics, western educators’ English-only policies forced
music, dance, and other expressions of traditional Native culture to go underground.

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Repression of Native culture by western educators and missionaries was common all over Alaska and is a major
reason why many Alaska Native languages are threatened today. In the first part of the twentieth century, traditional
dance and music became associated with the old ways and were looked down upon. After the 1960s, a strong revitalization movement arose. Today there is a renaissance in traditional music and dance practices. In Wales and other Seward
Peninsula communities, the younger people, who make up a large percentage of the population, have a great thirst for
30 learning to sing and dance their traditional songs.
25

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1.

2.

3.

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4.

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5.

6.

Which of the following best reflects the main idea of the passage?
A.

There has been a recent surge in interest in Native cultures everywhere.

B.

Native Alaskans have always tried to preserve their history and culture.

C.

Western expansion into Alaska resulted in loss of native cultures.

D.

Native Alaskan traditions were revived in the 1960s.

What can you infer about how the U.S. civil rights movement of the 1960s might have influenced the Native Solidarity
Movement?
A.

It was a catalyst for the Native Solidarity Movement, which provided an avenue for political activity and renewed
cultural identity.

B.

It led to new laws that give the Native Alaskan people the right to practice their religion and express their native
culture.

C.

It allowed the Native Alaskan people to rebel against the forced repression of their culture.

D.

It revived Native Alaskan cultural practices that had been lost.

What was the relationship between the missionaries in Alaska and the Native Alaskans?
A.

The Native Alaskans and missionaries lived in harmony because they had the same religious beliefs.

B.

The missionaries embraced the Native Alaskans and rescued them from epidemics of disease.

C.

The Native Alaskans resented the missionaries and tried to make them leave.

D.

The missionaries repressed native culture and the Native Alaskans rebelled by holding on to their culture.

What evidence does the passage provide to suggest that Alaskan culture was influenced by Russia?
A.

Lines 3–4: (“Along with … indigenous people”)

B.

Line 17: (“The Fifth Annual … dance group”)

C.

Lines 18–19: (“Kingikmiut, or Wales, … Seward Peninsula.”)

D.

Line 21: (“Because of … Kingikmiut flourished.”)

What conclusion could you infer from the passage?
A.

Native Alaskan cultures are still thriving.

B.

Cultural ties are very strong and can’t be easily extinguished.

C.

Many minor native languages are being lost.

D.

Music and dance is a common way to express one’s culture.

As used in line 24, “go underground” most nearly means
A.

hide in a hut.

B.

be practiced in an ice hut.

C.

practice in secret.

D.

be wiped out.

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Questions 7–11 are based on the following passage.
The following is an excerpt from “The Purloined Letter,” a short story by Edgar Allan Poe. Poe is best known for writing poems and stories
in the horror and mystery genre. However, he is also considered the inventor of detective fiction. The Mystery Writers of America call
their awards for excellence in the genre “Edgars,” in honor of Poe.
The Purloined Letter
… “Well, then; I have received personal information, from a very high quarter, that a certain document of the last
importance, has been purloined from the royal apartments. The individual who purloined it is known; this beyond a
doubt; he was seen to take it. It is known, also, that it still remains in his possession.”
Line
5

“How is this known?” asked Dupin.
“It is clearly inferred,” replied the Prefect, “from the nature of the document, and from the non-appearance of certain
results which would at once arise from its passing out of the robber’s possession; that is to say, from his employing it as
he must design in the end to employ it.”
“Be a little more explicit,” I said.

“Well, I may venture so far as to say that the paper gives its holder a certain power in a certain quarter where such
10 power is immensely valuable.” The Prefect was fond of the cant of diplomacy.
“Still I do not quite understand,” said Dupin.
“No? Well; the disclosure of the document to a third person, who shall be nameless, would bring in question the
honor of a personage of most exalted station; and this fact gives the holder of the document an ascendancy over the
illustrious personage whose honor and peace are so jeopardized.”
15

“But this ascendancy,” I interposed, “would depend upon the robber’s knowledge of the loser’s knowledge of the
robber. Who would dare—”

“The thief,” said G., “is the Minister D—, who dares all things, those unbecoming as well as those becoming a man.
The method of the theft was not less ingenious than bold. The document in question—a letter, to be frank—had been
received by the personage robbed while alone in the royal boudoir. During its perusal she was suddenly interrupted
20 by the entrance of the other exalted personage from whom especially it was her wish to conceal it. After a hurried and
vain endeavor to thrust it in a drawer, she was forced to place it, open as it was, upon a table. The address, however, was
uppermost, and, the contents thus unexposed, the letter escaped notice. At this juncture enters the Minister D—. His lynx
eye immediately perceives the paper, recognises the handwriting of the address, observes the confusion of the personage
addressed, and fathoms her secret. After some business transactions, hurried through in his ordinary manner, he produces
25 a letter somewhat similar to the one in question, opens it, pretends to read it, and then places it in close juxtaposition to
the other. Again he converses, for some fifteen minutes, upon the public affairs. At length, in taking leave, he takes also
from the table the letter to which he had no claim. Its rightful owner saw, but, of course, dared not call attention to the
act, in the presence of the third personage who stood at her elbow. The minister decamped; leaving his own letter—one
of no importance—upon the table.” …
30

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“You looked among D—’s papers, of course, and into the books of the library?”

“Certainly; we opened every package and parcel; we not only opened every book, but we turned over every leaf in
each volume, not contenting ourselves with a mere shake, according to the fashion of some of our police officers. We
also measured the thickness of every book-cover, with the most accurate ad measurement, and applied to each the most
jealous scrutiny of the microscope. Had any of the bindings been recently meddled with, it would have been utterly
35 impossible that the fact should have escaped observation. Some five or six volumes, just from the hands of the binder,
we carefully probed, longitudinally, with the needles.”
“You explored the floors beneath the carpets?”

Peterson’s SAT® Prep Guide 2017

“Beyond doubt. We removed every carpet, and examined the boards with the microscope.”
“And the paper on the walls?”
“Yes.”

40

“You looked into the cellars?”
“We did.”
“Then,” I said, “you have been making a miscalculation, and the letter is not upon the premises, as you suppose.”
“I fear you are right there,” said the Prefect. “And now, Dupin, what would you advise me to do?”
“To make a thorough re-search of the premises.”

45

“That is absolutely needless,” replied G—. “I am not more sure that I breathe than I am that the letter is not at the Hotel.”

7.

8.

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9.

Which of the following best describes the mystery to be solved in “The Purloined Letter”?
A.

What information is in the letter?

B.

What will happen if the letter is exposed?

C.

Where is the letter?

D.

Who has the letter?

Who is being blackmailed, and by whom?
A.

The royal lady is being blackmailed by the Minister D.

B.

The Minister D is being blackmailed by the Prefect G.

C.

The Prefect G is being blackmailed by Dupin.

D.

The royal lady is being blackmailed by the Prefect G.

What is the most likely reason that Dupin asks the Prefect to describe the search in such detail?
A.

To make sure the police haven’t missed anything

B.

To look for other clues

C.

To hear a good story

D.

To verify his own ideas

10. As used in line 10, “cant” most nearly means
A.

inclination.

B.

jargon.

C.

music.

D.

inability.

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11. Which of the following is a line that could be in the letter?
A.

It would be such an honor to have you in attendance at this surprise gala.

B.

You know how much I would like to be in your employ again.

C.

I’m so sorry that this is late notice, but can I meet with you and the prince next week?

D.

I beg of you to meet me on Monday when the prince is in Monaco.

Questions 12–17 are based on the following passage and supplementary material.
This passage is the introduction to a report from the Office of the Chief Technologist at the U.S. space agency NASA, entitled “Emerging
Space: The Evolving Landscape of the 21st Century American Spaceflight”
(http://www.nasa.gov/sites/default/files/files/Emerging_Space_Report.pdf).
America stands today at the opening of a second Space Age. Innovative NASA programs and American entrepreneurs
together are transforming the space industry. These initiatives—both at NASA and in the private sector—are expanding
the nation’s opportunities for exploration and for the economic development of the solar system.
Line

Today’s space economy extends some 36,000 kilometers (22,369 miles) from the surface of the Earth and includes an
5 array of evidence-based technologies—satellite communications, global positioning satellites, and imaging satellites—on
which our economy depends. These technologies are now an integral part of our economy, and they would not exist
if not for the over 50 years of research, development, and investment in the enabling technologies by NASA and other
government agencies that seeded these efforts and allowed them to bloom. As we expand our activities in the solar
system over the next decades, NASA programs and investments will provide the seed and soil that encourage economic
10 development increasingly farther from Earth. The first signs of this are already visible.
The next era of space exploration will see governments pushing technological development and the American
private sector using these technologies as they expand their economic activities to new worlds. NASA’s next objectives
for exploration—visits to asteroids and Mars— are more complex than any previous space mission attempted. They will
happen in the context of relatively smaller NASA budgets and an expanding commercial space economy. Teaming with
15 private-sector partners to develop keystone markets like low Earth orbit (LEO) transportation and technological capabilities like asteroid mining will help NASA achieve its mission goals, help the space economy evolve to embrace new
ambitions, and provide large economic returns to the taxpayer through the stimulation and growth of new businesses
and 21st-century American jobs.

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Motivated by an intrinsic desire to explore space, successful American entrepreneurs have pledged and spent
20 hundreds of millions of dollars to develop technologies aimed at fundamentally improving space access. Since 2003,

commercial human spaceflight has received $2.5 billion in private investment.1 At the same time, a new generation of
space enthusiasts are engaging directly though small-scale projects. Through cubesats, suborbital and orbital adventures,
and citizen science opportunities, the United States is transitioning from a spacefaring nation to a nation of spacefarers.
In addition to executing its scientific and human spaceflight programs, NASA also has a legislated responsibility to
25 “encourage, to the maximum extent possible, the fullest commercial use of space.” As part of fulfilling this responsibility,

this report examines how NASA has collaborated with American private-sector individuals and companies investing in
space exploration, collectively known as “emerging space.” Today, more than fifty years after the creation of NASA, our
goal is no longer just to reach a destination. Our goal is to develop the capabilities that will allow the American people to
explore and expand our economic sphere into the solar system. Although when NASA was founded only a government
30 program could undertake a voyage from the Earth to the Moon, this may not be true in the future. By taking full advantage
of the combined talents of government and the American private sector, our next journeys beyond Earth will come sooner
and we will catalyze new industries and economic growth in the process.

1. 2013 Commercial Spaceflight Industry Indicators, Commercial Spaceflight Federation

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NASA provides a number of resources for people willing to contribute as citizen scientists. All are available online, meaning all you need
is access to the Internet. Software tools are also provided. More than 1.2 million people from 80 countries have participated in NASA’s
citizen science projects. This table captures just a few of the projects.

Project

Citizen Scientist Role

Number of Participants

Be a Martian

Tag rover images and map craters
from satellite pictures

1,230,000

HiTranslate

Help translate NASA’s HiRISE project
captions into different languages

1,021 new in 2012

International Space
Apps Challenge

Develop mobile applications,
software, hardware, data
visualization, and platforms to
address current challenges relevant
to space exploration and social
need

2,083 from 17 countries in
2012

Lunar Impacts

Independent observers can
monitor the rates and sizes of large
meteoroids striking the far side of
the Moon

26 impact candidates

Rock Around the World

Help Mars scientists better
understand the red planet by
sending rocks to NASA for analysis

12,461 rocks received

Stardust at Home

Search for the first samples of
solid matter from outside the solar
system

30,649 from 2006 to 2012

Target Asteroids!

Observe asteroids, to help scientists
refine orbits and determine the
composition of near-Earth objects
(NEOs) in support of the OSIRIS-Rex
mission

104 registered users from 23
countries

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12. How did the government investment in space boost the economy?
A.

It expanded the knowledge about space beyond our solar system.

B.

It led to the development of popular commercial products.

C.

It led to human spaceflight programs, which required specialized products.

D.

It expanded space exploration farther from the Earth.

13. How will the next era of space exploration be different from the past?
A.

It will include private and public investment.

B.

It will require citizen participation.

C.

It will send people to explore and perhaps live on other planets.

D.

It will be much more expensive.

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14. What is meant by: “the United States is transitioning from a spacefaring nation to a nation of spacefarers.” (line 23)?
A.

The United States will no longer be able to use space for warfare.

B.

People will be more interested in space exploration.

C.

The United States will be able to dominate space exploration.

D.

People will be able to travel in space.

15. Which of the following is the best summary of the passage?
A.

NASA is ushering in a new chapter in the space age that will allow the commercialization of space.

B.

In the next decades, ordinary people will be able to travel in space.

C.

NASA is the U.S. agency that is charged with developing space programs.

D.

The Second Space Age will expand the economy and increase complex technologies in space exploration.

Questions 16 and 17 refer to the table.

16. What is the most likely reason that the “Be a Martian” project has so many more participants than the other projects?
A.

More people are interested in exploring Mars than in other aspects of the program.

B.

Other projects require more sophisticated/complex technology skills.

C.

It is the only project that is designed for young people.

D.

The other projects all require more time as a volunteer.

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17. What skills are needed to participate in the NASA projects as a citizen-scientist?
A.

The ability to identify different kinds of rocks

B.

The ability to use a telescope

C.

The ability to use software technology and the Internet

D.

The ability to locate and recognize the planets and other celestial bodies

Chapter 3
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Questions 18–23 are based on the following two passages.

The following passages are excerpted from narratives written by two explorers. Passage 1 is by Sir Earnest Shackleton from an account
he wrote entitled: South! The Story of Shackleton’s Last Expedition (1914–1917). Passage 2 is part of an account by Hiram Bingham
III, from “The Discovery of Machu Picchu,” first published in Harper’s Monthly magazine in 1913.
PASSAGE 1
Some intangible feeling of uneasiness made me leave my tent about 11 p.m. that night and glance around the
quiet camp. The stars between the snow-flurries showed that the floe had swung round and was end on to the swell, a
position exposing it to sudden strains. I started to walk across the floe in order to warn the watchman to look carefully
Line for cracks, and as I was passing the men’s tent the floe lifted on the crest of a swell and cracked right under my feet. The
5 men were in one of the dome-shaped tents, and it began to stretch apart as the ice opened. A muffled sound, suggestive
of suffocation, came from beneath the stretching tent. I rushed forward, helped some emerging men from under the
canvas, and called out, “Are you all right?”

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“There are two in the water,” somebody answered. The crack had widened to about four feet, and as I threw myself
down at the edge, I saw a whitish object floating in the water. It was a sleeping-bag with a man inside. I was able to
10 grasp it, and with a heave lifted man and bag on to the floe. A few seconds later the ice-edges came together again with
tremendous force. Fortunately, there had been but one man in the water, or the incident might have been a tragedy. The
rescued bag contained Holness, who was wet down to the waist but otherwise unscathed. The crack was now opening
again. The James Caird and my tent were on one side of the opening and the remaining two boats and the rest of the
camp on the other side. With two or three men to help me I struck my tent; then all hands manned the painter and rushed
15 the James Caird across the opening crack. We held to the rope while, one by one, the men left on our side of the floe
jumped the channel or scrambled over by means of the boat. Finally I was left alone. The night had swallowed all the
others and the rapid movement of the ice forced me to let go the painter. For a moment I felt that my piece of rocking
floe was the loneliest place in the world. Peering into the darkness; I could just see the dark figures on the other floe.
PASSAGE 2
Nor was I in a great hurry to move. The water was cool, the wooden bench, covered with a woolen poncho, seemed
20 most comfortable, and the view was marvelous. On both sides tremendous precipices fell away to the white rapids of

the Urubamba River below. In front was the solitary peak of Huay-na Picchu, seemingly inaccessible on all sides. Behind
us were rocky heights and impassable cliffs. Down the face of one precipice the Indians had made a perilous path, which
was their only means of egress in the wet season, when the bridge over which we had come would be washed away. Of
the other precipice we had already had a taste. We were not surprised to hear the Indians say they only went away from
25 home about once a month.

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Leaving the huts, we climbed still farther up the ridge. Around a slight promontory the character of the stone-faced
andenes began to improve, and suddenly we found ourselves in the midst of a jungle-covered maze of small and large
walls, the ruins of buildings made of blocks of white granite, most carefully cut and beautifully fitted together without
cement. Surprise followed surprise until there came the realization that we were in the midst of as wonderful ruins as any
30 ever found in Peru. It seemed almost incredible that this city, only five days’ journey from Cuzco, should have remained
so long undescribed and comparatively unknown. Yet so far as I have been able to discover, there is no reference in the
Spanish chronicles to Machu Picchu. It is possible that not even the conquistadors ever saw this wonderful place. From
some rude scrawls on the stones of a temple we learned that it was visited in 1902 by one Lizarraga, a local muleteer.
It must have been known long before that, because, as we said above, Wiener [an Austrian-French explorer], who was
35 in Ollantaytambo in the 70’s, speaks of having heard of ruins at a place named “Matcho Picchu,” which he did not find.
18. How do the two passages differ in their tone?
A.

Passage 1 has a tone of surprise, and Passage 2 has a tone of fear.

B.

Passage 1 has a threatening tone, and Passage 2 has an adventurous tone.

C.

Passage 1 exhibits a tone of danger, and Passage 2, a tone of awe.

D.

Passage 1 features a gloomy tone, and Passage 2, a festive tone.

19. What does the passage reveal about Shackleton’s character?
A.

He is fearful for himself and others.

B.

He is a risk-taker who likes adventure.

C.

He is a heroic man who likes attention.

D.

He is a leader who puts others first.

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20. Which of the following best describes a purpose common to both passages?
A.

They want to tell the world about the dangers of undeveloped places.

B.

They want to tell the world about new and undiscovered places.

C.

They want to persuade others to visit undeveloped places.

D.

They want to persuade people to help develop the locales described.

21. As used in line 12, “unscathed” most nearly means
A.

fearless.

B.

not whole.

C.

not harmed .

D.

harmless.

22. What idea in the text leads to the conclusion that Bingham thought he discovered Machu Pichu?
A.

It would take five days to get there from the closest city of Cuzco.

B.

The Native Indians didn’t seem to know about it.

C.

He dismisses the others who may have been there.

D.

It was hidden behind thick jungle growth.

23. Based on the two passages, what can be inferred about the nature of expeditions?
A.

They are often dangerous and can’t be undertaken alone.

B.

They usually add to the knowledge about a place.

C.

They are good travel destinations for people who enjoy going to little-known places.

D.

They represent undiscovered parts of the world.

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ANSWER KEY AND EXPLANATIONS
1. C

6. C

11. D

16. B

20. B

2. A

7. C

12. B

17. C

21. C

3. D

8. A

13. A

18. C

22. C

4. B

9. D

14. D

19. D

23. B

5. B

10. B

15. D

1. The correct answer is C. The first paragraph in the passage provides a summary. It explicitly states the reasons
that the Native Alaskan culture was almost wiped out and
what needs to be done to ensure that it is not lost forever.
The rest of the passage supports the concepts introduced
here.

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2. The correct answer is A. Lines 13–15 explain that the
Native Solidarity Movement led to increased political
activity. Although the passage doesn’t mention the civil
rights movement by name, the question identifies its era,
and the passage states that the Native Solidarity Movement
occurred during the same time period. A logical inference,
therefore, could be that the civil rights movement had some
impact on the Native American Solidarity Movement. There
is no information about laws that might have affected
Native Alaskans, choice B. The passage does not indicate
that the Native Alaskans rebelled, choice C. The passage
does indicate that the cultural practices have been revived,
but the text does not connect the revival, even indirectly,
to the civil rights movement.
3. The correct answer is D. The passage does not directly
state the relationship of the Native Alaskan people to the
missionaries, but it does describe how the missionaries
imposed Christianity on them and tried to force the Native
Alaskans to abandon their own belief systems. There is no
indication of living in harmony, choice A, nor of the missionaries rescuing them in the face of epidemic disease, choice
B. Although the passage suggests that Native Alaskans
may have had reason to resent the missionaries, there is
no indication that they tried to make them leave, choice C.
4. The correct answer is B. The presence of a Russian dance
group among other native groups indicates that the Russian
culture had been mixed with that of the Native Alaskan
groups. Choice A does not explain any influences on culture.
There is no information that explains the proximity of the
Seward Peninsula to Russia, choice C. Kingikmuit is located
on the Seward Peninsula, as described in the passage, but,

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as in choice C, the passage does not explain its geographic
relationship to Russia, choice D.
5. The correct answer is B. The main idea of the text shows
that although missionaries tried to impose their beliefs on
the Native Alaskans, they were not completely successful.
The Native Alaskans maintained their belief systems and
passed on their traditions in secret when it was not possible to be open about them. Today, these traditions are no
longer repressed and are thriving. Overall, this suggests
the conclusion in choice B. Although choice A is true, it is
neither a conclusion nor an inference; that idea is stated in
the text. Both answer choices C and D are general concepts
that could be applied to the Native Alaskan culture, but
nothing in the text suggests such a generality.
6. The correct answer is C. The idiom “go underground”
means doing something in secret. In this case, the western educators who had come to Alaska forced their own
culture onto the Native Alaskans, who then practiced their
traditions in secret rather than give them up.
7. The correct answer is C. The conversation in the excerpt
reveals, in general terms, the responses listed in the other
choices A, B, and D. The mystery to be solved by either the
Prefect or Dupin is in locating the letter, choice C.
8. The correct answer is A. It is the royal lady who has told
the Prefect the story, which he retells to Dupin and the
narrator (line 1: “I have received personal information,
from a very high quarter.”). His retelling also describes the
identity of the thief (minister D), and the importance of
the document (line 9–10: “that the paper gives its holder
a certain power in a certain quarter where such power is
immensely valuable.”).
9. The correct answer is D. We can infer from his advice (line
45: “To make a thorough re-search of the premises.”) that
Dupin has an idea about the whereabouts of the letter,
which he wants to confirm through the details of the search.
Dupin listens carefully, demonstrating that he is interested

in the specifics of the investigation. The details confirm his
own ideas.
10. The correct answer is B. The word “cant” is used in a statement made by the unnamed narrator. He is commenting
about the language of the Prefect’s statement.“Jargon”(the
language or idiom of a particular group) is the only choice
related to language.
11. The correct answer is D. We know that the royal lady is
being blackmailed. Therefore, the contents must reveal
something she is hiding from the man in the room with
her, most likely her husband. Choice D is the only one that
contains information that is to be kept from the prince.
12. The correct answer is B. The passage describes the space
economy and the many products that were developed
because of space exploration and then applied to commercial markets. Lines 6–8 explain that these products
are now part of our economy. The space program was
responsible for introducing new products to the market
and new products that people want and buy increase
economic activity.
13. The correct answer is A. The passage discusses the inclusion of private investment (lines 11–12). Commercial
companies are already gearing up to provide new space
services based on the ability to travel in space and explore
places beyond Earth. Formerly, space travel was only done
by NASA.
14. The correct answer is D. People have always been interested in space but the passage talks about how the next
phase of space exploration will include ordinary citizens
who will be able to take advantage of the commercialization
of space exploration and travel.
15. The correct answer is D. This statement represents the
best summary because it states the main idea by providing
the two most important aspects of the commercialization
of space exploration.
16. The correct answer is B. The table shows that the “Be a
Martian” project involves tagging on the Internet, and the
table caption explains that participants are provided with
any needed software. According to the descriptions of the
other projects, they all require some additional skill, for
example, translating text or doing more complex searches.

18. The correct answer is C. The first line of Passage 1 sets
the tone of danger (feeling of uneasiness) that continues
after the crack in the ice. Although the men aren’t killed,
the path to the boat was nevertheless full of danger. Passage 2 begins with Bingham’s observations that show his
appreciation of the beauty of the place. He marvels at the
Indians who make their way down the steep precipice on
a regular basis (lines 22–23). As Bingham makes his way
through the jungle and sees Machu Picchu for the first
time, detailed descriptions show awe and surprise at the
“wonderful ruins” (line 29).
19. The correct answer is D. Shackleton describes the scene
and how he warned to “look carefully for cracks” (lines 3–4),
which shows he was checking the ice to make sure he and
his men were safe. When he saw the ice cracking, his first
instinct was to throw himself down at the edge (lines 8–9)
and save one of the men. He made sure the others were
safe, leading them back to the boat; he was the last in line
to board.
20. The correct answer is B. Both passages record the experiences of men who are drawn to exploring places that most
people don’t ever see. Both use detailed descriptions of
the physical terrain of remote places that are void of other
people. There is no call inviting others to join them—just
descriptions that inform.
21. The correct answer is C. The surrounding text describes
the condition of the man (who was wet down to the waist),
and we know from the rest of the text that the water was
bitter cold. The word “otherwise” shows that what follows
is an exception, so he is—not harmed—except for being
wet (and presumably cold).
22. The correct answer is C. In lines 32–35, Bingham describes
the others who may have come before him. He remarks on
the beauty of the ancient city and how incredible it is that
others missed it. Surely the conquistadors would have told
others about it; Weiner never found it; and the muleteer
didn’t understand what he was looking at.

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23. The correct answer is B. Both passages describe places
about which little was known at the time. Both men undertook the trip and wrote detailed accounts of their experiences so that others could learn about them and perhaps
follow their footsteps to gain even more knowledge.

17. The correct answer is C. Reading the descriptions, the skill
required in all of the projects is how to use the Internet to
conduct searches. Even for projects that involve language
translation, a participant would have to access the Internet
to get the text that needs to be translated.

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SUMMING IT UP
• You do not need information beyond what is provided by the passage to answer any question.
• Complete familiar and interesting passages first.
• Read the introduction; it often provides background that will help form an overview of the passage.
• Read the questions and their answer choices.
• Read the passage as quickly as possible, marking the text to note information that may be relevant to the questions. Let the
questions drive your focus and the notations you make.

• Don’t get bogged down in details. Most questions will not be focused on details unless they are used to support a major idea
or theme.

• Go back into the passage to find answers as needed.
• Reading Test questions are ordered from those related to the central ideas and overall themes to those involving structural
and language-related concepts. Approach each passage by first looking for the big ideas and then the more structural
concepts.

• For any question you’re not sure of, eliminate obviously wrong answers and take your best guess. Wrong answers are not
counted against you, so answer every question.

• Answer every question for a passage before starting the next passage.

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• Advanced Question Types
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• Analyzing Structure
• Common Question Types
• Hard Prose Passages
• Hard Science Passages
• Other Reading Questions
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• Point of View
• Quantitative Information
• Reading Actively
• Understanding Difficult Text
• Wrong Answer Types
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part iv: writing
strategies for the sat ®

Chapter 4: Writing and Language Test Strategies
Chapter 5: English Language Conventions

Chapter 4:
Writing and Language
Test Strategies
OVERVIEW
A Closer Look at the Writing and Language Test
The Three Most Common Multiple-Choice Editing
Questions
Expression of Ideas Questions: Words in Context
Expression of Ideas Questions: Adding or
Deleting Text
Expression of Ideas Questions: Reordering
Sentences
Expression of Ideas Questions: Combining
Sentences and Using Transitional Words and
Phrases Correctly
Graphic Organizer Questions
Exercise: Writing and Language Test
Answer Keys and Explanations
Summing It Up

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A CLOSER LOOK AT THE WRITING AND LANGUAGE TEST
The Writing and Language Test gives you opportunities to demonstrate your college and career readiness by revising and editing
four passages. Each passage is 400–450 words long. There are 11 multiple-choice questions about each one—a total of 44
questions in all. You have 35 minutes to complete this section; that is about 48 seconds per question. If that doesn’t sound like
enough time to you, be assured that you will be able to answer many of the questions in fewer than 48 seconds. You can save up
your extra seconds for the harder questions you’ll encounter.
One passage of the four will be career-related; for example, this chapter includes a passage on technical writing careers. Another
passage will be humanities-related; it might be about visual art, music, theater arts, or literature. For example, this chapter includes
a short critical essay on a nineteenth-century novel by British author Jane Austen. The other two passages will be about history/
social studies and science. Some of the passages will be accompanied by graphic organizers such as tables, charts, or graphs.
The passages’ writing modes will include argument, informative/explanatory text, and nonfiction narrative. For example, this
chapter’s sample passage on technical writing is an informative/explanatory text. The essay on Jane Austen that appears later in
this chapter includes both argument and nonfiction narrative.
Answering the multiple-choice questions on each passage will place you in an editor’s role. You will be revising and editing the
work of an unspecified writer. You will be asked to improve each passage’s development, organization, and use of language. Your

Peterson’s SAT® Prep Guide 2017

tasks will include making sure that each passage conforms to standard rules of English grammar, usage, and punctuation. When a
passage is accompanied by one or more graphic organizers, you may need to correct the passage’s inaccurate interpretation of data.
These editing and revising goals may sound overwhelming, but don’t worry. Every answer is right there on your test page. All you
have to do is to select one out of four possible solutions [A, B, C, or D] to choose the best use of language.

THE THREE MOST COMMON MULTIPLE-CHOICE EDITING QUESTIONS
The Writing and Language Test contains three primary categories of multiple-choice questions:

1. Expression of Ideas Questions
More than half of the questions fall into this category. This group includes questions about the following:

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•
•
•
•
•
•
•
•
•

Words in context
Adding, deleting, or changing text
Transitional language that smoothly and clearly takes the reader from one idea to another
Relevant (or irrelevant) details
Combining sentences to make text more concise and less “choppy-sounding”
Eliminating awkward language and wordiness
Reordering sentences so that paragraphs make better sense
Consistency of style and tone
Cohesion and precision of language

You will learn how to approach Expression of Ideas questions later in this chapter.

2. Standard English Conventions Questions
About 45 percent of the questions fall into this category of grammar, usage, and punctuation rules. It includes questions that
require you to demonstrate your knowledge of the following:

•
•
•
•

Consistent (or inconsistent) verb tenses
Punctuation
Sentence structure
Correct (or incorrect) word usage

The Exercise section of this chapter provides practice with answering some questions from this category. In Chapter 5, you will
learn more about grammar, usage, and punctuation questions.

3. Graphic Organizer Questions
This is the smallest percentage of the three primary categories. There may be only a few questions that deal with graphic organizers on the Writing and Language Test. This type of question asks you to make revising and editing decisions about passages
in light of information and ideas conveyed through graphic organizers such as tables, charts, and graphs. However, you will not
need to do any mathematical computation in order to answer the questions in this category. Later in this chapter, you will learn
how to approach Graphic Organizer questions.

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EXPRESSION OF IDEAS QUESTIONS: WORDS IN CONTEXT
Words-in-Context questions are perhaps the easiest type of question on the Writing and Language Test. Most of the questions
on the test, including words in context, do not have a question right before the answer choices. Instead, you should choose the
response that corrects the sentence or paragraph and makes the writing stronger. Review the example below.

Jane Austen and Fanny Price

4

In real life, one 1 was sometimes left out because of

A.

NO CHANGE

actual purposeful wrongdoing on the parts of those doing

B.

Fairy tales

the leaving out, but sometimes one is simply left out—and

C.

Stories

D.

Articles

2 realism is beside the point. 3 The second case is
much less satisfying to the left-out person, but it is also much
more usual. 4 Novels such as “Cinderella” are satisfying
because, in them, it is clearly the nastiness of the villains
and villainesses that causes the heroes and heroines to be
excluded from pleasurable activities.

First, quickly read the paragraph to get a general sense of its meaning—you don’t need to understand every word. Right now
you are answering Question 4 only, so don’t worry about any errors you might spot in the rest of the paragraph—you will deal
with those later in the “Exercise” portion of this chapter.
Question 4 asks you to decide which word best fits the context. Your four choices are:

157

A. NO CHANGE (Novels); B. Fairy tales; C. Stories; and D. Articles.
Use the context clue Cinderella to make the best choice. Right away you can eliminate choice D: “Cinderella” is not an article—
most articles are nonfiction. Choice C is a possibility: “Cinderella” is a story—set this choice aside for a moment. Is “Cinderella” a
novel? No—novels are long, and the story of Cinderella is fairly short. Eliminate choice A. Is Cinderella a fairytale? Yes, it is: it has
magical elements, and it is a traditional tale that has been passed down for many generations. Is Fairy tales a better answer than
Stories? Yes, it is, because this description is more precise. Fairy tales are a specific type of story. The correct answer is choice B.

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Let’s try a words-in-context question that goes with a different passage.

A Technical Writing Career

11

Technical 11 communicators, better known as “technical

A.

NO CHANGE

writers,” plan, write, and edit instruction manuals, print and

B.

engineers

online articles, and other documents that transform 12

C.

manuals

D.

workers

intense technical information into simpler language that end
users can understand.

Peterson’s SAT® Prep Guide 2017

Quickly read the one-sentence paragraph to figure out what it is mainly about. Again, focus on the question you’re answering
(Question 11).
Here are some clue words and phrases that will help you figure out which word belongs after the numeral 11 : writers; write,
and edit; and simpler language that . . . users can understand. To which answer choice do these clues direct you? You can eliminate
choice C, manuals: a manual is a thing (a set of instructions), not a person. Might engineers, choice B, and workers, choice D, be
writers who write and edit text?
Maybe, but the word communicators is the best choice because it is most precise—a writer’s main job is to communicate with
others by writing understandable sentences, paragraphs, and so on.
Since the word communicators already appears in the paragraph after the 11 , the correct answer is choice A, NO CHANGE.

If you are somewhat stuck, but not totally, make an educated guess. If you can
eliminate at least one answer choice that you know is wrong (eliminating two
is even better), you won’t be guessing at random. Remember that you will not
be penalized for wrong answers, so educated guessing is a fine strategy to use.

EXPRESSION OF IDEAS QUESTIONS: ADDING OR DELETING TEXT
Here is a question that asks you whether it is a good or bad idea to delete a certain sentence.
When I was in elementary school, I was a shy little girl. . . .

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The stories I made up always had the same plot: I was carried

5

The writer is considering deleting the underlined sentence. Should the writer do this?

off by a prince (David) on a flying horse to his castle where

A.

Yes, because it adds unnecessary technical details.

I became his wife and got to live in the lap of luxury. 5

B.

Yes, because it makes the grown-up writer seem
silly and childish.

C.

No, because it adds funny details and helps to
show that the narrator was a child at the time.

D.

No, because, without this sentence, the last
sentence in the paragraph would not make sense.

From there I would go into elaborate detail about the décor
of the castle, how many horses we owned, what colors
they were, and so on. It was a silly, childish fantasy, but it
comforted me.

This question truly casts you in an editor’s role. You’re asked whether the paragraph would be better or worse if this sentence
were deleted. Not only that, you’re asked why your choice is the correct one.
You can eliminate choice B. The underlined sentence doesn’t make the grown-up writer seem “silly and childish”—it makes her
subject (her younger self ) seem so. The writer explicitly states this in the last sentence of the paragraph—she is having fun making
fun of her younger self.
Also eliminate choice A: This sentence does contain details, but they are not technical. How about choice D? Would the paragraph’s
last sentence fail to make sense if the underlined sentence were deleted? Read the first two sentences and the last one without
the middle (underlined) one. The last sentence still makes sense, so you can eliminate choice D.
You are left with choice C. Even if you disagree that the underlined sentence is funny, it definitely “helps to show that the narrator
was a child at the time.” The correct answer is choice C.

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EXPRESSION OF IDEAS QUESTIONS: REORDERING SENTENCES
Next, let’s try a question that asks you to reorder sentences in a paragraph.

[1] A few years ago, U.S. government experts predicted that
employment of technical writers would grow 1.5 percent

16 For the sake of cohesion, sentence 4 should
be placed

from 2012 to 2022, a gain of about 7,400 jobs per year.

A.

where it is now.

[2] (This is faster than the average for all occupations on

B.

before sentence 1.

C.

after sentence 1.

D.

after sentence 2.

which the U.S. Department of Labor gathers statistics.) [3]
This causes a greater need for professionals with the talent
and skills to write instructional manuals that users can
easily understand and follow. 16 [4] The high-tech and
electronics industries continue to change and grow.

In this type of question, each sentence in a paragraph is numbered with a numeral in brackets. Your job is to decide whether a
specific sentence should stay where it is; move to a different spot in the paragraph; and if it should move, where it should go.
The best way to answer this question would be to read the paragraph out loud to yourself. During the SAT®, you won’t be able
to do that, but try it now if possible. You will probably notice that sentence 4 sounds odd at the end of the paragraph—it seems
“tacked on” somehow. So it needs to be moved, but where?
Try each option one at a time. You will discover that this sentence belongs right after sentence 2—before sentence 3. Sentence
3 says that “This causes a greater need . . . [for good technical writers].” What causes this need? The cause is the fact that “the
high-tech and electronics industries continue to change and grow.” If sentences 3 and 4 were to swap places, the paragraph would
be “most logical”—it would make better sense than it does now, for sure. The correct answer is choice D.

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If a particular question seems overwhelming, circle it on
your test booklet and go on to the next question. When
you’re done with all of the easier ones, come back to any
questions you circled.

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Peterson’s SAT® Prep Guide 2017

EXPRESSION OF IDEAS QUESTIONS: COMBINING SENTENCES AND
USING TRANSITIONAL WORDS AND PHRASES CORRECTLY
Here is a question that asks you to complete two tasks at once: combine two shorter sentences into one longer one and choose
the transitional word or phrase that makes the best sense in the new, longer sentence.
Most novel readers do not like it when story events seem

7

artificially “rigged” by the author in order to teach a moralistic

Which choice most effectively combines the two
sentences at the underlined portion?

lesson. In this novel, Jane Austen rigs 7 events. Whenever

A.

events, but whenever Fanny is left out,

Fanny is left out, we can be sure that one or some of the

B.

events so that whenever Fanny is left out,

C.

events, because, whenever Fanny is left out,

D.

events, and the cause is that whenever Fanny is
left out,

other characters are engaged in something sinful. This is an
unrealistic (fairytale) element in what is otherwise a highly
developed, realistic novel.

Again, the best way to solve this editing problem is to imagine reading the paragraph out loud. If you try one answer choice at a
time, you will soon find the one that makes the best sense. The writer is saying that Jane Austen heavy-handedly rigs events in
her novel in order that such and such happens. The transitional words and phrases in the other answer choices (A: but; C: because;
D: and the cause is that) do not relay that same idea; only so that communicates this thought clearly. The correct answer is choice B.

GRAPHIC ORGANIZER QUESTIONS

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Every Writing and Language Test contains one or more passages with graphic organizers such as tables, charts, and graphs. One
or more of the questions following such a passage deals with its organizers. This type of question asks you to compare information given in the passage to similar information or data that the graphic organizer presents. If the two sets of information are
inconsistent, you will need to make editing changes to the passage.
Here is an example:

A TECHNICAL WRITING CAREER
Quick Facts: Technical Writers
2012 Median Pay

$65,500 per year
$31.49 per hour

Entry-level Education

Bachelor’s degree

Work Experience in a Related Occupation

Less than 5 years

On-the-job Training

Short-term on-the-job training

Number of Jobs, 2012

49,500

Job Outlook, 2012–22

15% (faster than average)

Employment Change, 2012–22

7,400

[Source: http://www.bls.gov/ooh/Media-and-Communication/Technical-writers.htm]

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Technical communicators, better known as “technical
writers,” plan, write, and edit instruction manuals, print and

17 Which choice most accurately and effectively represents
the information in the chart?

online articles, and other documents. Requirements for this

A.

NO CHANGE

well-paid profession include 17 a bachelor’s degree and

B.

a bachelor’s degree and less than ten years of
on-the-job work experience in a related
occupation

C.

a master’s degree, less than five years of work
experience in a related occupation, and a short
period of on-the-job training

D.

a bachelor’s degree, less than five years of work
experience in a related occupation, and a short
period of on-the-job training

five to ten years of on-the-job training in a technical field.

To find the correct answer choice, you will need to pay close attention to details in the chart. In this case, carefully read the three
rows beginning with “Entry-level Education” and ending with “On-the-job Training.” Choice A is incorrect because the chart does
not specify “five to ten years of on-the-job training in a technical field.” Choice B is incorrect because the chart does not specify
“less than ten years of on-the-job work experience in a related occupation.” Choice C is incorrect because the chart lists a bachelor’s
degree, not a master’s, as a prerequisite for an entry-level technical writing job. The only answer choice that perfectly matches
the chart is choice D. The correct answer is choice D.

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EXERCISE: WRITING AND LANGUAGE TEST
18 Minutes—22 Questions
DIRECTIONS: Each of the following passages is accompanied by a set of questions. For some questions, you will consider
how the passage might be revised to improve the expression of ideas. For other questions, you will consider how the
passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage or a question may be
accompanied by one or more graphics (such as a table, chart, graph, or photograph) that you will consider as you make
revising and editing decisions.
Some questions will direct you to an underlined portion of a passage. Other questions will direct you to a location in a
passage or ask you to think about the passage as a whole.
After reading each passage, choose the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage conform to the conventions of Standard Written English. Many questions include a
“NO CHANGE” option. Choose that option if you think the best choice is to leave the relevant portion of the passage as it is.

Questions 1–11 are based on the following passage.

1

Jane Austen and Fanny Price
. . . In real life, one 1 was sometimes left out because of
actual purposeful wrongdoing on the parts of those doing

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the leaving out, but sometimes one is simply left out—and
2 realism is beside the point. 3 The second case is

NO CHANGE

B.

is

C.

will be

D.

may have been

A.

NO CHANGE

B.

purpose

C.

culpability

D.

satisfaction

2

much less satisfying to the left-out person, but it is also
much more usual. Fairy tales such as “Cinderella” are
satisfying because, in them, it is clearly the nastiness of the
villains and villainesses that causes the heroes and heroines
to be excluded from pleasurable activities.
3

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A.

The writer is considering deleting the underlined sentence. Should the writer do this?
A.

Yes, because it does not provide a good transition
between the first and third sentences in the
paragraph.

B.

Yes, because it fails to support the main argument
of the passage: that Mansfield Park presents a
fairytale conception of being left out.

C.

No, because it identifies important distinctions
among three different “cases.”

D.

No, because it provides a good transition between
the first and third sentences in the paragraph.

[1] When I was in elementary school, I was a shy little girl

4

not unlike Fanny Price of Jane Austen’s 4 Mansfield Park.
[2] Sometimes when I was feeling left out, I would sit on a

The writer is considering adding the phrase “magnificent
work of art” here. Should the writer do this?
A.

Yes, because it identifies the genre of Mansfield
Park.

B.

Yes, because it sums up the writer’s true opinion of
the book.

C.

No, because it is an unnecessary and possibly
confusing addition.

D.

No, because it contradicts the writer’s previous,
more critical statement.

bench at the very edge of the playground and put spit on my
cheeks to simulate tears, in case David Gould, 5 a boy I
knew, should pass by and take pity on me. 6 [3] I also had
a fairytale conception of being left out (as Fanny and Jane
Austen have in this novel). [4] He never did, but it didn’t really
7 matter. My imagination would take over from that point.
[5] The stories I made up always had the same plot: I was
carried off by a prince (David) on a flying horse to his castle

5

where I became his wife and got to live in the lap of luxury.
[6] (From there I would go into elaborate detail about the
décor of the castle, how many horses we owned, 8 what
colors they were and so on.

6

7

Which choice provides the most relevant detail?
A.

NO CHANGE

B.

the shortest boy in my classroom

C.

the handsomest boy in the school

D.

my sister’s best friend’s boyfriend

To make this paragraph most logical, sentence 3 should
be placed
A.

where it is now.

B.

after sentence 1.

C.

after sentence 4.

D.

after sentence 6.

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Chapter 4

Which choice most effectively combines the two sentences at the underlined portion?
A.

matter, because my imagination

B.

matter; for example, my imagination

C.

matter; in other words, my imagination

D.

matter—consequently, my imagination

A.

NO CHANGE

B.

what colors they are and so on.

C.

what colors they will be, and so on.)

D.

what colors they were, and so on.)

Writing and
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8

Peterson’s SAT® Prep Guide 2017

In the course of Mansfield Park, Fanny goes through one big

9

suffer-and-be-vindicated cycle (her 9 ultimate marriage to

A.

NO CHANGE

B.

ill-advised

C.

initial

D.

volatile

A.

NO CHANGE

B.

yet,

C.

predictably,

D.

on the other hand,

A.

NO CHANGE

that I felt at the moment in my David Gould fantasy when

B.

sinful, this

he would suddenly appear and sweep me up and away from

C.

sinful: this

my wrongfully left-out state into one of well-deserved bliss.

D.

sinful (this

Edmund after many, many years of being left out) and many
little suffer-and-be-comforted cycles:
“Edmund . . . going quietly to another table
. . . brought a glass of Madeira to Fanny [who had
a headache as a result of being deprived of proper
exercise by the thoughtless disregard of others],
and obliged her to drink the greater part. She
wished to be able to decline it, but the tears which
a variety of feelings created, made it easier to
swallow than to speak.” [Mansfield Park, page 513;
from The Complete Novels of Jane Austen, Modern
Library edition]
The little gush of passionate, passive gratefulness that Fanny

10

11

feels when Edmund “obliges” her to drink the Madeira feels
to me similar to the sweet rush of vindicated personal pathos

This way of thinking is childish, self-pitying, and self-deluded;

164

10 accordingly, Jane Austen (who is usually far more
astute) lets Fanny get away with it.

Chapter 4
The author rigs things so that whenever Fanny is left out,
Writing and
Language
Test
Strategies

we can be sure that one or some of the other characters
are engaged in something 11 sinful; this is an unrealistic
(fairytale) element in what is otherwise a highly developed,
realistic novel.

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Questions 12–22 are based on the following passage and
supplementary material.

12

A Technical Writing Career
Technical communicators, better known as “technical writers,”
plan, write, and edit instruction manuals, print and online
articles, and other documents that transform 12 intense

A.

NO CHANGE

B.

ordinary

C.

complex

D.

varied

A.

NO CHANGE

B.

determines end users’ needs.

C.

determines and decides end users’ needs.

D.

determines the needs of end users and people
who will be using the product.

13

technical information into simpler language that end users
can understand.
A typical technical writer

•

13 determines end users’ needs and requirements.

• studies product samples and discusses them with
designers and developers.

• outlines, writes, and edits documents that support a
variety of technical products.

• gathers and/or creates graphics that illustrate instructions
and other technical documents.

14 Which choice provides the most relevant list of
details?
A.

NO CHANGE

B.

(books, magazines, newspapers, television news
shows)

C.

(drawing, painting, sculpture, computer-generated graphics)

D.

(keyboards, monitors, hard drives, software, cloud
computing)

• writes scripts for online instructional videos.
• decides which medium 14 (how-to manuals, “frequently asked questions” pages, online videos) will most
effectively convey the information.

• gathers feedback on products’ usability from customers,

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designers, and manufacturers.

• revises documents to fit product changes.
• works with customer service specialists to improve the
end-user experience through product design changes.

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Technical writers must be able to fully comprehend complex
information. Their work colleagues may include computer

15 Which change most effectively ends this paragraph and
is also consistent with information provided in the chart?

hardware engineers, scientists, computer support specialists,

A.

NO CHANGE

and software developers.

B.

Prior knowledge about such colleagues’ fields
enables technical writers to understand and
translate “tech speak” into clear, useful instructions
for users.

C.

It takes years of graduate study to enable a
technical writer to understand various work
colleagues’ fields—a master’s degree or Ph.D. in
technical writing is advisable.

D.

DELETE the underlined sentence and do not
replace it.

15 How else can they be expected to communicate with
people from such an array of professional backgrounds?

Quick Facts: Technical Writers
2012 Median Pay

$65,500 per year
$31.49 per hour

Entry-Level Education

Bachelor’s degree

Work Experience in a Related Occupation

Less than 5 years

Chapter 4

On-the-job Training

Short-term on-the-job training

Writing and
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Number of Jobs, 2012

49,500

Job Outlook, 2012–22

15% (Faster than average)

Employment Change, 2012–22

7,400

166

[Source: http://www.bls.gov/ooh/Media-and-Communication/Technical-writers.htm]

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16 [1] Why is the technical writing field growing so quickly?

16 For the sake of cohesion, sentence 1 should be placed

[2] A few years ago, U.S. government experts predicted
that employment of technical writers would grow 17 1.5
percent from 2012 to 2022, a gain of about 7,400 jobs per
year. [3] (This is faster than the average for all occupations on
which the U.S. Department of Labor gathers statistics.) [4] As
the high-tech and electronics industries continue to change
and grow, they 18 reflect a greater need for professionals

A.

where it is now.

B.

after sentence 2.

C.

after sentence 3.

D.

after sentence 4.

17 Which choice most accurately and effectively represents
the information in the chart (on the previous page)?

with the talent and skills to write instructional manuals that
users can easily understand and follow.

A.

NO CHANGE

B.

7.5 percent from 2012 to 2022, a gain of about
7,500 jobs per year.

C.

15 percent from 2012 to 2022, a gain of about
7,400 jobs per year.

D.

15 percent from 2012 to 2022, a gain of about
7,400 jobs total.

A.

NO CHANGE

B.

generate

C.

effect

D.

obligate

18

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Job opportunities 19 abound. This is especially true
for applicants with both technical skills and writing skills.

19 Which choice most effectively combines the two sentences
at the underlined portion?

Increasingly, consumers rely on technologically sophisticated

A.

abound, especially for applicants with

products in the home as well as in the workplace. 20 In

B.

abound, especially is this the case for applicants
with

C.

abound; especially positively impacted are
applicants with

D.

abound—and especially for those lucky applicants
who have acquired

A.

NO CHANGE

B.

And another thing: for many people,

C.

I need to make one last point—for many people—

D.

In contrast, for many people,

A.

NO CHANGE

B.

As older technical writers retire,

C.

Baby Boomers are retiring these days, so

D.

Smarter job seekers will recall that, as older
workers retire,

A.

NO CHANGE

B.

competitive

C.

apparent

D.

stagnant

addition—for many people—ordinary daily life requires us
to understand complex medical and scientific information.
All of these factors are combining to create many new
opportunities for technical writers. 21 Remember now, that
as older workers retire, their jobs will become vacant. Yet,
competition among freelance technical writers will remain

20

22 lively.

21

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22

ANSWER KEYS AND EXPLANATIONS
PASSAGE 1

1. B

4. C

6. B

8. D

10. B

2. C

5. C

7. A

9. A

11. A

3. D

1. The correct answer is B. Except for this verb, was, the
writer uses the present tense throughout the paragraph.
Therefore, to be consistent, the correct answer is choice B.
2. The correct answer is C. The writer is making a distinction
between times when a person is left out because other(s)
have misbehaved and times when a person is left out, but
no one else is at fault, or culpable. Since a noun is needed
in the sentence here, culpability, choice C, is the correct
answer.
3. The correct answer is D. The writer should not delete the
sentence because it provides a good transition between
the first and third sentences in the paragraph.
4. The correct answer is C. The writer should not add this
phrase here because it is unnecessary and may confuse
readers into thinking Mansfield Park is a work of visual art,
such as a painting.
5. The correct answer is C. It makes sense that a girl would
cast the handsomest boy in the school in the role of a prince
who saves her from her unhappy state. Choices A, B, and
D are incorrect because, while they are possible choices,
they are not as relevant as choice C.

6. The correct answer is B. Sentence 3 makes the best sense
when it follows sentence 1.
7. The correct answer is A. The linking word because makes
sense in context: the writer is explaining why it did not
matter that David Gould never noticed or pitied her when
she was a shy little girl.
8. The correct answer is D. Choice D correctly includes a
needed comma following the word were and includes a
missing close parenthesis mark.
9. The correct answer is A. The writer is referring to an event
that occurs near the end of the novel (“after many, many
years of being left out,” Fanny finally marries Edmund). The
correct choice is A, NO CHANGE: ultimate, meaning “final.”
10. The correct answer is B. The transitional word yet makes
sense in context: the writer is explaining that, even though
Jane Austen is usually astute about her characters, in this
case, the author “lets Fanny get away with” childishness,
self-pity, and self-delusion.
11. The correct answer is A. No change is needed because
this phrase is correctly punctuated with a semicolon.

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PASSAGE 2

12. C

15. B

17. D

19. A

21. B

13. B

16. C

18. B

20. A

22. A

14. A
12. The correct answer is C. The writer is referring to technical
ideas that are the opposite of “simple.” The correct choice
is C: complex.
13. The correct answer is B. Only choice B offers clear and
concise wording without redundancy. Choice A is incorrect
because end users’“needs and requirements”is redundant.
Choice C eliminates the original redundancy, but then
it creates a new one: “determines” and “decides” mean
the same thing. Choice D is incorrect because it, too, is
redundant: “end users” and “people who will be using the
product” mean the same thing.
14. The correct answer is A. No change is needed because
the writer is using the word medium to refer to a genre or
method of effectively conveying technical information.
15. The correct answer is B. This sentence clarifies information
presented earlier in the paragraph.

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16. The correct answer is C. Sentence 1 makes the most sense
when it follows sentence 3.
17. The correct answer is D. The last two lines of the chart say
that the projected job outlook for technical writers during
the ten years from 2012 to 2022 is 15 percent growth and
that, during those ten years, the technical writing field
will gain 7,400 jobs total. Choices A, B, and C are incorrect
because the statistics they give do not match those shown
in the chart.

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18. The correct answer is B. The writer is referring to certain
changes in the U.S. economy that will produce, result in, or
generate more technical writing jobs. The correct choice
is B: generate.
19. The correct answer is A. This is the simplest, clearest way
to combine the two sentences. Choices B, C, and D are
incorrect because each is either awkward or too wordy or
does not match the rest of the passage’s style and tone.
20. The correct answer is A. No change is needed because
the existing wording is the simplest, clearest way to make
this point. It matches the style and tone of the passage
while including necessary transitional language.
21. The correct answer is B. This phrase is appropriately specific
and best matches the rest of the passage’s style and tone.
22. The correct answer is A. The writer’s point is that even
though many older technical writers will be vacating their
jobs as they retire, freelance technical writers will still face
competition as they vie for available jobs; thus, the competition will be lively.

SUMMING IT UP
• In the Writing and Language Test section of the SAT®, there are four passages and 44 multiple-choice questions (eleven questions about each passage). You will have 35 minutes to complete this section.

• The multiple-choice questions in this section put you in an editor’s role. Each question consists of an “editing problem” with
four possible solutions.

• Some passages are accompanied by informational graphics, such as graphs, charts, tables, and photographs. You’ll need to
refer to these supplementary graphics to answer a question or two, but no math will be required in this section.

• There are three main categories of multiple-choice questions:
1.

Expression of Ideas questions, including questions on words in context; adding, deleting, or changing text; transitional language; relevant details; combining sentences; eliminating awkward language and wordiness; reordering
sentences so that paragraphs make better sense; consistency of style and tone; cohesion and precision of language

2.

Standard English Conventions questions covering grammar, usage, and punctuation

3.

Graphic Organizer questions that ask you to compare information that is in the passage to similar information or
data that are presented in a chart, graph, table, or photograph

• In addition to your Writing and Language Test score, the following subscores and cross-test scores will be provided:
ºº Command of Evidence: Questions that ask you to interpret and use evidence in the passages and informational
graphics, such as graphs, tables, and charts

ºº Expression of Ideas: Questions that focus on topic development, organization, and rhetorically effective use of
ºº
ºº
ºº
ºº

language
Words in Context: Questions that address the meaning of a particular word or phrase in context
Standard English Conventions: Questions that focus on sentence structure, usage, and punctuation
Analysis in History/Social Studies: Questions based on history/social studies–related passages
Analysis in Science: Questions based on science-related passages

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• Frequently Confused Words
• Grammar Question Types
• Organization Questions
• Pacing in Writing
• Parallelism
• Pronouns
• Punctuation
• Style Questions
• Verb Tenses
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Chapter 5:
English Language
Conventions
OVERVIEW
Sentence Formation
Verb Tense, Mood, and Voice
Conventions of Usage
Agreement
Frequently Confused Words
Conventions of Punctuation
Summing It Up

This chapter reviews standard English language conventions. While we’re not attempting to teach you all the rules of punctuation
and grammar, we do want you to review those rules that may be tested or that you may need to call on for your own writing.
Each of the three main domains covered in this chapter—sentence structure, conventions of usage, and conventions of punctuation—is broken down into smaller sections. These instructional sections are followed by exercises with answers and explanations.
Be sure to read all the answer explanations, even for the questions you answered correctly. Review is an important part of your
SAT® exam preparation.

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SENTENCE FORMATION
Sentence Boundaries
Fragments
Basic Rule
Every sentence must have a complete subject and verb and express a full idea. A group of words that is missing one of these
elements is called a sentence fragment or an incomplete sentence.
There are three ways to correct incomplete sentences:
1.

Add the fragment to the sentence that precedes it.
Incorrect: Zoologists and wildlife biologists study animals and other wildlife. How they interact with their
ecosystems.
Correct: Zoologists and wildlife biologists study animals and other wildlife and how they interact with their
ecosystems.
Explanation: The fragment is added to the sentence that precedes it by adding the word and.

2.

Add the fragment to the sentence that follows it.
Incorrect: By studying animal behaviors. Wildlife biologists seek to understand how animals interact with their
ecosystems.
Correct: By studying animal behaviors, wildlife biologists seek to understand how animals interact with their
ecosystems.

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Explanation: The fragment is added to the sentence that follows it by inserting a comma.

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3.

Add a subject and verb to the fragment.
Incorrect: Considerable time studying animals in their natural habitats.
Correct: Wildlife biologists may spend considerable time studying animals in their natural habitats.
Explanation: A subject (wildlife biologists) and verb (may spend) are added to the fragment.

Run-ons
A run-on sentence occurs when a writer fails to use either end-stop punctuation to divide complete thoughts or suitable conjunctions to join two ideas.
The following rules will help you avoid and fix run-on sentences:
1.

Though the result can be short, choppy sentences, the most common way to correct a run-on sentence is to simply divide
the sentence using end-stop punctuation.
Incorrect: Zoologists need a bachelor’s degree for entry-level positions a master’s degree or Ph.D. is often needed
for advancement.

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Correct: Zoologists need a bachelor’s degree for entry-level positions. A master’s degree or Ph.D. is often needed
for advancement.
2.

A more advanced technique is to create a compound sentence by joining independent clauses using a coordinating conjunction (e.g., and, but, or so).
Incorrect: Zoologists need a bachelor’s degree for entry-level positions a master’s degree is often needed for
advancement.
Correct: Zoologists need a bachelor’s degree for entry-level position, but a master’s degree is often needed for
advancement. (Remember that a comma is required when you use a coordinating conjunction to join two independent clauses.

3.

Another option is to create a complex sentence by adding a subordinating conjunction (e.g., because, although, or while),
making one of the independent clauses a dependent clause.
Incorrect: Zoologists need only a bachelor’s degree for entry-level positions a master’s degree is often needed for
advancement.
Correct: Zoologists need only a bachelor’s degree for entry-level positions although a master’s degree is often
needed for advancement. (In general, commas are not required when the dependent clause follows the
independent clause.)
Also Correct: Although a master’s degree is often needed for advancement, zoologists need only a bachelor’s
degree for entry-level positions. (Commas are required when the dependent clause precedes the independent
clause.)

4.

Use a semicolon when ideas are very closely related in meaning and full end-stop punctuation seems too strong.
Incorrect: Zoologists and wildlife biologists study how animals and other wildlife interact with their ecosystems
these scientists work in offices, laboratories, or outdoors.

175

Correct: Zoologists and wildlife biologists study how animals and other wildlife interact with their ecosystems;
these scientists work in offices, laboratories, or outdoors.

Chapter 5
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Skill Builder: Fragments and Run-ons
DIRECTIONS: Revise the following sentences to correct fragments and eliminate run-ons.

1. Zoologists and wildlife biologists perform a variety of scientific tests and experiments for example, they take blood samples
from animals to assess their levels of nutrition, check animals for disease and parasites, and tag animals in order to track
them.

2. In order to track potential threats to wildlife. Wildlife biologists often use computer programs.

3. Zoologists and wildlife biologists work to expand our knowledge of wildlife species. Work closely with public officials to
develop wildlife management and conservation plans.

Peterson’s SAT® Prep Guide 2017

4. Herpetologists study reptiles, such as snakes. And amphibians, such as frogs.

5. Some wildlife biologists develop conservation plans and make recommendations on conservation and management issues.
To policymakers and the general public.

6. Ecologists study ecosystems. And the relationships between organisms and the surrounding environments.

7. Evolutionary biologists study the origins of species. The changes in their inherited characteristics over generations.

8. Zoologists and wildlife biologists conduct experimental studies they also collect biological data for analysis.

Answers
In some cases, there are many possible correct answers. Here are some examples:
1. Zoologists and wildlife biologists perform a variety of scientific tests and experiments. For example, they take blood samples
from animals to assess their levels of nutrition, check animals for disease and parasites, and tag animals in order to track
them.
2. In order to track potential threats to wildlife, wildlife biologists often use computer programs.

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3. Zoologists and wildlife biologists work to expand our knowledge of wildlife species and work closely with public officials to
develop wildlife management and conservation plans.
4. Herpetologists study reptiles and amphibians, such as snakes and frogs.
5. Some wildlife biologists develop conservation plans and make recommendations on conservation and management issues
to policymakers and the general public.
6. Ecologists study ecosystems and the relationships between organisms and the surrounding environments.
7. Evolutionary biologists study the origins of species and the changes in their inherited characteristics over generations.
8. Zoologists and wildlife biologists conduct experimental studies and collect biological data for analysis.

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Coordination and Subordination
Basic Rule
Coordinating and subordinating conjunctions are used to join together clauses and form compound and complex sentences.
Some common coordinating and subordinating conjunctions are:

Coordinating conjunctions

Subordinating conjunctions

and, but, for, nor, or, so, yet

after, although, as, as if, because, before, even if,
even though, if, if only, rather than, since, that, though,
unless, until, when, where, whereas, wherever,
whether, which, while

Basic Rule of Coordinating Conjunctions
Coordinating conjunctions are used to join independent clauses to make compound sentences. In these sentences, each piece
of information carries the same weight.
Independent clauses: There was a Treaty of Paris signed in 1763. There was also one signed in 1783.
Joined together: There were Treaties of Paris signed in 1763 and 1783.
When two clauses are joined, if the second remains an independent clause, a comma must be used before the coordinating
conjunction.

177

Independent clauses: There was a Treaty of Paris signed in 1763. There was also one signed in 1783.
Chapter 5
Joined together: There was a Treaty of Paris signed in 1763, but there was another Treaty of Paris signed in 1783.

Basic Rule of Subordinating Conjunctions

English
Language
Conventions

Subordinating conjunctions are used to join independent and dependent clauses to make complex sentences. In these sentences,
the dependent clause establishes a place, a time, a reason, a condition, a concession, or a comparison for the independent clause.
Independent clauses: A tax on imported goods from another country is called a tariff. A tax on imported goods
from another country to protect a home industry is called a protective tariff.
Joined together: A tax on imported goods from another country is called a tariff, while a tax on imported goods
from another country to protect a home industry is called a protective tariff.

Peterson’s SAT® Prep Guide 2017

Here, the subordinate clause is at the end. You can also place a subordinate clause at the beginning of a sentence, as long as you
use a comma.
Independent clauses: A tax on imported goods from another country is called a tariff. A tax on imported goods
from another country to protect a home industry is called a protective tariff.
Joined together: While a tax on imported goods from another country is called a tariff, a tax on imported goods
from another country to protect a home industry is called a protective tariff.

Skill Builder: Subordination and Coordination
DIRECTIONS: Join the following sentences using subordinating or coordinating conjunctions.

1. A democracy is a form of government that is run for the people. It is also run by the people.

2. A primary source is an original record of an event. A secondary source is something that was written later.

3. The Industrial Revolution ushered in a time of unparalleled human progress. People often forget the damage that this
progress did, and continues to do, to the environment.

178

4. Elizabeth Cady Stanton became famous as an advocate of women’s rights. During the Civil War, she was also an ardent
abolitionist.

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Answers
In some cases, there are many possible correct answers. Here are some examples:
1. A democracy is a form of government that is run for the people, and it is also run by the people.
2. Whereas a primary source is an original record of an event, a secondary source is something that was written later.
3. While the Industrial Revolution ushered in a time of unparalleled human progress, people often forget the damage that this
progress did, and continues to do, to the environment.
4. Elizabeth Cady Stanton became famous as an advocate of women’s rights, and, during the Civil War, she was also an ardent
abolitionist.

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Parallel Structure
Parallel structure is the repetition of a grammatical form within a sentence. Parallel structure is a hallmark of effective writing
and is often used to emphasize ideas and present compared items in an equal light. Coordinating conjunctions are often used
in parallel constructions.
Non-parallel structure: As a child, George Washington Carver enjoyed reading, learned about plants, and he
made art.
Parallel structure: As a child, George Washington Carver enjoyed reading, learning about plants, and making art.

Modifier Placement
A modifier is a word, phrase, or clause that adds detail to a sentence. In order to avoid confusion, modifiers should be placed as
close as possible to the things they modify.
Examples of different modifiers are underlined in the sentences below.
Within the field of marine biology, employment is highly competitive. (The phrase “within the field of marine biology” modifies
the subject of the sentence, which is “employment.” The word “highly” modifies our understanding of the competitive nature of
finding employment. )
The abundant supply of marine scientists far exceeds the demands, and the number of federal and state government jobs is
limited. (“Abundant” modifies “supply.” “Marine” modifies “scientists.” “Limited” modifies our understanding of “jobs.”)
When the subject of a modifier is unclear or is not included in the sentence, it is considered a dangling modifier.

179

Incorrect: Not realizing that the job title of marine biologist rarely exists, “marine biology” is a term recognized by
most people. (What is the first phrase modifying?)

Chapter 5

Possible revision: Not realizing that the job title of marine biologist rarely exists, most people recognize the term
“marine biology.”

English
Language
Conventions

Misplaced modifiers occur when a modifier is poorly placed and it doesn’t express the writer’s intent accurately.
Incorrect: The term “marine biologist” is used to almost describe all of the disciplines and jobs that deal with the
study of marine life, not just those that deal with the physical properties of the sea.
Possible revision: The term “marine biologist” is used to describe almost all of the disciplines and jobs that deal
with the study of marine life, not just those that deal with the physical properties of the sea.

Peterson’s SAT® Prep Guide 2017

Skill Builder: Modifier Placement
DIRECTIONS: Revise the following sentences to eliminate problems with modifier placement.

1. Critical for getting a competitive edge in the job market, fishery science requires a strong background in advanced mathematics and computer skills.

2. A fishery scientist studies population dynamics of fish and marine mammals after taking course work in the animal and
aquatic sciences.

3. Another increasingly important field within marine biology, more universities are starting to offer programs in fisheries or
wildlife management.

4. As well as their interactions, biological oceanographers study both the biological and physical aspects of the sea.

5. A student may take course work weighted heavily in physics, mathematics, and computer modeling in the field of physical
oceanography.

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Answers
In some cases, there are many possible correct answers. Here are some examples:

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Conventions

1. A strong background in advanced mathematics and computer skills is critical for getting a competitive edge in the fishery
science job market.
2. After taking course work in the animal and aquatic sciences, a fishery scientist studies fish and marine mammal population
dynamics.
3. More universities are starting to offer programs in fisheries or wildlife management, another increasingly important field
within marine biology.
4. Biological oceanographers study both the biological and physical aspects of the sea, as well as their interactions.
5. A student in the field of physical oceanography may take course work weighted heavily in physics, mathematics, and computer modeling.

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VERB TENSE, MOOD, AND VOICE
Basic Rule
Use the same verb tense whenever possible within a sentence or paragraph. Do not shift from one tense to another unless there
is a valid reason.
Incorrect: The Magna Carta was signed in 1215 by King John of England and has been the first document of its
kind to limit the power of the British monarchy.
Correct: The Magna Carta was signed in 1215 by King John of England and was the first document of its kind to
limit the power of the British monarchy.

When to Use the Perfect Tenses
Basic Rule
Use present perfect for an action begun in the past and extended to the present.
Example: Scientists at NASA have seen an alarming increase in the accumulation of greenhouse gases.
Explanation: In this case, scientists at NASA saw would be incorrect. What they have seen (present perfect) began
in the past and extends to the present.

181

Basic Rule
Use past perfect for an action begun and completed in the past before some other past action.

Chapter 5

Example: Despite their preparations, Lewis and Clark had never encountered the kinds of challenges that awaited
them before their expedition.

English
Language
Conventions

Explanation: In this case, never encountered would be incorrect. The action had never encountered (past perfect) is
used because it is referring to events prior to their expedition.

Basic Rule
Use future perfect for an action begun at any time and completed in the future.
Example: When the American astronauts arrive, the Russian cosmonauts will have been on the International Space
Station for six months.
Explanation: In this case, although both actions occur in the future, the Russian cosmonauts will have been on the
space station before the American astronauts arrive. When there are two future actions, the action completed first
is expressed in the future perfect tense.

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Skill Builder: Verb Tense
DIRECTIONS: Circle the word with the correct verb tense for each sentence.

1. (was, has been) Founded in Jamestown, Virginia, the House of Burgesses ___ the first representative body founded in the
new world.
2. (have been, were) There ___ many great American explorers, but some scholars argue that none is as historically significant
as Lewis and Clark.
3. (had never been, never was) Before 1804, Meriwether Lewis ___ on an expedition of any significance, let alone led one.
4. (will have added, has added) By the time this article is published, the United States ___ 250,000 new jobs.
5. (was, has been) Civil Disobedience, or the refusal to obey a government law or laws, ___ one of Martin Luther King, Jr.’s key
tactics during the Civil Rights Movement.

Answers
1. The correct answer is was. The past tense is used because the action occurred in the past.
2. The correct answer is have been. The present perfect tense is used because the sentence refers to action that began in the
past and extended to the present.
3. The correct answer is had never been. The past perfect tense is used because the sentence contains a past tense action
that occurred before another action.

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4. The correct answer is will have added. The future perfect tense is used because the sentence refers to action begun at
any time and completed in the future.
5. The correct answer is was. The past tense is used because the action occurred in the past.

Mood
Basic Rule
Mood, as it relates to verb forms, refers to the kind of message the writer intends to communicate.
The indicative mood is the most common mood and is used to state facts or opinions.
Example: Zora Neale Hurston’s novel Their Eyes Were Watching God was forgotten for many years but is now
considered a literary classic.
The imperative mood is used when a writer wants to give a directive or make a request. Though not stated, the subject of an
imperative sentence is you.
Example: Stop pretending that it doesn’t matter.
Example: George Washington peered across the Potomac as the frigid wind lashed his face. “Hurry!” he exclaimed.
(Peered is in the indicative. Hurry is in the imperative.)

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The subjunctive mood expresses a condition contrary to fact, a wish, a supposition, or an indirect command. Although it is going
out of use in English, the subjunctive can still be seen in the following forms:

• To express a wish not likely to be fulfilled or impossible to be realized
Example: I wish it were possible for us to approve his transfer at this time. (It is not possible.)

• In a subordinate clause after a verb that expresses a command, a request, or a suggestion
Example: It was recommended by the White House that the Office of Homeland Security be responsible for preparing the statements.

• To express a condition known or supposed to be contrary to fact
Example: If Ann were chosen to be our company’s president, women would earn more than their male
counterparts.

• After as if or as though. In formal writing and speech, as if and as though are followed by the subjunctive, since they
introduce as supposition something not factual. In informal writing and speaking, the indicative is sometimes used.
Example: Before defecting to the British Army, Benedict Arnold talked as if he were a true American patriot.
(He was not.)

Avoid shifts in mood. Once you have decided on the mood that properly expresses
your message, use that mood throughout the sentence or the paragraph. A shift in
mood is confusing to the listener or reader; it indicates that the speaker or writer
himself has changed his way of looking at the conditions.
Incorrect: It is requested by the White House that a report of Congressional
proceedings be prepared and copies should be distributed to all citizens. (Be is
subjunctive; should be, indicative.)
Correct: It is requested by the White House that a report of the Congressional
proceedings be prepared and that copies be distributed to all citizens.

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Voice
Basic Rule
Voice tells us whether the subject of a sentence is the actor or is acted upon. In formal writing, active voice is preferred because
it is more immediate and places the reader closer to the action.
Active voice example: According to legend, George Washington chopped down the whole cherry tree.
Passive voice example: According to legend, the cherry tree was chopped down by George Washington.

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Skill Builder: Mood and Voice
DIRECTIONS: In the following sentences, choose the correct mood or voice.

1. (was, were) The team of Russian engineers ___ unable to prevent the nuclear reactor in Chernobyl from melting down.
2. (was, were) If climate change ___ not such a threat to life on this planet, the scientific community would not be making such
a big deal about carbon emissions.
3. (is, were) If inflation ___ to continue to rise, the effects on the economy would be disastrous.
4. (be, should be) The President asked that the Speaker of the House ___ present when the special announcement was made.
5. (passive or active voice) The stony coral polyps were placed in a cup made of calcium carbonate.
6. (passive or active voice) For over 40 years, Henry Clay played a central role on the national political stage.

Answers and Explanations
1. The correct answer is was. This sentence uses the indicative mood and requires the simple past tense.
2. The correct answer is were. The subjunctive is correct because the sentence is making a supposition.
3. The correct answer is were. The subjunctive is correct because the sentence is making a supposition.
4. The correct answer is be. The subjunctive is correct because the subordinate clause after the verb is making a request.
5. The correct answer is passive voice. This sentence is passive because the subject of the sentence is acted upon.
6. The correct answer is active voice. This sentence is active because the subject of the sentence is the actor.

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CONVENTIONS OF USAGE
Pronouns
Pronouns substitute for nouns.
Examples: George Washington was born on February 22, 1732, in Pope’s Creek, Virginia; he was the first American
president.
Did you know that Besty Ross and George Washington both went to the same church? It was called Christ Church,
and it was located in Philadelphia.

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The following pronoun chart may prove helpful:

Number

Singular

Plural

Person

Subjective
Case

Objective
Case

Possessive
Case

1st person

I

me

mine

2nd person

you

you

yours

3rd person

he, she, it, who

him, her, it, whom

his, hers, whose

1st person

we

us

ours

2nd person

you

you

yours

3rd person

they, who

them, whom

theirs, whose

Basic Rule
A pronoun uses the subjective case when it is the subject of the sentence or when it renames the subject as a subject complement.
Incorrect: That night, George Washington, Robert Morris, and him asked Betsy Ross to sew the first flag.
Correct: That night, George Washington, Robert Morris, and he asked Betsy Ross to sew the first flag. (He is part of
the subject of the sentence.)
Incorrect: George Ross is him.

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Correct: George Ross is he. (He renames the subject.)

Basic Rule

Chapter 5

If a pronoun is the object of a verb or preposition, it is placed in the objective case.

English
Language
Conventions

Incorrect: After the plot was discovered, they accused Benedict Arnold and he of treason.
Correct: After the plot was discovered, they accused Benedict Arnold and him of treason. (Him is the object of the
verb accused.)
Incorrect: Despite the fact that we turned in our marine biology paper late, “A” grades were given to Franklin and I.
Correct: Despite the fact that we turned in our marine biology paper late, “A” grades were given to Franklin and
me. (Me is the object of the verb given.)

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Pronoun Clarity
Avoid ambiguity and confusion by placing a pronoun as close as possible to its antecedent (the word it refers to) and by making
sure that the antecedent is clear.
Incorrect: At the height of his career, Frank Lloyd Wright told an architectural scholar that he thought his work was
improving. (Is Wright talking about his own work or the work of the scholar?)
Correct: At the height of his career, Frank Lloyd Wright told an architectural scholar that he thought his own work
was improving.
Incorrect: Frank Lloyd Wright and his wife Olgivanna founded a school for aspiring artists in Spring Green,
Wisconsin, where they could “learn by doing.” (Does they refer to the Wrights or the artists?)
Correct: Frank Lloyd Wright and his wife Olgivanna founded a school in Spring Green, Wisconsin, where aspiring
artists could “learn by doing.”

Possessive Determiners
When a pronoun expresses ownership, it is placed in the possessive case.

Possessive determiners (its, your, their), contractions (it’s, you’re, they’re), and adverbs
(there) are often confused. Remember that personal pronouns that express ownership
never require an apostrophe.

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Incorrect: Frank Lloyd Wright believed that an architectural structure should be
in harmony with it’s environment.

Chapter 5

Correct: Frank Lloyd Wright believed that an architectural structure should be
in harmony with its environment.

English
Language
Conventions

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Skill Builder: Pronouns
DIRECTIONS: In the space provided, identify and explain the pronoun error contained in each statement.

1. The Battle of Yorktown was an important turning point in the American Revolution and the British defeat signaled
the end of it.

2. The American Bill of Rights was based on the English Bill of Rights; it protected the rights of the citizens.

3. While the Articles of Confederation is less famous than other historical documents like the Declaration of Independence and
the Constitution, it’s historical significance cannot be overstated.

4. Federalists and Anti-Federalists felt differently about the division of power between national and state governments. They
preferred more power be given to the states.

5. Thomas Paine was an American patriot who’s pamphlets Common Sense and The Crisis helped stir the American independence movement.

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Answers and Explanations

Chapter 5

1. It is unclear whether the “it” at the end of the sentence refers to the American Revolution or the Battle of Yorktown.
2. It is unclear whether the “it” that follows the semicolon refers to the American or English Bill or Rights or both.
3. “It’s” is a contraction; the correct word should be the possessive pronoun “its.”

English
Language
Conventions

4. It is unclear whether “they” refers to the Federalists or the Anti-Federalists.
5. “Who’s” is a contraction; the correct word should be the possessive pronoun “whose.”

Peterson’s SAT® Prep Guide 2017

AGREEMENT
Pronoun-Antecedent Agreement
A pronoun agrees with its antecedent in both person and number.
Example: The archaeologists examined the fossilized bone with great care to make sure they didn’t damage it.
Explanation: The pronoun they refers to archaeologists, its antecedent. The pronoun it refers to bone, its
antecedent.

Remember to use a singular pronoun when you refer to indefinite pronouns such as
everyone, everybody, each, every, anyone, anybody, nobody, none, no one, one, either,
and neither.
Examples:
Although Union High School’s male lacrosse players operate as a team, each
knows it’s his (not their) responsibility to arrive on time and in uniform.
Despite the fact that many of the women came from wealthy families,
everyone who attended the Seneca Falls conference on women’s rights risked
her (not their) life and reputation.
When the programmers were questioned, neither could be certain if it was
his or her (not their) mistake that caused the computer network to crash.

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Subject-Verb Agreement

Chapter 5
English
Language
Conventions

Basic Rule
A verb agrees in number with its subject. A singular subject takes a singular verb. A plural subject takes a plural verb.
Examples: Coral reefs are an important part of the marine ecosystem.
V
S
My teacher believes that coral reefs are an important part of the marine ecosystem.
S
V
V
S

For the following sentence, choose the correct verb: (is, am, are)
Booker T. Washington, Frederick Douglass, and W.E.B. DuBois _____ all important historical figures.
Explanation: Remember that the verb must agree with the subject. Since the subject is plural—subjects joined
by and are plural—a plural verb is needed. The correct response therefore should be:
Booker T. Washington, Frederick Douglass, and W.E.B. DuBois are all important historical figures.

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Sometimes the subject comes after the verb, but the rule still applies.
Choose the correct verb: (is, are)
While the lecture has lasted 2 hours already, there ____ still 3 more speakers.
Explanation: The correct choice is are since the subject speakers is plural and requires a plural verb.

There is one major exception to this rule. When the sentence is introduced by the
word “there” and the verb is followed by a compound (double) subject, the first part
of the subject dictates whether the verb should be singular or plural.
Example: There is one American astronaut in the shuttle and four Russian
astronauts in the space station.

When compound subjects are joined by either-or or neither-nor, the verb agrees with the subject closest to the verb.
Examples:
Neither the violinist nor the other musicians have had much experience performing for an audience.
Neither you nor I am willing to make the sacrifices required of a professional musician.
Explanation:
In the first example, musicians (plural) is closest to the verb; in the second example, I (singular) is closest
to the verb.
Sometimes a word or a group of words may come between the subject and the verb. The verb still must agree with the simple
subject, and the simple subject is never part of a prepositional phrase.

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Example:
Stephen King, the author of hundreds of best-selling novels, novellas, and short stories, is also a guitarist
and singer in a band.
The simple subject is Stephen King, a singular noun. The verb must be is.
Choose the correct verb: (was, were)
The causes of the deterioration of coral reefs ____ not known until recently.
Explanation:
The simple subject is causes; “of the deterioration of coral reefs” is a prepositional phrase. Since the
subject is plural, the plural verb were is required. So, the correct answer is were.
The third person singular of most verbs ends in “s.” First person: I, we speak;
second person: you speak; third person: he, she, it speaks. Examples:
He runs. She jogs. It jumps. The man sees. Mary laughs. The child walks.

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Collective Nouns
Collective nouns present special problems. A collective noun names a group of people or things. Although usually singular in
form, it is treated as either singular or plural according to the sense of the sentence:

• A collective is treated as singular when members of the group act, or are considered, as a unit:
Example: The citizens’ assembly is drafting a petition that would seek to protect local aquifers from chemical run-off
and hazardous waste.

• A collective is treated as plural when the members act, or are considered, as multiple individuals:
Example: After one of the longest and most fabled droughts in baseball history, the Boston Red Sox have finally
overcome the “Curse of the Bambino” to win another World Series.
Common collective nouns include:
assembly, association, audience, board, cabinet, class, commission, committee, company, corporation, council,
counsel, couple, crowd, department, family, firm, group, jury, majority, minority, number, pair, press, public, staff,
United States
The following short words—though seldom listed as collective nouns—are governed by the same rules. They are singular or
plural according to the intended meaning of the sentence.
all, any, more, most, some, who, which

Skill Builder: Agreement

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Conventions

DIRECTIONS: Follow the principles of agreement and choose the correct word.
1. (is, are) The President and Vice President of the United States of America ___ expected to attend tomorrow’s historic ceremony
honoring Rosa Parks.
2. (have, has) Either the chair of the department or one of the professors ___ the necessary paperwork.
3. (was, were) In the time of the first settlers, there ___ no antibiotics to prevent outbreaks of disease.
4. (its, their) Because of ___ biodiversity, coral reefs are often called “the rainforests of the sea.”
5. (her, their) After a brief introduction, each of the doctors presented ___ findings at the medical conference.
6. (is, are) Many young people are surprised to find out that the music of Verdi’s operas ____ as vibrant and fun as anything on
the radio.
7. (his, their) As the conductor took the podium, the musicians finished tuning ___ instruments.
8. (know, knows) Neither Sherlock Holmes nor the detectives of Scotland Yard ___ who the perpetrator is.
9. (is, are) According to preliminary market reports, either Xiaomi or Huawei ___ the biggest smartphone provider in China.
10. (is, are) However, neither the Republicans nor the Democrats ___ satisfied with the language of the new nuclear weapons
treaty.

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Answers and Explanations
1. The correct answer is are. The plural subject President and Vice President requires the plural are.
2. The correct answer is has. The verb must agree with the subject closest to it, in this case the singular one.
3. The correct answer is were. The plural subject antibiotics requires the plural were.
4. The correct answer is their. The plural subject coral reefs requires the plural their.
5. The correct answer is her. The singular subject each requires the singular her.
6. The correct answer is is. The singular subject music requires the singular is.
7. The correct answer is their. The plural antecedent musicians requires the plural their.
8. The correct answer is know. In a neither-nor construction, the verb is governed by the closest subject, detectives.
9. The correct answer is is. The singular determiner either requires the singular verb is.
10. The correct answer is are. In a neither-nor construction, the verb is governed by the closest subject, Democrats.

Skill Builder: Agreement
DIRECTIONS: Revise the underlined words to eliminate agreement errors. If the underlined word is grammatically
correct, write C above it. If a change is necessary, indicate the change and give a grammatical reason for it. Do not make
unnecessary changes.

Joseph, one of my best friends, are considering becoming a medical doctor. He and I believe that medicine, compared to
1
2
other professions, are an exciting and fulfilling field. In order to help him decide, he asked each of his friends to give his or her
3
opinion about why medicine would or would not be a fulfilling career choice. After that, he also asked his parents for their

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Language
Conventions

opinions. It seems that his friends and his mother is in agreement, but his father do not agree.
5
4
Jacob’s father feels strongly that the medical profession, unlike other professions, requires an excessive amount of study and is
6
too emotionally taxing. On the other hand, his friends and his mother agree that while the schooling is rigorous, the practice
7
itself would be very rewarding.

Jacob is still deciding what he wants to be, but he and I has learned that there is always many possible answers to a question.
8
9
10

Peterson’s SAT® Prep Guide 2017

Answers and Explanations
1. The correct answer is is. The subject, Joseph, is singular.
2. The correct answer is C. The subject, He and I, is plural.
3. The correct answer is is. The subject, medicine, is singular.
4. The correct answer is are. The subject, his friends and his mother, is plural.
5. The correct answer is does. The subject, father, is singular.
6. The correct answer is C. The subject, medical profession, is singular.
7. The correct answer is C. The subject, friends and mother, is plural.
8. The correct answer is C. The subject, Jacob, is singular.
9. The correct answer is have. The subject, he and I, is plural.
10. The correct answer is are. The subject, answers, is plural.

FREQUENTLY CONFUSED WORDS
The following pages review groups of words that are similar in sound and/or meaning and are generally found to be confusing
to students and adults alike. Misunderstanding what they mean or how they are used results in various usage problems. The
word groups have been broken down into manageable sections to help you learn them more easily. Do not try to master all the
information at once. Study one section at a time.

192

At the end of each section there is a practice exercise. See how well you do on the exercise by checking your answers against
the answers and explanations given. If you do well, go on to the next section. If you find that you have made a number of errors,
review the section. It is important that you master each section before moving on to the next one.

Chapter 5
English
Language
Conventions

Frequently Confused Words: Group 1
a is used before words that start with a consonant sound
an is used before words that start with a vowel sound
Please give the baby a toy.
He is an only child. We put up a united front. (United begins with a consonant sound—y.)
We spent an hour together. (Hour begins with a vowel sound, since the h is silent.)
and is used to join words or ideas
We enjoy shopping and sightseeing.
She is a very serious student, and her grades are the best in the class.

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accept means to receive or to agree to something
except means to exclude or excluding
I’ll accept the gift from you.
Everyone except my uncle went home.
My uncle was excepted from the group of losers.
advice means counsel (noun), opinion
advise means to offer advice (verb)
Let me give you some free advice.
I’d advise you to see your doctor.
affect means to influence (verb)
effect means to cause or bring about (verb) or a result (noun)
The pollution can affect your health.
The landmark decision will effect a change in the law.
The effect of the storm could not be measured.
all ready means everybody or everything ready
already means previously
They were all ready to write when the test began.
They had already written the letter.
all together means everybody or everything together
altogether means completely
The boys and girls stood all together in line.

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His action was altogether strange for a person of his type.
desert (DEZZ-ert) means an arid area
desert (di-ZERT) means to abandon, or a reward or punishment (usually plural)
dessert (di-ZERT) means the final course of a meal
I have seen several movies set in the Sahara desert.
The soldier was warned not to desert his company.
We’re certain that execution is a just desert for his crime.
He received his just deserts.
We had strawberry shortcake for dessert.

Peterson’s SAT® Prep Guide 2017

in is used to indicate inclusion, location, or motion within limits
into is used for motion toward one place from another
The spoons are in the drawer.
We were walking in the room.
I put the spoons into the drawer.
She walked into the room.
it’s is the contraction of it is or it has
its is a possessive pronoun meaning belonging to it
It’s a very difficult assignment.
We tried to analyze its meaning.
lay means to put
lie means to recline
To lay:
(present)		

I lay

(past)			

I laid the gift on the table.

(present perfect)

I have laid

To lie:

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(present)		

I lie

(past)			

I lay on my blanket at the beach.

(present perfect)

I have lain

lets is third person singular present of let
let’s is a contraction for let us
He lets me park my car in his garage.
Let’s go home early today.
loose means not fastened or restrained, or not tight-fitting
lose means to mislay, to be unable to keep, to be defeated
The dog got loose from the leash.
Try not to lose your umbrella.
passed is the past tense of to pass
past means just preceding or an earlier time
The week passed very quickly.
The past week was a very exciting one.

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principal means chief or main (adjective), or a leader, or a sum of money (noun)
principle means a fundamental truth or belief
His principal support comes from the real estate industry.
The principal of the school called a meeting of the faculty.
He earned 10 percent interest on the principal he invested last year.
As a matter of principle, he refused to register for the draft.
quiet means silent, still
quit means to give up, to discontinue
quite means very or exactly, to the greatest extent
My brother is very shy and quiet.
I quit the team last week.
His analysis is quite correct.
raise means to lift, to erect
raze means to tear down
rise means to get up, to move from a lower to a higher position, to increase in value
The neighbors helped him raise a new barn.
The demolition crew razed the old building.
The price of silver will rise again this month.
set means to place something down (mainly)
sit means to seat oneself (mainly)
To set:
(present)		

He sets

(past)			

He set the lamp on the table.

(present perfect)

He has set

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To sit:
(present)		

He sits

(past)			

He sat on the chair.

(present perfect)

He has sat

stationary means standing still
stationery means writing material
In ancient times, people thought that the earth was stationary.
We bought our school supplies at the stationery store.

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suppose means to assume or guess
supposed is the past tense and also past participle of suppose
supposed also means ought to or should (when followed by to)
I suppose you will be home early.
I supposed you would be home early.
I had supposed you would be there.
I am supposed to be in school tomorrow.
than is used to express comparison
then is used to express time or a result or consequence
Jim ate more than we could put on the large plate.
I knocked on the door, and then I entered.
If you go, then I will go, too.
their means belonging to them
there means in that place
they’re is the contraction for they are
We took their books home with us.

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Your books are over there on the desk.
They’re coming over for dinner.
though means although or as if
thought is the past tense of to think, or an idea (noun)
through means in one side and out another, by way of, finished
Though he is my friend, I can’t recommend him for this job.
I thought you were serious!
We enjoyed running through the snow.
to means in the direction of (preposition); it is also used before a verb to indicate the infinitive
too means very, also
two is the numeral 2
We shall go to school.
It is too hot today.
We shall go, too.
I ate two sandwiches for lunch.

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use means to employ, put into service
used is the past tense and the past participle of use
I want to use your chair.
I used your chair.
used meaning in the habit of or accustomed to, is followed by to
used is an adjective meaning not new
I am used to your comments.
I bought a used car.
weather refers to atmospheric conditions
whether introduces a choice; it should not be preceded by of or as to
I don’t like the weather in San Francisco.
He inquired whether we were going to the dance.
were is a past tense of be
we’re is a contraction of we are
where refers to place or location
They were there yesterday.
We’re in charge of the decorations.
Where are we meeting your brother?
who’s is the contraction for who is (or who has)
whose means of whom, implying ownership

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Who’s the next batter?
Whose notebook is on the desk?
your is a possessive, showing ownership
you’re is a contraction for you are
Please give him your notebook.
You’re very sweet.

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Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.

1. The patriot Samuel Adams was one of the (principal, principle) organizers of the Boston Tea Party.
2. Merchants in Boston refused to (accept, except) the taxes imposed upon them by the Tea Act of 1773.
3. Though the significance of the Tea Act of 1773 cannot be overrestimated, (weather, whether) or not the Tea Act of 1773 led
to the American Revolution is hard to say.
4. In late November of 1773, the ship the Dartmouth sailed (in, into) Boston Harbor.
5. Governor Hutchinson was determined to collect the taxes and (adviced, advised) the tea consignees not to back down.
6. More (than, then) 40 tons of tea were thrown into the water during the Boston Tea Party.
7. Tea smuggling was (all ready, already) a significant problem, especially in New York and Philadelphia.
8. The overall (affect, effect) of the Boston Tea Party was to bolster the revolutionary fervor that was sweeping New England.
9. The British Crown reacted swiftly and harshly in order to dispel the idea that they were (loosing, losing) control of the colonies.
10. (All together, Altogether) 342 chests of tea, weighing over 92,000 pounds, were dumped into the water.

Answers
1. principal
2. accept

198

3. whether

Chapter 5

5. advised

English
Language
Conventions

4. into

6. than
7. already
8. effect
9. losing
10. altogether

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Frequently Confused Words: Group 2
abbreviate means to shorten by omitting
abridge means to shorten by condensing
New York is abbreviated to NY.
In order to save time in the reading, the report was abridged.
ad is used informally, but in formal usage advertisement is correct; similarly: exam (examination), auto (automobile), phone
(telephone), gym (gymnasium)
advantage means a superior position
benefit means a favor conferred or earned (as a profit)
He had an advantage in experience over his opponent.
The rules were changed for his benefit.
aggravate means to make worse
annoy means to bother or to irritate
Your nasty comments aggravated a bad situation.
Your nasty comments annoyed him. (Not: Your nasty comments aggravated him.)
ain’t is an unacceptable contraction for am not, are not, or is not, although ain’t is sometimes heard in very informal speech
alibi is an explanation on the basis of being in another place
excuse is an explanation on any basis
The accused man’s alibi was that he was in another town when the robbery occurred.
Whenever he is late, he makes up a new excuse.

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all ways means in every possible way
always means at all times
He was in all ways acceptable to the voters.
He was always ready to help.
almost means nearly, not quite
most refers to the greatest amount or number or to the largest part, a majority
We are almost finished writing the book.
Most of the credit should be given to his uncle.
alongside of means side by side with
alongside means parallel to the side

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He stood alongside of her at the corner.
Park the car alongside the curb.
allot means to give or apportion
I will allot 3 hours for painting the table.
alot is a misspelling of a lot
He earned a lot of money. (Better: He earned a great deal of money.)
alright is now often employed in common usage to mean all right (In formal usage, all right is still preferred by most authorities.)
all right means satisfactory, very well, uninjured, or without doubt
I’m alright, thank you.
It was his responsibility, all right.
alternate, as a noun, means a substitute or second choice
alternate, as a verb, means to perform by turns
alternative means a choice between two things, only one of which may be accepted
She served as an alternate delegate to the convention.
The cook alternated green beans and cauliflower on the menu.
Is there an alternative to the proposition? (In less formal usage, alternative is not always limited to a choice between two.)

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Language
Conventions

alumna means a female graduate (plural: alumnae; ae rhymes with key)
alumnus means a male graduate (plural: alumni; ni rhymes with high)
She is an alumna of Mrs. Brown’s School for Young Women.
He is an alumnus of City College.
among is used to discuss more than two items
between is used to discuss two items only
The work was divided among the four brothers.
She divided the pie between Joe and Marie.
amount is used to refer to a quantity not individually countable
number is used to refer to items that can be counted individually
A tremendous amount of work had piled up on my desk.
We ate a great number of cookies at the party.
annual means yearly
biannual means twice a year (also semiannual)

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biennial means once in two years or every two years
Are you going to the annual holiday party?
I received biannual car insurance statements in April and in October.
He gets a new car biennially.
anxious means worried
eager means keenly desirous
We were anxious about our first airplane flight.
I am eager to see you again.
anyways is an incorrect form for anyway
anywheres is an incorrect form for anywhere
I didn’t want to go anyway.
I couldn’t locate her anywhere.
aren’t I is used informally, but in formal usage am I not is correct
Am I not entitled to an explanation?
as is not always as clear as because, for, or since (also see like)
She wants to cry because she is very sad.

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as, used as a conjunction, is followed by a verb
like, used as a preposition, is not followed by a verb

Chapter 5

Do as I do, not as I say.

English
Language
Conventions

Try not to behave like a child.
as … as is used in an affirmative statement
so … as is used in a negative statement
She is as talented as any other actress in the show.
He is not so reliable as his older brother.
as good as is used for comparisons, not to mean practically
This bicycle is as good as the other one.
They practically promised us a place in the hall. (Not: They as good as promised us a place in the hall.)
astonish means to strike with sudden wonder
surprise means to catch unaware
The extreme violence of the hurricane astonished everybody.
A heat wave in April would surprise us.

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at should be avoided when it does not contribute to the meaning of an idea
Where do you live at? may be heard in informal usage, but Where do you live? is the correct form.
The group will arrive about noon. (not at about noon)
awfully is sometimes heard in informal usage. In formal usage, very is correct.
This pie is very good. (not awfully good)
a while is used after a preposition (noun)
awhile is used in other cases (adverb)
I coached the team for a while.
I coached the team awhile.
backward and backwards both may be used as adverbs
We tried to skate backward. (Or: We tried to skate backwards.)
bad is used after verbs that refer to the senses, such as look, feel (adjective)
badly means greatly, in a bad manner (adverb)
He felt bad that he could not attend the meeting.
The young man needs a part-time job very badly.

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been is the past participle of to be, used after helping verbs have, has, or had
being is the -ing form of to be, usually used after helping verbs is, am, are, was, and were
I have been living here for six years.
He was being a troublemaker, so we told him to stay away from us.
being as and being that should not be used in standard English. Because and since are preferable.
Since it was dark, we turned on the lights.
Because he is my friend, I give him a gift.

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Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.
1. The (abbreviated, abridged) jobs report omitted jobs in the arts in order to make the report more manageable.
2. Detectives often ask suspects if they have an (alibi, excuse) for where they were on the night of a given crime.
3. Animal trainers must (allot, a lot) a significant amount of their work time to building a relationship with their animals.
4. The famous dog trainer Felix Ho is an (alumna, alumnus) of La Trobe University in Melbourne, Australia.
5. Animal care and service workers often divide their time (among, between) training, feeding, grooming, and exercising their
animals.
6. Learning how to be an effective animal trainer requires a tremendous (amount, number) of work.
7. Animals form very real bonds with their trainers; likewise, trainers are often (anxious, eager) to see their animals when they
have been away.
8. While horse trainers rarely have formal schooling in their field, they can’t get their training just (anywhere, anywheres).
9. Becoming a good animal trainer requires experience that can be (awfully, very) difficult to attain.
10. Many animal trainers feel (bad, badly) when they have to leave their animals for long periods of time.
11. (Because, Being that) zookeepers and marine mammal trainers require formal education, they tend to make more money
than other animal care professionals.

Answers
1. abbreviated

203

2. alibi

Chapter 5

3. allot

English
Language
Conventions

4. alumnus
5. among
6. amount
7. eager
8. anywhere
9. very
10. bad
11. Because

Peterson’s SAT® Prep Guide 2017

Frequently Confused Words: Group 3
beside means at the side of
besides means in addition to
In our tennis game, he played beside me at the net.
We entertained Jim, Sue, and Louise, besides the members of the chorus.
better means recovering
well means completely recovered
better is used with the verb had to show desirability
He is better now than he was a week ago.
In a few more weeks, he will be well.
He had better (not he better) follow instructions or pay the penalty.
between you and I is the incorrect form, since the object of the preposition between should be the objective case me, not the
subjective case I
Between you and me, he has not been very helpful this week.
both means two considered together

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each means one of two or more
Both of the applicants qualified for the position.
Each applicant was given a good reference.
bring means to carry toward the speaker
take means to carry away from the speaker
Bring the coat to me.
Take money for carfare when you leave.
bunch is used informally to describe a group of people, but in formal usage group is preferred
When he returned to his office, he learned that a group of students was waiting for him.
burst is used in present and past tenses to mean to explode (or to break)
bust and busted are incorrect forms of burst
I do hope the balloon will not burst.
He cried when the balloon burst. (not busted)
but that is sometimes heard in informal usage, but in formal usage that is correct
He never doubted that she would visit him.

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can means able
may implies permission or possibility
I can eat both desserts.
May I eat both desserts?
It may snow tonight.
cannot seem is sometimes used informally, but in formal usage seems unable is correct
My elderly uncle seems unable to remember his own phone number.
complected should not be used for complexioned
At the beach, the fair-complexioned boy stayed under an umbrella.
consistently means in harmony
constantly means regularly, steadily
If you give me advice, you should act consistently with that advice.
I constantly warned him about leaving the door unlocked.
continual means happening again and again at short intervals
continuous means without interruption
The teacher gave the class continual warnings.

205

Noah experienced continuous rain for forty days.
could of is an incorrect form of could have, which can be contracted to could’ve in speech or informal writing
I wish that I could’ve gone. (Better: I wish that I could have gone.)

Chapter 5
English
Language
Conventions

couple refers to two; several or a few refers to more than two
Alex and Frieda are the most graceful couple on the dance floor.
A few of my cousins—Mary, Margie, Alice, and Barbara—will be at the reunion tonight.
data is the Latin plural of datum, meaning information (data is preferred with plural verbs and pronouns, but is now acceptable
in the singular)
These data were very significant to the study. (Or: This data was very significant to the study.)
did is the past tense of do
done is the past participle of do
I did whatever was required to complete the job.
I have done what you requested.

Peterson’s SAT® Prep Guide 2017

different than is often used informally, but in formal usage different from is correct
Jack is different from his brother.
disinterested means impartial
uninterested means not interested
The judge must be a disinterested party in a trial.
I’m an uninterested bystander, so I find the proceedings boring.
doesn’t is a contraction of does not (third person singular)
don’t is a contraction of do not and is not a substitute for doesn’t
She doesn’t go to school.
They don’t go to school.
doubt whether is often heard in informal usage, but doubt that is the correct form
I doubt that I will be home this evening.
due to is sometimes used informally at the beginning of a sentence, but in formal usage because of, on account of, or some similar
expression is preferred
Because of (not due to) the rain, the game was postponed. (But: The postponement was due to the rain.)
each other refers to two persons

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Language
Conventions

one another refers to more than two persons
Jane and Jessica have known each other for many years.
Several of the girls have known one another for many years.
either … or is used to refer to choices
neither … nor is the negative form
Either Lou or Jim will drive you home.
Neither Alice nor Carol will be home tonight.
else than is sometimes heard in informal usage, but in formal usage other than is correct
Shakespeare was rarely regarded by students as anything other than the writer of plays.
enthuse or enthused should be avoided; use enthusiastic
We were enthusiastic when given the chance to travel abroad.
equally as good is an incorrect form; equally good or just as good is correct
This bicycle is just as good as that one.

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etc. is the abbreviation for the Latin term et cetera, meaning and so forth, and other things. In general, it is better to be specific
and not use etc.
I think that oranges, peaches, cherries, etc., are healthful. (Etc. is not preceded by and)
everyone, written as one word, is a pronoun
every one, written as two words, is used to refer to each individual
Everyone present voted for the proposal.
Every one of the voters accepted the proposal.
every bit is incorrect usage for just as
You are just as (not every bit as) clever as she is.
ever so often means frequently or repeatedly
every so often means occasionally or now and again
He sees his brother ever so often, practically every day.
Since tickets are so expensive, we only attend the theater every so often.
expect is sometimes used incorrectly to mean assume or presume
I assume (not expect) that he won the race.

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Language
Conventions

Peterson’s SAT® Prep Guide 2017

Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.
1. (Beside, Besides) needing a bachelor’s degree in marine biology, animal science, biology, or a related field, marine mammal
trainers often need to have SCUBA certification.
2. Between you and (me, I), training lions does not sound like fun!
3. After a rigorous application process, (both, each) of the trainers were hired.
4. A dog trainer might begin with a simple task, such as training a dog to (bring, take) a rubber ball back to him.
5. Young students often ask zookeepers, “(Can, May) I help you feed the animals?”
6. While job opportunities in kennels, grooming shops, and pet stores are increasing, many advanced animal care professionals,
such as zookeepers and marine mammal trainers, (cannot seem, seem unable) to find work.
7. In jobs surveys, the percentage of nonfarm animal caretakers (consistently, constantly) outnumbers the number of actual
animal trainers.
8. Here are a (couple, few) examples of what an animal care specialist might do: give food and water to animals; clean equipment and the living spaces of animals; monitor animals and record details of their diet, physical condition, and behavior;
and examine animals for signs of illness or injury.
9. Even though they sound the same, the job of a pet groomer is very (different from, different than) the job of a horse groom.
10. (Because of, Due to) employment growth and high job turnover, job opportunities in the animal care and services field will
continue to grow.

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Language
Conventions

11. The starting salary for animal care and service workers is (equally as good, just as good) as the starting salary for nonfarm
animal caretakers.

Answers
1. Besides
2. me
3. both
4. bring
5. May
6. seem unable
7. constantly
8. few
9. different from
10. Because of
11. just as good

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Frequently Confused Words: Group 4
fewer is used to refer to items that can be counted
less is used to refer to something viewed as a mass, not as a series of individual items
I made fewer repairs on the new car than on the old one.
After the scandal, the company enjoyed less prestige than it had the previous year.
finalized is used to mean concluded or completed, usually in informal usage; in formal usage, completed is preferred
Labor and management completed arrangements for a settlement.
flaunt means to make a display of
flout means to show contempt, scorn
He flaunted his new wealth in an ostentatious manner.
She flouted the policeman’s authority.
former means the first of two
latter means the second of two
The former half of the story was in prose.
The latter half of the story was in poetry.
good is an adjective; good is often used informally as an adverb, but the correct word is well
She is a good singer.
She sings well.
graduated is followed by the preposition from when it indicates completion of a course of study
graduated also means divided into categories or marked intervals

209
Chapter 5
English
Language
Conventions

He graduated from high school last year. (Or: He was graduated from high school last year.)
A graduated test tube is one that has markings on it to indicate divisions.
guess is sometimes used informally to mean think or suppose, but it is incorrect in formal use
I think (not guess) I’ll go home now.
habit means an individual tendency to repeat a thing
custom means group habit
He had a habit of breaking glasses before each recital.
The custom of the country was to betroth girls at an early age.

Peterson’s SAT® Prep Guide 2017

had ought is an incorrect form for ought or should
hadn’t ought is an incorrect form for should not or ought not
The men ought (not had ought) to go to the game now.
He ought not (not hadn’t ought) to have spoken.
He should not (not hadn’t ought) have spoken.
hanged is used in reference to a person
hung is used in reference to a thing
The prisoner was hanged in the town square.
The drapes were hung unevenly.
have got is incorrect usage; got should be omitted
I have an umbrella.
healthful is used to express whatever gives health
healthy is used to express whatever has health
He follows a healthful diet.
He is a healthy person.
hisself is a misspelling of himself

210
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Language
Conventions

Let him do it himself.
humans is used informally to refer to human beings, but in formal usage human beings is correct
He says that love is a basic need of all human beings. (But used as an adjective: He says that love is a basic human need.)
if introduces a condition
whether introduces a choice
I shall go to Greece if I win the prize.
He asked me whether I intended to go to Greece.
if it was implies that something might have been true in the past
if it were implies doubt or indicates something that is contrary to fact
If your book was there last night, it is there now.
If it were summer now, we would all go swimming.
imply means to suggest or hint at (the speaker implies)
infer means to deduce or conclude (the listener infers)
Are you implying that I have disobeyed orders?
From your carefree tone, what else are we to infer?

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in back of means behind
in the back of (or at the back of) means in the rear of
The shovel is in back of (behind) the barn.
John is sitting in the back of the theater.
in regards to is an incorrect form for in regard to
He called me in regard to your letter.
instance where is sometimes used informally, but the correct term is instance in which
Can you tell me of one instance in which such a terrible thing occurred?
irregardless in an incorrect form for regardless
I’ll be your friend regardless of what people say, even if the people are accurate.
is when and is where are sometimes used informally, but in formal usage occurs when and is a place where are correct
The best scene occurs when the audience least expects it.
My favorite vacation spot is a place where there are no telephones.
kind of and sort of are informal expressions that should be rephrased in formal writing—for instance, somewhat or rather are
preferable
I am rather sorry he retired.
He was somewhat late for the meeting.
kid is used informally to mean child (noun) or to make fun of (verb) but is incorrect in formal usage
My cousin is a very sweet child.
They always laugh when you make fun of me.
learn means to acquire knowledge

211
Chapter 5
English
Language
Conventions

teach means to give knowledge
We can learn many things just by observing carefully.
He is one actor who likes to teach his craft to others.
least means the smallest in degree or lowest rank
less means the smaller or lower of two
This is the least desirable of all the apartments we have seen.
This apartment is less spacious than the one we saw yesterday.

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leave means to go away from (a verb is NOT used with leave)
let means to permit (a verb IS used with let)
Leave this house at once.
Let me remain in peace in my own house.
lend is a verb meaning to give to
loan is a noun denoting what is given
borrow means to take from
The bank was willing to lend him $500.
He was granted a loan of $500.
I’d like to borrow your electric drill for an hour.
liable means responsible according to the law
likely suggests probable behavior
If he falls down the stairs, we may be liable for damages.
A cat, if annoyed, is likely to scratch.
libel is a written and published statement injurious to a person’s character

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Conventions

slander is a spoken statement of the same sort
The unsubstantiated negative comments about me in your book constitute libel.
When you say these vicious things about me, you are committing slander.
like is a preposition used to introduce a phrase
as if is used to introduce a clause (a subject and a verb)
as is a conjunction used to introduce a clause
like if is an incorrect form for like, as, or as if
It seems like a sunny day.
It seems as if it is going to be a sunny day.
He acted as he was expected to act.
many refers to a number
much refers to a quantity or amount
How many inches of rain fell last night?
Much rain fell last night.
may of is an incorrect form for may have
might of is an incorrect form for might have

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NOTE: Contractions of these terms are unacceptable in formal usage.
He may have been there, but I didn’t see him.
I might have gone to the party if I hadn’t been ill.

Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.
1. As of 2012, the median annual wage for nonfarm animal caretakers is (less, fewer) than $20,000.
2. During the interrogation, the lawyer (flaunted, flouted) his authority as he questioned the accused thief.
3. In addition to being patient with animals, animal caretakers must also work (good, well) with people!
4. She is one of 2,200 people to (graduate, graduate from) the National Association of Professional Pet Sitters’ certification program.
5. While in captivity, many animals develop nervous (customs, habits), such as pacing and over-grooming.
6. While it is usually not required, animal caretakers in shelters (ought, had ought) to attend training programs through the
Humane Society of the United States and the American Humane Association.
7. Keepers in zoos plan diets, monitor eating patterns, and clean enclosures in order to maintain (healthful, healthy) animals.
8. Often, the difference between the needs of animals and (human beings, humans) is not as great as you think.
9. (Irregardless, Regardless) of one’s education, the number one trait an animal trainer must have is a love for animals.
10. While it does happen, it is (rather, sort of ) rare for a groom to be hired who does not have significant prior experience with
horses.

213

11. Animal trainers take good care of their animals because when animals are neglected, they are more (liable, likely) to become
aggressive and dangerous.

Chapter 5

Answers

English
Language
Conventions

1. less
2. flaunted
3. well
4. graduate from
5. habits
6. ought
7. healthy
8. human beings
9. Regardless
10. rather
11. likely

Peterson’s SAT® Prep Guide 2017

Frequently Confused Words: Group 5
maybe means perhaps, possibly (adverb)
may be shows possibility (verb)
Maybe he will meet us later.
He may be here later.
mighty means powerful or great; it should not be used in formal writing to mean very
He was very (not mighty) sleepy.
media is the Latin plural of medium; it refers to a means of mass communication or artistic expression and is used with a plural verb
Most media that report the news realize their responsibility to the public.
That artist’s favorite medium is watercolor.
must of is an incorrect form for must have
I must have been sleeping when you called. (A contraction of this term is unacceptable in formal usage.)
myself is used as an intensifier if the subject of the verb is I
myself instead of I or me is not correct
Since I know myself better, let me try it my way.
My daughter and I (not myself) will play.

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Language
Conventions

They gave my son and me (not myself) some food.
nice is used informally to mean pleasing, good, fine, but a more exact, less overused word is preferred
This is sunny (or good or fine) weather (not nice weather).
He is a good (or kind) person.
nowheres is incorrect usage for nowhere
The dog was nowhere to be found.
off of is sometimes used informally, but off is correct in formal usage
Joe was taken off the team.
okay (O.K.) is used informally but is to be avoided in formal writing
Informal: His work is okay.
Formal: His work is acceptable (or good).
on account of is an incorrect form of because
We could not meet you because we did not receive your message in time.
oral means spoken
verbal means expressed in words, either spoken or written

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Instead of writing a note, she gave him an oral message.
Shorthand must usually be transcribed into verbal form.
outdoor is an adjective
outdoors is an adverb
We spent the summer at an outdoor music camp.
We played string quartets outdoors.
owing to is used informally, but in formal usage because is preferred
Because of a change of management, his company canceled the takeover attempt.
people comprise a united or collective group of individuals
persons are individuals who are separate and unrelated
The people of our city will vote next week.
Only ten persons remained in the theater after the first act.
per is a Latin term used mainly in business: per diem (by the day), per hour (by the hour). In formal writing, according to or by the
is preferred
As per your instructions... (Better: According to your instructions...)
plan on is used informally, but in formal usage plan to is correct
Do you plan to go (not plan on going) to the lecture?
plenty means abundance (noun)
plenty is incorrect as an adverb or adjective
There is plenty of room in that compact car.
That compact car is very large (not plenty large).

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Conventions

prefer that than is the incorrect form for prefer that to
I prefer that to anything else you might suggest.
put in is incorrect for to spend, make, or devote
Every good student should spend (not put in) several hours a day doing homework.
Be sure to make (not put in) an appearance at the meeting.
quit is sometimes used informally to mean stop, but in formal usage stop is preferred
Please stop your complaining.
quite is used to mean very in informal usage, but in formal usage very is preferred
Your comment was very (not quite) intelligent.

Peterson’s SAT® Prep Guide 2017

quite a few is used to mean many in informal usage, but in formal usage many is preferred
My car has many (not quite a few) dents.
read where is heard in informal usage, but in formal usage read that is correct
I read that the troops were being reviewed today.
real is sometimes used informally instead of really or very, but in formal usage really is correct
He’s a very (not real) good ballplayer.
He plays really (not real) well with the band.
reason is because is used informally in speech, but in formal usage the reason is that is correct
The reason she calls is that (not because) she is lonely. (Or: She calls because she is lonely.)
refer back/report back: since re means back or again, the word back is redundant and should be omitted
Please refer to your notes.
Please report to the supervisor.
repeat again is redundant; again should be omitted
Please repeat the instructions.
respectfully means with respect and decency
respectively means as relating to each, in the order given

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Conventions

The students listened respectfully to the principal.
Jane and Lena are the daughters respectively of Mrs. Smith and Mrs. Jones.
run is used informally to mean conduct, manage, but in formal usage conduct or a similar word is preferred
He wants to conduct (not run) the operation on a profitable basis.
said is sometimes used in business or law to mean the or this; in formal usage, the or this is correct
said is also used incorrectly to mean told someone
When the (not said) coat was returned, it was badly torn.
The professor told us (not said) to study for the examination.
same as is an incorrect form for in the same way as or just as
The owner’s son was treated in the same way as any other worker.
says is present tense of say
said is past tense of say
He says what he means.
He said what he meant. (Goes or went should not be used instead of says or said.)

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Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.
1. If you are interested in the social and organizational side of businesses, the field of organizational psychology (may be,
maybe) the field for you.
2. As the economy continues to grow and more businesses are created, organizational psychology is becoming a (mighty, very)
important field.
3. (Because of, On account of ) their collaborative work with social workers and healthcare professionals, demand for psychologists is expected to increase in tandem with the healthcare industry overall.
4. (Nowhere, Nowheres) is the demand for psychologists growing more than in the field of organization psychology.
5. Because of the importance of talking with patients, clinical psychologists are expected to have good (oral, verbal) communication skills.
6. Psychologists typically work in offices, so if you prefer working (outdoor, outdoors), this might not be the job for you.
7. Over the next decade, the job market for psychologists will continue to grow in large part (because of, owing to)
increased demand for psychological services in schools, hospitals, mental health centers, and social services agencies.
8. Most (people, persons) don’t realize that there is a difference between a Ph.D. in psychology (a research degree) and a Psy.D.
(a clinical degree).
9. While a master’s degree is sufficient for some positions, most aspiring psychologists (plan on getting, plan to get) a Ph.D. or
a Psy.D.
10. In addition to formal schooling, most clinical psychologists (put in, spend) hundreds of unpaid hours as interns in their fields
of specialization.
11. The reason most aspiring psychologists get Ph.D.’s and Psy.D.’s is (because, that) there are more jobs available for psychologists
with terminal degrees.

Answers

217
Chapter 5
English
Language
Conventions

1. may be
2. very
3. Because of
4. Nowhere
5. oral
6. outdoors
7. because of
8. people
9. plan to get
10. spend
11. that

Peterson’s SAT® Prep Guide 2017

Frequently Confused Words: Group 6
saw is the past tense of see
seen is the past participle of see
We saw a play yesterday.
I have never seen a Broadway show.
seem is used in informal speech and writing in the expressions I couldn’t seem to and I don’t seem to but in formal usage:
We can’t find the address. (Not: We can’t seem to find the address.)
seldom ever is used informally, but in formal usage ever is redundant and should be omitted, or if should be inserted
I seldom swim in January.
I seldom if ever swim in January.
shall is used with I and we in formal usage; informally, I will (would) may be used
will is used with you, he, she, it, they
When an emphatic statement is intended, the rule is reversed
I shall be there today.
We shall pay the rent tomorrow.
I certainly will be there.

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Language
Conventions

They shall not pass.
shape is incorrect when used to mean state or condition
The refugees were in serious condition (not shape) when they arrived here.
should of is an incorrect form for should have, which can be contracted to should’ve in speech or informal writing
You should’ve returned that sweater. (Better: You should have returned that sweater.)
sink down is sometimes heard in informal usage, but down is redundant and should be omitted
You can sink into the mud if you are not careful.
some time means a segment of time
sometime means at an indefinite time in the future
sometimes means occasionally
I’ll need some time to make a decision.
Let’s meet sometime next week.
Sometimes I have an urge to watch a late movie on television.

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stayed means remained
stood means took or remained in an upright position or erect
He stayed in bed for three days.
The scouts stood at attention while the flag was lowered.
still more yet is redundant; yet should be omitted
There is still more to be said.
sure is used informally to mean surely or certainly, but in formal usage surely or certainly is preferred
She certainly (not sure) is pretty!
We will surely be in trouble unless we get home soon.
testimony means information given orally
evidence means information given orally or in writing; an object that is presented as proof
He gave testimony to the grand jury.
He presented written evidence to the judge.
than any is used informally in a comparison, but in formal usage than any other is preferred
He is smarter than any other boy in the class.
the both is used informally, but in formal usage the should be omitted

219

I intend to treat both of you to lunch.
their, in informal usage, often appears in the construction, “Anyone can lose their card,” but because anyone takes a singular
personal pronoun, his or her is the correct form

Chapter 5
English
Language
Conventions

theirselves is an incorrect form for themselves
They are able to care for themselves while their parents are at work.
them is the objective case of they; it is not used instead of those (the plural of that) before a noun
Give me those (not them) books!
try and is sometimes used informally instead of try to, but in formal usage try to is correct
My acting teacher is going to try to attend the opening of my play.
unbeknownst to is unacceptable for without the knowledge of
The young couple decided to get married without the knowledge of (not unbeknownst to) their parents.
upwards of is an incorrect form for more than
There are more than (not upwards of) 60,000 people at the football game.

Peterson’s SAT® Prep Guide 2017

valuable means of great worth
valued means held in high regard
invaluable means priceless
This is a valuable manuscript.
You are a valued friend.
A good name is an invaluable possession.
wait on is sometimes used informally, but in formal usage wait for is correct
We waited for (not on) him for over an hour.
which is sometimes used incorrectly to refer to people; it refers to things
who is used to refer to people
that is used to refer to people or things
He decided to wear his orange striped tie, which had been a gift from his daughter.
I am looking for the girl who made the call.
He finally returned the books that he had borrowed.
while is unacceptable for and, but, whereas, or though
The library is situated on the south side, whereas (not while) the laboratory is on the north side.

220

Though (not while) I disagree with you, I shall not interfere with your right to express your opinion.
who is, who am is used with these constructions:

Chapter 5
English
Language
Conventions

It is I who am the most experienced.
It is he who is...
It is he or I who am...
It is I or he who is...
It is he and I who are...
who, whom To determine whether to use who or whom (without grammar rules), use he, him:
(Who, Whom) do you think should represent our company?
Step 1:

Change the who—whom part of the sentence to its natural order:

		

Do you think (who, whom) should represent our company?

Step 2:

Substitute he for who, and him for whom:

		

Do you think (he, him) should represent our company?

Step 3:

Since he would be used in this case, the correct form is:

		

Who do you think should represent our company?

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whoever, whomever (see who, whom above)
Give the chair to whoever wants it (subject of verb wants).
Speak to whomever you see (object of preposition to).
win is used when you win a game
beat is used when you beat another player; beat is incorrect usage for swindle
We won the contest.
We beat (not won) the other team.
The hustler swindled the gambler out of twenty dollars.
without is incorrect usage for unless
You will not receive the tickets unless (not without) you pay for them in advance.
worst kind and worst way are incorrect usages for terms such as very badly or extremely
The school is greatly in need of more teachers (not needs teachers in the worst way).
would of is an incorrect form for would have, which can be contracted to would’ve in informal usage
He would’ve treated you to the movies. (Better: He would have treated you to the movies.)
would have is not used instead of had in an if clause
If I had (not would have) gone, I would have helped him.

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Peterson’s SAT® Prep Guide 2017

Skill Builder: Usage
DIRECTIONS: Circle the correct word to complete the sentence while adhering to formal American-English conventions.
1. In Sir Arthur Conan Doyle’s story, “A Scandal in Bohemia,” Sherlock Holmes (can’t believe, can’t seem to believe) that he’s been
outsmarted by the beautiful and alluring Irene Adler.
2. Forest conservation workers are (seldom, seldom ever) required to have education beyond a basic bachelor’s degree.
3. According to his fictional biography, Sherlock Holmes’s friend, John H. Watson, returns to England in serious (condition,
shape) after being wounded in the Second Anglo-Afghan War.
4. (Some time, Sometime) in the near future, the U.S. Forest Service may be forced to undertake its own fire suppression duties,
which will result in higher levels of employment.
5. At the end of all Sherlock Holmes stories, Holmes presents (evidence, testimony) that shows how a crime was committed
and whom it was committed by.
6. According to some scholars, Sherlock Holmes is more recognizable (than any, than any other) fictional detective in the world.
7. The complexity of the Tube, Britain’s underground railway system, makes it possible for anyone to lose (his or her, their) way.
8. In the event that they get lost, forest service workers need to be able to take care of (theirselves, themselves) in the wild.
9. If formal schooling is unavailable, aspiring forest and conservation services workers should (try and, try to) gain experience
working in forestry-related fields.
10. As of 2012, there were (more than, upwards of ) 10,000 jobs in the forest and conservation services field.

222
Chapter 5
English
Language
Conventions

Answers
1. can’t believe
2. seldom
3. condition
4. Some time
5. evidence
6. than any other
7. his or her
8. themselves
9. try to
10. more than

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Conventional Expressions
A conventional expression is a phrase or clause that has become a characteristic way of expressing a certain idea. Ironically,
despite these expressions being conventional, they are often misused.
Here is a list of commonly misused conventional expressions and their correct usages.

Incorrect Usage

Correct Usage

It’s a doggy-dog world

It’s a dog-eat-dog world

For all intensive purposes

For all intents and purposes

I’m suppose to go running

...supposed to…

statue of limitations

statute of limitations

I could care less

I couldn’t care less

Fall by the waste side

Fall by the wayside

Irregardless

Regardless

Escape goat

Scapegoat

I guess we’ll make due

...make do...

Peak my interest

Pique my interest

The criminal got away scott free

...scot free...

I’m waiting with baited breath

...bated breath...

Without further adieu

Without further ado

The boy had free reign

...free rein...

Hunger pains

Hunger pangs

I should of called

...should have...

Don’t step foot on this carpet

...set foot...

Nipped in the butt

Nipped in the bud

The waiter was at his beckon call

...beck and call...

The lawyer made a mute point

...moot point...

Case and point

Case in point

The cops were starting to hone in

...home in...

One in the same

One and the same

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Language
Conventions

Peterson’s SAT® Prep Guide 2017

Logical Comparison
Basic Rule
In order for a comparison to make sense, it must be logical and complete.
In an incomplete comparison, what is being compared is unclear.
Incomplete: According to some scholars of U.S. history, the Magna Carta is more important because it was the first
document to limit the powers of the King of England.
Complete: According to some scholars of U.S. history, the Magna Carta is more important than the Declaration of
Independence because it was the first document to limit the powers of the King of England.
Incomplete: At 864,000 miles across, the Sun is more than 100 times the size.
Complete: At 864,000 miles across, the Sun is more than 100 times the size of Earth.
For a comparison to be logical, you must be comparing the same things.
Illogical: Despite popular opinion, many scholars believe that the political achievements of Thomas Jefferson were
much more significant to American history than George Washington. (Thomas Jefferson’s achievements are being
compared to the person George Washington.)
Logical: Despite popular opinion, many scholars believe that the political achievements of Thomas Jefferson were
much more significant to American history than the achievements of George Washington.

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Illogical: The distance from the Sun to the planet Neptune is 30 times greater than the Sun and Earth. (This distance
from the Sun to Neptune is being compared to the Sun and Earth, not the distance between them.)

Chapter 5

Logical: The distance from the Sun to the planet Neptune is 30 times greater than the distance from the Sun to
Earth.

English
Language
Conventions

Skill Builder: Logical Comparisons
DIRECTIONS: Revise the following comparisons to make sure they are logical.

1. According to scientists, the brain mass of a dolphin is actually slightly greater than a human.

2. Although they are on the same hemisphere, the average rainfall in South America differs greatly from North America.

3. In the 2015 World Happiness Report, the people of Switzerland ranked happier than America.

4. The tallest mountain in the United States is still 9,000 feet shorter than Nepal.

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Answers
1. According to scientists, the brain mass of a dolphin is actually slightly greater than the brain mass of a human.
2. Although they are on the same hemisphere, the average rainfall in South America differs greatly from the average rainfall
in North America.
3. In the 2015 World Happiness Report, the people of Switzerland ranked happier than the people of America.
4. The tallest mountain in the United States is still 9,000 feet shorter than the tallest mountain in Nepal.

CONVENTIONS OF PUNCTUATION
End-of-Sentence Punctuation
There are three types of punctuation used to end a sentence: the period, the question mark, and the exclamation mark.
1.

A period is used at the end of a sentence that makes a statement.
Examples:
Toni Morrison’s first novel, The Bluest Eye, was published in 1970.
In 1620, the Pilgrims in Plymouth signed the Mayflower Compact.

2.

A question mark is used after a direct question. A period is used after an indirect question.
Examples:
Direct Question—Were The Federalist Papers written by James Madison, John Jay, or Alexander Hamilton?
Indirect Question—Profession Mahin wanted to know if you knew who wrote The Federalist Papers.

3.

An exclamation mark is used after an expression that shows strong emotion or issues a command. It may follow a word, a
phrase, or a sentence.
Examples:

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Koko the gorilla knows more than 1,000 sign-language signs and can communicate with humans.
Amazing!
One of the most famous quotes in American history is Patrick Henry’s, “Give me liberty or give me
death!”

Peterson’s SAT® Prep Guide 2017

Within-Sentence Punctuation
The Colon
Basic Rule
The colon is used to precede a list of three or more items or a long quotation.
Examples:
Christopher Columbus led three ships to the New World: La Nina, La Pinta, and La Santa Maria.
In the United States, there are three branches of government: the Executive, the Legislative, and the
Judicial.

Avoid using the colon after a verb. It can interrupt the natural flow of language.
Incorrect: The Louisiana Purchase included territory that would become:
Montana, South Dakota, Nebraska, Kansas, Oklahoma, Arkansas, Louisiana, and
Missouri.
Correct: The Louisiana Purchase included territory that would become many of
today’s states: Montana, South Dakota, Nebraska, Kansas, Oklahoma, Arkansas,
Louisiana, and Missouri.

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The Semicolon
Basic Rule
A semicolon may be used to separate two complete ideas (independent clauses) in a sentence when the two ideas have a close
relationship and are not connected with a coordinating conjunction.
Example: “Inalienable rights” are basic human rights that many believe cannot and should not be given up or taken
away; life, liberty, and the pursuit of happiness are some of those rights.
The semicolon is often used between independent clauses connected by conjunctive adverbs such as consequently, therefore,
also, furthermore, for example, however, nevertheless, still, yet, moreover, and otherwise.
Example: In 1867, critics thought William H. Seward foolish for buying the largely unexplored territory of Alaska
for the astronomical price of $7 million; however, history has proven that it was an inspired purchase.
Do not use the semicolon between an independent clause and a phrase or
subordinate clause.
Incorrect: While eating ice cream for dessert; Clarence and Undine
discussed their next business venture.
Correct: While eating ice cream for dessert, Clarence and Undine discussed
their next business venture.

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Skill Builder: Punctuation
DIRECTIONS: Decide whether the colons and semicolons are correctly placed in the following sentences or whether another
mark of punctuation would be better. Write the correct punctuation in the space provided.

1. He is an excellent student and a fine person; as a result, he has many friends.

2. Because he is such an industrious student; he has many friends.

3. We tried our best to purchase the books; but we were unsuccessful.

4. The students were required to pass the following exit tests: English, science, math, and social studies.

5. The rebuilt vacuum cleaner was in excellent condition; saving us a good deal of expense since we didn’t have to purchase
a new one.

6. Marie has a very soft voice; however, it is clear and distinct.

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7. Don’t open the door; the floor is still wet.

Chapter 5

8. Don’t open the door; because the floor is still wet.

English
Language
Conventions

9. To the campers from the city, every noise in the night sounded like a bear: a huge, ferocious, meat-eating bear.

10. We worked for three days painting the house; nevertheless, we still needed more time to complete the job.

11. The telephone rang several times, as a result; his sleep was interrupted.

12. Peter was chosen recently to be vice president of the business; and will take over his duties in a few days.

Peterson’s SAT® Prep Guide 2017

Answers
1. Correct.
2. Substitute a comma for the semicolon.
3. Substitute a comma for the semicolon.
4. Correct.
5. Substitute a comma for the semicolon.
6. Correct.
7. Correct.
8. Delete the semicolon.
9. Substitute a comma for the colon.
10. Correct.
11. The telephone rang several times; as a result, his sleep was interrupted. (Note the two punctuation changes. The semicolon
is placed in front of the conjunctive adverb and the comma after it.)
12. Delete the semicolon; no punctuation is necessary in its place.

The Em-Dash
Basic Rule

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Em-dashes are used to set off parenthetical material that you want to emphasize.
Example: Benjamin Franklin’s many intellectual pursuits—from printmaking to politics—exemplify his eclectic
personality.
Em-dashes can also be used when you are renaming a nearby noun. Typically, you would use a comma to set this clause off, but
since it includes commas already, you use an em-dash.
Example: Benjamin Franklin—a printer, writer, inventor, and statesman—was the son of a soap maker.
An em-dash also indicates a list, a restatement, an amplification, or a dramatic shift in tone or thought.
Example: Eager to write for his brother’s newspaper, young Benjamin began submitting letters to the editor under
the pseudonym, Silence Dogood—they were a hit!

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Skill Builder: Punctuation
DIRECTIONS: Revise the following sentences to eliminate end-of-sentence and within-sentence punctuation errors.
1. Architects design houses, office buildings, and other structures!
2. On any given day, architects might perform the following tasks; prepare structural specifications; meet with clients to determine objectives and structural requirements; direct workers to prepare drawings and documents.
3. Architects are responsible for designing the places where we live: work: play: learn: shop: and eat?
4. Architects—design both indoor and outdoor—spaces on public and private projects.
5. Architects often provide various predesign services: from environmental impact studies to cost analyses: depending on a
project’s needs.
6. For actual blueprints, traditional paper-and-pencil drafting has been replaced by computer-aided design and drafting (CADD):
however, hand-drawing skills are still important during the conceptual stages of a project.
7. Did you know that BIM stands for business information modeling.
8. Architects often collaborate with workers in related fields; civil engineers, urban planners, interior designers, and landscape
architects.
9. In addition to years of schooling, being a good architect requires a mix of artistic talent and mathematical ability: it’s not
easy!
10. The path to becoming an architect requires a college education: a five-year Bachelor of Architecture degree program is
typical.

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Answers

Chapter 5

1. Architects design houses, office buildings, and other structures.
2. On any given day, architects might perform the following tasks: prepare structural specifications, meet with clients to determine objectives and structural requirements, and direct workers to prepare drawings and documents.

English
Language
Conventions

3. Architects are responsible for designing the places where we live, work, play, learn, shop, and eat.
4. Architects design both indoor and outdoor spaces on public and private projects.
5. Architects often provide various predesign services—from environmental impact studies to cost analyses—depending on
a project’s needs.
6. For actual blueprints, traditional paper-and-pencil drafting has been replaced by computer-aided design and drafting (CADD);
however, hand-drawing skills are still important during the conceptual stages of a project.
7. Did you know that BIM stands for business information modeling?
8. Architects often collaborate with workers in related fields: civil engineers, urban planners, interior designers, and landscape
architects.
9. In addition to years of schooling, being a good architect requires a mix of artistic talent and mathematical ability—it’s not
easy!
10. The path to becoming an architect requires a college education; a five-year Bachelor of Architecture degree program is
typical.

Peterson’s SAT® Prep Guide 2017

The Apostrophe
The apostrophe is usually either misused or omitted because of the writer’s failure to proofread his paper or because he is not
certain about its use. The apostrophe is used in the following situations:

• To indicate the possessive case of nouns: If the noun does not end in s—whether singular or plural—add an ’s; if the noun ends
in s simply add the ’. Some writers like to add ’s to all nouns, even those that already end in s.
Examples:
The impact of Allen Ginsberg’s poem “Howl” on the cultural landscape of the United States cannot be overstated.
A car’s headlights are typically wired in parallel so that if one burns out the other will keep functioning.
The women’s club sponsored many charity events.
Charles Mingus’ (or Mingus’s) skill as a jazz musician is widely recognized.

Do not use apostrophes with possessive pronouns such pronouns as yours, hers, ours, theirs,
and whose, which indicate possession already.

• To indicate a contraction—the omission of one or more letters: Place the apostrophe exactly where the missing letters occur.

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Examples:
can’t = cannot
it’s = it is
we’re = we are

• To indicate plurals of letters, abbreviations, and numbers: Usually, the apostrophe is used to form the plurals of lowercase letters
(a’s, b’s, c’s, and so on) and numbers (3’s, 6’s). With capital letters, abbreviations without periods (PhD, RN), and even with
numbers when no confusion results, you have a choice. In either case, the writer should be consistent in his or her style.
Examples:
Tiffani signed her texts with x’s and o’s.
The class learned their multiplication tables for 2’s and 4’s.
BUT:
Jocelyn recited her ABCs for her parents.
The room was filled with those who had earned their PhDs.

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Skill Builder: Apostrophe Use
DIRECTIONS: Revise the following sentences to correct any apostrophe errors.

1. Poet William Wordsworths most famous work is The Prelude, which was published in 1850.
2. Its how Wordsworth uses the language of the “common man” that strikes most readers.
3. While most of his poems are considered classics, The Prelude stands as one of the crowning achievements of British Romanticism.
4. Wordsworths poem The Prelude was published by his wife Mary three months after his death.
5. Sonnet 18s theme revolves around the idea of expressing ones self through language.
6. What proportion of humans exposure to plastic ingredients and environmental pollutants occurs through seafood?
7. The use of student’s personal information for anything other than educational purposes is a violation of privacy.

Answers
1. Poet William Wordsworth’s most famous work is The Prelude, which was published in 1850.
2. It’s how Wordsworth uses the language of the “common man” that strikes most readers.
3. While most of his poems are considered classics, The Prelude stands as one of the crowning achievements of British Romanticism.
4. Wordsworth’s poem The Prelude was published by his wife Mary three months after his death.
5. Sonnet 18’s theme revolves around the idea of expressing one’s self through language.
6. Do you know what proportion of humans’ exposure to plastic ingredients and environmental pollutants occurs through
seafood?
7. The use of students’ personal information for anything other than educational purposes is a violation of privacy.

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Peterson’s SAT® Prep Guide 2017

Skill Builder: Apostrophe Use
DIRECTIONS: Circle the word with the correct spelling in the following sentences.

1. According to (statistics, statistic’s), 55 percent of the nursing workforce holds a (bachelors, bachelor’s) degree or higher.
2. Over the past decade, the average age of (nurses, nurse’s) has increased by almost two years for (RNs, RN’s) and 1.75 years
for (LPNs, LPN’s).
3. According to the Board of Registered (Nurse’s, Nurses’) list of (regulations, regulation’s), registered (nurses, nurse’s) must have
a high school diploma, appropriate pre-licensure schooling, and required certification.
4. Despite teaching similar (skills, skill’s), one nursing (program, program’s) (requirements, requirement’s) can be very different
from another (programs, program’s) (requirements, requirement’s).
5. Many future (RNs, RN’s) attend the following types of pre-licensure degree (programs, program’s): Associate Degree in Nursing
(ADN); Bachelor of Science in Nursing (BSN); Entry-Level Master’s Program in Nursing (ELM).
6. Based on recent (studies, studies’), an (RNs, RN’s) salary is about $50,000 a year.

Answers
1. statistics; bachelor’s
2. nurses; RNs; LPNs
3. Nurses’; regulations; nurses

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4. skills; program’s; requirements; program’s; requirements
5. RNs; programs
6. studies; RN’s

Items in a Series
Basic Rule
Use a comma between items in a series when three or more items are present. Items can be expressed as words, phrases, or clauses.
Example: The following wildlife biologists study animals based on where they live: limnologists, marine biologists,
and terrestrial biologists.
When the items themselves contain commas, use a semicolon to separate them.
Example: Some kinds of biologists study specific species of animals. For example, cetologists study marine mammals,
such as whales and dolphins; entomologists study insects, such as beetles and butterflies; and ichthyologists study
wild fish, such as sharks and lungfish.

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Skill Builder: Items in a Series
DIRECTIONS: Revise the following sentences to make sure the items in a series are punctuated correctly.
1. A typical architectural program includes courses on such topics as architectural history, building design, computer-aided
design, and math.
2. Architects must possess certain qualities: analytical skills, in order to understand the content of designs, communication skills,
in order to communicate with clients, creativity, in order to develop attractive and functional structures, and organizational
skills, in order to keep track of big projects.
3. In order to be hired as an architect, you typically need to: complete a professional degree in architecture: gain relevant
experience through a paid internship: and pass the Architect Registration Exam.
4. Because of growing concerns about the environment, today’s architects need to understand sustainable design, which
emphasizes the efficient use of resources, such as energy and water conservation, waste and pollution reduction, and environmentally friendly specifications and materials.
5. In addition to structural plans architects often provide drawings of the air-conditioning heating and ventilating systems
electrical systems communications systems plumbing and possibly site and landscape plans.

Answers
1. No corrections are needed. The sentence reads fine as: A typical architectural program includes courses on such topics as
architectural history, building design, computer-aided design, and math.
2. Architects must possess certain qualities: analytical skills, in order to understand the content of designs; communication skills,
in order to communicate with clients; creativity, in order to develop attractive and functional structures; and organizational
skills, in order to keep track of big projects.
3. In order to be hired as an architect, you typically need to complete a professional degree in architecture, gain relevant experience through a paid internship, and pass the Architect Registration Exam.
4. Because of growing concerns about the environment, today’s architects need to understand sustainable design, which
emphasizes the efficient use of such resources as energy and water; waste and pollution reduction; and environmentally
friendly specifications and materials.

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5. In addition to structural plans, architects often provide drawings of the air-conditioning, heating, and ventilating systems;
electrical systems; communications systems; plumbing; and possibly site and landscape plans.

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Nonrestrictive and Parenthetical Elements
Basic Rule
Nonrestrictive and parenthetical elements provide extra information that is not essential to the meaning or grammatical correctness of a sentence. A nonrestrictive or parenthetical element can be removed from a sentence without making the sentence
grammatically incorrect and without interfering with the rest of the sentence’s meaning.
Parenthetical elements are identified by commas, parentheses, or em-dashes. While each of these punctuation marks serves a
similar purpose, the difference between them is one of emphasis.
Commas indicate a slight interruption.
Example: Toni Morrison, who won the Nobel Prize in Literature in 1993, is a Professor Emeritus at Princeton University.
Parentheses are seen as “quieter” than commas and are reserved for asides that are less important and more tangential than
those indicated by commas. They also allow the inclusion of material that doesn’t have a specific grammatical connection to the
rest of the sentence.
Example: Toni Morrison’s novel Beloved (1987) explores the themes of love and the supernatural.
Example: While at Princeton, Toni Morrison (the writer) established a special creative workshop for writers and
performances called the Princeton Atelier.
If parentheses are used for “quiet” asides, dashes are used when you want to call attention to something. Dashes interrupt the
flow of your sentence, thereby calling attention to the information they contain.

234

Example: Toni Morrison—winner of both the Pulitzer and Nobel Prizes in Literature—is considered one of the
greatest writers of her generation.

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Conventions

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Skill Builder: Nonrestrictive and Parenthetical Elements
DIRECTIONS: Select a comma, parentheses, or em-dash to set off the underlined portion of each sentence.

1. Samuel Clemens 1835–1910 was born in Florida‚ Missouri, to John and Jane Clemens.
2. Mark Twain whose given name was Samuel Clemens was the sixth of seven children.
3. In 1861, Sam’s dreams of becoming a steamboat pilot ended abruptly the Civil War started.
4. Sam’s commitment to the Confederate cause was short-lived he quit the army after just two weeks.
5. Twain’s “big break” came with the publication of his short story‚ “Jim Smiley and His Jumping Frog” 1865, which was picked
up by papers across the country.
6. After the success of his story, “Jim Smiley and His Jumping Frog,” Clemens was hired by the Sacramento Union to visit and
report on the Sandwich Islands now Hawaii.
7. Clemens’ writings for the Sacramento Union were so popular that upon his return he was asked to undertake a lecture tour
across the United States.
8. Like all good writers‚ Mark Twain Samuel Clemens spent his life observing and writing about life as he saw it, with all of its
joys and horrors.

Answers
1. Samuel Clemens (1835–1910) was born in Florida‚ Missouri, to John and Jane Clemens.
2. Mark Twain, whose given name was Samuel Clemens, was the sixth of seven children. (Em-dashes might also be acceptable
here if the writer wished to emphasize the information.)
3. In 1861, Sam’s dreams of becoming a steamboat pilot ended abruptly—the Civil War started.
4. Sam’s commitment to the Confederate cause was short-lived—he quit the army after just two weeks.
5. Twain’s “big break” came with the publication of his short story‚ “Jim Smiley and His Jumping Frog” (1865), which was picked
up by papers across the country.

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6. After the success of his story, “Jim Smiley and His Jumping Frog,” Clemens was hired by the Sacramento Union to visit and
report on the Sandwich Islands (now Hawaii).
7. Clemens’ writings for the Sacramento Union were so popular that, upon his return, he was asked to undertake a lecture tour
across the United States.
8. Like all good writers‚ Mark Twain (Samuel Clemens) spent his life observing and writing about life as he saw it, with all of its
joys and horrors.

Peterson’s SAT® Prep Guide 2017

The Comma
Basic Rule
In previous sections, we covered the way that commas are used to separate the following:

• Independent clauses that are connected by a coordinating conjunction
• Items in a series
• Nonrestrictive elements
In addition to these uses, commas have several other purposes:

• To set off introductory clauses and phrases.
Example: The year after winning her Nobel Prize, Toni Morrison published the novel Jazz.

• To set off nouns that are being addressed directly.
Example: Toni Morrison, the Nobel Prize committee commends you on your achievements and thanks you for your
contribution to world literature.

• To separate the different parts of dates, addresses, and geographical names.
Example: Toni Morrison was born on February 18, 1931, in Lorain, Ohio, to Ramah and George Wofford.

• To introduce a titles and quotations.

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Example: Toni Morrison began her lecture, “The Future of Time: Literature and Diminished Expectations,” with the
line, “Time, it seems, has no future.”

• To separate contrasted elements or to indicate a distinct pause or shift.
Examples: To her handlers, Koko the gorilla seemed thoughtful, almost human.
You’re one of the senator’s close friends, aren’t you?

• To separate coordinate adjectives that precede the noun they describe. Coordinate adjectives are of equal importance and
related meaning.
Examples: Toni Morrison is rumored to be a fun, entertaining speaker.

Note how the word and can be substituted for the comma. If you cannot
substitute and without changing the meaning, the adjectives are not
coordinate, and no comma is needed.
Example: Toni Morrison is a well-respected American writer.

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Unnecessary Punctuation
Unnecessary punctuation can break a sentence into confusing and illogical fragments.
Here are some common mistakes to look out for.

• Don’t use a comma to connect independent clauses. This is called a comma splice.
Incorrect: Toni Morrison grew up in an integrated neighborhood, she did not become fully aware of racial divisions
until she was in her teens.
Possible revision: Toni Morrison grew up in an integrated neighborhood and did not become fully aware of racial
divisions until she was in her teens.

• Don’t use a comma between compound elements that are not independent clauses.
Incorrect: In 1998, Oprah Winfrey, and Danny Glover starred in a film adaptation of Morrison’s novel Beloved.
Possible revision: In 1998, Oprah Winfrey and Danny Glover starred in a film adaptation of Morrison’s novel Beloved.

• Do not use an apostrophe when making a noun plural.
Incorrect: In 2006, the New York Times Book Review named Beloved the best American novel published in the last
25 year’s.
Possible revision: In 2006, the New York Times Book Review named Beloved the best American novel published in
the last 25 years.

237
While any punctuation mark can be misused, overused commas tend to
be a common problem.

Chapter 5
English
Language
Conventions

Peterson’s SAT® Prep Guide 2017

Skill Builder: Commas and Unnecessary Punctuation
DIRECTIONS: Revise the following sentences to correct errors, with special attention to unnecessary, misused, and missing
punctuation marks. In some cases, there are multiple ways to fix these errors. Consider the answers a partial list of possible
revisions.

1. The job of an art director is a creative one he or she is responsible for the visual style and images in magazines newspapers
product packaging, and movie and television productions.

2. An art director’s job includes creating the overall design of a project; and directing others who develop artwork and layouts.

3. People interested in becoming art director’s often work as graphic designer’s, illustrator’s, copy editor’s, or photographer’s,
or in some other types of art and design occupations.

4. Some art directors work for advertising and public relations firms and others work in print media and entertainment.

5. In order to become an art director you typically need at least a bachelor’s degree in an art or design subject, and previous
work experience.

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6. Art direction is a management position, that oversees the work of other designers and artists.

Chapter 5
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Conventions

7. An art director might choose the overall style or tone, desired for a project, and communicate this vision to the artists he or
she manages.

8. In the movie industry an art director might collaborate with a director; in order to determine the look and style of a movie.

9. As of 2012: art directors held about 74,800 jobs.

10. Even though the majority of art directors are self-employed they often work under pressure to meet strict deadlines.

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Answers
1. The job of an art director is a creative one; he or she is responsible for the visual style and images in magazines, newspapers,
product packaging, and movie and television productions.
2. An art director’s job includes creating the overall design of a project and directing others who develop artwork and layouts.
3. People interested in becoming art directors often work as graphic designers, illustrators, copy editors, or photographers or
in some other types of art and design occupations.
4. Some art directors work for advertising and public relations firms, and others work in print media and entertainment.
5. In order to become an art director, you typically need at least a bachelor’s degree in an art or design subject and previous
work experience.
6. Art direction is a management position that oversees the work of other designers and artists.
7. An art director might choose the overall style or tone desired for a project and communicate this vision to the artists he or
she manages.
8. In the movie industry, an art director might collaborate with a director in order to determine the look and style of a movie.
9. As of 2012, art directors held about 74,800 jobs.
10. Even though the majority of art directors are self-employed, they often work under pressure to meet strict deadlines.

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SUMMING IT UP
• The SAT® Writing and Language Test is designed to test your mastery of Standard English conventions. On the test, you will
read multiple passages that may cover careers, science, history, or the humanities. The questions will require you to read the
passages and select the answers that improve the writing in the passage. The correct answer will be the one that best
follows Standard English conventions.

• The Standard English conventions reviewed in this lesson are keys to good writing. When you utilize proper sentence
structure, grammar, and punctuation, your writing is stronger, clearer, and more focused. That is why the use of standard
English conventions is important for both college writing and any writing you will do in your future career.

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Access more practice questions, lessons, helpful tips, and expert strategies for the following English language conventions
topics in Peterson’s SAT® Online Course:

• Comparisons
• Modifiers
• Noun Agreement
• Parallelism
• Pronoun Case
• Pronouns

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• Punctuation
• Sentence Improvements
• Subject-Verb Agreement
• Verb Tenses
• What Makes a Sentence?
To purchase and access the course, go to www.petersons.com/sat.

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part v:
sat ® writing strategies
Chapter 6: The SAT® Essay

Chapter 6:

The SAT® Essay
OVERVIEW
A Closer Look at the Essay Question
Pacing Your Writing
Prewriting
Writing the Introduction
Developing Your Ideas
Writing the Conclusion
The Scoring Rubric for the SAT® Essay
Exercise: Practicing Your Essay Skills
Additional Essay Writing Practice
Summing It Up

The Essay section of the SAT® exam is 50 minutes long. In this time, you need to read the essay prompt and plan and write your
essay. It doesn’t need to be—and isn’t supposed to be—a final, polished version. The high school and college English teachers
who will score your essay are trained to view the essays as first drafts. They will be assessing your essay and hundreds of others
against a rubric that guides them to look at the essays holistically. They are reading for an overall general impression of your
reading, writing, and analyzing skills. Later in this chapter, you will analyze a rubric that is similar to the one the scorers will use.

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A CLOSER LOOK AT THE ESSAY QUESTION
You will be given one essay prompt and asked to write an analytical essay in response. You won’t have a choice of questions to
answer. This is good because it saves you time, as you don’t have to decide which one to choose. The essay section is made up of
a prompt that directs you to read and analyze a high-quality source text. In this text, the author makes an argument or examines
a current debate, idea, or trend.
Once you have closely read and analyzed the source text, you can begin your planning. You don’t need any specific subject-area
knowledge to write your essay. The purpose of the essay is to demonstrate for the scorers that you can then analyze it in writing
using your own critical reasoning and evidence drawn from the source text.

PACING YOUR WRITING
You want to use everything you’ve been taught in English class about the writing process—but sped up to fit within 50 minutes.
Pacing yourself is important so that you are able to get your ideas down on paper in a complete, coherent, and unified essay. As
you practice writing essays in this chapter and in the practice tests in this book, work out a pacing schedule for yourself. Begin by
trying out the following timetable and see how it works for you. If necessary, adjust it as you practice, but be sure to give yourself
enough time to finish a complete draft.

244

•
•
•
•
•
•

Prewriting: 10 to 15 minutes
Writing the introduction: 4 to 5 minutes
Writing the body of the essay: 15 to 20 minutes
Writing the conclusion: 3 to 4 minutes
Revising: 3 to 5 minutes
Proofing: 3 to 5 minutes

NOTE: Remember that the readers do not take off points for specific errors in grammar,
usage, and mechanics, but they will take note of a pattern of errors. These can contribute
to a lower score. Check the rubric (later in this chapter).

Chapter 6
The SAT®
Essay

PREWRITING
Before you begin to write your analysis, read the prompt and the source text. Pay attention to the text author’s key claims.
Underline the author’s key claims. Then circle or highlight evidence the author uses to support those claims. Finally, take notes
on important stylistic features or persuasive techniques the author uses in the source text.
You want to spend about 10 to 15 minutes on prewriting, as this will give you time to carefully read the prompt and then read
and analyze the source text. Your goals in this planning stage are to:

• Identify and underline the author’s key claims
• Find and then circle or highlight specific evidence the author uses to support his or her key claims
• Take notes on ways the author has used logic, reasoning, rhetoric (persuasive language techniques), and evidence to
convince readers that his or her key claims are valid

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Familiarizing Yourself with the Prompt and the Passage
The Essay prompt will not change much at all, no matter when and where you are taking the SAT®. This is great news because it
means you can become very familiar and comfortable with the prompt before you take the test. The source text (passage) that
accompanies the prompt will be new to you; however, it will share important qualities with other passages you will read and
analyze as you prepare to write the SAT® Essay.
All passages:

•
•
•
•
•
•
•
•
•
•

Come from high-quality, previously published sources
Contain arguments written for a broad audience
Examine ideas, opinions, views, debates, or trends
Discuss topics in the arts; the sciences; or civic, cultural, or political life
Are interesting, relevant, and accessible to college-bound students at your grade level
Tend NOT to consist of simple pro/con debates on issues
Strive to convey nuanced views on complex subjects
Use evidence, logical reasoning, and/or stylistic and persuasive elements
Are similarly complex: all are challenging—but not too difficult—for readers at your grade level
Do NOT require test-takers to possess prior knowledge of specific topics

The prompt that introduces the passage will be identical or very similar to this:

As you read the passage below, consider how [the author] uses the following:

• Evidence, such as facts or examples, to support claims

245

• Reasoning to develop ideas and to connect claims and evidence
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power to the ideas
expressed

Chapter 6
The SAT®
Essay

After the passage, the prompt will continue as follows:

Write an essay in which you explain how [the author] builds an argument to persuade [his/her] audience
that [the author’s claim is true or valid]. In your essay, analyze how [the author] uses one or more of the
features listed above [see bullet points above] (or features of your own choice) to strengthen the logic
and persuasiveness of [his/her] argument. Be sure that your analysis focuses on the most relevant aspects
of the passage. Your essay should not explain whether you agree with [the author’s] claims, but rather
explain how [he/she] builds an argument to persuade [his/her] audience.

It is vital that you read, reread, and thoroughly understand everything the prompt asks you to do. Pay particular attention to the
bullet points that tell you exactly what to look for in the passage. Also note that the prompt gives you the option of mentioning
other “features of your own choice.” Finally, let’s take a close look at the last sentence in the prompt (we have capitalized and
underlined the word not):

Your essay should NOT explain whether you agree with [the author’s] claims, but rather explain how [he/
she] builds an argument to persuade [his/her] audience.

Peterson’s SAT® Prep Guide 2017

In other words, your task is not to present your own arguments—the passage author has already done that. Your task is to analyze
the author’s argument: “explain how the author builds an argument to persuade [his/her] audience.”
The people who develop the SAT® believe that if you complete this essay-writing task, your work will exhibit three types of skills:
1.

Close reading skills

2.

Analyzing skills

3.

Writing skills

Organizing Your Essay
Decide how many paragraphs you need to write to develop your analysis of the passage. Remember that length is not a valid
substitute for strength. Your answer booklet provides a certain number of pages for your essay. You can’t write more than the
lines provided, but you can write less. It is more important to do a good job of analyzing the passage than it is to fill up all the
lines. However, an essay of five sentences won’t earn you a high score.
A safe number of paragraphs is five. Use the first paragraph for the introduction and the last one for the conclusion. That gives
you three paragraphs to develop your ideas. That doesn’t mean that you can’t write a fourth or even fifth paragraph in the body
of your essay to develop your ideas. It’s more important to have a tightly written and well-developed shorter essay than a longer,
rambling, repetitious one that you didn’t have time to revise or proofread. There is a limit to what you can write in 50 minutes.
Use the opportunity that you have for practice in this book to work on your pacing and see how much you can plan and write
well in 50 minutes.

WRITING THE INTRODUCTION

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Essay

®

Now it’s time to write. You’ve analyzed the prompt and the passage in your prewriting step and identified the author’s key claims,
use of evidence and reasoning, and stylistic or persuasive language features. Now begin writing your introduction.
In your introduction, it is important to introduce the source text to your reader. State the author’s name and the title of the passage.
Then give a brief summary of the author’s key claim. Two to four sentences should accomplish these tasks.
As you practice writing essays in this book, and as you write the real one on test day, keep the following five ideas in mind:
1.

In writing your introduction, keep the key words and phrases of the prompt in mind.

2.

Avoid being cute, funny, ironic, satiric, overly emotional, or too dramatic. Set the tone or attitude in your first sentence.
You want to be sincere, clear, and straightforward.

3.

Don’t bother repeating the key claims from the source text word for word. A paraphrase in your own words is far
better than just copying the words of the source text.

4.

In your first paragraph, in addition to introducing the passage’s author, title, topic, and the author’s key claim about
the topic, make it clear to your readers that you are about to analyze the passage and explain how the author accomplishes his or her persuasive purpose. This can be accomplished in a clear topic sentence.

5.

Each sentence should advance your topic and be interesting to your reader.

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Skill Builder: Topic Sentence
DIRECTIONS: Which of the following is the best topic sentence?
1.

I agree with the author that the use of motorized boats and watercraft should be limited in freshwater streams and lakes.

2.

The author believes that the use of motorized boats and other watercraft should be limited in freshwater ecosystems in
order to decrease pollution.

3.

In this essay, I will examine the author’s argument in favor of limiting the use of motorized boats and watercraft in freshwater
streams and lakes.

4.

The author introduces her argument with startling statistics on the negative effects of motorized watercraft on freshwater
ecosystems; she then builds on those statistics with careful reasoning to reach the logical conclusion that we should limit
the use of motorized watercraft in freshwater ecosystems.

Answer and Explanation
Of the four sentences presented, choice 4 is the best answer since it states the topic clearly, limits the scope of the essay, and
presents the key points of the analysis. Sentence 4 also implies that the essay writer will expand on these key points in the body
of the essay.
ALERT: Remember that you are writing an analysis of the passage author’s work. You are NOT writing a persuasive
essay on the author’s topic.

Recognizing Effective Introductions
An effective introduction often refers to the subject of the essay, explains the value of the topic, or attracts the attention of the
reader by giving a pertinent illustration. Ineffective beginnings often contain unrelated material, ramble, and lack clarity.

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Skill Builder: Effective Introductions

The SAT®
Essay

DIRECTIONS: Examine the following excerpts from five introductory paragraphs and decide whether each is effective
or ineffective. Be able to defend your decision.
1.

The pollution of freshwater streams and lakes has become a pretty big problem in the United States. Part of the problem is
due to the unrestricted use of motorized boats and other stuff. I mostly agree with the author that something needs to be
done about it, but I don’t know that you should tell people where they can drive their boats.

2.

Freshwater lakes and streams are popular recreational destinations for many Americans. These bodies of water are also
the principal ecosystems of many different animals and plants. In her essay, “Bringing Fresh Back to Freshwater Lakes and
Streams,” activist River Pura makes the claim that the unrestricted use of motorized watercraft is to blame for polluting these
ecosystems.

3.

River Pura makes a very persuasive argument to persuade her audience that motorized boats should be restricted in freshwater streams and lakes. She persuades her audience with some facts and emotional appeals.

4.

The author makes an argument to persuade her audience about what she is thought about. It’s pollution.

5.

Pollution in freshwater ecosystems has been growing over the past decade. Author River Pura, in her essay titled “Bringing
Fresh Back to Freshwater Streams and Lakes,” claims that motorized watercraft are the primary source of that pollution.
While Pura presents her readers with startling statistical information, her argument is anticlimactic and builds to no logical
conclusion.

Peterson’s SAT® Prep Guide 2017

Answers and Explanations
1.

Ineffective. This paragraph is focused on the topic of the source text, not on the author’s writing. Although the prompt specifically says not to present opinions on the topic, the writer states that he or she “mostly agrees” with the passage author.
Also, the writer uses vague, informal expressions: “pretty big” and “mostly agree.”

2.

Effective. This paragraph effectively introduces the author, the passage title, and the topic. The paragraph also identifies the
author’s key claim and begins to analyze the author’s work.

3.

Ineffective. While this paragraph identifies the author’s key claim, nonspecific phrases like “some facts” and “emotional appeal”
weaken the paragraph. Also, the writer uses three different forms of the word persuade, which sounds repetitious.

4.

Ineffective. The paragraph does not introduce the author, the passage title, or the author’s key claim. It does not explain that
the writer is going to analyze the passage. The writing is poorly constructed and misuses verb tense.

5.

Effective. This paragraph clearly introduces the source text, highlights the author’s key claim, and explains how the passage
author fails to build an effective argument.

DEVELOPING YOUR IDEAS
The heart of your essay is the development, or middle paragraphs. In these paragraphs, you must use explanations, details, and
examples from the source text to support the main ideas in your essay. All the sentences in the development paragraphs must
explain and support your analysis of the source text and must not digress.
In the limited time you have on the Essay section of the SAT®, you can take only 15 to 20 minutes to write the body of your essay. In
this time, you need to support your analysis of the author’s work with careful reasoning, and back up your analysis with evidence
from the source text. Your writing must be coherent, logical, unified, and organized.
Avoid the following three pitfalls in the development of your essay:

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Chapter 6
The SAT®
Essay

1.

Using sentences that are irrelevant and contain extraneous material

2.

Using sentences that do not follow a logical sequence of thought but seem to jump from one idea to another

3.

Using sentences that do not relate to the topic sentence or do not flow from the preceding sentence

Using Transitions
The successful writer uses transitional words and phrases to connect thoughts and provide a logical sequence of ideas. Become
familiar with the following list of transitions and use them in your practice essays. They will help make your writing smoother:

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therefore

for example

nevertheless

first of all

in any case

but

then

consequently

still

moreover

for instance

yet

second

on the other hand

also

indeed

of course

in addition

however

finally

furthermore

Skill Builder: Using Transitions
DIRECTIONS: In the following three samples, the transition is missing. Supply a transitional word or phrase that will allow
the second sentence to follow smoothly or logically from the first.

1.

Freshwater ecosystems hold only 0.01% of Earth’s water supply. Over half of the people on Earth live near freshwater
ecosystems.

2.

Human activity comprises the primary threat to freshwater ecosystems. Damming lakes, extracting water, and filling shallow
wetlands all lead to the destruction of these ecosystems.

3.

Constructing dams and levees can lead to a significant loss of habitat for land animals and plant species. The restricted
water flow changes natural water temperatures and impacts marine life.

Answers and Explanations
1.

The sentences require a transition that indicates contrast, such as yet, but, however, still, although and either . . . or.
Although freshwater ecosystems hold only 0.01% of Earth’s water supply, over half of the people on Earth live near these
ecosystems.

2.

These sentences require a transition that indicates an example is to follow.
Human activity comprises the primary threat to freshwater ecosystems; for example, damming lakes, extracting water, and
filling shallow wetlands all lead to the destruction of these ecosystems.

3.

These sentences require a transition that indicates additional information is to follow.
The construction of dams and levees can lead to a significant loss of habitat for land animals and plant species. Furthermore,
the restricted water flow changes natural water temperatures and impacts marine life.

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Writing Effectively

Chapter 6

There are three important elements that will be considered in scoring an SAT® essay:
1.

Reading

2.

Analysis

3.

Writing

The SAT®
Essay

Essays are scored according to how well they meet these three basic criteria. To improve an essay you are writing, ask yourself
these questions:

Reading
•
•
•
•

Does my essay demonstrate a thorough understanding of the source text?
Does my essay identify the author’s key claims?
Does my essay explain how the author uses evidence to support his or her key claims?
Does my essay effectively use evidence from the source text?

Peterson’s SAT® Prep Guide 2017

Analysis
• Does my essay offer an in-depth evaluation of the author’s use of evidence in building and supporting an argument?
• Does my essay offer an in-depth evaluation of the author’s use of stylistic or persuasive language features to build and
support his or her argument?

• Does my essay use supporting evidence from the passage that is relevant and focused on my task (analyzing the
passage)?

Writing
• Does my essay include a precise central claim that is supported with body paragraphs?
• Does my essay include an effective introduction and a strong conclusion?
• Does my essay incorporate a variety of sentence structures? Is each of my sentences clearly written? Does each sentence
flow well?

• Is my essay virtually error-free in spelling, grammar, usage, and mechanics?

WRITING THE CONCLUSION
Lewis Carroll, the author of Alice in Wonderland, once gave some very good advice for writers. He said, “When you come to the
end, stop!”
When you come to the end of your ideas, stop writing the development—and begin writing your conclusion. You can’t just end your
essay with your last development paragraph. You need to draw your comments together in a strong, clear concluding paragraph.

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The SAT®
Essay

A good concluding paragraph for your essay should assure your scorers that you have successfully read, understood, and analyzed
the source text. You should be able to do this in three to six sentences written in 3 to 4 minutes. The following are three possible
ways to end your essay:
1.

Through a restatement of your most important or most central idea

2.

Through a summary of the material covered in the essay

3.

Through a clear statement about the effectiveness of the passage author’s work

Keep in mind that a good conclusion is an integral part of your essay. It may be a review or a restatement, or it may leave your
readers with an intriguing question to think about (one that is closely related to your essay, of course). In any case, your conclusion
must be strong, clear, and effective.

What Not to Say in Your Conclusion
Just as there are good techniques, there are also some very ineffective methods that essay writers may be tempted to use in
drawing a composition to a close. Try to avoid falling into the following three traps:
1.

Apologizing for your inability to more thoroughly analyze the passage in the allotted time

2.

Complaining that the source text did not interest you or that you don’t think it was fair to be asked to write an analysis
of the source text without giving your own opinions on the topic

3.

Introducing material that you will not develop, rambling on about nonpertinent matters, using material that is trite
or unrelated, or making a sarcastic joke that indicates your disdain for the topic you just spent 50 minutes writing
about

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Recognizing Effective Conclusions
Remember that an effective concluding paragraph may restate or summarize main idea(s) in your essay, draw a logical conclusion,
or offer a strong opinion about the effectiveness of the author’s work. An ineffective final paragraph introduces new material in a
scanty fashion, apologizes for the ineffectiveness of your essay, or is illogical or unclear. Use the following skill-builder exercises
to test yourself.

Skill Builder: Effective Conclusions
DIRECTIONS: Why are the following sentences ineffective in a concluding paragraph?
1.

I wish I had more time to write a better, more in-depth analysis, but I find that in the allotted time this is all that I could do.

2.

Although I have not mentioned this before, my family enjoys boating on freshwater lakes. We often pick up litter from the
water in the hopes of decreasing pollution.

3.

This passage was incredibly difficult to understand, and I felt like the author droned on and on about nothing.

DIRECTIONS: Examine the following five excerpts from concluding paragraphs and decide whether each is effective or
ineffective.
4.

That’s all I have to say about the topic. I know I’m not an expert, but at least this is an actual analysis of the work. I also used
a lot of supporting details from the source text. So, I think you should give me at least a 3.

5.

While River Pura is a passionate spokesperson for freshwater ecosystems, her argument for limiting the use of motorized
watercraft lacks cohesion. Furthermore, a careful examination of the issue shows that motorized watercraft are not the
main cause of pollution in freshwater ecosystems. Had Pura taken the time to structure her impassioned pleas around valid
statistical evidence, her argument would be stronger.

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I forgot to mention earlier that the author uses a variety of descriptive words and phrases to appeal to the emotions of
readers. She also uses figurative language and makes some illusions to other articles the reader may have read.

Chapter 6

6.
7.

Protecting the biodiversity of freshwater ecosystems is a topic of importance for all of those who depend upon these
ecosystems for survival. River Pura makes a solid case for the restriction of motorized watercraft in freshwater areas. Pura
begins her argument with startling facts and statistics designed to capture the reader’s attention. She then moves into a
well-reasoned discourse that effectively negates any counter-claims opponents might make.

8.

In conclusion, the author makes a pretty good case for protecting freshwater ecosystems. However, most people I know
aren’t going to stop boating because an environmentalist says they should.

The SAT®
Essay

Answers and Explanations
1.

Ineffective. Don’t apologize for doing a poor job. (Maybe your essay is better than you think. And if it is bad, why would you
want to call attention to its weaknesses?) Also, don’t blame the fact that you did a poor job on the time limit.

2.

Ineffective. Don’t include asides like this anywhere in your essay—but especially not in your conclusion. You’re supposed to
be concluding your analysis, not cramming in extra details that are only loosely related to the topic.

3.

Ineffective. Do not complain about the task in the conclusion. Your essay should maintain a formal tone throughout.

4.

Ineffective. Do not speak directly to or “butter up” the scorers in your concluding paragraph. Maintain a formal tone.

5.

Effective. This paragraph sums up the key points of the analysis and states the essay writer’s opinion of the passage author’s
persuasive writing.

Peterson’s SAT® Prep Guide 2017

6.

Ineffective. Do not introduce new ideas into a concluding paragraph. If you have more information to add that would improve
or add depth to your analysis, consider adding another body paragraph. Also, the essay writer has misused the word illusion:
he or she should have used allusion.

7.

Effective. This paragraph effectively summarizes the key points of the analysis.

8.

Ineffective. This paragraph gives only a vague summary of the analysis and offers an opinion that is irrelevant to the essaywriting task.

THE SCORING RUBRIC FOR THE SAT® ESSAY
The SAT® Essay will be scored based on a 4-point rubric. Points will be awarded in three areas: reading, analysis, and writing. Each
essay will be scored by two graders who will give a score of 1 to 4 in each of the three areas. Scores in each area will be reported
separately from the other two. For example, a test-taker might earn a score of 3/4/3. This means that the test-taker scored 3 out
of 4 points in both reading and writing and 4 out of 4 points in analysis.
All the scorers read the essays against the same rubric developed by the College Board, which administers the SAT®. This rubric
guides the scorers in considering overall impression, development, organization, diction, sentence structure, grammar, usage,
and mechanics. The rubric also directs scorers in evaluating essay writers’ comprehension of the source text, use of relevant evidence from the passage, and their analysis of the passage author’s argument. The scoring guidelines are similar to the following:

Essay Scoring 4 (Advanced)
• Reading: shows a comprehensive understanding of the source text, including the author’s key claims, use of details and
evidence, and the relationship between the two

• Analysis: offers an “insightful” and in-depth evaluation of the author’s use of evidence and stylistic or persuasive features

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Essay

in building an argument; uses relevant supporting details that address the task

• Writing: includes all of the features of a strong essay, including a precise central claim, body paragraphs, and a strong
conclusion; incorporates a variety of sentence structures; is virtually free of all convention errors

Essay Scoring 3 (Proficient)
• Reading: shows an appropriate understanding of the source text, including the author’s key claims and use of details
in developing an argument

• Analysis: offers an effective evaluation of the author’s use of evidence and stylistic or persuasive features in building an
argument; uses appropriate supporting details and evidence that are relevant and focused on the task

• Writing: includes all of the features of an effective essay, including a precise central claim, body paragraphs, and a strong
conclusion; incorporates a variety of sentence structures and is relatively free of common grammatical errors

Essay Scoring 2 (Partial)
• Reading: shows some understanding of the source text, including the author’s key claims; uses limited textual evidence;
incorporates unimportant details

• Analysis: offers a limited evaluation of the author’s use of evidence and stylistic or persuasive features in building an
argument; supporting details are lacking and/or irrelevant to task

• Writing: does not provide a precise central claim, nor an effective introduction, body paragraphs, and conclusion;
incorporates little variety of sentence structures and contains numerous errors in grammar and conventions

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Essay Scoring 1 (Inadequate)
• Reading: demonstrates little or no understanding of the source text or the author’s use of key claims
• Analysis: offers no clear evaluation of the author’s use of evidence and stylistic or persuasive features in building an
argument; supporting details and evidence are nonexistent or irrelevant to task

• Writing: lacks any form of cohesion or structure; incorporates little variety in sentence structure and includes significant
errors in convention that make it difficult to read
Read the rubric several times. As you practice writing essays for the SAT®, keep this rubric in mind. As you write each essay, try to
focus on one or two qualities of good writing that the rubric measures. After you have finished writing your essay, come back to
the rubric and see how your essay measures up.
Use the following table to help you. Give yourself anywhere from 1 to 4 points for each quality of good writing.

PRACTICE TEST SCORING TABLE
Reading:
Analysis:
Writing:
Final Score:

__________
__________
__________
__________ / __________ / __________

EXERCISE: PRACTICING YOUR ESSAY SKILLS
Use the following prompt to practice writing an effective essay. Carefully read the prompt and write a response. Make use of the
effective writing techniques discussed in this chapter. Use the scoring rubric to evaluate your work. Then read and evaluate the
three sample responses.

As you read the passage below, consider how the writer uses the following:

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Chapter 6

• Evidence, such as facts or examples, to support claims

The SAT®
Essay

• Reasoning to develop ideas and to connect claims and evidence
• Stylistic or persuasive elements, such as word choice, emotional appeal, intellectual appeal, or
ethical appeal, to add power to the ideas expressed

Henry Clay (1777–1852) served several terms in Congress and was Secretary of State in 1825. In the following speech, given in 1818, he
argues that the United States should support South America in gaining independence from Spain.

The Emancipation of South America
1

Spain has undoubtedly given us abundant and just cause for war. But it is not every cause of war that should lead to
war. . . . If we are to have war with Spain, I have, however, no hesitation in saying that no mode of bringing it about
could be less fortunate than that of seizing, at this time, upon her adjoining province. There was a time, under certain
circumstances, when we might have occupied East Florida with safety; had we then taken it, our posture in the
negotiation with Spain would have been totally different from what it is.

2

But we have permitted that time, not with my consent, to pass by unimproved. If we were now to seize upon Florida after
a great change in those circumstances, and after declaring our intention to acquiesce in the procrastination desired by
Spain, in what light should we be viewed by foreign powers—particularly Great Britain? We have already been accused

Peterson’s SAT® Prep Guide 2017

of inordinate ambition, and of seeking to aggrandize ourselves by an extension, on all sides, of our limits. Should we not,
by such an act of violence, give color to the accusation? No, Mr. Chairman; if we are to be involved in a war with Spain, let
us have the credit of disinterestedness. Let us put her yet more in the wrong. Let us command the respect which is never
withheld from those who act a noble and generous part. I hope to communicate to the committee the conviction which I
so strongly feel, that the adoption of the amendment which I intend to propose would not hazard, in the slightest degree,
the peace of the country… .

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3

In contemplating the great struggle in which Spanish America is now engaged, our attention is fixed first by the
immensity and character of the country which Spain seeks again to subjugate. Stretching on the Pacific Ocean from about
the fortieth degree of north latitude to about the fifty-fifth degree of south latitude, and extending from the mouth of the
Rio del Norte (exclusive of East Florida), around the Gulf of Mexico and along the South Atlantic to near Cape Horn, it is
nearly five thousand miles in length, and in some places nearly three thousand in breadth… .

4

Throughout all the extent of that great portion of the world which I have attempted thus hastily to describe, the spirit
of revolt against the dominion of Spain has manifested itself. The Revolution has been attended with various degrees of
success in the several parts of Spanish America. In some it has been already crowned, as I shall endeavor to show, with
complete success, and in all I am persuaded that independence has struck such deep root, that the power of Spain can
never eradicate it. What are the causes of this great movement?

5

Three hundred years ago, upon the ruins of the thrones of Montezuma and the Incas of Peru, Spain erected the most
stupendous system of colonial despotism that the world has ever seen—the most vigorous, the most exclusive. The great
principle and object of this system have been to render one of the largest portions of the world exclusively subservient, in
all its faculties, to the interests of an inconsiderable spot in Europe….

6

Thus upon the ground of strict right, upon the footing of a mere legal question, governed by forensic rules, the Colonies,
being absolved by the acts of the parent country from the duty of subjection to it, had an indisputable right to set up for
themselves. But I take a broader and a bolder position. I maintain that an oppressed people are authorized, whenever
they can, to rise and break their fetters. This was the great principle of the English Revolution. It was the great principle of
our own… .

7

In the establishment of the independence of Spanish America, the United States have the deepest interest. I have no
hesitation in asserting my firm belief that there is no question in the foreign policy of this country, which has ever arisen,
or which I can conceive as ever occurring, in the decision of which we have had or can have so much at stake. This interest
concerns our politics, our commerce, our navigation… .

8

I would invoke the spirits of our departed fathers. Was it for yourselves only that you nobly fought? No, no! It was the
chains that were forging for your posterity that made you fly to arms, and, scattering the elements of these chains to the
winds, you transmitted to us the rich inheritance of liberty.

Chapter 6
The SAT®
Essay

Write an essay in which you explain how Henry Clay builds an argument to persuade his audience that
the United States should support South America in its efforts to secure freedom from Spain. In your essay,
analyze how Clay uses one or more of the features previously listed (or features of your own choice) to
strengthen the logic and persuasiveness of his argument. Be sure that your analysis focuses on the most
relevant aspects of the passage.
Your essay should not explain whether you agree with Clay’s claims, but rather explain how he builds
an argument to persuade his audience.

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Use the following scoring guide to help you evaluate Sample Essay 1. Then, read our analysis of the essay, as well as suggestions
for improvement.

Score Point

4
(Advanced)

3
(Proficient)

2
(Partial)

1
(Inadequate)

Reading

Analysis

Writing

The essay shows
a comprehensive
understanding of the
source text, including the
author’s key claims, use
of details and evidence,
and the relationship
between the two.

The essay offers an
“insightful” and in-depth
evaluation of the author’s
use of evidence and stylistic
or persuasive features in
building an argument.
Supporting details and
evidence are relevant and
focus on those details that
address the task.

The essay includes all of the
features of a strong essay,
including a precise central
claim, body paragraphs,
and a strong conclusion.
There is a variety of
sentence structures used in
the essay, and it is virtually
free of all convention errors.

The essay shows an
appropriate understanding
of the source text,
including the author’s key
claims and use of details in
developing an argument.

The essay offers an
“effective” evaluation of the
author’s use of evidence
and stylistic or persuasive
features in building an
argument. Supporting
details and evidence are
appropriate and focus
on those details that
address the task.

The essay includes all
of the features of an
effective essay, including
a precise central claim,
body paragraphs, and a
strong conclusion. There
is a variety of sentence
structures used in the essay,
and it is free of significant
convention errors.

The essay shows some
understanding of the
source text, including
the author’s key claims,
but uses limited textual
evidence and/or
unimportant details.

The essay offers limited
evaluation of the author’s
use of evidence and
stylistic or persuasive
features in building an
argument. Supporting
details and evidence are
lacking and/or are not
relevant to the task.

The essay does not provide
a precise central claim,
nor does it provide an
effective introduction,
body paragraphs, and
conclusion. There is
little variety of sentence
structure used in the essay,
and there are numerous
errors in grammar
and conventions.

The essay demonstrates
little or no understanding
of the source text or the
author’s use of key claims.

The essay offers no clear
evaluation of the author’s
use of evidence and
stylistic or persuasive
features in building an
argument. Supporting
details and evidence are
nonexistent or irrelevant
to the task.

The essay lacks any form
of cohesion or structure.
There is little variety
of sentence structures,
and significant errors
in convention make it
difficult to read.

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Sample Essay 1
In his speech to Congress, Henry Clay emphasizes the importance of supporting South America in their revolt against Spain. Clay
begins his argument by talking about the significance of the state of Florida, which isn’t actually a state yet. Clay urges Congress
not to invade Florida (which apparently has been captured by Spain) because it would make the U.S. look bad. Clay’s goal is for
Spain to be “in the wrong” and for the U.S. to “command the respect which is never withheld from those who act a noble and
generous part.”
Clay goes on to remind his listeners that the majority of South America is already involved in a Revolution against Spain. This
is a key point of persuasion. Finally, Clay makes the comparison between the Revolution in South America and the Revolution
against Great Britain. He even goes so far as to “invoke the spirits of our departed fathers” and uses other images like “fly to arms”
and “the rich inheritance of liberty.” While Clay’s argument is okay, it’s long-winded and focuses too much on emotional appeal.

Analysis of Sample Essay 1
This response scored a 2/2/2.

• Reading—2: The writer demonstrates some comprehension of the source text. In the first paragraph, the writer conveys
the basic central claim—the importance of supporting South America in their revolt against Spain. The writer also shows
a partial understanding of Clay’s position on Florida—Clay’s goal is for Spain to be “in the wrong”—but does not effectively
tie it to the central claim. In the following paragraph, the writer correctly identifies Clay’s comparison of the South
American Revolution to the U.S. Revolution. However, there is little demonstration of the relationship between the
central claim and the supporting details. Overall, the writer shows a partial understanding of the source text.

• Analysis—2: The response offers a limited analysis of the source text, showing only partial understanding of the task.
The writer mentions the significance of the state of Florida but then does not elaborate on this significance or explain
how Florida’s significance contributes to Clay’s argument. In the second paragraph, the writer makes note of a key point
of persuasion; however, there is no further discussion of why South America’s revolution against Spain is a key point of
persuasion. Furthermore, the writer does not develop the effect of Clay’s comparison of the South American Revolution
to the U.S. Revolution. While the writer includes the use of emotional appeal in the analysis, there is no explanation of
it. Overall, this response is only a partially successful analysis.

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• Writing—2: This response reflects limited cohesion and some skill in the use of language. There is no precise central
claim, nor is there an effective introduction and conclusion. Phrases like isn’t actually a state yet and which apparently
has been captured by Spain use an informal, almost flippant tone. Calling the source text long-winded is subjective and
inappropriate for a formal analysis. Overall, this response represents a partially developed essay.

Suggestions for Improvement
1.

The response needs a clearly developed introduction that establishes the topic and presents a precise central claim.
While the first paragraph makes a start, a precise central claim should briefly summarize the key points that the writer
will make in his or her analysis.

2.

Each body paragraph should begin with a topic sentence that summarizes the key point of the paragraph. For instance,
the writer could begin the second paragraph with the sentence: Clay begins his argument with reason rather than
rhetoric, logically appealing to those who are hesitant to engage in open warfare.

3.

The use of evidence from the source text should directly support key aspects of the essay writer’s analysis. Look at this
sentence from paragraph 2 of Sample Essay 1: He even goes so far as to “invoke the spirits of our departed fathers”
and uses other images like “fly to arms” and “the rich inheritance of liberty.” The quotations here do not support the
writer’s analysis of the source text. A better use of quotations might be:

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Clay uses emotionally powerful language as a persuasive tool in making the correlation between the U.S. quest for
independence from Great Britain and South America’s quest for independence from Spain. He wants to inspire the
same passionate support for South America’s struggle that most of his listeners feel about their own country’s revolution, so he uses emotional phrases like “invoke the spirits of our departed fathers,” “fly to arms,” and “rich inheritance of
liberty.”
4.

The response should include a strong conclusion that restates the thesis, recaps the most important parts of the
analysis, or leaves the reader with a final thought. The conclusion should provide a sense of closure on the topic.

5.

All SAT® essays should maintain a formal and objective tone. The writer should limit the use of contractions and refrain
from using derogatory adjectives like long-winded to describe the source text.

Sample Essay 2
In Henry Clay’s 1818 address to Congress, he is building an argument to persuade his listeners to support South America in their
revolution against Spain. He builds his argument in three different ways. Clay demonstrates an understanding of his audience,
underscores the action that they need to take, and closes with an emotional appeal for liberty by referencing the Revolutionary War.
Clay begins building his argument by demonstrating an understanding of his audience. He demonstrates an understanding of his
audience when he assures them at the outset of his speech that he is not calling for open warfare against Spain. This is significant
because many members of Congress still remembered the bloodshed from the Revolutionary War. Clay reassures his audience
and seeks to get them on his side by stating “it is not every cause of war that should lead to war.” Once Congresses minds are put
at ease, Clay can move onto talking about his central claim.
After Clay reassures his listeners, he then attempts to underscore the amount of involvement they would have to take in the
conflict. He is seeking to minimize the nature of the conflict in order to win support for it. Clay says that, “The Revolution has
been attended with various degrees of success in the several parts of Spanish America. In some it has been already crowned, as
I shall endeavor to show, with complete success. . . .”
Finally, Clay seeks to draw a parallel for his listeners between the revolution they had recently won and the revolution being fought
in South America. This is his emotional appeal. Clay is telling his listeners, “Remember your fight for independence? Remember
how greatly you desired freedom? This is the same thing.” By getting his listeners to remember how passionately they desired
freedom from Great Britain, he is hoping to sway their emotions in favor of supporting South America against Spain.
Henry Clay uses logic, minimizing, and emotional appeal to build an argument. He shows that he understands his audience and
seeks to give them what they need so that they will agree with him.

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Analysis of Sample Essay 2
This essay scored a 3/3/3.

• Reading—3: This response demonstrates effective understanding of the source text with appropriate use of evidence
through the analysis. In the second paragraph, the author discusses Clay’s understanding of his audience and what the
audience most fears. Although the source text does not refer explicitly to this fear, the writer picks up on it from a careful
reading of the passage. In the next paragraph, the writer cites and discusses a claim Clay makes that supporting South
America requires a minimal response. Finally, the last body paragraph paraphrases Clay’s emotional call to remember
the principles that guided the American Revolution. The writer shows an effective understanding of both the central
idea and important details.

• Analysis—3: The writer shows an effective understanding of the task by identifying three ways Clay builds his argument
(Clay demonstrates an understanding of his audience, underscores the action that they need to take, and closes with an
emotional appeal . . .) and then elaborating on each point in the body paragraphs. Each body paragraph carefully evaluates how pieces of evidence from the source text, the author’s use of reasoning, or stylistic or persuasive features are

Peterson’s SAT® Prep Guide 2017

used to develop an argument. For example, in the final body paragraph the writer claims that Clay is getting his listeners
to remember how passionately they desired freedom from Great Britain and explains that this is to sway their emotions in
favor of supporting South America against Spain. The response could have made stronger use of evidence from the text,
offering a direct quote rather than a paraphrase. However, this response shows an effective analysis of the source text
using relevant support.

• Writing—3: This essay includes most of the features of an effective essay, including a precise central claim and body
paragraphs. The introduction and conclusion lack development, although the introduction presents the central claim
and the conclusion restates it. There is appropriate variety of sentence structure, and the few errors of convention and
grammar do not detract from the overall reading of the response. Overall, this analysis is proficient.

Suggestions for Improvements
1.

The author should work to develop a stronger introduction and conclusion. For example, the introduction could
explain the significance of the topic, and the conclusion might provide a final thought or statement.

2.

Paragraph 3 could further discuss Clay’s reasons for minimizing the support needed in South America. While the
writer effectively points out Clay’s use of minimization, the importance of this technique to Clay’s argument is not
fully clear.

3.

In paragraph 4, the writer paraphrases Clay’s emotional appeal. When discussing an author’s use of emotional language
to persuade listeners to share his point of view or take a certain action, direct quotes from the source text are best.

Sample Essay 3

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Essay

In 1818, South America was rising in revolt against Spain. Congressman Henry Clay believed that it was in America’s best interest
to support their neighbors to the south. In his speech to the 1818 Congress, Clay builds an argument tailor-made for his audience,
outlining action steps Congress should take while at the same time appealing to their passionate belief in democracy. Through
a combination of careful rhetoric, logic, and emotional appeal, Clay hopes to convince Congress to adopt an amendment that
would put the U.S. at war with Spain.
Clay begins his argument with careful rhetoric designed specifically for his audience. Clay understands that some may be thinking
of the bloodshed of the American Revolution and have no desire to engage in another war. “It is not every cause of war that
should lead to war …” Clay maintains. However, Clay goes on to suggest to his audience that, had they acted prior to this moment
in time, war might have been avoided. In essence, Clay is telling his audience that he does not condone war; however, Congress
has brought about the necessity to engage in war by previous inaction. Clay tells his audience, “There was a time . . . ”when . . .
our posture in the negotiation with Spain would have been totally different . . . ” Yet, Clay maintains, that time has passed. Now
is the time for more heavy-handed action.
Clay furthers the appeal of his argument by insisting that the action steps he proposes would not lead the country into another
violent conflict. Rather, Clay maintains “ . . . ” the adoption of the amendment which I intend to propose would not hazard, in the
slightest degree, the peace of the country. . . . ” He uses logic to reason that, because of the size of South America, and because of
the success that some South American people have already had in their fight against Spain, the revolution in some areas is already
“a complete success.” Therefore, Clay is demonstrating to his audience that supporting his amendment poses no risk to them.
Finally, Clay uses an emotional appeal to ultimately convince Congress to pass the amendment. Clay draws a parallel between
the ideals of freedom and democracy that underscored the fight for American independence and the ideals of freedom and
democracy that are bolstering the fight in South America. His emotional appeal is summed up in the last paragraph of the speech:
“I would invoke the spirits of our departed fathers. Was it for yourselves only that you nobly fought? No, no! It was the chains that
were forging for your posterity that made you fly to arms . . . ””
Speaking to Congress of the imminent threat of Spain, Henry Clay seeks to persuade his listeners to pass an amendment that
would essentially put the fledgling nation at war with another European nation. With careful rhetoric, logic, and emotional appeals,
Clay seeks to convince his listeners that freedom is something for which one should always be willing to fight.

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Analysis of Sample Essay 3
This essay scored a 4/4/4.

• Reading—4: This response demonstrates thorough understanding of the source text with skillful use of paraphrases
and direct quotations. The writer briefly summarizes the main idea of Clay’s argument (Clay believed that it was in America’s
best interest to support their neighbors to the south) and presents many details from the text, including Clay’s reflection
that Congress had an opportunity to negotiate with Spain but missed it, to demonstrate why Clay’s argument is significant. There are few long direct quotations from the source text. Instead, the author accurately and precisely paraphrases
the key points of the speech.

• Analysis—4: The writer demonstrates an insightful understanding of the task by identifying three ways Clay builds his
argument (Through a combination of careful rhetoric, logic, and emotional appeal . . .) and then elaborating on each point
in the body paragraphs. Each body paragraph carefully evaluates how pieces of evidence from the source text, the
author’s use of reasoning, or stylistic or persuasive features are used to develop an argument. For example, in the final
body paragraph the writer claims that Clay “draws a parallel between the ideals of freedom and democracy that underscored the fight for American independence and the ideals of freedom and democracy that are bolstering the fight in
South America.” The response demonstrates a thorough understanding of both the source text and its effect on the
audience.

• Writing—4: This essay is cohesive and shows an effective command of language, including a precise central claim and
body paragraphs. The introduction and conclusion are well developed. There is ample variety of sentence structures
and no errors of convention and grammar that detract from the overall reading of the response. Overall, this analysis
shows advanced writing proficiency.

ADDITIONAL ESSAY WRITING PRACTICE
For more practice, carefully read the following prompt and source text. Then write an analysis of the passage. Score your analytical
response using the rubric provided.

As you read the passage below, consider how the writer uses the following:

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Chapter 6

• Evidence, such as facts or examples, to support claims

The SAT®
Essay

• Reasoning to develop ideas and to connect claims and evidence
• Stylistic or persuasive elements, such as word choice, emotional appeal, intellectual appeal, and ethical
appeal, to add power to the ideas expressed

Padre Island National Seashore separates the Gulf of Mexico from the Laguna Madre, one of a few hypersaline lagoons in the world.
The park protects 70 miles of coastline, dunes, prairies, and wind tidal flats teeming with life. It is a safe nesting ground for the Kemp’s
Ridley sea turtle and a haven for 380 bird species. It also has a rich history, including the Spanish shipwrecks of 1554.

The Importance of the 1554 Shipwrecks
1

In April, 1554, three Spanish naos (a type of cargo and passenger ship similar to Columbus’s Santa Maria) went aground
on Padre Island following a storm that had blown them across the Gulf of Mexico from the coast of Cuba. At the time this
was the greatest disaster to ever befall the Spanish fleet in the New World. Tons of treasure bound for Spain was lost in
addition to the lives of approximately three hundred passengers and crew who died from hunger, thirst, and attacks by
natives as they attempted to walk back to the port of Vera Cruz.

Peterson’s SAT® Prep Guide 2017

2

But the story of the 1554 shipwreck does not end there, nor does it end with the conclusion of the salvage operations that
took place later that year. As with any important historical event, its effects resonate through the centuries and can still be
felt today—if one looks for them.

3

First of all, the wrecks were the first documented occurrence of Europeans on the island and one of the first occurrences
of Europeans in what was to become Texas. The salvage operation was the first documented instance of Europeans
intentionally coming to the island and staying for an extended period.

4

Second, the three ships that wrecked (the Santa Maria de Yciar, the Espiritu Santo, and the San Esteban) are the oldest
shipwrecks ever found in North America (excluding the Caribbean and Latin America).

5

Third, when the remains of the ships were discovered in 1967, a private company called Platoro, Ltd. began excavating
them. This set off a long legal battle over ownership of the remains, as Texas had no laws governing antiquities at the
time. In the long run, the state won its case and the remains were turned over to the National Park Service, which has
transferred curation of the artifacts to the Corpus Christi Museum of Science and History, where they may now be viewed.

6

Historian and Marine Archeologist Dr. Donald Keith, President of the Ships of Discovery at the Corpus Christi Museum of
Science and History, notes that:

7

“The 1554 shipwrecks are important for a lot of reasons. The ‘mining’ of them by Platoro caused the state of Texas to realize
that shipwrecks and archaeological sites in general are important, and the property of the people and the state. They are
cultural resources that have to be cared for. Some of the earliest experiments in the conservation of artifacts from the
sea were done on the objects and hull remains that were recovered from the sites that Platoro and the State worked. . . .
The Platoro conflict did lead to the establishment of the Texas Antiquities Committee, which led to the Texas Historical
Commission, which led to the discovery and excavation of La Belle [the ship of the French explorer La Salle, found on the
Texas coast within the past few years] among other accomplishments.”

8

This third and last effect on our present society is undoubtedly the most important, because it resulted in new Texas laws
to protect archeological resources. These laws follow the federal Antiquities Act in spirit, which gives federal agencies
custody of relics found within their jurisdictions so that they may be properly protected and studied. Thus, instead of
ending up in private collections where they become curiosities for a fortunate few, the knowledge derived from the
artifacts goes to the public in the form of publications and exhibits in museums and on websites.

9

Bits and pieces of the 1554 wrecks and many other historical events still wash up on the island or can be found emerging
from the sands. If you discover something, please remember that the right thing to do is leave it where it is and report it
to us, so that we may conduct a proper archeological dig and learn more about the rich history of the island and share our
findings (and yours) with the world.

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Essay

Write an essay in which you explain how the writer builds an argument to persuade his or her audience
of the importance of the 1554 shipwrecks. In your essay, analyze how the author uses one or more of the
features listed previously (or features of your own choice) to strengthen the logic and persuasiveness
of his/her argument. Be sure that your analysis focuses on the most relevant aspects of the passage.
Your essay should not explain whether you agree with the writer’s claims, but rather explain how the
writer builds an argument to persuade his or her audience.

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Score Point

4
(Advanced)

3
(Proficient)

2
(Partial)

1
(Inadequate)

Reading

Analysis

Writing

The essay shows
a comprehensive
understanding of the
source text, including the
author’s key claims, use of
details and evidence, and
the relationship between
the two.

The essay offers an
“insightful” and in-depth
evaluation of the author’s
use of evidence and stylistic
or persuasive features in
building an argument.
Supporting details and
evidence are relevant and
focus on those details that
address the task.

The essay includes all
of the features of a
strong essay, including
a precise central claim,
body paragraphs, and a
strong conclusion. There
is a variety of sentence
structures used in the
essay, and it is virtually
free of all convention
errors.

The essay shows an
appropriate understanding
of the source text, including
the author’s key claims and
use of details in developing
an argument.

The essay offers an
“effective” evaluation of the
author’s use of evidence
and stylistic or persuasive
features in building an
argument. Supporting
details and evidence are
appropriate and focus
on those details that
address the task.

The essay includes all
of the features of an
effective essay, including
a precise central claim,
body paragraphs, and a
strong conclusion. There
is a variety of sentence
structures used in the essay,
and it is free of significant
convention errors.

The essay shows some
understanding of the
source text, including
the author’s key claims,
but uses limited textual
evidence and/or
unimportant details.

The essay offers limited
evaluation of the author’s
use of evidence and stylistic
or persuasive features in
building an argument.
Supporting details and
evidence are lacking and/or
are not relevant to the task.

The essay does not provide
a precise central claim,
nor does it provide an
effective introduction,
body paragraphs, and
conclusion. There is
little variety of sentence
structure used in the essay,
and there are numerous
errors in grammar
and conventions.

The essay demonstrates
little or no understanding
of the source text or the
author’s use of key claims.

The essay offers no clear
evaluation of the author’s
use of evidence and stylistic
or persuasive features in
building an argument.
Supporting details and
evidence are nonexistent or
irrelevant to the task.

The essay lacks any form of
cohesion or structure. There
is little variety of sentence
structures, and significant
errors in convention make
it difficult to read.

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SUMMING IT UP
• Remember that your essay should not explain whether you agree with the author’s claims, but, rather, it should explain how
the author builds an argument to persuade his or her audience.

• SAT® essays are scored based on how well they meet the following three criteria:
1.

Reading—Does the essay demonstrate a thorough understanding of the source text, identify the author’s key claims
and explain how he or she uses evidence to support them, and use evidence from the source text effectively?

2.

Analysis—Does the essay offer in-depth evaluations of the author’s use of evidence and stylistic or persuasive language features to build and support his or her argument? Does the essay include relevant supporting evidence from
the passage to aid in its analysis?

3.

Writing—Does the essay include an effective introduction, a precise central claim supported by body paragraphs,
and a strong conclusion? Does the essay include a variety of clearly written sentences that flow well together? Is the
essay mostly error-free in grammar, usage, and mechanics?

• Practice pacing yourself so that you are able to get your ideas down on paper in a complete, coherent, and unified essay.
• Prewriting should take 10 to 15 minutes. Use this time to:
ºº Identify and underline the author’s key claims
ºº Find and then circle or highlight specific evidence the author uses to support his or her key claims
ºº Take notes on ways the author has used logic, reasoning, and rhetoric (persuasive language techniques), and evidence
to convince readers that his or her key claims are valid

• Writing the introduction should take 4 to 5 minutes. Keep these five ideas in mind:

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Essay

1.

Keep the key words and phrases of the prompt in mind.

2.

Be sincere, clear, and straightforward. Avoid being cute, funny, ironic, satiric, overly emotional, or too dramatic.

3.

Paraphrase key claims from the source text.

4.

Write a clear topic sentence that introduces the passage’s author, title, topic and the author’s key claim about the topic,
and makes it clear to your readers that you are about to analyze the passage and explain how the author accomplishes
his or her persuasive purpose.

5.

Write sentences that advance the topic and interest the reader.

• Writing the body of the essay should take 15 to 20 minutes. Support your analysis of the author’s work with careful
reasoning, and back up your analysis with evidence from the source text. Your writing must be coherent, logical, unified,
and organized.

• Writing the conclusion should take 3 to 4 minutes. A good concluding paragraph should assure your scorers that you have
successfully read, understood, and analyzed the source text. There are three possible ways to end your essay:
1.

Through a restatement of your most important or most central idea

2.

Through a summary of the material covered in the essay

3.

Through a clear statement about the effectiveness of the passage author’s work

• Revising (3 to 5 minutes) and proofing (3 to 5 minutes) are important steps in the writing process. Be sure to leave yourself
enough time to polish your essay, even though it is considered a first draft by the test graders.

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ONLINE
PREP

Want to Know More?

Access more practice questions, valuable lessons, helpful tips, and expert strategies for the following essay writing topics in
Peterson’s SAT® Online Course:

• Avoiding Common Errors
• Effective Style in Essays
• Essay Scoring
• Essay Writing Method
• Organize and Develop Ideas
• Putting It All Together
To purchase and access the course, go to www.petersons.com/sat.

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Essay

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part vi: math strategies
for the sat ®

Chapter 7:
Chapter 8:
Chapter 9:
Chapter 10: 	
Chapter 11: 	
Chapter 12: 	
Chapter 13: 	

Multiple-Choice Math
Grid-In Strategies
Numbers and Operations
Basic Algebra
Geometry
Functions and Intermediate Algebra
Data Analysis

Chapter 7:
Multiple-Choice Math
OVERVIEW
Why Multiple-Choice Math Is Easier
Question Format
Solving Multiple-Choice Math Questions
Know When to Use Your Calculator
Learn the Most Important Multiple-Choice
Math Tips
Exercises: Multiple-Choice Math
Summing It Up

267

WHY MULTIPLE-CHOICE MATH IS EASIER
How can one kind of math possibly be easier than another? SAT® multiple-choice math is easier than the math tests you take
in class because the answers are right there in front of you. As you know from taking other standardized tests, multiple-choice
questions always give you the answer. You just have to figure out which answer is the correct one. So even if you aren’t sure and
have to guess, you can use estimating to narrow your choices and improve your odds.

Chapter 7
MultipleChoice Math

The questions in each multiple-choice math section are arranged from easiest to most difficult. The questions don’t stick to one
content area. They jump around from algebra to geometry to advanced math to data analysis to statistics and back to algebra
in no particular pattern.

Peterson’s SAT® Prep Guide 2017

QUESTION FORMAT
On the SAT® Math test, each set of multiple-choice math questions starts with directions and a reference section that look like this:
DIRECTIONS: For Questions 1–30, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 31–38, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 31 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:

• The use of a calculator is permitted (In the Math Test—No Calculator section, this will say: “The use of a calculator is not
permitted.)

• All variables and expressions used represent real numbers unless otherwise indicated.
• Figures provided in this test are drawn to scale unless otherwise indicated.
• All figures lie in a plane unless otherwise indicated.
• Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which is f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

Chapter 7

V = lwh

MultipleChoice Math

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
l

h

w

Rectangular
Solid:

268

Triangle:

x

x

Special Right Triangles

a2 + b2 = c2
Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

The information in the reference section should all be familiar to you from your schoolwork. Know that it’s there in case you need
it. But remember: the formulas themselves aren’t the answers to any problems. You have to know when to use them and how
to apply them.
Some multiple-choice questions ask to solve a given equation or system of equations, while others are presented in the form of
word problems. Some include graphs, charts, or tables that you will be asked to interpret. All of the questions have four answer
choices. These choices are arranged in order when the answers are numbers, usually from smallest to largest, but occasionally
from largest to smallest.

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SOLVING MULTIPLE-CHOICE MATH QUESTIONS
These five steps will help you solve multiple-choice math questions:
1. Read the question carefully and determine what’s being asked.
2. Decide which math principles apply and use them to solve the problem.
3. Look for your answer among the choices. If it’s there, mark it and go on.
4. If the answer you found is not there, recheck the question and your calculations.
5. If you still can’t solve the problem, eliminate obviously wrong answers and take your best guess.
Now let’s try out these steps on a couple of SAT®-type multiple-choice math questions.
Example:

Q

15°

x°
P

S

R

PQ = PS

269

In the figure above, x =
A.

15°

B.

30°

C.

60°

D.

75°

Chapter 7
MultipleChoice Math

Solution:
1. The problem asks you to find the measure of one angle of right triangle PQR.
2. Two math principles apply: (1) the sum of the measures in degrees of the angles of a triangle is 180, and (2)
45-45-90 right triangles have certain special properties. Since PQ = PS, PQS is a 45-45-90 right triangle.
Therefore, angle PQS = 45° and angle PQR = 45 + 15 = 60°. Therefore, angle x = 180 − 90 − 60 = 30°.
3. Look to see if 30° is among the answer choices. You’ll see that it’s choice B. No further steps are needed.
The correct answer is choice B.

Peterson’s SAT® Prep Guide 2017

Example:

If x and y are negative numbers, which of the following is negative?
A.

xy

B.

(xy)2

C.

(x − y)2

D.

x+y

Solution:
1. The problem asks you to pick an answer choice that is a negative number.
2. The principles that apply are those governing operations with signed numbers. Since x and y are negative, choice
A must be positive. As for choices B and C, as long as x and y are not equal to each other, both expressions must
be positive. (If they’re equal, the expression equals zero, and any number other than zero squared gives a positive
result.) Choice D, however, is negative since it represents the sum of two negative numbers.
3. Looking among the answer choices, you can see that the correct answer is choice D. If you have trouble working
with letters, try substituting easy numbers for x and y in each choice.

KNOW WHEN TO USE YOUR CALCULATOR

270
Chapter 7
MultipleChoice Math

Calculators are allowed in the SAT® Math Test—Calculator section, but you won’t need a calculator to solve any SAT® math questions. Calculators can be helpful in solving most of the problems, whether you use the calculator for simplifying expressions or
graphing equations. But remember that your calculator is not some sort of magic brain. If you don’t understand the questions in
the first place, the calculator won’t give you a solution.
Most calculators that you would use in class are allowed. It is best to use whichever calculator you are already comfortable using
instead of trying to learn how to use a new one.
The most important thing to remember is to set up your work on paper first, and then plug the information into the calculator.
For example, if you have a question that deals with an equation, set up the equation on your scratch paper. Then make your
number substitutions on the calculator. This way, you always have something to refer to without having to think, “Oh, nuts, how
did I set that up?” as the seconds tick by.
When you use your calculator, check the display each time you enter numbers to make sure you entered them correctly. Make
sure to hit the Clear key after each finished operation; otherwise, it could get ugly.

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LEARN THE MOST IMPORTANT MULTIPLE-CHOICE MATH TIPS
You’ve probably heard some of these tips before, but some will be new to you. Whatever the case, read them, learn them, and
remember them. They will help you.

ALERT: Don’t automatically reach for your calculator. If it can’t help you solve the problem, you’ll just waste time fiddling
with it. Save the calculator for what it does best, especially simplifying numeric expressions.

The Question Number Tells You How Hard the Question Is
Just as in most of the other SAT® sections, the questions go from easy to hard as you work toward the end. The first third of the
questions is easy, the middle third is average but harder, and the final third gets more and more difficult. Take a look at these
three examples. Don’t solve them yet (you’ll be doing that in a couple of minutes); just get an idea of how the level of difficulty
changes from Question 1 to Question 12 to Question 25.
1.

12.

If

a+5
= m, and m = 9, what is the value of a?
6

A.

24

B.

49

C.

59

D.

84

Line a intersects the x-axis at (3, 0) and the y-axis at (0, –2). Line b passes through the origin and is parallel to line a. Which
of the following is an equation of line b?
A.

3
y= x
2

B.

2
y= x
3

C.

3
y=− x
2

D.

2
y=− x
3

271
Chapter 7
MultipleChoice Math

Peterson’s SAT® Prep Guide 2017

25.

Yasmine owns a coffee shop and orders both coffee and tea from a wholesale supplier. The supplier will send no more than
600 kg in a shipment. Coffee beans come in packages that weigh 18.5 kg, and tea leaves come in packages that weigh 10 kg.
Yasmine wants to buy at least twice as many packages of coffee as packages of tea. If c stands for the number of packages
of coffee, and t stands for the number of packages of tea, which of the following systems of inequalities best represents
Yasmine’s order? Both c and t are nonnegative integers.
A.

18.5c + 10t ≤ 600
c ≥ 2t

B.

18.5c + 10t ≤ 600
2c ≥ t

C.

37c + 10t ≤ 600
c ≥ 2t

D.

37c + 10t ≤ 600
2c ≥ t

Look for shortcuts. SAT® math problems test your math reasoning, not your ability to make
endless calculations. If you find yourself calculating too much, you’ve probably missed a
shortcut that would have made your work easier.

Can you see the difference? You can probably do Question 1 very quickly. For Question 12, you might have to think for a bit.
Question 25 may cause you to wince a little and then get started on some heavy-duty thinking.

272
Chapter 7
MultipleChoice Math

Easy Questions Have Easy Answers—Difficult Questions Don’t
The easy questions are straightforward and don’t have any hidden tricks. The obvious answer is almost always the correct answer.
So for Question 1, the answer is indeed choice B.
When you hit the difficult stuff, you have to think harder. The information is not straightforward, and the answers aren’t obvious.
You can bet that your first-choice, easy answer will be wrong. If you don’t believe it, let’s take another look at Question 25.
Example:
25.

Yasmine owns a coffee shop and orders both coffee and tea from a wholesale supplier. The supplier will send no more than
600 kg in a shipment. Coffee beans come in packages that weigh 18.5 kg, and tea leaves come in packages that weigh 10 kg.
Yasmine wants to buy at least twice as many packages of coffee as packages of tea. If c stands for the number of packages
of coffee, and t stands for the number of packages of tea, which of the following systems of inequalities best represents
Yasmine’s order? Both c and t are nonnegative integers.
A.

18.5c + 10t ≤ 600
c ≥ 2t

B.

18.5c + 10t ≤ 600
2c ≥ t

C.

37c + 10t ≤ 600
c ≥ 2t

D.

37c + 10t ≤ 600
2c ≥ t

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Solution:
This question is difficult mostly because it takes a little longer to think through the problem and set up the inequalities laid out in the question stem. Let’s tackle this step by step.
We will use the variables c for coffee beans and t for tea. The total weight, in kg, of coffee beans and tea that the
wholesale supplier sends can be expressed as the weight of each package multiplied by the number of each type of
package, which is 18.5c for coffee beans and 10t for tea leaves. Since the supplier will not send shipments that weigh
more than 600 kg, it follows that 18.5c + 10t ≤ 600 expresses the first part of the problem.
Since Yasmine wants to buy at least twice as many packages of coffee beans as packages of tea leaves, the number of
packages of coffee beans should be greater than or equal to two times the number of packages of tea leaves. This
can be expressed by c ≥ 2t.
Thus, the correct answer is choice A.
Why are the other answers wrong? Choice B is incorrect because it misrepresents the relationship between the
numbers of each package that Yasmine wants to buy. Choice C is incorrect because the first inequality of the system
incorrectly doubles the weight per package of coffee beans. The weight of each package of coffee beans is 18.5 kg,
not 37 kg. Choice D is incorrect because it doubles the weight per package of coffee beans and transposes the relationship between the numbers of packages.
ALERT: Beware of the obvious. Don’t be fooled by what look like obvious answers to difficult questions. The answers to
difficult questions require some digging. They never jump out at you.

Be Certain to Answer the Question Being Asked

273

Suppose that you were asked to solve the following problem:

Chapter 7

Example:

MultipleChoice Math

If 5x + 11 = 31, what is the value of x + 4?
A.

4

B.

6

C.

8

D.

10

Solution:
The first step is to solve the equation 5x + 11 = 31.
5 x + 11 = 31 Subtract 11 from both sides.
5 x = 20 Divide both siides by 5.
x=4
Remember that the problem does not ask for the value of x, it asks for the value of x + 4, so the answer is actually 8.
Make certain that the answer you select is the answer to the question that is being asked. The correct answer is
choice C.

Peterson’s SAT® Prep Guide 2017

When Guessing at Hard Questions, You Can Toss Out Easy Answers
Now that you know the difficult questions won’t have easy or obvious answers, use a guessing strategy. (Use all the help you can
get!) When you have less than a clue about a difficult question, scan the answer choices and eliminate the ones that seem easy
or obvious, such as any that just restate the information in the question. Then take your best guess.

Questions of Average Difficulty Won’t Have Trick Answers
Let’s look again at Question 12:
12.

274
Chapter 7
MultipleChoice Math

Line a intersects the x-axis at (3, 0) and the y-axis at (0, –2). Line b passes through the origin and is parallel to
line a. Which of the following is an equation of line b?

A.

y=

3
x
2

B.

y=

2
x
3

C.

3
y=− x
2

D.

2
y=− x
3

This is a bit more difficult than Question 1, but it’s still pretty straightforward. Since we know points on line a, we can calculate
the slope of this line:
y 2 − y1 −2 − 0 2
=
=
x 2 − x1 0 − 3 3
2
. The problem tells us that line b passes through the origin,
3
2
which means that it intercepts the y-axis at 0. Thus, line b can be expressed by the equation y = x . The correct answer is choice B.
3

Since line b is parallel to line a, the two have the same slope, that is,

It’s Smart to Work Backward
Every standard multiple-choice math problem includes four answer choices. One of them has to be correct; the other three are
wrong. This means that it’s always possible to solve a problem by testing each of the answer choices. Just plug each choice into
the problem and sooner or later you’ll find the one that works! Testing answer choices can often be a much easier and surer way
of solving a problem than attempting a lengthy calculation.

When Working Backward, Always Start from the Middle
When working on multiple-choice math questions, remember that all of the numeric answer choices are presented in order—
either smallest to largest, or vice versa. As a result, it’s always best to begin with a middle option, choice B or choice C. This way,
if you start with choice C and it’s too large, you’ll only have to concentrate on the smaller choices. There, you’ve just knocked off
at least two choices in a heartbeat! Now let’s give it a test run!

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Example:
If

8
9
y = , what is the value of y?
9
4

A.

32
81

B.

1
2

C.

2

D.

81
32

Solution:
8
16 9
Start with choice C, because it will be easier to compute with than choice B: (2) =
< .
9
9 4
Since choice C is too small, the only possible answer is choice D.
You can check that

8  81 9
 = .
9  32  4

The correct answer is choice D.
Now try this testing business with a more difficult question:
Example:
In the xy-plane, the line determined by the points (8, c) and (c, 18) passes through the origin. Which of the following
could be the value of c?
A.

10

B.

11

C.

12

D.

13

275
Chapter 7
MultipleChoice Math

Solution:
Start with choice C, because it may be easier to compute with than choice B. The line through (8, 12) and (12, 18)
3
18 − 12
x + b. This equation simplifies to y = x , which is a line through the origin.
2
12 − 8
3
Plug (8, 12) or (12, 18) into y = x , and both sides will be equal.
2
is y =

3
3
12 = (8 ) or 18 = (12)
2
2
12 = 12
18 = 18
The other values of c will not result in an equivalent equation. The correct answer is choice C.

Peterson’s SAT® Prep Guide 2017

It’s Easier to Work with Numbers Than with Letters
Because numbers are more meaningful than letters, try plugging them into equations and formulas in place of variables. This
technique can make problems much easier to solve. Here are some examples:
Example:
If x − 4 is 2 greater than y, then x + 5 is how much greater than y?
A.

3

B.

7

C.

9

D.

11

Solution:
Choose any value for x. Let’s say you decide to make x = 4. All right, 4 − 4 = 0, and 0 is 2 greater than y. So y = −2.
If x = 4, then x + 5 = 4 + 5 = 9, and so x + 5 is 11 more than y. The correct answer is choice D.
Example:
The cost of renting office space in a building is $2.50 per square foot per month. Which of the following represents
the total cost c, in dollars, to rent p square feet of office space each year in the building?

276

A.

c = 2.50(12p)

B.

c = 2.50p + 12

C.

c=

2.50 p
12

D.

c=

12 p
2.50

Chapter 7
MultipleChoice Math

Solution:
Let p = 100, then the rent for one month is $250 and the rent for one year is $3,000. The only equation that will
provide that answer is c = 2.50(12p). The correct answer is choice A.
If a question asks for an odd integer or an even integer, go ahead and pick any odd or even integer you like.

Leave a paper trail! If you need to set up an equation, jot it down in your
test booklet. That way, if you come back to recheck your work, you’ll know
what you were originally thinking.

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Solving for Variables with Restricted Values
When solving problems involving variables, you must pay careful attention to any restrictions on the possible values of the
variables
Consider the following question:
Example:
If x ≥ 2, which of the following is a solution to the equation x(x − 3)(x + 4)(x + 2)(3x − 5) = 0?
A.

2

B.

3

C.

4

D.

5

Solution:
This equation has five solutions, but the problem is looking only for a solution that is at least 2. Set each of the factors
equal to 0 and solve for x. The only answer that is greater than or equal to 2 is 3. The correct answer is choice B.
Now, consider this slightly different version of the same problem.
Example:

277

If x < –2, which of the following is a solution to the equation x(x − 3)(x + 4)(x + 2)(3x − 5) = 0?
A.

–3

Chapter 7

B.

–4

C.

–5

MultipleChoice Math

D.

There is more than one solution.

Solution:
The solutions to the equation can be found by setting each of the factors equal to zero. So x = 0, x – 3 = 0, x + 4 = 0,
x + 2 = 0, and 3x – 5 = 0.
These lead to the solutions x = 0, 3, –4, –2, and

5
respectively.
3

Of these five solutions only –4, choice B, is less than –2. The correct answer is choice B.

The test booklet is yours, so feel free to use it for your scratchwork.
Also, go ahead and mark up any diagrams with length or angle information; it helps. But don’t waste time trying to redraw diagrams; it’s
just not worth it.

Peterson’s SAT® Prep Guide 2017

5
3

Solving Equations in the Three-Statement Format
You may find a three-statement format in certain questions in the multiple-choice math section. The best way to answer this
kind of question is by process of elimination, tackling one statement at a time and marking it as true or false. Here is an example:

Example:

k

p° q°
r°

m
s°

t° v°
w° x°

n

Note: Figure not drawn to scale.

In the figure above, lines k and m intersect at a point, and lines k and n intersect at a different point. If v + s = p + q,
which of the following statements must be true?

278
Chapter 7
MultipleChoice Math

I.

r=w

II.

t=s

III.

q=x

A.

I only

B.

II only

C.

I and II only

D.

I, II, and III

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Solution:
Because v + s = p + q, we know that p + q = 180. Because they both make a straight line, lines m and n must be parallel. Since m and n are parallel, then statements I and II, must be true. While statement III might be true, it is only true
if line k is perpendicular to lines m and n, and that does not have to be true.
The correct answer is choice C.

For multiple-choice math questions, circle what’s being asked so that
you don’t pick a wrong answer by mistake. That way, for example, you
won’t pick an answer that gives perimeter when the question asks for
an area.

Solving Equations Involving Square Roots or Algebraic Fractions
The procedure for solving equations involving square roots or algebraic fractions occasionally results in what are known as
extraneous solutions. An extraneous solution is a number that is correctly obtained from the equation-solving process but doesn’t
actually solve the equation, be sure to check your answer.
Example:
Solve for x:

x + 4 + 15 = 10

A.

−29

B.

−21

C.

21

D.

There are no solutions.

279
Chapter 7

Solution:

MultipleChoice Math

First, solve the equation.
x + 4 + 15 = 10

Subtract 15 from both sides.

x + 4 = −5

(

x+4

)

2

Squaare both sides.

= ( −5)

2

x + 4 = 25
x = 21

It appears that the solution is choice C. However, if you check the solution x = 21 in the original equation, you will see
that it doesn’t solve it.
x + 4 + 15 = 10 ?
21+ 4 + 15 = 10 ?
25 + 15 = 10 ?
5 + 15 ≠ 10.
The correct answer is choice D.

Peterson’s SAT® Prep Guide 2017

Solving Geometry Problems of Measure
When you are asked to find the measure of a side or angle of a figure, using the measure of an angle or a side of another shape
can help you find the measure you need.
Example:
In the figure, what is the length of NP?
A.

8

B.

9

C.

12

D.

15

N
20

M

9

7
P

O

Solution:
This figure is really two right triangles, NMO and NMP. Since NM is a side of both triangles, once you find its length,
you can find the length of NP. The Pythagorean theorem is what you need:
NM2 + MO2 = NO2

280
Chapter 7
MultipleChoice Math

NM2 + (16)2 = (20)2
Note that 16 and 20 are multiples of 4 and 5, respectively, so you now know that this is a 3-4-5 right triangle, which
means that NM = 12.
Since you just found out that triangle NMP has sides of 9 and 12, it’s also a 3-4-5 right triangle, so NP must be 15.
The correct answer is choice D.

Draw a diagram if none is supplied. Drawing a diagram is a great way to
organize information. Mark it up with the information you’re given, and
you’ll have a better idea of what you’re looking for.

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Solving Right Triangles Using the Pythagorean Theorem
The Pythagorean theorem is usually needed to solve problems involving a right triangle for which you are given the lengths
of some of the sides. The Pythagorean theorem enables you to compute the length of the third side of a right triangle if you
know the lengths of the other two sides. It is one of the most useful and common SAT® geometry facts. Consider the problem
below.
Example:
Line segment PQ is tangent to the circle with center O at point T. If T is the midpoint of PQ, OQ = 13, and the radius
of the circle is 5, what is the length of PQ?
A.

10

B.

12

C.

24

D.

26

P
T
O

Q

Solution:
This is a tricky question since, at the moment, it doesn’t appear to involve any triangles at all. However, you are told
that the radius of the circle is 5, and if you draw in radius OT , you will create triangle OTQ. Use the fact that a tangent
line to a circle is perpendicular to the radius at the point of contact to deduce that ∠OTQ is a right angle.

281

P
T

Q

Chapter 7
O

MultipleChoice Math

The diagram now depicts right triangle OTQ, and OT = 5 and OQ = 13. Now, use the Pythagorean theorem to
determine that TQ = 12, as shown here:

OT 2 + TQ 2 = OQ 2
52 + TQ 2 = 132
25 + TQ 2 = 169
TQ 2 = 144
TQ = 12
Finally, since T is the midpoint of line segment PQ, the entire length of the line segment is 12 + 12 = 24.
The correct answer is choice C.

Peterson’s SAT® Prep Guide 2017

Eliminate Answers That Can’t Possibly Be Right
Knowing whether your calculations should produce a number that’s larger or smaller than the quantity you started with can point
you toward the right answer. It’s also an effective way of eliminating wrong answers. Here’s an example:
Example:
Daryl can set up the display for the science fair in 20 minutes. It takes Francisco 30 minutes to set it up. How long will
it take the two boys to complete the setup if they work together?
A.

8 minutes

B.

12 minutes

C.

20 minutes

D.

30 minutes

Solution:
Immediately you can see that choices C and D are impossible because the two boys working together will have to
complete the job in less time than either one of them working alone.

Actual time spentt
Time needed to do entire job alone

282

Daryl
x
20

x
x
+
=1
20 30

Chapter 7
MultipleChoice Math

Multiply by 60 to clear fractions:
3 x + 2 x = 60
5 x = 60
x = 12
The correct answer is choice B.

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Francisco
x
30

Your Eye Is a Good Estimator
Figures in the standard multiple-choice math section are always drawn to scale unless you see the warning “Note: Figure not
drawn to scale.” That means you can sometimes solve a problem just by looking at the picture and estimating the answer. Here’s
how this works:
Example:

4

f (x)

2

–2

0

2

4

6

–2
g (x)
–4

f ( x ) = ( x − 3) − 3
2

283

g ( x ) = −2 ( x − 3) + 3
2

Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does
f(x) + g(x) = 0?

Chapter 7

A.

1

MultipleChoice Math

B.

2

C.

3

D.

4

Solution:
The sum of the function values is 0 when the function values for f and g are opposites. That appears to be true at
x = 3. The correct answer is choice C.

If Some Questions Always Give You Trouble, Save Them for Last
You know which little demons haunt your math skills. If you find questions that you know will give you nightmares, save them for
last. They will take up a lot of your time, especially if you’re panicking, and you can use that time to do more of the easier questions.

Peterson’s SAT® Prep Guide 2017

EXERCISES: MULTIPLE-CHOICE MATH
Exercise 1
18 Minutes—15 Questions
For Questions 1–15, solve each problem, choose the best answer from the choices provided, and put a circle around the
correct answer. You may use any available space for scratch work.

ADDITIONAL INFORMATION:

• The use of a calculator is permitted.
• All variables and expressions used represent real numbers unless otherwise indicated.
• Figures provided in this test are drawn to scale unless otherwise indicated.
• All figures lie in a plane unless otherwise indicated.
• Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

284

l
A = lw

Rectangular
Solid:

MultipleChoice Math

l
V = lwh

h

w

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w

Chapter 7

Triangle:

x

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

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x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

1
V = �r2h
3

l

w
1
3

V = lwh

1.

2.

3.

4.

In a linear function f(x) with a graph that has a slope of
–2.5, if f(5) = 8, what is the value of f(1)?
A.

–2

B.

3

C.

13

D.

18

Which of the following expressions is equal to 0 for some
value of p?
A.

|p – 2| − 2

B.

|2 − p| + 2

C.

|p + 2| + 2

D.

|p – 2| + 2

If f(x) = –3x + 4, what is f(–4x)?
A.

–12x – 4

B.

12x + 4

C.

12x – 4

D.

12x2 – 20x

y
=4
x
5 ( x − 1) = y
If (x, y) is the solution to the system of equations above,
what is the value of x?

5.

SHOW YOUR WORK HERE

A.

–20

B.

–5

C.

5

D.

20

285
Chapter 7
MultipleChoice Math

Which of the following is equivalent to the expression
5(3x – 2)(2x + 1)?
A.

15x

B.

30x2 – 10

C.

30x2 – 5x –10

D.

25x2 – 5

Peterson’s SAT® Prep Guide 2017

6.

7.

Kathleen is preparing to run her first road race. She begins training by doing intervals of running and walking.
The longest interval of running increases by a constant
amount each week. The first week she runs for intervals
of up to 2 minutes at a time. By the ninth week, she runs
for intervals of up to 40 minutes at a time. Which of the
following best describes how the time Kathleen spends
running changes between her first and ninth weeks?
A.

Kathleen increases the time of her longest run by
5 minutes each week.

B.

Kathleen increases the time of her longest run by
4.75 minutes each week.

C.

Kathleen increases the time of her longest run by
4.5 minutes each week.

D.

Kathleen increases the time of her longest run by
4.25 minutes each week.

If

x+y 5
= , which of the following must also be true?
y
9

A.

x
4
=−
y
9

B.

286

x 14
=
y 9

C.

4
x−y
=−
9
y

Chapter 7

D.

x − 2y
13
=−
y
9

MultipleChoice Math

8.

Which of the following shows the solution set to the
equation x − 1 = x − 7 ?
A.

{5, 10}

B.

{1}

C.

{5}

D.

{10}

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SHOW YOUR WORK HERE

9.

A circle whose center is at the origin passes through the
point whose coordinates are (1, 1). What is the area of this
circle?

10.

A.

π

B.

2π

C.

2p

D.

2 2p

SHOW YOUR WORK HERE

In triangle ABC, AB = BC, and AC is extended to D. If
angle BCD measures 100°, find the number of degrees in
angle B.

B

A

11.

C
A.

20

B.

40

C.

50

D.

80

D

Which of the following represents a line that is perpendicular to the line with equation y = 4 – 2x?
A.

y = 2x + 5

B.

y = –2x + 3

C.

y – 2x = 1

D.

2y – x = 6

287
Chapter 7
MultipleChoice Math

x = 3y

12.

( x − 3) + ( y − 1)2 = 10
2

How many ordered pairs satisfy the system of equations
above?
A.

0

B.

1

C.

2

D.

infinitely many

Peterson’s SAT® Prep Guide 2017

13.

14.

15.

If

z+6
= 5 , what is the value of z?
z −5

A.

19
6

B.

35
6

C.

25
4

D.

31
4

If the expression (4 + 3i)(2 – 7i) is rewritten in the form
a + bi, where a and b are real numbers, what is the value
of a? (Note: i = −1 )
A.

29

B.

8

C.

–13

D.

–22

x 2 − 6dx =

e
2

In the quadratic equation above, d and e are
constants. What are the solutions for x?

288
Chapter 7
MultipleChoice Math

A.

x = 3d ±

6 d − 2e
2

B.

x = 3d ±

6 d + 2e
2

C.

x = 3d ±

36d 2 − 2e
2

D.

x = 3d ±

36d 2 + 2e
2

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SHOW YOUR WORK HERE

Exercise 2
12 Minutes—10 Questions
For Questions 1–10, solve each problem, choose the best answer from the choices provided, and put a circle around the
correct answer. You may use any available space for scratch work.

ADDITIONAL INFORMATION:

• The use of a calculator is permitted.
• All variables and expressions used represent real numbers unless otherwise indicated.
• Figures provided in this test are drawn to scale unless otherwise indicated.
• All figures lie in a plane unless otherwise indicated.
• Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h
r

4
3

V = �r3
The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
3

289

h

V = �r2h

l

w
1
3

V = lwh

Chapter 7
MultipleChoice Math

Peterson’s SAT® Prep Guide 2017

1.

2.

3.

290
Chapter 7
MultipleChoice Math

4.

Mario has made 58 successful 3-point shots in basketball
this season. The school record is 92 3-point shots. If he
makes 3 more 3-point shots each game, which of the
following shows how many 3-point shots he will have
made after g additional games?
A.

3 + 58g

B.

92 + 3g

C.

58 + 3g

D.

58 – 3g

If a = 5b, then
A.

5b
3

B.

3b

C.

3b
5

D.

b
3

3
a=
5

A rectangular door measures 5 feet by 6 feet 8 inches.
What is the distance from one corner of the door to the
diagonally opposite corner?
A.

8 feet 2 inches

B.

8 feet 4 inches

C.

8 feet 8 inches

D.

9 feet 6 inches

Two ships leave from the same port at 11:30 a.m. If one
sails due east at 20 miles per hour and the other due south
at 15 miles per hour, how many miles apart are the ships
at 2:30 p.m.?
A.

25

B.

50

C.

75

D.

80

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SHOW YOUR WORK HERE

5.

6.

7.

8.

The line y = ax – 5, where a is a constant, is graphed in the
xy-plane. If the line contains the point (b, c), which does
not lie on either the x- or y-axis, what is the slope of the
line in terms of b and c?

A.

c +5
b

B.

b+5
c

C.

c −5
b

D.

b−5
c

SHOW YOUR WORK HERE

Ken received grades of 90, 88, and 75 on three tests. What
grade must he receive on the next test so that his average
for these four tests is 85?
A.

87

B.

89

C.

90

D.

92

There is enough food at a picnic to feed 20 adults or 32
children. If there are 15 adults at the picnic, how many
children can still be fed?

291

A.

6

Chapter 7

B.

8

C.

12

MultipleChoice Math

D.

16

In parallelogram ABCD, angle A measures 60°. What is the
sum of angle B and angle D?
A.

180°

B.

240°

C.

280°

D.

300°

Peterson’s SAT® Prep Guide 2017

9.

10.

If 4x – 7 ≤ 1, what is the greatest possible value of 4x + 2?
A.

10

B.

7

C.

3

D.

1

If a train covers 14 miles in 10 minutes, what is the rate of
the train in miles per hour?
A.

64

B.

76

C.

84

D.

98

292
Chapter 7
MultipleChoice Math

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SHOW YOUR WORK HERE

ANSWER KEYS AND EXPLANATIONS
Exercise 1

1.

1. D

4. C

7. A

10. A

13. D

2. A

5. C

8. D

11. D

14. A

3. B

6. B

9. B

12. C

15. D

The correct answer is D. If the slope is –2.5 and
f(5) = 8, then use the slope formula to find f(1).

7.

18 = f (1)

2.

3.

4.

5.

8.

The correct answer is D.
x −1 = x − 7

The correct answer is A. The absolute value of an
expression is always greater than or equal to 0, so
adding a number to the expression will never result in
0. Choice A, which states |p – 2| − 2 = 0 when p = 0 or
4, is correct.

x − 1 = ( x − 7)

2

x − 1 = x 2 − 14 x + 49
0 = x 2 − 15 x + 50

293

Consequently, x = 5 or x = 10. Plug these values into
the original equation to see if they make it true.

Chapter 7

0 = ( x − 5) ( x − 10)

The correct answer is B. If f(x) = –3x + 4, then
f(–4x) = –3(–4x) + 4, and –3(–4x) + 4 = 12x +4.

5 −1 = 5 − 7?
2 ≠ −2

y
= 4 and 5(x – 1) = y, then
x
y = 4x and y = 5x –5. So, 4x = 5x – 5 and x = 5.

The correct answer is C. If

The correct answer is C. Multiply the expression to
find the equivalent one. Use FOIL.

x+y 5
= , then
9
y

x y 5
+ =
y y 9
x y
5
+ − 1= − 1
y y
9
x
4
=−
y
9

8 − f (1)
= −2.5
5 −1
8 − f (1)
= −2.5
4
8 − f (1) = −10
8 + 10 = f (1)

The correct answer is A. If

MultipleChoice Math

10 − 1 = 10 − 7 ?
3=3
9.

The correct answer is B.

5(3 x − 2)(2 x + 1) = 5(6 x 2 + 3 x − 4 x − 2)

(1, 1)

= 5(6 x 2 − x − 2)
= 30 x − 5 x − 10
2

1
6.

The correct answer is B. To find the average increase,
divide the change in increase by the number of weeks:
40 − 2 38
=
= 4.75
9 −1
8

1

12 + 12 = r2
2 = r2
Area = πr2 = 2π

Peterson’s SAT® Prep Guide 2017

10.

The correct answer is A.

14.

(4 + 3i) (2 – 7i) = 8 – 28i + 6i – 21i2

		Angle BCA = Angle BAC = 80°.
		

(4 + 3i) (2 – 7i) = 8 – 22i – 21(–1)

There are 20° left for angle B.
		

11.

The correct answer is D. A line that is perpendicular to
the line with the equation y = 4 – 2x will have a slope
equal to 0.5. If all equations are written in slope–
intercept form, only choice D, 2y – x = 6, will be correct.

The correct answer is A.

15.

(4 + 3i) (2 – 7i) = 29 – 22i
The correct answer is D. Write the equation in
standard form, then plug the numbers into the
quadratic formula and simplify.

12.

The correct answer is C. Graph the system of
equations. Note that the second equation is a circle
that is intersected twice by the line.

e
=0
2
The quadratic formula is:

13.

The correct answer is D.

b 2 − 4 ac
−b
±
2a
2a
So, applyiing that:

z+6
=5
z −5
z + 6 = 5 z − 25
31 = 4 z
31
=z
4

294
Chapter 7
MultipleChoice Math

www.petersons.com

x 2 − 6dx −

x=

x=

− ( −6d )
±
2(1)

x = 3d ±

( −6d ) 2 − 4 (1)  −
2 (1)

2

36d + 2e
2

1 
e
2 

Exercise 2
1. C

3. B

5. A

7. B

9. A

2. B

4. C

6. A

8. B

10. C

1.

The correct answer is C. If Mario already has made 58
shots and will make an additional 3 shots each game,
then he will make an additional 3g 3-point shots in g
games, for a total of 58 + 3g.

6.

The correct answer is A. Ken must score as many
points above 85 as below. So far he has 8 above and 10
below. He needs another 2 above, making 87, choice A,
the correct answer.

2.

The correct answer is B.

7.

The correct answer is B. If 15 adults are fed, 3 of the
4
1
1
food is gone. of the food will feed × 32, or 8,
4
4
children.

8.

The correct answer is B.

3
i 5 b = 3b
5

3.

The correct answer is B.
5 feet = 60 inches

If angle A = 60°, then angle B = 120°.

6 feet 8 inches = 80 inches

Angle B = Angle D. Their sum is 240°.

This is a 6-8-10 triangle, making the diagonal 100
inches, which is 8 feet 4 inches.
4.

5.

9.

If 4x –7 ≤ 1, then 4x + 2 must be at most 10.

The correct answer is C. In 3 hours, one ship went
60 miles, the other 45 miles. This is a 3-4-5 triangle, as
45 = 3(15), and 60 = 4(15). The hypotenuse will be
5(15), or 75.
The correct answer is A. Substitute the point (b, c)
into the equation y = ax – 5 and solve for a to find that
c +5
c = ab – 5 and a =
.
b

The correct answer is A.

4 x − 7 + 9 ≤ 1+ 9
4 x + 2 ≤ 10
10.

The correct answer is C.
10 minutes =

295
Chapter 7

1
hour
6

MultipleChoice Math

In one hour, the train will cover 6(14), or 84, miles.

Peterson’s SAT® Prep Guide 2017

SUMMING IT UP
• Follow the five-step plan for answering basic multiple-choice math questions:
1.

Read the question carefully and determine what’s being asked.

2.

Decide which math principles apply and use them to solve the problem.

3.

Look for your answer among the choices. If it’s there, mark it and go on.

4.	If the answer you found is not there, recheck the question and your calculations.
5.	If you still can’t solve the problem, eliminate obviously wrong answers and take your best guess.

• In the Math Test—Calculator section, use a calculator where it can help the most: on basic arithmetic calculations, when
calculating square roots and percentages, and comparing and converting fractions.

• Always set up your work on paper, then enter the numbers in your calculator; that way, if your calculation becomes confused, you don’t have to try to replicate your setup from memory.

• The question number tells you how hard the question will be, though some questions may be easier for you.
• Work backward from the answer choices. When you do, start with choice B or choice C.
• Try to work with numbers instead of letters. This will help you avoid unnecessary algebraic calculations.
• Figures in the math section are always drawn to scale unless you see a warning. So, if you need to do so, use your eye as an
estimator.

ONLINE
PREP

296
Chapter 7
MultipleChoice Math

Want to Know More?

Access more practice questions, valuable lessons, helpful tips, and expert strategies for the following multiple-choice math topics
in Peterson’s SAT® Online Course:

• Calculator Strategy
• Guessing in Math
• Pacing in Math
• Plugging in Numbers
• Problem Solving
• Working Backwards
To purchase and access the course, go to www.petersons.com/sat.

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Chapter 8:
Grid-In Strategies
OVERVIEW
Why Grid-Ins Are Easier Than You Think
How to Record Your Answers
Guessing on Grid-Ins Can’t Hurt You
Exercises: Grid-Ins
Summing It Up

WHY GRID-INS ARE EASIER THAN YOU THINK
Let’s take a quick break from multiple-choice questions and examine the other kind of question you will see on both the Math
Test—No Calculator and Math Test—Calculator sections: grid-ins. These are officially named “student-produced responses,”
because you have to do the calculations and find the answer on your own; there are no multiple-choice answers from which
to choose.

297
Chapter 8

Many students are intimidated by grid-ins. Don’t be! Grid-in questions test the exact same mathematical concepts as the
multiple-choice questions. The only difference is that there are no answer choices with which to work.

Grid-In
Strategies

The grid-in questions are in a section of their own and arranged in order of difficulty from easy to hard.

Take a Look at a Grid
The special answer grid has some very different sections. There are blank boxes at the top so you can actually write in your answer.
Below the boxes are some circles that have fraction slashes and decimal points. You fill these in if your answer needs them. The
largest section has circles with numbers in them. You have to fill in the circles to correspond to the answer you have written in
the boxes. Yes, it’s a lot to think about, but once you understand how to use the grid-ins, it’s not a big deal.

Peterson’s SAT® Prep Guide 2017

Here is a sample grid:

/
.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

6

7
8

7
8

7
8

7
8

9

9

9

9

NOTE: Remember that the student-produced responses will not be negative numbers
and won’t be greater than 9999.

1

ALERT: If the correct answer is a mixed number such as 5 , you must grid it as 21/4 or as 5.25. If you grid it as “51/4,” it will
4
read as “fifty-one fourths,” and it will be marked incorrect.

298
Chapter 8
Grid-In
Strategies

HOW TO RECORD YOUR ANSWERS
On the SAT® exam, each set of grid-in questions starts with directions that look approximately like this:

DIRECTIONS: For these questions, solve the problem and enter your answer in the grid, as described below, on the
answer sheet.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
7
1
5. Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
		
If 3

1
is entered into the grid as
2

www.petersons.com

, it will be interpreted as

1
31
, not 3 .
2
2

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.

7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

1

1

2

2

2

1

1

3

3

3

3

3

4

4

4

4

4

5

5

5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

0

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

299

2
Acceptable ways to grid are:
3
.

1

0

0

0

1

1

1

2

2

2

1

Chapter 8
.

Grid-In
Strategies

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

7

7

7

8

8

8

8

8

9

9

9

9

9

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

7

7

7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

Once you understand the following six rules, you can concentrate just on solving the math problems in this section.

Peterson’s SAT® Prep Guide 2017

1. Write your answer in the boxes at the top of the grid.
2. Mark the corresponding circles, one per column.
3. Start in any column.
4. Work with decimals or fractions.
5. Express mixed numbers as decimals or improper fractions.
6. If more than one answer is possible, grid any one.

NOTE: Don’t use a comma in a number larger than 999. Just fill in the four digits and the corresponding circles.
You only have circles for numbers, decimal points, and fraction slashes; there aren’t any for commas.
Now let’s look at these rules in more detail:
1.

Write your answer in the boxes at the top of the grid. Technically, this isn’t required by the SAT®. Realistically, it gives you
something to follow as you fill in the circles. Do it—it will help you.

2.

Make sure to mark the circles that correspond to the answer you entered in the boxes, one per column. The machine that
scores the test can only read the circles, so if you don’t fill them in, you won’t get credit. Just entering your answer in the
boxes is not enough!

3.

You can start entering your answer in any column, if space permits. Unused columns should be left blank; don’t put in zeroes.
Look at this example:
Here are two ways to enter an answer of “150.”

300

/
.
0

Chapter 8
2

Grid-In
Strategies

4.

/
.

.
0

0

1

1

1

1

2

2

2

2

0

/
.
0
2

/
.

.

0
1

1

2

2

3

3

3

3

3

3

3

3

4
5

4

4
5

4
5

4
5

4
5

4

4
5

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

You can write your answer as a decimal or a fraction. For example, an answer can be expressed as 3 or as .75. You don’t have
4
to put a zero in front of a decimal that is less than 1. Just remember that you have only four spaces to work with and that a
decimal point or a fraction slash uses up one of the spaces.

www.petersons.com

ALERT: Take the time to write your answer in the spaces. It will lessen your chances of filling in an incorrect circle.

For decimal answers, be as accurate as possible but keep it within four spaces. Say you get an answer of .1777,
here are your options:

.

.
/
.

0

0

1
2

2

/
.

.

/
.

0

0

0

1

1

1

2

2

2

0
2

/
.

.

0

0

1

1

2

2

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

7
8

7
8

8

8

7
8

7
8

8

9

9

9

9

9

9

9

7
9

Answers .177 and .178 would both be marked correct.

Fractions do not have to be simplified unless they don’t fit in the answer grid. For example, you can grid

4
, but you can’t
10

12
3
grid 16 because you’d need five spaces. So, you would simplify it and grid 4 .
5.

301
3

A mixed number has to be expressed as a decimal or as an improper fraction. If you tried to grid 1 , it would be scored as
4
7
13
, which would give you a wrong answer. Instead, you could grid the answer as 1.75 or as .
4
4

Chapter 8
Grid-In
Strategies

.
/

/
.

.

.

/
.

/
.

.

.

0

0

0

0

0

0

0

1

1

1

1

1

1

1

0

2

2

2

2

2

2

2
3

.
0
2

2

/
.

/
.

.
0

0

0

1

1

1

2

2

2

3

3

4
5

4
5

5

3

3

3

3

3

3

3

4
5

4
5

4
5

4

4
5

4
5

4
5

5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

8

7
8

7
8

8

7
8

7
8

9

9

9

9

9

9

9

9

7
8

7
8

7
8

7
8

9

9

9

9

The above answers are acceptable.

3

The above answer is unacceptable as

3
4

representing the fraction 1 .

Peterson’s SAT® Prep Guide 2017

6.

Sometimes, the problems in this section will have more than one correct answer. Choose one and grid it.
For example, if a question asks for a prime number between 5 and 13, the answer could be 7 or 11. Grid 7 or grid 11, but
don’t put in both answers.

/
.

/
.

.

0

0

0

0

1

1

2

2

2

2

2

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

7
8

7
8

8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

/
.

/
.

.

.

0

0

0

0

1

1

1

1

2

2

2

3

3

3

4
5

4
5

6
7
8
9

.

Either answer is acceptable but not both.

GUESSING ON GRID-INS CAN’T HURT YOU

302

Unfortunately, you cannot receive partial credit for grid-ins. Your answers are either completely correct or completely wrong. But
no points are deducted for incorrect responses, so guessing is better than leaving a question blank.

Chapter 8
Grid-In
Strategies

www.petersons.com

EXERCISES: GRID-INS
Exercise 1
15 Minutes—10 Questions
DIRECTIONS: For these questions, solve the problem and enter your answer in the grid following each question, as
described below.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
7
1
5. Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
		
If 3

1
is entered into the grid as
2

, it will be interpreted as

1
31
, not 3 .
2
2

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
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Answer:

Answer: 2.5

Write answer
in boxes.

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1. If 3x + y = 4 and x + 3y = 5, what is the value of x + y?

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2. Marion is paid $24 for 5 hours of work in the school office.
Janet works 3 hours and makes $10.95. How much more
per hour does Marion make than Janet? (Ignore the dollar
sign when gridding your answer.)

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3. If the outer diameter of a cylindrical oil tank is 54.28 inches
and the inner diameter is 48.7 inches, what is the thickness
of the wall of the tank, in inches?

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4. A car has an average mileage of 30 miles per gallon. If one
gallon of gasoline costs $3.75, how many miles can the car
travel on $20 worth of gasoline?

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5. If r = 25 − s, what is the value of 4(r + s)?

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6. Arc AB is on circle O. If the radius of circle O is 5 centimeters,
and angle AOB measures 30°, what is the length of arc AB
rounded to the nearest tenth of a centimeter?

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7.

SHOW YOUR WORK HERE

4x + 5 = 6
If x is a solution of the equation above, what is the
value of 4x?

8.

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9.

10.

In May, Carter’s Electronics sold 40 smartphones. In
June, because of a special promotion, the store sold 80
smartphones. What is the percent of increase in the
number of smartphones sold?

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ANSWER KEY AND EXPLANATIONS

1.

1. 9/4

3. 2.79

5. 100

7. 31

9. 100

2. 1.15

4. 160

6. 2.6

8. 72.9

10. 18

3x + y = 4
x + 3y = 5
Add the two equations to get:

6.

30
(10p) ≈ 2.6
360

4x + 4y = 9

The correct answer is 2.6.

4( x + y) = 9
x+y=

The circumference of the circle is 2p (5) = 10p .

9
4

4x + 5 = 6
4 x + 5 = 36

7.

The correct answer is 9/4 or 2.25.

4 x = 31
2.

Marion’s hourly wage is

$24
, or $4.80.
5

$10.95
Janet’s hourly wage is
, or $3.65.
3

The correct answer is 31.
8.		 The formula for volume of a cube is s3.
Therefore, 33 = 27.

$4.80 − $3.65 = $1.15

27(2.7) = 72.9

The correct answer is 1.15. (You do not need to grid
in the dollar sign.)
3.

The difference of 5.58 must be divided between
both sides. The thickness on each side is 2.79 inches.

The correct answer is 72.9.
9.

so

Chapter 8
Grid-In
Strategies

40
× 100 = 100% increase.
40

The correct answer is 100.

The correct answer is 160.

4(r + s) = 4(25) = 100

difference
×100. In this case, the difference is
original

80 – 40, which is 40. The original amount sold was 40,

 20 
30 
= 160
 3.75 

5.		r + s = 25

When computing the percent of increase (or decrease),
use

The correct answer is 2.79.
4.

309

10.

(3 2 )(3 2 ) = 9 i 2 = 18
The correct answer is 18.

The correct answer is 100.

Peterson’s SAT® Prep Guide 2017

Exercise 2
15 Minutes—10 Questions
DIRECTIONS: For these questions, solve the problem and enter your answer in the grid following each question, as
described below.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
7
1
5. Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
		
If 3

1
is entered into the grid as
2

, it will be interpreted as

1
31
, not 3 .
2
2

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

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Answer: 201
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1. 53 percent of the 2,500 students at Jackson High are girls.
How many boys are there in the school?

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SHOW YOUR WORK HERE

2 centimeters and

6 centimeters. What is the length of the hypotenuse of
the right triangle to the nearest tenth of a centimeter?

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3. In a group of 40 students, 25 applied to Columbia and
30 applied to Cornell. If 3 students applied to neither
Columbia nor Cornell, how many students applied to both
schools?

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5. A gallon of water is added to 6 quarts of a solution that is
50% acid. What percent of the new solution is acid?

6. A gasoline tank is

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1
full. After 10 gallons of gasoline are
4

added to the tank, its gauge indicates that the tank is

2
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full. Find the capacity of the tank in gallons.

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Grid-In
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Peterson’s SAT® Prep Guide 2017

7. A plane flies over Denver at 11:20 a.m. It passes over
Coolidge, 120 miles from Denver, at 11:32 a.m. Find the
rate of the plane in miles per hour.

8.

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x +1
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x −1

		
What value of x is a solution of the equation above?

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9. What is the median of the set of numbers
2, 3, 4, 5, 6, 7, 8, and 9?

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2
10. y = x − 8 x + 7
y = x −1

		
If (x, y) is a solution of the system of equations above, what
is a possible value of x + y?

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Chapter 8
Grid-In
Strategies

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS
1. 1175

3. 18

5. 30

7. 600

9. 5.5

2. 2.8

4. 5

6. 24

8. 1.5

10. 15 or 1

1. 		 47 percent of 2,500 are boys.

6. 		 10 gallons is

(0.47)(2,500) = 1,175 boys

2 + 6 = (hypotenuse ) 2

2 1 8−3 5
=
− =
3 4
12 12
5
x = 10
12
5 x = 120
x = 24

8 = (hypotenuse ) 2

The correct answer is 24.

The correct answer is 1175. (Do not include the
comma)
2.

2 1
−
of the tank.
3 4

( 2) + ( 6)
2

2

= (hypotenuse ) 2

1
hour.
7. 		 The plane covers 120 miles in 12 minutes, or
5
5
In , or 1 hour, it covers 5(120), or 600 miles.
5

8 = hyypotenuse
2.8 ≈ hypotenuse

The correct answer is 2.8.

The correct answer is 600.

3.

8.

25 – x

x

30 – x

x +1
=5
x −1
x + 1 = 5 ( x − 1)
x + 1= 5x − 5
6 = 4x

316

6
=x
4
x = 1.5

25 − x + x + 30 − x = 37
55 − x = 37
18 = x
18

Chapter 8
Grid-In
Strategies

The correct answer is 1.5.
9.

The correct answer is 18.
4.

The median is equal to the arithmetic mean of the two
numbers in the middle, 5 and 6.

5 + 6 11
= = 5.5
2
2
The correct answer is 5.5.

x 2 − y 2 = ( x − y )( x + y )
100 = 20 ( x + y )
5 = ( x + y)
5

The correct answer is 5.

10.

5.
No. of
quarts

%
acid

Amount
of acid

Original

6

50

3

Added

4

0

0

New

10

3

3
= 30%
10
The correct answer is 30. (Ignore the percent
symbol when griding your answer.)

www.petersons.com

y = x 2 − 8x + 7
y = x −1
x 2 − 8x + 7 = x −1
x 2 − 9x + 8 = 0

( x − 8) ( x − 1) = 0
x = 8 or x = 1
If x = 8, then y = 8 – 1 = 7
If x = 1, then y = 1 – 1 = 0
x + y = 15 or x + y = 1
The correct answer is 15 or 1 (both answers are
acceptable.

SUMMING IT UP
• When you grid answers to student-produced response questions, follow these six rules:
1. Write your answer in the boxes at the top of the grid.
2. Mark the corresponding circles, one per column.
3. Start in any column.
4. Work with decimals or fractions.
5. Express mixed numbers as decimals or improper fractions.
6. If more than one answer is possible, grid any one.

• Remember that grid-ins test the same concepts as multiple-choice math.
• The most important advice for grid-ins? Don’t be intimidated.
•

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topics in Peterson’s SAT® Online Course:

• Grid-Ins
• Problem Solving
• Word Problems
To purchase and access the course, go to www.petersons.com/sat.

317
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Strategies

Peterson’s SAT® Prep Guide 2017

Chapter 9:
Numbers and Operations
OVERVIEW
Operations with Fractions
Test for Divisibility
Exercises: Operations with Fractions
Word Problems Involving Fractions
Exercises: Word Problems Involving Fractions
Complex Numbers
Exercises: Complex Numbers
Direct and Inverse Variation
Exercises: Direct and Inverse Variation
Finding Percents
Exercises: Finding Percents

319

Percent Word Problems

Chapter 9

Exercises: Percent Word Problems

Numbers and
Operations

Summing It Up

Peterson’s SAT® Prep Guide 2017

OPERATIONS WITH FRACTIONS
The four basic arithmetic operations are addition, subtraction, multiplication, and division.

Adding and Subtracting
In adding or subtracting fractions, you must remember that the numbers must have the same (common) denominator.
Example:
Add

1 2 3
+ + .
3 5 4

Solution:
The least number that is divisible by 3, 5, and 4 is 60. Therefore, use 60 as the common denominator. Convert each
fraction to fractions with the common denominator, 60, by multiplying each numerator by the same factor as you
must multiply the denominator by to result in the common denominator of 60.
20 24 45 89
+
+
=
60 60 60 60
29
=1
60

320
Chapter 9
Numbers and
Operations

Fractions should be written in the simplest form. Often, in multiple-choice questions, you may find that the answer
you have correctly computed is not among the choices but an equivalent fraction is. Be careful!
In simplifying fractions involving large numbers, it is helpful to be able to tell whether a factor is common to both
numerator and denominator before a lengthy trial division. Certain tests for divisibility help with this.

TEST FOR DIVISIBILITY
To test if a number is divisible by:

Check to see:

2

if it is even

3

if the sum of the digits is divisible by 3

4

if the number formed by the last two digits is divisible by 4

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5

if its last digit is a 5 or 0

6

if it is even and the sum of the digits is divisible by 3

8

if the number formed by the last three digits is divisible by 8

9

if the sum of the digits is divisible by 9

10

if its last digit is 0

Example:
Simplify:

3, 525
4 , 341

Solution:
This fraction can be simplified by dividing by 3, since the sum of the digits of the numerator is 15 and those of the
denominator add up to 12, both are divisible by 3.

3, 525 1,175
=
4 , 341 1, 447
The resulting fraction meets no further divisibility tests and therefore has no common factor listed above. Larger
divisors would be unlikely on the SAT®.
To add or subtract mixed numbers, it is again important to remember common denominators. In subtraction, you
must borrow in terms of the common denominator.
Addition:

2
6
43 = 43
5
15
1
5
+ 8 =+ 8
3
15
11
51
15

2
6
21
Subtraction: 43 = 43 = 42
5
15
15
2
10
10
−6 = −6 = −6
3
15
15
11
36
15

321
Chapter 9
Numbers and
Operations

Multiplying
To multiply fractions, always try to divide common factors where possible before actually multiplying. In multiplying mixed
numbers, always rename them as improper fractions first.
2

9

2
10
99 18
i
i
=
Multiply:
5
11
110 55
55

Multiply: 4
3

1
2
1
i1 i 5
3
5
2
13

9
5
26
i
i
= 39
2
3
5

Peterson’s SAT® Prep Guide 2017

Dividing
To divide fractions or mixed numbers, remember to multiply by the reciprocal of the divisor (the number after the division sign).
3

2

1 3 9
4
Divide: 4 ÷ =
i
=6
2 4 2
3
25

1
1
125
1
Divide: 62 ÷ 5 =
i
= 12
2
2
2
5
To simplify complex fractions (fractions within fractions), multiply every term by the least common multiple of all denominators
in order to clear all fractions in the given numerator and denominator.
Example:
1 1
+
2 3
1 1
+
4 6

Solution:
The least number that can be used to clear all fractions is 12. Multiplying each term by 12 yields:

1 1 12 12
+
+
2 3 = 2 3 = 6 + 4 = 10 = 2
1 1 12 12 3 + 2 5
+
+
4 6 4 6

322
Chapter 9

Example:

Numbers and
Operations

3 2
+
4 3
1
1−
2
Solution:
Again, multiply by 12.
3 2 36 24
+
+
4 3= 4
3 = 9 + 8 = 17 = 2 5
1
12 12 − 6 6
6
1−
12 −
2
2

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EXERCISES: OPERATIONS WITH FRACTIONS
DIRECTIONS: Work out each problem in the space provided.
Add:
5
3
1
1. 12 + 2 + 21
6
8
4

2.

1 1 1 1 1
+ + + +
2 3 4 5 6

Divide:
1
÷5
7.
5

8. 3 2 ÷ 1 5
3 6

Simplify:
Subtract:
3. 15

9.

3
1
from 10
4
2

5 1
−
6 3
1
2+
5

1
4
10.
1
5−
2
3+

4. 17

2
from 50
3

323
Chapter 9
Numbers and
Operations

Solve:

Multiply:
1
5
5. 5 i 1
4
7

1 1
11. 4  + 
 6 12 

12.
6. 3 i 3 i 3
4 4 4

2  1 1
 + 
5  3 4

13. 4 + 7 − 4
9 18 5

Peterson’s SAT® Prep Guide 2017

ANSWERS AND EXPLANATIONS
1.

2.

324
Chapter 9

5
20
12 = 12
6
24
3
9
2 = 2
8
24
1
6
+21 = 21
4
24
35
11
35 = 36
24
24
1 30
=
2 60
1 20
=
3 60
1 15
=
4 60
1 12
=
5 60
1 10
+ =
6 60
9
87 27
=1 =1
60 20
60

1
3
6
3. 10 = 9 = 9
2
2
4
3
−5
4
3
4
4

7.

1 1 1
i =
5 5 25

8.

11 6
i
=2
3 11

9.

25 − 10 15 5
=
=
60 + 6 66 22

2

Each term was multiplied by 30.
10.

Each term was multiplied by 4.
1 1
2
1
11. 4  +  = 4  + 
 12 12 
 6 12 
 3
= 4 
 12 
 12 
= 
 12 
=1
12.

Numbers and
Operations

4.

49

3
3
2
−17
3
1
32
3
50

3

5.

13.

3

21 12
i
=9
4
7

6. 3 i 3 i 3 = 27
4 4 4 64

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12 + 1 13
=
20 − 2 18

2  1 1 2  4 3 
 + =  + 
5  3 4  5  12 12 
=

21  7 
5  12 6 

=

7
30

4 7 4 8 7 4
+ − = + −
9 18 5 18 18 5
15 4
= −
18 5
5 4
= −
6 5
25 24
=
−
30 30
1
=
30

WORD PROBLEMS INVOLVING FRACTIONS
Fraction problems deal with parts of a whole.
Example:
If a class consists of 12 boys and 18 girls, what part of the class is boys?
Solution:
The class consists of 12 boys out of 30 total students, or

2
12 2
of the class.
= . So, boys represent
5
30 5

Notice that, to find the solution, you must add the boys and girls to find the total number of students. Problems may
require more than one calculation as you can see in this example.
Example:
One-quarter of this year’s seniors have averages above 90. One-half of the remainder have averages between 80 and
90 inclusive. What part of the senior class have averages below 80?
Solution:
We know that

1
have averages above 90.
4

3
1
3
of
, or , have averages between 80 and 90 inclusive.
8
2
4
1 3 2 3 5
+ = + = have averages 80 and above.
4 8 8 8 8

325
Chapter 9

3
Therefore,
of the class have averages below 80.
8

Numbers and
Operations

Example:
14 is

2
of what number?
3

Solution:
14 =
Divide each side of the equation by

2
x
3

2
3
, which is the same as multiplying the reciprocal, or .
2
3
21 = x

Peterson’s SAT® Prep Guide 2017

Example:
If John has p hours of homework and has worked for r hours, what part of his homework is yet to be done?
Solution:

If John had 5 hours of homework and had worked for 3 hours, you would first find he had 5 − 3 hours, or 2 hours, yet
2
of his work. Using letters, his remaining work is represented by p − r .
to do. This represents
5
p

If a problem is given with letters in place of numbers, the same reasoning
must be applied as for numbers. If you are not sure how to proceed, replace
the letters with numbers to determine the steps that must be taken.

326
Chapter 9
Numbers and
Operations

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EXERCISES: WORD PROBLEMS INVOLVING FRACTIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

A team played 30 games, of which it won 24. What part
of the games played did the team lose?
A.

4
5

B.

1
4

C.

1
5

D.

3
4

If Germaine earns $X a week, and he saves $Y, what part
of his weekly salary does he spend?
A.

X
Y

B.

X −Y
X

C.

X −Y
Y

D.

3.

SHOW YOUR WORK HERE

Y−X
X

327
Chapter 9
Numbers and
Operations

What part of an hour elapses between 11:50 a.m. and
12:14 p.m.?
A.

2
5

B.

7
30

C.

17
30

Peterson’s SAT® Prep Guide 2017

D.
4.

5.

1
6

SHOW YOUR WORK HERE

One half of the employees of Acme Co. earn salaries
above $18,000 annually. One third of the remainder earn
salaries between $15,000 and $18,000. What part of the
staff earns below $15,000?
A.

1
6

B.

2
3

C.

1
2

D.

1
3

David received his allowance on Sunday. He spends

1
4

2
of the remainder on
3
Tuesday. What part of his allowance is left for the rest of
the week?
of his allowance on Monday and

328
Chapter 9
Numbers and
Operations

6.

A.

1
13

B.

1
9

C.

1
4

D.

1
3

12 is

3
of what number?
4

A.
B.
C.
D.
7.

16
9
36
20

A piece of fabric is cut into three sections so that the first is
three times as long as the second, and the second section
is three times as long as the third. What part of the entire
piece is the smallest section?
A.

1
13

B.

1
9

C.

1
4

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D.
8.

9.

1
3

SHOW YOUR WORK HERE

If a number is added to both the numerator and denom4
8
inator of , the result is . What is the number?
7
9
A.

2

B.

9

C.

18

D.

20

A factory employs M men and W women. What part of its
employees are women?

10.

11.

A.

M
W

B.

M +W
W

C.

W
M −W

D.

W
M +W

A motion was passed by a vote of 5:3. What part of the
votes cast were in favor of the motion?
A.

5
8

B.

5
3

C.

3
5

D.

3
8

329
Chapter 9
Numbers and
Operations

If the ratio of x:y is 9:7, what is the value of x + y?
A.

2

B.

16

C.

63

Peterson’s SAT® Prep Guide 2017

D.

12.

13.

330

14.

Chapter 9
Numbers and
Operations

15.

It cannot be determined from the information
given.

In a certain class, the ratio of men to women is 3:5. If the
class has 24 people in it, how many are women?
A.

9

B.

12

C.

15

D.

18

1
gallons of water. In the morn2
1
ing, 23 gallons are used. The level of the rain barrel after
4
3
it rains increases by 16 gallons. How many gallons are
4
in the tank after it rains?
A rain barrel contains 56

A.

16

B.

50

C.

64

D.

96

If x is

1
2

1
2

2
3
of y and y is of z, what is the ratio of z:x?
4
3

A.

1:2

B.

1:1

C.

2:1

D.

3:2

Teagan can paint a house in 5 hours and Kevin can paint
a house in 8 hours. How many hours will it take them to
paint a house if they work together?
A.

3

B.

3

1
13

C.

6

1
2

D.

13

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

2.

1. C

4. D

7. A

10. A

13. B

2. B

5. C

8. D

11. D

14. C

3. A

6. A

9. D

12. C

15. B

The correct answer is C. The team lost 6 games out
6 1
=
of 30.
30 5

8.

4+n 8
= ; 9 ( 4 + n) = 8 (7 + n) ;
7+n 9

The correct answer is B. Germaine spends X − Y
out of X. X − Y
X

3.

4.

36 + 9n = 56 + 8n; n = 20

The correct answer is A. 10 minutes elapse by noon,
and another 14 after noon, making a total of 24
24 2
minutes. There are 60 minutes in an hour.
=
60 5
The correct answer is D. One half earn over $18,000.
1
1
One third of the other , or , earn between $15,000
6
2
and $18,000. This accounts for

1 1
3 1 4 2
+ , or + = =
2 6
6 6 6 3

1
to earn below $15,000.
3
The correct answer is C. David spends 1 on Monday
4
2
3
1
of the other , or , on Tuesday, leaving only
and
3
4
2
1
for the rest of the week.
4
3
The correct answer is A. 12 = x. Multiply each side
4
4
by . 16 = x.
3

9.

The correct answer is D. The factory employs M + W
people, out of which W are women.

10.

The correct answer is A. For every 5 votes in favor, 3
were cast against. 5 out of every 8 votes cast were in
favor of the motion.

11.

The correct answer is D. Remember, a ratio is a
fraction. If x is 18 and y is 14, the ratio x:y is 9:7, but x + y
is 32. The point of this problem is that x and y can take
on many possible values, just as long as the ratio 9:7 is
preserved. Given the multiplicity of possible values, it is
not possible here to establish one definite value for the
sum of x and y.

of the staff, leaving

5.

6.

7.

The correct answer is D. Let n be the number that is
being added.

The correct answer is A. Let the third or shortest
section = x. Then the second section = 3x, and the first
section = 9x. The entire piece of fabric is then 13x, and
x
1
the shortest piece represents
, of the
, or
13
13 x
entire piece.

12.

The correct answer is C. The ratio of women to the
total number of people is 5:8. We can set up a pro5 x
portion. If =
, then x = 15.
8 24

13.

The correct answer is B. To find the water remaining
in the tank, solve:
1
1
3
56 − 23 + 16 .
2
4
4

331
Chapter 9
Numbers and
Operations

2
1
3
The result is 56 − 23 + 16 = 50 gallons.
4
4
4

Peterson’s SAT® Prep Guide 2017

14.

The correct answer is C. There are several ways to
2
2
attack this problem. If x is of y, then x = i y .
3
3
If y is

4
4
3
of z, then z is
of y, or z = i y. Therefore,
3
3
4

z = 2x. The ratio of z:x is 2:1. You could also plug in a
real number and solve. If x is 2, figure out what y and z
would be. Therefore, y would be 3 and z would be 4, so
the ratio of z to x is 2:1.

332
Chapter 9
Numbers and
Operations

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15.

The correct answer is B. To find how long it will take
x x
them to paint the house together solve: + = 1 .
5 8
The result is: 8 x + 5 x = 40
13 x = 40
1
x =3
13

COMPLEX NUMBERS
A complex number is a number made up of a real number and an imaginary number. It can be written in standard form a + bi,
where a and b are real numbers and i is an imaginary unit.

i = −1 , i 2 = −1
For example, in the complex number 2 + 3i the real number is 2 and the imaginary number is 3i.
Complex numbers can be added, subtracted, multiplied, and divided.

Adding Complex Numbers
To add complex numbers, add the real numbers and the imaginary numbers separately.
Sum: (a + bi) + (c + di) = (a + c) + (b + d)i
Example:
Add: (2 + 3i) + (8 + 4i)
Solution:
Add the real numbers and then the imaginary numbers.
(2 + 8) + (3i + 4i) = 10 + 7i

333
Chapter 9

Subtracting Complex Numbers

Numbers and
Operations

To subtract complex numbers, subtract the real numbers and the imaginary numbers separately.
Difference: (a + bi) – (c + di) = (a – c) + (b – d)i
Example:
Subtract: (2 + 3i) – (8 + 4i)
Solution:
Subtract the real numbers and then the imaginary numbers.
(2 + 3i) – (8 + 4i) = (2 – 8) + (3i – 4i) = –6 – i

Peterson’s SAT® Prep Guide 2017

Multiplying Complex Numbers
Multiplying complex numbers is like multiplying polynomials by using the distributive property or the FOIL method.
Product: (a + bi) (c + di) = (ac) + (adi) + (bci) + (bd)i2
Example:
Multiply: 3i (–2 + 9i)
Solution:
Distribute 3i to all of the terms in the parentheses.
3i ( −2 + 9i ) = (3i ) ( −2) + (3i )(9i )
= (3i ) ( −2) + 27i 2
i2 =

( −1)( −1) = −1

= −6i + 27 ( −1)
= −27 − 6i
Example:
Multiply: (2 + 3i) (8 + 4i)

334
Chapter 9
Numbers and
Operations

Solution:
Find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.
The acronym FOIL stands for First Outer Inner Last and will help you to remember how to multiply two binomials.
When simplifying an expression that involves complex numbers, simplify i2 to –1.

(2 + 3i ) (8 + 4i ) = (2 i 8) + (2 i 4i ) + (8 i 3i ) + (3i i 4i )
= 16 + 8i + 24 i + 12i 2
= 16 + 32i + 12 ( −1)
= 4 + 32i
Simplify and write in standard form a + bi.

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Dividing Complex Numbers
Dividing complex numbers is more complicated because the denominator cannot contain a radical. This process is called rationalizing the denominator. In order to make the denominator rational, you must use its complex conjugate. The product of two
complex conjugates is always a real number a2 + b2. The numbers 2 + 8i and 2 – 8i are examples of complex conjugates, and their
product is the real number 22 + 82 = 4 + 64 = 68.
Complex conjugates: (a + bi) and (a – bi)
Product of complex conjugates: (a + bi) (a – bi) = a2 + b2
Example:
Simplify:

8
7i

Solution:
Rationalize the denominator by multiplying the numerator and denominator by i.
8 8 i 8i
8i
8i
= i = 2=
=
7i 7i i 7i
7 ( −1) −7
Example:
Simplify:

4 + 2i
−3 + 5i

335

Solution:
Rationalize the denominator by multiplying the numerator and denominator by the conjugate for the denominator.
Then simplify by combining like terms.

Chapter 9
Numbers and
Operations

4 + 2i
4 + 2i −3 − 5i
=
i
−3 + 5i −3 + 5i −3 − 5i
=

−12 − 20i − 6i − 10

9 + 15i − 15i − 25i 2
−12 − 20i − 6i − 10 ( −1)
=
9 + 15i − 15i − 25 ( −1)
−2 − 26i
9 + 25
−2 − 6i
=
34
−2 26i
−
=
34 34
−1 13i
= −
17 17
=

Recall that i2 = –1.

Peterson’s SAT® Prep Guide 2017

EXERCISES: COMPLEX NUMBERS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

3.

336
Chapter 9
Numbers and
Operations

4.

5.

Add: (8 + 2i) + (2 – 3i)
A.

15i

B.

5 + 4i

C.

6+i

D.

10 – i

Add: (–2 – 5i) + (6 + 9i)
A.

4 + 4i

B.

7+i

C.

8i

D.

8 + 14i

Subtract: (–9 + 4i) – (3 + 7i)
A.

–6 – 3i

B.

–2 + i

C.

–12 – 3i

D.

–i

Subtract: (6 + 3i) – (2 + 9i)
A.

4 – 6i

B.

4 + 12i

C.

8 – 6i

D.

10i

Multiply: (2i)(32i)
A.

64

B.

–64

C.

64i

D.

–64i

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SHOW YOUR WORK HERE

6.

7.

8.

9.

10.

Multiply: (–5i)(12 – 3i)
A.

8 + 17i

B.

–15 – 60i

C.

15 + 60i

D.

–8 + 17i

SHOW YOUR WORK HERE

Multiply: (4 – 6i)(1 – 2i)
A.

4 + 12i

B.

4 – 12i

C.

8 + 14i

D.

–8 – 14i

Multiply: (–5 + 3i)(20 – 7i)
A.

–100 – 4i

B.

100 + 21i

C.

–79 + 95i

D.

121 + 95i

Simplify:

−5i
4 i + 11

A.

–4 – 11i

B.

20 − 55i
137

C.

−20 − 55i
137

D.

4 +11i

Simplify:

337
Chapter 9
Numbers and
Operations

17 − i
3i

A.

1 17
− i
3 3

B.

1 7
+ i
3 3

C.

34 2
+ i
5 5

D.

1 17
− − i
3 3

Peterson’s SAT® Prep Guide 2017

11. Simplify:

22 2
− i
3 3

A.

−

B.

1 7
+ i
3 3

C.

34 2
+ i
5 5

D.

1 17
− − i
3 3

12. Simplify:

338

6 + 14 i
1 + 2i

−3 + 5i
−3 − 4 i

29 27
− i
5
5

A.

−

B.

−11 27
− i
25 25

C.

21 27
− i
25 25

D.

11 27
+ i
7 7

Chapter 9
Numbers and
Operations

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

1. D

4. A

7. D

9. C

11. C

2. A

5. B

8. C

10. D

12. B

3. C

6. B
9.

The correct answer is D.
(8 + 2i) + (2 – 3i) = (8 + 2) + (2i – 3i) = 10 – i

2.

The correct answer is C.
−5i
−5i
11− 4 i
=
i
11+ 4 i 11+ 4 i 11− 4 i
−5i (11− 4 i )
=
(11+ 4i ) (11− 4i )

The correct answer is A.
(–2 – 5i) + (6 + 9i) = (–2 + 6) + (–5i + 9i) = 4 + 4i

=

3.

121− 44 i + 44 i + 16i 2
−20 − 55i
=
121+ 16
−20 − 55i
=
137

The correct answer is C.

( −9 + 4i ) − (3 + 7i ) = ( −9 − 3) + ( 4i − 7i )
= −12 − 3i
4.

The correct answer is A.

(6 + 3i ) − (2 + 9i ) = (6 − 2) + (3i − 9i )

10.

= 4 − 6i
5.

The correct answer is D.
17 − i 17 − i i
i
=
3i
3i
i
17 − i )(i )
(
=
3i 2

The correct answer is B.
(2i)(32i) = 64i = 642(−1) = −64

6.

−55i + 20i 2

=

The correct answer is B.

17i − i 2
3 ( −1)

1+ 17i
=
−3
1 17
=− − i
3 3

( −5i ) (12 − 3i ) = ( −5i )(12) + ( −5i ) ( −3i )
= −60i + 15i 2

= −60i + 15 ( −1)

339
Chapter 9
Numbers and
Operations

= −15 − 60i

7.

The correct answer is D.

( 4 − 6i ) (1− 2i ) = ( 4) + ( −8i ) + ( −6i ) + (12i 2 )
= 4 + ( −14 i ) + ( −12)
= −8 − 14 i

8.

The correct answer is C.

( −5 + 3i ) (20 − 7i ) = −100 + ( −5) ( −7i ) + (3i )(20) + (3i ) ( −7i )

(

= −100 + 35i + 60i + −21i 2

)

= −100 + 95i + 21
= −79 + 95i

Peterson’s SAT® Prep Guide 2017

11.

The correct answer is C.
6 + 14 i 6 + 14 i 1− 2i
=
i
1 + 2i
1 + 2i 1 − 2i
(6 + 14i ) (1− 2i )
=
(1+ 2i ) (1− 2i )
=

6 − 12i + 14 i − 28i 2

1 − 2i + 2i − 4 i 2
6 − 12i + 14 i − 28 (1)
=
1− 2i + 2i − 4 ( −1)

6 + 2 i + 28
1+ 4
34 + 2i
=
5
34 2
=
+ i
5 5
=

340
Chapter 9
Numbers and
Operations

www.petersons.com

12.

The correct answer is B.
−3 + 5i −3 + 5i −3 + 4 i
i
=
−3 − 4 i −3 − 4 i −3 + 4 i
( −3 + 5i ) ( −3 + 4i )
=
( −3 − 4i ) ( −3 + 4i )
=

9 − 12i − 15i + 20i 2

9 − 12i + 12i − 16i 2
9 − 12i − 15i + 20 ( −1)
=
9 − 12i + 12i − 16 ( −1)
=

9 − 27i + ( −20)
9 + ( −16) ( −1)

−11− 27i
25
−11 27
=
− i
25 25
=

DIRECT AND INVERSE VARIATION
Direct Variation
Two quantities are said to vary directly if as one increases, the other increases, and, as one decreases, the other decreases.
For example, the amount of sugar needed in a recipe varies directly with the amount of butter used. The number of inches between
two cities on a map varies directly with the number of miles between the cities. The equation y = ax represents direct variation
between x and y, and y is said to vary directly with x. The variable a is called the constant of variation. By dividing each side by x,
you can see that the ratio for the variable is the constant a.
Example:
Hooke’s Law states that the distance d a spring stretches varies directly with the force F that is applied to it. Suppose
a spring stretches 15 inches when a force of 9 lbs. is applied. Write an equation that relates d to F, and state the constant of variation.
Solution:
d F
You are comparing the distance that a spring stretches with the force that is applied, so = . Solving for d in terms
15 9
5
5
of F, you get d = F . The constant of variation is .
3
3
Example:
The weight of a person on the Moon varies directly with the weight of a person on Earth. A person who weighs 100
lbs. on Earth weighs 16.6 lbs. on the Moon. How much would a person who weighs 120 lbs. on Earth weigh on the
Moon?

341
Chapter 9
Numbers and
Operations

Solution:
Start with the equation y = ax, where y is the weight of a person on the Moon and x is the weight of a person on
Earth.
y = ax

16.6 = a (100)
0.166 = a
The equation y = 0.166x gives the weight y on the Moon of a person who weighs x pounds on Earth. To solve the
example, substitute x = 120 in the equation to determine the weight of the person on the Moon.
y = 0.166 x
y = 0.166(120 )
y = 19.92
A person who weighs 120 lbs. on Earth would weigh 19.92 lbs. on the Moon.

Peterson’s SAT® Prep Guide 2017

Inverse Variation
Two quantities are said to vary inversely if, as one increases, the other decreases.
For example, the number of workers hired to paint a house varies inversely with the number of days the job will take. A doctor’s
stock of flu vaccine varies inversely with the number of patients injected. The number of days a given supply of cat food lasts
varies inversely with the number of cats being fed.
The equation xy = a, where a ≠ 0, represents inverse variation between x and y, and y is said to vary inversely with x. The variable
a is called the constant of variation.

Whenever two quantities vary directly, you can find a missing term by
setting up a proportion. However, be very careful to compare the same
units, in the same order, on each side of the equal sign.
Example:
The number of songs that can be stored on a hard drive varies inversely with the size of the song. A certain hard
drive can store 3,000 songs when the average size of the song is 3.75 MB. Write an equation that gives the number of
songs y that will fit on the hard drive as a function of the average song size x.
Solution:
First, write an inverse variation equation that relates x and y. Then substitute 3,000 for y and 3.75 for x.

342

xy = a
a
y=
x

Chapter 9

a
3.75
11, 250 = a
3, 000 =

Numbers and
Operations

The inverse variation equation for this situation is y =

www.petersons.com

11, 250
.
x

EXERCISES: DIRECT AND INVERSE VARIATION
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

If 60 feet of uniform wire weighs 80 pounds, what is the
weight of 2 yards of the same wire?

B.

2
2 pounds
3
6 pounds

C.

8 pounds

D.

120 pounds

A.

2.

3.

4.

SHOW YOUR WORK HERE

A gear 50 inches in diameter turns a smaller gear 30 inches
in diameter. If the larger gear makes 15 revolutions, how
many revolutions does the smaller gear make in that
time?
A.

9

B.

12

C.

20

D.

25

The distance a spring stretches varies directly with the
force applied to it. If a 4-lb. weight stretches a spring 65.5
inches, how many inches will the spring stretch if a 12-lb.
weight is applied?
A.

262

B.

1
196
2

C.

21

1
3

D.

16

3
8

343
Chapter 9
Numbers and
Operations

If a furnace uses 40 gallons of oil in a week, how many
gallons, to the nearest gallon, does it use in 10 days?
A.

4

B.

28

C.

57

D.

58

Peterson’s SAT® Prep Guide 2017

5. A recipe requires 13 ounces of sugar and 18 ounces of flour.
If only 10 ounces of sugar are used, how much flour, to the
nearest ounce, should be used?
A.

13

B.

14

C.

15

D.

23

6. If a car can drive 25 miles on two gallons of gasoline, how
many gallons will be needed for a trip of 150 miles?
A.

12

B.

10

C.

7

D.

6

7. A school has enough bread to feed 30 children for 4 days. If
10 more children are added, how many days will the bread
last?

344
Chapter 9
Numbers and
Operations

1
3

A.

1

B.

2

C.

3

D.

5

2
3
1
3

8. The intensity of a sound, I, varies inversely with the square
of the distance, d, from the sound. If the distance is reduced
1
by a factor of , by what factor will the intensity of the
4
sound increase?
A.

4

B.

8

C.

12

D.

16

www.petersons.com

SHOW YOUR WORK HERE

9. If 3 miles are equivalent to 4.83 kilometers, then 11.27
kilometers are equivalent to how many miles?
A.

2

B.

5

C.

6

D.

7

SHOW YOUR WORK HERE

1
3
1
2

10. Suppose the variables x and y vary inversely. If x = –12
and y = 4, find y when x = –2.
A.

48

B.

24

C.

–24

D.

–48

345
Chapter 9
Numbers and
Operations

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. C

3. B

5. B

7. C

9. D

2. D

4. C

6. A

8. D

10. B

The correct answer is C. You are comparing feet with
pounds. The more feet, the more pounds. This is
DIRECT. Remember to rename yards as feet:
60 6
=
80 x
60 x = 480
x =8

2.

x = 196
4.

8.

5.

The correct answer is B. The more sugar, the more
flour. This is DIRECT.
13 10
=
18 x
13 x = 180
11
x = 13
13

www.petersons.com

The correct answer is D.

( )

I d2 =k
2

 d
I  = k
 4
d2
I  = k
 16 

1
2

The correct answer is C. The more days, the more oil.
This is DIRECT. Remember to rename the week as 7
days.
40 x
=
7 10
7 x = 400
1
x = 57
7

The correct answer is C. The more children, the fewer
days. This is INVERSE.
30 i 4 = 40 i x
120 = 40 x
3= x

4
12
=
65.5 x
4 x = 786

Chapter 9
Numbers and
Operations

7.

The correct answer is B. The more weight that is
applied the farther the spring will stretch.

346

The correct answer is A. The more miles, the more
gasoline. This is DIRECT.
25 150
=
2
x
25 x = 300
x = 12

The correct answer is D. The larger a gear, the fewer
times it revolves in a given period of time. This is
INVERSE.
50 i 15 = 30 i x
750 = 30 x
25 = x

3.

6.

( )

I d 2 = 16k

9.

The correct answer is D. The more miles, the more
kilometers. This is DIRECT.
3
x
=
4.83 11.27
4.83 x = 33.81
x =7

10.

The correct answer is B.
xy = k

( −12)( 4) = k
−48 = k
−2 y = −48
y = 24

FINDING PERCENTS
Percent Equivalents
“Percent” means “out of 100.” If you understand this concept, it becomes very easy to rename a percent as an equivalent decimal
or fraction.
5% =

2.6% =

c% =

5
= 0.05
100
2.6
= 0.026
100

c
1
i c = 0.01c
=
100 100

1
1 1
1
1
2
%=
=
i =
i 0.5 = 0.005
100 100 2 100
2

Certain fractional equivalents of common percents occur frequently enough that they should be memorized. Learning the values
in the following table will make your work with percent problems much easier.

Percent-Fraction Equivalents
50% =

1
2

1
25% =
4

347

9
10

1
1
12 % =
2
8

1
1
33 % =
3
3

1
3
37 % =
2
8

90% =

75% =

3
4

20% =

1
5

1
5
62 % =
2
8

10% =

1
10

40% =

2
5

1
7
87 % =
2
8

30% =

3
10

60% =

3
5

2
1
16 % =
3
6

70% =

7
10

80% =

4
5

1
5
83 % =
3
6

Chapter 9
Numbers and
Operations

Most percentage problems can be solved by using the following proportion:
part
%
=
100 whole

Peterson’s SAT® Prep Guide 2017

Although this method works, it often yields unnecessarily large numbers that are difficult to compute. Following are examples
of the four basic types of percent problems and different methods for solving them.

How to Solve Percentage Problems

• To change a % to a decimal, remove the % sign and divide by 100. This has the effect of moving
the decimal point two places to the LEFT.

• To change a decimal to a %, add the % sign and multiply by 100. This has the effect of moving
the decimal point two places to the RIGHT.

• To change a % to a fraction, remove the % sign and divide by 100. This has the effect of putting
the % over 100 and simplifying the resulting fraction.

• To change a fraction to a %, add the % sign and multiply by 100.

To Find a Percent of a Number
Example:
Find 27% of 92.
Solution:

348

Proportional Method

Chapter 9

Rename the percent as its decimal or fraction equivalent and
multiply. Use fractions only when they are among the familiar
ones given in the previous chart.

Numbers and
Operations

27
x
=
100 92
100 x = 2, 428
x = 24.84

www.petersons.com

Shorter Method

92
× 0.27
644
184
24.84

Example:
1
Find 12 % of 96.
2
Solution:

Proportional Method

Decimal Method

1
2= x
100 96
100 x = 1, 200

0.125
× 96

12

x = 12

Fractional Method

1
i 96 = 12
8

750
1125
12.000

Which method is easiest? It really pays to memorize those fractional equivalents.

To Find a Number When a Percent of It Is Given
Example:
7 is 5% of what number?

349

Solution:

Chapter 9

Proportional Method

Shorter Method

Numbers and
Operations

Translate the problem into an algebraic equation. In
doing this, the percent must be written as a fraction or
decimal.
5
7
=
100 x
5 x = 700
x = 140

7 = 0.05 x
700 = 5 x
140 = x

Peterson’s SAT® Prep Guide 2017

Example:
1
20 is 33 of what number?
2
Solution:

Proportional Method

Shorter Method

1
2 = 20
x
100
1
33 x = 2, 000
3
100
x = 2, 000
3
100 x = 6 , 000
x = 60
33

1
x
3
60 = x

20 =

1
1
Just think of the time you will save and the number of extra problems you will solve if you know that 33 % = .
3
3

To Find What Percent One Number Is of Another

350
Chapter 9
Numbers and
Operations

Example:
90 is what percent of 1,500?
Solution:

Proportional Method

Shorter Method

x
90
=
100 1, 500
1, 500 x = 9 , 000
15 x = 90
x =6

Put the part over the whole. Simplify the fraction and
multiply by 100.

Example:
7 is what percent of 35?

www.petersons.com

90
9
3
=
=
i 100 = 6
1, 500 150 50

Solution:

Proportional Method

Shorter Method

7
x
=
100 35
35 x = 700
x = 20

7 1
= = 20%
35 5

Example:
18 is what percent of 108?
Solution:

Proportional Method

Shorter Method

18
x
=
100 108
108 x = 1, 800

18
9 1
2
=
= = 16 %
108 54 6
3

Time-consuming long division is necessary to get:
x = 16

2
3

Once again, if you know the fraction equivalents of
common percents, computation can be done in a
few seconds.

351
Chapter 9

To Find a Percent Over 100

Numbers and
Operations

Example:
Find 125% of 64.
Solution:

Proportional Method

125 x
=
100 64
100 x = 8 , 000
x = 80

Decimal Method
64
× 1.25
320
128
64
80.00

Fractional Method
1
1 i 64
4
5
i 64 = 80
4

Peterson’s SAT® Prep Guide 2017

Example:
36 is 150% of what number?
Solution:

Proportional Method
150 36
=
100 x
150 x = 3, 600
15 x = 360
x = 24

Decimal Method

Fractional Method

36 = 1.50 x
360 = 15 x
24 = x

1
36 = 1 x
2
3
36 = x
2
72 = 3 x
24 = x

Example:
60 is what percent of 50?
Solution:

Proportional Method

352
Chapter 9
Numbers and
Operations

www.petersons.com

60
x
=
100 50
50 x = 6 , 000
5 x = 600
x = 120

Fractional Method

1
60 6
= = 1 = 120%
50 5 5

EXERCISES: FINDING PERCENTS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1. Write 0.2% as a decimal.

2.

A.

0.002

B.

0.02

C.

0.2

D.

20

Write 3.4% as a fraction.
A.

3.

4.

5.

SHOW YOUR WORK HERE

34
1, 000

B.

34
10

C.

34
100

D.

340
100

3
Write % as a decimal.
4
A.

0.75

B.

0.075

C.

0.0075

D.

0.00075

353
Chapter 9
Numbers and
Operations

Find 60% of 70.
A.

4,200

B.

420

C.

42

D.

4.2

What is 175% of 16?
A.

28

B.

24

C.

22

D.

12

Peterson’s SAT® Prep Guide 2017

6.

7.

8.

354

9.

What percent of 40 is 16?
A.

20%

B.

1
2 %
2

C.

1
33 %
3

D.

40%

What percent of 16 is 40?
A.

20%

B.

1
2 %
2

C.

200%

D.

250%

$4 is 20% of what?
A.

$5

B.

$20

C.

$200

D.

$500

12 is 150% of what number?

Chapter 9

A.

18

Numbers and
Operations

B.

15

C.

9

D.

8

10.

1
How many sixteenths are there in 87 % ?
2
A.

7

B.

13

C.

14

D.

15

www.petersons.com

SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

1. A

3. C

5. A

7. D

9. D

2. A

4. C

6. D

8. B

10. C

7.

The correct answer is A.

40 5
1
= = 2 = 250%
16 2
2

0.2% = 0.002
The decimal point moves to the
LEFT two places.
8.
2.

The correct answer is A.

3.4% =

3.

3.4
34
=
100 1, 000

9.

The correct answer is D.
150% = 1

3
5

3
i 70 = 42
5
10.

The correct answer is A.
7
i 16 = 28
4

The correct answer is D.

1
2

3
x = 12
2
3 x = 24
x =8

The correct answer is C.

3
175% = 1
4
6.

1
1 , so
4= x
5
5
20 = x

The correct answer is C.

60% =

5.

The correct answer is B.
20% =

3
% = 0.75% = 0.0075
4
4.

The correct answer is D.

The correct answer is C.

355

1
7 14
87 % = =
2
8 16

Chapter 9
Numbers and
Operations

16 2
= = 40%
40 5

Peterson’s SAT® Prep Guide 2017

PERCENT WORD PROBLEMS
Certain types of business situations are excellent applications of percent.

Percent of Increase or Decrease
The percent of increase or decrease is found by putting the amount of increase or decrease over the original amount and renaming
this fraction as a percent.

Example:
Over a five-year period, the enrollment at South High dropped from 1,000 students to 800. Find the percent of
decrease.
Solution:

1, 000 − 800 200
20
=
=
= 20%
1, 000
1, 000 100
Example:

356

A company normally employs 100 people. During a slow spell, the company fired 20% of its employees. By what
percent must the company now increase its staff to return to full capacity?
Solution:

Chapter 9
20% =

Numbers and
Operations

1
5

1
i 100 = 20%
5

20 1
The company now has 100 − 20 = 80 employees. If it then increases its staff by 20, the percent of increase is
= ,
80 4
or 25%.

In word problems, of can usually be interpreted to mean times (in other
words, multiply).

www.petersons.com

Discount
A discount is usually expressed as a percent of the marked price that will be deducted from the marked price to determine the
sale price.
Example:
Bill’s Hardware offers a 20% discount on all appliances during a sale week. If they take advantage of the sale, how
much must the Russells pay for a washing machine marked at $280?
Solution:

Long Method
20% =

1
5

1
i 280 = $56 discount
5

Shorter Method
If there is a 20% discount, the Russells will pay 80% of the
marked price.

$280 − $56 = $224 sale price
The danger inherent in this method is that $56 is sure to
be among the multiple-choice answers.

80% =

4
5

4
i 280 = $224 sale price
5

357

Example:
A store offers a television set marked at $340 less discounts of 10% and 5%. Another store offers the same television
set also marked at $340 with a single discount of 15%. How much does the buyer save by buying at the better price?

Chapter 9
Numbers and
Operations

Solution:
9
, of $340, which is $306. The additional 5%
10
discount means the buyer pays 95% of $306, or $290.70. Note that the second discount must be figured on the

In the first store, the initial discount means the buyer pays 90%, or

first sale price. Taking 5% off $306 is a smaller amount than taking the additional 5% off $340. The second store will
therefore have a lower sale price. In the second store, the buyer will pay 85% of $340, or $289, making the price $1.70
less than in the first store.

Peterson’s SAT® Prep Guide 2017

Commission
Many salespeople earn money on a commission basis. In order to encourage sales, they are paid a percentage of the value of
goods sold. This amount is called a commission.
Example:
A salesperson at Brown’s Department Store is paid $80 per week in salary plus a 4% commission on all her sales. How
much will that salesperson earn in a week in which she sells $4,032 worth of merchandise?
Solution:
Find 4% of $4,032 and add this amount to $80.

4032
× 0.04
$161.28 + $80 = $241.28
Example:
Bill Olson delivers frozen food for a delivery service and keeps 8% of all money collected. One month he was able to
keep $16. How much did he forward to the delivery service?
Solution:

358

First, determine how much he collected by finding the number that 16 is 8% of.
16 = 0.08 x
1, 600 = 8 x
200 = x

Chapter 9
Numbers and
Operations

If Bill collected $200 and kept $16, he gave the delivery service $200 − $16, or $184.

www.petersons.com

Taxes
Taxes are a percent of money spent or money earned.
Example:
Noname County collects a 7% sales tax on automobiles. If the price of a car is $8,532 before taxes, what will this car
cost once sales tax is added in?
Solution:
Find 7% of $8,532 to determine tax and then add it to $8,532. This can be done in one step by finding 107% of
$8,532.
$8532
× 1.07
59724
85320
$9129.24
Example:
If the tax rate in Anytown is $3.10 per $100, what is the annual real estate tax on a house assessed at $47,200?
Solution:
annual tax = tax rate • assessed value

 $3.10 
=
( 47, 200 )
 $100 
= (0.031)( 47, 200 )
= $1, 463.20

359
Chapter 9
Numbers and
Operations

Peterson’s SAT® Prep Guide 2017

EXERCISES: PERCENT WORD PROBLEMS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

3.

A suit marked at $80 is sold for $68. What is the rate of
discount?
A.

12%

B.

15%

C.

20%

D.

85%

What was the original price of a phone that sold for $70
during a 20%-off sale?
A.

$56

B.

$84

C.

$87.50

D.

$90

How many dollars does a salesperson earn on a sale of
$800 at a commission of 2.5%?

360

A.

20

B.

200

Chapter 9

C.

2,000

Numbers and
Operations

D.

20,000

4.

5.

At a selling price of $273, a refrigerator yields a 30%
profit on the cost. What selling price will yield a 10%
profit on the cost?
A.

$210

B.

$221

C.

$231

D.

$235

What single discount is equivalent to two successive
discounts of 10% and 15%?
A.

25%

B.

24.5%

C.

24%

D.

23.5%

www.petersons.com

SHOW YOUR WORK HERE

6.

7.

8.

The net price of a certain article is $306 after successive
discounts of 15% and 10% off the marked price. What is
the marked price?
A.

$234.09

B.

$382.50

C.

$400

D.

$408

SHOW YOUR WORK HERE

If a merchant makes a profit of 20% based on the selling
price of an article, what percent does the merchant make
on the cost?
A.

20

B.

25

C.

40

D.

80

A certain radio costs a merchant $72. At what price must
the merchant sell this radio in order to make a profit of
20% of the selling price?
A.

$86.40

B.

$90

C.

$92

D.

$144

361
Chapter 9

9.

10.

A baseball team has won 40 games out of 60 played. It
has 32 more games to play. How many of these must the
team win to make its record 75% for the season?
A.

26

B.

28

C.

29

D.

30

Numbers and
Operations

If prices are reduced 25% and sales increase 20%, what
is the net effect on gross receipts?
A.

They increase by 5%.

B.

They decrease by 5%.

C.

They increase by 10%.

D.

They decrease by 10%.

Peterson’s SAT® Prep Guide 2017

11.

12.

13.

362
Chapter 9
Numbers and
Operations

14.

A salesperson earns 5% on all sales between $200 and
$600, and 8% on the part of the sales over $600. What is
her commission in a week in which her sales total $800?
A.

$20

B.

$36

C.

$46

D.

$78

If the enrollment at State U. was 3,000 in 1998 and 12,000
in 2008, what was the percent of increase in enrollment?
A.

400%

B.

300%

C.

25%

D.

3%

2
If 6 students, representing 16 % of the class, failed
3
algebra, how many students passed the course?
A.

30

B.

32

C.

36

D.

42

If 95% of the residents of Coral Estates live in private
homes and 40% of these live in air-conditioned homes,
what percent of the residents of Coral Estates live in
air-conditioned homes?
A.

3%

B.

3.8%

C.

30%

D.

38%

15. A salesperson receives a salary of $100 a week and a commission of 5% on all sales. What must be the amount of
sales for a week in which the salesperson’s total weekly
income is $360?
A.

$6,200

B.

$5,200

C.

$2,600

D.

$720

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

4. C

7. B

10. D

13. A

2. C

5. D

8. B

11. C

14. D

3. A

6. C

9. C

12. B

15. B

The correct answer is B. The amount of discount is
$12. Rate of discount is figured on the original price.
12 3
=
80 20

2.

1. B

6.

If marked price = m, first sale price = 0.85m, and
net price = 0.90(0.85m) = 0.765m

3
i 100 = 15%
20

0.765m = 306
m = 400

The correct answer is C. $70 represents 80% of the
original price.

In this case, it would be easy to work from the answer
choices.

70 = 0.80 x
700 = 8 x
$87.50 = x
3.

The commission is
4.

15% of $400 is $60, making a first sale price of $340.
10% of this price is $34, making the net price $306.
Choices A, B, and D would not give a final answer in
whole dollars.

The correct answer is A.
2.5% =

2.5
100

7.

2.5
(800) = $20.
100

8.

The new price will add 10% of cost, or $21, for profit.
9.

Final sale price is 85% of $90, or $76.50
Total discount is $100 − $76.50 = $23.50
23.50
= 23.5%
100

Numbers and
Operations

3
The correct answer is C. The team must win 75%, or ,
4
of the games played during the entire season. With 60
games played and 32 more to play, the team must win
3
3
of 92 games, and i 92 = 69. Since 40 games have
4
4
already been won, the team must win 29 additional
games.

First sale price is 90% of $100, or $90

Percent of discount =

Chapter 9

90 = x

New price = $231
The correct answer is D. Work with a simple figure,
such as 100.

The correct answer is B. If the profit is to be 20% of
the selling price, the cost must be 80% of the selling
price.

363

72 = 0.80 x
720 = 8 x

$273 represents 130% of the cost.

5.

The correct answer is B. Use an easy amount of $100
for the selling price. If the profit is 20% of the selling
price, or $20, the cost is $80. Profit based on cost is
20 1
= = 25%
80 4

The correct answer is C.
1.30 x = 273
13 x = 2, 730
x = $210 = cost

The correct answer is C.

10.

The correct answer is D. Let original price = p, and
original sales = s. Therefore, original gross receipts = ps.
Let new price = 0.75p, and new sales = 1.20s. Therefore,
new gross receipts = 0.90ps. Gross receipts are only
90% of what they were.

Peterson’s SAT® Prep Guide 2017

11.

12.

The correct answer is C. Five percent of sales between
$200 and $600 is 0.05(600) = $30. Then, 8% of sales
over $600 is 0.08(200) = $16. Total commission =
$30 + $16 = $46.
The correct answer is B. There was an increase of
9,000 students. To determine the percent of this
increase in enrollment:
9 , 000
= 3 = 300%
3, 000

13.

The correct answer is A.
2
1
16 % =
3
6
1
6= x
6
36 = x
36 students in class: 6 failed, 30 passed

364
Chapter 9
Numbers and
Operations

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14.

The correct answer is D.
40% =

2
5

2
of 95% = 38%
5
15.

The correct answer is B.
Let s = sales
$100 + 0.05s = 360
0.05s = 260
5s = 26 , 000
s = $5, 200

SUMMING IT UP
• If the arithmetic looks complex, try to simplify it first.
• If a problem is given with letters in place of numbers, the same reasoning must be applied as for numbers. If you are not
sure how to proceed, replace the letters with numbers to determine the steps that must be taken.

• Fractions should be written in the simplest form. Often, in multiple-choice questions, you may find that the answer you
have correctly computed is not among the choices but an equivalent fraction is. Be careful!

• Whenever two quantities vary directly, you can find a missing term by setting up a proportion. However, be very careful to
compare the same units, in the same order, on each side of the equal sign.

• When solving percentage problems, remember the following:
ºº To change a % to a decimal, remove the % sign and divide by 100. This has the effect of moving the decimal point two
places to the LEFT.
ºº To change a decimal to a %, add the % sign and multiply by 100. This has the effect of moving the decimal point two
places to the RIGHT.
ºº To change a % to a fraction, remove the % sign and divide by 100. This has the effect of putting the % over 100 and
simplifying the resulting fraction.
ºº To change a fraction to a %, add the % sign and multiply by 100.

• In problems dealing with percent, you may be presented with certain types of business situations, such as taxes or commissions. For problems asking about the percent of increase or decrease, put the amount of increase or decrease over the
original amount and rename that fraction as a percent. A discount is usually expressed as a percent of the marked price that
will be deducted from the marked price to determine the sale price.

365

•

ONLINE
PREP

Want to Know More?

Chapter 9
Access additional practice questions, helpful lessons, valuable tips, and top-notch strategies for the following numbers and
operations review topics in Peterson’s SAT® Online Course:

Numbers and
Operations

• Arithmetic Strategy
• Hard Arithmetic
• Percent Word Problems
• Proportions and Rates
• Word Problems
• Working Backwards
To purchase and access the course, go to www.petersons.com/sat.

Peterson’s SAT® Prep Guide 2017

Chapter 10:
Basic Algebra
OVERVIEW
Signed Numbers

Roots and Radicals

Exercises: Signed
Numbers

Exercises: Roots and
Radicals

Linear Equations

Monomials and
Polynomials

Exercises: Linear
Equations
Simultaneous Equations
Exercises: Simultaneous
Equations
Exponents
Exercises: Exponents
Quadratic Equations
Exercises: Quadratic
Equations
Literal Equations

Exercises: Monomials and
Polynomials
Problem Solving in
Algebra
Exercises: Problem
Solving in Algebra
Inequalities

367

Exercises:
Inequalities

Chapter 10
Basic Algebra

Summing It Up

Exercises: Literal
Equations

SIGNED NUMBERS
To solve algebra problems, you must be able to compute accurately with signed numbers.
Addition: To add signed numbers with the same sign, add the magnitudes of the numbers and keep the same sign. To add signed
numbers with different signs, subtract the magnitudes of the numbers and use the sign of the number with the greater magnitude.
Subtraction: When subtracting a positive number from a negative number, add the magnitudes and make the difference (the
answer) negative. When subtracting a negative number from a positive number, add the magnitude and make the difference
positive. When asked to find the difference or a distance between a negative number and a positive number, the answer will
always be positive.

Peterson’s SAT® Prep Guide 2017

Multiplication: If there is an odd number of negative signs, the product is negative. An even number of negative signs gives a
positive product.
Division: If the signs are the same, the quotient is positive. If the signs are different, the quotient is negative.
Practicing these basic operations with signed numbers will help you on the more difficult problems on the SAT® in which these
and more complex skills are tested.

EXERCISES: SIGNED NUMBERS
DIRECTIONS: Work out each problem. Circle the letter next to your choice.

1.

2.

368
Chapter 10
Basic Algebra

3.

4.

When +3 is added to −5, what is the sum?
A.

−8

B.

+8

C.

−2

D.

+2

When −4 and −5 are added, what is the sum?
A.

−9

B.

+9

C.

−1

D.

+1

Subtract −6 from +3.
A.

−3

B.

+3

C.

+18

D.

+9

When −5 is subtracted from +10, what is the result?
A.

+5

B.

+15

C.

−5

D.

−15

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SHOW YOUR WORK HERE

5.

6.

7.

8.

(−6)(−3) equals
A.

−18

B.

+18

C.

+2

D.

−9

SHOW YOUR WORK HERE

 1
What is the product of ( −6)  +  ( −10) ?
 2
A.

−15

1
2

B.

+15

1
2

C.

−30

D.

+30

When the product of (−4) and (+3) is divided by (−2), the
quotient is

1
2

A.

+

B.

+15

C.

+6

D.

−

1
2

1
2

Last winter the meteorology class recorded the daily
temperatures. The coldest recorded temperature was
–37 degrees Fahrenheit, and the warmest was 38 degrees
Fahrenheit. How many degrees warmer was the warmest
day than the coldest day?
A.

–75

B.

–1

C.

1

D.

75

369
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

9.

10.

The highest point in California is Mt. Whitney with an
elevation of 14,494 feet. The lowest point is Death Valley
with an elevation of –294 feet. How much higher is the
base of a tree at the top of Mt. Whitney than a person
standing at the lowest point in Death Valley?
A.

294 feet

B.

14,200 feet

C.

14,494 feet

D.

14,788 feet

A submarine started at an elevation of –1,250 feet, or
1,250 feet below sea level, and it submerged another 25
feet per second. It continued to submerge for 10 seconds.
What was its new elevation?
A.

–1,500 feet

B.

–1,000 feet

C.

250 feet

D.

1,500 feet

370
Chapter 10
Basic Algebra

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS
1. C

3. D

5. B

7. C

9. D

2. A

4. B

6. D

8. D

10. A

1.

The correct answer is C. In adding numbers with
opposite signs, subtract their magnitudes (5 − 3 = 2)
and use the sign of the number with the greater
magnitude (negative).

2.

The correct answer is A. In adding numbers with the
same sign, add their magnitudes (4 + 5 = 9) and keep
the same sign.

3.

The correct answer is D. Change the sign of the
second number and follow the rules for addition.

8.

The correct answer is D. When subtracting a positive
number from a negative number, you add the
magnitude and make the difference positive. This is
like a distance question. It’s really asking what the
distance is on the number line from –37 to +38. Try to
picture the number line. Add the magnitudes and
make the answer positive:
–37 – 38 = –75

+ 3
+ 6
+ 9
4.

+ 15

6.

The correct answer is B. The product of two negative
numbers is a positive number.
The correct answer is D. The product of an even
number of negative numbers is positive.
6  1
  (10) = 30
1  2

7.

9.

The correct answer is D. This question is really asking
about distance between two things, so the answer will
be positive. You can figure it is 14,494 feet from the top
of Mt. Whitney to sea level, and then another 294 feet
to get to the lowest point of Death Valley. Add the two
numbers: 14,494 + 294 = 14,788.

10.

The correct answer is A. Find the additional distance
submerged. Multiply –25 by 10. When multiplying a
negative number by a positive, the product is negative.

The correct answer is B. Change the sign of the
second number and follow the rules for addition.
+ 10
+ 5

5.

The difference is 75 degrees.

–25 × 10 = –250
Subtract 250 from –1,250. When subtracting a positive number from a negative number, add the magnitude and make the difference (the answer) negative:

371
Chapter 10
Basic Algebra

1,250 + 250 = 1,500
The answer is –1,500.

The correct answer is C.
(−4)(+3) = −12
Dividing a negative number by a negative number
gives a positive quotient.
−12
= +6
−2

Peterson’s SAT® Prep Guide 2017

LINEAR EQUATIONS
The next step in solving algebra problems is mastering linear equations. Whether an equation involves numbers or only variables,
the basic steps are the same.

Four-Step Strategy
1.

If there are fractions or decimals, remove them by multiplication.

2.

Collect all terms containing the unknown for which you are solving on the same side of the equation. Remember that
whenever a term crosses the equal sign from one side of the equation to the other, it must “pay a toll.” That is, it must
change its sign.

3.

Determine the coefficient of the unknown by combining similar terms or factoring when terms cannot be combined.

4.

Divide both sides of the equation by this coefficient.

If you have a string of multiplications and divisions to do and the
number of negative factors is even, the result will be positive; if the
number of negative factors is odd, the result will be negative.

Example:
Solve for x: 5x − 3 = 3x + 5

372

Solution:

Chapter 10

2x = 8
x=4

Basic Algebra

Example:
Solve for x:

3
2
x +2= x +3
4
3

Solution:
Multiply by 12:
9 x + 24 = 8 x + 36
x = 12

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Example:
Solve for x: 0.7x + 0.04 = 2.49
Solution:
Multiply by 100:
70 x + 4 = 249
70 x = 245
x = 3.5
An equation that is true for every value of the variable is called an identity. It has infinitely many solutions. An
equation has no solution if no value for the variable will make the equation true.
Example:
Solve for x: 0.5(6x + 4) = 3x + 2
Solution:
First, simplify each side of the equation. Then solve for x:
3x + 2 = 3x + 2
3x = 3x
x=x

373

Since x = x is always true, the original equation has infinitely many solutions and is called an identity.

Chapter 10
Basic Algebra

Example:
Solve for x: 9x + 7 = x + 2(4x + 3)
Solution:
First, simplify each side of the equation. Then solve for x:
9x + 7 = x + 8x + 6
9x + 7 = 9x + 6
7=6
Since 7 ≠ 6, the original equation has no solution.
If you eliminate the variable in the process of solving the equation, then you will have either infinitely many solutions
or no solution.

Peterson’s SAT® Prep Guide 2017

Example:
In the equation ax + 7 = 2x + 3, for which values of a will the equation have no solutions?

Solution:
If a = 2, the original equation becomes 2x + 7 = 2x + 3. Since 2x + 7 ≠ 2x + 3 there are no solutions that make the
equation true.

Real-World Linear Equations
A literal equation is an equation that involves two or more variables. You can solve for one variable in terms of the others using
the properties of equalities. A formula is a literal equation that defines a relationship among quantities. For example, the perimeter
of a rectangle can be found using the formula P = 2l + 2w, where P = perimeter, l = length, and w = width.
Example:
What is the width of a rectangle with perimeter 42 and length 8?
Solution:
Using the formula P = 2l + 2w, where P = perimeter, l = length, and w = width, solve for the variable w.

374

Substitute the values that you know into the formula.

Chapter 10

42 = 2 (8) + 2w

Basic Algebra

42 = 16 + 2w
42 − 16 = 2w
26 = 2w
26
=w
2
13 = w

The width of the rectangle is 13 units.

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Example:
The drama club sold student and adult tickets to its spring play. The adult tickets cost $15 each, and the student
tickets cost $10 each. Tickets sales were $4,050. If 120 adult tickets were sold, how many student tickets were sold?
Solution:
Using the formula R = 15a + 10s, where R = revenue from ticket sales, a = adult tickets, and s = student tickets, solve it
for the variable s.
Substitute the values that you know into the formula.
4 , 050 = 15 (120) + 10 s
4 , 050 = 1, 800 + 10 s
4 , 050 − 1, 800 = 10 s
2, 250 = 10 s
2, 250
=s
10
225 = s

The drama club sold 225 student tickets.

EXERCISES: LINEAR EQUATIONS

375

DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

If 5x + 6 = 10, then x equals
A.

16
5

B.

5
16

C.

−

D.

4
5

SHOW YOUR WORK HERE

Chapter 10
Basic Algebra

5
4

Solve for x: 2x – 3 = 4x – 15
A.

–6

B.

–3

C.

3

D.

6

Peterson’s SAT® Prep Guide 2017

3.

Solve for k:
A.
B.
C.
D.

4.

5.

376

6.

Chapter 10
Basic Algebra

7.

k k
+ =1
3 4

8
11
7
12
12
7
1
7

If x + y = 12 and x – y = 2, what is the value of xy?
A.

10

B.

12

C.

20

D.

35

If 7x = 3x + 12, then 2x + 5 =
A.

10

B.

11

C.

12

D.

13

Solve for x: 6x + 7 = 2(3x – 5)
A.

0

B.

4

C.

No solution

D.

Infinitely many solutions

Solve for x:

2x + 9 3x + 8
=
2
7

A.

No solution

B.

Infinitely many solutions

C.

17
38

D.

−

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38
17

SHOW YOUR WORK HERE

8.

9.

10.

11.

12.

Solve for x:

1
1
(2 x + 8) = 4  x + 1
2
4

A.

Infinitely many solutions

B.

No solution

C.

0

D.

8

SHOW YOUR WORK HERE

1
The formula for the area of a triangle is A = bh . Find the
2
base of the triangle if the area is 28 in.2 and its height is
7 in.
A.

2 in.

B.

8 in.

C.

98 in.

D.

196 in.

For what values of n is n + 5 equal to n − 5?
A.

No value

B.

0

C.

All positive values

D.

All values

Membership to Iron Gym costs $40 per month plus a $30
registration fee. The monthly cost is deducted automatically from your account. If your starting balance is $350,
how many months will you be able to go to the gym
before you have to add money to your account?
A.

6

B.

7

C.

8

D.

9

377
Chapter 10
Basic Algebra

Your cell phone plan costs $45 per month plus $0.08 per
text message. Your latest bill is $66.04. How many text
messages were included in this bill?
A.

825

B.

562

C.

420

D.

263

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. D

4. D

7. D

10. A

2. D

5. B

8. A

11. C

3. C

6. C

9. B

12. D

The correct answer is D.

6.

5x = 4
4
x=
5
2.

6 x + 7 = 6 x − 10
7 = −10
Since 7 ≠ –10, there are no values of x that will satisfy
the equation. There is no solution.
7.

4 x + 18 = 21x + 56
−17 x = 38
38
x=−
17

4 k + 3k = 12
7k = 12
12
k=
7
4.

Basic Algebra

The correct answer is D. Add the two equations to
cancel the y-variable and solve for x.

8.

7 + y = 12
y =5
xy = 35
5.

The correct answer is B. Solve for x:
4 x = 12
x =3

2 x + 5 = 3 (3) + 5 = 11

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The correct answer is A.
1
1
(2 x + 8) = 4  x + 1
2
4
x+4= x+4
x=x

x + y = 12
x−y =2
2 x = 14
x =7
Substitute the value of x into the addition equation to
find the value of y.

The correct answer is D.
2x + 9 3x + 8
=
2
7
2 (2 x + 9 ) = 7 (3 x + 8 )

The correct answer is C. Multiply by 12:

378
Chapter 10

6 x + 7 = 2 (3 x − 5)

The correct answer is D.
2 x − 3 = 4 x − 15
−2 x − 3 = −15
−2 x = −12
x =6

3.

The correct answer is C.

All values of x will make this equation true, so there
are infinitely many solutions.
9.

The correct answer is B. Solve the formula for b. Then
substitute in the values of the variables.
1
A = bh
2
2A
=b
h
2 (28)
=b
7
8=b

10.

11.

The correct answer is A. There is no number such
that, when 5 is added, you get the same result as when
5 is subtracted. Do not confuse choices A and B. Choice
B would mean that the number 0 satisfies the
equation, which it does not.
The correct answer is C.
40 x + 30 = 350
40 x = 320
x =8

12.

The correct answer is D. Write an equation to model
your monthly cell phone bill. Use the variable B for your
total bill and t for the number of text messages. Then
plug in the given values and solve for t.
B = 45 + 0.08t
B − 45
=t
0.08
66.04 − 45
=t
0.08
263 = t
Your latest bill included charges for 263 text
messages.

379
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

SIMULTANEOUS EQUATIONS
In solving equations with two unknowns, you must work with two equations simultaneously. The object is to eliminate one of
the two unknowns and solve for the resulting single unknown.
Example:
Solve for x: 2 x − 4 y = 2
3 x + 5 y = 14
Solution:
Multiply the first equation by 5:
10x − 20y = 10
Multiply the second equation by 4:
12x + 20y = 56
Since the y-terms now have the same numerical coefficients, but with opposite signs, you can eliminate them by
adding the two equations. If they had the same signs, you would eliminate them by subtracting the equations.
Add the equations:
10 x − 20 y = 10
12 x + 20 y = 56
22x = 66

380

x =3
Chapter 10
Basic Algebra

Since you were only asked to solve for x, stop here. If you were asked to solve for both x and y, you would now substitute 3 for x in either equation and solve the resulting equation for y.
3 (3) + 5 y = 14
9 + 5 y = 14
5y = 5
y =1
In the previous example, the system of equations has exactly one solution (3, 1). It is also possible for a system of
equations to have no solution or infinitely many solutions.
Example:
Solve the system: −12 x + 8 y = 2
3x − 2y = 7

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Solution:
Multiply the second equation by 4, so that the x-terms and y-terms have the same numerical coefficients:
−12 x + 8 y = 2
12 x − 8 y = 28
Now add the equations:
−12 x + 8 y = 2
12 x − 8 y = 28
0 = 30
Since 0 ≠ 30, there is no solution to the system.
Example:
Solve the system: 3 x − 2 y = −15
2
x − y = −5
3
Solution:
Multiply the second equation by 3, so that the x- and y-terms have the same numerical coefficients:
3 x − 2 y = −15
3 x − 2 y = −15

381
Chapter 10

Now subtract the equations:

Basic Algebra

3 x − 2 y = −15
3 x − 2 y = −15
0 = 0
Since 0 = 0 is an identity, there are infinitely many solutions to the system.

Peterson’s SAT® Prep Guide 2017

Example:
For which value of a will the system

3 x − 4 y = 12
have infinitely many solutions?
ax − 3 y = 9

Solution:
Consider solving each equation for y:
3
x −3
4
a
y=
3x − 3
y=

To have infinitely many solutions,
9
So a = .
4

3 a
= .
4 3

Example:
Solve the system: x 2 + y = 9

x − y = −3
Solution:

382

Add the equations to eliminate the y-variable:

Chapter 10

x2 + y = 9
x − y = −3

Basic Algebra

x2 + x = 6
Set the equation equal to 0 and solve for x:
x2 + x – 6 = 0
Factor to solve for x:
(x – 2)(x + 3) = 0
x = 2 or x = –3
Find the corresponding y-values by substituting each value of x into the linear equation.
2 – y = –3; y = 5 and
–3 – y = –3; y = 0

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There are 2 possible solutions for the system: (2, 5) and (–3, 0). Check each in both equations.

( )

1st equation: x 2 + y = 9 and

( 2 )2 + 5 = 9

( x )2 + y = 9
( −3)2 + 0 = 9
9=9

9=9
2nd equation: ( x ) − y = −3

(2) − 5 = −3

( x ) − y = −3
( −3) − 0 = −3

−3 = −3

−3 = −3

and

The solutions to the system are (2, 5) and (–3, 0).

Applications of Systems
Systems of equations can be used to solve many real-life problems.
Example:
Computer Connect, Inc. makes and sells computer parts. The material for each part costs $3.00 and sells for $12.75
each. The company spends $1,200 on additional expenses each month. How many computer parts must the
company sell each month in order to break even?

Solution:
The break-even point is when the income equals the expenses. The first equation 12.75x = y represents the income.
The second equation 3x + 1,200 = y represents expenses.
y = 12.75 x
y = 3.00 x + 1, 200

383
Chapter 10
Basic Algebra

Solve the system by subtracting the second equation from the first.
y = 12.75 x
y = 3.00 x + 1, 200
0 = 9.75 x − 1,2
200
−9.75 x = −1, 200
−1, 200
x=
− 9.75
x ≈ 123.08
To break even, the company would have to sell at least 124 computer parts.

Peterson’s SAT® Prep Guide 2017

Example:
Jordan and Alex are planning a vacation. They plan to spend some of the time in Naples, Florida, and the rest of time
in Key West. They estimate that it will cost $250 per day in Naples and $325 per day in Key West. If they plan to
vacation a total of 8 days and have a budget of $2,375. How many days should they spend in each city?

Solution
To write the equations, let x = the number of days in Naples and y = the number of days in Key West. The first
equation x + y = 8 represents the total number of days on vacation. The second equation, 250x + 325y = 2,375,
represents total cost.
The system of equations is:

x+y =8
250 x + 325 y = 2, 375

Solve the system by multiplying the first equation by 325 and then subtract the second equation from the first.
325 x + 325 y = 2, 600
250 x + 325 y = 2, 375
75 x = 225
x=
3
Since x + y = 8, if x = 3 then y = 5. The couple can spend 3 days in Naples and 5 days in Key West.

384
Chapter 10

Solving Systems of Inequalities by Graphing
Systems of inequalities are solved using the same methods as systems of equations. Recall that you must reverse the sign of the
inequality if you multiply or divide by a negative value.

Basic Algebra

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You can graph a system of linear inequalities in the coordinate plane. The solution of the system is where the graphs of the
inequalities overlap. Recall, that an inequality with a < or > sign, is graphed as a dashed line, while an inequality with a ≤ or ≥ is
graphed with a solid line. A solid line shows that answers along the line are included in the solution set for that inequality.
Example:
What system of inequalities is represented by the graph shown?

4

2

–4

–2

0

2

4

–2
–2

–
4
–4

385
Chapter 10

Solution

Basic Algebra

First write the inequality that represents the region bounded by the solid line, using two points along the line and
the slope-intercept formula y = mx + b, replacing the equal sign with a comparison symbol.
y ≥ –0.5x + 2
Then write the inequality that represents the region bounded by the dashed line.
y < 2x + 1
The graph shows the intersection of the system y ≥ –0.5x + 2
					
y < 2x + 1

Peterson’s SAT® Prep Guide 2017

Example:
Solve the system of inequalities by graphing: x + 2 y ≤ 8
3x − y ≥ 3
Solution
First solve each inequality for y to rewrite in slope-intercept form:
			

1st inequality: x + 2 y ≤ 8
2y ≤ − x + 8
1
y≤− x+4
2

2nd inequality: 3 x − y ≥ 3
− y ≥ −3 x + 3
y ≤ 3x − 3

Then graph each inequality.

10
8
6
4
2

386

–1
10
–10

–8
–8

–6
–6

4
–4

2
–2

–
2
–2
4
–4

Chapter 10

–6
–6

Basic Algebra

–8
–8
–10
–10
–1

The solution is the region where the graphs overlap.

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2

4

6

8

10
10

EXERCISES: SIMULTANEOUS EQUATIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

Solve the system for x:

SHOW YOUR WORK HERE

− x + 2y = 7
3 x − 2 y = −3

2.

A.

4.5

B.

2

C.

–2

D.

–11

Solve the system for y:
2x − 9y = 4
−x + y = 5

3.

A.

7

B.

2

C.

–2

D.

–7

Solve the system:
2 y = x + 16
1
− x + y = −2
2

4.

387

A.

No solution

B.

Infinitely many solutions

C.

0

D.

All positive values

Chapter 10
Basic Algebra

Solve the system for y:
x − y2 = 2
2x + 5y = 7
A.

y = 11, 2.25

B.

y = 0.5, –3

C.

y = 1.75, 17

D.

Infinitely many solutions

Peterson’s SAT® Prep Guide 2017

5.

SHOW YOUR WORK HERE

Solve the system:
14 y = −2 x + 23

2 ( x + 7 y ) = 23

6.

A.

0

B.

All negative values

C.

No solution

D.

Infinitely many solutions

What system of inequalities is shown in the graph?
y

5
4
3
2
1
–5

–4

–3 –2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

388
Chapter 10

A.

y < 4 x −1
2x + y ≥ 5

B.

y > 4 x −1
−2 x + y ≥ 5

C.

y > 4x +1
2x − y ≥ 5

D.

y ≥ 4 x −1
2 x + y ≥ −5

Basic Algebra

7.

Speedy Rent-A-Car charges $45 a day plus $0.60 per mile
driven to rent a car. Zippy Rental charges $40 a day plus
$0.70 per mile driven to rent a car. After how many miles
would it cost the same amount to rent a car from either
Speedy Rent-A-Car or Zippy Rental?
A.

25 miles

B.

50 miles

C.

75 miles

D.

100 miles

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8.

A used bookstore sells hardcover books for $5 each
and paperback books for $1 each. You buy 13 books for
summer reading, and you spend $45. How many more
hardcover books than paperback books did you buy?
A.

8

B.

5

C.

4

D.

3

SHOW YOUR WORK HERE

389
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. B

3. A

5. D

7. B

2. C

4. B

6. A

8. D

The correct answer is B. Add the equations to
eliminate y.

4.

The correct answer is B. Eliminate the x-variable and
solve for y.

− x + 2y = 7
3 x − 2 y = −3

x − y2 = 2
2x + 5y = 7

2x = 4
x= 2
2.

2x − 2y2 = 4
2xx + 5 y = 7
2y2 + 5y = 3

The correct answer is C. Rewrite the equations and
multiply the second equation by 2. Then add the
equations to eliminate x.

2y + 5y − 3 = 0
2

(2 y − 1) ( y + 3) = 0
1
y = , −3
2

2x − 9y = 4
−x + y = 5
2x − 9y = 4
−2 x + 2 y = 10

5.

14 y = −2 x + 23

− 7 y = 14
y = −2

390

3.

2 ( x + 7 y ) = 23
2 x + 14 y = 23
2 x + 14 y = 23

The correct answer is A. Multiply the second equation
by 2 and add to eliminate a variable.
2 y = x + 16
1
− x + y = −2
2
− x + 2 y = 16
x − 2y = 4

Chapter 10
Basic Algebra

0 = 20
Since 0 ≠ 20, there is no solution.

The correct answer is D.

0=0

Since 0 = 0 is always true, there are infinitely many
solutions.
6.

The correct answer is A. First write the inequality that
represents the region bounded by the dashed line
using two points and the slope intercept formula.
y < 4x –1
Then write the inequality that represents the region
bounded by the solid line.
y ≥ –2x + 5
The graph shows the intersection of the system:
y < 4x –1
2x + y ≥ 5

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7.

The correct answer is B. The system of equations that
represents the cost of renting a car from the places is:
y = 45 + 0.6x
y = 40 + 0.7x
Solve this system by subtracting the second equation
from the first. The solution is 50 miles.
Rewrite the equations so that you can eliminate the y
variable. So:
40 = −0.7 x + y
−45 = 0.6 x − y
Add the second equation to the first to eliminate the
y variable: –5 = –0.1x. When simplified, x = 50. Therefore, 50 is the number of miles it would take for the
cost (y) of both rental companies to be equal.

8.

The correct answer is D. The system of equations that
represents this situation is:
x + y = 13
5 x + y = 45
Where x represents the number of hardcover books
purchased and y represents the number of paperback
books purchased. Solve this system by subtracting
the first equation from the second.
5 x + y = 45
− x − y = −13
You are left with 4x = 32 or x = 8. If 8 hardcover
books are purchased, then 5 paperback books are
purchased. This means that you purchased 3 more
hardcover books than paperback books.

391
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

EXPONENTS
An exponent is a mathematical notation indicating that a number, called the base, has been multiplied one or more times by
itself. For example, in the term 23, the 2 is the base and the 3 is the exponent. This term means “two times two times two” and is
read “two to the third power.” The word power tells how many times the base number appears in the multiplication.
x 3 = x times x times x
x 2 = x times x
x1 = x
x0 = 1

Commit to memory small powers of small numbers that come up in many
questions. For example, the powers of 2: 2, 4, 8, 16, 32, . . . the powers of
3: 3, 9, 27, 81, . . . and so on.

The Five Rules of Exponents
1.

To multiply powers of the same base, add the exponents.
x2 times x3 = x2 + 3 = x5
x5 times x4 = x5 + 4 = x9

2.

To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend.

x6
= x6 − 2 = x4
x2
x 10
= x 10 − 3 = x 7
x3

392
Chapter 10
Basic Algebra

3.

Negative powers represent reciprocals.
x −1 =
 x3 
 y 5 

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−2

1
x
2

 y5 
y 10
= 3 = 6
x
x 

4.

To find the power of a power, multiply the exponents.
(x2)3 = x(2)(3) = x6
(x3y5)2 = x(3)(2)y(5)(2) = x6y10
A variable base with an even exponent has two values, one positive and one negative.
x2 = 25; x could be positive 5 or negative 5.
A variable base can be zero (unless otherwise stated in the problem). In that case, no matter what the exponent, the value
of the term is zero.
Is x4 always greater than x2? No; if x is zero, then x4 and x2 are equal.
When the base is a fraction between 0 and 1, the larger the exponent, the smaller the value of the term.
2
1
 37 
 37 
 37 
 37 
Which is greater,   or   ? The correct answer is   because   is almost ,
2
 73 
 73 
 73 
 73 
2
 37 
1
while   is about .
73
4

5.

Fractional exponents represent roots.
1

x2 = x
1

x3 =3 x
2

x5 =

( x)
5

5

= x2

2

393
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

EXERCISES: EXPONENTS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

394
Chapter 10

p8 × q4 × p4 × q8 =
A.

p12q12

B.

p4q4

C.

p32q32

D.

p64q64

(x2y3)4 =
A.

x6y7

B.

x8y12

C.

x12y8

D.

x2y

x 16 y 6
=
x4 y2
A.

x20y8

B.

x4y3

C.

x12y3

D.

x12y4

Basic Algebra

4.

If x4 = 16 and y2 = 36, then the maximum possible value
for x − y is
A.

–14

B.

–4

C.

8

D.

20

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SHOW YOUR WORK HERE

5.

a −4 × a−3 =
1

A.

a 12
1

B.

6.

SHOW YOUR WORK HERE

a7

C.

a7

D.

a12
2

1

x 3x 2 =
A.

3

x

B.

5

x3

C.

( x)

D.

5

6

7

1
x2

395
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. A

3. D

5. B

2. B

4. C

6. C

The correct answer is A. The multiplication signs do
not change the fact that this is the multiplication of
terms with a common base and different exponents.
Solve this kind of problem by adding the exponents.
p

8+4

4+8

×q

5.

a −4 × a −3 = a −4

12 12

=p q

2.

The correct answer is B. To raise a power to a power,
multiply the exponents. x(2)(4)y(3)(4) = x8y12

3.

The correct answer is D. All fractions are implied
division. When dividing terms with a common base
and different exponents, subtract the exponents.
Therefore, 16 − 4 = 12 and 6 − 2 = 4.

The correct answer is B. To multiply, add the exponents. The resulting exponent will be negative, which
means you need to take the reciprocal.

= a −7
1
= 7
a

6.

The correct answer is C. To multiply, add the exponents.
Then, use the rules for rational exponents to convert to
root form.

x
4.

396

The correct answer is C. First, determine the value for
x and the value for y, and you will find that x could be 2
or –2, and y could be 6 or –6. Therefore, the four
possible values for x − y are as follows:
2 − 6 = −4

2 − ( −6) = 8

Chapter 10

−2 − 6 = −8

−2 − ( −6) = 4

Basic Algebra

The maximum value would be 8.

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+ ( −3)

2 1
3x 2

=x

2 1
+
3 2

=x

7
6

=

( x)
6

7

QUADRATIC EQUATIONS
Roots and Factoring
In solving quadratic equations, remember that there will always be two roots, even though these roots may be equal. A complete
quadratic equation is of the form ax2 + bx + c = 0.

ALERT: Don’t forget: In working with any equation, if you move a term from one side of the equal sign to the other, you must
change its sign.

Example:
Factor: x2 + 7x + 12 = 0
Solution:
(x + 3)(x + 4) = 0
The last term of the equation is positive; therefore, both factors must have the same sign, since the last two terms
multiply to a positive product. The middle term is also positive; therefore, both factors must be positive, since they
also add to a positive sum.
(x + 4)(x + 3) = 0
If the product of two factors is 0, each factor may be set equal to 0, yielding the values for x of −4 or −3.

397

Example:
Chapter 10
Factor: x2 + 7x − 18 = 0

Basic Algebra

Solution:
(x + 9)(x − 2) = 0
Now you are looking for two numbers with a product of −18; therefore, they must have opposite signs. To yield + 7 as
a middle coefficient, the numbers must be + 9 and −2.
(x + 9)(x − 2) = 0
This equation gives the roots −9 and + 2.
Incomplete quadratic equations are those in which b or c is equal to 0.

Peterson’s SAT® Prep Guide 2017

Example:
Solve for x: x2 − 16 = 0
Solution:
x2 = 16
x = ±4
Remember, there must be two roots.
Example:
Solve for x: 4x2 − 9 = 0
Solution:

4 x2 = 9
9
x2 =
4
x=±

3
2

Example:

398
Chapter 10

Solve for x: x2 + 4x = 0
Solution:

Basic Algebra

Never divide through an equation by the unknown, as this would yield an equation of lower degree having fewer
roots than the original equation. Always factor this type of equation.
x(x + 4) = 0
The roots are 0 and −4.

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Example:
Solve for x: 4x2 − 9x = 0
Solution:
x(4x − 9) = 0
The roots are 0 and

9
.
4

The quadratic formula can also be used to find the solutions to quadratic equations ax2 + bx + c = 0 where a, b, and c are real
numbers and a ≠ 0.

x=

−b ± b 2 − 4 ac
2a

Example:
Use the quadratic formula to solve for x: 2x2 + 7x = 3
Solution:
Write the equation in standard form: 2x2 + 7x – 3 = 0. Then, identify the values of a, b, and c and substitute them into
the quadratic formula.
a = 2, b = 7, and c = −3
−b ± b 2 − 4 ac
x=
2a
x=
x=

The solutions are x =

−7 ±

399
Chapter 10
Basic Algebra

(7) 2 − 4 (2) ( −3)
2 ( 2)

−7 ± 73
4

−7 − 73
−7 + 73
≈ −3.886
≈ 0.386 or x =
4
4

Peterson’s SAT® Prep Guide 2017

EXERCISES: QUADRATIC EQUATIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

3.

Solve for x: x2 − 2x − 15 = 0
A.

+5 or −3

B.

−5 or +3

C.

−5 or −3

D.

+5 or +3

Solve for x: x2 + 12 = 8x
A.

+6 or −2

B.

−6 or +2

C.

−6 or −2

D.

+6 or +2

Solve for x: 4x2 = 12
A.

400

B.

Chapter 10
Basic Algebra

4.

3
3 or −3

C.

3 or − 3

D.

3 or

−3

Solve for x: 3x2 = 4x
A.

4
3

B.

4
or 0
3

C.

4
− or 0
3

D.

4
4
or −
3
3

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SHOW YOUR WORK HERE

5.

Solve for x: 2x2 + 3x = 7
A.

x=

3 − 47
3 + 47
,x=
4
4

B.

x=

3 + 65
3 − 65
,x=
4
4

C.

x=

−3 + 47
−3 − 47
,x=
4
4

D.

x=

−3 + 47
−3 − 47
,x=
4
4

SHOW YOUR WORK HERE

401
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS
1. A

1.

2. D

The correct answer is A.

5.

( x − 5) ( x + 3) =
x = 5 or − 3
2.

3. C

The correct answer is D.

4. B

5. D

The correct answer is D. Write the equation in
standard form:
2x2 + 3x – 7 = 0.
a = 2, b = 3, and c = –7.

x 2 − 8 x + 12 = 0

( x − 6 ) ( x − 2) = 0

x = 6 or 2
3.

The correct answer is C.
x2 = 3

The correct answer is B.
3x 2 − 4 x = 0

402
Chapter 10
Basic Algebra

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−3 ± (3)2 − 4(2)( −7)
2(2)

x=

−3 ± 65
4

The solutions are x =

x = 3 or − 3
4.

x=

x (3 x − 4 ) = 0
x = 0 or

4
3

−3 − 65
−3 + 65
.
or x =
4
4

LITERAL EQUATIONS
There are many equations that can be used to represent common problems, such as distance. The equation to find distance, given
rate and time, is written as d = rt. This type of equation is called a literal equation in which the equation is solved for one variable
in particular, such as d in the distance formula. Here are some examples:
Example:
Solve for l in the equation P = 2l + 2w.
Solution:
Subtract 2w from both sides of the equation. This will eliminate it from the right side of the equation.
P – 2w = 2l
Divide both sides of the equation to solve for l.
P − 2w P
; −w = l
2
2

Example:
Solve for c in the equation E = mc2.
Solution:

Divide both sides by m. This will eliminate it from the right side of the equation.
E
= c2
m

403
Chapter 10
Basic Algebra

Take the square root of both sides to solve for c.
E
=c
m
Example:
1
The volume of a cone can be found using the formula V = pr 2h . Solve for r.
3
Solution:

Divide both sides by h:
Divide both sides by pi:

v 1 2
= pr
h 3
v

ph

1
= r2
3

Multiply both sides by 3: 3 ×

v

ph

1
= r2 × 3
3

v
Take the square root of both sides: 3 × ph = r

Peterson’s SAT® Prep Guide 2017

EXERCISES: LITERAL EQUATIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

404

Solve for x in the equation z = 5x – 25xy
A.

z
=x
−20 y

B.

z
=x
1− 5 y

C.

z
=x
5 − 25 y

D.

z
=x
30 y

A bakery orders vanilla beans at a cost of $12.45 for a
package of 10. There is a shipping cost of $6.00 for all sizes
of shipments. Which of the following shows the equation
solved for p, the total number of packages purchased,
where c is the total cost of the order.
A.

p = 6c + 12.45

B.

p = 12.45c + 6

C.

p=

c
−6
12.45

D.

p=

c −6
12.45

Chapter 10
Basic Algebra

3.

The distance between two points is determined by the
equation below, where x1 and x2 are the x-coordinates of
two points, and y1 and y2 are the y-coordinates of the two
points.
d=

( x2 − x1)2 + ( y2 − y1)2

Which shows the equation solved for y2?
A.

y 2 = d 2 − ( x 2 − x1 ) + y1

B.

y 2 = d − ( x 2 − x1 ) + y1

C.

y 2 = d − ( x 2 − x1 ) + y1

D.

y 2 = d 2 − ( x 2 − x1 ) + y1

2

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2

SHOW YOUR WORK HERE

4.

5.

The surface area of a cylinder is found using the formula
SA = 2πrh + 2πr2. Which shows the equation solved for
h, the height of the cylinder, in simplest form?

A.

SA − 2pr 2
=h
2pr

B.

SA
-r =h
2pr

C.

SA
=h
2pr

D.

SA
=h
4 pr

SHOW YOUR WORK HERE

The formula for converting degrees Fahrenheit to degrees
Celsius is shown below.
C=

5
(F − 32)
9

Which equation shows the formula correctly solved for F?

A.

9
(C + 32) = F
5

C
B. 		 − 32 = F
9
5

6.

C.

9
C − 32 = F
5

D.

9
C + 32 = F
5

Solve for f:

405
Chapter 10
Basic Algebra

1 1 1
= +
f a b

A.

f = a+ b

B.

f=

C.

f = ab

D.

f=

ab
a+b

ba
b−a

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. C

3. A

5. D

2. D

4. B

6. B

The correct answer is C. Factor out an x from both terms
on the right side of the equation: z = x(5 – 25y)

5.

Divide both sides by 5 – 25y:

The correct answer is D. To solve for F, divide both sides
5
9
by or multiply both sides by .
9
5
9
C = F − 32
5

z
=x
5 − 25 y
2.

by the equation 12.45p + 6 = c. To solve for p, subtract
6 from both sides. Then, divide both sides by 12.45 to
isolate p.
3.

Add 32 to both sides to isolate F.

The correct answer is D. The total cost, c, is determined

The correct answer is A. Solve for y2 by squaring both
sides to remove the square root from the right side.

9
C + 32 = F
5
6.

The correct answer is B. To solve for f, first multiply both
sides of the equation by f to move it into the numerator.

1=

d2 = (x2 – x1)2 + (y2 – y1)2
Subtract the term (x2 – x1)2 from both sides.

406

Multiply by b and then by a to write the fractions with
a common denominator, ab.

d2 – (x2 – x1)2 = (y2 – y1)2
1=

Take the square root of both sides to eliminate the
exponent on the right side.

Chapter 10

f f
+
a b

fb fa
+
ab ab

Add the fractions.

Basic Algebra

d 2 − ( x 2 − x1 ) = y 2 − y1
2

Add y1 to both sides of the equation.
d 2 − ( x 2 − x1 ) + y1 = y 2
2

4.

The correct answer is B. To solve for the height, h, factor
out 2πr from the terms on the right side of the equation.
SA = 2πr(h + r)
Divide both sides of the equation by 2πr.
SA
= h+r
2pr
Subtract r from both sides of the equation.
SA
−r =h
2pr

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1=

fb + fa
ab

Multiply both sides of the equation by ab.
ab = fb + fa
Factor f out of the terms on the right side of the
equation.
ab = f(b + a)
Divide both sides of the equation by (b + a).
ab
=f
a+b

ROOTS AND RADICALS
Adding and Subtracting
Rules for adding and subtracting radicals are much the same as for adding and subtracting variables. Radicals must be exactly
the same if they are to be added or subtracted, and they merely serve as a label that does not change.
4 2 +3 2 =7 2
2 +2 2 =3 2
2 + 3 cannot be added
Sometimes, when radicals are not the same, simplification of one or more radicals will make them the same. Remember that
radicals are simplified by factoring out any perfect square factors.
27 + 75
9 i 3 + 25 i 3
3 3 +5 3 =8 3

Multiplying and Dividing
In multiplying and dividing, treat radicals in the same way as you treat variables. They are factors and must be handled as such.

2i 3= 6

407

2 5 i 3 7 = 6 35

(2 3 )

2

= 2 3 i 2 3 = 4 i 3 = 12

75
= 25 = 5
3

Chapter 10
Basic Algebra

10 3
=2
5 3

Simplifying
To simplify radicals that contain a sum or difference under the radical sign, add or subtract first, then take the square root.
16 x 2 + 9 x 2
25 x 2 5 x
x2 x2
+
=
=
=
9 16
144
144
12

If you take the square root of each term before combining, you would have
clearly not the same answer. Remember that

x x
7x
+ , or
, which is
12
3 4

25 is 5. However, if you write that

25 as

16 + 9 , you cannot say it is

4 + 3, or 7. Always combine the quantities within a radical sign into a single term before taking the square root.

Peterson’s SAT® Prep Guide 2017

Radicals
In solving equations containing radicals, always get the radical alone on one side of the equation; then square both sides to
remove the radical and solve. Remember that all solutions to radical equations must be checked, as squaring both sides may
sometimes result in extraneous roots.
Example:
Solve for x:

x +5 =7

Solution:
x + 5 = 49
x = 44
Checking, we have 49 = 7 , which is true.
Example:
Solve for x: x = − 6
Solution:
You may have written the answer: x = 36.

408
Chapter 10
Basic Algebra

Checking, we have 36 = − 6, which is not true, as the radical sign means the positive, or principal, square root only.
This equation has no solution because 36 = 6 , not −6.
Example:
Solve for x:

x2+ 6 − 3 = x

Solution:

x 2 +6 −3= x
x2 +6 = x +3
x 2 + 6 = x 2 + 6x + 9
6 = 6x + 9
−3 = 6 x
1
− =x
2

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Checking, we have

6

1
1
−3= −
4
2

25
1
−3= −
4
2
5
1
−3= −
2
2
1
1
2 −3= −
2
2
1
1
− =−
2
2
This is a true statement. Therefore,

1
is a true root.
2

Roots as Fractional Powers
Roots can also be written as fractional exponents to make them easier for you to work with. The square root of 4 ( " 4 " ) , for example,
1

1

can also be written as 4 2 . The value of a square root includes both the positive and negative root, so

4 = ±2 and 4 2 = ± 2.

To write an nth root as a fractional exponent, use the root as the denominator of the fraction under 1 or

n

1

x = x n.

Use the laws of exponents to solve radical expressions and equations.
Example:
Simplify:

3x i

A.

9x2

B.

6x

C.

3x

D.

3x

409

3x

Chapter 10
2

Basic Algebra

Solution:

3x i

1

1

3 x = (3 x ) 2 i (3 x ) 2
1

= (3 x ) 2

+

1
2

= 3x

Peterson’s SAT® Prep Guide 2017

EXERCISES: ROOTS AND RADICALS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

410
Chapter 10
Basic Algebra

4.

5.

What is the sum of 12 + 27 ?
A.

29

B.

3 5

C.

13 3

D.

5 3

What is the difference between 150 and 54 ?
A.

2 6

B.

16 6

C.

96

D.

6 2

What is the product of 18x and 2x , where x is greater
than 0?
A.

6x2

B.

6x

C.

36x2

D.

6 x

If

1
= 0.25 , what does x equal?
x

A.

2

B.

0.5

C.

0.2

D.

20

Solve for x: 5 2 x 2 = 500
A.

10

B.

100

C.

2 5

D.

10

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SHOW YOUR WORK HERE

6.

A.

–2

B.

7.

2

D.

4

Which expression is equivalent to
A.

5

B.

10 x 5

C.

5

5

4x + 5 6x ?

10 x
1

10 + 2 x

(4 x )

1
5

+ (6 x )

1
5

Divide 6 45 by 3 5.
A.

6

B.

9

C.

15

D.

30
y2 y2
+
=
25 16

9.

A.

2y
9

B.

9y
20

C.

y
9

D.
10.

2

C.

D.
8.

SHOW YOUR WORK HERE

Solve for x: 8 x + 7 = 3 x + 17

y

411
Chapter 10
Basic Algebra

41
20

Which expression shows
form?
A.

3
2

B.

0
2

C.

4 − 13
2

D.

2 − 23
2 2

5

32 − 3 2
written in simplest
8

1

1

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. D

3. B

5. D

7. D

9. D

2. A

4. A

6. D

8. A

10. D

The correct answer is D.

6.

12 = 4 3 = 2 3

Subtract 3 x from each side: 5 x = 10.

27 = 9 3 = 3 3
2 3 +3 3 =5 3
2.

Divide each side by 5:

x = 2, x = 4 .

7.

The correct answer is D. The terms under the roots
cannot be added because they are not like terms. The
terms must remain as 4x and 6x. The fifth root can be
1
rewritten as an exponent of .
5

8.

The correct answer is A.

The correct answer is A.
150 = 25 6 = 5 6
54 = 9 6 = 3 6

The correct answer is D. Subtract 7 from each side of
the equation: 8 x = 3 x + 10 .

5 6 −3 6 =2 6
3.

The correct answer is B.
18 x i 2 x = 36 x 2 = 6 x

412

4.

9.

Chapter 10
Basic Algebra

The correct answer is D.

The correct answer is D.
16 y 2 + 25 y 2
y2 y2
+
=
25 16
400

The correct answer is A.
0.25 = 0.5
1
= 0.5
x
1 = 0.5 x
10 = 5 x
2= x

5.

6 45
=2 9 =2i 3=6
3 5

=

10.

y 41
41y 2
=
400
20

The correct answer is D. The fifth root of 32 is 2, because
2 × 2 × 2 × 2 × 2 = 32.
2−3 2
8

Factor 500 = 100 5 = 10 5 so you get:

The third root of 2 can be rewritten as

5 2 x 2 = 10 5.

The square root of 8 can be simplified:

Factor 5 from each side of the equation:
2x 2 = 2 5
Square each side:
2x2 = 4 × 5 = 20.   x2 = 10, so x = 10 .

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8 = 4×2 =2 2
1

2−23
2 2

1
23

1

2−23 .
:
8

MONOMIALS AND POLYNOMIALS
When we add a collection of expressions together, each expression is called a term. Monomial means one term. For example, we
might say that 2x + 3y2 + 7 is the sum of three terms, or three monomials. When we talk about a monomial, we generally mean
a term that is just the product of constants and variables, possibly raised to various powers. Examples might be 7, 2x, −3y2, and
4x2z5. The constant factor is called the coefficient of the variable factor. Thus, in −3y2, −3 is the coefficient of y2.
If we restrict our attention to monomials of the form Axn, the sums of such terms are called polynomials (in one variable). Expressions
like 3x + 5, 2x2 − 5x + 8, and x4 − 7x5 − 11 are all examples of polynomials. The highest power of the variable that appears is called
the degree of the polynomial. The three examples just given are of degree 1, 2, and 5, respectively.
In evaluating monomials and polynomials for negative values of the variable, the greatest pitfall is keeping track of the minus
signs. Always remember that in an expression like −x2, the power 2 is applied to the x, and the minus sign in front should be
thought of as (−1) times the expression. If you want to have the power apply to −x, you must write (−x)2.

Combining Monomials
Monomials with identical variable factors can be added together by adding their coefficients. So 3x2 + 4x2 = 7x2. Of course, subtraction is handled the same way, thus:
3x4 − 9x4 = −6x4
Monomials are multiplied by taking the product of their coefficients and taking the product of the variable part by adding exponents of factors with like bases. So, (3xy2)(2xy3) = 6x2y5.
Monomial fractions can be simplified to simplest form by dividing out common factors of the coefficients and then using the
usual rules for subtraction of exponents in division. An example might be:
6x 3y 5
2x 4 y 3

=

3y 2
x

413
Chapter 10
Basic Algebra

Example:
3
Combine into a single monomial: 8 x − 6 x
2

4x

Solution:
The fraction simplifies to 2x, and 2x − 6x = −4x.

Peterson’s SAT® Prep Guide 2017

Combining Polynomials and Monomials
Polynomials are added or subtracted by just combining like monomial terms in the appropriate manner. Thus,
(3x2 − 3x − 4) + (2x2 + 5x − 11)
is summed by removing the parentheses and combining like terms, to yield
5x2 + 2x − 15.
In subtraction, when you remove the parentheses with a minus sign in front, be careful to change the signs of all the terms within
the parentheses. So:

(3 x

2

) (

)

− 3 x − 4 − 2 x 2 + 5 x − 11 = 3 x 2 − 3 x − 4 − 2 x 2 − 5 x + 11
= x 2 − 8x + 7

(Did you notice that 3x2 − 2x2 = 1x2 but the “1” is not shown?)
To multiply a polynomial by a monomial, use the distributive property to multiply each term in the polynomial by the monomial
factor. For example, 2x(2x2 + 5x − 11) = 4x3 + 10x2 − 22x.
When multiplying a polynomial by a polynomial, you are actually repeatedly applying the distributive property to form all
possible products of the terms in the first polynomial with the terms in the second polynomial. The most common use of this is
in multiplying two binomials (polynomials with two terms), such as (x + 3)(x − 5). In this case, there are four terms in the result,
x • x = x 2; x(−5) = −5x; 3 • x = 3x; and 3 • (−5) = −15; but the two middle terms are added together to give −2x. Thus, the product
is x2 − 2x − 15.

414

This process is usually remembered as the FOIL method. That is, form the products of First, Outer, Inner, Last, as shown in the
figure below.

Chapter 10

O
F

Basic Algebra

(x + 3)(x – 5) = x2 + (–5x + 3x) – 15
I
L

Example:
If d is an integer, and (x + 2)(x + d) = x2 − kx −10, what is the value of k + d?
Solution:
The product of the two last terms, 2d, must be −10. Therefore, d = −5. If d = −5, then the sum of the outer and inner
products becomes −5x + 2x = −3x, which equals −kx. Hence, k = 3, and k + d = 3 + (−5) = −2.

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Factoring Monomials
Factoring a monomial simply involves reversing the distributive property. For example, if you are looking at 4x2 + 12xy, you should
see that 4x is a factor of both terms. Hence, you could just as well write this as 4x(x + 3y). Multiplication using the distributive
property will restore the original formulation.
Example:
If 3x − 4y = −2, what is the value of 9x − 12y?
Solution:
Although you seem to have one equation in two unknowns, you can still solve the problem, because you do not need to know
the values of the individual variables. Just rewrite:
9x − 12y = 3(3x − 4y).
Since 3x − 4y = −2, 9x − 12y is 3 times −2, or −6.

415
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

EXERCISES: MONOMIALS AND POLYNOMIALS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

416
Chapter 10
Basic Algebra

4.

SHOW YOUR WORK HERE

6x3(x 2)3 =
A.

6x7

B.

6x8

C.

6x9

D.

6x10

(3w  2y  3)4 =
A.

18w 8y12

B.

18w6y7

C.

81w6y7

D.

81w8y12

5x3(−3x8) =
A.

15x11

B.

−15x11

C.

−15x24

D.

15x24

3
2
Simplify: 3 x y − 9 x
2
xy

A.

−6 xy

B.

3 x ( xy − 3)

C.

3x 2 − 9 x
y

D.

3x2 – 9x

xy 2

y2

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5.

6.

7.

8.

(a3 + 4a2 – 11a + 4) – (8a2 + 2a + 4) =
A.

–3a2 – 13a

B.

a3 – 12a2 – 13a – 8

C.

a3 – 4a2 – 9a + 8

D.

a3 – 4a2 – 13a

SHOW YOUR WORK HERE

( 4 x 3 − 2 x + 5) + (8 x 2 − 2 x − 10 )

A.

4x3 + 8x2 – 4x – 5

B.

12x2 – 4x – 5

C.

12x3 – 5

D.

4x3 + 8x2 + 15

What is the product of 2x2 and 3x3 – x + 4?
A.

6x6 + 6x2

B.

6x5 – 2x3 + 8x2

C.

5x5 – x2 + 4

D.

6x5 + 2x3 + 8x2

Multiply: (x2 – 1)(2x3 + 5)

417

A.

2x5 + 5x2

B.

–2x3 – 5

C.

2x5 – 2x3 + 5x2 – 5

Chapter 10

D.

2x6 – 5x2 – 2x3 – 5

Basic Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. C

3. B

5. D

7. B

2. D

4. B

6. A

8. C

The correct answer is C.

5.

The correct answer is D. The term a3 will remain because there are no other like terms to subtract. Subtract
the squared terms: 4a2 – 8a2 = –4a2; the single variable
terms –11a – 2a = –13a; and the integer terms –4 – 4 = 0.
Combining these terms with a3 gives us a3 – 4a2 – 13a.

6.

The correct answer is A. The only like terms that may be
combined are

( ) = (6 i x ) i ( x )
3

6x 3 x 2

2 3

3

= 6 i x 3 i x (2 i 3)
=6i x3 i x6
=6i x9
= 6x 9

2.

The correct answer is D.

(3w y )

2 3 4

(–2x) + (–2x) = –4x and +5 + (–10) = 5 – 10 = –5.

= 81 i w 8 i y 12

7.

= 81w 8 y 12

3.

Combine all the terms to get 4x3 + 8x2 – 4x – 5.

4
= (3) i w (2 i 4) i y (3 i 4)

The correct answer is B.

418

(

2x 2 i 3x 3 = 6 x 5
2 x 2 i ( − x ) = −2 x 3

)

5 x 3 −3 x 8 = 5 i x 3 i ( −3) i x 8
3

= 5 i ( −3) i x i x

Chapter 10

= −15 i x 3+ 8

Basic Algebra

= −15 x 11

4.

The correct answer is B. Multiply each term in the polynomial by 2x2:

2x 2 i 4 = 8x 2

8

Combine the products to get 6x5 – 2x3 + 8x2.
8.

The correct answer is B. The variable x can be
factored out of the all the terms in the numerator and
denominator of the fraction:

The correct answer is C. Use the FOIL method to multiply:
First: (x2)(2x3) = 2x5
Outer: (x2)(5) = 5x2
Inner: (–1)(2x3) = –2x3

3

3x y − 9 x
xy 2

2

=
=

2

3x y − 9 x

1

(1) y 2

3x 2 y − 9 x
y2

Factor the term 3x out of the expression in the
numerator: 3x(xy – 3).
Because y appears in only one of the terms in the
numerator, it cannot be factored out of either the
numerator or the denominator.

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Last: (–1)(5) = –5
Combine the terms to get 2x5 – 2x3 + 5x2 – 5.

PROBLEM SOLVING IN ALGEBRA
When you are working with algebraic word problems, remember that before you begin solving the problem you should be
absolutely certain that you understand precisely what you need to answer. Once this is done, show what you are looking for
algebraically. Write an equation that translates the words of the problem to the symbols of mathematics. Then solve that equation
by using the techniques you just learned.
This section reviews the types of algebra problems most frequently encountered on the SAT® exam. Thoroughly familiarizing
yourself with the problems that follow will help you to translate and solve all kinds of word problems.

Solving Two Linear Equations in Two Unknowns
Many word problems lead to equations in two unknowns. Usually, one needs two equations to solve for both unknowns, although
there are exceptions. There are two generally used methods to solve two equations in two unknowns. They are the method of
substitution and the method of elimination by addition and subtraction.
We’ll illustrate both methods via example. Here is one that uses the method of substitution.
Example:
Mr. Green took his four children to the local craft fair. The total cost of their admission tickets was $14. Mr. and Mrs.
Molina and their six children had to pay $23. What was the cost of an adult ticket to the craft fair, and what was the
cost of a child’s ticket?
Solution:

419

Expressing all amounts in dollars, let x = cost of an adult ticket and let y = cost of a child’s ticket.
Chapter 10

For the Greens: x + 4y = 14

Basic Algebra

For the Molinas: 2x + 6y = 23
The idea of the method of substitution is to solve one equation for one variable in terms of the other and then
substitute that solution into the second equation. So we solve the first equation for x, because that is the simplest
one to isolate:
x = 14 − 4y
and substitute into the second equation:
2(14 − 4y) + 6y = 23
This gives us one equation in one unknown that we can solve:
28 − 8y + 6y = 23
−2y = −5; y = 2.5

Peterson’s SAT® Prep Guide 2017

Now that we know y = 2.5, we substitute this into x = 14 − 4y to get:
x = 14 − 4(2.5) = 4
Thus, the adult tickets were $4 each, and the children’s tickets were $2.50 each.

Here is an example using the method of elimination.
Example:
Paul and Denise both have after-school jobs. Two weeks ago, Paul worked 6 hours, Denise worked 3 hours, and they
earned a total of $39. Last week, Paul worked 12 hours, Denise worked 5 hours, and they earned a total of $75. What
is each one’s hourly wage?
Solution:
Again, let us express all amounts in dollars. Let x = Paul’s hourly wage, and let y = Denise’s hourly wage.
For the first week: 6x + 3y = 39
For the second week: 12x + 5y = 75

420

The idea of the method of elimination is that adding equal quantities to equal quantities gives a true result. So we
want to add some multiple of one equation to the other one so that if we add the two equations together, one
variable will be eliminated. In this case, it is not hard to see that if we multiply the first equation by −2, the coefficient
of x will become −12. Now when we add the two equations, x will be eliminated. Hence,
−12 x − 6 y = −78

Chapter 10

12 x + 5 y = 75
− y = −3

Basic Algebra

Thus, y = 3. We now substitute this into either of the two equations. Let’s use the first:
6x + (3)(3) = 39; x = 5.
Thus, Denise makes only $3 per hour, while Paul gets $5.

Word Problems in One or Two Unknowns
Word problems can be broken down into a number of categories. To do consecutive integer problems, you need to remember
that consecutive integers differ by 1, so a string of such numbers can be represented as n, n + 1, n + 2 . . .
Rate-time-distance problems require you to know the formula d = rt. That is, distance equals rate times time.
Here are some examples of several types of word problems.

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Example:
Movie tickets are $13.50 for adults and $8 for senior citizens. On Saturday night, a total of 436 adults and senior citizens attended, and the movie theater collected $4,885 from these adults and senior citizens. How many senior citizens were at the movie theater?
Solution:
To solve the problem, you must write two different equations using the data in the question. Let a be the number of
adults and s represent senior citizens.
a + s = 436
You also know that a × $13.50 can be used to find the total amount the movie theater collected for adult tickets and
s × $8 to find the total amount collected for senior citizen tickets. Together these dollar amounts total $4,885.
13.5a + 8s = 4,885
Solve using elimination, by multiplying the first equation by –8 to eliminate one of the variables during addition of
the equations:
(–8)(a + s) = (–8)(436)
–8a + –8s = –3,488
Add the equations:
− 8a + −8 s = −3, 488
+13.5a + 8 s = 4 , 885

421

5.5a = 1, 397
a = 254

Chapter 10

254 adults attended, so 436 – 254 = 182 senior citizens were at the movie theater.

Basic Algebra

Example:
A supermarket places two orders for regular and extra-large packages of paper towels. The first order had 48 regular
and 120 extra-large packages and cost $644.40. The second order had 60 regular and 40 extra-large and cost $338.
What is the difference in cost between a regular and extra-large package of paper towels?
Solution:
Write two equations using the data given in the question. Use r to represent a regular package of paper towels and e
to represent an extra-large package.
48r + 120e = 644.40
60r + 40e = 338
Multiply the bottom equation by –3 to eliminate e:

( −3) (60r + 40e) = ( −3)(338)
−180r − 120e = −1, 014

Peterson’s SAT® Prep Guide 2017

Add the 2 equations:
48r + 120e = 644.4
+ − 180r − 120e = −1, 014
− 132r = −369.6
r = 2.8

The price of a regular package of paper towels is $2.80. To find the price of an extra-large package, substitute 2.8 into
one of the equations:

( 48)(2.8) + 120e = 644.4
120e = 510
e = 4.25
The difference in cost between an extra-large package and a regular package of paper towels is:
$4.25 – $2.80 = $1.45
Example:
It took Andrew 15 minutes to drive downtown at 28 miles per hour to get a pizza. How fast did he have to drive back
in order to be home in 10 minutes?
Solution:

422
Chapter 10

1
of an hour. Hence, going 28 miles per hour, the distance to the pizza parlor can be computed using
4
1
1
 1
the formula d = rt; d = (28)   = 7 miles. Since 10 minutes is of an hour, we have the equation 7 = r . Multiplying
 4
6
6
by 6, r = 42 mph.

15 minutes is

Basic Algebra

Fraction Problems
2
, it does not mean the numerator must be 2 and the
3
denominator 3. The numerator and denominator could be 4 and 6, respectively, or 1 and 1.5, or 30 and 45, or any of infinitely
many combinations. All you know is that the ratio of numerator to denominator will be 2:3. Therefore, the numerator may be
2x
represented by 2x, the denominator by 3x, and the fraction by
.
3x

A fraction is a ratio between two numbers. If the value of a fraction is

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Example:
3
The value of a fraction is . If 3 is subtracted from the numerator and added to the denominator, the value of the
4
2
fraction is . Find the original fraction.
5
Solution:
Let the original fraction be represented by
the new fraction becomes

3x
. If 3 is subtracted from the numerator and added to the denominator,
4x

3x − 3
.
4x + 3

2
We know that the value of the new fraction is .
5
3x − 3 2
=
4x + 3 5
Cross-multiply to eliminate fractions.
15 x − 15 = 8 x + 6
7 x = 21
x =3

Therefore, the original fraction is

3x 9
= .
4 x 12

423
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

EXERCISES: PROBLEM SOLVING IN ALGEBRA
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

424

A train with a heavy load travels from Albany to Binghamton at 15 miles per hour. After unloading the load,
it travels back from Binghamton to Albany at 20 miles
per hour. The trip from Albany to Binghamton took 1.5
hours longer than the return trip. Which of the following
equations can be used to calculate the time, t, it took for
the train to go from Albany to Binghamton?
A.

1.5t = 20t

B.

15t = 20t – 30

C.

t = 20t – 30

D.

15t = 20 + 30

If a fleet of m buses uses g gallons of gasoline every two
days, how many gallons of gasoline will be used by 4
buses every five days?

A.

10g
m

B.

10gm

C.

10m
g

D.

20g
m

Chapter 10
Basic Algebra

3.

A faucet is dripping at a constant rate. If, at noon on
Sunday, 3 ounces of water have dripped from the faucet
into a holding tank and, at 5 p.m. on Sunday, a total of
7 ounces have dripped into the tank, how many ounces
will have dripped into the tank by 2:00 a.m. on Monday?
A.

10

B.

51
5

C.

12

D.

71
5

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SHOW YOUR WORK HERE

4.

Prior to the 2016 Summer Olympics, the world record
in 800-meter freestyle swimming was approximately 8
minutes and 15 seconds. Marta is recording her times in
seconds, s, for the 800-meter freestyle competition at her
school. Which expression below could be used to calculate Marta’s time as a percentage of that world record?
A.

s
× 100
8.25

B.

 s

 ÷ 8.15 × 100
60

C.

 s

 ÷ 495 × 100
60

D.

SHOW YOUR WORK HERE

s
× 100
495

425
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS
1. B

1.

2. A

The correct answer is B. Use the distance formula
d = rt. The train’s rate from Albany to Binghamton is
15mph. Its time can be expressed as t. The train’s rate
from Binghamton to Albany is 20mph. Its time can be
expressed as t – 1.5.

3. D

3.

For the trip from Binghamton to Albany:

7+

d = 20(t – 1.5) = 20t – 30

15t = 20t – 30
2.

426

The correct answer is A. Running m buses for two
days is the same as running one bus for 2m days. If we
g
use g gallons of gasoline, each bus uses
gallons
2m
each day. So if you multiply the number of gallons per
day used by each bus by the number of buses and the
number of days, you should get total gasoline usage.

Chapter 10
Basic Algebra

That is,

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10 g
g
.
× ( 4 )(5) =
2m
m

The correct answer is D. In 5 hours, 4 ounces (7 − 3)
4
have dripped. Therefore, the drip rate is of an ounce
5
per hour.
From 5:00 p.m. on Sunday until 2:00 a.m. on Monday
is 9 hours, which means the total will be:

For the trip from Albany to Binghamton: d = 15t

Since the distance from Albany to Binghamton is
equal to the distance from Binghamton to Albany, we
can set these two expressions equal to each other:

4. D

4.

4
36 71
×9=7 =
5
5
5

The correct answer is D. Convert the world record
of 8 minutes and 15 seconds to seconds by multiplying 8 minutes × 60 sec/min = 480 seconds. Add 15:
480 + 15 = 495 seconds.
s
495
and multiply by 100 to express it as a percent. So the
s
correct answer is
× 100.
495

Divide Marta’s time, s, by the world record, 495:

INEQUALITIES
Algebraic inequality statements are solved just as equations are solved. However, you must remember that whenever you multiply
or divide by a negative number, the order of the inequality, that is, the inequality symbol, must be reversed.
Example:
Solve for x: 3 − 5x > 18
Solution:
Add −3 to both sides:
−5x > 15
Divide by −5, remembering to reverse the inequality:
x < −3
Example:
Solve for x: 5x − 4 > 6x − 6
Solution:
Collect all x terms on the left and numerical terms on the right. As with equations, remember that if a term crosses
the inequality symbol, the term changes sign.

427

−x > −2

Chapter 10

Divide (or multiply) by −1:

Basic Algebra

x<2

Inequality Symbols
> greater than

< less than

≥ greater than or equal to

≤ less than or equal to

You can solve inequalities in the same way you solve linear equations, except in cases where you multiply or divide by a negative
number. In these situations, you must reverse the direction of the inequality symbol.

Peterson’s SAT® Prep Guide 2017

Properties of Inequalities
In the properties below, assume that a, b, and c are real numbers.

Addition Property of Inequality

Subtraction Property of Inequality

If a > b, then a + c > b + c

If a > b, then a – c > b – c

If a < b, then a + c < b + c

If a < b, then a – c < b – c

Multiplication Property of Inequality

Division Property of Inequality

c>0

c>0
If a > b, then ac > bc
If a < b, then ac < bc

If a > b, then

a b
>
c c

If a < b, then

a b
<
c c

c<0

c<0

a b
<
c c
a b
If a < b, then >
c c

If a > b, then
If a > b, then ac < bc
If a < b, then ac > bc

428

These properties are also true for inequalities that include the ≤ and ≥ symbols.
Example:

Chapter 10
Basic Algebra

The meeting room can hold at most 250 people. If 182 people have already been admitted, how many more people
can be allowed into the meeting room?
Solution:
Let x = number of people that can be admitted.
182 + x ≤ 250
182 − 182 + x ≤ 250 − 182
x ≤ 68
There can be at most 68 more people admitted to the meeting room.

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Example:
To stay healthy, an adult’s goal should be to walk at least 10,000 steps each day. A fitness tracker showed that a
person had walked 6,349 steps. What is the minimum number of steps this person can take to reach this goal?
Solution:
Let x = number of steps.
6 , 349 + x ≥ 10 , 000
6 , 349 − 6 , 349 + x ≥ 10 , 000 − 6 , 349
x ≥ 3, 651

The person must walk at least 3,651 more steps.
Example:
Alexander plans on mowing lawns this summer. He charges $20 per lawn. How many lawns will he have to mow in
order to earn at least $575?
Solution:
Let x = number of lawns.
20 x ≥ 575
20 x 575
≥
20
20
x ≥ 28.75

429
Chapter 10
Basic Algebra

Alexander must mow at least 29 lawns to earn at least $575.

Peterson’s SAT® Prep Guide 2017

Use properties of inequality to solve multi-step inequalities.

Example:
The marching band members are making a banner for the pep rally. The banner is in the shape of a rectangle that is
12 ft. long. They have no more than 32 ft. of fringe for the banner. What are the possible widths of the banner?
Solution:
Let w = width of the banner and l = length of the banner. Use the perimeter formula (2l + 2w ≤ P) to find the possible
allowable widths.
2 (12) + 2w ≤ 32
24 + 2w ≤ 32
2w ≤ 8
2w 8
≤
2 2
x≤4
The width of the banner can be 4 ft. or less.
Example:

430
Chapter 10
Basic Algebra

A prepaid cell phone has a balance of $40. Calls are $0.04 per minute, and texts are $0.07 per text. If 342 texts were
used, how many minutes can be used for calls?
Solution:
Let x = number of minutes used on calls and y = number of texts.

0.04 x + 0.07 y ≤ 40

0.04 x + 0.07 (342) ≤ 40
0.04 x + 23.94 ≤ 40
0.04 x ≤ 16.06
0.04 x 16.06
≤
0.04
0.04
x ≤ 401.5

The number of minutes that can be used for calls is 401 or less.

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EXERCISES: INEQUALITIES
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

4.

If 3x – 8 ≥ 4x, then
A.

–8 ≤ x

B.

–8 ≥ x

C.

–8 < x

D.

–8 > x

SHOW YOUR WORK HERE

If –9x + 7 < 43, then
A.

x ≥ –4

B.

x ≤ –4

C.

x > –4

D.

x < –4

The admission to the local carnival is $6. You want to play
games that cost $1.50 per game. If you have $30, how
many games can you play?
A.

At least 24

B.

No more than 20

C.

Less than or equal to 16

D.

Greater than or equal 20

You order a bouquet of flowers that contains roses and
carnations. You have only $48 to spend. Roses cost $3
each, and carnations cost $1.25 each. How many roses
can be in the bouquet if there are 18 carnations in the
bouquet? Let r represent the number of roses.
A.

r≥8

B.

r≤9

C.

r≥9

D.

r≤8

431
Chapter 10
Basic Algebra

Peterson’s SAT® Prep Guide 2017

5.

6.

Bike rentals cost $15 for the first 2 hours and $6 for any
additional hours. Ali wants to bike for more than 2 hours,
but she only has $35. Which inequality represents the
situation, where h is the total number of hours Ali can
bike?
A.

6 +15h ≤ 35

B.

6(h – 2) +15 ≤ 35

C.

6h +15 ≤ 35

D.

6(h + 2) +15 ≤ 35

Selena is adding trim to a rectangular tablecloth that
measures 108 in. long. If she has 330 in. of trim, what is
the greatest possible width of the tablecloth?
A.

At most 54 in.

B.

At most 57 in.

C.

At most 222 in.

D.

At most 114 in.

432
Chapter 10
Basic Algebra

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS
1. B

3. C

5. B

2. C

4. D

6. B

1.

The correct answer is B. Subtracting 3x from both sides
leaves –8 ≥ x.

2.

The correct answer is C.
−9 x + 7 < 43
−9 x < 36
x > −4
By dividing by –9, you reverse the inequality sign.

3.

The correct answer is C.

5.

The correct answer is B. The cost for the first 2 hours is
$15. Subtract the 2 hours from the total number of hours
(h), and multiply by $6 an hour to compute the cost for
the number of hours over 2. Be sure to add the initial $15
for the first 2 hours:
6(h – 2) + 15 ≤ 35

6.

The correct answer is B.

2l + 2w ≤ 330

2 (108) + 2w ≤ 330

6 + 1.5 x ≤ 30
1.5 x ≤ 24
1.5 x 24
≤
1.5 1.5
x ≤ 16
4.

The correct answer is D.
3r + 1.25c ≤ 48

3r + 1.25 (18) ≤ 48

3r + 22.5 ≤ 48
3r ≤ 25.5
3r 25.5
≤
3
3
r ≤ 8.5

216 + 2w ≤ 330
2w ≤ 114
2w 114
≤
2
2
w ≤ 57

The tablecloth can be at most 57 in. wide.

433
Chapter 10
Basic Algebra

There can only be at most 8 roses in the bouquet.

Peterson’s SAT® Prep Guide 2017

SUMMING IT UP
• In complex questions, don’t look for easy solutions.
• Always keep in mind what is being asked.
• Keep the negatives and positives straight when you’re doing polynomial math.
• Don’t be distracted by strange symbols.
• An equation can have one solution, infinitely many solutions, or no solutions.
• Let a, b, and c be real numbers.
ºº If a > b, then a + c > b + c
ºº If a < b, then a + c < b + c
ºº If a > b, then a – c > b – c
ºº If a < b, then a – c < b – c
ºº If c > 0, then if a > b, then ac > bc and if a < b, then ac < bc
ºº If c < 0, then if a > b, then ac < bc and if a < b, then ac > bc

• You can graph a system of linear inequalities in the coordinate plane. The solution of the system is where the graphs of the
inequalities overlap.

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PREP

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Access more practice questions, valuable lessons, helpful tips, and expert strategies for the following basic algebra review topics
in Peterson’s SAT® Online Course:

Chapter 10

• Algebra Strategy

Basic Algebra

• Inequalities
• Linear Equations
• Polynomials
• Quadratics
• Solving Equations
To purchase and access the course, go to www.petersons.com/sat.

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Chapter 11:
Geometry
OVERVIEW
Geometric Notation
Angle Measurement
Intersecting Lines
Area
Circles
Volume
Triangles
Parallel Lines
Coordinate Geometry

435

Exercises: Geometry
Answer Key and Explanations

Chapter 11

Summing It Up

Geometry

GEOMETRIC NOTATION
1.

A point is represented by a dot and denoted by a capital letter.
·P
Point P

2.

A line can be denoted in two different ways. First, a small letter can be placed next to the line. For example, the diagram
below depicts line l. The arrowheads on both ends of the line indicate that lines extend infinitely in both directions.
l

3.

A line can also be denoted by placing a small double-headed arrow over two of its points. The diagram below depicts

line AB.

A

B

Peterson’s SAT® Prep Guide 2017

4.

A line segment is the part of a line between two of its points, which are called the endpoints of the line segment. A line segment
is denoted by placing a small line segment over the two endpoints. The diagram below depicts the line segment AB.

A

5.

B

The length of a line segment is denoted by placing its two endpoints next to each other. In the diagram below, CD = 7.
C

D
7

6.

Two line segments that have the same length are said to be congruent. The symbol for congruence is ≅ . Thus, if AB = 12 and
EF = 12, then AB is congruent to EF , or AB ≅ EF .

7.

A ray is the part of a line beginning at one point, called the endpoint, and extending infinitely in one direction. A ray is denoted
by placing a small one-headed arrow over its endpoint and another point on the ray. The first diagram below depicts the
ray AB , and the second diagram depicts the ray AC .
A

B

A

C

8.

436

Two lines that cross each other are said to intersect. Two lines that do not intersect are said to be parallel. The symbol || is
used to represent parallel lines. In the diagrams below, line k intersects line l at point P, while lines m and n are parallel, that
is, m || n.
k

Chapter 11
Geometry
P

l

m

n

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ANGLE MEASUREMENT
1.

When two rays share a common endpoint, they form angles. The point at which the rays intersect is called the vertex of the
angle, and the rays themselves are called the sides of the angle.
Side

Vertex

2.

Side

The symbol for angle is ∠. Angles can be denoted in several different ways, as shown in the diagram below. The most common
way to denote an angle is to name a point on one side, then the vertex, and then a point on the other side as shown in the
diagram.
Angles can also be denoted by writing a letter or a number within the angle, as shown below.
If there is no ambiguity, an angle can be named by simply naming the vertex.

A

B

437

C
ABC or CBA

Chapter 11
Geometry
2

a
a

3.

2

A

A

The size of an angle is measured in degrees. The symbol for degree is °. A full circle contains 360°, and all other angles can
be measured as a fractional part of a full circle. Typically, the measure of an angle is written in the interior of the angle, near
the vertex.

120°

60°

30°

Peterson’s SAT® Prep Guide 2017

4.

A straight angle is an angle that measures 180°.

180°

5.

A right angle is an angle that measures 90°. Note, as shown in the diagram below, a “box” is used to represent a right angle.

90°

438

6.

The measure of an angle is denoted by writing the letter m followed by the name of the angle. For example, m∠ABC = 45°
tells that angle ABC has a measure of 45°.

7.

Two angles that have the same number of degrees are said to be congruent. Thus, if m∠P = m∠Q, then ∠P ≅ ∠Q.

8.

Two angles whose measures add up to 180° are said to be supplementary. Two angles whose measures add up to 90° are
said to be complementary.

Chapter 11
Geometry
E
G

C

A

B

D

F

ABC and CBD
are supplementary.

9.

To convert degrees to radians, multiply the degree measure by

www.petersons.com

H

EFG and GFH
are complementary.

p radians .
180°

Example:
Convert 85° to radians:
Solution:
 p radians  17p
85° = 85 
=
 180°  36

To convert from radians to degrees, multiply the radian measure by

180°

p radians

.

Example:
Convert

π
radians to degrees:
6

Solution:

p  p radians   180° 
=
= 30°
 
6 
6
p radians 

439

INTERSECTING LINES
1.

When two lines intersect, four angles are formed. The angles opposite each other are congruent.

Chapter 11
Geometry

∠1 ≅ ∠3 and ∠2 ≅ ∠4

1
2

4
3

Peterson’s SAT® Prep Guide 2017

2.

When two lines intersect, the angles adjacent to each other are supplementary.
m∠5 + m∠6 = 180°
m∠6 + m∠7 = 180°
m∠7 + m∠8 = 180°
m∠ 8 + m∠5 = 180°
8

5

6

7

If you know the measure of any one of the four angles formed when two lines intersect, you can determine the measures of
the other three. For example, if m∠1 = 45°, then m∠3 = 45°, and m∠2 = m∠4 = 180° − 45° = 135°.
3.

Two lines that intersect at right angles are said to be perpendicular. In the figure below, AB is perpendicular to CD . This can
be denoted as AB ⊥ CD .

C

440
Chapter 11

B

A

Geometry

D

Note that all four of the angles in the diagram above are right angles.

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AREA
Many of the geometry problems you will encounter on the SAT® will ask about the perimeter or area of a polygon. A polygon is
a closed plane figure that consists of straight line segments called sides. The perimeter of a closed plane figure is the distance
around the figure and is computed by adding all the lengths of the segments/sides that form its outer boundary. The area of a
two-dimensional plane figure is the number of unit squares needed to cover it. The units of area measure are square inches, square
feet, square yards, square centimeters, square meters, and so on. Following are useful area formulas for common plane figures:

1.

Rectangle = bh

3

Area = 6 i 3 = 18

2.

6

Parallelogram = bh

5

4

Area = 8 i 4 = 32
8

3.

Square = s2
Area = 62 = 36

6

441
Chapter 11
Geometry

1
Square = d 2 (d = diagonal)
2
1
Area = (10)(10) = 50
2

4.

Triangle =
Area =

1
bh
2

1
(12)( 4) = 24
2

10

4

12

Peterson’s SAT® Prep Guide 2017

6

5.

Trapezoid = 1 h (b1 + b2 )
2
1
Area = (5)(16) = 40
2

5

10

CIRCLES
1.

A circle is a closed flat figure formed by a set of points all of which are the same distance from a point called the center. The
boundary of the circle is called the circumference, and the distance from the center to any point on the circumference is
called the radius. A circle is denoted by naming the point at its center, that is, the circle whose center is at point P is called
circle P.

P

2.

442

A diameter of a circle is a line segment that passes through the center of the circle, and whose endpoints lie on the circle.
The diameter of a circle is twice as long as its radius. Typically, the letter r is used to represent the radius of a circle, and the
letter d is used to represent the diameter.
2r = d

r

Chapter 11
d

Geometry

3.

A chord of a circle is a line segment both of whose endpoints lie on the circumference of the circle. The chords of a circle
have different lengths, and the length of the longest chord is equal to the diameter.
AB, CD, and EF are chords of circle O. EF is also a diameter.
E

B

A

O

F D

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C

4.

A tangent is a line that intersects the circle at exactly one point. A radius drawn to the point of intersection is perpendicular
to the tangent line.
OQ ⊥ CD

O

C

5.

Q

D

A central angle is an angle that is formed by two radii of a circle. As the diagram below shows, the vertex of a central angle
is the center of the circle.

A

O
B

443

Central angle ∠ AOB

6.

A central angle is equal in degrees to the measure of the arc that it intercepts. That is, a 40° central angle intercepts a 40° arc,
and a 90° central angle intercepts a 90° arc.

Chapter 11
Geometry

90°
40°

40°

Peterson’s SAT® Prep Guide 2017

7.

An arc is a piece of the circumference of a circle. The symbol  placed on top of the two endpoints is used to denote an
 is indicated in the figure below.
arc. For example, MN
M


MN

N

8.

The measure of an arc is in degrees. The arc’s length depends on the size of the circle because it represents a fraction of the
circumference.


Length of AB


mAB
2pr
360

If the radius of a circle is 5 cm and the measure of the arc is 45°, then the length of the arc is
45°
5p
i 2p (5) =
cm
360°
4
= 1.25p cm
≈ 3.93 cm

444
Chapter 11
Geometry

9.

The area of a circle is measured using the formula pr 2. If the diameter of the circle is 12, its radius is 6:
Area of a circle = πr2
12

Area = π(6)2 = 36π

10. The area of a sector of a circle is the product of the ratio measure of the arc and the area of the circle. If the radius of a circle
360°
is 3 cm and the measure of the arc is 60°, then the area of the sector is
Area of sector AOB =


mAB
• pr 2
360

60°
i
360°

p (3)2 =

9 p 3p 2
=
cm .
6
2

A

O

60◦
3

B

When an SAT® exam problem asks you to find the area of a shaded region, you probably
won’t be able to calculate it directly. That’s OK— instead, think of the shaded region as being
whatever is left over when one region is subtracted or removed from a larger region. Use
the formulas you know to find those two regions and perform the necessary subtraction.

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 measure of the central angle 
11. The length of a chord of a circle is the product of 2r and sin 
 . If the radius of a circle is

2
 60° 
4 inches and the measure of the central angle is 60°, then the length of the chord is 2 ( 4 ) sin 
= 8 sin (30°) = 4 inches.
 2 
(In a right-angled triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
The abbreviation is sin.)

VOLUME
1.

The volume of a right rectangular prism is equal to the product of its length, width, and height.
V = lwh				

4

V = (6)(2)(4) = 48

2
6

2.

The volume of a cube is equal to the cube of an edge.
V = e3				
V = (5)3 = 125

445

5

Chapter 11
Geometry

5
5

3.

The volume of a right circular cylinder is equal to π times the square of the radius of the base times the height.
V = πr 2h
V = π(5)2(3) = 75π

3
5

Peterson’s SAT® Prep Guide 2017

4.

The volume of a sphere is equal to

4
p times the cube of the radius.
3

4 3
pr
3
4
3 4
v = p (3) = p (27) = 36 p
3
3

V=

5.

3

The volume of a right square pyramid is equal to

1
times the product of the square of the side and the height.
3

1
V = s2h
3
1 2
V = ( 2) ( 6 )
3
V =8

6

2
6.

1
3

The volume of a right circular cone is equal to p times the product of the square of the radius and the height.
1 2
pr h
3
1
2
V = p (6) (9)
3
V = 108 p
V=

446

1
9

Chapter 11
Geometry

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6

TRIANGLES
1.

A triangle is a polygon with three sides. A vertex of a triangle is a point at which two of its sides meet. The symbol for a triangle
is ∆, and a triangle can be named by writing its three vertices in any order.

∆ ABC contains sides AB , BC, and AC, and angles ∠A, ∠B, and ∠C.
B

A

C

2.

The sum of the measures of the angles in a triangle is 180°. Therefore, if the measures of any two of the angles in a triangle
are known, the measure of the third angle can be determined.

3.

In any triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. In the
triangle below, if a° > b° > c°, then BC > AC > AB.
c°

C

447
a°

b°

B

Chapter 11

A

Geometry

4.

If two sides of a triangle are congruent, the angles opposite these sides are also congruent.
If AB ≅ AC , then ∠B ≅ ∠C.

A

B

C

Peterson’s SAT® Prep Guide 2017

5.

If two angles of a triangle are congruent, the sides opposite these angles are also congruent.
If ∠B ≅ ∠C, then AB ≅ AC .

A

C

B
6.

In the following diagram, ∠1 is called an exterior angle. The measure of an exterior angle of a triangle is equal to the sum of
the measures of the two remote interior angles, that is, the two interior angles that are the farthest away from the exterior
angle.
A

m ∠1 = 115°

B

448
Chapter 11
Geometry

70°

7.

1

45°

C

D

If two angles of one triangle are congruent to two angles of a second triangle, the third angles are also congruent.
∠D ≅ ∠A
D

A

B

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C

E

F

Right Triangles
1.

Pythagorean theorem: The Pythagorean theorem states that the square of a hypotenuse (the leg opposite the right angle)
of a right triangle is equal to the sum of the squares of the other two legs a2 + b2 = c2.

(leg)2 + (leg)2 = (hypotenuse)2
4 2 + 52 = x 2
16 + 25 = x 2
41 = x 2
41 = x
5

x

4

Remember that in a right triangle, you can use the two legs (the two sides
other than the hypotenuse) as base and altitude.

2.

Pythagorean triples: These are sets of whole numbers that satisfy the Pythagorean theorem. When a given set of numbers,
such as 3-4-5, forms a Pythagorean triple (32 + 42 = 52), any multiples of this set, such as 6-8-10 or 15-20-25, also form a
Pythagorean triple. The most common Pythagorean triples that should be memorized are:

449
Chapter 11
Geometry

3-4-5
5-12-13
8-15-17
7-24-25

39

x

15

Peterson’s SAT® Prep Guide 2017

Squaring the numbers 15 and 39 in order to apply the Pythagorean theorem would take too much time. Instead, recognize
the hypotenuse as 3(13). Suspect a 5-12-13 triangle. Since the given leg is 3(5), the missing leg must be 3(12), or 36, with no
computation and a great saving of time.

Remember the well-known Pythagorean triples, that is, sets of whole numbers such as
3-4-5 for which a2 + b2 = c2. (Also watch for their multiples, such as 6-8-10 or 15-20-25.)
On the SAT®, you’ll encounter right triangles with sides whose lengths correspond to
these values. Other Pythagorean triples are: 5-12-13, 8-15-17, and 7-24-25.

3.

The 30°-60°-90° triangle is a special right triangle whose sides are in the ratio of x : 3 : 2 x.
1
i hypotenuse .
2
1
b. The leg opposite the 60° angle is i hypotenuse i 3 .
2
a. The leg opposite the 30° angle is

c. An altitude in an equilateral triangle forms a 30°–60°–90° triangle and is therefore equal to

30°

8
x

60°

4.

Geometry

30°

30°

10

5

x=4

450
Chapter 11

y

60°

8

z

1
i hypotenuse i
2

x

60°

The 45°–45°–90° triangle (isosceles right triangle) is a special right triangle whose sides are in the ratio of x: x : 2
a. Each leg is

1
i hypotenuse i
2

b. The hypotenuse is leg i

2.

2.

c. The diagonal in a square forms a 45°–45°–90° triangle and is therefore equal to the length of one side i

45°

45°

3 2

8

w

45°

x

45°
w=6

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2.

y

45°
x=8 2

6

10

z

45°
y=5 2

z=6 2

3.

5.

One way to solve SAT® questions that involve 30°–60°–90° triangles and 45°–45°–90° triangles is to use right triangle
trigonometric relationships. In the triangle below, side AB is called the side adjacent to ∠A, side BC is called the side
opposite ∠A, and side AC is the hypotenuse. Relative to ∠A, the trigonometric ratios sine, cosine, and tangent are defined as
shown.

opposite
sin e a° = sin a° =
hypotenuse
adjacent
cosine a° = cos a° =
hypotenuse
opposite
tangent a° = tan a° =
adjacent

C

		

p

Hy

se

nu

e
ot

Opposite

a°

A

B

Adjacent

The table below shows the values of the sine, cosine, and tangent for 30°, 45°, and 60°.

Angle a

sin a°

cos a°

tan a°

30°

1
2

3
2

3
3

45°

2
2

2
2

1

60°

3
2

1
2

3

451
Chapter 11

By using the values of sine, cosine, and tangent above, problems involving 30°–60°–90° triangles and 45°–45°–90° triangles
can also be solved. For example, consider the 30°-60°–90° triangle with hypotenuse of length 8. The computations that follow
show how to determine the lengths of the other two sides.

Geometry

Peterson’s SAT® Prep Guide 2017

30°

sine 60° =
or y =

8

y

opposite
y
y
3
= . Also, since , then =
. Cross-multiply to get 2 y = 8 3 ,
hypotenuse 8
8
2

8 3
= 4 3. Note that this is the same answer that would be obtained using the
2

properties of 30°-60°-90° triangles.
cos 60° =

1
adjacent
x
x 1
= . Also, since cos 60°= , then = . Cross-multiply to get
2
hypotenuse 8
8 2

2x = 8, or x = 4. This, again, is the same answer that would be obtained using the
60°

x

properties of 30°–60°–90° triangles above.

Here are two sample problems:

Example:
Suppose a building has a handicap ramp that rises 2.5 ft. and forms a 3° angle with the ground. How far from the
base of the building is the start of the ramp? Round your answer to the nearest tenth.
Solution:

452
Chapter 11
Geometry

www.petersons.com

2.5
x
2.5
x=
tan 3°
x = 47.7 feet

tan 3°=

Example:
Suppose a 26-ft. wire is attached to the top of a pole and staked in the ground at a 40-degree angle. Estimate the
height of the pole.

B

A

40°

C

Solution:
x
26
26 sin 40° = x
16.7 ft. ≈ x
sin 40° =

To find how far the stake is from the ground, you can use the Pythagorean theorem:
a2 + b 2 = c 2
16.72 + b 2 = 262
19.9 ft. ≈ x

453

PARALLEL LINES

Chapter 11
Geometry

1.

If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
If AB ⊥ CD , then
1 2

A

∠ 1 ≅ ∠3, and
∠2 ≅ ∠4.

B

4 3
C

2.

D

If two parallel lines are cut by a transversal, the corresponding angles are congruent.
If AB || CD , then
∠ 1 ≅ ∠ 5,

A

∠ 2 ≅ ∠ 6,
∠ 3 ≅ ∠ 7, and

C

1 2
4 3

5 6
8 7

B
D

∠ 4 ≅ ∠ 8.

Peterson’s SAT® Prep Guide 2017

3.

If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary.

If AB || CD , then
1

A

∠ 1 is supplementary to ∠ 4, and
∠ 2 is supplementary to∠ 3.

4

2

B

3

C

D

COORDINATE GEOMETRY
1.

Lines and other geometric figures can be positioned on a plane by means of the rectangular coordinate system. The rectangular coordinate system consists of two number lines that are perpendicular and cross each other at their origins (0 on each
of the number lines). The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.
y
6
5
4
3
2

454

–6 –5 –4 –3 –2 –1
–1
–2

Chapter 11

–3

Geometry

–4
–5
–6

www.petersons.com

x

1
1

2

3

4

5

6

2.

Any point on the plane can be designated by a pair of numbers. The first number is called the x-coordinate and indicates how
far to move to the left (negative) or to the right (positive) on the x-axis, and the second number is called the y-coordinate
and tells how far to move up (positive) or down (negative) on the y-axis. Generically, a point on the plane can be written as
(x, y). When two points need to be expressed generically, they are typically written as (x1, y1) and (x2, y2).
The points (2, 3), (−4, 1), (−5, −2), and (2 –4) are graphed on a coordinate system as shown below.
y
6
5
4

( 2, 3 )

3
2

( – 4, 1 )

1

–6 –5 –4 –3 –2 –1
–1
–2
( – 5, – 2 )
–3

x
1

–4

2

3

4

5

6

( 2, – 4)

–5
–6

3.

The slope of a straight line is a number that measures how steep the line is. Traditionally, the variable m is used to stand for
the slope of a line. By convention, a line that increases from left to right has a positive slope, and a line that decreases from
left to right has a negative slope. A horizontal line has a slope of 0 since it is “flat,” and a vertical line has an undefined slope.

455
Chapter 11
Geometry

y

y

x

Positive Slope

4.

y

x

Negative Slope

y

x

Zero Slope

If (x1, y1) and (x2, y2) are any two points on a line, the slope is given by the formula m =

x

Undefined Slope

( y 2 − y1 ) .
( x 2 − x1 )

3
7−4 3
= . A slope of represents
2
5−3 2
the fact that for every 2 units moved horizontally along the x-axis, the line rises vertically 3 units.

Therefore, for example, if a line contains the points (5, 7) and (3, 4), the slope would be m =

5.

An equation of degree one that contains the variables x and/or y raised to the first power, but no higher, will always have a
straight line as its graph. A very convenient way to write the equation of a line is in the slope-intercept form, y = mx + b. In
this form, m represents the slope of the line, and b is the y-intercept, that is, the point where the graph crosses the y-axis.

Peterson’s SAT® Prep Guide 2017

Example:
Consider the line represented by the equation 2x + 5y = 12.
Solution:
Begin by writing this equation in slope-intercept form.
2 x + 5 y = 12
5 y = −2 x + 12

Subtract 2x from both sides.
Divide both sides by 5.

2
12
y=− x+
5
5

2
12
Therefore, the slope of the line is − , and the y-intercept is . Here is the graph of this line.
5
5
y
6
5
4
3
2

456

1
–6

–5

–4

–3

–2

–1–1
–2

Chapter 11
Geometry

–3
–4
–5
–6

www.petersons.com

x
1

2

3

4

5

6

The following are sample problems:
Example:
Write the equation of the line containing the point (2, 1) and having slope 5.
Solution:
Begin by taking the slope-intercept form y = mx + b, and substituting m = 5, to obtain y = 5x + b. To determine the
value of the y-intercept b, substitute the coordinates of the point (2, 1) into the equation.
y = 5 x + b Substitute (2,1).
1 = 5(2) + b Solve for b.
1 = 10 + b
−9 = b
Therefore, the equation of the line is y = 5x − 9.
Example:
Graph the function f(x) = 2x + 5.
Solution:
Begin by recognizing that the slope is 2 and the y-intercept is (0, 5). To graph this function, first graph the point (0, 5).
Then move up 2 units and then to the right 1 unit. This location is (1, 7). Starting at (0, 5) again, go down 2 units and
then to the left 1 unit. This location is (–1, 3). Connect these points to form the graph of the function f(x) = 2x + 5.

457
Chapter 11
Geometry

7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
–1
–2
–3
–4
–5
–6
–7

Peterson’s SAT® Prep Guide 2017

You can write an equation of a line from a graph given any two points on the line. First, use the two points to find the
slope. Then use the point–slope form of an equation of a line: y – y1 = m(x – x1). As an example, consider the graph
shown below.
y

4
(0, 3)

2
(–1, 1)

–4

–2

0

2

4

x

–2

–4

You need to first find the slope using two points on the line.
The slope formula is m =

458
Chapter 11

y 2 − y1
. Use the points (0, 3) and (–1, 1) to find the slope.
x 2 − x1
m=

y 2 − y1 1− 3 −2
=
=
=2
x 2 − x1 −1− 0 −1

Use the point–slope form and either given point.
y − y 1 = m ( x − x 1)

Geometry

y − 1 = 2 ( x − ( −1))
y − 1 = 2 ( x + 1)

To write this equation in slope–intercept form, solve for y.
y − 1 = 2 ( x + 1)

y = 2 ( x + 1) + 1
y = 2x + 2 +1
y = 2x + 3

Here is a sample question of how to write an equation of a line from a word problem and then graph the equation
using the intercepts.

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Example:
You decide to purchase holiday gift cards for your family. You have $300 to spend on the cards, and you purchase
cards for either $20 or $30. What are three combinations of cards that you can purchase?
Solution:
To write an equation that represents this situation, first define your variables.
Let x = number of $20 gift cards purchased and y = number of $30 gift cards purchased.
Now write an equation to represent the situation.
20x + 30y = 300
Use the intercepts to draw the graph.
20 x + 30 y = 300

20 x + 30 y = 300

20 (0) + 30 y = 300

20 x + 30 (0) = 300

30 y = 300
y = 10

20 x = 300
x = 15

11

# of $30

10
9

459

8
7

Chapter 11

6

Geometry

5
4
3
2
1
1

2

3

4

5

6

7

8

9

10

11

12

13

# of $20

You cannot purchase a fraction of a card, so only the integer combinations can be solutions. You can purchase fifteen $20 cards
and zero $30 cards, six $20 cards and six $30 cards, or zero $20 cards and ten $30 cards. (Although the question only asked for
three answers, the other possible combinations are twelve $20 gift cards and two $30 gift cards, nine $20 gift cards and four $30
gift cards, and three $20 gift cards and eight $30 gift cards.)

Peterson’s SAT® Prep Guide 2017

6.

The standard form of the equation of a circle with center at (h, k) and radius r is (x – h)2 + (y – k)2 = r2. For example, to graph
y2 = –x2 + 64, first rewrite the equation in standard form: x2 + y2 = 64. Then identify the radius, r = 8, and the center, (0, 0).
Now plot points that are on the circle: (0, 8), (0, –8), (–8, 0), and (8, 0). Connect the points to draw the circle.
y
10
8
6
4
2
–10

–8

–6

–4

–2

2

4

6

8

10

x

–2
–4
–6
–8
–10

To graph (x – 1)2 + (y + 2)2 = 4, first identify the radius, r = 2, and the center, (1, –2). Next, plot points that are on the circle. The
easiest way to do this is to find points 2 units above, below, left, and right of the center: (1, 0), (1, –4), (–1, –2), and (3, –2). Connect
the points to draw the circle.

460

y
4

Chapter 11

3

Geometry

2
1
–4

–3

–2

–1

1
–1
–2
–3
–4

www.petersons.com

2

3

4

x

7.

Parallel lines have the same slope. Therefore, one way to tell whether two lines are parallel or not is to write them in slope-intercept form and compare the slopes. To write the equation of the line that is parallel to the line y = 3x + 7 and contains
the point (5, 2), begin by noting that the equation of the line we are looking for must have a slope of 3, just like the line
y = 3x + 7. Thus, it must be of the form y = 3x + b.

y = 3x + b
y = 3x + b
2 = 3(5) + b
2 = 15 + b
−13 = b

Substitute (5, 2).
Solve for b.

Therefore, the equation of the line is y = 3x − 13.
8.

a
, then the slope of
b
5
b
2
the perpendicular line would be − . Thus, the line perpendicular to the line with slope
would have a slope of − .
2
a
5
The slopes of perpendicular lines are negative reciprocals of each other. That is, if a line has a slope of

To write the equation of the line that is perpendicular to the line y =

1
x − 7 and contains the point (4, −3), begin by
2

noting that the equation of the line to be determined has a slope of −2. Thus, the equation must be of the form
y = −2x + b.
y = −2 x + b

Substitute ( 4 , −3).

−3 = −2 ( 4 ) + b Solve for b.
−3 = −8 + b
b=5

461

Therefore, the equation of the line is y = −2x + 5.
Chapter 11
Geometry

Peterson’s SAT® Prep Guide 2017

EXERCISES: GEOMETRY
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

If the angles of a triangle are in the ratio 2:3:7, what is the
measure of the smallest angle?
A.

15°

B.

30°

C.

45°

D.

105°

What is the volume of a square pyramid with height 34.2
feet and base edges of 25 feet?
A.

285 ft.3

B.

2,565 ft.3

C.

7,125 ft.3

D.

81,225 ft.3

If the radius of a circle is decreased by 10%, by what
percent is its area decreased?

462

A.

10

B.

19

Chapter 11

C.

21

Geometry

D.

81

4.

5.

A spotlight is mounted on the ceiling 5 feet from one wall
of a room and 10 feet from the adjacent wall. How many
feet is it from the intersection of the two walls?
A.

15

B.

5 2

C.

5 5

D.

10 2

A sphere has a diameter of 3 cm, and a cone has a height
of 10 cm and a radius of 1.5 cm. How much bigger is the
volume of the cone than the volume of the sphere?
A.

0.5π

B.

π

C.

3π

D.

4.5π

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SHOW YOUR WORK HERE

6.

7.

In parallelogram PQRS, angle P is 4 times angle Q. What
is the measure in degrees of angle P?
A.

36

B.

72

C.

125

D.

144

SHOW YOUR WORK HERE

If PQ ≅ QS , QR ≅ RS and the measure of angle
PRS = 100°, what is the measure, in degrees, of
angle QPS?
S

P

Q

R

Note: Figure not drawn to scale

8.

9.

A.

10

B.

15

C.

20

D.

25

A circle has a radius of 6 cm. What is the area of a sector
bounded by a 60° minor arc?
A.

p

B.

2p

C.

6p

D.

20p

463
Chapter 11
Geometry

A rectangular box with a square base contains 6 cubic
feet. If the height of the box is 18 inches, how many feet
are there in each side of the base?
A.

1

B.

2

C.

3

D.

3
3

Peterson’s SAT® Prep Guide 2017

10.

11.

12.

464

The surface area of a cube is 150 square feet. How many
cubic feet are there in the volume of the cube?
A.

30

B.

50

C.

100

D.

125

Peter lives 12 miles west of his school, and Bill lives north
of the school. Peter finds that the direct distance from his
house to Bill’s is 6 miles shorter than the distance by way
of his school. How many miles north of the school does
Bill live?
A.

6

B.

9

C.

10

D.

6 2

A square is inscribed in a circle of area 18 p. Find a side of
the square.
A.

3

B.

6

C.

3 2

D.

6 2

Chapter 11
Geometry

13.

14.

A carpet is y yards long and f feet wide. How many dollars
will it cost if the carpet sells for x cents per square foot?
A.

3xyf

B.

xyf
3

C.

0.03 yf
x

D.

0.03xyf

If a triangle of base 6 has the same area as a circle of
radius 6, what is the altitude of the triangle?
A.

6p

B.

8p

C.

10p

D.

12p

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SHOW YOUR WORK HERE

15.

16.

17.

18.

The vertex angle of an isosceles triangle is p°. How many
degrees are there in one of the base angles?
A.

180 − p

B.

90 −

C.

180 − 2p

D.

180 −

SHOW YOUR WORK HERE

p
2
p
2

In a circle with center O, the measure of arc RS = 132°.
How many degrees are there in angle RSO?
A.

66°

B.

48°

C.

24°

D.

22°

The ice compartment of a refrigerator is 8 inches long,
4 inches wide, and 5 inches high. How many ice cubes will
it hold if each cube is 2 inches on an edge?
A.

8

B.

10

C.

12

D.

16

465

In the figure, PQ is a straight line and RS is perpendicular to ST. If the measure of angle RSQ = 48°, how many

Chapter 11
Geometry

degrees are there in angle PST?

R

P

S

48°

Q
T

A.

48°

B.

90°

C.

132°

D.

138°

Peterson’s SAT® Prep Guide 2017

19.

A cylindrical pail has a radius of 7 inches and a height of
9 inches. If there are 231 cubic inches to a gallon, approximately how many gallons will this pail hold?

B.

12
7
6

C.

7.5

D.

8.2

A.

20.

In triangle PQR, QS and SR are angle bisectors (meaning
∠ PQS is congruent to ∠ SQR, and ∠ PRS is congruent
to ∠ SRQ), and the measure of angle P = 80°. How many
degrees are there in angle QSR?

P
80°

S

R

Q

466
Chapter 11
Geometry

21.

A.

115°

B.

120°

C.

125°

D.

130°

If the m∠a is six less than twice the m∠b, what is the
value of a?

O
a°

A
A.

28

B.

32

C.

48

D.

58

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b°

B

SHOW YOUR WORK HERE

22.

23.

24.

25.

One end of a wire is attached to the top of a 70-foothigh pole, and the other end is attached to a stake in the
ground. If the wire makes a 30° angle with the ground,
how long is the wire?
A.

70 feet

B.

70 3 feet

C.

140 feet

D.

140 2 feet

SHOW YOUR WORK HERE

What is the equation of the line containing the points
(4, 6) and (3, 8)?
A.

y = –2x + 14

B.

y = 2x + 14

C.

y = –2x + 2

D.

y = 2x – 2

Which of the following represents the equation of a line
with a slope of −7 and a y-intercept of 12?
A.

y = 7x − 12

B.

y = −7x + 12

C.

y = 7x + 12

D.

y = 12x − 7

Which of the following represents the equation of a line
parallel to the line y = 7x – 6 and containing the point
(1, 7)?
A.

y = 7x

B.

y = 7x − 7

C.

y = −7x + 7

D.

y = −7x

467
Chapter 11
Geometry

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. B

6. D

11. B

16. C

21. D

2. C

7. C

12. B

17. D

22. C

3. B

8. C

13. D

18. D

23. A

4. C

9. B

14. D

19. B

24. B

5. C

10. D

15. B

20. D

25. A

The correct answer is B. Represent the angles as 2x,
3x, and 7x.

5.

2 x + 3 x + 7 x = 180°
12 x = 180°
x = 15°

V=

Chapter 11

V=

The correct answer is C.
1
V = s 2h
3
1
2
V = (25) (34.2)
3

468

V = 7,125 ft. 3

3.

Geometry

4.

The correct answer is B. If the radii of the two circles
have a ratio of 10:9, the areas have a ratio of 100:81.
Therefore, the decrease is 19 out of 100, or 19%.
The correct answer is C.
5 2 + 10 2 = x 2
25 + 100 = x 2
x 2 = 125
x = 125 = 25 5 = 5 5

www.petersons.com

4
p (1.5) 3 = 4.5p
3

The volume of the cone is calculated using the
1
formula V = pr 2h :
3

The angles are 30°, 45°, and 105°. The smallest angle
is 30°.
2.

The correct answer is C. The volume of the sphere is
4
calculated using the formula V = pr 3 :
3

1
p (1.5) 2 (10) = 7.5p
3

Since 7.5p − 4.5p = 3p, the volume of the cone is 3p
bigger than the volume of the sphere.
6.

The correct answer is D. The consecutive angles of a
parallelogram are supplementary, so
x + 4 x = 180°
5 x = 180°
x = 36°
Angle P is 4(36), or 144°.

7.

The correct answer is C.

11.

The correct answer is B.

S
Bill

40°

x

P

140° 40°

100°

Q

R

Since QR ≅ RS, ∠RQS ≅ ∠RSQ. There are 80° left in
the triangle, so each of these angles is 40°.

Peter

School

12

∠SQP is supplementary to ∠SQR, making it 140°.
The direct distance from Peter’s house to Bill’s can be
represented by means of the Pythagorean theorem

Since QP ≅ QS, ∠QPS ≅ ∠QSP. There are 40° left in
the triangle, so each of these angles is 20°.
8.

as

The correct answer is C. The area of a sector of a circle
measure of the arc
and the
is the product of the ratio
360°
area of the circle. Since the radius of the circle is 6 cm

144 + x 2 = (12 + x ) − 6
144 + x 2 = x + 6
Square both sides.

and the measure of the arc is 60°, the area of the sector
60°
2
is
i p (6) = 6 p.
360°
9.

144 + x 2 = x 2 + 12 x + 36
144 = 12 x + 36
108 = 12 x
9= x

The correct answer is B. Change 18 inches to 1.5 feet.
Letting each side of the base be x, the volume is 1.5x2.
1.5 x 2 = 6
15 x 2 = 60

144 + x 2 . Then:

12.

The correct answer is B.

Chapter 11

2

x =4
x =2

10.

469
Geometry

The correct answer is D. The surface area of a cube is
made up of 6 equal squares. If each edge of the cube is
x, then
6 x 2 = 150
x 2 = 25
x =5

Volume = (edge)3 = 53 = 125
The diagonal of the square will be a diameter of the
circle.

pr 2 = 18p
r 2 = 18
r = 18 = 9 2 = 3 2

The diameter is 6 2 and, since the triangles are
45°–45°–90°, a side of the square is 6.

Peterson’s SAT® Prep Guide 2017

13.

The correct answer is D. To find the area in square
feet, change y yards to 3y feet. The area is then (3y)(f),
or 3yf square feet. If each square foot costs x cents,
change this to dollars by dividing x by 100. Thus, each
square foot costs x dollars. The cost of 3yf square
100
feet will then be

17.

The correct answer is D. The compartment will hold 2
layers, each of which contains 2 rows of 4 cubes each.
This leaves a height of 1 inch on top empty. Therefore,
the compartment can hold 16 cubes.

3 xyf
3
. Since
= 0.03, the correct
100
100
5"

answer is choice D.
14.

The correct answer is D. The area of the circle is (6)2 p ,
or 36 p . In the triangle,
18.

1
(6)(h) = 36p
2
3h = 36 p
h = 12p

15.

16.

8"

48°

138°

Q

42°

T
Since ∠RST is a right angle, 42° are left for ∠QST.
Since ∠PSQ is a straight angle of 180°, ∠PST contains
138°.

°

132

S

19.
R
O

Geometry

S

P

The correct answer is C.

Chapter 11

The correct answer is D.

R

The correct answer is B. There are (180 − p) degrees
left, which must be divided between 2 congruent
p
180 − p
angles. Each angle will contain
, or 90 −
2
2
degrees.

470

4"

The correct answer is B. The volume of the pail is
found using the formula V = pr 2h. Since the answers
are not in terms of p, it is best to use 22 as a value for
7
p because the 7 will divide out r  2:
V=

P

22 7
i 49 i 9
7

Rather than multiply this out, which will take unnecessary time, divide by 231 and cancel wherever
possible.

By extending SO until it hits the circle at P, arc PRS is
a semicircle. Therefore, the measure of arc PR = 48°,
and the measure of the inscribed angle RSO = 24°.

2
3
22 i 7 i 9
=6
231

21
3

20.

www.petersons.com

The correct answer is D. If m ∠P = 80°, there are 100°
left between ∠PQR and ∠PRQ. If they are both
bisected, there will be 50° between ∠SQR and ∠SRQ,
leaving 130° for ∠QSR.

21.

The correct answer is D. Since the sum of the three
angles in a triangle is 180°, the measures of the missing
angles must add to 90°. The m ∠a = 2(m∠b) – 6, so

23.

line is m =

( y 2 − y 1) , where (x , y ) and (x , y ) are any two
1 1
2 2
( x 2 − x 1)

points on the line. In this problem, the two points are
( y 2 − y 1) = 8 − 6 = 2 = −2
.
(4, 6) and (3, 8), so m =
( x 2 − x 1) 3 − 4 −1

b + (2b − 6 ) = 90
3b − 6 = 90
3b = 96
b = 32 .

Use either point and the slope to complete the
equation.

Then, to find the m ∠a:
a = 2(32) − 6
a = 58
22.

The correct answer is A. The formula for the slope of a

y = mx + b

6 = ( −2)( 4 ) + b
6 = −8 + b
14 = b

The correct answer is C. Begin by making a diagram
of the situation described in the problem.

So the equation of the line is y = –2x + 14.

70ft.

w

30°

Note: Figure not drawn to scale.

There are two ways to solve this problem. The first is
to notice that the triangle is a 30°-60°-90° triangle,
and in such a triangle, the length of the side opposite the 30° angle is half of the length of the hypotenuse. Thus, the length of the wire, which represents
by the hypotenuse in the triangle, would be
2 × 70 feet = 140 feet.
The problem can also be solved by using trigonometry. Let w stand for the length of the wire, then write
70 . Since sine 30° = 1 , the equation is
sine 30° =
2
w
70 1
= . Cross-multiply: w = 140 feet.
w 2

24.

The correct answer is B. In the formula y = mx + b,
m represents the slope of the line, and b represents the
y-intercept. Thus, the equation y = − 7x + 12 represents
the equation of a line with a slope of −7 and y-intercept
of 12.

25.

The correct answer is A. Since parallel lines have the
same slope, the slope of the line to be determined is the
same as the slope of y = 7x − 6, which is 7. Therefore, the
equation of the unknown line can be written as y = 7x +
b, where b represents the y-intercept. In order to find the
value of b, substitute the point (1, 7) into y = 7x + b.

471
Chapter 11

y = 7x + b

Substitute (1, 7)

Geometry

7 = 7 (1) + b
7=7+b
b=0
Therefore, the equation of the line is y = 7x. Note that
a faster way to solve this problem is the trial-and-error
method. Of the four answer possibilities, choices A
and B represent lines with slopes of 7, but only choice
A contains the point (1, 7).

Peterson’s SAT® Prep Guide 2017

SUMMING IT UP
• Lines and line segments are the basic building blocks for most geometry problems.
• If a geometry problem provides a figure, mine it for clues. If a geometry problem doesn’t provide a figure, sketch one.
• If a geometry problem deals with a quadrilateral or circle, look to form triangles by drawing lines through the figure.
• Geometry diagrams on the SAT® are not always drawn to scale. If the diagram is not drawn to scale, you may want to redraw it.
•

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Peterson’s SAT® Online Course:

• Angles
• Geometry Strategy
• Hard Geometry
• Quadrilaterals
• Radian Measures
• Right Triangles
• Triangle Properties
• Trigonometry

472

• Word Problems
To purchase and access the course, go to www.petersons.com/sat.

Chapter 11
Geometry

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Chapter 12:
Functions and
Intermediate Algebra
OVERVIEW
Functions
Exercises: Functions
Integer and Rational Exponents
Exercises: Integer and Rational Exponents
Solving Complex Equations
Exercises: Solving Complex Equations
Linear, Quadratic, and Exponential Functions
Exercises: Linear, Quadratic, and Exponential
Functions

473

Summing It Up

Chapter 12
Functions
and
Intermediate
Algebra

FUNCTIONS
Definitions and Notation
Let D and R be any two sets of numbers. A function is a rule that assigns to each element of D one and only one element of R.
The set D is called the domain of the function, and the set R is called the range. A function can be specified by listing all of the
elements in the first set next to the corresponding elements in the second set or by giving a rule or a formula by which elements
from the first set can be associated with elements from the second set.
As an example, let the set D = {1, 2, 3, 4} and set R = {5, 6, 7, 8}. The diagram below indicates a particular function, f, by showing
how each element of D is associated with an element of R.

5
6
7
8

1
2
3
4
D

R

Peterson’s SAT® Prep Guide 2017

This diagram shows that the domain value of 1 is associated with the range value of 5. Similarly, 2 is associated with 6, 3 is associated with 7, and 4 is associated with 8. The function f can also be described in words by saying that f is the function that assigns
to each domain value x the range value x + 4.
Typically, the letter x is used to represent the elements of the domain and the letter y is used to represent the elements of the
range. This enables us to write the equation y = x + 4 to express the rule of association for the function above.
Note that as soon as a domain value x is selected, a range value y is determined by this rule. For this reason, x is referred to as the
independent variable, and y is called the dependent variable.
Often, the rule of association for a function is written in function notation. In this notation, the symbol f(x), which is read “f of x,”
is used instead of y to represent the range value. Therefore, the rule for our function can be written f(x) = x + 4. If you were asked
to determine which range value was associated with the domain value of, say, 3, you would compute f(x) = f(3) = 3 + 4 = 7. Note
that, in this notation, the letter f is typically used to stand for “function,” although any other letter could also be used. Therefore,
this rule could also be written as g(x) = x + 4.
Example:
Using function notation, write the rule for a function that associates, to each number in the domain, a range value
that is 7 less than 5 times the domain value.
Solution:
f(x) = 5x − 7

474
Chapter 12
Functions
and
Intermediate
Algebra

Example:
Use the function from the problem above to determine the range value that is associated with a domain value
of −12.
Solution:
f(−12) = 5(−12) − 7 = −60 − 7 = −67
Example:
If f(x) = 8x + 9, determine the value of f(5), f(q), f(p2), and f(r + 3).
Solution:
f(5) = 8(5) + 9 = 40 + 9 = 49
In the same way, to determine the value of f(q), simply substitute q for the value of x in the rule for f(x). Therefore,
f(q) = 8q + 9.
Similarly, f(p2) = 8(p2) + 9 = 8p2 + 9.
Similarly, f(r + 3) = 8(r + 3) + 9 = 8r + 24 + 9 = 8r + 33.

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Families of Functions
A family of functions is a group of functions with similar characteristics. The parent function is the most basic function in a family.
A linear function is a function whose graph is a straight line. f(x) = x is the parent function for all linear functions. A quadratic
function is a function whose graph is a parabola. The graph shown, f(x) = x2, is the parent function for all quadratic functions.

y
5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

Example:
Compare f(x) = 2x2 to f(x) = x2.
Solution:

475
y

Chapter 12

5

Functions
and
Intermediate
Algebra

4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

The graphs f(x) = 2x2 and f(x) = x2 both open up, have (0, 0) as their vertices, and have the same axis of symmetry
x = 0. The graph f(x) = 2x2 is narrower than the graph of f(x) = x2.

Peterson’s SAT® Prep Guide 2017

Example:
How does the graph f(x) = x2 + 2 compare to the parent function f(x) = x2?
Solution:

y
5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

The graph f(x) = x2 + 2 is two units higher than f(x) = x2. The function f(x) = x2 has been shifted up 2 units. The shifting,
or translating, of a function is called a transformation. To move a function up, add a value b to the function:
f(x) = x2 + b. To move a function down, subtract a value b from the function: f(x) = x2 – b.

476

The function f(x) = (x + 2)2 looks like the following:

y

Chapter 12
5

Functions
and
Intermediate
Algebra

4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

Its graph has been shifted to the left 2 units. To shift a function to the left, add a value b to inside the function:
f(x) = (x + b)2. To shift a function to the right, subtract a value b to inside the function:
f(x) = (x – b)2.

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The function –f(x) is f(x) flipped upside down (across the x-axis), while f (–x) is the mirror of f (x) (flipped across the
y-axis):
y

–f (x)

5

–5

–4

–3

–2

y

f (–x)

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

1

2

3

4

5

x

Example:
Describe how the function f(x) = –2x2 + 3 compares with the graph f(x) = x2.
Solution:
Both graphs have the same axis of symmetry but the graph f(x) = –2x2 + 3 opens downward and is narrower than the
graph of f(x) = x2. The vertex of f(x) = –2x2 + 3 is 3 units higher than the vertex of f(x) = x2.

Perform Operations on Functions and Compositions

477
Chapter 12
Functions
and
Intermediate
Algebra

You can add, subtract, multiply, and divide any two functions.
Let f(x) = 4x2 and g(x) = x2 + 9x + 6
f(x) + g(x) = 4x2 + (x2 + 9x + 6) = 5x2 + 9x + 6
f(x) – g(x) = 4x2 – (x2 + 9x + 6) = 3x2 – 9x – 6
f(x) · g(x) = 4x2 (x2 + 9x + 6) = 4x4 + 36x3 + 24x2
f ( x)
4x 2
= 2
g( x) x + 9x + 6
The composition of functions involves applying two functions in succession. The composition of a function g(x) with a function
f(x) is written as g(f(x)), read as “g of f of x”.

Peterson’s SAT® Prep Guide 2017

Let f(x) = 6x3 + 2 and g(x) = 2x2 – 8.
Example:
Find f  (g(3)) and g(f(3)).
Solution:
To evaluate f(g(3)), first find g(3).
g(3) = 2(3)2 – 8 = 10
Then f  (g(3)) = f  (10) = 6(10)3 + 2 = 6,002.
To evaluate g(f  (3)), first find f  (3).
f  (3) = 6(3)3 + 2 = 164
Then g(f(164)) = g(164) = 2(164)2 – 8 = 53,784.
Generally, f  (g(x)) ≠ g(f  (x)).

478
Chapter 12
Functions
and
Intermediate
Algebra

www.petersons.com

EXERCISES: FUNCTIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

4.

What is the effect on the graph of the function
f(x) = 2x2 + 5 when it is changed to f(x) = 2x2 – 3?
A.

The graph gets narrower.

B.

The graph opens down.

C.

The graph gets wider.

D.

The graph shifts down the y-axis.

SHOW YOUR WORK HERE

Which function opens down?
A.

y = –7x2 – 3

B.

y = 0.5x2 + 2

C.

y = 10x2 – 1

D.

y = 7x2 + 9

3
If h(x) = 3x2 + 5, and j ( x ) =
2 , what is the value of
x − 4)
(
h(5) − j(5)?
A.

0

B.

77

C.

83

D.

87

The profit from selling x number of sweatshirts can be
described by the function p(x) = 22x – 230. What is the
profit if 200 sweatshirts are sold?
A.

$4,170

B.

$4,280

C.

$4,400

D.

$4,630

479
Chapter 12
Functions
and
Intermediate
Algebra

Peterson’s SAT® Prep Guide 2017

5.

6.

7.

480
Chapter 12
Functions
and
Intermediate
Algebra

8.

The number of blue blankets in stock can be modeled by
the equation f(x) = 2x2 – 8x + 20 and the number of red
blankets in stock can be modeled by the equation h(x) =
3x2 + 4x + 30. Which function models the total number
of blankets in stock?
A.

–x2 – 4x + 50

B.

5x2 – 12x + 50

C.

5x2 – 4x + 50

D.

–x2 + 4x + 20

A company sells designer keychains. Its monthly revenue
is modeled by R(x) = 27x, and its costs are modeled by
C(x) = 7x + 1,200, where x is the number of keychains
sold. Find R(x) – C(x).
A.

–34x + 1,200

B.

20x + 1,200

C.

20x – 1,200

D.

34x – 1,200

You have a $25 gift certificate to a clothing store. The store
is having a 30%-off sale. You decide to purchase an outfit
that costs $100 before the sale. What is the final cost of
the outfit if the gift certificate is applied before the 30%
discount?
A.

$22.50

B.

$30

C.

$45

D.

$52.50

You earn $17.50 per hour at your job. You are given a raise
of 2% after 5 months. In addition, you receive $1 per hour
for being a model employee. Find your new hourly wage
if the $1 raise is applied before the 2% raise.
A.

$18.13

B.

$18.15

C.

$18.85

D.

$18.87

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS
1. D

3. B

5. C

7. D

2. A

4. A

6. C

8. D

1.

The correct answer is D. The vertex of the graph
changes from (0, 5) to (0, –3). The original graph is
translated down.

2.

The correct answer is A. The graph opens down since
the coefficient in front of the x2-term is less than 0.

3.

The correct answer is B.

( )

h (5) − j (5) = 3 5 2 + 5 −

7.

The correct answer is D. Let x be the regular price. The
function for the gift certificate is f(x) = x – 25. The
function for the 30% discount is g(x) = x – 0.30x = 0.7x.
The composition g(f(x)) represents the sale price when
the $25 gift certificate is applied before the 30%
discount.
g (f ( x )) = g ( x − 25)

= 0.7 ( x − 25)

= 0.7 (100 − 25)

3

(5 − 4 )

2

= 0.7 (75)

= 3 (25) + 5 − 3 = 77

4.

The correct answer is A.
p(200) = 22(200) – 230 = 4,170. The profit is $4,170.

5.

The correct answer is C.
f ( x ) + h ( x ) = 2 x 2 − 8 x + 20 + 3 x 2 + 4 x + 30
= 5 x 2 − 4 x + 50

6.

= $52.50

The correct answer is C.
R ( x ) − C ( x ) = 27 x − (7 x + 1, 200)
= 27 x − 7 x − 1, 200
= 20 x − 1, 200

So, you pay $52.50.
8.

The correct answer is D. Let x be your hourly wage.
The function for the 2% raise is f(x) = x + . 02x = 1.02x.
The function for the $1 raise is g(x) = x + 1. The
composition f(g(x)) represents the hourly wage when
the $1 raise is applied before the 2% raise.
f ( g ( x )) = f ( x + 1)

481

= 1.02 ( x + 1)

Chapter 12

= 1.02 (18.50)

Functions
and
Intermediate
Algebra

= 1.02 (17.5 + 1)
= 18.87
So, your new hourly wage is $18.87.

Peterson’s SAT® Prep Guide 2017

INTEGER AND RATIONAL EXPONENTS
Chapter 10: “Basic Algebra” contains the definitions and the rules for positive integer exponents. The following section extends
these definitions to integer and rational exponents.

Integer Exponents
Negative exponents are defined in the following way:
For any positive integer n, x − n =
 2
Similarly,  
3

−4

1
x

n

. For example, 4 −2 =

1
4

2

=

1
.
16

4

3 4 81
 3
=  = 4 = .
 2
16
2

All of the properties of exponents discussed in Chapter 11 apply to expressions with negative exponents as well. Thus, the
1
y −5
−5 −( −11)
−3
= y −5+11.= y 6
expression x −7 • x 4 is equal to x = 3 , and −11 = y
x
y
Examples:
Determine the value of the following expressions:
a. 8−2 • 84
b. x5 • x−5

482
Chapter 12
Functions
and
Intermediate
Algebra

c.

y4
y −9

−2 9
d. x y

x 7y 3

Solutions:
a. 8−2 • 84 = 82 = 64
b. x5 • x−5 = x0 = x
c.

y4
y −9

= y 4 y 9 = y 13

−2 9
9 −3
y6
d. x y = y
=
9
x 7y 3
x 7 −( −2) x

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Examples:
a. If f(x) = 5−x, what is the value of f(−2)?
b. If f(x) = 5−x, what is the value of f(2)?
Solutions:
a. f(−2) = 5−(−2) = 52 = 25
b. f(2) = 5–2 =

1
1
=
2
5 25

Rational Exponents
The definition of exponents can also be extended to include rational numbers:
For a rational number, x to the power of

1
1
is defined as the nth root of x. In other words, x n is equal to n x .
n

1

Therefore, 5 can be written as 5 2.
1

Similarly, 8 3 represents

3

8 and is thus equal to 2.
1

m

Next, x n is defined to mean ( x n ) m , for x > 0 and n > 0. Therefore, when you are given a number with a rational exponent, the
numerator represents the power to which the number is to be raised, and the denominator represents the root to be taken. The
5

expression 16 4 tells you to take the fourth root of 16 and then raise the result to the fifth power. This expression can be evaluated

5
in the following way: 16 4

=

(4 16 )

5

= (2) = 32

483

5

In summary, all of the properties of exponents apply to expressions with rational exponents.
Examples:

Chapter 12
Functions
and
Intermediate
Algebra

Determine the value of the following expressions:
1

a. 27 3
b. 64

−

2
3

5

c. 2 x 6 i 3 x

−

1
3

Solutions:
1

a. 27 3 = 3 27 = 3
b. 64

−

2
3

2

2

2
1
 13  1 
 1
=  =3
=
  =

 64 
4
16
 64 

5

c. 2 x 6 i 3 x

−

1
3

5

= 6x 6

−

1
3

1

= 6x 2

Peterson’s SAT® Prep Guide 2017

Examples:
Simplify the following expressions:
a.

1
6 2

(25a )
1

b3

b.

b

−

2
3

 − 1 3
c.  c 8 d 4 


d.

4x 3 i

16

8x 5

Solutions:

a.

(

25a 6

)

1
2

1

b.

b3
b

484
Chapter 12

−

2
3

1

1 2

4x 3 i

Functions
and
Intermediate
Algebra

1

= b 3b 3 = b 3

 − 1 3
c.  c 8 d 4 



d.

( )

= 25 2 a 6

16

1
2

+

 −
= c

1

= 25a 3 = 5a 3

2
3

= b1 = b

1  16  3  16
8 d 4 





3

1

5

3

5

8x 5 = 4 2 x 2 i 8 2 x 2
1

1

= 4 2 i 82 x 2x 2

( )

3

=2 2 2 x 2
= 4 2x 4

www.petersons.com



+

5
2

= c − 2d 12 =

d 12
c2

EXERCISES: INTEGER AND RATIONAL EXPONENTS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

4.

Simplify the expression: 8 x i

4 x3

SHOW YOUR WORK HERE

3

A.

32 x 2

B.

16 2 x 4

C.

4x4

D.

4 2x2

Simplify the expression: 25 x 4 y 6 i 3 x 3 y 5
7

11

A.

3x 2 y 2

B.

5 3x 2 y 2

C.

15x12y11

D.

75x7 y11

7

11

Which of the following is equal to (xy−3)2?
A.

x
y

B.

x
y6

C.

x2
y6

D.

x2
y

Simplify the expression:
A.

a7
b6c

B.

a7 c
b2

C.

a3
b2c

D.

a3c 5
b2

485
Chapter 12
Functions
and
Intermediate
Algebra

a5b −2c −3
a −2b 4 c −2

Peterson’s SAT® Prep Guide 2017

5.

A.
B.

C.
D.

6.

b3
a 6c
b3
a 6c 7
a 8c 12
b 28
b 28
a 8c 12

(

Simplify the expression: 49 x 4 y 8 z −6
A.

49x2 y4z6

B.

7x3y4z3

C.
D.

7.

1
2

7x 2z 3
7x 2y 4
z3

Simplify the expression:
8x x

486

B.

16 x 6

C.

8x 4 x 4

Chapter 12

D.

32 x 2 x

8.

)

y4

A.

Functions
and
Intermediate
Algebra

SHOW YOUR WORK HERE

Simplify the expression: (a−2b7c−3)−4

4

256 x 2 i 16 x 4

3

−125 x 6 i

4

4

Simplify the expression:
A.

−40x6y9

B.

−20x2y

C.

−9 x 6 y

D.

20 x 3 y 3 x

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3

64 y 3

ANSWER KEY AND EXPLANATIONS

1.

1. D

3. C

5. C

7. A

2. B

4. A

6. D

8. B

5.

The correct answer is D.
8x i

4 x 3 = (8 x )

1
2

1
4x 3 2

( )

1 
3

=  2 2x 2  2x 2 

 


= 4 2x
2.

(a
6.

1
25 x 4 y 6 2

)(

1
3x 3y 5 2

)

(

= 5x 2 y 3 i

)

1
2

b 28

1

4

8

= 49 2 x 2 y 2 z

7 11
2y 2

=

7.

−6
2

The correct answer is C.

7x 2y 4
z3

The correct answer is A.
4

1

4

1

1

256 x 2 i 16 x 4 = 256 4 x 2 i 16 4 x 1
1

= x 2 y −6 =

x

= 4 x 2 i 2x

2

= 8x x

y6
8.

4.

a 8c 12

= a 8b −28c 12 =

49 x 4 y 8 z −6

1 3 5
32 x 2y 2

1
3
5
2+
3+
32 x 2y 2

= 5 3x

−3 2

b c

= 7 x 2 y 4 z −3

=5i

( xy )

)

−2 7 −3 −4

The correct answer is D.

2

The correct answer is B.

(

3.

The correct answer is C.

The correct answer is B.

The correct answer is A.
5 −2 −3

a b

c

a −2b 4 c −2

3

=a

5 −( −2) −2 − 4 −3 −( −2)

b

= a 7b −6c −1 =

c

a7
b 6c

−125 x 6 i

3

6
3
64 y 3 = −5 x 3  4 y 3 



= −20 x 2 y

487
Chapter 12
Functions
and
Intermediate
Algebra

Peterson’s SAT® Prep Guide 2017

SOLVING COMPLEX EQUATIONS
Chapter 10: “Basic Algebra” describes how to solve linear and quadratic equations. The following section discusses how to solve
some of the more complex equations and inequalities that appear on the SAT®exam.

Equations Involving Rational Expressions
A rational expression is a fraction that contains variables in the numerator and/or the denominator. The quickest way to solve
equations containing rational expressions is to determine the least common denominator (LCD) of all of the fractions in the
equation and then eliminate the fractions by multiplying each term in the equation by this LCD. The four steps in solving such
an equation are:
1.

Find the LCD of all of the rational expressions in the equation.

2.

Multiply every term on both sides of the equation by this LCD.

3.

Solve the resulting equation using the methods previously explained.

4.

Check the solution to make certain that it actually solves the equation.

Note that step 4, checking the solution, is crucial because sometimes the process produces a solution that does not actually solve
the equation. Such extraneous solutions need to be eliminated.

Example:
Solve for x:

488

7x 3
+ = 10
5 8

Solution:
The LCD of the two fractions in the equation is 40, so every term must be multiplied by 40.

Chapter 12
 3
 7x 
40   + 40   = 40 (10)
 5
 8

Functions
and
Intermediate
Algebra

Perform the multiplications.

8 (7 x ) + 5 (3) = 400

Subtract 15 from both sides.
56 x + 15 = 400
Divide both sides by 56.
56 x = 385
385 55
7
x=
=
=6
56
8
8

Check that the answer is correct by substituting 55 into the original equation.
8

www.petersons.com

Example:
Solve for x:

5
3
36
−
=
x − 4 x + 4 x 2 − 16

Solution:
Begin by finding the LCD of the three fractions. Note that since x2 − 16 = (x − 4) (x + 4), the LCD is (x − 4)(x + 4). Each
term must be multiplied by this.

( x − 4) ( x + 4) 

5 
 3   36 
 − ( x − 4 ) ( x + 4 ) 
 =
 ( x − 4) ( x + 4)
x−4
x + 4   x 2 − 16 

( x + 4)(5) − ( x − 4)(3) = 36

Distribute.

5 x + 20 − 3 x + 12 = 36 Combin
ne like terms.
2 x + 32 = 36 Subtract 32 from both sides.
2 x = 4 Divide by 2.
x =2
To check the solution, substitute 2 into the equation:
5
3
36
−
=
x − 4 x + 4 x 2 − 16
5
3
36
−
=
2 − 4 2 + 4 22 − 16
5 3
36
− − =−
2 6
12
−3 = −3
Therefore, the solution is x = 2.

Chapter 12

Example:
Solve for x:

489
Functions
and
Intermediate
Algebra

1 1 1
− =
5 6 x

Solution:
The LCD is 30x. Multiply all terms by the LCD.

(30 x ) 

1
 1 1
 − (30 x )   = (30 x )
6
5
x
6 x − 5 x = 30
x = 30

If you check the value x = 30 in the original equation, you will find that it works.

Peterson’s SAT® Prep Guide 2017

Radical Equations
Equations that have variables in their radicands are called radical equations. For example, x = 16 is a radical equation. To solve
this radical equation, square both sides:
x = 16

( x)

2

= 16 2

x = 256

Check x = 256 in the original equation.
x = 16
256 = 16 ?
16 = 16
The solution works.
Extraneous solutions may occur when you raise both sides of a radical equation to an even power. For example, if you square
both sides of the equation x = 5 you get x2 = 25. This new equation has two solutions, –5 and 5, but only 5 is the solution to the
original equation.
The steps to solve a radical equation are:

490
Chapter 12
Functions
and
Intermediate
Algebra

1.

Isolate the radical on one side of the equation.

2.

Raise both sides of the equation to the same power to eliminate the radical.

3.

Solve the resulting equation.

4.

Check the solution.

Examples:
Solve each equation.
2x + 3 = 7

a.
b.

3

4x − 5 = 3

c.

4

2x + 8 − 2 = 2

d. x + 2 = 11x + 12

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Solutions:
a.

2x + 3 = 7

(

)

2

2x + 3 = 7

2x + 3 = 7
2 (23) + 3 = 7?

2

49 = 7?
7=7

2 x + 3 = 49
2 x = 46
x = 23 Check the solution.

b.

3

(

4x − 5 = 3

)

3

3

4x − 5 = 3

3

3

3

4x − 5 = 3

4 (8) − 5 = 3?

4 x − 5 = 27
4 x = 32
x = 8 Check the solution.
c.

4

(

3

4

4

2x + 8 = 4

2x + 8

)

4

= (4)

4
4

d.

The solution is 8.

2x + 8 − 2 = 2

2 (124 ) + 8 − 2 = 2?
4

2 x + 8 = 256
2 x = 248
x = 124 Check the
e solution.

27 = 3?
3=3

2x + 8 − 2 = 2
4

The solution is 23.

256 − 2 = 2?
4 − 2 = 2?
2=2

The sollution is 124.

x + 2 = 11x + 12

( x + 2 )2 = (

11x + 12

491

)

2

x + 4 x + 4 = 11x + 12
2

Chapter 12

x2 − 7x − 8 = 0

( x − 8) ( x + 1) = 0

Functions
and
Intermediate
Algebra

x = 8 , x = −1

Check the solution x = 8.
x + 2 = 11x + 12
8 + 2 = 11(8) + 12 ?
10 = 100 ?
10 = 10
Check the solution x = –1.

The
e solution is 8.

x + 2 = 11x + 12
−1+ 2 = 11( −1) + 12 ?
1 = 1?
1= 1

The so
olution is −1.

The solutions are x = 8 and x = –1.

Peterson’s SAT® Prep Guide 2017

EXERCISES: SOLVING COMPLEX EQUATIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

3.

492
Chapter 12
Functions
and
Intermediate
Algebra

4.

5.

Solve for x:
A.

x = −4

B.

x = −2

C.

x=2

D.

x=4

Solve for y:

2
5
2
−
=
x − 2 x + 2 x2 − 4

4
3
12
−
=
y − 2 y + 2 y2 − 4

A.

y = −4

B.

y = −2

C.

y=2

D.

There are no solutions.

Solve for a:

3
5
7
+
=
a − 7 a2 − 13a + 42 a − 6

A.

a = −18

B.

a = −9

C.

a=9

D.

a = 18

Solve for b:
A.

b>4

B.

b>8

C.

b > 12

D.

b > 18

b b
b
+ +
>2
8 12 24

Solve the equation: 3 8 x = 4
A.

x=8

B.

x=6

C.

x=4

D.

x=2

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SHOW YOUR WORK HERE

6.

7.

8.

9.

10.

Solve the equation:
A.

x=1

B.

x=9

C.

x = 17

D.

x = 209

4

3x − 2 + 1= 6

SHOW YOUR WORK HERE

Solve the equation: −5 3 9 x + 10 = −5
A.

x=3

B.

x=1

C.

x = −1

D.

x = −3

Solve the equation: x = 16 x + 225
A.

x = 45

B.

x = 25

C.

x = −9

D.

x = −25

Solve for t:
A.

t ≤ 84

B.

t ≤ 42

C.

t ≥ 42

D.

t ≥ 84

t 2t 3t − 14
+ ≥
4 9
6

Solve the equation:
A.

x=

11
7

B.

x=

7
3

C.

x=2

D.

x=3

493
Chapter 12

16 x − 32 = 2 x + 10

Functions
and
Intermediate
Algebra

Peterson’s SAT® Prep Guide 2017

ANSWER KEY AND EXPLANATIONS

1.

1. D

3. C

5. A

7. A

9. A

2. D

4. B

6. D

8. B

10. D

The correct answer is D. The LCD of the fractions in the equation

2
5
2
−
=
is (x − 2)(x + 2).
x − 2 x + 2 x2 − 4

Multiply all terms by the LCD.

( x − 2) ( x + 2)

2
5
2
− ( x − 2) ( x + 2)
=
( x − 2) ( x + 2)
x −2
x + 2 x2 − 4
2 ( x + 2) − 5 ( x − 2) = 2
2 x + 4 − 5 x + 10 = 2
−3 x + 14 = 2
−3 x = −12
x=4

Remember that you should check the answer to make certain that it solves the equation.
2.

The correct answer is D. The LCD of the fractions in the equation is

( y − 2) ( y + 2)

494

4
3
12
is y 2 − 4.
−
=
y −2 y +2 y 2 −4

4
3
12
− ( y − 2) ( y + 2)
= ( y − 2) ( y + 2) 2
y −2
y +2
y −4
4 ( y + 2) − 3 ( y − 2) = 12

4 y + 8 − 3 y + 6 = 12
y + 14 = 12
y = −2

Chapter 12
Functions
and
Intermediate
Algebra

Note that when you substitute y = −2 into the equation, two of the denominators become 0 and are, therefore,
undefined. This means that y = −2 is an extraneous solution, and the equation actually has no solutions.
3.

The correct answer is C. Note that a2 − 13a + 42 = (a − 7)(a − 6), so the LCD of the fractions in the equation is
(a − 7)(a − 6).
Now, multiply by the LCD.

( a − 7) ( a − 6 )

3
5
7
+ ( a − 7) ( a − 6 )
=
( a − 7) ( a − 6 )
a−7
( a − 7) ( a − 6 ) a − 6
3a − 18 + 5 = 7 (a − 7)
3a − 13 = 7a − 49
4 a = 36
a=9

This solution checks.

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4.

The correct answer is B. In the inequality

8.

The correct answer is B.

b b
b
+ +
> 2 , multiply by the LCD of 24.
8 12 24

x = 16 x + 225
x 2 = 16 x + 225
x − 16 x − 225 = 0
2

(24)

( x − 25) ( x + 9) = 0

b
b
b
+ (24 ) + (24 ) > 2 (24 )
8
12
24
3b + 2b + b > 48
6b > 48

x = 25, − 9
Note when you substitute x = –9 into the equation,
you get –9 = 9. This means that –9 is an extraneous
solution. The only solution is 25.

b>8
5.

The correct answer is A.
9.
3

(

3

8x = 4

8x

)

3

= 43

(36)

8 x = 64
x =8
6.

3x − 2 + 1= 6
4

7.

3x − 2 = 5
3 x − 2 = 625
3 x = 627
x = 209

The correct answer is A.
−5 3 9 x + 10 = −5
−5 3 9 x = −15
3

9x = 3
9 x = 27
x =3

t
2t
3t − 14
+ (36)
≥ (36)
9
6
4
9t + 8t ≥ 6 (3t − 14 )
17t ≥ 18t − 84
−t ≥ −84
t ≤ 84

The correct answer is D.
4

t 2t 3t − 14
The correct answer is A. To solve + ≥
,
4 9
6
multiply by the LCD of 36.

10.

The correct answer is D.
16 x − 32 = 2 x + 10
16 x − 32 = 2 x + 10
14 x = 42
x =3

495
Chapter 12
Functions
and
Intermediate
Algebra

Peterson’s SAT® Prep Guide 2017

LINEAR, QUADRATIC, AND EXPONENTIAL FUNCTIONS
A linear function is a function of the form f(x) = mx + b, where m and b are real numbers. A quadratic function is a function of the
form g(x) = ax2 + bx + c, where a ≠ 0 and a, b, and c are real numbers. An exponential function is a function of the form f (x) = abx
where base b is a positive integer greater than 1. These functions are important, because they can be used to model many realworld occurrences.

Applications of Linear Functions
In order to manufacture a new car model, a carmaker must initially spend $750,000 to purchase the equipment needed to start
the production process. After this, it costs $7,500 to manufacture each car. In this case, the cost function that associates the cost
of manufacturing cars to the number of cars manufactured is C(x) = 7,500x + 750,000, where x represents the number of cars
manufactured, and C(x) represents the cost of x cars. For example, the cost of making 7 cars is C(7) = 7,500(7) + 750,000 = 52,500
+ 750,000 = $802,500.
The above cost function is a linear function with b = 750,000 and m = 7,500. What is the domain of this function? Note that even
though nothing has been specifically said about the domain, the only values that make sense as domain values are the nonnegative integers, 0, 1, 2, 3, 4, 5, … . In such a situation, assume that the domain only contains the values that make sense.

Example:
Using the cost function for the carmaker discussed in the example above, how much would it cost to make 24 cars?
Solution:

496

To solve this, you need to determine the value of C(24).
C(24) = 7,500(24) + 750,000 = 180,000 + 750,000 = $930,000

Chapter 12
Functions
and
Intermediate
Algebra

Example:
Using the same cost function, determine how many cars could be made for $990,000.
Solution:
In this problem, you are told that the value of C(x) is $990,000, and you need to find the value of x. To do this, solve
the equation:
990 , 000 = 75, 000 ( x ) + 750 , 000 Subtract 750,000 from both sidess.
240 , 000 = 7, 500 x
32 = x
Therefore, for $990,000, 32 cars can be manufactured.

www.petersons.com

Divide by 7,500.

Example:
In the town of Kenmore, a taxi ride costs $2.50 plus an extra $0.50 per mile. Write a function that represents the cost
of taking a taxi ride, using x to represent the number of miles traveled.
Solution:
C(x) = $2.50 + 0.50x
If a ride costs $0.50 a mile, then the cost for x miles will be $0.50x. Add to this the initial fee of $2.50 a ride.
Example:
You purchased shorts for $8 per pair, plus a shirt for $6. Write a function that represents the cost of your purchases,
where x represents the number of pairs of shorts you purchase. How much did you spend if you purchased 5 pairs of
shorts?
Solution:
f(x) = 8x +6
Let x = 5, so f(5) = 8(5) + 6 = 46.
Example:
A bus pass has a starting value of $60. Each ride costs $2.50. Write a function that represents the remaining balance
on the bus pass, where x represents the number of rides taken. How much money is left on the pass after 12 rides?

497
Chapter 12
Functions
and
Intermediate
Algebra

Solution:
f(x) = 60 – 2.5x
Let x = 12, so f(12) = 60 – 2.5(12) = 30.
There is $30 remaining on the pass after 12 rides.

The Graph of a Linear Function
Typically, when a function is graphed, the independent variable is graphed along the x-axis, and the dependent variable is
graphed along the y-axis.

Peterson’s SAT® Prep Guide 2017

The taxi ride function from the previous problem is a linear function. In order to graph this function, you must first determine
the domain. Note that the domain, once again, must consist of non-negative numbers. Next, determine a few values that satisfy
the rule for the function. For example, when x = 0, C(0) = $2.50 + 0.50(0) = $2.50. A few additional simple computations will lead
to the following table of values.

x

C(x)

0

$2.50

1

$3.00

2

$3.50

3

$4.00

If these points are plotted on a graph, you will see that they all lie on the same line. The entire graph of the taxi ride cost function
is shown here.

y

Price

6
5
4
3
2
1
1

498
Chapter 12
Functions
and
Intermediate
Algebra

2

3

4

5

6

x

Miles

In general, the graph of any linear function is either a straight line or (depending on the domain) a portion of a straight line. The
value of m represents the slope of the line, and the value of b is the y-intercept.

Applications of Quadratic Functions
Quadratic functions can also be used to model certain real-world happenings. To understand these functions better, suppose a
coffee manufacturer has a revenue function given by R(x) = 40,000x − 2,000x2, where x represents the amount of coffee produced
in tons per week. Let’s consider some of the values for this function.
If x = 0, R(x) = 40,000(0) − 2,000(0)2 = 0 represents the obvious fact that if no coffee is produced there is no revenue.
That R(1) = 40,000 − 2,000 = 38,000 tells that the revenue from 1 ton of coffee is $38,000.
Similar computations show that R(10) = $200,000 and R(11) = $198,000.
Note that the revenue is smaller if 11 tons of coffee are produced than if 10 tons are produced. There are a number of possible
reasons for this. Perhaps, for example, at the 11-ton level, more is produced than can be sold, and the coffee company must pay
to store the overage.

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The function h(t) = –16t2 + h0 models the height of an object dropped from an initial height h0 (in feet) after t seconds.
Example:
An object is dropped from the roof of a building that is 80 ft. tall. How long will it take the object to hit the ground?
Round your answer to the nearest hundredth of a second.
Solution:
h(t) = –16t2 + h0
Here h0 = 80, so h(t) = –16t2 + 80.
Substitute 0 in for h(t) and solve the equation for t.
0 = −16t 2 + 80
16t 2 = 80
t2 =5
t ≈ ±2.24
Example:
Suppose you drop a ball from a window that is 36 ft. above the ground and it lands on a porch that is 4 ft. above the
ground. How long does it take for the ball to land on the porch? Round your answer to the nearest hundredth of a
second.
Solution:

499
Chapter 12

h(t) = –16t2 + h0

Functions
and
Intermediate
Algebra

2

Here h0 = 36, so h(t) = –16t + 36.
Substitute 4 for h(t), because the ball will hit the porch at 4 feet above 0, or ground level. Solve the equation for t.
4 = −16t 2 + 36
16t 2 = 32
t2 =2
t ≈ ±1.41

It will take approximately 1.41 seconds for the object to land on the porch.

Peterson’s SAT® Prep Guide 2017

The Graph of a Quadratic Function
As you just saw, the graph of a linear function is always a straight line. To determine what the graph of a quadratic function looks
like, consider the graph of the quadratic function R(x) = 40,000x − 2,000x2. Negative numbers must be excluded from the domain.
A few computations lead to the table here.

x

R(x)

0

0

3

102,000

5

150,000

9

198,000

10

200,000

11

198,000

15

150,000

17

102,000

20

0

The graph of R(x) is shown here.

200,000

Revenue

500
Chapter 12
Functions
and
Intermediate
Algebra

150,000
100,000
50,000

2

4 6

8 10 12 14 16 18 20
Tons

The graph shown above is called a parabola. This parabola is said to “open down.” The highest point on the parabola, (10, 200,000),
is called the extreme point.
Recall that the general form of a quadratic function is g(x) = ax2 + bx + c. In general, the graph of any quadratic function will be a
parabola. If a > 0, the parabola will “open up,” and if a < 0, the parabola will “open down.” If the parabola opens up, its extreme point
is the minimum value of the function, and if the parabola opens down, its extreme point is the maximum value of the function.
 −b
The coordinates of the extreme point of a parabola are  ,
 2a

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 −b  
f   .
 2a  

Example:
Sketch the graph of the function f(x) = x2 − x − 2.
Solution:
Since the function is quadratic, the graph will be a parabola. Note that the value of a, the number in front of the
−b − (1) 1
= , and the
=
x2-term is 1, so the parabola opens up. The x-coordinate of the minimum point is x =
2a 2 (1) 2
y-coordinate of this point is
2

1
 1  1
f   =  − −2
 2  2
2
1 1
= − −2
4 2
1
= −2
4
In order to sketch a parabola, it is helpful to determine a few points on either side of the extreme point.

x

f(x)

–2

4

–1

0

0

–2

1

–2

2

0

3

4

501
Chapter 12

The graph is shown here.

Functions
and
Intermediate
Algebra

y
4
3
2
1
x
–4 –3 –2 –1
–1

1

2

3

4

–2
–3
–4

Peterson’s SAT® Prep Guide 2017

Example:
What is the relationship between the graph of the function h(x) = ax2 + bx and the graph of the function
j(x) = ax2 + bx + 7?
Solution:
If (x, y) is a point on the graph of h(x), then (x, y + 7) will be a point on the graph of j(x). Therefore, the two graphs have
exactly the same size and shape. The graph of j(x) can be obtained by taking the graph of h(x) and “lifting” each point 7
units, that is, increasing the y-coordinate of each point by 7.

Applications of Exponential Functions
If a > 0 and b > 1, then the function f (x) = abx is an exponential growth function and b is called the growth factor. If a > 0 and
0 < b < 1, then the function f (x) = abx is an exponential decay function and b is called the decay factor.
An exponential growth function can model the number of students in a high school. Suppose the number of students in 2011
is given by f(x) = 1,250(1.13)x, where x is the number of years since 2011. Let’s consider some of the values for this function. If
x = 0, then f(x) = 1,250(1.13)0 = 1,250 represents the student population in 2011. If x = 1, then f(x) = 1,250(1.13)1 =1,413 represents
the student population after 1 year. Similar computations show that f(x) = 1,596 when x = 2 and f(x) = 2,303 when x = 5.

502

An exponential decay function can model the value of an automobile. Suppose the value of the automobile is given by
f(x) = 35,000(0.85)x, where x is the number of years since the automobile was purchased. Let’s consider some of the values for this
function. If x = 0, then f(x) = 35,000(0.85)0 = 35,000 represents the value of the automobile at the time of purchase. If x = 2, then
f(x) = 35,000(0.85)2 = 25,287.50 represents the value of the automobile after 2 years. Similar computations show that
f(x) = 15,529.69 when x = 5 and f(x) = 3,057.40 when x = 15.

Chapter 12
Functions
and
Intermediate
Algebra

The Graph of an Exponential Function
To determine what the graph of an exponential function looks like, consider the graph of the exponential function
f(x) = 52,50(0.9)x, where f(x) is the value of a jet ski in dollars after x years.
The initial value of the jet ski is $5,250 and the percent of decrease per year is 10%. Some of the computations along with the
graph of f(x) is a curve that falls from left to right and gets less and less steep as x increases. The x-axis is a horizontal asymptote.

www.petersons.com

x

f(x)

0

5,250

1

4,725

5

3,100

8

2,260

12

1,482.8

15

1,080

25

339.21

Value $
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
2

4

6

8

10 12 14 16

18

Years

Comparing Linear and Exponential Growth Functions
Suppose you can choose how you will get your allowance. The first option is to get $5 a week every week. The second option is to
get $0.50 for the first week, $1 for the second week, $2 for the third, and so on, by doubling the amount each week. Which option
will pay you more?
Option 1: y = 5x, where x is the number of weeks you were paid your allowance and y is the total amount of money you
have been paid so far.
Option 2: y = (0.5)(2)x –1, where x is the number of weeks you were paid your allowance and y is the total amount of
money you have been paid so far.
As you can see from the tables, Option 1 pays more until the 8th week. After that, Option 2 will always pay more since you are
doubling a larger number.
Option 1: y = 5x

x (week)

1

2

3

4

5

6

7

8

9

10

y (total)

5

10

15

20

25

30

35

40

45

50

503
Chapter 12
Functions
and
Intermediate
Algebra

Option 2: y = (0.5)(2)x –1

x (week)

1

2

3

4

5

6

7

8

9

10

y (total)

0.5

1

2

4

8

16

32

64

128

256

Option 1 is a linear function that is increasing at a constant rate, and Option 2 is an exponential function that is
increasing rapidly as x gets bigger. You would chose Option 2 to be paid the most.

Peterson’s SAT® Prep Guide 2017

Value $
90

80

70

60

Option 2

50

Option 1
40

30

20

10

1

504
Chapter 12
Functions
and
Intermediate
Algebra

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2

3

4

5

6

7

8

9

10

11

12

Weeks

EXERCISES: LINEAR, QUADRATIC, AND EXPONENTIAL FUNCTIONS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

2.

3.

4.

A taxi company charges $2.25 for the first mile and $0.45
for each mile thereafter. If x stands for the number of miles
a passenger travels, which of the following functions
relates the length of the trip to its cost?
A.

f(x) = 2.25 + 0.45(x + 1)

B.

f(x) = 2.25 + 0.45(1 − x)

C.

f(x) = 2.25 + 0.45(x − 1)

D.

f(x) = 2.25 + 0.45x

SHOW YOUR WORK HERE

Amp Corporation manufactures home video systems. The
cost function for the Amp45 system is C(x) = 3x2 − 2x + 7,
where x represents the number of systems manufactured,
and the cost is in dollars. How much does it cost to manufacture 18 of these systems?
A.

$943

B.

$972

C.

$974

D.

$2,903

505

Which of the following best describes the graph of the
function f(x) = 5x − 7?

Chapter 12

A.

A horizontal line

B.

A line that increases from left to right

Functions
and
Intermediate
Algebra

C.

A line that decreases from left to right

D.

A parabola that opens up

Which of the following best describes the graph of the
function g(x) = −5x2 + 7x − 23?
A.

A horizontal line

B.

A line that increases from left to right

C.

A line that decreases from left to right

D.

A parabola that opens down

Peterson’s SAT® Prep Guide 2017

5.

6.

7.

At the Four Seasons bowling alley, it costs $1.50 to rent
shoes and $2.50 for each game played. Which of the following functions relates the number of games played, x,
to the cost in dollars?
A.

f(x) = 4.00x

B.

f(x) = 2.50 + 1.50x

C.

f(x) = 1.50x − 2.50

D.

f(x) = 2.50x + 1.50

In order to raise money for a charity, Deb makes cakes
to sell at a school bake sale. Her profit function is P(x) =
$4.50x − $15. How many cakes must she sell in order to
earn $66 for the charity?
A.

15

B.

16

C.

18

D.

20

For which domain value[s] of the function f(x) = x2 + 3x
− 10 does f(x) = 0?
A.

2

506

B.

−2

C.

−5

Chapter 12

D.

2 and −5

Functions
and
Intermediate
Algebra

8.

At which point does the graph of the function
g(x) = −12x + 6 cross the y-axis?
A.

(0, 6)

B.

(6, 0)

C.

(0, 2)

D.

 1
 0 , 
2

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SHOW YOUR WORK HERE

9.

10.

11.

12.

The functions f(x) = 16x − 7 and g(x) = 16x + 5 are graphed
on the same coordinate plane. Which of the following
best describes the appearance of the graph?
A.

Two intersecting lines, one with y-intercept of −7,
the other with y-intercept of 5

B.

Two parallel lines, one with y-intercept of −7, and
the other with y-intercept of 5

C.

Two parallel lines, one with y-intercept of 7, and
the other with y-intercept of −5

D.

Two intersecting lines, one with y-intercept of 7,
the other with y-intercept of −5

SHOW YOUR WORK HERE

What is the x-coordinate of the extreme point of the
function f(x) = 7x2 − 28x + 16?
1
2

A.

x=

B.

x=−

C.

x=2

D.

x = −2

1
2

You purchase a new bike for $850 and the value of the
bike decreases by 20% per year. Approximately, when will
the value of the bike will be less than $500?

507

A.

After 3 years

Chapter 12

B.

After 2.5 years

C.

After 2 years

D.

After 1.5 years

Functions
and
Intermediate
Algebra

What is the asymptote of the graph of f(x) = (0.75)x + 2?
A.

f(x) = –2

B.

f(x) = 0

C.

f(x) = 0.75

D.

f(x) = 2

Peterson’s SAT® Prep Guide 2017

13.

14.

A ball is dropped from a height of 20 ft. above the ground.
Given h(t) = –16t2 +h0, how long will it be before the ball
hits the ground?
A.

About 2.0 seconds

B.

About 1.56 seconds

C.

About 1.12 seconds

D.

About 0.89 seconds

The value of a car can be modeled by the equation
f(x) = 38,000(0.89)x, when x is the number of years since
the car was purchased and f(x) is the value of the car.
What is the approximate value of the car after 6 years?
A.

About $19,000

B.

About $22,000

C.

About $28,000

D.

About $30,000

508
Chapter 12
Functions
and
Intermediate
Algebra

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

2.

1. C

4. D

7. D

10. C

13. C

2. A

5. D

8. A

11. B

14. A

3. B

6. C

9. B

12. D

The correct answer is C. The cost for the first mile on
a trip of x miles is $2.25. After this, there are still x − 1
miles to go, and the cost for each of these miles is
$0.45. Therefore, the total cost of the trip, in dollars, is
2.25 + 0.45(x − 1).

4.

The correct answer is B. The function f(x) = 5x − 7 is a
linear function, which means that its graph is a straight
line. The slope of the line is the coefficient of x, that is, 5.
A line with a positive slope increases from left to right.

Thus, f(x) = x2 + 3x − 10 = 0 at x = −5 and x = 2.
8.

The correct answer is A. For a linear function, the
y-intercept is equal to the value of the constant.
Therefore, g(x) = −12x + 6 crosses the y-axis at (0, 6).

9.

The correct answer is B. The two functions are both
linear, so their graphs are straight lines. Note that the
coefficient of the x-term in each case is 16. Since this
coefficient represents the slope of the function, both
functions are lines with slopes of 16. Lines with the
same slopes are parallel. The constant term of a linear
function is the y-intercept, so one line has a y-intercept
of −7, and the other has a y-intercept of 5.

The correct answer is D. The function g(x) = −5x2 + 7x
− 23 is a quadratic function, so its graph will be a
parabola. Because the coefficient of the x2-term is
negative, the parabola opens down.

5.

The correct answer is D. The cost of x games, at $2.50
a game, is $2.50x. Adding the $1.50 cost of shoe rental
to this leads to the function f(x) = 2.50x + 1.50.

6.

The correct answer is C. You are asked to find the
value of x for which 4.50x – 15 = 66.

4.50 x − 15 = 66
4.50 x − 15 = 66 Add 15 to both sides.
4.50 x = 81 Divide by 4.50 (or 4.5).
x = 18
Therefore, Deb must sell 18 cakes to make $66.

The correct answer is D. In order to answer this
question, you need to solve the quadratic equation
x2 + 3x − 10 = 0.
x 2 + 3 x − 10 = 0 Factor the left-hand side.
( x + 5)( x − 2) = 0 Set each factor equal to 0.
x +5= 0 x −2 = 0
x = −5
x =2

The correct answer is A. You need to determine the
value of C(18).
C(18 ) = 3(18 ) 2 − 2(18 ) + 7
= 3(324 ) − 36 + 7
= 972 − 36 + 7
= 943

3.

7.

10.

Chapter 12
Functions
and
Intermediate
Algebra

The correct answer is C. The extreme point of a
−b
quadratic function is given by the formula x =
,
2a
2
where a is the coefficient of the x -term and b is the
coefficient of the x-term. In this case, then, the extreme
point is
x =

11.

509

−b
−( −28 )
28
=
=
= 2.
2a
2(7)
14

The correct answer is B. The model giving the bike’s
value f(x) in dollars after x years is: f (x) = 850(0.8)x .
Substitute 500 in for f(x) and solve the equation.
The value of the bike will be less than $500 after
approximately 2.5 years.

Peterson’s SAT® Prep Guide 2017

12.

The correct answer is D. The graph of f(x) = abx−h + k is
the translation of the graph of f(x) = abx.
So f(x) = (0.75)x + 2 is translated up 2 units. The graph’s
asymptote is the line f(x) = 2.

13.

The correct answer is C. The model giving the height
h of the ball (in feet) after t seconds is h(t) = −16t2 + 20 .
Substitute 0 in for h(t) and solve the equation. The ball
will hit the ground about 1.12 seconds after it is
dropped.

510
Chapter 12
Functions
and
Intermediate
Algebra

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14.

The correct answer is A. Substitute 6 for x in the
equation f(x) = 38,000(0.89)x, and solve the equation.
The car will be worth approximately $19,000 after 6
years.

SUMMING IT UP
• A function is a rule that assigns exactly one output to each input. In other words, each member of the domain corresponds
to exactly one member of the range.

• In function notation, the rule of association for a function is written as f(x) to represent the range value.
• For any positive integer n, x − n =

1
xn

1

• For a rational number, x to the power of 1 is defined as the nth root of x. In other words, x n is equal to n x .
n

• A linear function is a function of the form f(x) = mx + b, where m and b are real numbers.
ºº In general, the graph of any linear function is either a straight line or depending on the domain) a portion of a straight line.

• A quadratic function is a function of the form g(x) = ax2 + bx + c, where a ≠ 0 and a, b, and c are real numbers.
ºº In general, the graph of any quadratic function will be a parabola.

• An exponential function is a function of the form f(x) = abx where base b is a positive integer greater than 1.
ºº In general, the graph of any exponential function will curve sharply as it rapidly increases or decreases.

• The four steps in solving an equation involving rational expressions are:
1. Find the LCD of all of the rational expressions in the equation.
2. Multiply every term on both sides of the equation by this LCD.
3. Solve the resulting equation using the methods previously explained.
4. Check the solution to make certain that it actually solves the equation.

• The four steps to solve a radical equation are:
1. Isolate the radical on one side of the equation.

511

2. Raise both sides of the equation to the same power to eliminate the radical.
3. Solve the resulting equation.

Chapter 12

4. Check the solution.
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intermediate algebra in Peterson’s SAT® Online Course:

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• Functions
• Hard Algebra
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• Linear Equations
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• Quadratic Systems
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Peterson’s SAT® Prep Guide 2017

Chapter 13:
Data Analysis, Statistics,
and Probability
OVERVIEW
Averages
Weighted Average
Exercises: Averages
Probability
Exercises: Probability
Data Interpretation
Exercises: Data Interpretation
Statistics
Exercises: Statistics

513

Summing It Up

Chapter 13

AVERAGES

Data Analysis,
Statistics, and
Probability

Arithmetic Mean, Median, Mode, and Range
Typically, when asked to find the average of a group of n numbers, students add up all the numbers in the group and then
divide by n. This type of average, which is more precisely called the arithmetic mean, is just one of a number of different types of
averages, each of which is computed in a different way and conveys a different type of information. There are three additional
ways to describe a set of data. Two of these are also types of averages, known as the median and the mode of the data. A third
value, range, is used to describe data. These will also occasionally appear on the SAT® exam.
In order to avoid ambiguity, when a question involves the computation of the arithmetic mean, it will use the word average
followed by the words arithmetic mean in parentheses. When an average question involves the median, the mode, or the range,
the words median, mode, and range will be specifically used. The arithmetic mean is by far the most common type of average
used on the exam.

Peterson’s SAT® Prep Guide 2017

The Arithmetic Mean
To find the average (arithmetic mean) of a group of n numbers, simply add the numbers and divide by n.
Example:
Find the average (arithmetic mean) of 32, 50, and 47.
Solution:
32
50
+47
129

43
3 129

)

Another type of arithmetic mean problem gives you the arithmetic mean and asks for the missing term.
Example:
The average (arithmetic mean) of three numbers is 43. If two of the numbers are 32 and 50, find the third number.
Solution:

514

Using the definition of arithmetic mean, write the equation:
32 + 50 + x
= 43
3
32 + 50 + x = 129
82 + x = 129

Chapter 13
Data Analysis,
Statistics, and
Probability

x = 47

Median and Mode
In order to find the median of a group of numbers, list the numbers in numerical order from smallest to largest. The median is
the number in the middle. For example, the median of the numbers 3, 3, 5, 9, and 10 is 5. Note that, typically, the median and the
arithmetic mean are not the same. In this problem, for example, the arithmetic mean is 30 ÷ 5 = 6.
If there is an even number of numbers, the median is equal to the arithmetic mean of the two numbers in the middle. For example,
to find the median of 3, 3, 5, 7, 9, and 10, note that the two middle numbers are 5 and 7. The median, then, is

5+7
=6.
2

The mode of a group of numbers is simply the number that occurs most frequently. Therefore, the mode of the group of numbers
3, 3, 5, 7, 9, and 10 is 3. If all of the numbers in a group only appear once, then there is no mode.
Example:
What is the product of the arithmetic mean, the median, and the mode of the following group of eight numbers?
2, 7, 8, 9, 9, 9, 10, and 10

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Solution:
The sum of the eight numbers is 64, so the arithmetic mean is 64 ÷ 8 = 8.
The median is the arithmetic mean of the two numbers in the middle. Since these numbers are both 9, the median is
9+9
=9 .
2
The mode is the number that occurs most often, which is also 9. The product of these three “averages” is
8 × 9 × 9 = 648.

Range
The range, or the spread, of a data set is the difference between the greatest and least data values. To find the range of a set of
data, first write the values in ascending order to make sure that you have found the least and greatest values.
Example:
Celia kept track of the average price of a gallon of gas over the last 10 years. Her data is shown in the table below.
What is the range in the average price of gas?
Solution:

Year

Average price/gallon
in U.S. dollars

2006

2.00

2007

2.08

2008

2.44

2009

3.40

2010

2.85

2011

2.90

2012

3.50

2013

4.20

2014

3.80

2015

3.25

515
Chapter 13
Data Analysis,
Statistics, and
Probability

Write the data in order from least to greatest:
2.00 2.08 2.44 2.85 2.90 3.25 3.40 3.50 3.80 4.20
Subtract the least value from the greatest value: 4.20 – 2.00 = 2.20.
$2.20 is the range or spread of the data.

Peterson’s SAT® Prep Guide 2017

WEIGHTED AVERAGE
If asked to find the arithmetic mean of a group of numbers in which some of the numbers appear more than once, simplify the
computation by using the weighted average formula. For example, suppose the question asks for the average (arithmetic mean)
age of a group of 10 friends. If four of the friends are 17, and six of the friends are 19, determine the average in the usual way:
Average age =

17 + 17 + 17 + 17 + 19 + 19 + 19 + 19 + 19 + 19 182
=
= 18.2
10
10

However, the computation can be done more quickly by taking the weights of the ages into account. The age 17 is weighted four
times, and the age 19 is weighted six times. The average can then be computed as follows:
Average age =

4(17) + 6(19 ) 182
=
= 18.2
10
10

Example:
Andrea has four grades of 90 and two grades of 80 during the spring semester of calculus. What is her average (arithmetic mean) in the course for this semester?
Solution:
90
90
90
90
80
+80

516

)

6 520
2
3

or

90 i 4 = 360

+ 80 i 2 = 160

)

6 520
= 86

2
3

Chapter 13

= 86

Data Analysis,
Statistics, and
Probability

Be sure not to average 90 and 80, since there are four grades of 90 and only two grades of 80.

Average Rate
The average rate for a trip is the total distance covered, divided by the total time spent. Recall that distance can be
determined by multiplying the rate by the time, that is, d = rt.
Example:
In driving from New York to Boston, Mr. Portney drove for 3 hours at 40 miles per hour and 1 hour at 48 miles per
hour. What was his average rate for this portion of the trip?

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Solution:

Total distance
Total time
3 ( 40 ) + 1( 48 )
Average rate =
3 +1
168
Average rate =
= 42 miles per hour
4
Average rate =

Since more of the trip was driven at 40 mph than at 48 mph, the average should be closer to 40 than to 48, which it is.
This will help you to check your answer or to pick out the correct choice in a multiple-choice question.

EXERCISES: AVERAGES
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

Dan had an average (arithmetic mean) of 72 on his first
four math tests. After taking the next test, his average
(arithmetic mean) dropped to 70. Which of the following
is his most recent test grade?
A.

60

B.

62

C.

66

D.

68

What is the average (arithmetic mean) of 0.64 , 0.85,
9
and
?
10
A.

21
25

B.

2.55

C.

85%
4
5

D.

SHOW YOUR WORK HERE

517
Chapter 13
Data Analysis,
Statistics, and
Probability

Peterson’s SAT® Prep Guide 2017

3.

The costs of five different airlines’ tickets from Dallas to
Boston are shown in table below.

Airline

Ticket Cost

A

$356

B

$298

C

$312

D

$304

E

$283

A sixth airline also offers flights from Dallas to
Boston. The median price of the tickets from the six
airlines, including those shown in the table, is $308.
The range of the ticket prices is $77. What is the cost
of the sixth airline’s ticket?

518
Chapter 13

4.

A.

$385

B.

$360

C.

$279

D.

$231

A high school theater department is using sale information from previous years’ sales for the annual musical
to determine how many seats will be needed. The sale
information is shown in the table below.

Data Analysis,
Statistics, and
Probability

Year

Seats

2013

185

2014

203

2015

205

2016

197

Which correctly shows the median and range of the
data?
A.

Median = 200; Range = 20

B.

Median = 204; Range = 12

C.

Median = 200; Range = 12

D.

Median = 204; Range = 20

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SHOW YOUR WORK HERE

5.

6.

7.

What is the average (arithmetic mean) of the first 15
positive integers?
A.

7

B.

7.5

C.

8

D.

8.5

SHOW YOUR WORK HERE

A man travels a distance of 20 miles at 60 miles per hour
and then returns over the same route at 40 miles per
hour. What is his average rate for the round trip in miles
per hour?
A.

50

B.

48

C.

47

D.

46

Max is selling his car. He looks at the selling prices of the
same type of car at five local car dealerships to determine
a fair price for his car. The selling prices are listed below.
$7,505; $7,630; $7,995; $7,029; $7,135; $7,995
What is the approximate average (arithmetic mean)
selling price for the type of car Max is trying to sell?

8.

A.

$7,995

B.

$7,548

C.

$7,512

D.

$7,505

519
Chapter 13
Data Analysis,
Statistics, and
Probability

Susan has an average (arithmetic mean) of 86 in three
examinations. What grade must she receive on her next
test to raise her average (arithmetic mean) to 88?
A.

90

B.

94

C.

96

D.

100

Peterson’s SAT® Prep Guide 2017

9.

10.

The heights of the 5 high jumpers on Redwood High’s
track team are 5'11", 6'3", 6', 6'6", and 6'2". The average
(arithmetic mean) height of these players is
A.

6'2".

B.

6'3".

C.

6'4".

D.

6'5".

The ages of 14 U.S. Presidents at inauguration are listed
here in order of their presidencies. Which of the following correctly compares the average (arithmetic mean),
median, and mode of their ages?
54 51 60 62 43 55 56 61 52 69 64 46 54 47

11.

A.

mode < mean < median

B.

mode < median < mean

C.

median < mode < mean

D.

median < mean < mode

A basketball team has 5 top-scoring players. The average
(arithmetic mean) points per game scored by the 5 players during one season are shown in the list below.

520

15.5, 16.2, 18, 16.5, 17.4
There are 10 games during the season. What is the
average points scored per player for the season for
the 5 top scoring players?

Chapter 13
Data Analysis,
Statistics, and
Probability

12.

A.

16.72

B.

18.72

C.

134.8

D.

167.2

Amaya drives on two types of roads for her trip. She averages 53 miles per hour on city roads and 59 miles per
hour on the highway. Amaya drives her car on a trip that
has twice as many highway miles as city road miles. She
drives a total of 552 miles. What is her average speed for
the whole trip? Round your answer to the nearest whole.
A.

55 miles per hour

B.

56 miles per hour

C.

57 miles per hour

D.

58 miles per hour

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ANSWER KEY AND EXPLANATIONS

1.

1. B

3. B

5. C

7. B

9. A

11. D

2. C

4. A

6. B

8. B

10. B

12. C

The correct answer is B.

4.

4(72) + x
= 70
5
288 + x = 350

185, 197, 203, 205
The median is the middle value of the list. Since the
list does not have a distinct middle value, add the two
middle values 197 and 203, then divide by 2 to find
the median.

x = 62
2.

The correct answer is C. In order to find the average
(arithmetic mean) of these three numbers, they should
all be expressed as decimals.

197 + 203 = 400; 400 ÷ 2 = 200

0.64 = 0.8
0.85 = 0.85
9
= 0.9
10
0.8 + 0.85 + 0.9
Average =
3
2.55
=
= 0.85 (aarithmetic mean)
3

The median is 200.
To find the range, subtract the least from the greatest
value:
205 – 185 = 20
The range is 20.

This is equal to 85%.
3.

The correct answer is B. List the given ticket costs
from least to greatest:

The correct answer is A. List the given number of seats
from least to greatest:

5.

The correct answer is C. Positive integers begin with 1.

$283, $298, $304, $312, $356

1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11+ 12 + 13 + 14 + 15
15

Add $77 to the least cost to determine if the unknown cost is also the greatest cost:

Since these numbers are evenly spaced, the average
(arithmetic mean) will be the middle number, 8.

521
Chapter 13
Data Analysis,
Statistics, and
Probability

283 + 77 = 360
Use the value to find the median of the tickets:
$283, $298, $304, $312, $356, $360
Find the average (mean) of $304 and $312, which is
$308.
The unknown ticket cost is $360.

Peterson’s SAT® Prep Guide 2017

6.

The correct answer is B.

Average rate =

10.

Total distance
Total time

43, 46, 47, 51, 52, 54, 54, 55, 56, 60, 61, 62, 64, 69

Total distance = 20 + 20 = 40

Since time =

The mode of their ages is 54, which is the only
repeated age.
The median of their ages is the middle number, which
is the average of 54 and 55, or 54.5.

distance
, time for first part of the trip is
rate

20
1
, or hour, while time for the second part of the
60
3
trip is

20
1
, or hour.
2
40

1 1
5
Total time = + , or hour
3 2
6
Average rate =

7.

The average or arithmetic mean is found by adding
their ages and dividing by 14.
43 + 46 + 47 + 51+ 52 + 54 + 54 + 55 + 56 + 60 + 61+ 62 + 64 + 69
14
774
=
= 55.3
14
Now order the three values: 54 < 54.5 < 55.3, which
means that mode < median < mean.

40
6
= 40 i = 48 mph
5
5
6

11.

The correct answer is B.
7, 505 + 7, 630 + 7, 995 + 7, 029 + 7,135 + 7, 995 45, 289
=
6
6
= 7, 548.167
The approximate average of the cars’ selling prices is
$7,548.

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Chapter 13

8.

3(86 ) + x
= 88
4
258 + x = 352
x = 94
9.

The correct answer is A.

)

29 ’ 22 " = 5 30 ’10 "
6 ’2"

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Average points for the season:
155 + 162 + 180 + 165 + 174 836
=
= 167.2 points per season
5
5
12.

5 ’11"
6 ’ 3"
6’ 0"
6’ 6"
6’ 2"

The correct answer is D. To find the average points
scored for the season by all 5 players, you can first find
the total number of points each player scored during
the season. Each player played 10 games, so to find
their total number of points scored, multiply the
average points per game by 10 games.
15.5 × 10 = 155
16.2 × 10 = 162
18 × 10 = 180
16.5 × 10 = 165
17.4 × 10 = 174

The correct answer is B.

Data Analysis,
Statistics, and
Probability

The correct answer is B. First, put the ages of the
presidents in order.

The correct answer is C. Amaya drove for a time on
city roads at 53 miles/hour and twice as much time on
the highway at 59 miles/hour, so her average speed
was:
53 x + 59(2 x ) 171x
=
= 57
3x
3x
The average speed for the entire trip was 57 miles per
hour.

PROBABILITY
In the study of probability, an experiment is a process that yields one of a certain number of possible outcomes. For example,
tossing a coin is an experiment with two possible outcomes: heads or tails. Throwing a die is an experiment with six possible
outcomes because there are six sides: 1, 2, 3, 4, 5, and 6.
Probability is a numerical way of measuring the likelihood that a specific outcome will happen. The probability of a specific outcome
is always a number between 0 and 1. An outcome with a probability of 0 cannot possibly happen, and an event with a probability
of 1 will definitely happen. Therefore, the nearer the probability of an event is to 0, the less likely the event is to happen, and the
nearer the probability of an event is to 1, the more likely the event is to happen.
If an experiment has n possible, equally likely outcomes, the probability of each specific outcome is defined to be

1
. In the coinn

1
, since heads is one of the two equally likely outcomes. When a die is thrown,
2
3
1
the probability of tossing an odd number is , or , since tossing an odd number is three of six equally likely outcomes.
6
2

tossing experiment, the probability of heads is

Here is a helpful formula for computing simple probabilities:
The probability of an event occurring =

The number of favorable outcomes
The number of possible outtcomes

Conditional Probability
The probability of an event occurring after another event has already occurred is called conditional probability.
The notation for conditional probability is P(B|A), which is read “the probability of B given A.
If both events A and B are independent, where the result of B is not affected by the result of A, then the conditional probability
of B is equal to the probability of B only.

523
Chapter 13

(B )
P
= P(B )
( A)

Data Analysis,
Statistics, and
Probability

If both events A and B are dependent, where the result of B is affected by the result of A, then the conditional probability of B may
be calculated using a few different methods. In probability situations involving dependent events, the way in which the question
is asked will determine which of the following equations to use.
P( A and B )
P( A and B )
 B
OR
OR P( A and B ) = P( A) × P  
 A
P ( A)
P(B )
Example:
Of 100 people who work out at a gym, there are 45 people who take yoga classes, 55 people who take weightlifting
classes, and 15 people who take both yoga and weightlifting. What is the probability that one of the randomly
chosen people who work out at the gym takes both yoga and weightlifting classes?

Peterson’s SAT® Prep Guide 2017

Solution:
This question is asking you to find the probability that a person is taking both a yoga class and a weightlifting class
(A and B), given that the person is in a yoga class (A).
P( A and B ) 0.15 1
=
=
P ( A)
0.45 3
The conditional probability that a person who takes yoga is also in a weightlifting class is

1
.
3

Independent Events
If events A and B are independent, then the probability of event B is not affected by the result of event A.
Example:
What is the probability of tossing two coins that both land heads up, if the first coin has already been tossed and
landed heads up?
Solution:
The result of the first toss does not affect the result of the second toss, so the conditional probability is equal to the
probability of B (the second coin toss).

524
Chapter 13
Data Analysis,
Statistics, and
Probability

P(B ) =

1
2

Example:
What is the probability of tossing two coins and having them both land heads up?

Solution:
Neither coin has been tossed, so the conditional probability of both coins landing heads up is determined using the
probability of both events. In this case, the probability of event A and event B both happening is found by multiplying
the probability of each event.
P( A and B ) =

1 1 1
× =
2 2 4

The probability of tossing two coins and having them both land heads up is

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1
= 0.25.
4

Dependent Events
If events A and B are dependent, then the probability of event B is affected by the result of event A.
Example:
What is the probability of choosing a black 5 and then a red 5 from the same standard deck of cards?
Solution:
There are two red 5s and two black 5s in a standard deck of 52 cards. Removing a black 5 from the deck will leave only 51 cards
in the deck, so the probability can be found by:
P( A and B ) =

2 2
1
× =
52 51 663

Two-Way Tables and Probability
Data on the exam is often represented in two-way tables like the one in the example below. Be careful to read the correct row or
column that represents the information in the problem. These tables are often used for two or three problems in a row.
Example:
Hattie is a member of the honor society. All members of the society are polled to determine how many hours they
spend studying per week and whether they prefer math or science classes. The results are shown in the table below.

Science

Math

Total

0−3 hours per week

4

2

6

4−6 hours per week

6

7

13

Total

10

9

19

525
Chapter 13
Data Analysis,
Statistics, and
Probability

What is the probability that an honor society member selected at random prefers math, given that the member
studies 4–6 hours per week?
Solution:
There are a total of 13 students who study 4–6 hours per week, and 7 of them prefer math. So the probability is

7
.
13

Peterson’s SAT® Prep Guide 2017

EXERCISES: PROBABILITY
DIRECTIONS: Work out each problem. Circle the letter of your choice.

1.

2.

A school cafeteria offers students three meal choices:
salad, grilled chicken, and pot roast. There are four side
choices: grilled vegetables, baked potato, rice, or soup.
What is the probability that a student who randomly
chooses a meal and a side chooses the grilled vegetables
after having chosen the grilled chicken?
A.

1
3

B.

1
4

C.

1
7

D.

1
12

A poll asked 100 visitors at a national park the distance
they hiked during their visit. The table shows the data
collected based on the visitors’ ages and hiking distances.

18−25
years old

26−35
years old

Total

0−2 miles

16

22

38

Chapter 13

2−4 miles

20

17

37

Data Analysis,
Statistics, and
Probability

4+ miles

11

14

25

Total

47

53

100

526

What is the probability that a visitor hiked greater
than 4 miles, given that the visitor was 18–25 years
old?
A.

11
14

B.

11
25

C.

11
36

D.

11
47

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3.

A game uses letter tiles that are selected randomly out
of a bag. The letters that are remaining in the bag after
each player has taken four turns are shown below.

SHOW YOUR WORK HERE

S, U, G, R, A, O, E, T, V, E, A, H, S, E
What is the probability of the player selecting two
vowel tiles, if the player selects two tiles from the
letters that remain?

4.

A.

3
13

B.

1
4

C.

6
13

D.

1
2

In a movie theater, there are 32 people who bought
popcorn, 25 people who bought a drink, and 12 people
who bought popcorn and a drink. What is the probability
that a randomly selected person who bought popcorn
also bought a drink?
A.

3
8

B.

12
25

C.

25
32

D.

12
13

527
Chapter 13
Data Analysis,
Statistics, and
Probability

Peterson’s SAT® Prep Guide 2017

5.

The two-way frequency table below shows the results
of a poll regarding video game play. The poll asked 150
randomly selected people the amount of time they spend
playing video games each week and the type of game
they most like to play. The table shows relative frequencies of each category.

1−3
hours

3−5
hours

5+
hours

Total

Roleplaying

12

15

16

43

Platform

24

19

18

61

Action

33

35

28

96

Total

69

69

62

200

What is the probability that a person plays 3–5 hours
of games per week, given that they prefer platform
games?

528
Chapter 13
Data Analysis,
Statistics, and
Probability

6.

A.

19
35

B.

19
42

C.

19
61

D.

19
69

Which question below is the probability of two dependent events?
A.

Two coins are flipped. What is the probability of
the second coin landing heads up, if the first coin
landed tails up?

B.

Two number cubes are rolled. What is the
probability of rolling two even numbers?

C.

A card is selected from a deck of 52 cards. What is
the probability of selecting 3 hearts in a row, if
each card is replaced after being selected?

D.

A bag contains 5 red marbles and 6 blue marbles.
What is the probability of selecting two marbles
of different colors, without replacement of the
marbles?

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7.

A summer camp held a fishing tournament. The participants selected the type of bait they would use. The table below
shows the first type of fish caught by each participant and the bait they used.

Perch

Bass

Trout

Catfish

Total

Live Bait

10

4

4

6

24

Artificial Bait

5

5

2

0

12

Total

15

9

6

6

36

What is the probability that a participant will catch a
bass, given that artificial bait was used?

8.

A.

1
4

B.

5
9

C.

5
12

D.

5
36

At a school dance, the DJ offers five kinds of music: Electronic, Rap, Pop, Swing, and Rock. If the kind of music
played is selected at random, what is the probability that
the next two songs the DJ will play will be an Electronic
song and then a Pop song?
A.

1
25

B.

1
10

C.

1
5

D.

2
5

SHOW YOUR WORK HERE

529
Chapter 13
Data Analysis,
Statistics, and
Probability

Peterson’s SAT® Prep Guide 2017

9.

During a science experiment, two studies of chemical
reactions are conducted. Each experiment requires a
5
hypothesis. Hypothesis A is correct of the times the
7
3
experiment is conducted. Hypothesis B is correct
of
4
the times the experiment is conducted. If the two hypotheses do not affect each other, what is the probability that
both hypotheses A and B are correct?

10.

530

A.

15
28

B.

5
7

C.

3
4

D.

8
11

Gustav finds that during daily marching band practice he
correctly completes all steps 7 of the time. During daily
8
symphonic band practice he correctly plays each piece
11
of music
of the time. The probability that he completes
12
all steps in marching band and plays each piece of music
3
correctly in symphonic band during the same day is .
5

Chapter 13

What is the probability that he correctly completes all

Data Analysis,
Statistics, and
Probability

steps during marching band, given that he has attended
symphonic band?
A.

24
35

B.

36
55

C.

11
20

D.

21
40

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ANSWER KEY AND EXPLANATIONS

1.

1. B

3. A

5. C

7. C

9. A

2. D

4. B

6. D

8. A

10. B

The correct answer is B. The probability of choosing
grilled vegetables is independent of choosing grilled
chicken. There are four sides to choose from, and
grilled vegetables is one of those four choices, or

2.

The correct answer is D. There are a total of 47 visitors
who are 18–25 years old. In that age group, 11 of those

The correct answer is A. Seven of the 14 tiles are
vowels, so the probability of selecting one vowel is
7 1
= . For the second tile, there are only 13 tiles to
14 2
choose from and 6 vowel tiles remaining.
P( A and B ) = P( A) × (B )
1 6
= ×
2 13
6
=
26
3
=
13

4.

The correct answer is B. P(A and B) is the probability
of someone having both popcorn and a drink, and P(B)
is the probability of someone having a drink. So the
probability of selecting a person with both popcorn
and a drink is P( A and B ) = 12 .
25
P(B )

5.

The correct answer is D. Situations that state there is
no replacement have an event that is dependent on
the other. In this case, the second chosen marble is
dependent on the marble that was chosen first
because there will be one less marble in the bag and it
must be a different color.

7.

The correct answer is C. There are 12 total fish caught
using artificial bait. The number of bass caught out of
5
those 12 is 5, so the probability is
.
12

8.

The correct answer is A. The probability of each type
of song being played are independent of each other.
The probability of an Electronic song being played is
1
and the probability of a Pop song being played
5
is 1 . The probability that an Electronic song and then
5
1 1 1
a Pop song will be played is found by × = .
5 5 25

1
.
4

visitors walked more than 4 miles, so the probability is
11
.
47
3.

6.

The correct answer is C. There are 61 total people
who play platform games. Of those 61 people, 19 play
19
for 3–5 hours, so the probability is
.
61

9.

The correct answer is A. The probability of each
hypothesis is independent of the other. The probability
of both events occurring can be found by
5 3 15 .
P( A and B ) = P( A) × P(B ) = × =
7 4 28

10.

531
Chapter 13
Data Analysis,
Statistics, and
Probability

The correct answer is B. The probability of correctly
completing the marching steps, given he has attended
symphonic band, can be found by
3
P( A and B ) 5 3 12 36
.
=
= × =
11 5 11 55
P(B )
12

Peterson’s SAT® Prep Guide 2017

DATA INTERPRETATION
Working with Data in Tables
Some SAT® exam questions ask you to solve mathematical problems based on data contained in tables. All such problems are
based on problem-solving techniques that have already been reviewed. The trick when working with tables is to make certain
that you select the correct data needed to solve the problem. Take your time reading each table so that you understand exactly
what information the table contains. Carefully select data from the correct row and column. As you will see, things are even trickier
when a problem involves more than one table.
In order to illustrate problem solving with tables, consider the two tables below. The three questions that follow are based on
the data within these tables.
Paul, Mark, and Bob are computer salespeople. In addition to their regular salaries, they each receive a commission for each
computer they sell. The number of computers that each salesperson sold during a particular week, as well as their commission
amounts, is shown in the tables below.

Number of Computers Sold
Monday

Tuesday

Wednesday

Thursday

Friday

Paul

9

3

12

6

4

Mark

6

3

9

1

5

Bob

8

4

5

7

8

Commission per Sale

532
Chapter 13
Data Analysis,
Statistics, and
Probability

Paul

$15

Mark

$20

Bob

$25

Example:
What is the total amount of the commissions that Bob earned over the entire week?
Solution:
This problem concerns only Bob, so ignore the information for Mark and Paul. Over the course of the week, Bob sold
8 + 4 + 5 + 7 + 8 = 32 computers. The second table tells us that Bob earns $25 per sale, so the total amount of his
commission would be $25 × 32 = $800.

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Example:
What is the total amount of commission money earned by Paul, Mark, and Bob on Thursday?
Solution:
To solve this problem, focus only on what happened on Thursday. Ignore the data for the other four days. Be careful
not to add the number of computers sold by the three people, since they each earn a different commission per sale.

• On Thursday, Paul sold 6 computers and earned a $15 commission for each computer sold, so Paul earned $15 × 6 = $90.
• Mark sold 1 computer, so, based on his $20 commission, he earned $20.
• Bob sold 7 computers and earned a $25 commission per machine, so he made $25 × 7 = $175.
• Overall, the amount of commission on Thursday is $90 + $20 + $175 = $285.
Example:
On what day did Paul and Mark earn the same amount in commission?
Solution:
You can save yourself a lot of time if you look at the tables before you start to compute. Note that Mark’s commission
is larger than Paul’s, and so the only way they could have earned the same amount is if Paul sold more computers
than Mark. The only days that Paul sold more computers than Mark were Monday, Wednesday, and Thursday, so those
are the only days that need to be considered. By observation, you can see the following:

• On Thursday, Paul made much more in commission than Mark, so eliminate Thursday.

533

• On Monday, Paul earned $15 × 9 = $135 and Mark earned $20 × 6 = $120. This means that the answer must be Wednesday.
• To be certain, note that on Wednesday Paul earned $15 × 12 = $180, and Mark earned $20 × 9 = $180 also.

Chapter 13
Data Analysis,
Statistics, and
Probability

Correlation and Scatterplots
If two variables have a relationship such that when one variable changes, the other changes in a predictable way, the two variables
are correlated. For example, there is a correlation between the number of hours an employee works each week and the amount of
money the employee earns—the more hours the employee works, the more money the employee earns. Note that in this case,
as the first variable increases, the second variable increases as well. These two variables are positively correlated.
Sometimes, when one variable increases, a second variable decreases. For example, the more that a store charges for a particular
item, the fewer of that item will be sold. In this case, these two variables are negatively correlated.
Sometimes, two variables are not correlated, that is, a change in one variable does not affect the other variable in any way. For
example, the number of cans of soda that a person drinks each day is not correlated with the amount of money the person earns.

Peterson’s SAT® Prep Guide 2017

One way to determine whether two variables are correlated or not is to sketch a scatterplot. A scatterplot is a graph on which the
x-axis represents the value of one variable and the y-axis represents the value of the other variable. Several values of one variable
and the corresponding values of the other variable are measured and plotted on the graph:

• If the points appear to form a straight line, or are close to forming a straight line, then it is likely that the variables are
correlated.

• If the line has a positive slope (rises up left to right), the variables are positively correlated.
• If the line has a negative slope (goes down left to right), the variables are negatively correlated.
• If the points on the scatterplot seem to be located more or less at random, then it is likely that the variables are not
correlated.

Positive Correlation

534

y

y

y

x

Negative Correlation x

x

It is rare that the points on a scatterplot will all lie exactly on the same line. However, if there is a strong correlation, it is likely
that there will be a line that could be drawn on the scatterplot that comes close to all of the points. Statisticians call the line that
comes the closest to all of the points on a scatterplot the “line of best fit.” Without performing any computations, it is possible to
visualize the location of the line of best fit, as the diagrams below show:

Chapter 13
Data Analysis,
Statistics, and
Probability

No Correlation

y
y

x

www.petersons.com

x

Example:
Which of the following slopes is the closest to the slope of the line of best fit for the scatterplot shown here?
y

x
A.

3

B.

1

C.

0

D . −1
Solution:
Begin by sketching in the line of best fit in its approximate location.

535

y

Chapter 13
Data Analysis,
Statistics, and
Probability

x
This line has a negative slope, since it decreases from left to right. In addition, the slope appears to be about −1, because
if you move one unit horizontally from a point on the line, you need to move one unit vertically downward to return to
the line. The correct answer is choice D.

Peterson’s SAT® Prep Guide 2017

Equation of Line of Best Fit
You may see questions that ask you to create a line of best fit and give the equation for this line. Again, there is some approximation involved in determining a line of best fit. Look at the following scatterplot. Imagine a line that would come closest to all
the data points and include an equal number of data points on either side of the line.

y

x
Notice the line of best fit below has 8 points above and 8 points below the line.
y

536
Chapter 13
Data Analysis,
Statistics, and
Probability

x

Note that the line of best fit does not have to cross any of the data points. In this case, the line of best fit goes through the middle
of the data and does not include any of the actual data points.
To determine the equation of the line of best fit, choose two points that lay on the line of best fit. You may have to approximate
points if the line does not have points that are exactly on an intersection. The line appears to have points at (6, 8) and (12, 3).
Use these two points to determine the equation of the line of best fit. First, calculate the slope, m, using the slope formula
y 2 − y1
. Plug x- and y-values into the equation: 3 − 8 = −5 The slope-intercept formula is y = mx + b.
x 2 − x1
6
12 − 6
So far, we have y =

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−5
x +b
6

Plug in one point into x and y in the equation.
−5
(6) + b
6
8 = −5 + b
b = 13

(6, 8): 8 =

The equation of the line of best fit is: y =

−5
x + 13.
6

Making Predictions
Assume the same previous scatterplot has real-world data. The following scatterplot now shows the average number of books
borrowed on a weekly basis for years 2000–2009 at a local library.

Library Books Borrowed
10
9

Books Borrowed (100s)

8
7
6
5
4
3

537

2
1

Chapter 13

0
1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Year

Data Analysis,
Statistics, and
Probability

Example:
If the trend continued, about how many books were borrowed in 2010?
Solution:
Use the slope of the line to make predictions about data points that are not shown. According to the slope, the
average number of books borrowed weekly goes down approximately 0.6 × 100 = 60 books every year. Multiply
by 100 because, according to the title of the vertical axis, the numbers are in the 100s. The expected value for the
number of books borrowed in 2009 was 400. The slope says we should expect that number to decrease by 60 every
year, so you can predict that there were 340 books borrowed in 2010.

Peterson’s SAT® Prep Guide 2017

EXERCISES: DATA INTERPRETATION
DIRECTIONS: Work out each problem. Circle the letter of your choice.

Questions 1–3 refer to the following information.
The scatterplot below shows average monthly feed and labor costs in dollars to raise different numbers of heads of beef cattle.

Average Monthly Cost

Feed and Labor Costs
1,000
900
800
700
600
500
400
300
200
100
0
0

50

100

150

200

250

Number of Heads of Cattle

538
Chapter 13

1.

Data Analysis,
Statistics, and
Probability

2.

Which of the following is closest to the slope of a line of
best fit for this data?
A.

200

B.

1
2

C.

10
9

D.

2

Based on the scatterplot, what is the equation of the line
of best fit?
A.

y = 200x + 400

B.

y = 2x + 320

C.

y = 2x + 380
1
y = x + 380
2

D.

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SHOW YOUR WORK HERE

3.

If the trend continued, what would be the average monthly
feed and labor costs to raise 500 heads of beef cattle?
A.

$1,380.00

B.

$1,000.00

C.

$880.00

D.

$600.00

SHOW YOUR WORK HERE

Questions 4–6 refer to the following information.

Geographic Area

Attended
College

Did Not Attend
College

No Response

Total

Northeast

72,404

68,350

29,542

170,296

Northwest

88,960

125,487

48,960

263,407

Southeast

115,488

96,541

65,880

277,909

Southwest

79,880

65,874

13,840

159,594

Total

356,732

356,252

158,222

871,206

A survey was conducted in different geographic areas of a large state, covering the entire state population, about whether people
over the age of 30 attended college. The table above displays a summary of the survey results.

4.

According to the table, for which group did the highest
percentage of people report that they had attended
college?
A.

Northeast

B.

Northwest

C.

Southeast

D.

Southwest

SHOW YOUR WORK HERE

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Chapter 13
Data Analysis,
Statistics, and
Probability

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5.

6.

Of the people living in the northeast who reported that
they did not attend college, 1,000 people were selected at
random to do a follow-up survey where they were asked if
they were interested in attending adult education classes.
There were 665 people who said they were interested in
attending adult education classes. Using the data from
both the initial survey and the follow-up survey, which of
the following is most likely to be an accurate statement?
A.

About 48,149 people living in the northeast who
did not attend college would be interested in
adult education classes.

B.

About 45,453 people living in the northeast who
did not attend college would be interested in
adult education classes.

C.

About 19,645 people living in the northeast who
did not attend college would be interested in
adult education classes.

D.

Most people in the state are not interested in
taking adult education classes.

What is the relative frequency of the number of people
who attended college statewide, according to the survey?
A.

0.18

540

B.

0.41

C.

0.43

Chapter 13

D.

0.5

Data Analysis,
Statistics, and
Probability

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Questions 7–8 refer to the following information.
In this election, Haynes and Cogswell were the only ones who received votes.

7.

8.

9.

District A

District B

District C

District D

Cogswell

150

350

300

200

Haynes

100

200

450

150

What percent of the votes cast in District C did Haynes
receive?
A.

40%

B.

45%

C.

60%

D.

65%

SHOW YOUR WORK HERE

What is the ratio of the total number of votes received
by Cogswell to the total number of votes received by
Haynes?
A.

10:9

B.

9:10

C.

5:4

D.

4:5

541

The scatterplot below depicts the relationship between
two variables, x and y. Which of the following best describes the line that best fits the data in the scatterplot?

Chapter 13
Data Analysis,
Statistics, and
Probability

y

x
A.

The slope of the line of best fit is −3.

B.

The slope of the line of best fit is −1.

C.

The slope of the line of best fit is 1.

D.

The slope of the line of best fit is 3.

Peterson’s SAT® Prep Guide 2017

10.

Below is a scatterplot depicting the relationship between
the variable a and the variable b. Which of the following
best describes the relationship depicted in the graph?
b

a
A.

There is a strong positive correlation between the
two variables.

B.

There is a strong negative correlation between the
two variables.

C.

The two variables are not correlated.

D.

As the value of a increases, the value of b
decreases.

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

1. D

3. A

5. B

7. C

9. D

2. C

4. D

6. B

8. A

10. C

The correct answer is D. Use two points that would be on the line of best fit, which would look something like this:

Feed and Labor Costs
1,000

Average Monthly Cost

900
800
700
600
500
400
300
200
100
0
0

50

100

150

200

250

Number of Heads of Cattle

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Chapter 13

Choose two points on this line: (60, 500) and (160, 700) look like they lay on, or close to, the line.
Use these coordinates in the slope formula:

y 2 − y1 700 − 500 200
=
=
=2.
x 2 − x1 160 − 60 100

2.

The correct answer is C. Using m = 2 as the slope
(from Question 1), insert a set of xy-coordinates into
the point-slope formula y = mx+ b: 500 = (2)(60) + b;
500 – 120 = b; b = 380. This gives you the equation
y = 2x + 380.

3.

The correct answer is A. Use the equation of the line
of best fit to make predictions. Plug in 500 for the
x-value: y = 2(500) + 380 = 1,000 + 380 = 1,380.

4.

Data Analysis,
Statistics, and
Probability

The correct answer is D. The percentage of people
who attended college in the southwest region is
79 , 880
≅ 0.5 = 50% .
159 , 594
The percentages for the other areas are:
72, 404
= 0.425 ≅ 43%
170 , 296
88 , 960
Northwest =
= 0.337 ≅ 34%
263, 407
115, 488
Southeast =
= 0.415 ≅ 42%
277, 909
Northeast =

Peterson’s SAT® Prep Guide 2017

5.

The correct answer is B. Extrapolating from the
second survey, we can predict that

9.

665
= 66.5%
1, 000

of the total population of the northeast will likely be

The correct answer is D. The figure here shows the
scatterplot with the approximate line of best fit
sketched in.
y

interested in taking adult education classes. Applying
this to the total northeast population who reported
that they did not attend college: 68,350 × 0.665 =
45,453 people in this population are likely to be
interested in adult education classes.
6.

The correct answer is B. The relative frequency of
college graduates in the survey is calculated by taking
the total number of people who reported having
attended college and dividing by the total number of
people in the survey:

x

Since the line increases from left to right, the line
has a positive slope. Also note that, if you move one
unit horizontally away from a point on the line, you
need to move approximately 3 units vertically to
return to the line. Therefore, the slope of the line of
best fit is approximately 3.

356 , 732
= 0.409 ≅ 0.41 .
871, 206
7.

The correct answer is C. Haynes received 450 out of a
total of 450 + 300 = 750 votes. Therefore, he received
of the vote

8.

544

450
= 60% of the vote.
750

The correct answer is A. Cogswell received 1,000
votes in total, and Haynes received 900. The ratio of
Cogswell to Haynes, therefore, is 1,000 to 900, or 10:9.

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Statistics, and
Probability

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10.

The correct answer is C. The points on the scatterplot
appear to be randomly arranged on the graph. This is
an indication that the values of a and b are not
correlated.

STATISTICS
Comparing Data Sets Using Shape, Center, and Spread
Statistics questions on the SAT® exam require using measures of central tendency, meaning the mean (average), median, and
mode of a data set. You will need to be familiar with the shape, center, and spread of data. The shape of the data refers to the
normal distribution curve, which we examine below. The center could be the average (arithmetic mean) or the median of the data
values in the set. The spread is the range of the data, or the standard deviation of the data that describes the distance between
values in a data set.
Data may be presented in tables, bar graphs, and other methods, so it is important to be familiar with different types of data
presentation.

Standard Deviation—Normal Distribution
A standard deviation describes how far the data values in a set are from the mean or how much they “deviate” from the mean.
The graphs below are both normal distribution curves. In the graph on the left, because much of the data clusters closely around
the mean, there is a small standard deviation. In the graph on the right, because the data is more spread out, there is a large
standard deviation. If these were sets of test scores for Class A and Class B on a math exam, most of the scores in Class A would
be very close to the average score, but, in Class B, the scores would be more varied.

Class A

Class B

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Chapter 13
Data Analysis,
Statistics, and
Probability

What You Really Need to Know About Standard Deviation
You won’t have to calculate the standard deviation, but it is important to understand how to use it. If data has a normal distribution, the empirical rule states that:

• Approximately 68% of the data falls within 1 standard deviation of the mean.
• Approximately 95% of the data falls within 2 standard deviations of the mean.
• Approximately 99¾% of the data falls within 3 standard deviations of the mean.
Let’s see how this works with a table of data. The table below lists the number of students enrolled in six different sections of
algebra, A, B, C, D, E, and F, offered by a college. First calculate the mean.

Peterson’s SAT® Prep Guide 2017

Number of Students

A

B

C

D

E

F

18

23

15

19

28

11

mean =

18 + 23 + 15 + 19 + 28 + 11 114
=
= 19
6
6
99.74%
95.44%
68.26%

Standard
Deviations

13%

2.15%

4

13.59%

9

34.13% 34.13%

14

19

13.59%

24

2.15%

29

13%

34

The mean is always in the middle. Here, it is 19, and each standard deviation is a distance of 5 from the mean of 19.
The standard deviation of this data set is given as 5. In this example, the standard deviation of 5 means that approximately 68%
of the algebra sections have between 14 (19 – 5) and 24 (19 + 5) students, plus or minus 1 standard deviation.

546

Approximately 95% of the algebra sections lie within 2 standard deviations, meaning the sections have between 9 and 29
students.

Chapter 13
Data Analysis,
Statistics, and
Probability

Confidence Intervals and Measurement Errors
Measurement or sampling errors will usually occur when data cannot be collected about an entire population. If, for example, we
are trying to determine the mean salary of people living in a city with 3.5 million people, we would probably use a smaller random
sample of several hundred to several thousand people that was representative of the population. The difference between the
mean salary of the actual population and that of the sample population is called a measurement or sampling error. The sampling
error decreases as the sample size increases, because there is more data that should more accurately reflect the true population.
Here’s an example:
A packaging company is gathering data about how many oranges it can fit into a crate. It takes a sample of 36 crates out of a
total shipment of 5,540 crates. The sample mean is 102 oranges with a sampling error of 6 oranges at a 95% confidence interval.

What Does the Confidence Interval Mean?
In this case, it means that based on the sample, you can be 95% confident that the true population mean for the entire shipment
is between 102 – 6 and 102 + 6, or 96 and 108 oranges per crate.
A confidence interval tells you how close the sample mean is to the actual mean of the entire population.

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Comparing Data Sets Using Mean and Standard Deviation
You may have two sets of data with similar means and ranges but different standard deviations. For the data set with the greater
standard deviation, more of the data are farther from the mean.
Example:
A coach is deciding between 2 baseball players to recruit to his team. He is looking at player performance over the
past 10 seasons. Both players have the same mean batting average of 0.270 and the same range of batting averages
(0.080) over the past 10 seasons. However, Player A’s batting averages have a higher standard deviation than Player
B’s batting averages. What does this indicate about each player?
A.

Player A is more likely to hit better than his mean batting average.

B.

Player B is more likely to hit better than his mean batting average.

C.

Player A’s batting average is more erratic.

D.

Player B’s batting average is more erratic.

Solution:
A greater standard deviation in a data set means that the data values are more spread out, or erratic, meaning performance varied more. Essentially, Player B’s batting average is more dependable; he more frequently batted close to his
batting average than did Player A. So, if the manager is looking for reliability, he may want to choose Player B for his
team. The correct answer is choice C.

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Probability

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Making Inferences Using Sample Data
Frequently, a population is too large for every data value to be measured. Instead, a random sample of the population is used to
make inferences about the true population.
Example:
An online retailer wants to determine the average dollar value of an order that it receives on a daily basis. Based on a
random sample of 200 orders, the mean dollar value is $72.00 and the standard deviation is $5.00.
The normal distribution curve would look like this:

99.74%
95.44%
68.26%

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Chapter 13
Data Analysis,
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Probability

Standard
Deviations

13%

2.15%

13.59%

34.13% 34.13%

13.59%

2.15%

13%

$57.00 $62.00 $67.00 $72.00 $77.00 $82.00 $87.00

If the sample used is representative of the true population, what can be concluded about the true population of
shoppers?
A.

The mean of the true population is $72.00.

B.

Most shoppers spend between $62.00 and $82.00.

C.

All shoppers spend between $57.00 and $87.00.

D.

The mode of the size of an order is $72.00.

Solution:
Shoppers who spent between $62.00 and $82.00 fall within 2 standard deviations of the mean of the sample population.
Approximately 95% of the shoppers fall within 2 standard deviations of the mean. Thus, it can be concluded that most
shoppers spend between $62.00 and $82.00. Though the sample is representative, it does not indicate that the mean of
the true population is equal to the mean of the sample population, so choice A is incorrect. Approximately 99¾% of the
population lies within 3 standard deviations of the mean, which, in this case, is between $57.00 and $87.00—but this
is not all shoppers, so choice C is not fully supported. We don’t know the mode of the data, so choice D is not correct.
The correct answer is choice B.

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Comparing Data Sets Using Spread
The spread is simply the difference between the least and greatest value in a set.
Example:
Todd’s meteorology class researched weekly precipitation in a tropical region during two 6-week periods. The data in
Set A covers a period from January through mid-February, and the data in Set B is from July through mid-August. The
results appear in the tables below.

Set A: Weeks 1–6 (January–February)
0.43

1.73

1.93

0.28

0.08

1.18

0.04

0.00

Set B: Weeks 27–32 (July–August)
0.20

0.01

0.00

0.08

Which of the following is true of the above sets of data?
A.

The range of the data in Set A is greater than that of Set B.

B.

The mean of the data in Set B is greater than that of Set A.

C.

The mode of the data in Set A is equal to that of the data in Set B.

D.

The mode of the data in Set A is greater than that of the data in Set B.

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Solution:
To calculate range, write the data values in order from least to greatest for each set:
		

Set A: 0.08; 0.28; 0.43; 1.18; 1.73; 1.93

		

Set B: 0.00; 0.00; 0.01; 0.04; 0.08; 0.20

Chapter 13
Data Analysis,
Statistics, and
Probability

Find the difference between the least and greatest value for each set:
		

Set A: Range = 1.93 – 0.08 = 1.85

		

Set B: Range = 0.20 – 0.00 – 0.20

The range in Set A is greater. The correct answer is choice A.

Peterson’s SAT® Prep Guide 2017

Comparing Data Sets Using Median and Mode
Using the same data sets about tropical precipitation, let’s look at problems involving median and mode.
Example:

Set A: Weeks 3–8 (January–February)
0.43

1.73

1.93

0.28

0.08

1.18

0.04

0.00

Set B: Weeks 29–34 (July–August)
0.20

0.01

0.00

0.08

Which is true about the two sets of data above?
A.

The mode of Set A is greater than the mode of Set B.

B.

The mode of Set B is greater than the mode of Set A.

C.

The median of Set A is greater than the median of Set B.

D.

The median of Set B is greater than the median of Set A.

Solution:

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Chapter 13

In this case, Set A does not have a mode, because there is no data value that appears more than once. So we cannot
make any statements involving the mode of Set A.
Calculate the median of both sets of data. The median is the number in the middle of a data set when all the values
are written in increasing order:

Data Analysis,
Statistics, and
Probability

Set A: 0.08 0.28 0.43 1.18 1.73 1.93
Here, the two middle numbers are 0.43 and 1.18, so we take their average:
Median of Set A: 0.43 + 1.18 = 1.61 = 0.805
2
2
We perform the same set of calculations for set B:
Set B: 0.00 0.00 0.01 0.04 0.08 0.20
Median of Set B: 0.01+ 0.04 = 0.05 = 0.025
2
2
From this we can see that the median of Set A is greater than the median of Set B. The correct answer is choice C.

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Evaluating Reports and Surveys
To evaluate a report about a set of data, it is important to consider the appropriateness of the data collection method.
Example:
A local politician wants to gauge how her constituents feel about the installation of a gas pipeline that will border
her district. Which of the following would allow the politician to make a valid conclusion about the opinions of her
constituents?
A.

Sending an electronic survey via e-mail

B.

Surveying people at several local movie theaters

C.

Surveying people at several local supermarkets

D.

Having people call in their opinion to a local radio show

Solution:
Let’s analyze each of these options. First is the e-mail survey in choice A. This may seem like a good option, but does
everyone in the district have an e-mail address? Will a representative group respond? Next, choice B is the option to
survey people at local movie theaters. This may work, but it would exclude people who don’t go to the movies on a
regular basis. Choice C is probably best because everyone eats, and the probability is high that most, if not all, people in
the politician’s district go to the supermarket at some point. Finally, choice D is not correct, because few people will listen
to any particular radio show, and even fewer will voluntarily call to voice their opinion. The correct answer is choice C.

When considering whether the data in a report is representative of a population, it is important to consider the demographics of
the population being studied. Their habits, behaviors, and perhaps incomes will influence their decisions and even their ability
to be included in the report. The type of survey that will include the widest range of habits, behaviors, and incomes of the people
being studied is likely the most representative.

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Peterson’s SAT® Prep Guide 2017

EXERCISES: STATISTICS
DIRECTIONS: Work out each problem. Circle the letter of your choice.
1.

The tables below show the number of employees in two different groups of an organization in different age ranges.

Production
Age Range

Number of Employees

20–24

4

25–29

8

30–34

25

35–39

19

40–44

17

Design
Age Range

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Chapter 13
Data Analysis,
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Probability

Number of Employees

20–24

2

25–29

4

30–34

6

35–39

33

40–44

38

Which of the following conclusions can be made about the data above?
A.

The range of ages is greater in production than in design.

B.

The range of ages is greater in design than in production.

C.

The median age is greater in production than in design.

D.

The median age is greater in design than in production.

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A nursery wants to know if a certain fertilizer is helping its rose bushes grow more roses per bush. The nursery uses the
fertilizer on one plot, Plot A, of rose bushes but does not use fertilizer on another plot, Plot B. All the rose bushes in both
plots were planted at the same time. The charts below show the number of flowers on each bush for the two plots.

Number of Flowers Per Bush

Plot A
10
8
6
4
2
0
1

2

3

4

5

6

7

8

9

10

Rose Bushes

Plot B
12
Number of Flowers Per Bush

2.

10

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8

Chapter 13

6

Data Analysis,
Statistics, and
Probability

4
2
0
1

2

3

4

5

6

7

8

9

10

Rose Bushes

Which of the following conclusions could be logically drawn based on the data?
A.

The mean number of roses in Plot A is greater, so plot A likely benefited from the fertilizer.

B.

The mean number of roses in Plot B is greater; so plot B likely benefited from NOT having the fertilizer.

C.

The fertilizer had no effect on the rose bushes.

D.

There is not enough information to make any conclusion.

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3.

4.

SHOW YOUR WORK HERE

If two 90% confidence intervals are of different sizes, then
the smaller interval provides a
A.

more precise estimate of the population mean.

B.

less precise estimate of the population mean.

C.

larger standard deviation.

D.

smaller standard deviation.

A property development company wants to see if a new
movie complex would be a profitable venture in a suburban area. The location is 15 miles away from an existing
movie complex in a region with approximately 650,000
residents with a mean age of 48. The company conducts
a survey of 200 people coming out of a midnight movie
on a Wednesday evening to see what they think of the
idea.
What can be said about this data collection method?

554

A.

The population surveyed is likely a good representative population.

B.

The survey probably didn’t include movie theater
employees.

C.

The sample is likely skewed toward people
younger than the mean.

D.

The sample is likely skewed toward
out-of-towners.

Chapter 13
Data Analysis,
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5.

A coffee retailer kept track of number of customers during the same 6-hour period over the course of two days and recorded
them in the table below.

1–2 p.m.

2–3 p.m.

3–4 p.m.

4–5 p.m.

5–6 p.m.

6–7 p.m.

Sunday

24

22

28

35

38

35

Monday

11

18

18

22

44

30

Which of the following is a valid conclusion to be
drawn from the data in the tables?
A.

The coffee shop is busier later in the day.

B.

There are probably never more than 50 customers
in the coffee shop.

C.

The average number of customers is higher on the
weekends than during the week.

D.

The range of data on the two days is equal.

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SHOW YOUR WORK HERE

6.

7.

8.

A farmer weighs eggs produced by his chickens. He
samples 36 eggs from a population of over 2,000 eggs.
The sample mean weight is 63.8 grams, with a sampling
error of 9.2 grams at a 90% confidence interval. Which of
the following is true, based on the sample?
A.

You can be 90% confident that another sample
will have a mean for the eggs between 54.6 and 73
grams.

B.

You can be 90% confident that the true population
mean for the eggs is between 54.6 and 73 grams.

C.

You can be 90% confident that the standard
deviation of each measurement is 9.2 grams.

D.

You can be 90% confident that the true population
mean is 63.8 grams.

SHOW YOUR WORK HERE

Using the same data from question 6, if you calculate a
90% confidence interval for the mean given a sample size
of 72 eggs, what is the effect?
A.

It increases the sample mean.

B.

It decreases the sample mean.

C.

It decreases the margin of error.

D.

It increases the margin of error.

The margin of error is +/– 20 points for a 95% confidence
interval for a given set of data. The researcher in charge
of the data wants to report a lower margin of error. Which
of the following would give a true representation of the
data and a lower margin of error?
A.

Increase the confidence level to 98%.

B.

Decrease the confidence level to 90%.

C.

Increase the sample size.

D.

Decrease the sample size.

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9.

10.

556

A poll was taken by the local university to determine
which candidate is most likely to win the upcoming
congressional race. The poll was conducted by randomly
talking to people walking downtown in the largest city
of the congressional district. Which of the following best
describes the poll?
A.

The poll is a representative sample because it was
done in the largest city in the district.

B.

The poll is a representative sample because it was
done randomly.

C.

The poll is not a representative sample because it
was done only in the largest city in the district.

D.

The poll is not a representative sample because it
was done randomly.

The double occupancy room rates at 40 five-star hotels in
Los Angeles is normally distributed with a mean of $280
and a standard deviation of $48.25. Which is the range
of values, in dollars, around the mean that includes 95%
of the room rates?
A.

$280.00–$328.25

B.

$231.75–$280.00

C.

$231.75–$328.25

D.

$183.50–$376.50

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SHOW YOUR WORK HERE

ANSWER KEY AND EXPLANATIONS

1.

2.

1. D

3. D

5. A

7. C

9. C

2. A

4. C

6. B

8. B

10. D

The correct answer is D. We don’t have exact ages,
which is why we can’t conclude anything about the
range of ages and can eliminate choices A and B. There
are 73 employees in the production group, so the
median age is the 37th data value when the ages are
written in ascending order, which would be in the
30–34 age range. There are 83 employees in the design
group. The median age is the 42nd data value, which
falls in the 35–39 age range. Thus the median age for
the design group is higher.

movie theater employees, choice B, is not relevant to
the validity of the data.
5.

The correct answer is A. It is difficult to conclude that
there are never more than 50 customers in the shop, as
choice B says, because we don’t have enough data. As
for choice C, while the mean for Sunday is higher than
the mean for Monday, the sample size of 2 days is not
enough to make a conclusion about the weekends
versus the weekdays in general. The range of the two
data sets are not equal to each other, so choice D is
incorrect.

6.

The correct answer is B. The confidence interval gives
us the ability to estimate a range for the true mean of
the population, not for a sample mean.

7.

The correct answer is C. The mean will likely be
different, but there is no reason to believe it will only
increase or only decrease. But, increasing sample size
decreases the margin of error.

The correct answer is A. First focus on the mean
number of roses on the bushes in Plot A:
6 + 6 + 4 + 5 + 9 + 5 + 5 + 8 + 5 + 4 57
=
10
10
= 5.7
Then, look at those in Plot B:
3 + 3 + 5 + 2 + 5 + 8 + 11+ 0 + 5 + 1 43
=
10
10
= 4.3

8.

The correct answer is B. The data has already been
collected, so increasing or decreasing the sample size
is not possible without redoing the study, and it would
not be an accurate representation of this data.
Decreasing the confidence level would decrease the
margin of error.

9.

The correct answer is C. A representative sample
should allow for random selection within the entire
population, not just random selection from one part of
the population.

10.

The correct answer is D. Ninety-five percent of the
rates fall within 2 standard deviations of the mean,
meaning within $48.25 × 2 = $96.50 of the mean
price of $280.00 and 280.00 + 96.50 = 376.50 and
280.00 – 96.50 = 183.50.

On average, the bushes in Plot A grew more roses and
so likely benefited from the fertilizer.
3.

4.

The correct answer is D. A 90% confidence interval
means that those who conducted the survey have
proved with 90% precision that the estimate for the
mean is within a given range, so eliminate choices A
and B. If the range of a confidence interval is less, then
the standard deviation is also less, so choice D is
correct.
The correct answer is C. People who are out after
midnight are probably younger than the mean age,
since they are not likely to be getting up early after a
late-night movie. It is probably not representative of
the general population. There is no reason to believe
the sample is skewed toward out-of-towners, choice D,
and 200 people is probably not a good sample size, so
choice A is incorrect. Whether the survey included

557
Chapter 13
Data Analysis,
Statistics, and
Probability

Peterson’s SAT® Prep Guide 2017

SUMMING IT UP
• Not all problems that deal with averages will ask you to solve for the average of a set of quantities.
• The trick when working with tables is to make sure you select the correct data needed to solve the problem.
• Take your time reading each table.
• Observe trends with scatterplots, and use lines or curves to predict unknown values.
• Read data representations carefully when comparing data sets.
• Pay attention to sampling methods when you evaluate survey data.
ONLINE
PREP

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Access more practice questions, helpful lessons, valuable tips, and expert strategies for the following data analysis, statistics, and
probability topics in Peterson’s SAT® Online Course:

• Data Interpretation
• Mean, Median, and Mode
• Percent Word Problems
• Ratios
• Word Problems
To purchase and access the course, go to www.petersons.com/sat.

558
Chapter 13
Data Analysis,
Statistics, and
Probability

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PART VII:
PRACTICE TESTS
®
FOR THE SAT
Chapter 14: SAT® Practice Tests

Chapter 14:
SAT® Practice Tests
OVERVIEW
Practice Test 1
Practice Test 2
Practice Test 3
Practice Test 4
Practice Test 5

INTRODUCTION TO THE PRACTICE TESTS
On test day, you will see these important reminders on the first page of your exam booklet:

• You must use a No. 2 pencil when taking the test; you may not use a pen or mechanical pencil.
• You may not share any questions with anyone. This is considered a violation of College Board’s“Test Security and Fairness”
policies, and it could cause your scores to be canceled.

• You are not permitted to take the test booklet out of the testing room.

561
Chapter 14

In addition to filling in your name and Test Center information on your answer sheet, you’ll be asked to fill in two different codes
that will be on your test booklet. Each test booklet has a unique code, and there will be a grid-in form to fill in with your “TEST
ID” and “FORM CODE” letters and numbers.

SAT ®
Practice
Tests

The general directions for the test will look something like this:

• You may only work on one section at a time.
• If you complete a section before time is called, check your work on that section only. You are not permitted to work on
any other section.
The directions for marking your answers will likely include the following recommendations:

•
•
•
•
•

Mark your answer sheet properly—be sure to completely fill in the answer circle.
Be careful to mark only one answer for each question.
Don’t make any stray marks on the answer sheet.
If you need to erase your answer, make sure you do so completely.
Be sure to use the answer spaces that correspond to the question numbers.

You will be able to use your test booklet for scratch work, but you won’t get credit for any work done in your test booklet. When
time is called at the end of each section, you will not be permitted to transfer answers from your test booklet to your answer sheet.

Peterson’s SAT® Prep Guide 2017

Any information, ideas, or opinions presented in any of the passages you will see on the exam that have been taken from other
sources or published material do not represent the opinions of the College Board.
Scoring on the exam is as follows:

• You will receive one point for each correct answer.
• You will not lose points for wrong answers, so you should attempt to answer every question even if you aren’t completely
sure of the correct answer.
Your testing supervisor will announce when to open the test booklet, so be sure to wait until you’re told to do so. For the purposes
of this practice test, be sure you have a timer to set for 65 minutes for the Section 1: Reading Test.
The answer sheets for each test section, including lined paper for the essay, appear on the next pages.
Following the Answer Key and Explanations for thes Practice Tests, you will find details on how to score your work.

Good
Luck!

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Practice
Tests

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Practice Test 1—Answer Sheet
Section 1: Reading Test
1.

12.

23.

33.

43.

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52.

11.

22.

Section 2: Writing and Language Test
1.

10.

19.

28.

37.

2.

11.

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29.

38.

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44.

9.

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27.

36.

Section 3: Math Test—No Calculator
1.

4.

7.

10.

13.

2.

5.

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11.

14.

3.

6.

9.

12.

15.

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Section 4: Math Test—Calculator
1.

7.

13.

19.

25.

2.

8.

14.

20.

26.

3.

9.

15.

21.

27.

4.

10.

16.

22.

28.

5.

11.

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29.

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/
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Practice Test 1—Answer Sheet
Section 5: Essay
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Practice Test 1—Answer Sheet

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Practice Test 1
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

Questions 1–10 are based on the following passage.
PASSAGE I
The following passage has been taken from the “The Bride Comes
to Yellow Sky,” by Stephen Crane. It is a western short story that was
first published in 1898. The protagonist is Jack Potter, who returns
to the town of Yellow Sky with his bride.
		 The great Pullman was whirling onward with such
dignity of motion that a glance from the window seemed
simply to prove that the plains of Texas were pouring
Line eastward. Vast flats of green grass, dull-hued spaces
5 of mesquite and cactus, little groups of frame houses,
woods of light and tender trees, all were sweeping into
the east, sweeping over the horizon, a precipice.
		 A newly married pair had boarded this coach at San
Antonio. The man’s face was reddened from many days
10 in the wind and sun, and a direct result of his new black
clothes was that his brick-colored hands were constantly
performing in a most conscious fashion. From time to
time he looked down respectfully at his attire. He sat
with a hand on each knee, like a man waiting in a bar15 ber’s shop. The glances he devoted to other passengers
were furtive and shy.
		 The bride was not pretty, nor was she very young.
She wore a dress of blue cashmere, with small reservations of velvet here and there, and with steel buttons
20 abounding. She continually twisted her head to regard
her puff sleeves, very stiff, straight, and high. They
embarrassed her. It was quite apparent that she had
cooked, and that she expected to cook, dutifully. The
blushes caused by the careless scrutiny of some pas25 sengers as she had entered the car were strange to see
upon this plain, under-class countenance, which was
drawn in placid, almost emotionless lines.

		 “Great! And then after a while we’ll go forward
to the diner, and get a big layout. Finest meal in the
world. Charge a dollar.”
		

“Oh, do they?” cried the bride. “Charge a dollar?

35 Why, that’s too much—for us—ain’t it Jack?”

		 “Not this trip, anyhow,” he answered bravely.
“We’re going to go the whole thing.”
		 Later he explained to her about the trains. “You
see, it’s a thousand miles from one end of Texas to
40 the other; and this train runs right across it, and
never stops but for four times.” He had the pride of
an owner. He pointed out to her the dazzling fittings
of the coach, and in truth her eyes opened wider as
she contemplated the sea-green figured velvet, the
45 shining brass, silver, and glass, the wood that gleamed
as darkly brilliant as the surface of a pool of oil. At
one end a bronze figure sturdily held a support for a
separated chamber, and at convenient places on the
ceiling were frescoes in olive and silver.
50 		

To the minds of the pair, their surroundings
reflected the glory of their marriage that morning in
San Antonio. This was the environment of their new
estate; and the man’s face in particular beamed with
an elation that made him appear ridiculous to the
55 negro porter. This individual at times surveyed them
from afar with an amused and superior grin. On other
occasions he bullied them with skill in ways that did
not make it exactly plain to them that they were being
bullied. He subtly used all the manners of the most
60 unconquerable kind of snobbery. He oppressed them,
but of this oppression they had small knowledge,
and they speedily forgot that infrequently a number
of travelers covered them with stares of derisive
enjoyment. Historically, there was supposed to be
65 something infinitely humorous in their situation.

		 They were evidently very happy. “Ever been in a
parlor-car before?” he asked, smiling with delight.
30 		

“No,” she answered; “I never was. It’s fine, ain’t it?”

CONTINUE
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Practice Test 1
1

The passage might best be described as
A.

2

3

4

5

  570

6

Which choice provides the best evidence for the answer
to the previous question?

an analysis of a man’s acceptance of his social
status.

A.

Lines 4–7 (“Vast flats . . . precipice.”)

B.

an account of a couple’s anticipation of married life.

B.

Lines 12–16 (“From time . . . furtive and shy.)

C.

a description of train travel in nineteenth-century
Texas.

C.

Lines 30–33 (“‘No,’ she . . . a dollar’.”)

D.

Lines 50–55 (“To the . . . negro porter”)

D.

a criticism of class consciousness in the nineteenth
century.

7

It can be inferred from the passage that Jack

In lines 23–27 (“The blushes . . . emotionless lines.”), why
does the narrator note that the bride’s blushing seemed
so out of place on her face?

A.

wants to impress his new bride.

A.

B.

is likely a farmhand or rancher.

To emphasize the degree to which other passengers are staring

C.

is used to being treated as an inferior.

B.

To express the bride’s extreme happiness with her
marriage

D.

wants to change his station in life.

C.

To communicate that the bride is lacking in
self-confidence

D.

To underscore that the bride is strikingly
unattractive

Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 12–15 (“From time . . . barber’s shop.”)

B.

Lines 17–22 (“The bride . . . embarrassed her.”)

C.

Lines 31–37 (“‘Great! . . . whole thing.”)

A.

project.

D.

Lines 50–55 (“To the . . . negro porter.”)

B.

interests.

C.

property.

D.

standing.

8

As used in line 2, “dignity” most nearly means
A.

splendor.

B.

respectability.

C.

superiority.

D.

gracefulness.

9

As used in line 53, “estate” most nearly means

In lines 55–64 (“This individual . . . derisive enjoyment.”),
the narrator maintains that the
A.

porter mocks the couple, making Jack and his bride
believe they are being catered to.

Jack and his bride might best be described as

B.

couple barely notices the contemptuous way they
are treated by the porter.

A.

firm and resolute in their decisions.

C.

B.

nervous and fearful about their trip.

porter is openly hostile to the couple, making the
trip painful for them.

C.

awkward and self-conscious in the setting.

D.

D.

amazed and bewildered by the landscape.

couple has become used to the rude behavior of
the porter.

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Practice Test 1
10 What is the main rhetorical effect of lines 10–13 (“and a . . .
his attire”)?
A.

To illustrate how nervous and awkward the
groom is

B.

To show how much the groom is used to using his
hands

C.

To convey how unaccustomed the groom is to
wearing dress clothes

D.

To show how happy the groom is about being
married

Questions 11–21 are based on the following passage.
The following passage has been taken from American Ornithology
by Alexander Wilson, a Scottish-American naturalist. Dubbed “the
Father of American Ornithology,” Wilson is regarded as the greatest
American ornithologist after Audubon. His nine-volume American
Ornithology was published between 1808 and 1814.

Line
5

10

15

20

25

30

		 About the twenty-fifth of April the Hummingbird
usually arrives in Pennsylvania; and about the tenth of
May begins to build its nest. This is generally fixed on
the upper side of a horizontal branch, not among the
twigs, but on the body of the branch itself. Yet I have
known instances where it was attached by the side to
an old moss-grown trunk; and others where it was fastened on a strong rank stalk, or weed, in the garden; but
these cases are rare. In the woods it very often chooses
a white oak sapling to build on; and in the orchard, or
garden, selects a pear tree for that purpose. The branch
is seldom more than ten feet from the ground. The nest is
about an inch in diameter, and as much in depth. A very
complete one is now lying before me, and the materials
of which it is composed are as follows: —The outward
coat is formed of small pieces of bluish grey lichen that
vegetates on old trees and fences, thickly glued on with
the saliva of the bird, giving firmness and consistency
to the whole, as well as keeping out moisture. Within
this are thick matted layers of the fine wings of certain
flying seeds, closely laid together; and lastly, the downy
substance from the great mullein, and from the stalks of
the common fern, lines the whole. The base of the nest
is continued round the stem of the branch, to which it
closely adheres; and, when viewed from below, appears
a mere mossy knot or accidental protuberance. The
eggs are two, pure white, and of equal thickness at both
ends. . . . On a person’s approaching their nest, the little
proprietors dart around with a humming sound, passing
frequently within a few inches of one’s head; and should
the young be newly hatched, the female will resume her

place on the nest even while you stand within a yard or
two of the spot. The precise period of incubation I am
unable to give; but the young are in the habit, a short
35 time before they leave the nest, of thrusting their bills
into the mouths of their parents, and sucking what they
have brought them. I never could perceive that they
carried them any animal food; tho, from circumstances
that will presently be mentioned, I think it highly
40 probable they do. As I have found their nest with eggs
so late as the twelfth of July, I do not doubt but that they
frequently, and perhaps usually, raise two broods in the
same season.
45

50

55

60

65

70

75

		 The hummingbird is extremely fond of tubular
flowers, and I have often stopt, with pleasure, to observe
his maneuvers among the blossoms of the trumpet
flower. When arrived before a thicket of these that are full
blown, he poises, or suspends himself on wing, for the
space of two or three seconds, so steadily, that his wings
become invisible, or only like a mist; and you can plainly
distinguish the pupil of his eye looking round with great
quickness and circumspection; the glossy golden green
of his back, and the fire of his throat, dazzling in the sun,
form altogether a most interesting appearance. The
position into which his body is usually thrown while in
the act of thrusting his slender tubular tongue into the
flower, to extract its sweets, is exhibited in the figure
on the plate. When he alights, which is frequently, he
always prefers the small dead twigs of a tree, or bush,
where he dresses and arranges his plumage with great
dexterity. His only note is a single chirp, not louder than
that of a small cricket or grasshopper, generally uttered
while passing from flower to flower, or when engaged
in fight with his fellows; for when two males meet at
the same bush, or flower, a battle instantly takes place;
and the combatants ascend in the air, chirping, darting
and circling around each other, till the eye is no longer
able to follow them. The conqueror, however, generally
returns to the place, to reap the fruits of his victory. I
have seen him attack, and for a few moments tease the
King-bird; and have also seen him, in his turn, assaulted
by a humble-bee, which he soon put to flight. He is one
of those few birds that are universally beloved; and
amidst the sweet dewy serenity of a summer’s morning,
his appearance among the arbours of honeysuckles, and
beds of flowers, is truly interesting.

CONTINUE
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Practice Test 1
11 The author is mostly concerned with
A.

describing the characteristics of the hummingbird.

B.

explaining how hummingbirds build their nests.

C.

convincing the reader that hummingbirds are
interesting.

D.

interpreting the meaning of certain hummingbird
behaviors.

16 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 28–33 (“On a person’s . . . the spot.”)

B.

Lines 33–37 (“The precise . . . brought them.”)

C.

Lines 37–40 (“I never . . . they do.”)

D.

Lines 61–64 (“His only . . . with his fellows;”)

17 As it is used in line 60, “dresses” most nearly means
12 Based on lines 1–3 (“About the twenty-fifth of April . . . to
build its nest.”), it can generally be assumed that hummingbirds

oils.

B.

dons.

A.

take two weeks to build their nests.

C.

shuffles.

B.

migrate elsewhere for the winter.

D.

neatens.

C.

cannot be found in places farther north.

D.

are mostly solitary animals.

13 As used in line 3, “fixed” most nearly means
A.

adjusted.

B.

intended.

C.

aligned.

D.

secured.

14 In lines 13–26 (“A very complete one . . . accidental
protuberance.”), the author is mainly concerned with
how the hummingbird

18 In lines 49–50, the author notes that the hummingbird’s
“wings become invisible, or only like a mist” to
A.

show how transparent the wings are.

B.

emphasize how fast the wings are moving.

C.

point out that the sun reflects off the wings.

D.

reiterate that the hummingbird is beautiful.

19 In lines 68–69 (“The conqueror . . . fruits of his victory.”),
“fruits of his victory” refers to
A.

the dead twigs of a tree.

B.

Lines 58–61 (“When he alights, . . . dexterity.”)

A.

uses nearby plants in the nest.

C.

Lines 63–65 (“passing from . . . or flower”)

B.

builds compact, complicated nests.

D.

the other combatant.

C.

builds the nest over a period of time.

D.

constructs a nest that is waterproof.

15 It can be inferred from the passage that hummingbirds

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A.

A.

stay in the nest for years at a time.

B.

builds compact, complicated nests.

C.

builds the nest over a period of time.

D.

feed only on the sweet nectar of flowers.

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20 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 1–3 (“About the twenty-fifth . . . its nest.”)

B.

Lines 58–61 (“When he alights, . . . dexterity.”)

C.

Lines 63–65 (“passing from, . . . or flower.”)

D.

Lines 66–68 (“and the combatants . . . follow them.”)

Practice Test 1
21 The author most likely references the kingbird in lines
69–71 (“I have seen . . . King-bird.”) to
A.

highlight the many dangers that confront
hummingbirds.

B.

describe how the hummingbird stays close to its
nest.

C.

emphasize that the hummingbird is an aggressive
bird.

D.

introduce the idea that the hummingbird does not
only fight for self-defense.

Questions 22–31 are based on the following passage and
supplementary material.
The passage is excerpted from information provided by the
National Oceanic and Atmospheric Administration (NOAA) at
http://www.noaa.gov.
		 Over half a mile taller . . . than Mt. Everest, Mauna
Kea in Hawai’i is more than 6 miles tall, from its base
on the ocean floor to its summit two miles above the
Line surface of the Pacific Ocean. This island mountain is only
5 one of many features found on the ocean floor. Besides
being the base for islands, the ocean floor also includes
continental shelves and slopes, canyons, oceanic ridges,
trenches, fracture zones, abyssal hills, abyssal plains,
volcanoes, and seamounts. Not just rock and mud, these
10 locations are the sites of exotic ecosystems that have
rarely been seen or even explored.
Plate Tectonics and the Ocean Floor
		 The shape of the ocean floor, its bathymetry, is
largely a result of a process called plate tectonics. The
outer rocky layer of the Earth includes about a dozen
15 large sections called tectonic plates that are arranged
like a spherical jigsaw puzzle floating on top of the
Earth’s hot flowing mantle. Convection currents in the
molten mantle layer cause the plates to slowly move
about the Earth a few centimeters each year. Many ocean
20 floor features are a result of the interactions that occur
at the edges of these plates.
		 The shifting plates may collide (converge), move
away (diverge), or slide past (transform) each other. As
plates converge, one plate may dive under the other,
25 causing earthquakes, forming volcanoes, or creating
deep ocean trenches such as the Mariana Trench. Where
plates are pulled away (diverge) from each other, molten
magma flows upward between the plates, forming
mid-ocean ridges, underwater volcanoes, hydrothermal

30 vents, and new ocean floor crust. The Mid-Atlantic Ridge

is an example of this type of plate boundary. . . .
Marine Life and Exploration on the Ocean Floor
		 Over the last decade, more than 1500 new species
have been discovered in the ocean by marine biologists and other ocean scientists. Many of these newly
35 discovered species live deep on the ocean floor in
unique habitats dependent on processes resulting from
plate movement, underwater volcanoes, and cold water
seeps. The discovery of deep ocean hydrothermal vent
ecosystems in 1977 forced scientists to redefine living
40 systems on our planet. Considered one of the most
important scientific discoveries of the last century,
organisms in this deep, dark ecosystem rely on chemicals
and a process called chemosynthesis as the base of their
food web and not on sunlight and photosynthesis as in
45 other previously described ecosystems. . . .
		 Hydrothermal vents form along mid-ocean ridges,
in places where the sea floor moves apart very slowly (6
to 18 cm per year) as magma wells up from below. (This
is the engine that drives Earth’s tectonic plates apart,
50 moving continents and causing volcanic eruptions and
earthquakes.) When cold ocean water seeps through
cracks in the sea floor to hot spots below, hydrothermal
vents belch a mineral-rich broth of scalding water.
Sometimes, in very hot vents, the emerging fluid turns
55 black, creating a “black smoker,” because dissolved sulfides of metals (iron, copper, and several heavy metals)
instantaneously precipitate out of solution when they
mix with the cold surrounding seawater.
		

Unlike plants that rely on sunlight, bacteria living

60 in and around the dark vents extract their energy from

hydrogen sulfide (HS) and other molecules that billow
out of the seafloor. Just like plants, the bacteria use their
energy to build sugars out of carbon dioxide and water.
Sugars then provide fuel and raw material for the rest of
65 the microbes’ activities.
Why Is Chemosynthesis Important?
		 Chemosynthetic deep-sea bacteria form the base
of a varied food web that includes shrimp, tubeworms,
clams, fish, crabs, and octopi. All of these animals must
be adapted to endure the extreme environment of the
70 vents—complete darkness; water temperatures ranging
from 2°C (in ambient seawater) to about 400°C (at the
vent openings); pressures hundreds of times that at
sea level; and high concentrations of sulfides and other
noxious chemicals.

CONTINUE
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Practice Test 1
Why is photosynthesis important?
75 Aquatic and terrestrial plants form the base of varied food webs

that may include small fish and crabs, larger fish, and eventually,
humans.

plume
of black
‘smoke’
black
smoker
chimneys
containing
sulphides
cold
seawater

100 m

hydrothermal fluids
enter ocean at
up to 350°C
or more

cold
seawater
(typically
2–4°C)

sulphides
metalliferous
deposited
in cracks
sediment
and veins
(stockwork)
oceanic
crust
high permeability

seawater
leaching of
metal ions
from rock

low permeability

seawater

high-temperature
reaction zone
heat from magma

22 Which best describes the function of the opening sentence
(“Over half a mile taller . . . the Pacific Ocean.”)?

  574

A.

It shows how unusual and extraordinary some
ocean features are.

B.

It emphasizes that Mt. Everest is not the world’s
tallest mountain.

C.

It describes the geography of island mountains in
the Pacific Ocean.

D.

It compares the geography of Mt. Everest to that of
Mauna Kea.

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23 The author uses the simile “like a spherical jigsaw puzzle”
(line 16) to illustrate that
A.

each plate plays a critical role.

B.

the earth is sphere-shaped.

C.

each plate is symmetrical.

D.

the plates fit together.

Practice Test 1
24 The movement of the earth’s tectonic plates is a
function of

28 The author devotes the first half of the passage to an
explanation of plate tectonics in order to

A.

earthquakes and volcanoes.

A.

describe the geography of the ocean floor.

B.

the movement of ocean tides.

B.

C.

new ocean floor crust.

explain the conditions that create hydrothermal
vents.

D.

the moving molten mantle layer.

C.

compare hydrothermal vents to underwater
volcanoes.

D.

argue that hydrothermal vents are a unique
ecosystem.

25 Which inference can you make about scientists’ pre-1977
understanding of deep ocean hydrothermal vent ecosystems?
A.

Scientists did not know how organisms in deep
ocean hydrothermal vent ecosystems survived.

B.

Scientists believed that colliding plates caused the
formation of deep ocean hydrothermal vents.

C.

D.

Scientists determined that some sea life can move
easily between shallow waters and deep ocean
hydrothermal vent ecosystems.
Scientists believed minerals could be mined from
deep ocean hydrothermal vent ecosystems.

26 Which choice provides the best evidence for the answer
to the previous question?

29 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 5–9 (“Besides being . . . and seamounts.”)

B.

Lines 34–38 (“Many of . . . water seeps.”)

C.

Lines 46–48 (“Hydrothermal vents . . . from below.”)

D.

Lines 48–51 (“This is the engine . . . and
earthquakes.”)

30 As used in line 74, “noxious” most nearly means
A.

annoying.

B.

harmful.

A.

Lines 32–34 (“Over the . . . ocean scientists.”)

C.

offensive.

B.

Lines 40–44 (“Considered one . . . web.”)

D.

unusual.

C.

Lines 46–48 (“Hydrothermal vents . . . from below.”)

D.

Lines 54–58 (“Sometimes, in . . . surrounding
seawater.”)

27 As it is used in line 61, “billow” most nearly means

31 Based on the diagram, what happens to the sulfides inside
the black smoker?
A.

They are carried by ocean currents.

B.

They are pushed out into the atmosphere.

A.

flow.

C.

They remain inside of the black smoker’s veins.

B.

crest.

D.

They drop back into the black smoker.

C.

wave.

D.

inflate.

CONTINUE
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Practice Test 1
Questions 32–42 are based on the following passage
and supplementary material.
The passage is an excerpt from “How the Other Half Lives,” by Jacob
Riis. It was published in 1890 and documented the squalid living
conditions in the tenements of New York City.
		 The old question, what to do with the boy, assumes
a new and serious phase in the tenements. Under the
best conditions found there, it is not easily answered.
Line In nine cases out of ten he would make an excellent
5 mechanic, if trained early to work at a trade, for he is
neither dull nor slow, but the short-sighted despotism
of the trades unions has practically closed that avenue
to him. Trade-schools, however excellent, cannot supply
the opportunity thus denied him, and at the outset the
10 boy stands condemned by his own to low and ill-paid
drudgery, held down by the hand that of all should labor
to raise him.

15

20

25

30

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		 Home, the greatest factor of all in the training of
the young, means nothing to him but a pigeon-hole
in a coop along with so many other human animals. Its
influence is scarcely of the elevating kind, if it have any.
The very games at which he takes a hand in the street
become polluting in its atmosphere. With no steady
hand to guide him, the boy takes naturally to idle ways.
Caught in the street by the truant officer, or by the
agents of the Children’s Societies, peddling, perhaps, or
begging, to help out the family resources, he runs the
risk of being sent to a reformatory, where contact with
vicious boys older than himself soon develop the latent
possibilities for evil that lie hidden in him. The city has
no Truant Home in which to keep him, and all efforts
of the children’s friends to enforce school attendance
are paralyzed by this want. The risk of the reformatory
is too great. What is done in the end is to let him take
chances—with the chances all against him. The result is
the rough young savage, familiar from the street. Rough

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as he is, if any one doubt that this child of common clay
have in him the instinct of beauty, of love for the ideal of
which his life has no embodiment, let him put the matter
35 to the test. Let him take into a tenement block a handful
of flowers from the fields and watch the brightened
faces, the sudden abandonment of play and fight that
go ever hand in hand where there is no elbow-room,
the wild entreaty for “posies,” the eager love with which
40 the little messengers of peace are shielded, once possessed; then let him change his mind. I have seen an
armful of daisies keep the peace of a block better than
a policeman and his club, seen instincts awaken under
their gentle appeal, whose very existence the soil in
45 which they grew made seem a mockery. . . .
		 Yet, as I knew, that dismal alley with its bare brick
walls, between which no sun ever rose or set, was
the world of those children. It filled their young lives.
Probably not one of them had ever been out of the sight
50 of it. They were too dirty, too ragged, and too generally
disreputable, too well hidden in their slum besides, to
come into line with the Fresh Air summer boarders.
		 With such human instincts and cravings, forever
unsatisfied, turned into a haunting curse; with appetite
55 ground to keenest edge by a hunger that is never fed,
the children of the poor grow up in joyless homes to
lives of wearisome toil that claims them at an age when
the play of their happier fellows has but just begun. Has
a yard of turf been laid and a vine been coaxed to grow
60 within their reach, they are banished and barred out
from it as from a heaven that is not for such as they. I
came upon a couple of youngsters in a Mulberry Street
yard a while ago that were chalking on the fence their
first lesson in “writin’.”
65 		

And this is what they wrote: “Keeb of te Grass.” They
had it by heart, for there was not, I verily believe, a green
sod within a quarter of a mile. Home to them is an empty
name.

Practice Test 1
32 The passage is mainly concerned with establishing that
A.

there are very few job opportunities available for
poor people.

B.

the condition of the tenements condemns children
to lives of misery.

C.

more education is needed to help elevate the
children of the poor.

D.

children who live in poverty naturally turn to crime
to support themselves.

33 As it is used in line 18, “polluting” most nearly means

6 37

As it is used in line 19, “idle” most nearly means
A.

unproductive.

B.

vain.

C.

immature.

D.

simple.

38 The author suggests taking flowers to the tenement child
to show that
A.

he has the capacity to appreciate exquisite things.

B.

he is always bored and will play with anything.

A.

dirty.

C.

there are few flowers growing in the tenements.

B.

dangerous.

D.

the policemen patrolling the tenements are brutal.

C.

corrupting.

D.

rowdy.

34 In line 10, “condemned by his own” means that the boy is
A.

denounced because of his character.

B.

criticized by his family members.

C.

held back by his own community.

D.

ridiculed by teachers in his school.

35 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 17–18 (“The very . . . atmosphere.”)

B.

Lines 20–21 (“Caught . . . Societies”)

C.

Lines 25–26 (“The city . . . keep him”)

D.

Lines 29–30 (“What is done . . . against him.”)

36 In lines 14–15, the author uses the metaphor of the pigeon
coop to establish that the tenement is
A.

as filthy as a cage in which animal are kept.

B.

completely devoid of privacy for its tenants.

C.

the only housing available for any person.

D.

merely a place to live and lacks any positive
influences.

39 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 30–31 (“The result . . . the street.”)

B.

Lines 31–35 (“Rough as . . . the test.”)

C.

Lines 41–45 (“I have . . . a mockery.”)

D.

Lines 46–48 (“Yet, as . . . those children.”)

40 The photos suggest which of the following statements
about tenements that the author did not address?
A.

Tenements are extremely unsanitary.

B.

Tenements are joyless.

C.

Tenement are dangerous.

D.

Tenement offer no job opportunities.

41 The author provides the story of the “writin’” in the last
paragraph to show that tenement children
A.

do not know how to spell.

B.

are in need of good schools.

C.

have no access to green spaces.

D.

are prone to vandalism.

CONTINUE
Peterson's SAT® Prep Guide 2017

  577

Practice Test 1
42 The author suggests in lines 25–28 that a truant home
A.

is no different from a reformatory.

B.

does not enforce school attendance.

C.

is full of vicious young boys.

D.

is necessary but unavailable.

Questions 43–52 are based on the following two passages.
Passage 1 is a letter written by Robert Schumann to Clara Wieck
in 1838.

		 You cannot think how your letter has raised and
strengthened me. . . . You are splendid, and I have much
more reason to be proud of you than of me. I have made
up my mind, though, to read all your wishes in your face.
35 Then you will think, even though you don’t say it, that
your Robert is a really good sort, that he is entirely yours,
and loves you more than words can say. You shall indeed
have cause to think so in the happy future. I still see you
as you looked in your little cap that last evening. I still
40 hear you call me du. Clara, I heard nothing of what you
said but that du. Don’t you remember?
PASSAGE 2
Napoleon Bonaparte to
Josephine Bonaparte (1796)

Passage 2 is a letter from Napoleon Bonaparte to his wife Josephine,
written in 1796.
PASSAGE 1
Robert Schumann to Clara Wieck (1838)

Line
5

10

15

20

25

30

  578

		 I have a hundred things to write to you, great
and small, if only I could do it neatly, but my writing
grows more and more indistinct, a sign, I fear, of heart
weakness. There are terrible hours when your image
forsakes me, when I wonder anxiously whether I have
ordered my life as wisely as I might, whether I had any
right to bind you to me, my angel, or can really make you
as happy as I should wish. These doubts all arise, I am
inclined to think, from your father’s attitude towards me.
It is so easy to accept other people’s estimate of oneself.
Your father’s behaviour makes me ask myself if I am really
so bad—of such humble standing—as to invite such
treatment from anyone. Accustomed to easy victory over
difficulties, to the smiles of fortune, and to affection, I
have been spoiled by having things made too easy for
me, and now I have to face refusal, insult, and calumny.
I have read of many such things in novels, but I thought
too highly of myself to imagine I could ever be the hero
of a family tragedy of the Kotzebue sort myself. If I had
ever done your father an injury, he might well hate me;
but I cannot see why he should despise me and, as you
say, hate me without any reason. But my turn will come,
and I will then show him how I love you and himself; for
I will tell you, as a secret, that I really love and respect
your father for his many great and fine qualities, as no
one but yourself can do. I have a natural inborn devotion
and reverence for him, as for all strong characters, and
it makes his antipathy for me doubly painful. Well, he
may some time declare peace, and say to us, “Take each
other, then.”

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45

50

55

60

65

		 I have not spent a day without loving you; I have not
spent a night without embracing you; I have not so much
as drunk a single cup of tea without cursing the pride
and ambition which force me to remain separated from
the moving spirit of my life. In the midst of my duties,
whether I am at the head of my army or inspecting the
camps, my beloved Josephine stands alone in my heart,
occupies my mind, fills my thoughts. If I am moving away
from you with the speed of the Rhône torrent, it is only
that I may see you again more quickly. If I rise to work in
the middle of the night, it is because this may hasten by
a matter of days the arrival of my sweet love. Yet in your
letter of the 23rd and 26th Ventôse, you call me vous.
Vous yourself! Ah! wretch, how could you have written
this letter? How cold it is! And then there are those four
days between the 23rd and the 26th; what were you
doing that you failed to write to your husband? . . . Ah,
my love, that vous, those four days make me long for
my former indifference. Woe to the person responsible!
May he, as punishment and penalty, experience what my
convictions and the evidence (which is in your friend’s
favour) would make me experience! Hell has no torments
great enough! Vous! Vous! Ah! How will things stand in
two weeks? . . . My spirit is heavy; my heart is fettered
and I am terrified by my fantasies. . . . You love me less;
but you will get over the loss. One day you will love me
no longer; at least tell me; then I shall know how I have
come to deserve this misfortune. …

43 Both passages are primarily concerned with the subject of
A.

jealousy.

B.

commitment.

C.

work.

D.

being apart.

Practice Test 1
44 As it is used in line 28, “antipathy” most nearly means

49 As it is used in line 52, “hasten” most nearly means

A.

indifference.

A.

stretch out.

B.

mistrust.

B.

speed up.

C.

rudeness.

C.

force.

D.

dislike.

D.

cause.

45 We can infer from Passage 1 that Clara’s father’s feelings
about Robert have caused Robert to

50 We can infer that Clara’s letter to Robert was different from
Josephine’s letter to Napoleon in that Clara’s letter

A.

dislike Clara’s father.

A.

made Robert doubt himself.

B.

question his and Clara’s future.

B.

made Robert question her loyalty.

C.

doubt Clara’s love for him.

C.

left Robert feeling encouraged.

D.

question Clara’s character.

D.

left Robert feeling confused.

46 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 4–9 (“There are . . . towards me.”)

B.

Lines 11–13 (“Your father’s . . . from anyone.”)

C.

Lines 22–26 (“But my . . . can do.”)

D.

Lines 35–37 (“Then you . . . can say.”)

51 In each passage, the author recollects something his beloved said. But the effect of Josephine’s words (lines 53–56)
differ from the effect of Clara’s words (lines 39–41) in that
A.

Josephine’s words have hurt Napoleon.

B.

Clara’s words have offended Robert.

C.

Josephine’s words have calmed Napoleon.

D.

Clara’s words have humbled Robert.

47 Napoleon’s letter to Josephine suggests that she
52 We can infer that both Robert and Napoleon
A.

wishes she could fight alongside her husband.

B.

has little to occupy her time.

C.

is distracting him from his responsibilities.

D.

has never regretted her marriage to him.

A.

are modest people.

B.

anger quickly.

C.

tend to be indecisive.

D.

suffer from self-doubt.

48 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 42–43 (“I have . . . you”)

B.

Lines 43–46 (“I have . . . my life.”)

C.

Lines 46–48 (“In the . . . heart”)

D.

Lines 49–51 (“If I . . . quickly.”)

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
Peterson's SAT® Prep Guide 2017

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Practice Test 1
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you
will need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you
to consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).
Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.
After reading each passage, select the answer to each question that most effectively improves the quality of writing in the
passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following passage.
Burma: has it truly changed?
A rigid red-and-white sign 1 erected on a rural road in

1

Burma reads, “[The Military] AND THE PEOPLE IN ETERNAL

A.

NO CHANGE

B.

born

It’s no wonder that Burma, also known as Myanmar, inspired

C.

floated

two of the most well-known books about totalitarianism: 2

D.

dripped

the British Imperial Police Force in the 1920s. Five years after

A.

NO CHANGE

Eric Arthur Blair began his tour of duty in the far-flung, 3

B.

Animal Farm and Nineteen Eighty-Four.

obscure Asian colony, he returned to his homeland, shed his

C.

Animal Farm and Nineteen Eighty-Four,

uniform, changed his name to George Orwell, and started a

D.

Animal Farm and Nineteen Eighty-Four!

A.

NO CHANGE

B.

darkened

C.

obvious

D.

uncertain

UNITY. ANYONE ATTEMPTING TO DIVIDE THEM IS OUR ENEMY.”

Animal Farm and Nineteen Eighty-Four? The books sprang from
the mind of a man who, as a teenager, sought adventure with

2

new career as a novelist.
3

CONTINUE
Peterson's SAT® Prep Guide 2017

  581

Practice Test 1
The contrasts Orwell saw still exist. This land of haunting

4

beauty, with its history of human rights violations, 4 had
also sparked filmmaker Ron Fricke’s imagination. He and his
crew traveled to 25 countries to shoot images for his nonverbal film Samsara (2013). Samsara means “the ever-turning
wheel of life” in Sanskrit. The sequences shot in Bagan, Burma,
are almost dreamlike in quality, especially because, as in the

A.

NO CHANGE

B.

have also sparked

C.

also sparked

D.

will also spark

A.

NO CHANGE

B.

As they seemingly float above seas of green foliage,
only music accompanies scenes of hundreds of
Buddhist temples.

C.

Only music accompanies scenes, as they seemingly
float above seas of green foliage, of hundreds of
Buddhist temples.

D.

Only music accompanies scenes, of hundreds of
Buddhist temples, as they seemingly float above a
sea of green foliage.

A.

NO CHANGE

B.

the countries major industries

C.

the countrys major industries

D.

the countries’ major industries

5

rest of the film, there is no dialogue or narration. 5 Only
music accompanies scenes of hundreds of Buddhist temples
as they seemingly float upon seas of green foliage. Watching
these scenes, it is hard to believe that Burma has seen violent
years of civil war, ethnic cleansing, and forced labor. But
such problems, as well as those of economic stagnation
and corruption, can usually be traced back to the military
regime, which took power in 1962 through a coup. The
military manages 6 the country’s major industries and has
also been accused of controlling Burma’s substantial heroin
exports.

6

The Irish rock band U2 dedicated their song “Walk On”
to Burmese academic Aung San Suu Kyi, who was under
house arrest from 1989 until 2010 because of her prodemocracy stance. 7 The members of U2 have a history
of incorporating their political views into their music. Her
National League for Democracy (NLD) won the 1990 elections
with an overwhelming majority, but she was not allowed to
serve.

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7

The writer is considering deleting the underlined sentence.
Should the writer do this?
A.

Yes, because the sentence does not support the
main idea of the paragraph.

B.

Yes, because the sentence should be moved to the
beginning of the paragraph.

C.

No, because the sentence expands upon the main
idea of the paragraph.

D.

No, because the sentence introduces an important
detail about Burma.

Practice Test 1
8 An honor given out, in 1991 given out to people, by the

8

Nobel Committee since 1901, and organizations, she received

Which of the following most effectively presents the ideas
in this sentence?

the Nobel Peace Prize.

A.

NO CHANGE

B.

In 1991 she received the Nobel Peace Prize, an
honor given out to people and organizations by the
Nobel Committee since 1901.

C.

The Nobel Peace Prize, since 1901 by the Nobel
Committee, she received in 1991, an honor given
out to people and organizations.

D.

Given out to people, an honor in 1991, since 1901
and organizations, the Nobel Peace Prize she
received, and organizations.

A.

NO CHANGE

B.

Not surprisingly, the album was banned. Anyone
caught attempting to smuggle it into the country
would have been imprisoned for three to twenty
years.

C.

Not surprisingly, the album was banned and not
allowed to be distributed in Burma. Anyone caught
attempting to smuggle it into the country would
have been imprisoned for three to twenty years.

D.

Not surprisingly, the album was banned from
things that could be smuggled into Burma. Anyone
caught attempting to obtain it in the country
would have been imprisoned for three to twenty
years.

A.

NO CHANGE

B.

offering her

C.

offer them

D.

offered it

A.

NO CHANGE

B.

its isolation

C.

our isolation

D.

your isolation

The lyrics of U2’s song are about doing what’s right, even if it
requires personal sacrifice. 9 Not surprisingly, the album
was banned and not allowed to be distributed in Burma.
Anyone caught attempting to smuggle it into the country
would have been imprisoned for three to twenty years for
smuggling.
Military rule supposedly ended in 2011. Then-Secretary of
State Hillary Clinton visited in 2011 and President Obama

9

in 2012. Soon after, the European Union lifted sanctions
against Burma and 10 offering them financial aid. There are
signs that the country is emerging from 11 their isolation.
However, it’s too soon to be sure that the people of this land
are finally free of the ever-watching gaze of Big Brother.

10

11

CONTINUE
Peterson's SAT® Prep Guide 2017

  583

Practice Test 1
Questions 12–22 are based on the following passage.

12 Which choice provides the most relevant detail?

John Dewey and Education

A.

NO CHANGE

B.

sometimes called “the father of public education,”

C.

the son of a grocer in Burlington, Vermont,

D.

a university professor who taught ethics and logic,

Perhaps no one has written more widely on the subject in

A.

NO CHANGE

the United States than John Dewey, 12 a philosopher and

B.

as a social act, and the classroom, or learning
environment, as a replica of society

C.

as a social act and the classroom or learning
environment as a replica of society

D.

as a social act and the classroom, or learning
environment, as a replica of society

beings needed to maintain themselves through a process

A.

NO CHANGE

of renewal. Therefore, just as humans needed 15 sleep;

B.

it was

food; water; and shelter for physiological renewal, they also

C.

we were

needed education to renew their minds, assuring that their

D.

he was

A.

NO CHANGE

B.

sleep: food: water: and shelter

C.

sleep, food, water; and shelter

D.

sleep, food, water, and shelter

John Dewey, an American educator and philosopher of education,
was a prolific writer on the subject. He was particularly interested
in the place of education in a democratic republic.
The place of public education within a democratic society
has been widely discussed and debated through the years.

13

teacher, whose theories on education have a large social
component, that is, an emphasis on education 13 as a social
act, and the classroom or learning environment as a replica of
society.
Dewey defined various aspects or characteristics of education.
First, 14 they were a necessity of life inasmuch as living

14

socialization kept pace with physiological growth.
15
16 The main aspect of education was its social component,
which was to be accomplished by providing the young with
an environment that would provide a nurturing atmosphere
to encourage the growth of their as yet undeveloped social
customs.

16 The writer is considering revising the underlined portion
of the sentence to read:
A second aspect of education was its social component,
Should the writer make this revision here?

  584

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A.

Yes, because the change improves the organization.

B.

Yes, because the change clarifies the aspects of
education.

C.

No, because the change eliminates information that
supports the main idea of the paragraph.

D.

No, because the change makes the organization of
this part of the passage unclear.

Practice Test 1
A third aspect of public education was the provision of

17

direction to youngsters, who might otherwise 17 be left in

A.

NO CHANGE

B.

get wild and crazy if not for a teacher keeping them
in check.

C.

change direction, much like the wind, with no one
to guide them.

D.

be lost, forlorn without school to steer them toward
moral clarity.

A.

NO CHANGE

B.

uncertain

C.

overt

D.

abstract

the past was recapitulated. Instead, 20 education was a

A.

NO CHANGE

continuous reconstructions of experiences, grounded very

B.

Finally,

much in the present environment.

C.

In retrospect,

D.

Therefore,

A.

NO CHANGE

B.

educations were continuous reconstructions of
experiences

C.

education was a continuous reconstruction of
experience

D.

education was experiences being continuously
reconstructed

uncontrolled situations without the steadying and organizing
influences of school. Direction was not to be of an
18 autonomous nature, but rather indirect through the
selection of the school situations in which the youngster
participated.
19 On the other hand, Dewey saw public education as a
catalyst for growth. Since the young came to school capable of

18

growth, it was the role of education to provide opportunities
for that growth to occur. The successful school environment
is one in which a desire for continued growth is created—a
desire that extends throughout one’s life beyond the end of
formal education. . . .
19
Neither did Dewey’s model see education as a means by which

20

CONTINUE
Peterson's SAT® Prep Guide 2017

  585

Practice Test 1
21 The nature of the larger society that supports the

21

educational system, since Dewey’s model places a heavy
emphasis on the social component, is of paramount
importance. The ideal larger society, according to Dewey, is

A.

NO CHANGE

B.

The nature of the larger society that supports the
educational system is of paramount important
since Dewey’s model places a heavy emphasis on
the social component.

C.

Of paramount importance, since Dewey’s model
places a heavy emphasis on the social component,
is the nature of the larger society that supports the
educational system.

D.

Since Dewey’s model places a heavy emphasis on
the social component, the nature of the larger
society that supports the educational system is of
paramount importance.

A.

NO CHANGE

B.

negotiate

C.

complicate

D.

obfuscate

one in which the interests of a group are all shared by all of
its members and in which interactions with other groups are
free and full. According to Dewey, education in such a society
should provide members of the group a stake or interest in
social relationships and the ability to 22 subjugate change
without compromising the order and stability of the society.

22

  586

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Practice Test 1
Questions 23–33 are based on the following passage.
The study of plant life is very different from the study of animal life
because of unique plant characteristics. The following passage
provides an overview of those characteristics, along with some plant
classifications that are of interest to scientists.

23 Which of the following would make the most effective
introductory sentence to this passage?
A.

When it comes to the study of plants and animals,
there are distinct differences between each.

B.

When it comes to the study of plants and animals,
there are no obvious and discernible differences.

C.

Let’s learn more about some unique animals and
plants!

D.

Have you ever studied various life forms in science
class?

A.

NO CHANGE

B.

by sending out runners or rhizomes, a split at the
stem base, or the production of arching canes that
take root where they touch the ground.

C.

by sending out runners or rhizomes, splitting at the
stem base, or in the production of arching canes
that take root where they touch the ground.

D.

by sending out runners or rhizomes, splitting at the
stem base, or producing arching canes that take
root where they touch the ground.

days. Annuals are herbaceous, which means that they lack a

A.

NO CHANGE

secondary meristem that produces lateral, woody tissue. They

B.

it’s

complete their life cycle after seed production for several

C.

its’

reasons: nutrient depletion, hormone changes, or inability of

D.

it is

23 Compared to animals, plants present unique problems in
demographic studies. The idea of counting living individuals
becomes difficult given perennials that reproduce vegetatively
24 by sending out runners or rhizomes, splitting at the stem
base, or by producing arching canes that take root where
they touch the ground. In these ways some individuals, given

24

sufficient time, can extend out over a vast area.
Each plant life span has a basic associated life form. Annual
plants live for 1 year or less. Their average life span is 1–8
months, depending on the species and on the environment
where they are located (the same desert plant may complete
25 its life cycle in 8 months one year and in 1 month the
next, depending on the amount of rain it receives). Annuals
with extremely short life cycles are classified as ephemeral
plants. An example of an ephemeral is Boerrhavia repens of
the Sahara Desert, which can go from seed to seed in just 10

25

non-woody tissue to withstand unfavorable environmental
conditions following the growing season. A few species
can persist for more than a year in uncommonly favorable

26 The writer is considering deleting the underlined sentence.
Should the writer do this?

conditions.

A.

Yes, because it doesn’t support the main idea of the
paragraph.

Biennial plants are also herbaceous, but usually live for 2

B.

Yes, because it is out of place in the paragraph.

years. 26 Their first year is spent in vegetative growth,

C.

No, because it describes vegetative growth.

which generally takes place more below ground than above.

D.

No, because it describes what happens in the first
year.

Reproduction occurs in the second year, and this is followed
by the completion of the life cycle. Under poor growing
conditions, or by experimental manipulation, the vegetative
stage can be drawn out for more than 1 year.

CONTINUE
Peterson's SAT® Prep Guide 2017

  587

Practice Test 1
Herbaceous perennials typically live for 20–30 years, although
some species have been known to live for 400–800 years.

27 Which choice most effectively maintains the paragraph’s
focus on relevant information and ideas?

These plants die back to the root system and root crown at

A.

NO CHANGE

B.

Their initial vegetative state lasts 2–8 years, which is
an adaptation that is not seen in animals.

C.

Blooming and reproducing early, herbaceous
perennials include such plants as hollyhocks, aster,
and yarrow.

D.

They have a juvenile, vegetative stage for the first
2–8 years, then bloom and reproduce yearly.

A.

NO CHANGE

B.

hedging

between herbaceous perennials and true shrubs. They

C.

estimating

develop perennial, woody tissue only near the base of their

D.

valuing

A.

NO CHANGE

B.

Suffrutescent shrubs (hemixyles) fall

C.

Suffrutescent shrub (hemixyles) fall

D.

Suffrutescent shrubs (hemixyles) has fallen

the end of each growing season. The root system becomes
woody, but the above-ground system is herbaceous. 27 An
initial vegetative state first, popular landscaping plants, they
then bloom and reproduce yearly after making them popular
landscaping plants. Sometimes they bloom only once at the
conclusion of their life cycle. Because herbaceous perennials
have no growth rings, it is difficult to age them. Methods that
have been used to age them include counting leaf scars and

28

28 reducing the rate of spread in tussock (clumped) forms.
29 Suffrutescent shrubs (hemixyles) falls somewhere

30 stems. The rest of the shoot system is herbaceous and
dies back each year. They are small and short-lived compared

29

to true shrubs.
31 Woody perennials (trees and shrubs) have the longest
life spans. Shrubs live on average 30–50 years. Broadleaf trees
(angiosperm) average 200–300 years, and conifer (needles)
trees average 500–1,000 years. Woody perennials spend
approximately the first 10 percent of their life span in a

30 Which choice most effectively combines the two sentences
at the underlined portion?

juvenile, totally vegetative state before they enter a combined

A.

stems, the rest of the shoot system

reproductive and vegetative state, achieving a peak of

B.

stems because the rest of the shoot system

C.

stems: the rest of the shoot system

D.

stems; the rest of the shoot system

A.

NO CHANGE

B.

Woody perennials—trees and shrubs—have the
longest life spans.

C.

Woody perennials, trees and shrubs, have the
longest life spans.

D.

Woody perennials “trees and shrubs” have the
longest life spans.

reproduction several years before the conclusion of their life
cycle.

31

  588

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Practice Test 1
32 Irregardless of the life span, annual or perennial, one
can identify about eight important age states in an individual
plant or population. They are: (1) viable seed, (2) seedling,
(3) juvenile, (4) immature, (5) mature, (6) initial reproductive,
(7) maximum vigor (reproductive and vegetative), and (8)
senescent. If a population shows all eight states, it is 33
stable and is most likely a part of a climax community. If it
shows only the last four states, it may not maintain itself and
may be part of a seral community.

32
A.

NO CHANGE

B.

Regardless

C.

Inregardless

D.

Regarding less

33 Which choice is most consistent with the style and tone of
the passage?
A.

NO CHANGE

B.

diminishing

C.

ephemeral

D.

uniform

CONTINUE
Peterson's SAT® Prep Guide 2017

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Practice Test 1
Questions 34–44 are based on the following passage and
supplementary chart.

34 For the sake of the cohesion of this paragraph, sentence 1
should be placed

Variations in wage

A.

where it is now.

34 [1] Within certain fields, workers are especially likely to

B.

after sentence 2.

receive different salaries. [2] According to the Bureau of Labor

C.

after sentence 3.

Statistics (BLS), large differences in wages can be explained by

D.

after sentence 4.

median for all occupations in May 2014. [4] But that median

A.

NO CHANGE

figure 36 diminishes the fact that the gap between the 90th

B.

of $75,620 more than double

percentile wage and the 10th percentile wage was more than

C.

of $75,620; more than double

$100,000. [5] In other words, just because someone chooses to

D.

of $75,620—more than double

A.

NO CHANGE

B.

contradicts

C.

conceals

D.

equivocates

a variety of factors. [3] Commercial pilots, for example, had a
median annual wage 35 of $75,620: more than double the

35

be a commercial pilot does not necessarily mean he or she will
36

earn as much as the top earners in the field.

Wage
difference(2)

90th percentile wage(1)

10th percentile wage

Occupation

Median wage

Employment

Table 1. Arts, Entertainment, and Sports Occupations with
More than $100,000 Wage Difference, May 2014

Actors(3)

59,210

$41,230

$18,720

>$187,200

>$168,480

Athletes and sports competitors

11,520

43,350

20,190

>187,200

>167,010

Producers and directors

97,300

69,100

31,380

>187,200

>155,820

Broadcast news analysts

4,310

61,450

28,210

182,470

154,260

Art directors

33,140

85,610

45,060

168,040

122,980

Film and video editors

24,460

57,210

25,520

145,620

120,100

Musicians and singers

38,900

50,250

18,680

137,510

118,830

(3)

Footnotes:
(1) BLS does not publish specific estimates for percentile wages above $187,200 per year. Where the percentile wage
is greater than $187,200, the wage is shown with a greater-than sign (>).
(2) Wage differences with a greater-than sign (>) were calculated using $187,200, the highest percentile wage that
BLS publishes.
(3) In occupations in which workers typically are paid by the hour and work less than the standard 2,080 hours per
year, BLS reports only hourly wages. For comparison purposes in calculating wage differences, the hourly wage was
multiplied by 2,080 to get an annual wage.
Source: Occupational Employment Statistics survey, Bureau of Labor Statistics

  590

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Practice Test 1
Why wages vary

37

37 Everyone is unique. Each person comes to a position

A.

NO CHANGE

B.

common

C.

normal

D.

typical

A.

NO CHANGE

B.

our

C.

its

D.

her

opportunities for advancement and higher pay than other

A.

NO CHANGE

occupations. Nevertheless, there are a variety of factors that

B.

tenuous

C.

impractical

D.

incidental

A.

NO CHANGE

B.

noticeable

Experience. Experienced workers usually earn more than

C.

small

those newer to the field. Employers will pay more for a skilled

D.

productive

A.

NO CHANGE

B.

affect

C.

infect

D.

reflect

with her own set of skills, a capacity for adapting to the
demands of the job, and 38 their own personal strengths
and weaknesses. In addition, job titles can be 39 deceiving.
No two jobs are identical. In some fields, this allows for
opportunity to advance dramatically in terms of rank and

38

earnings. There are the fields in which these differences are
very obvious, such as professional sports or the entertainment
field.
In occupations with less variability among workers, wage
differences are usually 40 vast. Fast food cooks, for example,
earn similar wages. Workers in this occupation have fewer

39

41 effect how much a person earns.
Credentials. In some jobs, having advanced education is
necessary for advancement. In other careers, holding a

40

professional license or training credentials will increase a
worker’s wage.

employee, especially in fields in which they are in high demand.
41

CONTINUE
Peterson's SAT® Prep Guide 2017

  591

Practice Test 1
Job tasks. Jobs that are more complex or that demand more
responsibility often pay more. 42

42 Which of the following, if added to the passage, would best
support the author’s point of view regarding job tasks in
the previous sentence?

Location. In the U.S., a worker doing the same job as another

A.

Even within the same company, two workers with
the same job title will sometimes be given the
exact same tasks and receive different wages as a
result.

B.

Even within the same company, two workers with
the same job title will sometimes be given different
tasks and receive different wages as a result.

C.

Even within the same company, two workers with
the same job title will sometimes be given different
tasks and receive the same wages as a result.

D.

Even within the same company, two workers with
the same job title will sometimes be given the same
tasks and receive the same wages as a result.

A.

NO CHANGE

B.

Cost of living and the local demand for the skill:
some of the factors behind this variation.

C.

Some of the factors behind this variation, cost of
living and the local demand for the skill.

D.

Some of the factors behind this variation include
cost of living and the local demand for the skill.

in a different state may earn a very different salary. 43 Some
of the factors—cost of living and the local demand for the skill
these are—behind this, variation. For example, in New York
City, the cost of living is high and workers will be paid more
than their counterparts in Billings, Montana.
Performance. In highly competitive fields, such as sports, only
a small percentage of athletes will experience great success.
There will be many athletes who experience only little or
moderate success, 44 and consequently their median wage
will rank below everyone except broadcast news analysts.
43

44 Which choice completes the sentence with accurate data
based on the supplementary table?
A.

NO CHANGE.

B.

and consequently their median wage will rank
below everyone except actors.

C.

and consequently their median wage will rank
above only singers and musicians.

D.

and consequently their median wage will rank
above only film and video editors.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  592

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Practice Test 1
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions

CONTINUE
Peterson's SAT® Prep Guide 2017

  593

Practice Test 1
1

2

One angle of a triangle measures 82°. The other two angles have a ratio of 2:5. Find the number of degrees in the
smallest angle of the triangle.
A.

14

B.

28

C.

38

D.

82

The total force required to move an object through the
air is given by T = F x2 + F y2 + F z2 , where Fx is the x-component of the force, Fy is the y-component of the force,
and Fz is the z-component of the force. If the total force is
15 Newtons and the x- and z-components are both equal
to twice the y-component of the force, what is the value
of Fz?
A.

15 Newtons

B.

10 Newtons

C.

5 Newtons

D.
3

4

  594

5 Newtons

If f(x) = x2 + 2 and g(x) = x − 1, which expression represents
f (g(a))?
A.

a2 + 1

B.

a2 − 2

C.

a2 + 2a − 3

D.

a2 − 2a + 3

Which expression is equivalent to –(y + 3x)2 –2(2x2 –3y2)?
A.

–4y2 –13x2

B.

–4y2 – 6xy – 13x2

C.

5y2 + 6xy + 13x2

D.

5y2 – 6xy – 13x2

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SHOW YOUR WORK HERE

Practice Test 1
5

SHOW YOUR WORK HERE

Simplify:
x2 − y2
x−y

6

7

8

A.

xy
x+y

B.

x+y
xy

C.

x+y

D.

xy

Which of the following complex numbers is
equivalent to (3 − i )(8 + 4i )?
A.

20 − (− 4i )

B.

20 + 4i

C.

24 − 4i

D.

28 + 4i

Which of these expressions is equivalent
to (x + y)2 − (x − y)2?
A.

0

B.

2y2

C.

4xy

D.

4xy + 2y2

An economist studied the labor forces in several randomly
selected states. He found the average minimum wage of
these states was $7.50, with a 95% confidence interval of
±0.25. How should the economist interpret the data?
A.

States that have a minimum wage below $7.75
represent 95% of the states.

B.

States that have a minimum wage above $7.25
represent 95% of the states.

C.

There is a 95% probability that a randomly selected
state will have a minimum wage between $7.25
and $7.75

D.

There is a 95% probability that the actual average
minimum wage of all states is between $7.25 and
$7.75.

CONTINUE
Peterson's SAT® Prep Guide 2017

  595

Practice Test 1
9

SHOW YOUR WORK HERE

y
7
6
5
4
3
2
1

–4

–3

–2

–1

0

1

2

3

4

5

6

x

–1
–2
–3

The curve shown on the xy-plane represents the function
f(x). Which of these equations represents the same function?
1 2
x − 2x
2

A.

y=

B.

y = x2 − 4x

C.

y = x2 + 4x

D.

y=

1 2
x + 2x
2

10 A 10% saline solution is to be mixed with a 40% saline
solution to obtain 5 liters of a 20% saline solution. Which
system of equations can be used to find the number of liters
of the 10% solution, x, that will be needed to be combined
with the number of liters of the 40% solution, y?

  596

A.

0.1x + 0.4 y = 1
x+ y =5

B.

0.1x + 0.4 y = 5
x+ y =5

C.

0.1x + 0.4 y = 1
x + y =1

D.

0.1x + 0.4 y = 5
x + y =1

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Practice Test 1
11 The path that a javelin follows once having been
thrown can be modeled using the quadratic function
f(x) = –0.036(x – 29.11)2 + 35.42, where x is the horizontal
distance that it has traveled (measured in feet) and the
output, f(x), is the height above the ground (in feet). What
does the 35.42 represent in this function?

12

A.

The maximum height attained throughout the
javelin’s path.

B.

The horizontal distance traveled by the javelin at
precisely the time when the maximum height is
attained.

C.

The speed at which the javelin is initially thrown.

D.

The total horizontal distance the javelin travels from
the instant it is thrown to the moment when it hits
the ground.

SHOW YOUR WORK HERE

2x + 3y = 3
x = 2 − 9y
If (x, y) is the solution of the system of equations above,
what is the value of y?
7
15

A.

−

B.

1
15

C.

2
9

D.

3
2

13 What is the equation of the line that is parallel to y = 5x + 7
and contains the point (1, 3)?
A.

y = −5x + 8

B.

y = 5x − 2

C.

y = 5x + 3

D.

y = 5x + 2

CONTINUE
Peterson's SAT® Prep Guide 2017

  597

Practice Test 1
14 When Rafael parked his car in the city garage for 3 hours,
the charge was $5. When he parked his car for 5 hours, the
charge was $6.50. If the cost of parking a car in the city
garage is a linear function of time in hours, which function
represents the charge, y, to park for x hours?

SHOW YOUR WORK HERE

5
x
3

A.

y=

B.

y = 1.3x

C.

y = 3x + 5

D.

y = 0.75x + 2.75

15 What is the solution of the equation
3(x − 9) = 4x + 3(1 − 2x)?
A.

−4

B.

6

C.

12

D.

30

CONTINUE
  598

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Practice Test 1

DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.

1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
1
7
5.  	 Mixed numbers such as 3 2 must be gridded as 3.5 or 2 .
1
If 3 2 is entered into the grid as

31
1
, it will be interpreted as 2 , not 3 2 .)

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
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Decimal
point

0

Answer: 201
Either position is correct.

0
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Acceptable ways to grid

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are:
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CONTINUE
Peterson's SAT® Prep Guide 2017

  599

Practice Test 1
16 What is the length of the arc of a circle with diameter 5
inches corresponding to a central angle of 144°? Round
your answer to the nearest hundredth of an inch.

17

If x is the solution of the equation
what is the value of x2?

SHOW YOUR WORK HERE

1
1 
1
 2 − x  = x − ( x − 3),
4
3
3

18 What is a solution of x2 + 4 = 9x − x2?

19 What is the x-intercept of the graph of y − 3 = 5(x − 2)?

20 Find a solution of

x + 3 = x − 3.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  600

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Practice Test 1
SECTION 4: MATH TEST—CALCULATOR
55 Minutes—38 Questions

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a2 + b2 = c2
Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  601

Practice Test 1
1

A salesperson earns twice as much in December as in each
of the other months of a year. What part of this salesperson’s entire year’s earnings is earned in December?
A.
B.
C.
D.

2

1
7
2
13
1
6
2
11

Village A has a population of 6,800 that is decreasing at a
rate of 120 per year. Village B has a population of 4,200 that
is increasing at a rate of 80 per year. Which equation can be
used to find the number of years, y, until the population
of the two villages will be equal?
A.

6,800 − 120y = 4,200 + 80y

B.

6,800 + 120y = 4,200 − 80y

C.

6,800 − 120y = 4,200 − 80y

D.

6,800 + 120y = 4,200 + 80y

Candidate B

Candidate C

Candidate D

Male
Female

Candidate A

3

27

29

35

24

24

49

45

17

The table above shows the results of a survey of a random
sample of likely voters. What is the probability that a male
voter who responded to the survey supports candidate C?

  602

A.

7
50

B.

7
23

C.

7
16

D.

7
9

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SHOW YOUR WORK HERE

Practice Test 1
4

5

6

7

The formula for converting temperatures from degrees
5
Fahrenheit to degrees Celsius is C = (F − 32) Solve the
9
formula for F.
A.

5
F = (C + 32)
9

B.

5
F = (C − 32)
9

C.

9
F = C − 32
5

D.

9
F = C + 32
5

SHOW YOUR WORK HERE

A recent study showed that 15% of the salmon that pass
through a turbine in hydroelectric dams are killed. If an
initial population of 50,000 salmon must pass through n
turbines, which function models the number of salmon
that will survive?
A.

A(n) = 50,000 − 0.15n

B.

A(n) = 50,000 − 0.85n

C.

A(n) = 50,000 × 0.15n

D.

A(n) = 50,000 × 0.85n

The equation f(x) = 1.5x + 15 models the growth of a bamboo shoot, where x represents the number of days and f (x)
represents the height of the shoot in feet. Determine how
many days it will take the bamboo shoot to reach a height
of 19.5 feet.
A.

1

B.

2

C.

3

D.

4

A small 24-degree wedge must be removed from a metal
washer in order for it to fit perfectly on a pipe. What part
of the total quantity is represented by a 24-degree sector
of an entire circular washer?
A.

2
6 %
3

B.

12%

C.

1
13 %
3

D.

15%

CONTINUE
Peterson's SAT® Prep Guide 2017

  603

Practice Test 1
8

A high school principal wanted to estimate the mean of
the grade point averages of students in her school. She
randomly selected a group of students and found the
mean grade point average to be 2.8 on a four-point scale,
with a 95% confidence interval of ±0.2. How should the
principal interpret the data?
A.

Students with a grade point average below 3.0
make up 95% of the students in the school.

B.

Students with a grade point average above 2.6
make up 95% of the students in the school.

C.

There is a 95% probability that a randomly selected
student will have a grade point average between
2.6 and 3.0.

D.

There is a 95% probability that the actual mean
grade point average of all students in the school is
between 2.6 and 3.0.

9

9"

6"

A pulley having a 9-inch diameter is belted to a pulley
having a 6-inch diameter, as shown in the figure. The ratio
of the number of revolutions per minute of these pulleys is
9:6. The small pulley is turned by a motor. When the small
pulley turns, the larger pulley also turns. If the large pulley
runs at 120 rpm, how fast does the small pulley run, in
revolutions per minute?

  604

A.

80

B.

100

C.

160

D.

180

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SHOW YOUR WORK HERE

Practice Test 1
10

y = x 2 − 7 x + 10
x−y=4

SHOW YOUR WORK HERE

If (x, y) is a solution of the system of equations above, what
is the value of y2?
A.

2

C.

9
2
18 − 8 2

D.

14

B.

11 The water level of a swimming pool, 75 feet by 42 feet, is
to be raised 4 inches. How many gallons of water must be
added to accomplish this? (7.48 gal. = 1 cubic ft.)
A.

1,684

B.

7,854

C.

12,600

D.

94,248

12 If 3 of a bucket can be filled in 1 minute, how many
7
minutes will it take to fill the rest of the bucket?
A.

7
3

B.

4
3

C.

3
4

D.

4
7

13 The distance from the center of a circle to a chord is 5. If the
length of the chord is 24, what is the length of the radius
of the circle?
A.

5

B.

10

C.

13

D.

26

CONTINUE
Peterson's SAT® Prep Guide 2017

  605

Practice Test 1
14 A 40-pound bag of garden soil contains 0.8 cubic feet
of soil. What is the weight, in pounds, of the garden soil
needed to cover a 12-foot by 12-foot square garden to a
depth of 3 inches?
A.

1,152

B.

1,800

C.

4,608

D.

5,760

15 The demand for a certain product can be defined by the
function y = 500 − 12x, where y is the number of units of
the product that can be sold at a price of x dollars. Which
statement must be true?

  606

A.

If the price of the product decreases by $1, the
number of units that can be sold decreases by 12.

B.

If the price of the product increases by $12, the
number of units that can be sold decreases by 1.

C.

The y-intercept of the graph of the function
represents the units of the product that can be sold
at a cost of $1.

D.

The x-intercept of the graph of the function
represents the price at which no units of the
product will be sold.

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SHOW YOUR WORK HERE

Practice Test 1

DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.

1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
1
7
5.  	 Mixed numbers such as 3 2 must be gridded as 3.5 or 2 .
1
If 3 2 is entered into the grid as

31
1
, it will be interpreted as 2 , not 3 2 .)

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

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8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

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2

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1

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1

2

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2

2

1

3

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4

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Acceptable ways to grid

2
are:
3

.

1

0

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6

CONTINUE
Peterson's SAT® Prep Guide 2017

  607

Practice Test 1
16

SHOW YOUR WORK HERE

y = (x − 5)(x + 1)
The equation above represents a parabola. Which of the
following equivalent forms of the equation shows the
coordinates of the vertex of the parabola as constants or
coefficients?
A.

y = x2 − 4x − 5

B.

y = (x − 2)2 − 9

C.

y = x(x − 4) − 5

D.

y + 5 = x2 − 4x

Questions 17–19 refer to the following graph.
100
90

Chemistry Test Score

80
70
60
50
40
30
20
10
0
0

10

20

30

40

50

60

70

80

90

100

Algebra Test Score

The scatterplot above shows the scores for 10 students on
their most recent Algebra and Chemistry tests.
17

  608

What is the arithmetic mean of the students’ algebra test
scores?
A.

68

B.

70

C.

79

D.

80

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Practice Test 1
18 A line of best fit of the data is given by y = 0.76x + 27.6,
where x is a student’s algebra test score and y is a student’s
chemistry test score. Which interpretation is valid?
A.

The average chemistry test score is 27.6 points
higher than the average algebra test score.

B.

The average algebra test score is 0.76 times the
average chemistry test score.

C.

Students with higher algebra test scores tended to
have higher chemistry test scores.

D.

There is not enough information to determine a
relationship between the students’ chemistry test
scores and their algebra test scores.

SHOW YOUR WORK HERE

19 Using the line of best fit, y = 0.76x + 27.6, what is the predicted algebra test score of a student with a chemistry test
score of 70, rounded to the nearest whole number?

20

A.

50

B.

56

C.

77

D.

81

The velocity of an object dropped from a tower is given by
the function v(t) = −9.8t, where t is the number of seconds
after the object was dropped and v(t) is given in meters per
second. If the object hits the ground at 4 seconds, which
inequality shows the possible values of v(t)?
A.

−39.2 ≤ v(t) ≤ 0

B.

−2.45 ≤ v(t) ≤ 0

C.

0 ≤ v(t) ≤ 2.45

D.

0 ≤ v(t) ≤ 39.2

21 To predict the results of an election for city council, a
polling company surveyed 200 randomly selected likely
voters within the city. Of those surveyed, 80 planned to
vote for candidate A. The polling company reported a
margin of error of 3.5%. What is a reasonable estimate of
the percentage of likely voters who support candidate A?
A.

Between 36.5% and 43.5%

B.

Between 46.5% and 53.5%

C.

Between 56.5% and 63.5%

D.

Between 76.5% and 83.5%

CONTINUE
Peterson's SAT® Prep Guide 2017

  609

Practice Test 1
22 Corporate Average Fuel Economy sets targets for fuel
economy for cars and light trucks. The target for the year
2020 is 42 miles per gallon, and for 2025, it is 54.5 miles per
gallon. Which function can be used to estimate progress
toward the goal y years after 2020 until 2025?
A.

g(y) = 54.5 – 2.5y

B.

g(y) = 42 – 2.5y

C.

g(y) = 54.5 + 2.5y

D.

g(y) = 42 + 2.5y

23 A municipal light plant buys energy from windmill farms
that have two sizes of windmills. Small windmills produce
1.45 megawatts of power, and large windmills produce
2.75 megawatts of power. Which inequality represents
the number of small windmills, x, and large windmills, y,
needed to supply the light plant with a total power supply
of at least 200 megawatts?

24

A.

2.75x + 1.45y ≤ 200

B.

1.45x + 2.75y ≥ 200

C.

2.75x + 1.45y ≥ 200

D.

1.45x + 2.75y ≤ 200

If x1 and x2 are the solutions of x2 − 4x = 3, what is |x2 − x1|?
A.

0

B.

2

C.

4

D.

2 7

25 A group of 18 coins has a total value of $3.10. If the coins
consist only of quarters and nickels, how many more
quarters are there than nickels?

  610

A.

3

B.

4

C.

7

D.

11

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SHOW YOUR WORK HERE

Practice Test 1
26 Which graph would be drawn to represent an economy
that is growing at a fixed percentage rate?

SHOW YOUR WORK HERE

A.

B.

C.

D.

27 You are at the top of a 150-foot cliff and wish to repel down
to the ground. You can safely descend at a rate of 4 feet per
second. Which of the following functions expresses your
elevation above the ground, d, as a function of time, t?
A.

d(t) = 4t + 150

B.

d(t) = 150t – 4

C.

d(t) = –4t + 150

D.

d(t) = 4t – 150

CONTINUE
Peterson's SAT® Prep Guide 2017

  611

Practice Test 1
28 Which quadrant does the solution set for the system of
inequalities below NOT intersect?
−2 y > 3( x − 6 )

 2y > 6 − 3x
A.

Quadrant I

B.

Quadrant II

C.

Quadrant III

D.

Quadrant IV

29

y
4
3
2
1
–4 –3 –2 –1
–1
–2

1

2

3

4

x

–3
–4

A polynomial function p(x) is shown on the xy-coordinate
plane. If q(x) is a quadratic function, which of these equations can represent p(x)?
A.

p(x) = (x − 1)q(x)

B.

p(x) = (x + 2)q(x)

C.

p(x) = (x − 3)q(x)

D.

p(x) = (x + 4)q(x)

30 The points (−3, 2) and (3, 2) are the endpoints of a diameter
of a circle. Which equation represents the circle?

  612

A.

(x – 2)2 + y2 = 3

B.

(x − 2)2 + y2 = 6

C.

x2 + (y − 2)2 = 9

D.

x2 + (y − 2)2 = 16

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SHOW YOUR WORK HERE

Practice Test 1
DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
		

If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

31
1
, not 3 .
2
2

, it will be interpreted as

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

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4

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5

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5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

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4

4

4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

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1

2

2

2

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1

.

0

0

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1

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CONTINUE
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Practice Test 1
31 A local politician requested donations to pay for the cost of
a radio ad. Twelve donors offered to split the cost equally,
so they each paid $75. If the politician was able to find 20
donors to equally split the same cost, how much would
each pay?

32 You want to buy a wall-to-wall rectangular rug for the
family room. The length of the family room is 2 feet less
than twice the width, and the distance from one corner of
the room to the corner diagonally across from it is 2 feet
more than twice the width. What is the area of the rug
needed, in square feet?

33 Jessica caught five fish with an average weight of 10
pounds. If three of the fish weigh 6, 7, and 15 pounds,
respectively, what is the average (arithmetic mean) weight
of the other two fish?

34 In 2012, Algeria had a population of approximately 37.44
million. In 2013, the population had grown to 38.19 million.
If the function p(t) = a i b t is used to model the population
in millions, p(t), t years after 2012, what is the value of b?
Round your answer to the nearest hundredth.

35 Juliette begins an exercise program in preparation for a
half-marathon. She plans to run 20 miles during Week 1.
For each subsequent week, she intends to increase the
miles run for that week by 10% of the number she ran
the previous week. How many miles will Juliette then run
during Week 3?

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SHOW YOUR WORK HERE

Practice Test 1
36 You have 160 yards of fencing material. If you want to
construct a rectangular pen whose width is between 10
and 20 yards, inclusive, what is the longest that such a pen
can be, in yards?

SHOW YOUR WORK HERE

37 3.6 x + 2.4 y = 12
x−y =2
If (x, y) is a solution of the system of equations above, what
is the value of y?
38 The function f(x) = x2 − 4 is translated 3 units to the right
to create function g(x). What is the value of g(9)?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

CONTINUE
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Practice Test 1
SECTION 5: ESSAY
50 Minutes—1 Essay

DIRECTIONS: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

As you read the passage below, consider how Elizabeth Roberts-Pedersen uses the following:

• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed.

Adapted from “From Shell Shock to PTSD: Proof of War’s Traumatic History” by Elizabeth Roberts-Pedersen, originally published
by The Conversation on April 14, 2015. Elizabeth Roberts-Pedersen is a lecturer in history at the University of Western Sydney in
Australia. (This passage was edited for length. To read the complete article, see http://theconversation.com.)
1

2015 marks several important First World War anniversaries: the centenary of the first use of poison gas in January; the
centenary of the Gallipoli landings and the Armenian genocide in April. It is also 100 years since The Lancet published
Charles S. Myers’ article, “A Contribution to the Study of Shell Shock.”
The study of shell shock

2

Myers’ article is generally regarded as the first use of the term “shell shock” in medical literature. It was used as a descriptor
for “three cases of loss of memory, vision, smell and taste” in British soldiers admitted to a military hospital in France.

3

While Myers presented these cases as evidence of the spectacular concussive effects of artillery on the Western Front,
British medical opinion soon came to regard these symptoms as psychological in origin. The men presenting to medical
officers with tics, tremors, and palpitations, as well as more serious symptoms of “functional” blindness, paralysis, and loss
of speech, were not concussed—but nor were they necessarily cowards or malingerers.

4

Instead, these were men simply worn down by the unprecedented stresses of trench warfare—in particular, the effort
required to push out of one’s mind the prospect of joining the ranks of the maimed or the corpses lying in no man’s
land. . . .

5

For contemporaries and later for historians, shell shock came to encapsulate all the horror of this new form of industrialized
warfare. As historian Jay Winter suggests, it moved “from a diagnosis into a metaphor.” . . .
Developing a diagnosis

6

It is tempting to view shell shock as the unambiguous turning point in psychiatry’s history, popularizing the idea that
unconscious processes might produce symptoms that operate separately from moral qualities such as endurance and
courage. However, scholarship over the last 15 years suggests that this position was far from widely accepted.

7

. . . The notion that many patients had some “predisposing” weakness—independent of their combat experiences—persisted
throughout the interwar period and into the Second World War.

CONTINUE
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Practice Test 1
8

It wasn’t until the Vietnam War that this formulation was reversed, which in turn bridged the gap between combatant
syndromes and the civilian sphere.

9

This development is only comprehensible as part of a broader political context. The notion that the Vietnam War exacted a
form of psychic damage on American soldiers was championed by the anti-war activists of Vietnam Veterans Against the War
(VVAW) and psychiatrists Chaim Shatan and Robert Jay Lifton. “Post-Vietnam syndrome,” Shatan wrote, was caused by the
“unconsummated grief” of a brutal and brutalizing war.

10

The VVAW’s advocacy was instrumental in securing official recognition for this condition. It was included in 1980 in the third
edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-III) as “post-traumatic stress disorder.”

11

PTSD’s inclusion in DSM-III legitimated the suffering of Vietnam veterans and held out the possibility of subsidized medical
care and compensation. But the DSM-III definition of PTSD was significant in two additional ways.

12

First, it identified the disorder as a condition that could afflict soldiers and civilians alike—not a diagnosis exclusive to
combat, like shell shock.

13

Second, it focused attention on the continuing effects of a traumatic experience, rather than on the personality and
constitution of the patient.

14

The ramifications of these changes have been immense. PTSD and a broader field of “traumatology” are now entrenched
in psychiatric and popular discourse. In Australia, we now assume that warfare is objectively traumatizing, and that
governments ought to provide medical and financial support for affected service personnel, even if a recent Four Corners
program confirmed that this is not always the case.
How is PTSD viewed today?

15

Though PTSD has its origins in opposition to the Vietnam War, the politics of the condition are now largely ambivalent, with
its significance shifting according to circumstance.

16

This point is well illustrated by the film American Sniper, which demonstrates the possibility of two contrary positions. After
his return to civilian life, SEAL sniper Chris Kyle (Bradley Cooper) is shown to be suffering from some characteristic aftereffects of combat. …
…

17

The real Chris Kyle was shot dead by Eddie Ray Routh [another veteran] in 2013. At trial, the accused’s lawyers pursued a
defense of insanity, compounded by the inadequate care provided by veterans’ mental health services. Routh was found
guilty of Kyle’s murder in March of 2015.

18

In the 100 years since Myers’ article on shell shock, the psychological consequences of war remain as relevant as ever.
Write an essay in which you explain how the writer builds an argument to persuade her audience that
she is offering proof of war’s traumatic history. In your essay, analyze how Elizabeth Roberts-Pedersen
uses one or more of the features listed above (or features of your own choice) to strengthen the logic
and persuasiveness of her argument. Be sure that your analysis focuses on the most relevant aspects
of the passage.
Your essay should not explain whether you agree with Elizabeth Roberts-Pedersen’s claims, but rather
explain how she builds an argument to persuade her audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  618

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Answer Keys and Explanations
Section 1: Reading Test

1. B

12. B

23. D

34. C

45. B

2. A

13. D

24. D

35. B

46. A

3. C

14. B

25. A

36. D

47. C

4. D

15. B

26. B

37. A

48. C

5. C

16. A

27. A

38. A

49. B

6. B

17. D

28. B

39. B

50. C

7. A

18. B

29. C

40. A

51. A

8. D

19. C

30. B

41. C

52. D

9. B

20. C

31. B

42. D

10. C

21. C

32. B

43. B

11. A

22. A

33. C

44. D

READING TEST RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is B. The narrator’s description of
Jack and his bride, of their wonder at their surroundings
and happiness at their marriage, makes choice B the
correct answer. Choice A is incorrect because though
Jack seems awkward in his surroundings, he does not
seem aware of his lower social standing compared to
other passengers. Though the passage provides a great
deal of insight about the people who traveled on trains
and the luxury in which they traveled, choice C is
incorrect because the primary focus is on the newly
married couple and their interactions. While Jack and
his bride do seem self-conscious on the train, and while
other passengers seem to regard them with derision,
the passage does not delve deeply into issue of class
and class consciousness, so choice D is also incorrect.
The correct answer is A. The couple’s trip on the
opulent train, as well as specific luxuries that Jack points
out to his bride, makes choice A the correct answer.
Choice B is misleading, as Jack’s face is “reddened from
many days in the wind and sun,” suggesting that he
works outside but not necessarily as a farmhand or
rancher. Choice C is incorrect because, while the couple
seem to shrug off the stares of other passengers,
readers get the distinct impression that they are not
used to being around people of a higher social

standing. Choice D is not correct because Jack does
not suggest through deeds or words that he wants
more than he has.
3.

The correct answer is C. Jack’s enthusiastic tone in
responding to his bride’s delight (“Great!”) and his
“brave” assurance that they are “going to go the
whole thing” when she questions if they can afford
the dining car make choice C the correct answer.
While choice A suggests that Jack is aware of his
formal clothes and may want to make a good
impression, it is not clear that he wants to impress
his bride with his appearance. Therefore, choice A is
incorrect. Because it involves the bride and the
other passengers’ perceptions of her, choice B is
also incorrect. Though choice D suggests that the
couple views their marriage favorably, there is no
indication in these lines that Jack wants to impress
his bride.

4.

The correct answer is D. In the first sentence, the
phrase “whirling onward with such dignity of
motion that a glance from the window seemed
simply to prove that the plains of Texas were
pouring eastward” suggests that the train was
moving very smoothly, so choice D is the correct
answer as “gracefulness” suggests a lack of

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Answer Keys and Explanations
standing as a married couple, so choice D is correct.
While “estate” can refer to social standing, in this case,
the couple’s newly married status helps to give context
to the word, so choice A is incorrect. Choice B is
off-base, as “interests” do not fit the context. While
“estate” does refer to property, the context of the
sentence does not support this definition of the word.
Therefore, choice C is incorrect.

turbulence. Choices A and C are incorrect because,
while they may suggest that the ride is better than
expected, they do not describe the smooth movement
that the sentence emphasizes. Choice B is a synonym of
“dignity,” but it does not suit the context of the
sentence.
5.

6.

7.

8.

  620

The correct answer is C. The expressions of both Jack
and his bride, as well as the intimation that they are not
wholly comfortable in their attire, make choice C
correct. The pair seems happy about their marriage, but
there is no suggestion that they are resolute about their
decision to marry or about any other decision, so choice
A is incorrect. Choice B is a distortion because, while
they seem slightly nervous, there is no evidence to
suggest that they are nervous about the trip itself.
Choice D is incorrect because, although they are
amazed at the train’s interior, they do not seem to notice
the landscape.
The correct answer is B. The couple’s awkwardness and
self-consciousness is best supported by Jack’s nervous
and shy countenance, choice B. The description of the
landscape is a distraction and does not support the
inference that the couple feels self-conscious, so choice
A is incorrect. Choice C is off-base because it suggests
the bride is concerned about the cost, rather than how
the couple might appear to others. Choice D is incorrect
because the narrator’s likening the state of their
marriage to their surroundings does not suggest that
they were either comfortable or uncomfortable in their
surroundings.
The correct answer is A. The narrator notes the other
passengers’ “careless scrutiny” and emphasizes that the
bride’s countenance is “emotionless.” The inference is
that the other passengers were staring to such a degree
that the bride’s usually “placid” face flushed red with
embarrassment, making choice A correct. While the
narrator notes in the following sentence that the pair
are “very happy,” there is no evidence to suggest that
she is blushing from happiness, so choice B is not
correct. While the “careless scrutiny” likely led to
self-consciousness, there is no evidence to support the
idea that the bride is generally lacking in self-confidence. Therefore, choice C is incorrect. Choice D is
misleading, because the narrator notes only that the
bride is plain, not unattractive.
The correct answer is D. In the preceding sentence the
narrator notes that “their surroundings reflected the
glory of their marriage that morning in San Antonio.”
The glory of their new estate, then, refers to their new

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9.

The correct answer is B. The narrator notes that the
couple “had small knowledge” of the porter’s bullying,
so choice B is correct. There is no indication they are
being openly mocked, nor that the couple feels catered
to, so choice A is incorrect. The narrator describes the
couple’s enjoyment and does not suggest that anyone
was openly hostile to them, thus choice C is not correct.
The couple “had small knowledge” of the porter’s
bullying, so choice D cannot be correct because they
could not have become used to behavior they had small
knowledge of.

10.

The correct answer is C. Because the author describes
the new black suit as the cause when he says the
groom’s “brick-colored hands were constantly performing in a most conscious fashion,” choice C is the
correct answer. Although the groom is nervous in
general, here the focus is on how his clothes have led to
certain hand gestures, so choice A is insufficient
because it does not take that important detail into
consideration; it only focuses on the groom’s awkwardness and not what is causing that awkwardness.
Choice B is incorrect, because although the author
brings up the weathered condition of the groom’s
hands, he uses it as a contrast to the new clothes; the
fact that the groom’s hands are “brick-colored,” which
may indicate that he works with his hands, is not the
most important message conveyed by these lines.
Choice D is also incorrect because the groom’s happiness is not described in this part of the story, and
when he expresses happiness, it is with a natural
openness. For example, he smiles with delight or beams
with elation.

11.

The correct answer is A. The passage covers nest
building, feeding, and other behaviors, so choice A is
correct. Choice B is incorrect, because how hummingbirds build their nests is just one detail in the passage,
and it fails to capture the idea of the passage as a whole.
Choice C is also incorrect because while the author
notes that the hummingbird is interesting, the author is
more concerned with detailing the hummingbird’s
behavior neutrally than convincing the reader of
anything. Choice D is incorrect because the author does

Answer Keys and Explanations
are “not louder than that of a small cricket or grasshopper,” it is also noted that a hummingbird’s “only note
is a single chirp,” making choice C incorrect. The author
notes that the females most likely carry “animal food” to
their young, so choice D is also incorrect.

not, for example, explain why the hummingbird builds
nests where it does but rather describes its behavior.
Interpretation is not as important as description in this
particular passage.
12.

13.

14.

15.

The correct answer is B. By noting that the birds arrive
“about the twenty-fifth of April,” the author is implying
that hummingbirds are elsewhere before that, and since
winter ends only one month before the twenty-fifth of
April, it is reasonable to conclude that birds migrate
elsewhere during the wintertime. The time span the
author gives is between the time the birds arrive and
the time they begin building their nest, so there is not
enough information in these lines to support choice A.
There is no indication that some birds do not migrate
farther north of Pennsylvania, so choice C is not a
correct assumption. By referring to “the hummingbird,”
the author is not referring to a singular one, but rather
to those species that migrate to Pennsylvania. Therefore,
choice D is not the best answer choice.
The correct answer is D. The author is describing how
the nest is stuck to the branch and provides a context
clue in the form of a synonym (“attached”) in line 6, so
choice D is correct. Because neither choice A nor choice
B make sense in the context of the sentence, they are
incorrect. While choice C makes sense in the context, it
does not make sense when the synonym (“attached”) in
line 6 is taken into account, and so it is incorrect.
The correct answer is B. The author notes the materials
in each layer and uses phrases like “firmness and
consistency” and “closely laid together,” making choice B
the correct answer since it covers the entirety of lines
13–26. While the author does cite a number of different
plants that go into the nest, this is just a single detail in
lines 13–26 and not the main focus of the section as a
whole, so choice A is incorrect. Though it might be
assumed that such an intricate nest takes time to build,
the author does not note time as a factor, so choice C is
not the best answer. While the author notes that the
bird’s saliva helps keep out moisture, this is not the
main focus of lines 13–26 as a whole, so choice D is also
incorrect.
The correct answer is B. The author notes the female’s
bold reaction to people approaching her nest, which
makes choice B correct. There is no specific mention of
how long hummingbirds stay in their nest, but based on
the suggestion that they migrate and that their young
only stay in their nests a “short time” (lines 34–35), it is
reasonable to conclude that choice A is incorrect.
Though the author mentions that hummingbird chirps

16.

The correct answer is A. These lines reveal that the
hummingbird will dart around a person’s head to
protect its eggs and young, which is a bold reaction
from such a tiny creature. Choice B refers to the duration
that chicks are in the nest, and thus does not support
the inference. Choice C refers to what hummingbirds
eat, and it also does not support the inference. Choice D
is incorrect because it includes details about a hummingbird’s voice and does not support the idea that the
female guards her young.

17.

The correct answer is D. Choice D is correct because
the bird is putting its feathers in order, or neatening
them, which the author’s use of the word “arrange”
supports. Choice A is incorrect because there is no
suggestion that the hummingbird oils itself at all in this
passage. Choice B is a synonym for “wears,” but in this
context, it suggests that the hummingbird is not always
wearing its feathers, which does not make sense. It is
not clear what it would mean for a bird to “shuffle” its
feathers, so choice C does not make much sense either.

18.

The correct answer is B. When something moves
extremely fast, it can be nearly impossible to see,
making it seem almost invisible, which makes choice B
the most plausible answer. Birds do not have transparent wings, and if the hummingbird did, this would
probably be an amazing enough detail for the author to
note. Since there is no specific mention of the hummingbird having transparent wings, choice A is not a
strong answer. The sun reflecting off the wings might
make them seem shiny, but it would not make them
“become invisible,” so choice C is also incorrect.
Something needs to be visible in order to be beautiful,
so choice D does not make sense.

19.

The correct answer is C. In lines 64–65, the author
notes that, “for when two males meet at the same bush,
or flower, a battle instantly takes place.” When the
author says the victor “returns to the same place,” the
reference must be the bush or flower, a conclusion
reinforced by line 57 in which the author describes how
the hummingbird “extracts its sweets” from the flower.
Thus, choice C is correct. Though the author notes in
line 59 that the hummingbird tends to alight on the
“dead twigs of a tree,” there is no indication that this is
the place the bird returns to after battle, so choice A is

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Answer Keys and Explanations
the author refers to the spherical shape of the Earth in
these lines, it is not the Earth’s shape that is most
important here, so choice B is incorrect. Because the
author does not describe the shape of each plate,
choice C is not a conclusion that can be reached based
on the information in line 16.

incorrect. Similarly, although the two combatants are
male, the author has not indicated that the males are
battling over females. Rather, the battle seems to be
over access to food, so choice B is also incorrect. Choice
D is off-base, as the author only mentions the conqueror
returning “to the same place.”
20.

21.

The correct answer is C. These lines describe the
hummingbird as attacking another bird, which
emphasizes its aggressive nature. These lines portray
the hummingbird as a danger, rather than a bird
vulnerable to dangers, so choice A does not make sense.
Choice B is also incorrect, as the author describes the
female hummingbird as staying on its nest, and these
lines, which refer to the male, have nothing to do with
the bird’s proximity to its nest. Choice D is incorrect
because the description of how male hummingbirds
attack each other that appeared earlier in the paragraph
already introduced the idea that they do not only fight
for self-defense.

22.

The correct answer is A. By invoking Mt. Everest, the
world’s tallest mountain, the author is intent on
showing that there are equally extraordinary and exotic
geographical features on the ocean floor, making choice
A the correct answer. While the author does emphasize
that Mauna Kea is actually taller, that isn’t the point of
the opening sentence. Instead, the author continues
describing the many geographical features found on
the ocean floor. Therefore, choice B is incorrect. The
author does not describe the geography of Mauna Kea
or any other island mountain, so choice C is incorrect.
Because there is no other mention of Mt. Everest in the
passage, choice D is also incorrect.

23.

  622

The correct answer is C. In these lines, the author
explains how the hummingbird moves from flower to
flower and how the two male combatants meet over a
flower, which implies that they are fighting over that
flower and the nectar it contains. So choice C is correct.
While the author begins the passage with a description
of the nesting habits of females, nesting and mating are
not discussed in the second paragraph, so choice A is
incorrect. The mention of dead twigs does not refer to
any specific territory, making choice B incorrect. The
reference to another male hummingbird provides no
support for the idea that “fruits of his victory” refers to
the nectar of flowers, so choice D is incorrect.

The correct answer is D.The pieces of a jigsaw puzzle
fit together as the tectonic plates do, so choice D is
correct. As the author does not note individual plates
and the role each plays, choice A is incorrect. Although

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24.

The correct answer is D. The author describes the
tectonic plates as “floating on top of the Earth’s hot
flowing mantle” and notes that “convection currents in
the molten mantle layer cause the plates to slowly
move,” so choice D is correct. Earthquakes and volcanoes are a result of the movement of the plates, so
choice A is incorrect. There is no mention of ocean tides
in this passage, so choice B is also incorrect. The upward
flow of magma in diverging plates causes new ocean
floor crust, which does not cause the tectonic plates to
move, so choice C is not correct.

25.

The correct answer is A. The passage indicates that the
major discovery of 1977 was that organisms in deep
ocean hydrothermal vent ecosystems eat chemicals.
Since eating is key to survival, this supports choice A.
The passage does not specify when scientists came to
believe that colliding plates caused the formation of
deep ocean hydrothermal vents, so choice B is not the
best answer. In lines 66–76, the author describes the
food web found in this ecosystem and notes that these
animals must be adapted to survive in the extreme
environment. There is no indication that the animals
move between environments, so choice C is incorrect.
While there are many metals that spew from the vents,
there is no indication that scientists had any interest in
whether or not these minerals could be mined, so
choice D is also incorrect.

26.

The correct answer is B. In lines 39–44, the author
notes that the discovery forced scientists to “redefine
living systems on our planet” and then goes on to note
“other previously described ecosystems” that rely on
sunlight and photosynthesis as the basis of their food
web. This makes choice B the correct answer. Lines
32–34 do not provide evidence because the author has
not yet tied the new species to the existence of an
ecosystem that relies on chemosynthesis, so choice A is
incorrect. The way hydrothermal vents are formed does
not support the inference about organisms in deep
ocean hydrothermal vent ecosystems, so choice C is
incorrect. Similarly, the kinds of metals that spew from
the vents support bacteria that form the base of the
chemosynthetic food web, but the existence of these
metals does not support the inference about what
scientists knew about organisms in deep ocean

Answer Keys and Explanations
hydrothermal vent ecosystems before 1977. Thus,
choice D is also incorrect.
27.

28.

29.

The correct answer is A. In line 61, the author describes
“molecules that billow out of the seafloor.” Because of
the context, we know that the molecules are somehow
emerging from the seafloor, but there is no indication
that it is forceful, so choice A seems the most reasonable answer. “Crest” indicates a very specific
movement, and since there is no indication of a cresting
pattern in the passage, choice B is not the best answer.
“Wave” indicates a movement and can be used as a
synonym for “billow,” but it does not indicate the
continuous forward movement indicated in line 61, so
choice C is not the best answer. Choice D implies that
the molecules change size, which is not implied in the
passage.
The correct answer is B. At the beginning of the
second paragraph, the author notes, “The shape of the
ocean floor, its bathymetry, is largely a result of a
process called plate tectonics.” The author goes on to
describe how the movement of plates causes hydrothermal vents, so choice B is the correct answer. While
the author does describe the geography of the ocean
floor, this description is general, and the geography of
the ocean’s floor is not the passage’s main idea, so
choice A is incorrect. The suggestion that the same
forces that create volcanoes also create hydrothermal
vents is tangential and has little impact on the passage’s
main idea, thus choice C is also incorrect. While the
author describes the ecosystems around hydrothermal
vents as different from those that rely on photosynthesis, the discussion of plate tectonics does not
support the inference that they are unusual. Therefore,
choice D is not correct.
The correct answer is C. The passage describes the
features of hydrothermal vents, so the discussion of
plate tectonics serves to explain how hydrothermal
vents are formed. In lines 46–48, the author explains
how the movement of the plates causes the formation
of hydrothermal vents, so choice C is correct. In lines
5–9, the author introduces the geography of the ocean
floor but has not yet mentioned hydrothermal vents, so
choice A is incorrect. In lines 34–38, the author notes
that many species have been discovered in this unique
environment, but there is no general discussion of the
formation of hydrothermal vents. Thus, choice B is not
correct. Lines 48–51 note that the main causes of
hydrothermal vents are also responsible for volcanoes
and earthquakes, but the information is parenthetical
and not as extensive as in the previous lines, so choice D
is also incorrect.

30.

The correct answer is B. The description of an “extreme
environment,” including darkness and extreme temperatures that would kill most other forms of life, signals
that choice B, “harmful,” is the answer. Though they
could be used as synonyms for “noxious” in another
context, choices A and C are not strong enough to
support the idea of the extremely inhospitable
environment that the author is describing in the
paragraph. Likewise, choice D is incorrect because while
the environment described is unusual, the focus is more
on the idea that it is inhospitable, i.e., harmful to most
forms of life that we know even though animals in this
region are adapted to survive exposure to these
chemicals.

31.

The correct answer is B. The diagram shows that the
black smoker contains sulfides, produces smoke that
contains these sulfides, and pushes a plume of that
smoke into the atmosphere. All of these details support
the conclusion in choice B. The diagram only indicates
that smoke-containing sulfides exit the black smoker
through its top; there is no indication they are carried
out at ocean level, so choice A is incorrect. Choice C is
incorrect because the diagram details a movement of
those sulfides, not the period in which they remain
within the black smoker’s cracks. Where the sulfides go
after exiting the black smoker is not clear based on the
diagram alone, and there is certainly no evidence that
they return to the depths of the black smoker, so choice
D is not a logical conclusion.

32.

The correct answer is B. The passage begins with a
sentence that focuses on boys who live in the tenements. The passage ends with the idea that “Home to
them is an empty name,” referring again to the tenements, so choice B is correct. Though much of the first
paragraph is a discussion of the lack of job opportunities, the main focus of the passage is on the lack of
opportunities for children living in the tenements, so
choice A is not correct. The author does allude to
education in the last paragraph, but again, it is not the
main focus of the passage, thus choice C is also
incorrect. The second paragraph deals with delinquency
but only within the context of the tenements. Since the
main focus of the passage as a whole is not how
impoverished children often turn to crime, choice D is
incorrect.

33.

The correct answer is C. Both the preceding and
following sentences discuss the idea that the tenements
are not “elevating” and contribute to “idle” ways, so the
context makes choice C the correct answer. While
polluting can mean “dirty,” the author here is concerned

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Answer Keys and Explanations
ways will lead to trouble does not support choice B,
“vain,” as an answer. Similarly, there is no indication that
the boy acts younger than he is, so choice C is incorrect.
Actions can be simple without being unproductive, so
choice D is not the best interpretation of how the
author uses “idle” in this context.

more with the child’s character development, so choice
A is incorrect. There is no evidence to suggest that the
games are dangerous, thus choice B is also incorrect.
Similarly, the context does not suggest that the author
is referring to the games as having a noisy character, so
choice D is not correct.
34.

The correct answer is C. The context of the tenements
helps make clear that the author is referring to the
people who make up the child’s community when he
writes that “the boy stands condemned by his own …,”
so choice C is the correct answer. Because the author’s
reference to “the boy” is a reference to all boys in the
tenement, choice A cannot be correct. Choice B is
incorrect because the author’s discussion is more about
the corrosive effects of the entire community, not of the
smaller family unit. There is no indication that the
children go to school, so choice D is also incorrect.

35.

The correct answer is B. Lines 20–21 provide examples
of the boy’s “own,” the people who should be helping
him but are letting him down: the truant officer and the
agents of the Children’s Societies. Choice A deals with
the games the boy plays, not the people who are failing
to protect him. Choice C is about environments—the
city and the Truant Home—not the people who run
them and fail the boy. Choice D refers to factors
affecting the boy in a vague way that does not place
any blame on specific people who should be helping
him.

36.

37.

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The correct answer is D. Again, the author’s focus is on
the tenements as spirit-crushing, which is supported by
the following sentence: “Its influence is scarcely of the
elevating kind, if it have any.” Thus, choice D is the
correct answer. While the author speaks of “so many
other human animals,” creating an image of packed
cages, there is no suggestion that the tenements are
filthy, only that they don’t provide an environment that
helps grow a boy’s character, so choice A is not the best
answer. Choice B assumes that the biggest problem
with tenement life is the lack of privacy, and since the
author never suggests that this is true, this is not a very
logical interpretation of the pigeon coop metaphor.
Choice C makes an incorrect generalization, suggesting
that every person lives in a tenement, which is simply
untrue.
The correct answer is A. The author demonstrates the
meaning of “idle” in the sentence that follows the word,
in which the author describes the boy doing things that
will not help him and may lead him into trouble. Thus,
choice A is the correct answer. The implication that “idle”

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38.

The correct answer is A. The author notes in lines
31–35: “Rough as he is, if any one doubt that this child
of common clay have in him the instinct of beauty, of
love for the ideal of which his life has no embodiment,
let him put the matter to the test.” Thus, choice A is the
correct answer. Because the context suggests the
author is speaking of the child’s “instinct for beauty,”
choice B is incorrect. While there is a suggestion that no
flowers grow in the tenements, choice C is incorrect
because the author’s focus here is on the child and his
(or her) potential, as evidenced by the sentence cited
above. Similarly, the reference to the police and their
tactics suggests brutality in dealing with the children.
The focus, again, is on the child’s potential, so choice D
is incorrect.

39.

The correct answer is B. The lines, “if anyone doubt
that this child of common clay have in him the instinct
of beauty, of love for the ideal of which his life has no
embodiment,” support the idea that the tenement child
has a capacity to appreciate beauty, so choice B is the
correct answer. Neither choice A nor choice D suggests
the child has the capacity to appreciate beauty, given
his (or her) surroundings. While choice C suggests the
calming effect of flowers and juxtaposes this with the
image of a policeman’s brutal tactics, it does not
suggest the capacity to appreciate the “ideal.”

40.

The correct answer is A. The photos depict dirty
children in dirty, cluttered environments. Although the
author briefly refers to tenement children as being dirty
in line 50, he does not address how extremely unsanitary the tenements, themselves, are. These photos
support that idea that is not really addressed in the
passage. However, the author does explicitly state that
tenement homes are “joyless” in line 56, so choice B is
not the best answer. The author does not really address
the dangerousness of tenement life, but these photos
do not really depict a dangerous environment either;
they only show a dismal and dirty environment, so
choice C is not the best answer. The author mentions
that there are few job opportunities in tenement
environments in the first paragraph, but “few job
opportunities” is not the same as “no job opportunities,”
and the photos do not support the conclusion in choice
D either. In fact, the left-hand photo seems to depict

Answer Keys and Explanations
8–9, “These doubts all arise, I am inclined to think, from
your father’s attitude towards me.” Thus, choice B is
correct. Choice A is incorrect, as Robert notes in lines
24–25, “I really love and respect your father.” There is no
indication that he doubts Clara’s love for him. In fact,
lines 31–32 suggest otherwise: “You cannot think how
your letter has raised and strengthened me.” Therefore,
choice C is incorrect. In lines 32–33, Robert writes, “You
are splendid, and I have much more reason to be proud
of you than of me,” so choice D is also incorrect.

people working in some sort of makeshift factory set up
inside of a tenement.
41.

42.

43.

The correct answer is C. In lines 58–61, the author
notes that tenement children “banished and barred”
from “a yard of turf” as from “a heaven that is not for
such as they,” and notes later that there was not “a green
sod within a quarter of a mile,” making choice C is the
correct answer. While the author notes that this is “their
first lesson in ‘writin’,” the point is more about what they
wrote, so choice A is not correct. Similarly, choice B is
incorrect, as the author does not mention lack of
schooling in this paragraph. There is no support for
choice D, as the focus in this paragraph is on children’s
play.
The correct answer is D. The correct answer is D. The
author notes that “The city has no Truant Home” and
that efforts to get the child to go to school “are paralyzed by this want,” or this need for a truant home, so
choice D is the correct answer. The author notes in the
lines that precede lines 25–28 that a reformatory is full
of “vicious boys,” but the author sees a “want” or need
for a truant home, so choices A and C are incorrect. The
suggestion that the city needs a truant home because
the boy won’t go to school suggests the opposite of
choice B.
The correct answer is B. In line 36, Robert expresses his
devotion to Clara by saying that he is “entirely yours,”
and likewise, Napoleon begins his letter by noting that
“I have not spent a day without loving you; I have not
spent a night without embracing you.” Both letters
express a devotion and commitment to the relationship,
so choice B is the correct answer. While Napoleon’s
letter betrays his jealousy, Robert’s letter contains no
note of jealousy, so choice A is incorrect. Napoleon’s
letter notes his “pride and ambition” that force him away
from Josephine, a reference to his work, but Robert’s
letter mentions no such reference, so choice C is
incorrect. Likewise, choice D is incorrect, as Robert’s
letter does not lament that the two are apart.

44.

The correct answer is D. The author notes in lines
21–22, “but I cannot see why he should despise me and,
as you say, hate me without any reason.” Thus, choice D
is correct. The synonyms “despise” and “hate” suggest
that choice A is incorrect, as indifference implies little
feeling. Similarly, choices B and C are incorrect, as “hate”
and “despise” suggest dislike, not mistrust or rudeness.

45.

The correct answer is B. In lines 5–7, the author notes,
“I wonder anxiously whether . . . I had any right to bind
you to me, my angel” and then goes on to write in lines

46.

The correct answer is A. In lines 5–7, the author notes,
“I wonder anxiously whether … I had any right to bind
you to me, my angel” and then goes on to write in lines
8–9, “These doubts all arise, I am inclined to think, from
your father’s attitude towards me.” Thus, choice A is
correct. Choice B is incorrect, as Robert doubts himself
in these lines, not his relationship with Clara. In lines
22–26, Robert expresses his admiration for Clara’s father,
sentiments that do not support the inference, so choice
C is incorrect. Likewise, choice D suggests a new
commitment by Robert to their relationship, which is
also incorrect.

47.

The correct answer is C. Napoleon makes it clear that
he spends so much time thinking about how much he
misses Josephine that it is distracting him from his
responsibilities as a military leader, so choice C is the
best answer. There is no indication in the letter that
Josephine wishes she could fight alongside her
husband, so choice A is incorrect. Choice B is also
incorrect, as Napoleon questions whether she is too
busy to write to her husband, which implies that she
might have quite a few things to occupy her time.
Napoleon imagines that Josephine may no longer love
him one day, or has even found someone else to love
already, which indicates that she could regret marrying
him, so choice D is not the best answer.

48.

The correct answer is C. Napoleon writes in lines
46–48: “In the midst of my duties, whether I am at the
head of my army or inspecting the camps, my beloved
Josephine stands alone in my heart,” suggesting that he
is thinking about Josephine when he should be
thinking about his responsibilities as a military leader. In
choice A, he is merely stating that he thinks about
Josephine constantly without implying that those
thoughts distract him from anything. Choice B may
support the idea that thoughts of Josephine distracted
Napoleon from enjoying a cup of tea, but they do not
support the idea that those thoughts distracted him
from his responsibilities. Choice D indicates the efforts
he is taking to return to Josephine as quickly as possible

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Answer Keys and Explanations
without suggesting that these efforts distract him from
his responsibilities as a military leader.
49.

50.

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The correct answer is B. The context—Napoleon’s
desire to see Josephine—and the phrase “by a matter of
days” suggest that choice B is the correct answer. Choice
A is incorrect, as stretching out the time would delay his
ability to see Josephine. “Force” does not make sense
when added to the phrase “by a matter of days,” so
choice C is incorrect. Likewise, choice D is incorrect
because “cause” does not suggest the idea that
Napoleon wants to make the days go by more quickly.
The correct answer is C. In lines 31–32, Robert writes to
Clara: “You cannot think how your letter has raised and
strengthened me. …” whereas Napoleon writes to
Josephine in lines 55–56: “Ah! wretch, how could you
have written this letter? How cold it is!” Thus, choice C is
the correct answer. While Robert does indeed express
doubts, those doubts seem to stem from the attitude of
Clara’s father, not Clara’s letter, so choice A is incorrect.
Robert does not question Clara’s loyalty, though
Napoleon does question Josephine’s, thus choice B is
also incorrect. Clara’s letter to Robert only seems to have
strengthened his love for her, rather than made him feel
confused, so choice D is not correct.

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51.

The correct answer is A. Napoleon is incensed and
crushed that Josephine used vous (a formal way of
addressing someone) in her letter, whereas Robert is
delighted by the memory of Clara calling him du.
Therefore, choice A is the correct answer, and choice B is
incorrect. Likewise, choice C is incorrect because rather
than calming Napoleon, the use of vous has made him
angry. Choice D is incorrect, as there is no evidence that
Robert feels humbled by her words.

52.

The correct answer is D. In line 10, Robert notes, “It is
so easy to accept other people’s estimate of oneself.”
Similarly, Napoleon writes in lines 66–69, “You love me
less; but you will get over the loss. One day you will love
me no longer; at least tell me; then I shall know how I
have come to deserve this misfortune. . . .” Choice D
then is the correct answer. Neither Robert nor Napoleon
show any evidence of being modest, thus choice A is
incorrect. There is no evidence to support the idea that
Robert angers quickly, whereas Napoleon seems quick
to anger. Thus, choice B is not correct. While Robert
seems indecisive, Napoleon does not. In fact, he seems
to make up his mind about Josephine quickly, so choice
C is also incorrect.

Answer Keys and Explanations
Section 2: Writing and Language Test

1. A

11. B

21. D

31. A

41. B

2. B

12. B

22. B

32. B

42. B

3. A

13. C

23. A

33. A

43. D

4. C

14. B

24. D

34. B

44. B

5. A

15. D

25. A

35. D

6. A

16. A

26. D

36. C

7. A

17. A

27. D

37. A

8. B

18. C

28. C

38. D

9. B

19. B

29. B

39. A

10. D

20. C

30. D

40. C

WRITING AND LANGUAGE TEST RAW SCORE
(Number of correct answers)

1.

The correct answer is A. This choice makes the most
sense given the context of the sentence. A standing
structure added to an area, like a sign on a road, is
typically erected. It is not born, so choice B is incorrect. It
is also unlikely that the sign floated or dripped, so
choices C and D are incorrect.

2.

The correct answer is B. Choice B is correct because
the sentence is declarative and therefore requires a
period. Choice A is incorrect because the sentence is not
a question. Choice C is incorrect because it creates a
run-on. Choice D is incorrect because the sentence is
not an exclamation.

3.

4.

The correct answer is A. Choice A is correct because
“obscure” supports the characterization of the colony as
“far-flung” and out-of-the-way. Choice B is incorrect
because there is no indication that the colony is not
well-lit. Choice C is incorrect because the colony is the
opposite of obvious. Choice D is incorrect because the
word implies vagueness, which isn’t intended here.
The correct answer is C. Choice C is correct because
the sentence requires the simple past tense. Choice A is
incorrect because this is past perfect tense. Choice B is
incorrect because it is in the plural past tense, and it
should be singular. Choice D is incorrect because it is in
the future tense.

5.

The correct answer is A. Choice A is correct because
the phrase “as they seemingly float above seas of green
foliage” modifies, and thus must follow, “Buddhist
temples.” Choices B and C are incorrect because they
make it unclear what the modifying clause refers to.
Choice C is incorrect because the use of commas is
wrong.

6.

The correct answer is A. Choice A is correct because
“country’s” is a singular possessive noun referring to
Burma. Choice B is incorrect because it is plural, not
possessive. Choice C is incorrect because it requires an
apostrophe before the s. Choice D is incorrect because it
is plural possessive.

7.

The correct answer is A. The sentence should be
deleted because it is irrelevant to the passage. Choice B
is incorrect because it does not belong in the passage at
all. Choice C is incorrect because it does not expand
upon the main idea but introduces an unrelated detail.
Choice D is incorrect, because it is a detail about the
rock band, not the country.

8.

The correct answer is B. This version most effectively
and clearly presents the ideas in this sentence. The
disorganization of ideas and information in choices A, C,
and D creates confusion.

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Answer Keys and Explanations
9.

10.

The correct answer is D. This sentence opens with the
phrase “soon after,” which implies that the events have
already happened. Another indication is the use of the
past tense “lifted” in the sentence. Therefore, to maintain
correct parallel structure—along with the correct
pronoun “it” when referring to Burma—the correct
version of the underlined phrase is “offered it,” choice D.
Choice A incorrectly uses the present verb tense and
plural pronoun “them.” Choice B incorrectly uses the
present verb tense and feminine pronoun “her.” Choice
C also uses the incorrect verb tense and plural pronoun.

11.

The correct answer is B. Choice B is correct because
the pronoun “its” refers to “the country,” which is a
singular noun. Choices A, C, and D are wrong because
they do not correctly refer to the antecedent, “the
country.”

12.

The correct answer is B. Noting that Dewey is known
as “the father of public education” sets up the rest of the
passage and provides information that supports the
main idea of the passage. Although accurate, choices A,
C, and D do not support the main idea of the paragraph
and introduce ideas that are not developed in the
passage.

13.

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The correct answer is B. Only choice B eliminates
redundancies while still communicating that the album
was banned and that smugglers were punished. Choice
A is incorrect because “not allowed to be distributed in
Burma” and “for smuggling” are redundant. Choice C is
incorrect because “not allowed to be distributed in
Burma” is redundant. Choice D is incorrect; as written, it
implies that some things can be legally smuggled into
Burma. It also inaccurately suggests that merely trying
to obtain the album in Burma, not smuggle it in, carried
a possible sentence of imprisonment for three to twenty
years.

The correct answer is C. Choice C is correct because
this part of an extended prepositional phrase introduced by the phrase “emphasis on.” Because of this, no
commas are necessary as they would separate the
preposition from its other subjects (“the classroom” or
“learning environment”). Choice A is incorrect because
the comma causes confusion about the subject of the
preposition “on.” Choice B is incorrect for the same
reason and also because “or learning environment” is a
restrictive phrase and does not require commas. Choice
D is incorrect because “or learning environment” is a
restrictive phrase and does not require commas.

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14.

The correct answer is B. Choice B is correct because
the antecedent is “education,” which means the pronoun
should be “it.” Choice A is incorrect because it implies
that the antecedent is “aspects or characteristics.” Choice
C is incorrect because the passage is not written in the
first person and there is no antecedent it could logically
refer to. Choice D is incorrect because it implies that the
antecedent is Dewey, which is incorrect.

15.

The correct answer is D. Choice D is correct because
semicolons are only necessary when the list items
themselves contain commas. Since they don’t, this
series only requires commas. Choices A and C are
incorrect because they misuse semicolons. Choice B is
incorrect because it misuses colons.

16.

The correct answer is A. Changing “another” to “a
second” improves the organization because it includes
an ordinal number as the previous and following
paragraphs do. Choice B is incorrect because it does not
clarify the aspects of education. Choice C is incorrect
because the change does not eliminate supporting
information. Choice D is incorrect because the change
does not negatively affect the organization.

17.

The correct answer is A. Choice A is correct because it
matches and maintains the formal and objective tone of
the passage. Choice B is incorrect because the tone and
diction are informal. Choice C is incorrect because, while
the diction is formal, the tone is overly dramatic. Choice
D is incorrect because the tone is subjective.

18.

The correct answer is C. Choice C is correct because
the context clue “but rather” suggests a word that is the
opposite of “indirect,” and “overt” comes closest to this
meaning. Choices A, B, and D are incorrect because they
do not make sense in the context of the sentence.

19.

The correct answer is B. Choice B is correct because it
effectively sets up the fourth and final item in a list of
examples. Choice A is incorrect because it implies a
contrast which is unsupported by the context. Choice C
is incorrect because it suggests the author is looking
back, which is unsupported by the context. Choice D is
incorrect because it suggests a conclusion, which the
paragraph is not.

20.

The correct answer is C. Choice C is correct because
the noun “education” must agree in number with
“reconstruction.” Choices A, B, and D are incorrect
because “education” must be singular in order to be in
agreement with “reconstruction.”

21.

The correct answer is D. In choice D, the subordinate
clause that begins with “since” should precede the

Answer Keys and Explanations
second part of the sentence that it qualifies. Choice A is
incorrect because the subordinate clause is illogical in
the middle of the sentence. Choice B is incorrect
because the subordinate clause helps set up the rest of
the sentence and belongs at the beginning. Choice C is
incorrect because the arrangement of the clauses is
awkward and difficult to follow.
22.

The correct answer is B. Choice B supports the
implication that members of the group could find a way
to enact and undergo change without causing social
instability. Choice A is incorrect because it suggests that
change is a negative thing that must be overcome.
Choices C and D are incorrect because they both imply
meanings that are not supported by the context of the
sentence.

23.

The correct answer is A. An effective opening sentence
for this paragraph and passage would introduce the
notion of differences between the study of plants and
the study of animals, a notion further elaborated upon
in the following sentence, so choice A is correct. Choice
B is incorrect because it provides information that
refutes this notion. Choice C is incorrect because the
exploration of unique animals and plants is not the
focus or intent of the passage. Choice D is incorrect
because a school-level study of various life forms does
not effectively introduce the main ideas in the passage.

24.

The correct answer is D. Choice D accurately employs
parallel structure. Choice A is incorrect because the
word “by” before “producing arching canes” is unnecessary and prevents the clause from being parallel.
Choice B is incorrect because each part of the clause is
constructed in a different way (“by sending,” “a split,” “the
production”). Choice C is incorrect because the last part
of the clause (“in the production . . .”) is not constructed
like the rest of the clause.

25.

The correct answer is A. Choice A is correct because
“its” is a possessive determiner that refers to “desert
plant.” Choice B is incorrect because it is a contraction of
“it is.” Choice C is incorrect because it is not a word.
Choice D is incorrect because it does not make sense in
the sentence.

26.

The correct answer is D. This sentence should not be
deleted because it provides useful and relevant
information regarding the lifecycles of biennial plants
Choice A is incorrect because this information does
support the main idea of the paragraph. Choice B is
incorrect because the current placement of the
sentence is correct in the organization of the paragraph.
Choice C is incorrect because the information in this

sentence does not provide a helpful illustrative contrast
of presented ideas for readers.
27.

The correct answer is D. This version most effectively
and clearly presents the ideas in this sentence. The
disorganization of ideas and information in choices A,
B, and C create confusion.

28.

The correct answer is C. Choice C is correct because
the context of the sentence suggests a word that refers
to an attempt to determine a number. Choices A and B
are incorrect because “reducing” and “hedging” suggest
actions that are not supported by the context of the
sentence. Choice D is incorrect because it suggests a
valuation of quality and worth rather than an attempt at
counting.

29.

The correct answer is B. Choice B is correct because
the subject “suffrutescent shrubs (hemixyles)” is plural
and must be followed by the plural verb, “fall.” Choice A
is incorrect because the subject is plural and the verb is
singular. Choice C is incorrect because the subject is
singular and the verb is plural. Choice D is incorrect
because the subject is plural and the verb is singular
and not in the present tense.

30.

The correct answer is D. Choice D is correct because
both sentences are closely related, independent clauses.
Choice A is incorrect because a comma is not sufficient
to join two independent clauses. Choice B is incorrect
because there is no cause/effect relationship present,
which the word “because” implies. Choice C is incorrect
because a colon is only used to separate independent
clauses when the second clause explains or amplifies
the first, which is not the case here.

31.

The correct answer is A. The parentheses in choice A
correctly indicate that the phrase “trees and shrubs” is
supplemental information and not necessary for
understanding the rest of the sentence. Choice B is
incorrect because dashes are used to call attention to
the text that they surround, which is not intended here.
Choice C is incorrect because it makes it unclear
whether woody perennials are trees and shrubs, or if the
author is talking about them in addition to trees and
shrubs. Choice D is not correct because quotation marks
are not used to set off extraneous information, but
rather to highlight specific words or to cast doubt on a
word or phrase.

32.

The correct answer is B. Choice B is correct because
“regardless” is the correct form of this conventional
expression. Choices A, C, and D are incorrect variations
of this phrase.

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33.

The correct answer is A. Choice A is correct because
the context suggests that if the eight age states exist,
the population is healthy, viable, and not going
anywhere. Choice B is incorrect because it suggests the
population is shrinking, which is not implied by the
context. Choice C is incorrect because it suggests
impermanence, which is not implied by the text. Choice
D is incorrect because it suggests that the population is
homogenous, which is not implied by the context.

39.

The correct answer is A. Choice A is correct because
the author’s point is that “no two jobs are identical” and
that because of this, job titles can be misleading. Choice
B is incorrect as it suggests a weak or unconvincing
connection, which doesn’t make sense in the context of
the sentence. Choice C is incorrect because the
sentence is not talking about the practicality of job
titles. Choice D is incorrect because the sentence is not
suggesting job titles are unplanned or unimportant.

34.

The correct answer is B. Choice B is correct because
sentence 2 makes a broad statement about differences
in wages and makes the most sense as an introductory
statement. Choice A is incorrect because sentence 1 is
not the best introductory statement. Choices C and D
are incorrect because sentences 3 and 4 expand on an
idea presented in sentence 2.

40.

The correct answer is C. This sentence is highlighting
the reduced variability in certain occupations, which
would indicate that wage differences, if any, would be
small. Referring to these wage differences as vast,
noticeable, or productive wouldn’t support the notion
of reduced variability, so answer choices A, B, and D are
incorrect.

35.

The correct answer is D. Choice D is correct because
the dash helps draw attention to the supplemental
information that follows it. Choice A is incorrect because
a colon is not used to introduce a dependent clause that
expands on an independent clause. Choice B is incorrect
because there should be punctuation to separate the
number from the rest of the sentence. Choice C is
incorrect because a semicolon is used to join two
independent clauses.

41.

The correct answer is B. Choice B is correct because
the author is listing the factors that influence, lead to, or
affect, how much a person earns. Choice A is incorrect
because the verb “effect” is used to suggest someone
has succeeded in making something happen, which is
not intended here. Choices C and D are incorrect
because they do not make sense in the context of the
sentence.

42.

36.

The correct answer is C. Choice C is correct because
the context implies that the author wants to suggest
that the median figure hides the fact that the gap was
more than $100,000. Choice A is incorrect because it
does not make sense in the sentence—the median
figure doesn’t reduce the fact. Choice B is incorrect
because the author is not presenting a disagreement.
Choice D is incorrect because the context does not
suggest vagueness and it is grammatically incorrect.

The correct answer is B. The author’s point of view
regarding job tasks, as evidenced in the previous
sentence, is that jobs with different responsibilities will
result in different wages. Choice B is the only option
that supports this notion. Choices A, C, and D either
don’t support this or directly negate this notion.

43.

The correct answer is D. Choice D corrects the fact that
this sentence lacks a verb and is incomplete by adding
“include.” Choices A, B, and C are incorrect because they
are not complete sentences.

44.

The correct answer is B. Choice B is correct because
the only job with a lower median wage than athletes is
actor. Choice A is incorrect because broadcast news
analysts do not have a lower median wage than actors.
Choices C and D are incorrect because only actors have
a median wage lower than athletes’ median wage.

37.

The correct answer is A. The point being made in this
paragraph is that everyone is different and comes with
an individualized set of skills for different jobs.
Therefore, describing them as unique is most appropriate. The adjectives in the other answer choices don’t
support this notion and are incorrect.

38.

The correct answer is D. Choice D is correct because
the antecedent in this sentence is “each person,” and the
pronoun “she” was used previously to refer to the
antecedent. Choices A, B, and C are incorrect because
they do not align with “her” in number and gender.

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Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. B

5. C

9. A

13. B

17. 4/9 or 0.44

2. B

6. D

10. A

14. D

18. 4 or 1/2

3. D

7. C

11. A

15. B

19. 1.4 or 7/5

4. D

8. D

12. B

16. 6.28

20. 6

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B. Let the other two angles be 2x
and 5x. Thus,

4.

−( y + 3 x ) 2 − 2(2 x 2 − 3 y 2 ) = −( y 2 + 6 xy + 9 x 2 ) − 4 x 2 + 6 y 2

2 x + 5 x + 82 = 180
7 x = 98
x = 14
2 x = 28
5 x = 70

= − y 2 − 6 xy − 9 x 2 − 4 x 2 + 6 y 2
= 5 y 2 − 6 xy − 13 x 2

5.

The smallest angle = 28°.
2.

The correct answer is B. Solve the following equation
for Fy:

(2 F y )

2

( )

+ F y2 + 2F y

2

6.

15 = 3F y

= 28 + 4 i

5 = Fy

3.

The correct answer is D.
g ( a) = a − 1
f (a − 1) = (a − 1) + 2 = a 2 − 2a + 1+ 2
2

The correct answer is D.

(3 − i ) (8 + 4i ) = 24 + 12i − 8i − 4i 2
= 24 + 4 i − ( −4 )

15 = 9F y2

Therefore, Fz = 2 × Fy = 10 Newtons.

The correct answer is C. The numerator is the difference between perfect squares; x2 − y2 is equal to the
product of (x + y) and (x − y). Therefore,
x 2 + y 2 ( x + y )( x − y )
=x+y
=
x−y
x−y

T = F x2 + F y2 + F z2
15 =

The correct answer is D.

7.

The correct answer is C.

( x + y ) 2 − ( x − y ) 2 = x 2 + 2 xy + y 2 − ( x 2 − 2 xy + y 2 )
= x 2 + 2 xy + y 2 − x 2 + 2 xy − y 2
= 4 xy

f ( g ( a ) ) = a 2 − 2a + 3

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Answer Keys and Explanations
8.

9.

The correct answer is D. The confidence interval
indicates the interval that the estimated population
parameter is likely to fall within. A 95% confidence
interval of ±0.25 means that it can be said, with 95%
confidence, that the average minimum wage of all
states will fall $0.25 above the average of the randomly
selected states and $0.25 below the average of the
randomly selected states. The economist found the
average of the randomly selected states to be $7.50, so
$7.50 + $0.25 = $7.75, and $7.50 – $0.25 = $7.25.
Therefore, the average minimum wage of all states will
be found within the range of $7.25 and $7.75, with 95%
confidence.

12.

2 (2 − 9 y ) + 3 y = 3
4 − 18 y + 3 y = 3
4 − 15 y = 3
−15 y = −1
1
y=
15
13.

The correct answer is A. Since we know the roots of
the quadratic function are 0 and 4, the equation must
take the form y = ax(x − 4). We can use the vertex,
(2, −2), to find the value of a:
−2 = a(2)(2 − 4 ) = −4 a → a =

Thus, the equation of the line is y = 5x – 2.
14.

1
x ( x − 4)
2
1
= x 2 − 2x
2

y=

10.

11.

The correct answer is A. The amount of the solutions x
and y combined must equal 5 liters, so x + y = 5. The
amount of salt in the two solutions, 0.1x and 0.4y, must
combine to equal the amount of salt in the total:
(0.2)(5) = 1

The correct answer is B. The slope of the line y = 5x + 7
is 5, and a line parallel to this line would have the same
slope. Therefore, the desired line is of the form y = 5x + b.
Substitute (1, 3) into this equation to compute the value
of b:
3 = 5 × 1+ b
−2 = b

1
2

Substituting this value into the equation, we get:

The correct answer is B. Substitute the expression
equivalent to x from the second equation into the first
equation and solve:

The correct answer is D. Find the equation of a line
that passes through the points (3, 5) and (5, 6.5) by
finding the slope, then substituting one of the ordered
pairs in the slope−intercept form of an equation to
find b.
6.5 − 5
= 0.75
5−3
5 = 0.75(3) + b → b = 5 − 0.75 (3) = 2.75

m=

y = 0.75 x + 2.75
15.

The correct answer is A. The vertex of the graph of f(x)
is (29.11, 35.42). Since the coefficient of the squared
term is negative, this parabola opens downward. So, the
maximum value of f(x) is 35.42. Since this represents the
height above the ground, this number represents the
maximum height attained throughout the javelin’s path.

The correct answer is B.
3 ( x − 9) = 4 x + 3 (1− 2 x )
3 x − 27 = 4 x + 3 − 6 x
3 x − 27 = −2 x + 3
5 x = 30
x =6

16.

The correct answer is 6.28. First, convert the central
angle to radians by multiplying 144° by

p ; this gives

180∞

4p
radians. Next, the diameter of the circle is 5 inches,
5

so its radius is 2.5 inches. Therefore, the length of the
 4π 
desired arc is S = rθ = (2.5 inches) i   ≈ 6.28 inches.
 5

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Answer Keys and Explanations
17.

The correct answer is

4
(4/9) or 0.44.
9

19.

1
1 
1
 2 − x  = x − ( x − 3)
4
3
3

The correct answer is 1.4 or

To find the x-intercept, set y equal to 0 and solve for x:
0 − 3 = 5 ( x − 2)

1 

3  2 + x  = 12 x − 4 ( x − 3)

3 
6 − x = 12 x − 4 x + 12
6 − x = 8 x + 12
−6 = 9 x
6
− =x
9
2
− =x
3
2

4
 2
So, x =  −  = .
 3
9
2

18.

−3 = 5 x − 10
7 = 5x
7
=x
5
20.

The correct answer is 6.

x +3 = x −3

(

1
The correct answer is 4 or
(1/2). (Either is
2
acceptable.)
x 2 + 4 = 9x − x 2
2x 2 − 9x + 4 = 0

(2 x − 1) ( x − 4) = 0
x=

7
(7/5).
5

x +3

)

2

= ( x − 3)

2

x + 3 = x 2 − 6x + 9
0 = x 2 − 7x + 6

0 = ( x − 6) ( x − 1)
x = 6 orr x = 1

Because 1+ 3 = 2 ≠ 1− 3 = −2 , only x = 6 is an actual
solution.

1
or x = 4
2

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Answer Keys and Explanations
Section 4: Math Test—Calculator

1. B

9. D

17. A

25. B

33. 11

2. A

10. A

18. C

26. A

34. 1.02

3. B

11. B

19. B

27. C

35. 24.2

4. D

12. B

20. A

28. C

36. 70

5. D

13. C

21. A

29. A

37. 0.8

6. C

14. B

22. D

30. C

38. 32

7. A

15. D

23. B

31. 45

8. D

16. B

24. D

32. 480

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B. Let x = amount earned each
month. Since the salesperson earned twice as much in
December as in every other month, 2x = amount earned
in December. Then, the entire earnings are

5.

The correct answer is D. Because this is a recursive
percent decrease, an exponential model is appropriate.
A model for exponential decay is f(t) = a(1 − r)t, where a
is the initial amount, and r is the decay rate. The initial
amount is 50,000 and the decay rate is 0.15, so the
appropriate model in this case is
A(n) = 50,000(1 − 0.15)n = 50,000 × 0.85n.

6.

The correct answer is C. Substitute 19.5 for f(x) and
solve the resulting equation for x:

11x + 2x = 13x. 2 x = 2 .
13 x 13
2.

3.

The correct answer is A. Because the population of
village A is decreasing by 120 per year, the population in
year y will be 6,800 − 120y. Because the population of
village B is increasing by 80 per year, the population in
year y will be 4,200 + 80y. Set the two expressions equal
to find when the populations will be the same:
6,800 − 120y = 4,200 + 80y.

The correct answer is D.
C=

5
(F − 32)
9

9
C = F − 32
5
9
C + 32 = F
5
9
F = C + 32
5

  634

7.

The correct answer is B. There are a total of 27 + 29 +
35 + 24 = 115 males who responded to the survey. Of
the 115 males, 35 support candidate C:
35
7
=
115 23

4.

19.5 = 1.5 x + 15
4.5 = 1.5 x
3= x

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The correct answer is A. There are 360 degrees in a
circle. A 24-degree sector is
2
6 % of a circle.
3

24
= 0.067 , or about
360

8.

The correct answer is D. The confidence interval
indicates the interval into which the estimated population parameter is likely to fall.

9.

The correct answer is D. This is an inverse proportion,
that is:
9
x
=
6 120
6 x = 1, 080
x = 180

Answer Keys and Explanations
10.

The correct answer is A. Since x − y = 4, y = x − 4. Set
the equations equal to each other. Then combine like
terms and use the quadratic formula to solve for x. To
solve for y, substitute the value for x into one of the
given equations. The answer will be y2:

14.

x pounds
40 pounds
=
36 cubic feet 0.8 cubic feet
( 40)(36)
x=
0.8
x = 1, 800

2

x − 4 = x − 7 x + 10
0 = x 2 − 8 x + 14
x=

−( −8 ) ± ( −8 ) 2 − 4(1)(14 )
=4± 2
2(1)

y = x − 4 = (4 ± 2 ) − 4 = ± 2
y2 =2

11.

The correct answer is B. Four inches is

1
ft.
3

15.

The correct answer is D. The x-intercept occurs at the
point where y = 0, or where no products will be sold.

16.

The correct answer is B. To find the equation that
shows the vertex of the parabola, change from factored
form to standard form, and then complete the square:

The volume of the added level is:
1
75 × 42 × = 1, 050 cubic ft. There are 7.48 gallons in
3
1 cubic ft., so 1,050 cubic ft. × 7.48 gal./cubic ft. =
7,854 gallons.
12.

The correct answer is B. Let x = number of minutes to
4
fill
of bucket. Then,
7
3 4
3 4
7 = 7 , or =
1 x
1 x
3x = 4
4
x=
3

13.

y = (x − 5)(x + 1)
y = x2 − 4x – 5
y = x2 − 4x + 4 – 5 – 4
y = (x – 2)2 − 9
17.

The correct answer is A. The arithmetic mean of the
algebra test scores is 50 + 50 + 60 + 60 + 70 + 70 + 70 +
80 + 80 + 90 = 680 ÷ 10 = 68.

18.

The correct answer is C. The slope of the line of best fit
is positive, indicating that the y-variable tends to
increase as the x-variable increases.

19.

The correct answer is B. Set y = 70 and solve for x:

The correct answer is C.

12
r

70 = 0.76 x + 27.6
42.4 = 0.76 x
42.4
x=
≈ 56
0.76

12
5

A radius drawn perpendicular to a chord bisects the
chord. Construct the radius as shown above.
52 + 122 = r 2
25 + 144 = r 2
169 = r 2
13 = r

The correct answer is B. Three inches equal 0.25 feet.
To cover the garden, we’ll need 12 feet × 12 feet × 0.25
feet = 36 cubic feet of garden soil.

20.

The correct answer is A. At t = 0, the object is moving
at –9.8(0) = 0 meters per second. At t = 4 seconds, the
object is moving at –9.8(4) = –39.2 meters per second.
The velocity must be equal to or between these two
extremes.

21.

The correct answer is A.
80
= 40%
200
40% − 3.5% = 36.5%
40% + 3.5% = 43.5%

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Answer Keys and Explanations
22.

The correct answer is D. Since we are interpolating, we
can use a linear model as the basis for the estimate. The
54.5 − 42
rate of change is
= 2.5 . In 2020, the target
2025 − 2020

28.

The correct answer is C. The following is the solution
set:
y

is 42, and the target increases by 2.5 each year.
23.

24.

The correct answer is B. Multiply 1.45 by x and 2.75 by
y. The total power supply must be at least 200, so the
inequality is 1.45x + 2.75y ≥ 200.

9
y=

The correct answer is D. First, find the solutions:

–3
(x– 6)
2

3

x − 4x = 3
2

2

x2 − 4 x + 4 = 7

y=

( x − 2 )2 = 7

x

6

–3
(x– 2)
2

x −2 = ± 7
x =2± 7
Then, find the absolute value of the difference of the
solutions:

(2 + 7 ) − (2 − 7 ) = 2
25.

7

The correct answer is B. Let n be the number of nickels
and q be the number of quarters. Then, solve the
resulting system of equations:
0.05n + 0.25q = 3.10
n + q = 18 → q = 18 − n
0.05n + 0.25(18 − n) = 3.10
0.05n + 4.5 − 0.25n = 3.10
−0.2n = −1.4
n=7

Notice, the solution set does not intersect Quadrant III.
29.

The correct answer is A. Since 1 is a 0 of the graph,
(x − 1) is a factor of the polynomial.

30.

The correct answer is C. Since (−3, 2) and (3, 2) are the
endpoints of a diameter of a circle, the center of the
circle is at (0, 2) and the radius of the circle is 3. The
general form of the equation of a circle with center (a, b)
and radius r is (x − a)2 + (y − b)2 = r2. Substituting the
values for a, b, and r, we obtain x2 + (y − 2)2 = 9.

31.

The correct answer is 45.
x
= 75
12
x = 900
900
= 45
20

Since there are 7 nickels, there must be 11 quarters:
11 − 7 = 4.
26.

The correct answer is A. Because the rate of growth is a
fixed percentage, an exponential graph is appropriate.

27.

The correct answer is C. The slope is –4 feet per second
(since you are descending as time t increases) and the
initial height is 150 feet at t = 0. So, the linear function is
d(t) = –4t + 150.

32.

The correct answer is 480. Let x represent the width of
the family room. The dimensions are given in the
following diagram:
Family Room

2x

+

2

2x – 2

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x

Answer Keys and Explanations
Use the Pythagorean theorem to obtain the equation
x2 +(2x – 2)2 = (2x + 2)2.

36.

Solve for x:
x 2 + (2 x − 2 ) 2 = (2 x + 2 ) 2
x 2 + 4x 2 − 8x + 4 = 4x 2 + 8x + 4

2l + 2(10 ) = 160
2l + 20 = 160
2l = 140
l = 70

x 2 − 16 x = 0
x ( x − 16 ) = 0
x = 0 ,16
So, the width of the family room is 16 feet and its
length is 2(16) – 2 = 30 feet. Therefore, the area is
(16 feet)(30 feet) = 480 square feet.
33.

So, the longest that such a pen can be is 70 yards.
37.

6 + 7 + 15 + x + y
= 10
5
28 + x + y = 50
x + y = 22

Multiply the second equation by 3.6 and subtract it
from the first equation. Then, solve for y:
3.6 x + 2.4 y = 12
3.6 x − 3.6 y = 7.2
6 y = 4.8
y = 0.8

The average of x and y is:

34.

35.

The correct answer is 1.02. Because this is an exponential growth model, divide the population in 2013 by
the population in 2012 to find the value of b:
(38.19 million) ÷ (37.44 million) ≈ 1.02.
The correct answer is 24.2.

The correct answer is 0.8.
3.6 x + 2.4 y = 12
x−y =2

The correct answer is 11.

x + y 22
=
= 11
2
2

The correct answer is 70 yards. The perimeter, P, of a
rectangle is 2l + 2w = P. We are given that P = 160. The
largest value of l occurs when the smallest value of w is
used. So, using w = 10 yards and P = 160 yards in this
formula yields:

38.

The correct answer is 32. Since g(x) is a translation of
f(x) 3 units to the right, g(x) = f(x − 3):
g(9 ) = f (9 − 3)
= f (6)
= 62 − 4
= 32

20 × 1.1 = 22
22 × 1.1 = 24.2

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Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
In the right-hand column, you will find an analysis of the passage by Elizabeth Roberts-Pedersen, noting how the writer used evidence, reasoning, and stylistic or persuasive elements to support her claims, connect the claims and evidence, and add power to
the ideas she expressed. Check to see if you evaluated the passage in a similar way.

1

2015 marks several important First World War
anniversaries: the centenary of the first use of poison gas
in January; the centenary of the Gallipoli landings and the
Armenian genocide in April. It is also 100 years since The
Lancet published Charles S. Myers’ article, “A Contribution
to the Study of Shell Shock.”

1

The writer provides a historical context to
support her central idea: people have long
known that war is psychologically traumatic.

The study of shell shock

  638

2

Myers’ article is generally regarded as the first use of the
term “shell shock” in medical literature. It was used as
a descriptor for “three cases of loss of memory, vision,
smell and taste” in British soldiers admitted to a military
hospital in France.

2

The writer lays the groundwork for her
argument by providing facts about and
describing the symptoms of this trauma, which
was initially called “shell shock.”

3

While Myers presented these cases as evidence of the
spectacular concussive effects of artillery on the Western
Front, British medical opinion soon came to regard these
symptoms as psychological in origin.

3

The writer supports her argument with facts
that show that “shell shock,” which was at
first used to describe symptoms caused by
“concussive effects of artillery,” came to be seen
as “psychological in origin.”

4

The men presenting to medical officers with tics, tremors,
and palpitations, as well as more serious symptoms of
“functional” blindness, paralysis, and loss of speech, were
not concussed—but nor were they necessarily cowards or
malingerers.

4

The writer strengthens her argument with facts
that demonstrate those suffering from shell
shock were suffering genuine psychological
trauma, and were not, as often believed,
cowards or people trying to avoid combat. The
author’s examples of “functional” problems
shows that even without physical damage,
people can become deaf, mute, or paralyzed
because of psychological damage.

5

Instead, these were men simply worn down by the
unprecedented stresses of trench warfare—in particular,
the effort required to push out of one’s mind the prospect
of joining the ranks of the maimed or the corpses lying in
no man’s land. . . .

5

The writer offers evidence that shows the
psychological effects of combat.

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Answer Keys and Explanations
6

For contemporaries and later for historians, shell shock
came to encapsulate all the horror of this new form of
industrialized warfare. As historian Jay Winter suggests, it
moved “from a diagnosis into a metaphor.”

6

The writer quotes a historian who views shell
shock not only as devastating in itself, but as
absolute confirmation of the horrors of war.

...
Developing a diagnosis
7

It is tempting to view shell shock as the unambiguous
turning point in psychiatry’s history, popularizing the idea
that unconscious processes might produce symptoms
that operate separately from moral qualities such as
endurance and courage. However, scholarship over the
last 15 years suggests that this position was far from
widely accepted.

7

The writer makes the point that even though
shell shock was being generally accepted as a
legitimate condition, there was still resistance
to the idea.

8

… The notion that many patients had some
“predisposing” weakness—independent of their combat
experiences—persisted throughout the interwar period
and into the Second World War.

8

Continuing to trace resistance to the validity
of shell shock, the writer cites one opposing
argument. She also provides additional
historical perspective, saying that resistance
continued even into WWII.

9

It wasn’t until the Vietnam War that this formulation
was reversed, which in turn bridged the gap between
combatant syndromes and the civilian sphere.

9

The writer completes this part of her argument,
providing a specific time frame (the Vietnam
War) for when shell shock was fully legitimized
as a combat-related condition. She also
identifies this period as a time when the
concept of trauma-caused damage began to
be extended to civilian experiences outside of
military participation.

10 This development is only comprehensible as part of a
broader political context. The notion that the Vietnam
War exacted a form of psychic damage on American
soldiers was championed by the anti-war activists
of Vietnam Veterans Against the War (VVAW) and
psychiatrists Chaim Shatan and Robert Jay Lifton.

10

The writer provides historical, political, and
social contexts for this acceptance.

11 “Post-Vietnam syndrome,” Shatan wrote, was caused by
the “unconsummated grief” of a brutal and brutalizing
war.

11

The writer uses the evocative words brutal and
brutalizing to communicate the particular
horrors of the Vietnam War.

12 The VVAW’s advocacy was instrumental in securing official
recognition for this condition. It was included in 1980 in
the third edition of the Diagnostic and Statistical Manual
of Mental Disorders (DSM-III) as “post-traumatic stress
disorder.”

12

The writer provides facts and dates to show
when “shell shock” was officially recognized
as a legitimate condition and when it was
renamed post-traumatic stress disorder (PTSD).

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Answer Keys and Explanations
13

PTSD’s inclusion in DSM-III legitimated the suffering
of Vietnam veterans and held out the possibility
of subsidized medical care and compensation. But
the DSM-III definition of PTSD was significant in two
additional ways.

13

The writer explains why official recognition
of PTSD was so important. She details how
the shift in emphasis from the patient to the
experience removed the stigma from those
suffering from PTSD.

14

The writer cites benefits that sufferers of PTSD
can now receive as a consequence of the
improved attitude toward PTSD.

15

The writer addresses the perception of PTSD
today, citing two recent examples of former
soldiers linked to PTSD.

16

The writer concludes her argument by
juxtaposing these modern instances of PTSD
with the article that introduced the term “shell
shock” and restating her central idea: The
psychological consequences of war are as
relevant and deserving of attention today as
they were 100 years ago. By referring to the
100 years since Myers’ article on shell shock,
the writer reinforces her central idea that she is
offering “proof of war’s traumatic history.”

First, it identified the disorder as a condition that could
afflict soldiers and civilians alike—not a diagnosis
exclusive to combat, like shell shock.
Second, it focused attention on the continuing effects of
a traumatic experience, rather than on the personality
and constitution of the patient.
14 The ramifications of these changes have been immense.
PTSD and a broader field of “traumatology” are now
entrenched in psychiatric and popular discourse. In
Australia, we now assume that warfare is objectively
traumatizing, and that governments ought to provide
medical and financial support for affected service
personnel, even if a recent Four Corners program
confirmed that this is not always the case.
How is PTSD viewed today?
15 Though PTSD has its origins in opposition to the Vietnam
War, the politics of the condition are now largely
ambivalent, with its significance shifting according to
circumstance.
This point is well illustrated by the film American Sniper,
which demonstrates the possibility of two contrary
positions. After his return to civilian life, SEAL sniper Chris
Kyle (Bradley Cooper) is shown to be suffering from some
characteristic after-effects of combat. . . .
…
The real Chris Kyle was shot dead by Eddie Ray Routh
[another veteran], in 2013. At trial, the accused’s lawyers
pursued a defense of insanity, compounded by the
inadequate care provided by veterans’ mental health
services. Routh was found guilty of Kyle’s murder in March
of 2015.
16

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In the 100 years since Myers’ article on shell shock, the
psychological consequences of war remain as relevant as
ever.

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Answer Keys and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Elizabeth Roberts-Pedersen.

High-Scoring Essay
Elizabeth Roberts-Pedersen claims that the psychological consequences of war have always been with us; it just took time for
us to realize it. To convince us, she uses evidence and reasoning that carefully develop and reinforce her premise. With a few
persuasive elements, her article brings us to the same conclusion: war has severe consequences that don’t disappear when
peace is declared.
Roberts-Pedersen begins the discussion of PTSD by citing an article published 100 years ago that contained the first mention
of a condition known at the time as shell shock. Soldiers suffering from shell shock were described as having physical
symptoms, such as blindness and paralysis. At first attributed to the effects of artillery, the medical community soon accepted
the cause as the stress and exhaustion of combat rather than physical injury. Unfortunately, the men were considered to be
weak individuals by popular medical opinion of the time.
In the section titled “Developing a diagnosis,” Roberts-Pedersen uses reason to explain how popular opinion toward this
condition changed and uses evidence to prove that the change occurred. She credits the Vietnam War and the public’s
response to the war for the change. Anti-war activists and psychiatrists promoted a description of Vietnam veterans’ condition
as grief caused by a “brutal and brutalizing war.” The phrasing shows us that the soldiers with this condition are victims of the
war, just as soldiers who are physically wounded in combat are. The image of veterans with shell shock morphed from “weak
individuals” to “noble heroes who suffer from brutal acts of war.” The evidence she cites for this claim is the addition of posttraumatic stress disorder (PTSD) to the official medical manual, Diagnostic and Statistical Manual of Mental Disorders (DSM-III).
She explains the consequences by showing the cause (including the condition in the manual) with its effects (people with
PTSD are now treated well by the military).
In the final section, Roberts-Pedersen reminds us of the American Sniper movie. Both the hero and the villain in the movie
have combat experience. Regardless of the men’s conditions, the audience easily distinguishes the hero from the villain.
Understanding of the medical condition first described 100 years ago is needed to understand the movie. This final piece of
evidence persuades us that PTSD is a condition that continues to affect lives today, and we need to see it with clear eyes.

Low-Scoring Essay
Elizabeth Roberts-Pedersen is a writer familiar with shell shock, which is called PTSD today. She first discovered shell shock
100 years ago and wrote about it in a medical book. Shell shock was a head injury that happens when men close to the
bomb are shocked when the bomb explodes. The light is bright enough to blind them and the sound can make them deaf
and dumb or paralyze them. They studied this in three British soldiers who were in a French hospital.
Doctors studied this a long time and changed the name to PTSD. They changed the name because the same thing can
happen when people who aren’t in the military get shocked by something bad. Now, it’s a stress disorder that doctors can
treat with medicine. Civilians can get it now after a bad thing happens like a riot or a bombing but they don’t get as stressed
about it anymore. Now they can cure it or at least treat it.
The writer uses a movie I saw called American Sniper. The sniper does some stuff during the war and gets PTSD. A bad guy
who was also in a military unit killed the sniper. He tries to tell people that he had PTSD and that’s why he killed the sniper.
The writer says that the story in the movie, which is true, is proof that PTSD still happens today. You hear about it in the news
pretty often. That makes it important for people to know about, which is why she wrote about it and why we should know
about it.

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Computing Your Scores
COMPUTING YOUR SCORES
Now that you’ve completed this practice test , it’s time to compute your scores. Simply follow the instructions on the following pages,
and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation as
possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then you’ll calculate the total score. It sounds a little confusing, but we’ll take
you through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test..
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for
wrong answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page 646. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1.  	 Count the number of correct answers you got on the Section 3: Math Test—No Calculator and the Section 4: Math Test—
No Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2.  	 Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—No Calculator.
3.  	 Use the Raw Score Conversion Table 1: Section and Test Scores on page 646 and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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Computing Your Scores
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test that focus on linear equations and inequalities.

• Add up your total correct answers from these sections:
•
•

ºº Math Test—No Calculator: Questions 3, 9, 12, 13–15, 17–19
ºº Math Test—Calculator: Questions 2, 6, 10, 15, 20, 22, 23, 27, 29, 37, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
the interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 8, 10
ºº Math Test—Calculator: Questions 1, 3, 5, 7–9, 11, 12, 14, 17–19, 21, 26, 33, 35
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability
to progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations,
and interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 2–4, 6, 9, 11, 16
ºº Math Test—Calculator: Questions 4, 10, 16, 24, 29, 34, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Passport to Advanced Math subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 1, 3, 7–9, 16–19, 22, 23, 26–28, 30, 33, 34, 36, 37, 39, 42, 44

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 2, 4–6, 11, 13–15, 20, 21, 24, 25, 29, 31, 32, 35, 38, 40, 41, 43

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Standard English Conventions subscore.
  644

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Computing Your Scores
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 4, 8, 13, 17, 27, 30, 33, 37, 44, 49
ºº Writing and Language Test: Questions 1, 3, 18, 22, 28, 33, 36, 39
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts.

• Add up your total correct answers from Sections 1 and 2:
•
•

ºº Reading Test: Questions 3, 6, 16, 20, 26, 29, 39, 42, 46, 48
ºº Writing and Language Test: Questions 7, 8, 12, 16, 23, 26, 27, 42, 44
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 647 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these questions:
ºº
ºº
ºº
ºº
ºº
ºº

Reading Test: Questions 32–52
Writing and Language Test: Questions 7–9, 43
Math Test—No Calculator: Question 8
Math Test—Calculator: Questions 2, 3, 21, 22, 26, 31, 34
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 648 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 11–31
ºº Writing and Language Test: Questions 23, 26, 27, 29, 31
ºº Math Test—No Calculator: Questions 10, 11
ºº Math Test—Calculator: Questions 4–6, 9, 20, 23
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 648 to determine your Analysis in Science cross-test
score.

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  645

Computing Your Scores

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

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TOTAL SAT® SCORE
(400–1600)

Computing Your Scores

Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

2

1

1

2

2

5

2

2

3

2

2

3

3

6

3

3

4

3

2

4

4

7

4

4

5

4

3

5

5

8

5

5

6

5

4

6

6

9

6

6

7

6

5

6

7

10

6

7

8

6

6

7

8

11

7

8

9

7

6

8

8

11

8

8

10

7

7

8

9

12

8

9

11

8

7

9

10

12

9

10

12

8

8

9

10

13

9

10

13

9

8

9

11

13

10

11

14

9

9

10

12

14

11

12

15

10

10

10

13

14

12

13

16

10

10

11

14

15

13

14

17

11

11

12

15

14

15

18

11

12

13

15

15

19

12

13

15

20

12

15

21

13

22

14

23

14

24

15

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Computing Your Scores
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

1

10

11

19

29

27

2

11

12

20

30

27

3

12

13

21

30

28

4

14

14

22

31

29

5

15

15

23

32

30

6

16

16

24

32

30

7

17

17

25

33

31

8

18

18

26

34

32

9

20

19

27

35

33

10

21

20

28

35

33

11

22

20

29

36

34

12

23

21

30

37

35

13

24

22

31

38

36

14

25

23

32

38

37

15

26

24

33

39

38

16

27

24

34

40

39

17

28

25

35

40

40

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Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

Computing Your Scores
Conversion Equation 3: Cross-Test Scores

ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

RAW SCORE

ANALYSIS IN SCIENCE
QUESTIONS

Reading Test

32–52

11–31

Writing and
Language Test

7–9, 43

23, 26, 27, 29, 31

Math Test—No
Calculator

8

10, 11

Math
Test—Calculator

2. 3. 21, 22, 26, 31,
34

4–6, 9, 20, 23

RAW SCORE

TOTAL

ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (10–40)

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Practice Test 2—Answer Sheet
Section 1: Reading Test
1.

12.

23.

33.

43.

2.

13.

24.

34.

44.

3.

14.

25.

35.

45.

4.

15.

26.

36.

46.

5.

16.

27.

37.

47.

6.

17.

28.

38.

48.

7.

18.

29.

39.

49.

8.

19.

30.

40.

50.

9.

20.

31.

41.

51.

10.

21.

32.

42.

52.

11.

22.

Section 2: Writing and Language Test
1.

10.

19.

28.

37.

2.

11.

20.

29.

38.

3.

12.

21.

30.

39.

4.

13.

22.

31.

40.

5.

14.

23.

32.

41.

6.

15.

24.

33.

42.

7.

16.

25.

34.

43.

8.

17.

26.

35.

44.

9.

18.

27.

36.

Section 3: Math Test—No Calculator
1.

4.

7.

10.

13.

2.

5.

8.

11.

14.

3.

6.

9.

12.

15.

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Practice Test 2—Answer Sheet
Section 3: Math Test—No Calculator
16.

17.

18.

19.

20.

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2

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2

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2

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3

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3

3

3

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3

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3

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3

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4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

Section 4: Math Test—Calculator
1.

7.

13.

19.

25.

2.

8.

14.

20.

26.

3.

9.

15.

21.

27.

4.

10.

16.

22.

28.

5.

11.

17.

23.

29.

6.

12.

18.

24.

30.

31.

32.
.

/
.

/
.

.

0

0

0

1

1

2

2

3

.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

7
8

7
8

7
8

9

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34.
.

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.

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0

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3

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4
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4
5

4
5

4
5

6

6

6

6

7
8

7
8

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9

36.

  652

33.
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0

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2

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2

2

2

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Practice Test 2—Answer Sheet
Section 5: Essay
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Practice Test 2
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

Questions 1–11 are based on the following
passage and supplementary material.
“A Menace to U.S. Public Health” was authored by Rob Wilkins, a
member of the National Federation of Professional Trainers (NFPT).
The NFPT certifies personal fitness trainers to understand the fundamental exercise science principles in order to provide safe and
effective fitness programs to individuals or small groups. The article
appears on NFPT’s website, http://www.nfpt.com.

Line
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25

“In the United States, even the Grim Reaper is flabby.”
– Dr. Frank W. Booth, University of Missouri-Columbia
Being fat and physically inactive now has a name—
Sedentary Death Syndrome or “SeDS.” Approximately 2.5
million Americans will die prematurely in the next ten
years due to SeDS, a number greater than all alcohol,
guns, motor vehicles, illicit drug use, and sexual behavior
related deaths combined.
Research has identified SeDS as the second
largest threat to public health (heart disease remains
the number one cause of death for Americans) and is
expected to add as much as $3 trillion to healthcare
costs over ten years, more than twice the tax cut recently
passed by the U.S. Senate. Frank W. Booth, a professor
at the University of Missouri-Columbia, stated that he
invented the term SeDS to emphasis his point that, in
the United States, even the Grim Reaper is flabby.
Professor Booth’s goal is to make the public and
the federal government pay more attention and spend
more money on getting the average American to
become more physically active. “We knew that there
were approximately 250,000 people in the United
States each year dying of inactivity-related diseases,
but the phrase inactivity-related disease lacks pizzazz,”
Booth said. Without a catchy name, the condition wasn’t
getting enough attention, he said. “One day while I was
out jogging, it hit me: Why not call it SeDS?”
Approximately two-thirds of American adults are
currently overweight or obese according to the Center

30 for Science in the Public Interest (CSPI). Due to the

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65

fact that more than one-fourth of Americans are not
physically active in their leisure time, obesity has
doubled, and Type 2 diabetes (also known as adultonset diabetes) has increased tenfold. Type 2 diabetes
is a devastating disease that may lead to complications
such as blindness, kidney failure, heart disease, circulatory problems that can result in amputation, and
premature death.
Between 1982–1994, one third of all new cases of
Type 2 diabetes were among people ages 10–19. The
then-Surgeon General of the United States recently
observed that, “We are raising the most overweight
youngsters in American history.” In 2011–2012, 8.4%
of 2- to 5-year-olds had obesity compared with 17.7%
of 6- to 11-year-olds, and 20.5% of 12- to 19-year-olds.
Studies indicate that currently about 17% of
the nation’s children are obese. This is not surprising,
considering that the average American child spends
900 hours per year in school but 1,200 hours watching
television, according to the TV-Turnoff Network.
The problem is made worse by the fact that
fewer than 3 in 10 high school students get at least
60 minutes of physical activity every day. Less than
half (48%) of all adults meet the 2008 Physical Activity
Guidelines.
“Our bodies were designed to be physically
active,” said Scott Gordon of East Carolina University.
The trouble is that hard work, from farming to simply
doing household chores without appliances, is no
longer part of ordinary life for most people, he said.
Gordon called for activity to be put back in. “In adults,
this may mean planning exercise into your daily
routine,” he said. “However, it may be as simple as
taking the stairs instead of the elevator a couple of
times a day.” Booth and his supporters said a special
effort must be made to reach children, so they won’t
turn fat and weak like their parents and, also like their

CONTINUE
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Practice Test 2

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parents, get sick and die early. “Perhaps the greatest
tragedy is that ailments previously associated with
the middle-aged and older population will now affect
our children and will serve to drastically decrease their
quality of life,” said researcher Ron Gomes of the University of Delaware.
All Americans may incur a severe decline in their
health due to consistent physical inactivity. Thirty-five
known conditions are exacerbated by physical inactivity;
they include arthritis pain, arrhythmias, breast cancer,
colon cancer, congestive heart failure, depression,
gallstone disease, heart attack, hypertension, obesity,
osteoporosis, peripheral vascular disease, respiratory
problems, Type 2 diabetes, sleep apnea, and stroke.
Providing enjoyable experiences is a potent
strategy for increasing activity levels in youth, their
attitude about the value of exercise, and ultimately
long-term health outcome. Introducing and making
exercise fun for young children may help them develop
commitment and a positive attitude toward physical
activity as they go through adolescence and adulthood.

1

2

The author most likely selected the particular causes of
death in lines 6–7 (“alcohol . . . behavior”) to
A.

shock the reader with the various ways one could
die.

B.

prove that SeDS has become the most common
cause of death.

C.

show that some of the most common causes of
death are not as common as SeDS.

D.

prevent the reader from engaging in destructive
and self-destructive behavior.

The structure of the article is designed to
A.

present opinions backed up by factual detail.

B.

frighten readers who are ignoring their weight
issues.

C.

offer testimonials from those who are most
affected.

D.

focus on statistical data and how it is being
interpreted.

Number (in thousands)

Number in Thousands of New Cases of Diagnosed Diabetes Among
Adults Aged 18 –79 Years, U.S. 1980–2011
1,900
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
900
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Practice Test 2
3

4

5

6

7

The author includes a quote featuring the Grim Reaper in
line 1 to
A.

indicate the gravity of a problem.

B.

lighten the tone of an otherwise serious article.

C.

to make the concept of death more understandable.

D.

frighten the reader with a scary image.

Based on the passage, which choice best describes the
relationship between the design of our bodies and the fact
that obesity has doubled?
A.

Humans are naturally prone to obesity.

B.

Weight gain is passed from parents to children.

C.

People eat more in order to perform modern
activities.

D.

Physical work is no longer part of most people’s lives.

As used in line 4, “sedentary” most nearly means
A.

inactive.

B.

robust.

C.

sudden.

D.

obese.

The author indicates that SeDS
A.

may soon surpass heart disease as the number one
cause of death.

B.

has made Dr. Frank W. Booth a respected and
well-known professor.

C.

does not affect young people significantly.

D.

has financial negative impacts as well as physical
ones.

8

9

It can reasonably be inferred from the passage and the chart
that drastic increases in new cases of Type 2 diabetes began
around
A.

1980.

B.

1988.

C.

1998.

D.

2009.

As used in line 24, “pizzazz” most nearly means
A.

research.

B.

oomph.

C.

seriousness.

D.

clarity.

10 The passage most strongly suggests which of the following?
A.

A catchy name will motivate people to lose weight.

B.

Moving the body is essential to health.

C.

Type 2 diabetes is another form of obesity.

D.

Children can have good habits despite poor role
models.

11 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 18–21 (“Professor . . . active”)

B.

Lines 30–34 (“Due to . . . tenfold”)

C.

Lines 34–38 (“Type 2 . . . death”)

D.

Lines 68–73 (“Perhaps . . . Delaware”)

Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 11–13 (“and is . . . ten years”)

B.

Lines 14–15 (“Frank . . . Columbia”)

C.

Lines 18–20 (“Professor . . . money”)

D.

Lines 21–23 (“We knew . . . diseases”)

CONTINUE
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Practice Test 2
Questions 12–22 are based on the following passage.
This passage is excerpted from Helen Hunt Jackson’s A Century of
Dishonor, published in 1881. In 1879, Jackson became a Native
American rights activist after witnessing a speech by Ponca chief
Standing Bear.

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There are within the limits of the United States
between two hundred and fifty and three hundred
thousand Indians, exclusive of those in Alaska. The
names of the different tribes and bands as entered in
the statistical table, so the Indian Office Reports, number
nearly three hundred.
There is not among these three hundred bands of
Indians one which has not suffered cruelly at the hands
either of the Government or of white settlers. The poorer,
the more insignificant, the more helpless the band, the
more certain the cruelty and outrage to which they have
been subjected. This is especially true of the bands on
the Pacific slope. These Indians found themselves all
of a sudden surrounded by and caught up in the great
influx of gold-seeking settlers, as helpless creatures on a
shore are caught up in a tidal wave. There was not time
for the Government to make treaties; not even time for
communities to make laws. The tale of the wrongs, the
oppressions, the murders of the Pacific-slope Indians in
the last thirty years would be a volume by itself, and is
too monstrous to be believed.
It makes little difference, however, where one opens
the record of the history of the Indians; every page and
every year has its dark stain. The story of one tribe is the
story of all, varied only by differences of time and place;
but neither time nor place makes any difference in the
main facts. Colorado is as greedy and unjust in 1880 as
was Georgia in 1830, and Ohio in 1795; and the United
States Government breaks promises now as deftly as
then, and with an added ingenuity from long practice.
One of its strongest supports in so doing is the
wide-spread sentiment among the people of dislike to
the Indian, of impatience with his presence as a “barrier
to civilization” and distrust of it as a possible danger.
The old tales of the frontier life, with its horrors of Indian
warfare, have gradually, by two or three generations’
telling, produced in the average mind something like
an hereditary instinct of questioning and unreasoning
aversion which it is almost impossible to dislodge or
soften.
President after president has appointed commission after commission to inquire into and report
upon Indian affairs, and to make suggestions as to
the best methods of managing them. The reports are

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Indians, of perfidies on the part of the Government; they
counsel, as earnestly as words can, a trial of the simple
and unperplexing expedients of telling truth, keeping
promises, making fair bargains, dealing justly in all ways
and all things. These reports are bound up with the Government’s Annual Reports, and that is the end of them.
The history of the Government connections with
the Indians is a shameful record of broken treaties and
unfulfilled promises. The history of the border white
man’s connection with the Indians is a sickening record
of murder, outrage, robbery, and wrongs committed by
the former, as the rule, and occasional savage outbreaks
and unspeakably barbarous deeds of retaliation by the
latter, as the exception.
Taught by the Government that they had rights
entitled to respect, when those rights have been assailed
by the rapacity of the white man, the arm which should
have been raised to protect them has ever been ready
to sustain the aggressor.
The testimony of some of the highest military
officers of the United States is on record to the effect
that, in our Indian wars, almost without exception, the
first aggressions have been made by the white man. . . .
Every crime committed by a white man against an Indian
is concealed and palliated. Every offense committed by
an Indian against a white man is borne on the wings
of the post or the telegraph to the remotest corner of
the land, clothed with all the horrors which the reality
or imagination can throw around it. Against such influences as these are the people of the United States need
to be warned.

12 The author’s description of government inquiries into the
handling of Native American affairs in lines 41–51 suggests
that the author
A.

claims no responsibility for the unjust treatment
Native Americans have suffered historically.

B.

believes that the government reports were more
concerned with voicing insincere support for Native
Americans than making substantive changes.

C.

supposes that presidents have not been critical of
how Native Americans have been treated
historically.

D.

acknowledges that the government understands
the problem and is well equipped to determine a
viable solution.

Practice Test 2
13 The author refers to different states and different times
(lines 22–30) as a way of
A.
B.
C.
D.

showing that abuses against Native Americans are
widespread across geography and history.
pointing out which states had the worst records of
abuse against Native Americans.
showing that these abuses against Native Americans
no longer occur in America.

17 The author is primarily concerned with
A.

explaining how the government can atone for the
abuses it has committed against Native Americans.

B.

arguing that Native Americans have been systematically abused throughout U.S. history.

C.

explaining the causes and effects of the government’s abuses against Native Americans.

D.

presenting opposing viewpoints as to why the
United States has had conflicts with Native
Americans.

defining where abuses against Native Americans in
the southern United States occurred.

14 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 22–23 (“It makes . . . the Indians”)

B.

Lines 24–25 (“The story . . . place”)

C.

Lines 28–30 (“the United . . . as then”)

D.

Line 30 (“with . . . practice”)

15 What explanation does the author give for why abuses
against Native Americans were allowed to go unchecked
and unpunished in lines 16–18?
A.

Old tales of Native Americans attacks on the frontier
were persistent.

B.

The government tended to break treaties and abuse
its own laws.

C.

The government sympathized with gold-seeking
settlers instead of Native Americans.

D.

The Pacific slope was lawless and chaotic during the
gold rush.

16 The author states that the abuses Native Americans suffered
were not
A.

completely unjustified.

B.

limited to a particular tribe.

C.

well documented enough.

D.

recorded before 1795.

18 As used in line 70, “palliated” most nearly means
A.

intensified.

B.

misunderstood.

C.

eased.

D.

excused.

19 Which of the following summaries of the last paragraph is
the most accurate?
A.

The generals of the U.S. Army suggest that they had
to be aggressive to keep Native Americans from
defeating them and that sometimes there were
crimes committed against Native Americans. Both
sides spread their interpretation of events across the
nation.

B.

In court hearings, soldiers discussed how the white
man often took the fight to Native Americans in
order to move them off the land and that there were
occasions when this resulted in savage behavior by
both parties.

C.

Proof that the white man was the aggressor in almost
every conflict comes from the U.S. Army itself and the
offenses of white men are disguised while the few
offenses of Native Americans are widely exaggerated.

D.

The history of the conflicts between Native
Americans and white men is one of gross injustice
and extreme crimes against the tribes most of the
time, while horrible crimes against white people are
generally few and far between.

CONTINUE
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Practice Test 2
Questions 23–32 are based on the following
passage and supplementary material.

20 The author suggests that the government has
A.

tried to convince Native Americans that they have
the same rights as all other Americans.

B.

only just begun to make efforts to ensure that
Native Americans are treated fairly.

C.

made a conscious effort to force Native Americans
out of the United States.

D.

tried to conceal the crimes that Native Americans
have committed against white men.

Robert E. Lee and his family lived on a plantation estate in
Arlington, Virginia, up until 1861. When the Civil War broke out,
he and his family departed for safer quarters. Lee became the
commander of the Rebel field forces in 1862. His former home
is now a National Park site. The full-length text of the following
passage, provided by the National Park Service, can be found at
http://www.nps.gov/arho/learn/historyculture/slavery.htm.
Slavery at Arlington

21 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 60–61 (“Taught by . . . respect”)

B.

Lines 62–64 (“the arm . . . aggressor”)

C.

Lines 65–68 (“The testimony . . . white man…”)

D.

Lines 70–73 (“Every offense . . . land”)

22 As used in line 58, “barbarous” most nearly means
A.

silent.

B.

steadfast.

C.

calculated.

D.

brutal.

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From its earliest days, Arlington House was home
not only to the Custis and Lee families who occupied the
mansion, but to dozens of slaves who lived and labored
on the estate.
For nearly sixty years, Arlington functioned as a
complex society made up of owners and slaves, whites
and blacks. To some observers, on the surface, Arlington
appeared as a harmonious community in which owner
and slave often lived and worked side by side. Yet an
invisible gulf separated the two, as slaves were the legal
property of their owners. The enslaved possessed no
rights, could not enter into legally binding contracts,
and could be permanently separated from their families
at a moment’s notice.
In 1802, the first slaves to inhabit Arlington arrived
with their owner, George Washington Parke Custis. The
grandson of Martha Washington and adopted grandson
of George Washington, Custis had grown up at Mount
Vernon, as had many of his slaves. Upon Martha Washington’s death, Custis inherited her slaves and purchased
others who belonged to his mother. In all, Custis owned
nearly 200 slaves and as many as 63 lived and worked
at Arlington. The others worked on his other two plantations near Richmond, Virginia.
Once at Arlington, the slaves constructed log cabins
for their homes and began work on the main house.
Using the red clay soil from the property and shells
from the Potomac river, they made the bricks and stucco
for the walls and exterior of the house. The slaves also
harvested timber from the Arlington forest, which was
used for the interior flooring and supports. The slaves
were responsible for keeping up the house and laboring
on the plantation, working to harvest corn and wheat,
which was sold at market in Washington.
Custis saw his daughter marry Lt. Robert E. Lee at
Arlington in 1831. Robert and Mary Anna came to call
Arlington home and Custis was a prominent figure in
the lives of the seven Lee children. In his later years,
Custis did not stray far from Arlington. He made his

Practice Test 2
40 will in 1855, and he increasingly relied on his son-in-law,

45

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Col. Lee, to handle his tangled business affairs. Until his
death, Custis retained his old bedchamber in the north
wing of the mansion, where he died after a short illness
on October 10, 1857.
Some slaves had very close relationships with the
family members, though these relationships were governed by the racial hierarchy that existed between slaves
and slaveholders. Mr. Custis relied heavily on his carriage
driver, Daniel Dotson, and Mrs. Lee had a personal relationship with the head housekeeper, Selina Gray. As Mary’s
arthritis increasingly restricted her activities through the
years, she depended on Selina for assistance. As evidence
of their close bond, Mrs. Lee entrusted Selina with the
keys to the plantation at the time of the Lees’ evacuation
in May 1861.
There is evidence that some slaves at Arlington had
opportunities not widely afforded to slaves elsewhere.
Mrs. Custis, a devout Episcopalian, tutored slaves in basic
reading and writing so that they could read the Bible.
Mrs. Lee and her daughters continued this practice even

65

70

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80

though Virginia law had prohibited the education of slaves
by the 1840s. Mrs. Custis also persuaded her husband to
free several women and children.
Some of these emancipated slaves settled on the
Arlington estate, including Maria Carter Syphax who lived
with her husband on a seventeen-acre plot given to her by
the Custises at the time of her emancipation around 1826.
While such allowances may have improved the
quality of life for the Arlington slaves, most black men
and women on the estate remained legally in bondage
until the Civil War. In his will, Custis stipulated that all
the Arlington slaves should be freed upon his death if
the estate was found to be in good financial standing
or within five years otherwise. When Custis died in 1857,
Robert E. Lee—the executor of the estate—determined
that the slave labor was necessary to improve Arlington’s
financial status. The Arlington slaves found Lee to be a
more stringent taskmaster than his predecessor. Eleven
slaves were “hired out” while others were sent to the other
estates. In accordance with Custis’s instructions, Lee officially freed the slaves on December 29, 1862.

The room at the east end on the lower level housed the summer kitchen, with cooks’ quarters above. The center room at the lower level was a washroom, with
the washerwoman’s quarters above. The rooms at the west end housed various domestic slaves, including the coachmen, gardener, and housekeeper.

CONTINUE
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  663

Practice Test 2
23 What is the most likely purpose of the passage?
A.

To inform people about the evils of slavery

B.

To persuade people that slavery was not so terrible

C.

To describe the history of Arlington House

D.

To illustrate how slaves lived before the Civil War

24 Why did Mrs. Custis teach her slaves to read?
A.

So they could teach other slaves and become
self-sufficient

B.

So they could read their contracts with their owners

C.

So they could teach her children to read

D.

So they could read the Bible

25 According to the information in the passage, what did
George Washington Parke Custis inherit from his grandmother Martha Washington?
A.

Land and slaves

B.

Slaves

C.

A house with land and slaves

D.

Three plantations

26 According to the information in the passage, how was the
life of Selina Gray different from that of other slaves?
A.

She didn’t have to work as hard.

B.

She was trusted by Mrs. Lee.

C.

She took care of the Lee children.

D.

She ran the whole plantation.

27 Which of the following statements is most likely true based
on the graphic and the passage?

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A.

The slaves lived in one enormous house built just
for slaves.

B.

The slaves’ quarters were adequate for the needs of
the slaves.

C.

Selina Gray lived in the west end of the building in
the diagram.

D.

Maria Carter Syphax lived in the building in the
diagram.

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28 How was Robert E. Lee related to George Washington?
A.

Lee married the daughter of Washington’s
grandson.

B.

Lee married George Washington’s granddaughter.

C.

Lee’s son married Martha Washington’s
granddaughter.

D.

Lee’s father was Martha Washington’s nephew.

29 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 15–16 (“the first slaves . . . Parker Custis.”)

B.

Lines 19–21 (“Upon Martha . . . his mother.”)

C.

Lines 35–36 (“Curtis saw . . . in 1831.”)

D.

Lines 36–38 (“Robert . . . Lee children.”)

30 Which of the following best illustrates that slaves were
considered property in the era described in the passage?
A.

Lines 5–7 (“Arlington functioned . . . and blacks”)

B.

Lines 20–21 (“Custis inherited . . . his mother”)

C.

Lines 60–62 (“Mrs. Lee . . . the 1840s”)

D.

Lines 62–63 (“Mrs. Custis . . . and children”)

31 How does the author use the phrase “invisible gulf”
(line 10)?
A.

As a figure of speech—related to differences in
stature.

B.

As a maritime definition—related to a hidden body
of water.

C.

As a geographical reference—related to a ravine or
abyss.

D.

As an architectural description—related to building
placement.

32 In the context of the passage, what is the best definition
of the word “afforded” (line 57)?
A.

Spared or given up without risk

B.

Had sufficient money to pay for

C.

Provided or supplied

D.

Purchased in exchange for

Practice Test 2
Questions 33–42 are based on the following passages.
Passage 1 is excerpted from the U.S. Environmental Protection
Agency website. Passage 2 is excerpted from the article “Science
Has Spoken: Global Warming Is a Myth” by Oregon Institute of
Science and Medicine chemists, Arthur B. Robinson and Zachary
W. Robinson. This article was published in the Wall Street Journal
in 1997.
PASSAGE 1
Climate change is happening

Line
5

10

15

20

25

30

35

40

Our Earth is warming. Earth’s average temperature
has risen by 1.4°F over the past century and is projected
to rise another 2 to 11.5°F over the next hundred years.
Small changes in the average temperature of the planet
can translate to large and potentially dangerous shifts in
climate and weather.
The evidence is clear. Rising global temperatures have
been accompanied by changes in weather and climate.
Many places have seen changes in rainfall, resulting in more
floods, droughts, or intense rain, as well as more frequent
and severe heat waves. The planet’s oceans and glaciers have
also experienced some big changes—oceans are warming
and becoming more acidic, ice caps are melting, and sea
levels are rising. As these and other changes become more
pronounced in the coming decades, they will likely present
challenges to our society and our environment.
Humans are largely responsible for recent climate
change. Over the past century, human activities have
released large amounts of carbon dioxide and other
greenhouse gases into the atmosphere. The majority
of greenhouse gases come from burning fossil fuels to
produce energy, although deforestation, industrial processes, and some agricultural practices also emit gases
into the atmosphere.
Greenhouse gases act like a blanket around Earth,
trapping energy in the atmosphere and causing it to warm.
This phenomenon is called the greenhouse effect and is
natural and necessary to support life on Earth. However,
the buildup of greenhouse gases can change Earth’s
climate and result in dangerous effects to human health
and welfare and to ecosystems.
Our lives are connected to the climate. Human
societies have adapted to the relatively stable climate we
have enjoyed since the last ice age, which ended several
thousand years ago. A warming climate will bring changes
that can affect our water supplies, agriculture, power and
transportation systems, the natural environment, and even
our own health and safety.
Some changes to the climate are unavoidable.
Carbon dioxide can stay in the atmosphere for nearly a

century, so Earth will continue to warm in the coming
decades. The warmer it gets, the greater the risk for
more severe changes to the climate and Earth’s system.
Although it’s difficult to predict the exact impacts of
45 climate change, what’s clear is that the climate we are
accustomed to is no longer a reliable guide for what to
expect in the future.
We can reduce the risks we will face from climate
change. By making choices that reduce greenhouse gas
50 pollution and preparing for the changes that are already
underway, we can reduce risks from climate change. Our
decisions today will shape the world our children and
grandchildren will live in.
PASSAGE 2
[The global warming] hypothesis predicts that
55 global temperatures will rise significantly, indeed cata-

60

65

70

75

80

85

strophically, if atmospheric carbon dioxide rises. Most of
the increase in atmospheric carbon dioxide has occurred
during the past 50 years, and the increase has continued
during the past 20 years. Yet there has been no significant
increase in atmospheric temperature during those 50
years, and during the 20 years with the highest carbon
dioxide levels, temperatures have decreased.
In science, the ultimate test is the process of experiment. If a hypothesis fails the experimental test, it must be
discarded. Therefore, the scientific method requires that
the global warming hypothesis be rejected.
Why, then, is there continuing scientific interest in
“global warming”? There is a field of inquiry in which
scientists are using computers to try to predict the
weather—even global weather over very long periods.
But global weather is so complicated that current data
and computer methods are insufficient to make such
predictions. Although it is reasonable to hope that these
methods will eventually become useful, for now computer
climate models are very unreliable.
So we needn’t worry about human use of hydrocarbons warming the Earth. We also needn’t worry about
environmental calamities, even if the current, natural
warming trend continues: After all the Earth has been much
warmer during the past 3,000 years without ill effects.
But we should worry about the effects of the hydrocarbon rationing being proposed at Kyoto. Hydrocarbon
use has major environmental benefits. A great deal of
research has shown that increases in atmospheric carbon
dioxide accelerate the growth rates of plants and also
permit plants to grow in drier regions. Animal life, which
depends upon plants, also increases.

CONTINUE
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Practice Test 2
33 Upon which concepts do both passages fully agree?

38 As used in line 15, “pronounced” most nearly means

A.

That global warming has been proven by evidence

A.

articulated.

B.

That an increase in overall temperature is
manageable

B.

announced.

C.

inconspicuous.

C.

That levels of atmospheric carbon dioxide have
increased

D.

noticeable.

D.

That usual weather patterns have been affected

34 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 4–6 (“Small changes . . . and weather.”)

B.

Lines 28–31 (“However, the . . . to ecosystems.”)

C.

Lines 56–61 (“Most of the . . . 20 years.”)

D.

Lines 81–82 (“But we should . . . at Kyoto.”)

39 In both passages, the authors present information by
A.

listing a sequence of events that begins in the past
and continues into the future.

B.

discussing the causes of a situation and the
resulting lack of effects.

C.

comparing two different approaches to a problem
and determining which will be most effective.

D.

defining the problems the world faces and then
offering solutions to them.

35 Which point of view characterizes both passages?
A.

One of scientists taking neutral positions

B.

One of fanatics defending a cause

C.

One of humans concerned for global well-being

D.

One of debaters directly addressing readers as “you”

36 Both the author of Passage 1 and the author of Passage 2
agree that humans

A.

hydrocarbons should be controlled.

B.

climate and weather can be modified by humans.

C.

atmospheric elements pose a threat to human life.

D.

the production of hydrocarbons is a natural result
of human activity.

41 Which choice provides the best evidence for the answer
to the previous question?

A.

can have positive impacts on the environment.

B.

are accountable for the rise of global warming.

C.

have proven to be able to adapt to climate changes
throughout history.

A.

Lines 20–24 (“The majority . . . into the
atmosphere.”)

D.

shouldn’t worry about hydrocarbons warming the
Earth.

B.

Lines 40–42 (“Carbon dioxide . . . coming decades”)

C.

Lines 54–56 (“The global . . . dioxide rises”)

D.

Lines 83–86 (“A great . . . drier regions”)

37 The terms such as “potentially dangerous, severe, dangerous effects” in Passage 1 and terms such as “no significant,
insufficient, unreliable” in Passage 2 create tones that are

  666

40 The essential difference between the arguments the two
sets of authors present is whether or not

A.

the same because they both create a sense of
danger.

B.

different because one is based on scientific
evidence and the other is speculative.

C.

the same because they are both very technical.

D.

different because one is alarming and the other is
assuring.

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42 As used in line 5, “translate” most nearly means
A.

comprehend.

B.

expand.

C.

transform.

D.

explain.

Practice Test 2
Questions 43–52 are based on the following passage.

She was told every week of her life that the poor
45 children would never have had to lift a finger if their

The following is an excerpt from a short story, “Miss Tempy’s
Watchers,” by Sarah Orne Jewett, a novelist and short-story writer
who lived from 1849–1909. In the story, two women watch over
their deceased friend on the evening before her funeral and share
their memories of her.

Line
5

10

15

20

25

30

35

40

The time of year was April; the place was a small
farming town in New Hampshire, remote from any
railroad. One by one the lights had been blown out in
the scattered houses near Miss Tempy Dent’s, but as her
neighbors took a last look out of doors, their eyes turned
with instinctive curiosity toward the old house where a
lamp burned steadily. They gave a little sigh. “Poor Miss
Tempy!” said more than one bereft acquaintance; for
the good woman lay dead in her north chamber, and
the lamp was a watcher’s light. The funeral was set for
the next day at one o’clock.
The watchers were two of her oldest friends. Mrs.
Crowe and Sarah Ann Binson. They were sitting in the
kitchen because it seemed less awesome than the
unused best room, and they beguiled the long hours by
steady conversation. One would think that neither topics
nor opinions would hold out, at that rate, all through
the long spring night, but there was a certain degree of
excitement just then, and the two women had risen to
an unusual level of expressiveness and confidence. Each
had already told the other more than one fact that she
had determined to keep secret; they were again and
again tempted into statements that either would have
found impossible by daylight. Mrs. Crowe was knitting a
blue yarn stocking for her husband; the foot was already
so long that it seemed as if she must have forgotten to
narrow it at the proper time. Mrs. Crowe knew exactly
what she was about, however; she was of a much cooler
disposition than Sister Binson, who made futile attempts
at some sewing, only to drop her work into her lap
whenever the talk was most engaging.
Their faces were interesting—of the dry, shrewd,
quick-witted New England type, and thin hair twisted
neatly back out of the way. Mrs. Crowe could look
vague and benignant, and Miss Binson was, to quote
her neighbors, a little too sharp-set, but the world
knew that she had need to be, with the load she must
carry supporting an inefficient widowed sister and six
unpromising and unwilling nieces and nephews. The
eldest boy was at last placed with a good man to learn
the mason’s trade. Sarah Ann Binson, for all her sharp,
anxious aspect never defended herself, when her sister
whined and fretted.

father had lived, and yet she had kept her steadfast
way with the little farm, and patiently taught the young
people many useful things for which, as everybody said,
they would live to thank her. However pleasureless her
50 life appeared to outward view, it was brimful of pleasure
to herself.
Mrs. Crowe, on the contrary, was well-to-do, her
husband being a rich farmer and an easy-going man.
She was a stingy woman, but for all of that she looked
55 kindly; and when she gave away anything, or lifted a
finger to help anybody, it was thought a great piece
of beneficence, and a compliment, indeed, which the
recipient accepted with twice as much gratitude as
double the gift that came from a poorer and more
60 generous acquaintance. Everybody liked to be on good
terms with Mrs. Crowe. Socially, she stood much higher
than Sarah Ann Binson.
43 The two women are in Miss Tempy Dent’s house because
they are
A.

waiting to tell other friends and family that she has
died.

B.

staying with the body so it isn’t alone until it is
buried.

C.

conducting a funeral service following Miss Tempy’s
requests.

D.

visiting Miss Tempy Dent, but she has died.

44 The theme of this excerpt can best be described as
A.

old friends often grow closer when they lose a
friend.

B.

the bonds of friendship remain strong even in
death.

C.

trying to stay awake all night isn’t hard for dear
friends.

D.

the living carry on the traditions of the dead.

CONTINUE
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Practice Test 2
45 In lines 24–27, the author describes the stocking Mrs.
Crowe was knitting to show that she
A.

was too distracted to do a good job.

B.

had never knitted anything before.

C.

had forgotten her husband’s measurements.

D.

did not really want to be where she was.

46 Even though these two women are very different, the
author shows that they are getting closer by
A.

having them sit in the kitchen instead of the best
room.

B.

having Mrs. Crowe give Sarah Ann something nice.

C.

explaining that Sarah Ann was actually very happy.

D.

describing the intimacy of their conversation.

49 Mrs. Crowe and Sarah Ann Binson are
A.

not very trusting.

B.

the same age.

C.

focused on their work.

D.

from different social standings.

50 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 1–3 (“The time of . . . any railroad.”)

B.

Lines 13–16 (“They were . . . conversation.”)

C.

Lines 49–53 (“However . . . easy-going man.”)

D.

Lines 60–61 (“Everybody . . . Mrs. Crowe.”)

51 As used in line 36, “sharp-set” most nearly means

47 Which choice provides the best evidence for the answer
to the previous question?

A.

eager.

B.

bored.

A.

Lines 16–20 (“One would . . . and confidence.”)

C.

absentminded.

B.

Lines 20–24 (“Each had . . . daylight.”)

D.

cheap.

C.

Lines 27–29 (“Mrs. Crowe . . . Binson”)

D.

Lines 29–31 (“who made . . . engaging.”)

52 As used in line 42, “aspect” most nearly means

48 Which choice provides the best summary of what happened between Mrs. Crowe and Sarah Ann Binson in Miss
Tempy’s kitchen?
A.

Both women found it hard to fill up the long hours.

B.

Both women had become excited by the intimacy
they shared.

C.

Mrs. Crowe did not reveal as much as Sarah Ann
Binson.

D.

Sarah Ann Binson revealed her love of pleasure and
freedom.

A.

face.

B.

angle.

C.

attitude.

D.

component.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

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Practice Test 2
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you will
need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you to
consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).
Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.
After reading each passage, select the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following passage.
Code Talking
In September of 1992, a group of American heroes who had
gone unrecognized for many years was honored by the United
States Pentagon. 1 Consisted of thirty-five Navajo code
talkers.

1
A.

NO CHANGE

B.

Having consisted of

C.

A group which were made of

D.

It consisted of

CONTINUE
Peterson's SAT® Prep Guide 2017

  669

Practice Test 2
During World War II, the United States Marines needed

2

to develop a 2 code, for communicating top-secret
information. 3 It being the case that they would then have
access to information about United States Marines tactics and
troop movements, it was crucial that enemy forces not be able
to decipher the code.

A.

NO CHANGE

B.

code for communicating

C.

code, for communicating,

D.

code for communicating,

A.

NO CHANGE

B.

It was crucial to the United States, that enemy
forces not be able to decipher the code, having
access to information about Marines tactics and
troop movements.

C.

It was crucial that enemy forces be unable to
decipher the code because, if they did, they would
have access to information about the Marines’
tactics and troop movements.

D.

Crucially, the enemy forces were unable to decipher
the code, which would have access to the Marines’
tactics and troop movements.

3

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Practice Test 2
The military recruited a small group of Navajos to create a

4

code based on their language. 4 The Navajo language

Which choice most effectively sets up the information that
follows?

was chosen because many of the top military officials at the

A.

NO CHANGE

time were Navajo. First, it was extremely difficult to learn

B.

The Navajo language was chosen because the
Navajo people were famous for their military
history.

C.

The Navajo people had often been called on to
help the American government in the past.

D.

The Navajo language made an excellent code for a
few essential reasons.

A.

NO CHANGE

B.

Furthermore

being sent to a Marine unit. Once they were stationed with a

C.

Likewise

unit, the code talkers used telephones and radios to transmit

D.

As a result

While the Navajo language was complicated, the code was

A.

NO CHANGE

even more complex. A code talker receiving a message heard

B.

uncertainty

C.

beauty

D.

clarity

and virtually unknown outside the Navajo community in the
American Southwest. 5 However, the Navajo language
does not have a written form; it uses no alphabet. Its
complexity and 6 obscurity made it the perfect basis for a
code.
The first group of Navajo recruits attended boot camp in 1942.

5

Afterward, they set to work developing a vast dictionary of
code words for military terms based on the Navajo language.
Each code talker had to memorize the dictionary before

encoded orders and information.

6

a stream of Navajo words. 7 The receiver had to translate
the words into English. Then the receiver had to use the first
letter of each English equivalent to spell out a word. Adding
to the difficulty of breaking the code was the fact that most
letters could be indicated by the code talkers with more than
one Navajo word.

7

Which choice most effectively joins the two sentences?
A.

The receiver had to translate the words into English,
and then the receiver had to use the first letter of
each English equivalent to spell out a word.

B.

The receiver had to translate the words into English,
and then use the first letter of each English
equivalent to spell out a word.

C.

The receiver had to translate the words into English
even though the receiver had to then use the first
letter of each English equivalent to spell out a word.

D.

The receiver had to translate the words into English
because the receiver had to use the first letter of
each English equivalent to spell out a word.

CONTINUE
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  671

Practice Test 2
Though able to crack the codes of other military branches,

8

enemy forces never managed to 8 perceive what the

A.

NO CHANGE

B.

fathom

C.

elucidate

D.

decipher

unacknowledged until quite recently. Half a century later,

A.

NO CHANGE

in 1992, thirty-five former code talkers and their families

B.

speed, and accuracy

attended the dedication of the Navajo Code Talker Exhibit at

C.

speed and accuracy

the United States Pentagon, and officially took their place in

D.

speed and accuracy,

A.

NO CHANGE

B.

will work

C.

are working

D.

have been working

Marines’ Navajo code talkers said. The code talkers were
renowned for the 9 speed, and accuracy, with which they
10 worked.
11 Because the Navajo language was common only in the
American Southwest, the work of the code talkers remained

9

military history.
10

11 Which choice provides information that best supports the
claim made by the sentence?

  672

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A.

NO CHANGE

B.

had to be translated into English words and letters

C.

took a long time to decode by people who didn’t
speak English

D.

remained part of a classified code for many years

Practice Test 2
Questions 12–22 are based on the following passage.

12

Dian Fossey
Who was 12 Dian Fossey. Dian Fossey was a researcher, a
visionary, and a pioneer in the field of animal conservation.

A.

NO CHANGE

B.

Dian Fossey?

C.

Dian Fossey,

D.

Dian Fossey!

More specifically, Fossey dedicated her life to preserving
Africa’s endangered mountain gorilla.

13 The writer is considering deleting the underlined portion
of the sentence. Should the writer make this deletion?

Fossey 13 was born in San Francisco and made her first
trip to Africa in 1963. At the time, she was 31 years old. In the
course of her trip, she met Dr. Louis Leakey, a 14 prominent

A.

Yes, because this information should be provided
earlier in the passage.

B.

Yes, because this information doesn’t support the
main idea of the paragraph.

C.

No, because this information supports the main
idea of the paragraph.

D.

No, because this information is important to the
organization of the passage.

A.

NO CHANGE

B.

imminent

C.

infamous

D.

egregious

A.

NO CHANGE

B.

After accepting the research challenge from Dr.
Leakey, Fossey chose mountain gorillas as the topic
of her research.

C.

Mountain gorillas, after accepting the research
challenge from Dr. Leakey, became the topic of
Fossey’s research.

D.

Fossey chose mountain gorillas after accepting the
research challenge from Dr. Leakey, as her research
topic.

archaeologist and anthropologist. Dr. Leakey believed in
the importance of research on large apes and encouraged
Fossey to undertake such a study. 15 After accepting the
research challenge from Dr. Leakey, mountain gorillas became
a research topic.
14

15

CONTINUE
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  673

Practice Test 2
Fossey began her work in the African country of Zaire, but

16

was forced to leave because of political unrest. She moved

A.

NO CHANGE

B.

Their

C.

There

D.

Where

A.

NO CHANGE

B.

undertake

Spending so much time observing the gorillas, Fossey

C.

assume

naturally distinguished among them and had particular

D.

accept

A.

NO CHANGE

B.

Fossey was crushed.

C.

Fossey was super-duper sad.

D.

Fossey was stunned and saddened.

A.

NO CHANGE

B.

it was predicted

C.

it is predicted

D.

he is predicting

to another African country, Rwanda, where she established
a research camp in a national park. 16 They’re, she spent
thousands of hours observing the behavior of gorillas. Her
steadfast patience won the trust of the animals, and they
began to 17 except her presence among them. As a result,

17

she was able to observe behaviors that had never been seen
by humans before.

favorites. One of these favorites was a young male gorilla
named Digit. Digit was later killed by a poacher, an illegal

18

hunter of protected animals. 18 Fossey was really, really sad.
She began a public campaign to raise awareness about the
problem of gorilla poaching, a practice that threatened their
continued existence. In 1989, 19 it will be predicted that
there were only 620 mountain gorillas left. Fossey’s campaign
earned worldwide attention and support, and she continued
to live and work in Africa for many years thereafter.

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19

Practice Test 2
20 In 1980, Fossey took a teaching position at Cornell
University and wrote a book, Gorillas in the Mist, that brought

20 At this point, the writer is considering adding the following
sentence:
She had always been interested in dancing and learning
new and interesting dance moves.

further attention to the 21 deteriorating numbers of
mountain gorillas. Afterward, Fossey returned to Rwanda,

Should the writer make this addition here?

and spent the rest of her life working to protect the mountain
gorilla. Even after her mysterious death, Fossey’s work

A.

Yes, because this information provides information
necessary to understand the paragraph.

B.

Yes, because this information makes a good
transition from the previous paragraph.

C.

No, because this information is not necessary and
doesn’t support the main idea of the paragraph.

D.

No, because this information should be placed at
the end of the passage.

A.

NO CHANGE

B.

declining

C.

demeaning

D.

degrading

A.

NO CHANGE

B.

the population of mountain gorillas in Rwanda are
rising.

C.

the population of mountain gorillas in Rwanda
were rising.

D.

there are higher population of mountain gorillas in
Rwanda, which is rising.

continued make an impact.
Today, 22 the population of mountain gorillas in Rwanda is
rising thanks to the legacy of Dian Fossey.

21

22

CONTINUE
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Practice Test 2
Questions 23–33 are based on the following
passage and supplementary material.

23

Tamarin Families
Deep in the rainforests of Brazil, tiny creatures known as “kings
of the jungle” inhabit the trees. These creatures, similar in size
to squirrels, have bright, reddish-orange coats and hairless
faces; their fur 23 obscures their faces like the mane of a

A.

NO CHANGE

B.

surrounds

C.

covers

D.

marks

24 The writer is considering deleting the underlined sentence.
Should the writer do this?

lion. Accordingly, these highly endangered monkeys are called

A.

No, because this is useful and relevant contextual
information.

B.

No, because it explains why family units are
relatively small.

C.

Yes, because it should be placed earlier in the
paragraph.

D.

Yes, because this information interrupts the flow of
the paragraph.

A.

NO CHANGE

B.

better parents than tamarins that do not.

C.

better parents than other tamarins.

D.

better parents than older tamarins.

golden lion tamarins.
Tamarins live in small family units of up to nine individuals.
24 Offspring are generally born in pairs, and all members
of the group will pitch in to help care for them. Tamarins
that participate in caring for their newborn siblings tend to
become 25 better parents.
25

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Practice Test 2
[1] Tamarins are diurnal, meaning 26 they are active during

26

the daytime. [2] At night, they seek shelter in tree hollows. [3]
They are omnivorous, eating fruits, insects, and occasionally
small lizards and snakes, which are 27 one in the same to
them. [4] Tamarins spend their time in trees, using their fingers
to grip the branches. 28 [5] However, they dislike direct
sunlight, and so are well-suited to the dense foliage of the

A.

NO CHANGE

B.

it is

C.

he is

D.

it will be

A.

NO CHANGE

B.

one with the same

C.

one and the same

D.

one the same

27

forest.

28 To make this paragraph the most logical, sentence 5 should
be placed
A.

where it is now.

B.

before sentence 1.

C.

before sentence 2.

D.

before sentence 4.

160

600

140

500

120

100
80

300

60

# Zoos

# Animals

400

200
40

Animals
Zoos

100

20

0

0
1970

1974

1979

1982

1986

1990

1994

1996

2002

2006

Year
Used with permission. Ballou, J. D., J. Mickelberg, D. Field, and N. Lindsey. 2009. Population Management Recommendations for the International Ex-situ
Population of Golden Lion Tamarins (Leontopithecus rosalia). National Zoological Park, Washington, D.C.

CONTINUE
Peterson's SAT® Prep Guide 2017

  677

Practice Test 2
Golden lion tamarins inhabit a distinct ecological 29 niche,

29

they are found only in the eastern rainforests of Brazil. As
farmers clear the rainforest to grow cash crops, the habitat of
the tamarins has decreased drastically; as a result, the survival
of the species is in extreme danger. Ecologists estimate that
there are only one thousand tamarins remaining in the wild.
In the 1970s, a conservation campaign was initiated to
save the tamarins. At this time, there 30 were about 140
participating zoos. The movement began as a collaborative
effort by the National Zoological Park in Washington, the

A.

NO CHANGE

B.

niche they,

C.

niche they

D.

niche; they

30 At this point, the writer wants to add specific information
that supports the main idea of the paragraph. Which
choice most effectively completes the sentence with
relevant and accurate information based on the graph
(previous page)?
A.

NO CHANGE

31 It has grown to address the problem from several angles,

B.

were about 300 participating zoos.

including managing and restoring the disappearing habitat of

C.

were fewer than 200 tamarins in the world’s zoos.

the tamarins, breeding tamarins in captivity and in the wild,

D.

were more than 200 tamarins in the world’s zoos.

A.

NO CHANGE

B.

The campaign

C.

The problem

D.

They

Smithsonian Institute, and the Rio de Janeiro Primate Center.

and reintroducing tamarins into their natural environment.
As part of this effort, a number of zoos around the world have
participated in helping to breed tamarins in captivity. 32

31

32 Which choice adds accurate data to the paragraph based
on the graph (previous page)?

  678

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A.

Unfortunately, the participation rate among zoos
has fallen dramatically while the tamarin population has climbed.

B.

While the population of tamarins in captivity has
fluctuated since 2000, the number of participating
zoos has remained relatively steady.

C.

Although the population of tamarins has fallen
since 2000, the participation rate of zoos has risen
substantially in recent years.

D.

Sadly, both the number of participating zoos and
the population of tamarins has fallen significantly
since 2000.

Practice Test 2
So far, efforts to return these animals back into their
natural habitat have been 33 fruitful, making the golden
lion tamarin one of very few species to be successfully
reintroduced into the wild.

33
A.

NO CHANGE

B.

problematic

C.

lucrative

D.

delayed

CONTINUE
Peterson's SAT® Prep Guide 2017

  679

Practice Test 2
Questions 34–44 are based on the following passage.
Classical architecture, the origins of which can be traced to
ancient Rome, is characterized by a strict and 34 terminable
adherence to the principles of coherence, exactness, and
detail.
35 The basis of the classical style was the manner in which a
building’s space was divided so as to create a coherent whole.
An example of a plan for the division of a building’s space was
36 the tripartite plan. This plan would divide the space in a
particular building into three equal parts. Such a plan would

34
A.

NO CHANGE

B.

inclement

C.

rigorous

D.

contentious

35 At this point, the writer is considering adding the following
sentence:
Over time, the classical tripartite plan spilled over from
architecture to other arts—music, poetry, and dance—and
it is not uncommon to have a three-part hierarchy within
those artistic areas as well.

be followed no matter what the purpose of the building—

Should the writer make this addition here?

churches, homes, or public government buildings could all

A.

Yes, because it adds interesting detail to the
paragraph.

B.

Yes, because it provides an accurate introduction to
the paragraph.

C.

No, because this information should be added at
the end of the paragraph.

D.

No, because this information does not support the
main idea of the paragraph.

be designed with such a plan. Even gardens, designed in the
classical style, might have a three-part plan.

36 Which choice most effectively combines the sentences at
the underlined portion?

  680

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A.

the tripartite plan, and this plan would

B.

the tripartite plan would

C.

the tripartite plan, it would

D.

the tripartite plan, which would

Practice Test 2
Once the framework of a building designed in the classical

37

style was established, architectural elements were added.
While 37 columns are fairly typical architectural element,
there are five types in particular that are the most 38
common: the Doric, Ionic, Corinthian, Tuscan, and Composite.
Each column was distinctive and of a certain specified
proportion, base to top. Just as the building follows a

A.

NO CHANGE

B.

columns are fairly typical architectural elements

C.

column is a fairly typical architectural elements

D.

columns is fairly typical architectural elements

A.

NO CHANGE

B.

common: the Doric and Ionic, Corinthian, and
Tuscan, and Composite.

C.

common; the Doric Ionic; and Corinthian; Tuscan
and Composite.

D.

common: the Doric and Ionic; Corinthian, Tuscan,
and Composite.

A.

NO CHANGE

B.

cornice, frieze, and the architrave.

C.

the cornice, the frieze, and the architrave.

D.

the cornice, the frieze, and architrave.

38

tripartite plan, so the columns themselves have a three-part
organization. Above the column is a horizontal piece, called
the entablature; then comes the column itself, which is tall and
cylindrical; and finally comes the platform, or crepidoma, upon
which the column rests.
Each of these elements also maintains a three-part
organization. The entablature is divided into three parts—
39 cornice, the frieze, and the architrave. The column
includes the capital, the shaft, and the base. 40

39

40 Which of the following sentences, if added here, support
the author’s ideas in the first sentence of the paragraph?
A.

The crepidoma was a single solid mass of steps that
supported the rest of the column.

B.

The crepidoma sometimes included a sloping ramp,
particularly in large temples.

C.

The crepidoma maintains the three-part division
with its three steps.

D.

The crepidoma, though, was not often used in
Doric columns.

CONTINUE
Peterson's SAT® Prep Guide 2017

  681

Practice Test 2
Classical architecture is filled with conventions that while

41

not obvious to most viewers, become apparent upon closer
analysis. For example, 41 classical buildings must stand
free; it cannot touch the sides of other buildings because, in
the view of the classicist, each building is a world within a
world of 42 his own. Consequently, organizing groups of
buildings became problematic for rule-following, classical

A.

NO CHANGE

B.

a classical building must stand free; we cannot
touch

C.

classical buildings must stand free; you cannot
touch

D.

classical buildings must stand free; they cannot
touch

A.

NO CHANGE

B.

their

C.

its

D.

the buildings

A.

NO CHANGE

B.

perceived

C.

comprehended

D.

extricated

architects because of 43 differentiated violations of spatial
conventions. The classical mode required adherence to formal
rules that were sometimes impossible to impose on groups of

42

buildings. 44

43

44 Which choice most effectively establishes the main topic
of the final paragraph?
A.

The rules of classical architecture include dividing a
building and its features into tripartite groups of
three.

B.

Classical architects were all quite interested in
building on a mass scale during the time in which
they lived.

C.

A classical building must stand free and be a world
unto itself, which is why no classical buildings
connect to each other.

D.

The numerous and strict conventions of classical
architecture, such as the idea that a building must
stand on its own, were not always easy for classical
builders to abide by.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  682

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Practice Test 2
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions
TURN TO SECTION 3 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  683

Practice Test 2
1

2

Simplify the expression (4x2 – 5x + 8) – (3x2 – 5 – 2x).
A.

x2 – 3x + 13

B.

x2 – 3x + 3

C.

x2 – 7x + 13

D.

x2 – 7x + 3
2

Which expression is equivalent to x 3 i x
A.

−3 x8

B.

−3 x2

C.

3

D.

3

−4
3

?

x2
1

3

4

x2

Simplify the expression: –2[x(1 – 3x) + 3x]2.
A.

–18x4 +48x3 – 32x2

B.

–18x4 – 24x3 + 16x2

C.

–2x2

D.

36x4 – 96x3 + 64x2

8x – 9 = x2 – y
Which of the following is an equivalent form of the above
equation from which the coordinates of the vertex are
readily identified as constants appearing in the equation?

5

  684

A.

y = (x + 1)(x – 9)

B.

y = (x – 4)2 – 7

C.

y = x2 – 8x + 9

D.

x = y +7 + 4

If a + 4b = 16, what is the value of –5[–3a + 2(4b + a) –12b]?
A.

80

B.

16

C.

−16

D.

−80

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SHOW YOUR WORK HERE

Practice Test 2
6

S = 2πr2 + 2πrh

SHOW YOUR WORK HERE

The formula above relates the surface area S of a cylinder
to an expression involving the radius r and the height h.
Which of the following gives h in terms of S and r?

7

8

A.

h=

S
−r
2π r

B.

h=

S
+r
2π r

C.

h=

2π r 2 − S
2π r

D.

h=

S + 2π r 2
2π r

A group of economists performed a study on the decreasing population in a small town for a time period of
10 years. They determined that as a result of factors such
as loss of jobs and a poor economy, the population of the
town decreased by about 3.5% each year. Which of the
following equations accurately describes the population
of the town, P, in terms of its initial population, P0, and n,
the number of years of the study?
A.

P = P0(0.965)n

B.

P = P0(0.965)n

C.

P = P0(1.035)n

D.

P = P0(1.035)n

If f is a linear function and f(4) = 2 and f(6) = 10, which of
the following could be the function f ?
A.

f(x) = x – 2

B.

f(x) = 2x – 2

C.

f(x) = 2x – 6

D.

f(x) = 4x – 14

CONTINUE
Peterson's SAT® Prep Guide 2017

  685

Practice Test 2
SHOW YOUR WORK HERE

9

y
(4, 6)

q
p

x
Note: Figure not drawn to scale.

In the figure above, lines p and q are parallel. If y = x + 1
represents the equation of line p, what is the y-intercept
of line q?
A.

2

B.

3

C.

4

D.

5

10 A certain brand of yogurt is sold in either large or small
cups. If 3 small cups and 2 large cups hold 30 ounces of
yogurt, and 4 small cups and 1 large cup hold 25 ounces
of yogurt, how much yogurt, in ounces, does a large cup
of yogurt hold?

  686

A.

2 ounces

B.

4 ounces

C.

7 ounces

D.

9 ounces

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Practice Test 2
11

SHOW YOUR WORK HERE

A

D

B

2

4

E

C

Note: Figure not drawn to scale.

In the figure above, DE is parallel to BC and AD = 3. What
is the length of segment BD?
A.

2

B.

3

C.

4

D.

6

12 The sales for gasoline at a local station during a given year
are described by the function p(x) = –3(x – 5)2 + 173, where
x = 1, 2, . . .12; x = 1 corresponds to the month of June; and
p(x) is measured in hundred thousands of dollars. What
does the number 173 in the formula represent?
A.

The number of thousands of gallons sold, on
average.

B.

The total profit (in hundred thousands of dollars)
for the year.

C.

The maximum monthly sales (in hundred thousands of dollars) for the months of the year being
described.

D.

The month during which the sales were the
highest.

13 If (x + 2)2 – (x – 3)2 = 0, which of the following are possible
values of x?

B.

1
only
2
−2 and 3

C.

−3 and 2

D.

no solution

A.

CONTINUE
Peterson's SAT® Prep Guide 2017

  687

Practice Test 2
14 What is the equation of the circle for which the points
(–2, 3) and (4, 9) are the endpoints of one of its diameters?

15

A.

( x − 1) 2 + ( y − 6 ) 2 = 2 3

B.

(x + 1)2 + (y + 6)2 =18

C.

(x − 1)2 + (y − 6)2 =18

D.

( x + 1) 2 − ( y + 6 ) 2 = 2 3

4
passes through
5
the point (3, 4). Which of the following points lies on the

A line in the xy-plane with the slope −

line?

  688

A.

(–5, 12)

B.

(–2, 0)

C.

(7, –1)

D.

(13, −4)

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SHOW YOUR WORK HERE

Practice Test 2

DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
If 3

1
7
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

31
1
, not 3 .)
2
2

, it will be interpreted as

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

1

1

2

2

2

1

1

3

3

3

3

3

4

4

4

4

4

5

5

5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

7

7

7

8

8

8

8

8

9

9

9

9

9

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

7

7

7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

CONTINUE
Peterson's SAT® Prep Guide 2017

  689

Practice Test 2
16 Miguel is making a new garden. He is buying a new wheelbarrow and bags of peat moss. Each bag weighs 30 pounds
and the wheelbarrow weighs 50 pounds. If his truck can
carry a maximum of 1,500 pounds in the bed, what is the
greatest number of whole bags of peat moss he can carry
in the bed of his truck, along with the wheelbarrow?

17

SHOW YOUR WORK HERE

6
8

A sign is made by cutting four identical right triangles out
of a square, as shown above. What is the perimeter of the
sign, in inches?

18 What is the value for b that will make the equation below
true?
5x + 2
b
= 5+
x −4
x −4
19

y = 3x − 4
y = 2x −5
According to the system of equations above, what is the
value of xy?

20

6 x − 5y = 9
−18 x + by = −27
What value of b will make the system of equations above
have infinitely many solutions?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  690

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Practice Test 2
SECTION 4: MATH TEST—CALCULATOR
55 Minutes—38 Questions
TURN TO SECTION 4 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–30, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 31–38, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 31 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a2 + b2 = c2
Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  691

Practice Test 2
1

2

3

4

  692

A purse contains $11.20 in change consisting of nickels,
dimes, and quarters in the ratio of 1:3:5. How many dimes
are in this collection?
A.

7

B.

21

C.

28

D.

35

If 2[–3 – (2 – 4x)] = –32 + x, what is the value of x–2?
A.

361

B.

49

C.

14

D.

9

In the 1908 London Olympics, the 400-meter race was
introduced. Wyndham Halswelle of Great Britain won with
a time of 50.0 seconds. In 1996, Michael Johnson of the
United States ran the 400-meter race with a time of 43.18
seconds. If they had been racing together, approximately
how many meters would Halswelle still have had to run
after Johnson finished the race?
A.

10

B.

25

C.

55

D.

100

If 18 – 6x is 4 less than −8, what is the value of –3x?
A.

–15

B.

–5

C.

5

D.

15

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Practice Test 2
5

1,000 milligrams = 1 gram

SHOW YOUR WORK HERE

1,000 grams = 1 kilogram
Ibuprofen is an over-the-counter drug used to treat arthritis and relieve pain, fever, and swelling. The dose contained
in a standard tablet is 200 mg. If ibuprofen is sold in cartons
of 24 bottles, with 250 standard tablets per bottle, how
much pain medication is in the carton in all?

6

A.

0.12 kilograms

B.

1.2 kilograms

C.

12 kilograms

D.

120 kilograms

A local newspaper reported a poll of 100 adults that found
80% of respondents were in favor of building a new school.
The poll was taken by asking random parents picking up
their students after school. Which of the following statements about the sampling method for this poll is NOT true?
A.

The sampling method was not representative of the
town as a whole because some students take the
bus home.

B.

The sampling method was not representative of the
town as a whole because not everyone has children
who go to school.

C.

The sampling method was not representative of the
town as a whole because the population of the
town is much greater than 100.

D.

The sampling method was not representative of the
town as a whole because people who do not have
students in school are less likely to support a new
school.

CONTINUE
Peterson's SAT® Prep Guide 2017

  693

Practice Test 2
Questions 7 and 8 refer to the following information.
The graph below shows the population of a small town, from
the years 2007 through 2015.
1, 000
900

Population

800
700
600
500
400
300
200
100
2007

2009

2011

2013

2015

Years

7

8

  694

Assuming that the population growth trend continues,
what is the best prediction for the difference in the town’s
population from 2011 to 2014?
A.

663

B.

515

C.

358

D.

305

Assuming the data is described by the function P(x) = Aebx,
which of the following values of b is the best choice if the
points (2009, 250) and (2013, 500) lie on its graph?
A.

ln16

B.

ln2

C.

1
ln2
4

D.

4

ln2

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Practice Test 2
9

The median salary at a large biotech company is $45,000.
The mean income is $60,000. Which of the following statements best explains the difference between the mean and
the median?
A.

There are a few people at the biotech company
with very low salaries.

B.

There are a few people at the biotech company
with very high salaries.

C.

Most of the salaries at the biotech company are
between $45,000 and $60,000.

D.

All of the salaries at the biotech company are within
a small range.

SHOW YOUR WORK HERE

10 Mount Asgard in Auyuittuq (pronounced: ow-you-eettook) National Park, Baffin Island, Nunavut, was used in
the opening scene for the James Bond movie The Spy Who
Loved Me. A stuntman skis off the edge of the mountain,
free-falls for several seconds, and then opens a parachute.
The height, h, in meters, of the stuntman above the ground
t seconds after he opens the parachute is represented by
the equation h(t) = –10.5t + 980. What does the 980 in the
equation represent?
A.

The speed of the stuntman

B.

The height of the mountain

C.

The height of the stuntman when he opens the
parachute

D.

The total length of time the stuntman is in the air

11 According to Einstein’s theory of relativity, an object cannot
travel faster than the speed of light, which is approximately
180,000 miles per second. If x represents the speed of an
object (measured in miles per hour), which inequality
represents the range of possible speeds for the object?
A.

x ≤ 648,000,000

B.

x ≥ 648,000,000

C.

x ≤ 180,000

D.

x ≥ 180,000

CONTINUE
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  695

Practice Test 2
SHOW YOUR WORK HERE

12 Consider the following diagram:

B

l

37°

100°

A

x°

C

y°

m

Assuming that lines l and m are parallel, determine the
value of x.
A.

37

B.

43

C.

137

D.

143

13 The price of one 1 GB memory card is x dollars. A coupon
for 15% is applied to the cost of a purchase of T memory
cards, and a 6% tax is then applied to the discounted
amount. Finally, a special state employee discount of 10%
is applied to the final amount. Which of the following
expressions represents the savings in the absence of any
discount?
A.

0.910(x + T) dollars

B.

0.8109xT dollars

C.

0.2491xT dollars

D.

0.1581(x + T) dollars

14 What values of z, if any, satisfy the equation
1
4
=
+1 ?
1+ z z + z 2

  696

A.

No solution

B.

0

C.

–2 only

D.

–2 and 2

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Practice Test 2
15 A food truck sells sandwiches for $5.95 each and beverages
in cans or bottles. A beverage in a bottle costs the same
as a beverage in a can. Which of the following statements
is true about the equation that represents the food truck
revenue, 5.95x − 1.75y = z?

16

A.

x is the number of customers served

B.

z is the number of customers served

C.

y is the number of beverages sold

D.

y is the number of sandwiches sold

SHOW YOUR WORK HERE

2x + y ≥ a
x +2y ≥ b
In the xy-plane, if (–1, –1) is a solution to the system of
inequalities above, which of the following relationships
must be true about a and b?
A.

a>b>0

B.

a 2y

CONTINUE
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Practice Test 2
18 Which of the following equals x, if 3 x + 8 = 20?
A.

4

B.

8

C.

12

D.

16

19 According to historians, Archimedes proved that a crown
made for his king was not pure gold. Suppose the crown
had a density of 800 grams and a volume of 50 grams. The
density of gold is about 19 grams per cc, and the density of
silver is about 10.5 grams per cc. The system below models
this relationship (G = volume of gold, S = volume of silver).
G + S = 50
19G + 10.5S = 800
If the crown contained both silver and gold, about what
percent of the crown is silver?

  698

A.

19 percent

B.

36 percent

C.

62 percent

D.

81 percent

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SHOW YOUR WORK HERE

Practice Test 2
SHOW YOUR WORK HERE

Questions 20 and 21 refer to the following information.
1,000

Revenue (dollars)

800
600
400
200
0

5

10

15

20

25

30

35

Temperature (degrees Celsius)
The graph above displays the total revenue R in dollars
for an ice cream shop when the temperature is T degrees
Celsius.

20 Which of the following best describes the association
between R and T?
A.

Strong positive correlation

B.

Strong negative correlation

C.

Weak positive correlation

D.

Weak negative correlation

21 Which of the following is the line of best fit for the data in
the graph?
A.

y = 500 + 1.2x

B.

y = 1.33x

C.

y = 20x + 250

D.

y = 725

22 For which of the following values of a does the equation
ax2 – x + 2 have two complex conjugate solutions?
A.

–5

B.

−

C.

1
8

D.

2
3

1
2

CONTINUE
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  699

Practice Test 2
23 If (x – 1) and (x + 5) are the only linear factors of f(x), which
of the following graphs shows a possible graph of the
function f?

4

2

–6

–4

–2

0

2

–2

–4

A.

4

2

–6

–4

–2

0

2

–2

–4

B.

4

2

–2

0

2

4

6

4

6

8

–2

–4

C.

4

2

0

2

–2

–4

D.

  700

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SHOW YOUR WORK HERE

Practice Test 2
24 The graph of a parabola has x-intercepts at 4 and –2 and
a y-intercept at 8. Which of the following could be the
equation of the graph?
A.

y = –(x – 1)2 + 9

B.

y = x2 – 2x + 8

C.

y = (x – 1)2 – 9

D.

y = x2 + 2x – 8

SHOW YOUR WORK HERE

25 A population of bacteria in a sample increases in number
by 30% every hour. Which best describes the relation
between the time h in hours and the number of bacteria
B in the sample?
A.

The relation between B and h is linear, because the
population increases by the same percent each
hour.

B.

The relation between B and h is linear, because the
population increases by the same amount each
hour.

C.

The relation between B and h is exponential,
because the population increases by the same
percent each hour.

D.

The relation between B and h is exponential,
because the population increases by the same
amount each hour.

CONTINUE
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  701

Practice Test 2
26 If k is a negative constant less than –1, which of the following could be the graph of y = kx2 + bx + c?

4

2

–8

–6

–4

–2

0
–2

–4

–6

A.

4

2

–4

–2

0

2

4

4

6

2

4

–2

–4

–6

B.

4

2

–2

0

2

–2

–4

–6

C.
4

2

–4

–2

0

–2

–4

–6

D.

  702

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SHOW YOUR WORK HERE

Practice Test 2
Questions 27 and 28 refer to the following information.

SHOW YOUR WORK HERE

Liberal

Moderate

Conservative

An educational researcher chose 200 randomly selected students at a local college and asked them how they would best
categorize their political inclinations. The results are shown in
the table below.

Seniors

6

18

34

Juniors

20

42

30

Sophomores

8

6

4

Freshmen

22

8

2

27 What is the probability that a junior of this group is a
conservative?
A.

17
29

B.

9
15

C.

2
9

D.

15
46

28 Given a total of 4,000 students at the college, about how
many of those students would categorize themselves as
moderates?
A.

About 74

B.

About 1,120

C.

About 1,400

D.

About 1,480

CONTINUE
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  703

Practice Test 2
29 A recent poll found that 11% of the respondents approve
of the job that the U.S. Congress is doing. The margin of
error for the poll was ± 3% with 95% confidence interval.
Which of the following statements is a conclusion that can
accurately be drawn from this poll?
A.

95% of the time that such a poll is conducted, the
true approval rate is between 8% and 14%.

B.

The true percentage of people who approve of the
job that the U.S. Congress is doing is between 8%
and 14%.

C.

The pollsters are 95% confident that the true
percentage of people who approve of the job that
the U.S. Congress is doing is between 86% and 92%.

D.

The pollsters are 95% confident that the true
percentage of people who approve of the job that
the U.S. Congress is doing is between 8% and 14%.

30 Line m intersects the x-axis at (3, 0) and the y-axis at (0, –2).
Line n passes through the origin and is perpendicular to
line m. Which of the following is an equation of line n?

  704

A.

3
y= x
2

B.

2
y= x
3

C.

3
y =− x
2

D.

2
y =− x
3

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SHOW YOUR WORK HERE

Practice Test 2
DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

31
1
, not 3 .
2
2

, it will be interpreted as

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

1

1

2

2

2

1

1

3

3

3

3

3

4

4

4

4

4

5

5

5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

7

7

7

8

8

8

8

8

9

9

9

9

9

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

7

7

7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

CONTINUE
Peterson's SAT® Prep Guide 2017

  705

Practice Test 2
31 A baboon troop has 60 members, 35% of which are male.
What is the ratio of males to females in the baboon troop?
(Grid your answer as a fraction.)

SHOW YOUR WORK HERE

32 During a recent baseball season, 2 hitters on a team had
a total of 66 home runs. Batter B had 14 fewer home runs
than batter A. How many home runs did batter A hit?

33 A community radio station operates 24 hours per day,
every day of the week. Each radio show lasts 90 minutes.
What is the total number of shows that the radio station
will broadcast Monday through Friday?

34 3(5 – 2x) = –4(cx + 4)
What value for c in the equation above will make the
equation have no solutions?

35 The base of a circular cylinder has a radius that is equal to
twice its height. The diameter of a sphere is the same as
the height of the cylinder. How many times larger is the
volume of the cylinder as compared to the volume of the
sphere?

36

f ( x ) = 3x 2 − 4 x + 8
g( x ) = 2 x − 5
Use the functions above to find the value of g(f(–2)).

37

y = 2x −3
y = −3( x − 1)2 + 4
According to the system of equations above, what is one
value of x?

38 The total rainfall in Plainville increased by 25% from 2012
to 2013. The rainfall decreased by 30% from 2013 to 2014.
Then, it increased again by 40% from 2014 to 2015. What
was the percent of increase in rainfall from 2012 to 2015?
Express your final answer as a decimal.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  706

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Practice Test 2
SECTION 5: ESSAY
50 Minutes—1 Essay
DIRECTIONS: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

As you read the passage below, consider how Jessica Smartt Gullion uses the following:
• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed.

Will guns on campus lead to grade inflation?
Adapted from “Will Guns on Campus Lead to Grade Inflation?” by Jessica Smartt Gullion, originally published in The Conversation on
April 27, 2015. Jessica Smartt Gullion is an assistant professor of sociology at Texas Woman’s University.
1

Texas college professors may soon face a dilemma between upholding professional ethics and protecting their lives.

2

The Texas legislature appears poised to approve a bill that would allow college students to carry firearms to class. Called
“campus carry,” public universities in Texas will not be allowed to ban guns on their campuses, once the law is passed,
although private schools could enact their own prohibitions.

3

Its backers argue that students have the right to protect themselves on campuses with handguns. The lobbying extends to
sponsoring crash courses such as the NRA University, a two-hour seminar course for college students.

4

With this proposed law, a question coming up for many academics is whether they would be forced to give As to
undeserving students, just so they can avoid being shot.

5

This is not as farfetched as it sounds. In my five years as a college professor, I have had experience with a number of
emotionally distressed students who resort to intimidation when they receive a lesser grade than what they feel they
deserve.
Threats on campus

6

Here is an example of one such threatening experience: One evening in a graduate course, after I handed back students’
papers, a young woman stood up and pointed at me. “This is unacceptable!” she screamed as her body shook in rage.

7

She moved toward the front of the class waving her paper in my face and screamed again, “unacceptable!” After a heated
exchange, she left the room and stood outside the door sobbing.

8

All this was over receiving a B on a completely low-stakes assignment.

CONTINUE
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  707

Practice Test 2
9

What followed was even more startling. The following week, the student brought along a muscle-bound man to class. He
watched me through the doorway window for the entire three hours of the class, with his arms folded across his chest.

10

And if this wasn’t enough, the young woman’s classmates avoided me on campus because, they said, they were afraid of getting
caught in the crossfire should she decide to shoot me.

11

After that, every time she turned in a paper I cringed and prayed that it was good so that I wouldn’t have to give her anything less
than an A.

12

Learning from this experience, now I give papers back only at the end of the class or just “forget” to bring them with me.

13

I was lucky that the student didn’t have a gun in my classroom. Other professors have not been so lucky.

14

Last year, a student at Purdue shot his instructor in front of a classroom of students. In another incident in 2009, a student at
Northern Virginia Community College tried to shoot his math professor on campus. And, in 2000, a graduate student at the
University of Arkansas shot his English professor.

15

In each of these states, carrying handguns on campus was illegal at the time of the shooting, although a bill was introduced in
Arkansas earlier this year to allow students to carry guns.
Grade inflation

16

Despite these and other shootings, a new trend has emerged across the U.S. that supports guns on college campuses.

17

Eight states allow firearms onto college campuses, and 11 states are now considering similar legislation.

18

We know that some students will carry guns whether it is legal or not. One study found that close to 5 percent of undergraduates
had a gun on campus and that almost two percent had been threatened with a firearm while at school.
…

19

Who would want to give a student a low grade and then get shot for it?

20

Many majors are highly competitive and require certain GPAs for admission. Students on scholarships and other forms of
financial aid must maintain high grades to keep their funding. It’s no surprise that some students might resort to any means
necessary to keep up their GPAs.

21

An international student once cried in my office and begged me to change his F to an A, as without it, his country would no
longer pay for him to be in the U.S. I didn’t. He harassed me by posting threatening messages on Facebook.

22

So, the question is, will we soon see a new sort of grade inflation, with students earning a 4.0 GPA with their firepower rather
than brain power? And if so, what sort of future citizenry will we be building on our campuses?

Write an essay in which you explain how the writer builds an argument to persuade her audience that
she is offering proof of war’s traumatic history. In your essay, analyze how Jessica Smartt Gullion uses
one or more of the features listed previously (or features of your own choice) to strengthen the logic
and persuasiveness of her argument. Be sure that your analysis focuses on the most relevant aspects
of the passage.
Your essay should not explain whether you agree with Jessica Smartt Gullion’s claims, but rather
explain how she builds an argument to persuade her audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  708

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Answer Keys and Explanations
Section 1: Reading Test

1. C

12. B

23. C

34. C

45. A

2. A

13. A

24. D

35. C

46. D

3. B

14. B

25. B

36. A

47. B

4. D

15. D

26. B

37. D

48. B

5. A

16. B

27. C

38. D

49. D

6. D

17. B

28. A

39. D

50. C

7. A

18. D

29. C

40. C

51. A

8. C

19. C

30. B

41. C

52. C

9. B

20. A

31. A

42. C

10. B

21. A

32. C

43. B

11. B

22. D

33. C

44. A

READING TEST RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is C. The causes of death the author
lists are thought to be very common causes, but by
stating that SeDS is a more common cause than all of
those other causes combined shows that SeDS is more
severe than they are. Some of the causes of death may
be shocking to some readers, but the author has a much
more important reason for listing them than their shock
value, so choice A is not the best answer. The author
only shows that SeDS is more common than the causes
of death he lists in lines 6–7, and in the following
paragraph, he states that there is one cause of death
more common than SeDS, so choice B is incorrect. The
causes of death listed in lines 6–7 are all destructive or
self-destructive, but choice D implies that the author’s
main concern is stopping readers from engaging in
these forms of behavior when the overall purpose of the
passage is to explain the dangers of SeDS.
The correct answer is A. The article presents the
opinions of Frank Booth first, accompanied by factual
details. These are followed by quotes from Scott Gordon
and Ron Gomes, along with other facts and charts
illustrating statistics about diabetes. Choice B is
incorrect because the information is not presented in a
sensational manner; it is concerned with facts and
opinions from experts. Those affected are not quoted,
so choice C is also incorrect. Choice D focuses only on

statistics, and the article does not discuss how the
statistics are interpreted, so it is incorrect as well.
3.

The correct answer is B. The Grim Reaper is a
traditional image of a cloaked skeleton that
represents the inevitability of death, but the image
of a flabby skeleton is so absurd that it is comical.
Since the rest of the article is extremely serious, it is
reasonable to conclude that the author included
the humorous quote in line 1 to lighten the tone of
an otherwise serious article, so choice B is the best
answer. Choice A is incorrect because the silliness of
the image of a flabby Grim Reaper actually
undercuts the gravity of the problem of SeDS.
Choice C is incorrect because the idea of a flabby
Grim Reaper is intended to be silly and ironic, which
is almost the opposite effect of being relatable.
Choice D is incorrect because although images of
the Grim Reaper can be frightening, the silliness of
a flabby Grim Reaper undercuts that image’s
scariness.

4.

The correct answer is D. The article says that the
human body has evolved over time to do physical
work like farming and household chores, but
machines now do much of that work, which leads
to obesity. Choice A introduces an idea that

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  709

Answer Keys and Explanations
9.

The correct answer is B. Booth states that he wanted
to come up with “a catchy name” something that would
get people’s attention. Based on this statement, it is
logical to conclude that “pizzazz” means “oomph,” or
bold and attention getting. Choice A makes sense
within the context of the sentence, but it changes the
meaning of the sentence and doesn’t convey the idea of
a catchy name, which is what the sentence discusses.
Choice C suggests that “inactivity-related disease” is too
frivolous, with the author saying that it is not “catchy”
enough to grab the public’s attention, implying that
“inactivity-related disease” is too dry and serious. This
contradicts the conclusion in choice C. Choice D is
incorrect because “inactivity-related disease” is a much
clearer and more descriptive term than SeDS.

10.

The correct answer is D. The author refers to the heavy
cost of treating SeDS in the article, which supports
choice D. Although Dr. Frank W. Booth comes off as an
authority on SeDS in this article, there is no indication
that the syndrome is responsible for making him
respected or well known. The author’s discussion of how
many people between the ages of 10 and 19 suffer from
Type 2 diabetes caused by SeDS in lines 39–40 contradicts the conclusion in choice C.

The correct answer is B. The author includes quotes
stating that “Our bodies were designed to be physically
active” and that “this may mean planning exercise into
your daily routine,” which supports the conclusion in
choice B since physical inactivity causes SeDS. Choice A
is incorrect because the author sees a catchy name as
simply a way to make people aware of the problem.
Choice C is incorrect because although the article
connects the rise in Type 2 diabetes with obesity, it is
only one health issue the article discusses. Choice D is
also incorrect because of the narrowness of its focus.
The article brings up the importance of children
developing better habits than their parents, but is not
the overarching theme of the passage.

11.

The correct answer is A. Choice A discusses the heavy
healthcare costs ($3 trillion) of treating SeDS. Choice B is
incorrect because it merely introduces an authority on
SeDS; it makes no comment on the financial burden the
syndrome creates. While choice C refers to money by
stating that Dr. Booth believes the government should
spend more on preventing SeDS, he does not present
this proposal in a negative light, so choice C is not as
strong of an answer as choice A is. Choice D only
discusses the negative physical impacts of SeDS; it does
not refer to the financial ones.

The correct answer is B. Choice B establishes a clear
link between the number of Americans who are not
physically active and the doubling of the obesity rate.
Choice A mentions the fact that one person wants more
money to be allocated to helping Americans be more
active, but doesn’t link obesity to fitness. Choice C
describes the complications of Type 2 diabetes but
doesn’t refer to obesity. Choice D explains the connection between children and ailments associated with
obesity but doesn’t indicate how essential it is for all
human beings to be physically active.

12.

The correct answer is B. Although the government
professes that wrongs done to the Native Americans
should be corrected, the author’s use of the phrase
“simple and unperplexing expedients” suggests that the
author believes the government’s intentions are not
sincere, so choice B is correct. The lines state that the
government acknowledges that Native Americans have
suffered “wrongs” and that the government is responsible for committing such “perfidies,” or untrustworthy
actions, which contradicts choice A. The author states
that “President after president” initiated these reports

information in the article never supports. Children do
inherit different body types, but this article is not about
the dangers of a particular body type acquired naturally; it is about how inactivity can cause people to
become unnaturally obese, so choice B is not the best
answer. The author argues that people are now more
sedentary than in previous generations, but choice C
implies that people need to eat more because modern
life requires a great deal of physical activity. This
conclusion contradicts a main point in the passage.
5.

6.

7.

8.

  710

The correct answer is A. Frank Booth wanted to
emphasize that a lack of exercise or activity leads to
obesity and even death, so he chose “sedentary” as a
synonym for “inactive” to add pizzazz to a condition that
needs greater attention. Choice B is actually the
opposite meaning, referring to health and energy.
Choice C echoes another health issue: Sudden Infant
Death Syndrome, which refers to children who die
mysteriously as infants. The process the article discusses
is not sudden or restricted to children. Choice D
describes the result of inactivity, but does not define it.

The correct answer is C. In 1998, new cases of Type 2
diabetes began to drastically increase and grow
continuously every year, until the number peaked in
2009. Choice A is the start of the chart, and although it
shows an increasing trend overall, there are many
decreases as well. Choice D is the highest number of
new cases reported, but it is not the beginning of
continuing increases because the number of cases falls
off the following year.

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Answer Keys and Explanations
describing government injustices committed against
Native Americans, which contradicts choice C. While the
author may think the government has some understanding of the plight of Native Americans, she shows
that she does not believe that it is “well equipped to
determine a viable solution” by implying that the
government only voices insincere support for Native
Americans while failing to make substantive changes to
improve their situation.
13.

14.

15.

The correct answer is A. By citing abuses against
Native Americans in a variety of U.S. states across a
period of 85 years, the author shows how government
abuses against Native Americans are widespread across
geography and history. Choice B is not the best answer
because, although specific states are mentioned, they
are simply used as examples and there is no indication
that these states have the worst records of abuse
against Native Americans. Choice C implies that because
the dates cited are not recent, the problems have
stopped, yet the second half of the sentence explains
that the government “breaks promises now as deftly as
then.” Choice D is incorrect because it implies that the
lines are specifically focused on a particular region,
which is not true since the states mentioned are not all
southern states and the author suggests that abuses
against Native Americans have been committed in
different places.
The correct answer is B. Lines 24–25 state that “The
story of one tribe is the story of all, varied only by
differences of time and place,” and since this story is that
of the abuses Native Americans have suffered at the
hands of the government, the lines show that the
abuses have been committed across geography (“place”)
and history (“time”). So choice B is the best answer.
Choice A is less effective because it only refers to history
(“the record of the history of the Indians”), not geography. Choice C refers only to geography (“the United
States”), not history. Choice D is incorrect because it
merely refers to how the abuses are being committed
(“with added ingenuity”), not how they have been
committed across history and geography.
The correct answer is D. In lines 16–18 (“There . . .
laws”), the author talks about an area that was settled so
quickly that there wasn’t a chance to create laws to
protect Native Americans amidst the chaos of the gold
rush. Consequently, settlers could do whatever they
wanted to the tribes, unregulated by any treaty. While
the author mentions that the tales described in choice A
existed, she does not use them to explain why abuses
against Native Americans during the gold rush were
allowed to go unchecked and unpunished. Choice B is

incorrect because there were no treaties or laws to break
during the chaotic and lawless period described in lines
16–18. Choice C is incorrect because although white
settlers and the government were both responsible for
abuses against Native Americans, the author does not
suggest that there was any particular sympathy between
those two particular parties.
16.

The correct answer is B. In lines 24–25, the author
states that “The story of one tribe is the story of all,”
which is his way of saying that the abuses Native
Americans suffered were not limited to a particular
tribe. The author expresses nothing but outrage in
sympathy with Native Americans throughout the
passage, contradicting choice A completely. Choice C is
incorrect because the author regularly cites documentation of the abuses Native Americans suffered at the
hands of the government (“The reports are filled with
eloquent statements of wrongs done to the Indians . . .
The history of the Government connections with the
Indians is a shameful record of broken treaties and
unfulfilled promises.”). Choice D makes an unsubstantiated assumption based on the fact that 1795 is the
earliest year mentioned in this particular article.

17.

The correct answer is B. Throughout the article, the
author passionately argues that Native Americans have
been systematically abused by both the government
and white settlers, citing examples of such abuses as
“murder, outrage, [and] robbery.” However, the author
never explains how the government could atone for
those abuses, so choice A is incorrect. The author is
mainly concerned with detailing the government’s
abuse of Native Americans; she does not really get into
the causes and effects of those abuses, so choice C is
not the best answer. The author never presents
opposing viewpoints of why the United States has had
conflicts with Native Americans; she only argues her
own position that the government has been abusive, so
choice D is not the best answer either.

18.

The correct answer is D. The author repeatedly refers to
concealing or explaining away the offenses of white
settlers against Native Americans, so “excused” is the best
synonym for “palliated” as it is used in line 70. Choice A
has the opposite meaning of “palliated.” Choice B would
imply that there might be some justification for white
men’s crimes against Native Americans; that those crimes
are merely misunderstood. This contradicts the proNative American stance the author expresses throughout
the entire passage. “Eased” can be used as a synonym for
“palliated,” but it is not appropriate for this particular
context since one it does not really make sense to ease a
crime.

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Answer Keys and Explanations
19.

20.

21.

22.

  712

The correct answer is C. Choice C is the best summary
because it accurately states that the army admits they
were the aggressor. The few times Native Americans did
something horrible, the events were played up as worse
than they were, while the army’s crimes were played
down. Choice A gets some of the facts wrong and
makes assumptions that aren’t in the original paragraph. Choice B does the same and interprets “testimony” as literally referring to a courtroom. Choice D is
too simplistic and leaves out much of the pertinent
information of the paragraph.
The correct answer is A. While the author is clear that
she feels the government has denied Native Americans
their human rights, she also suggests that the government has tried to convince them that they have the
same rights as all other Americans. The author states
that the government’s abuse of Native Americans is
ongoing (“the United States Government breaks
promises now as deftly as then”), which contradicts
choice B. While she argues that the government’s
treatment of Native Americans has been extremely
unjust, she never accuses the government of having an
agenda to actually drive Native Americans out of the
country. The author acknowledges that Native
Americans have committed crimes against white men,
but states that these crimes are widely reported (lines
70–74 “Every offense committed by an Indian . . . around
it.”), which contradicts choice D.
The correct answer is A. These lines show that the
government has taught Native Americans that they
have rights even if the government has not honored its
own teachings. Choice B only comments on the
government’s failure to honor its teachings; it does not
explain what has been taught, which is necessary to
serve as evidence to support the previous question’s
answer. Choice C moves on to a new topic (white man’s
aggression toward Native Americans) that has nothing
to do with the previous question. Lines 70–73 deal with
Native American crimes against white people, and the
only answer choice related to that topic in the previous
question incorrectly suggests that the government has
tried to conceal these crimes, so choice D is incorrect
under any circumstances.
The correct answer is D. The author uses the word
“barbarous” to describe the retaliations of Native
Americans against white people that are “unspeakable.”
It is logical to conclude that the attacks are unspeakable
because they are so brutal and violent, so choice D is
the best answer. An attack can be silent, but this would
not make it unspeakable, so choice A does not make
much sense. “Steadfast” generally has positive

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connotations, meaning admirably consistent or loyal,
yet an attack would most likely be unspeakable because
it is horrible. Therefore, the correct answer should have
negative connotations, and that eliminates choice B.
Similarly, an attack can be calculated, but it is more
logical for an attack to be unspeakable because of its
brutality than its level of calculation, so choice C is not
the most sensible answer.
23.

The correct answer is C. The main theme in the
passage describes the people who lived at Arlington
House—slaves and owners—and includes information
about how the house was constructed and by whom as
well as the history of the plantation’s ownership. There
is no language that suggests the author wished to
persuade readers, choice B. Although the author makes
it clear how disadvantaged slaves were, the passage
does not focus on the evils of slavery, choice A.
Although the passage includes some information about
the lives of slaves, choice D, its overall focus is the
history of the plantation.

24.

The correct answer is D. The text explains that Mrs.
Custis “tutored slaves in basic reading and writing so
that they could read the Bible” (lines 58–59) because she
was a very religious woman. There is no indication that
she wanted them to be able to teach the skills to
anyone else, so choices A and C can be eliminated. The
passage never mentions any other reading material, so
choice B is incorrect.

25.

The correct answer is B. The text states that “Upon
Martha Washington’s death, Custis inherited her slaves”
(lines 19–20). It does not say how he acquired the land
for his plantations, so we cannot assume that it was
granted to him by Martha Washington, so even though
choice A mentions the slaves Custis inherited, it must be
eliminated. The passage describes how Custis went
about building the house, so it’s safe to say that he did
not inherit a house with land and slaves, so choice C is
incorrect. The text states that Custis had three plantations in all, but it does not say how he acquired them, so
choice D cannot be proven with information in this
particular passage.

26.

The correct answer is B. The text tells us that Selina
was given the keys to the plantation, which implies
great trust in the days of slavery. As head housekeeper,
she may also have cared for the Lee children, choice C,
but that information is not in the passage. Being head
of housekeeping is not the same as running the whole
plantation, choice D; while housekeeping of a large
mansion is hard work, the text doesn’t compare it to the
fieldwork of other slaves, choice A.

Answer Keys and Explanations
27.

28.

29.

30.

The correct answer is C. Lines 49–50 of the passage
state that Selina Gray was the head housekeeper at
Arlington, and the caption below the diagram indicates
that the west end of the building housed the housekeeper, which supports the conclusion in choice C.
According to the passage, “the slaves constructed log
cabins for their homes” (lines 25–26), and the diagram
does not depict a log cabin, so choice A is incorrect. The
diagram implies that a large number of people were
forced to live in a relatively small space, so choice B is
not the best conclusion. Lines 64–67 state that Maria
Carter Syphax was an emancipated slave “who lived
with her husband on a seventeen-acre plot given to her
by the Custises at the time of her emancipation around
1826.” There is no evidence that the house depicted in
the diagram was Syphax’s home on that seventeen-acre
plot, so choice D is not the best answer.
The correct answer is A. According to the passage,
Robert E. Lee was related to George Washington
through marriage. The fact that Lee married
Washington’s great granddaughter eliminates choice B.
The passage never mentions whether any of Lee’s seven
children were even sons, so choice B is incorrect. There
is no discussion of Lee’s father at all, which means there
is no evidence supporting choice D either.
The correct answer is C. These lines state that Robert E.
Lee married Custis’s daughter after the author had
already explained that Custis was George Washington’s
grandson. Lines 15–16 only introduce Custis and do not
explain his relationship to George Washington at all, so
choice A is not a strong answer. Lines 19–21 only show
that Custis had some sort of relationship with Martha
Washington, since he inherited slaves from her, but it
does not explain the exact nature of that relationship,
so choice B is not the best evidence for the previous
answer. Similarly, lines 36–38 show that Lee and Custis
had a relationship but fail to explain what that relationship is, so choice D is incorrect.
The correct answer is B. Custis could inherit slaves
because they were legally equivalent to any other
property—a good that could be bought and sold.
Choice B illustrates this point. Simply being able to free
a slave, choice D, doesn’t illustrate the concept of
property ownership; it illustrates the concept of physical
freedom. Choice A is a general description of the
complexity of the relationships on the plantation, but
doesn’t show how slaves were property to be bought
and sold.

31.

The correct answer is A. The “invisible gulf” the author
mentions is one of separation between slaves and
owners in terms of privilege and human rights. While
“gulf” can describe a body of water, as in choice B; a
chasm, as in choice C; or a physical gap, as in choice D,
here the author’s use is metaphorical.

32.

The correct answer is C. In this context, “afford” does
not refer to money as in choice B, but to things provided
to others. Since slaves were property, and treated as
such, few owners thought about teaching them to read
or write. There is no risk implied in this use of the word,
choice A, or any suggestion of the tutoring being given
in exchange for something else as in choice D.

33.

The correct answer is C. Both passages agree that the
amount of carbon dioxide in our atmosphere has
increased. However, choice A is disputed by the second
passage, and choice B is disputed by the first passage.
Choice D is refuted by the second passage as being too
complicated to prove or predict.

34.

The correct answer is C. Only choice C specifically
mentions carbon dioxide levels, which the first passage
implies the same by stating that “Carbon dioxide can
stay in the atmosphere for nearly a century, so Earth will
continue to warm in the coming decades” in lines
40–42. Choice A discusses some of the effects of carbon
dioxide levels but does not confirm their increase.
Choice B discusses the changes to the atmosphere
without specifically mentioning increased carbon
dioxide levels. Choice D directly counters any attempts
to limit carbon dioxide but doesn’t support the fact
there are increases.

35.

The correct answer is C. Both passages address the
reader as “we” or “our,” indicating a shared interest
among humans. Each passage is trying to persuade the
reader to one viewpoint, thus making choice A
incorrect. Choice B is too strong a description since both
passages try to convince with logic rather than pure
emotionalism. Choice D is incorrect because there are
no second-person or “you” statements in the passages.

36.

The correct answer is A. The author of Passage 1
believes that human actions could reduce the impact of
global warming on the environment and shows this by
stating “By making choices that reduce greenhouse gas
pollution and preparing for the changes that are already
underway, we can reduce risks from climate change”
(lines 49–51). The authors of Passage 2 do not believe in
global warming, but still believe in humans’ capacity to
improve the environment by advocating human
rationing of hydrocarbon and stating that “Hydrocarbon

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Answer Keys and Explanations
use has major environmental benefits” in lines 82–83.
Choice B is incorrect because the authors of Passage 2
do not even believe in global warming. Only the author
of Passage 1 discusses how humans have adapted to
climate changes throughout history, so choice C is
incorrect. Only the author of Passage 2 voices the
suggestion in choice D by stating that “we needn’t
worry about human use of hydrocarbons warming the
Earth” in lines 76–77.
37.

  714

The correct answer is D. The purpose of Passage 1 is to
convince readers that global warming is a danger, and
the alarming tone of language such as “potentially
dangerous, severe, dangerous effects” reinforces that
purpose. The second passage attempts to refute any
cause for concern by describing the evidence supporting global warming with terms such as “no
significant, insufficient, unreliable,” which attempts to
assure the reader that there is nothing to worry about.
Therefore, choice D is the best answer. Based on these
evaluations, only Passage 1 creates a sense of danger, so
choice A is incorrect. While one could certainly argue
that the first passage is based on scientific evidence and
the second is speculative, the terms in this answer
choice do not differ because one set is scientific and the
other is speculative, so choice B is not the best answer.
The passages are not overly technical, and the terms
repeated in this answer choice certainly do not refute
that fact, so choice C is not the best answer.

38.

The correct answer is D. The sentence refers to
symptoms of climate change becoming more recognizable. “Pronounced” can refer to the way something is
said; however, that meaning doesn’t fit the context,
choice A. Choice C has the opposite meaning from the
meaning of “pronounced” as used in the passage.
“Pronounced” can refer to a declaration or
announcement, choice B, but that meaning also does
not fit the context.

39.

The correct answer is D. Both passages define a
problem—the first discusses a lack of sufficient concern
about global warming and the second discusses
misplaced concern about global warming—and offer
solutions to those problems when the author Passage 1
implores the reader to reduce the risks of global
warning and the authors of Passage 2 recommend
greater use of hydrocarbons. Therefore, choice D is the
best answer. Choice A suggests a timeline of events.
Although both authors reference past and future
events, information is not presented sequentially. Only
the author of Passage 2 argues that there is a lack of
effects regarding global warming, so choice B fails to

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describe how information is presented in both passages. Neither passage compares two approaches to the
global warming problem, so choice C is incorrect.
40.

The correct answer is C. The first passage focuses only
on the negative effects of atmospheric carbon dioxide,
and the second passage states that hydrocarbons do not
have a negative effect. Choices A and D are incorrect
because there is no mention of hydrocarbons in Passage
1. The author of Passage 1 believes that human intervention could have a positive impact on global warming,
which indicates a belief that climate and weather can be
somewhat modified by humans, but the authors of
Passage 2 make no such suggestions, so choice B is
incorrect.

41.

The correct answer is C. The author of the second
passage is quoting those he or she disagrees with, such
as the author of the first passage. Choice A only
highlights the sources of greenhouse gases and does
not encapsulate the major differences between these
arguments. Choice B focuses on the long-term effects of
carbon dioxide but doesn’t summarize the two
competing arguments. Choice D focuses only on
beneficial effects of increased atmospheric carbon
dioxide.

42.

The correct answer is C. Choice C correctly fits with the
idea of changes becoming shifts and suggests that the
effects of climate change may be unpredictable.
Language translation, choice A, is the process of
converting words and meaning from one language into
another; however, that is not the way in which
“translate” is used here. The effects the authors mention
could include expansion, but that is too narrow a
definition for the context, which makes choice B
incorrect. Choice D refers to helping someone understand something, which does not fit the context of the
sentence.

43.

The correct answer is B. The two women are fulfilling a
tradition common to many cultures, in which the living
stay with the body of a friend or family member so it
doesn’t have to be alone. The tradition partly grew out
of the possibility that the deceased might revive, as
sometimes happened in the days before doctors were
readily available. Choice A is incorrect; it is clear that
word has already spread that Miss Tempy died. Choice C
has no supporting evidence in the story. Choice D is a
presumption that is also unsupported by details in the
story.

Answer Keys and Explanations
44.

The correct answer is A. While performing a duty to a
friend, two of her oldest, dearest friends draw closer to
each other. Choice B is incorrect because the focus of
the story is the relationship between the two remaining
friends. Choice C may be true but is incidental. Choice D
may also be true but is not central to the story.

45.

The correct answer is A. The author explains how
stimulating the conversation between the women was
(“the two women had risen to an unusual level of
expressiveness . . . they were again and again tempted
into statements that either would have found impossible by daylight”), so it is reasonable to assume that
Mrs. Crowe was so distracted by this conversation that
she failed to notice that the stocking she was knitting
was becoming too long. Choices B and C reach very
specific conclusions that evidence in the passage does
not support, and as already stated, the author’s
description of Mrs. Crowe’s conversation with Sarah Ann
Binson indicates a likelier answer to this question. That
stimulating conversation also indicates that Mrs. Crowe
did want to be where she was; otherwise, she would not
be very interested in the conversation, so choice D is
not the best conclusion either.

46.

The correct answer is D. Choice D shows that under
this special circumstance, the women are bonding.
Choice A is a minor detail that doesn’t reflect their
friendship. Choice B does not happen in the story,
although it is mentioned as a trait of Mrs. Crowe’s.
Choice C is part of the author’s description of Sarah Ann,
but it doesn’t indicate closeness to Mrs. Crowe.

47.

The correct answer is B. In these lines, the author
states that the two women were telling each other
secrets and saying things that they never would have
said under other circumstances (“statements that either
would have found impossible by daylight”), indicating
the intimacy of their conversation. Therefore, choice B is
the best answer. Choice A indicates the liveliness of the
conversation (“there was a certain degree of excitement
just then, and the two women had risen to an unusual
level of expressiveness and confidence”) but not the
intimacy of it. Choice C only describes a difference
between the two women. Choice D shows that the
conversation was “engaging,” but not that it was
especially intimate.

48.

The correct answer is B. During the long night
together talking, both women reveal secrets and say
things they would never have said under normal
circumstances. Choice A is a supposition the author
makes, presuming they wouldn’t have enough to talk

about all night long, but that doesn’t prove to be the
case. Choice C reflects the characterization of Mrs.
Crowe as “knowing exactly what she was about” and “a
cooler disposition,” yet she is so involved in her conversation that she doesn’t notice she is knitting a sock that
is too long. Choice D reflects the author’s comment that
her life is filled with pleasure, but she also says that, to
outward appearances, Sarah Ann Binson was burdened
by caring for her family.
49.

The correct answer is D. Choice D is correct because
despite Mrs. Crowe’s higher social standing the women
easily fill a long night with intimate talk. Their intimate
conversation indicates that they are very trusting, at
least when talking to each other, so choice A is not the
best answer. Choice B assumes they are the same age,
but this detail isn’t mentioned in the passage. Neither
seems overly concerned with her work (Mrs. Crowe is
not paying attention to her knitting and Sarah Ann
Binson keeps setting her sewing down to talk instead),
so choice C is not the best conclusion.

50.

The correct answer is C. These lines indicate that Sara
Ann Binson seemed to live a “pleasureless” life because
she had to work so hard on her small farm, while Mrs.
Crowe was “well-to-do” with a “rich” husband. Therefore,
choice C is the best answer. Choice A merely establishes
the passage’s setting and implies nothing about its two
main characters. Choice B establishes what the two
women are doing and suggests nothing about their
social standing. Choice D only indicates public perception of Mrs. Crowe, and its failure to mention Sarah
Ann Binson makes it weak evidence for the previous
answer.

51.

The correct answer is A. Sarah Ann would have to be
eager to carry the load of her family as discussed in the
rest of the sentence, and since the author seems to be
establishing a contrast between public perception of
Sarah Ann and the “vague” Mrs. Crowe, choice A is the
best contrast to Mrs. Crowe’s vagueness. That contrast
also eliminates choice C since “absentminded” is too
close in meaning to “vague.” Sarah Ann’s hard work
indicates that people would not view her as “bored,” so
choice B does not make much sense. While she may be
restless, the focus of the sentence is on how much
responsibility she shoulders for her relatives, which
makes choice B incorrect. The fact that Sarah Ann
Binson does not have much money does not mean that
she was cheap, since one who does not have much to
spend does not have the luxury of cheapness, so choice
D is not the best answer.

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52.

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The correct answer is C. Although several of the
answer choices are synonyms of “aspect,” the only one
that would truly make sense in place of the word in this
particular line is “attitude,” since it is Sarah Ann Binson’s
attitude that appears to be “sharp” and “anxious.” It
would not make sense to write “for all her sharp, anxious
face,” even though “face” can be used to mean “aspect”
in another context, so choice A is not the best answer.
Choice B is another synonym of “aspect” that would not
make sense in this context. Choice D is incorrect,
because although “aspect” is sometimes misused to
mean “component,” this is not exactly what it means,
and “component” would not make sense in this context
anyway.

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Answer Keys and Explanations
Section 2: Writing and Language Test
1. D

11. D

21. B

31. B

41. D

2. B

12. B

22. A

32. B

42. C

3. C

13. B

23. B

33. A

43. B

4. D

14. A

24. A

34. C

44. D

5. B

15. B

25. B

35. C

6. A

16. C

26. A

36. D

7. B

17. D

27. C

37. B

8. D

18. D

28. C

38. A

9. C

19. B

29. D

39. C

10. A

20. C

30. C

40. C

WRITING AND LANGUAGE TEST RAW SCORE
(Number of correct answers)
1.

The correct answer is D. This sentence is a fragment
requiring a subject, which the pronoun “it” provides.
Choices B and C do not work because the specific
subject doesn’t have a verb—“having” and “were” are
part of the descriptive phrase, not the direct action of
the subject.

2.

The correct answer is B. The phrase “for communicating” is set off by a comma in the passage, but
because the description “for communicating” modifies
“code” by defining the purpose of that code, “for
communicating” is a restrictive phrase and should not
be separated from the word or phrase it modifies. This
makes choices A and C incorrect because the comma
after “code” separates the restrictive phrase and the
word it modifies. Choice D is incorrect because the
comma after “communicating” is incorrect.

3.

4.

The correct answer is C. Choice C is the only choice
that makes clear who has the access and the only choice
that states the intended purpose concisely. Choice A is
incorrect because the construction “it being the case
that they would” is wordy. Choice D places “enemy
forces” near the beginning of the sentence, but it
creates confusion in the second clause that implies that
the code, not the enemy forces, would have access to
the tactics and troop movements. Choice B is incorrect
because “having access” is ambiguous.
The correct answer is D. This sentence accurately
supports the information in the paragraph and passage,

that the U.S. military selected the Navajo language as
the foundation for a secret code for a few specific
reasons—namely, its “complexity and obscurity.” There’s
no evidence to suggest that many of the top military
officials at the time were Navajo, so choice A is incorrect.
There’s also no evidence to support the notion that the
Navajo language was chosen because the Navajo
people were famous for their military history, so choice
B is incorrect. Furthermore, there’s no evidence to
support the notion that the Navajo people had often
been called on to help the American government in the
past, so choice C is also incorrect.
5.

The correct answer is B. This sentence provides an
additional reason why the Navajo language made an
excellent code, which makes “furthermore” the best
choice. Choice A is incorrect because “However”
indicates a contrast, which is not implied by the context.
Choice C is incorrect because “Likewise” would make
sense only if the sentence were making a comparison.
Choice D is incorrect because “As a result” suggests that
the sentence is drawing a conclusion, but this is not
supported by the context.

6.

The correct answer is A. Choice A maintains the
paragraph’s implication that the Navajo language is
largely unknown or obscure, a quality that would make
the language ideal for the Marines’ purpose. Choice B is
incorrect because it implies that the language is
nonsensical and incomprehensible, which is not the

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Answer Keys and Explanations
point. Choice C is incorrect because “beauty” would not
make a language perfect for a code. Choice D is
incorrect because “clarity” is not a desirable quality for a
code that is intended to be unbreakable.
7.

8.

9.

10.

11.

  718

The correct answer is B. Choice B correctly joins two
independent clauses with a comma and a coordinating
conjunction. Choice A does not effectively combine the
two sentences because it repeats the subject, forming
an awkward sentence. Choices C and D are incorrect
because they imply that the second clause is dependent
on the first clause, which changes the meaning of the
sentence.
The correct answer is D. Choice D accurately suggests
that the enemy forces attempted, but did not succeed,
in interpreting (or deciphering) the code. Choices A and
B are incorrect because they do not fit the intended
meaning of the sentence and therefore do not make
sense in the context. Choice C is incorrect because
“elucidate” means “explain something,” which is the
opposite of what the Marines tried to achieve by using
Navajo code talkers.
The correct answer is C. No commas are needed to
separate “speed and accuracy” from the rest of the
sentence, as this adverbial phrase does not need to be
set off from the verb (the work of the code talkers). For
this reason, choices A and D are incorrect. Choice B is
incorrect because “speed and accuracy” contains a
conjunction and does not require a comma.
The correct answer is A. Choice A maintains the simple
past tense, which is established earlier in the sentence.
Choices B, C, and D are incorrect because they contain
inappropriate shifts in verb tense.
The correct answer is D. This choice best supports the
claims made by the rest of this sentence. The work of
the code talkers had to remain largely a secret and
unacknowledged for many years because the code was
still being used actively. Choices A, B, and C don’t
explain why the work of the code talkers had to remain
unacknowledged, so they are incorrect.

12.

The correct answer is B. “Who was Dian Fossey” is a
question and thus requires a question mark. Choices A,
C, and D are incorrect because they do not include a
question mark.

13.

The correct answer is B. Knowing where Fossey was
born is irrelevant to the rest of the passage; it doesn’t
support the main idea of the paragraph or the passage,
which is Fossey’s work with gorillas. Therefore, choices C
and D are incorrect. Choice A is incorrect because this

www.petersons.com

information does not need to be included anywhere in
the passage.
14.

The correct answer is A. Choice A correctly portrays Dr.
Louis Leakey as a well-known and well-respected
scholar in the field. Choice B is incorrect because
“imminent” refers to something that is about to happen
and therefore does not make sense. Choices C and D
both imply that Dr. Leakey is bad or disreputable, which
is not supported by the context.

15.

The correct answer is B. Choice B corrects the dangling
modifier by making it clear that Fossey decided to focus
her research on mountain gorillas. Choice A is incorrect
because it contains a dangling modifier. Choice C and D
are incorrect because they contain misplaced modifiers.

16.

The correct answer is C. The sentence is attempting to
show where Fossey observed gorillas, so “There” is the
correct word to start the sentence. Choice A is incorrect
because “they’re”, a contraction that means “they are,”
does not fit within the context of the sentence. Choice B
is incorrect because it is a possessive determiner and
does not fit in this context. Choice D is incorrect
because it makes the sentence a fragment.

17.

The correct answer is D. Choice D is correct because
the sentence is talking about how the animals welcomed Fossey. Choice A is incorrect because it confuses
“except,” which refers to something that is apart from
other things, with the word “accept.” Choices B and C are
incorrect because they are used incorrectly in this
context.

18.

The correct answer is D. Only choice D maintains the
tone and style of the rest of the passage. Choices A, B,
and C are incorrect because they are much more
informal than the rest of the passage.

19.

The correct answer is B. The opening of the sentence
(In 1989) indicates that the action in this sentence has
already happened, so the past tense is required.
Therefore, choice B is correct. Choices A, C, and D
employ incorrect verb tense forms.

20.

The correct answer is C. The writer should not add the
sentence because, while the information might or
might not be true, the writer doesn’t expand on it, and it
doesn’t support the main idea of the paragraph—that
Fossey continued to work to save gorillas for the rest of
her life. Choice A is incorrect because the information
does not support the main idea of the paragraph.
Choice B is incorrect because the information is not

Answer Keys and Explanations
necessary to the transition between paragraphs. Choice
D is incorrect because the information is not necessary
anywhere in the passage.
21.

22.

23.

24.

25.

26.

The correct answer is B. Choice B is correct because
“declining” accurately communicates that the number
of gorillas as falling. Choice A is incorrect because it
suggests a diminishment of quality, not number.
Choices C and D both imply humiliation, which is not
supported by the context.
The correct answer is A. Choice A is the correct answer
because the singular verb “is rising” agrees with the
singular noun “population.” Choice B is incorrect
because the verb “are” is plural. Choice C is incorrect
because the verb “were” is plural and past tense. Choice
D is incorrect because the correct verb form to match
the singular “population“ is “there is.”
The correct answer is B. Choice B is correct because
“surrounds” maintains the comparison the author makes
between a tamarin’s fur and a lion’s mane. Choices A
and C are incorrect because the first part of the
sentence describes their “hairless faces,” so the notion of
fur obscuring or covering the face is inappropriate.
Choice D is incorrect because it is vague and
ambiguous.
The correct answer is A. The writer should not delete
the underlined sentence. This information supports the
main idea of the paragraph, and the sentence appears
in the correct place in the logical organization of the
paragraph. Choice B is incorrect because this sentence
does not explain the previous sentence; rather, it adds a
detail that is further explained in the next sentence.
Choice C is incorrect because moving the sentence
would interrupt the organizational flow of the paragraph. Choice D is incorrect because this information
does not interrupt the flow of ideas in the paragraph.
The correct answer is B. Choice B clarifies the comparison between tamarins that assist in the care of
newborns with those that do not. Choice A is incorrect
because the failure to note what is being compared
leads to confusion. Choices C and D are incorrect
because the comparisons are vague or incorrect.
The correct answer is A. The pronoun “they” correctly
refers to the plural antecedent “tamarins” and the verb
“are” is in the present tense like the rest of the paragraph. Choices B and D are incorrect because the
pronoun “it” is singular. Choice C is incorrect because
“tamarins” are gender-neutral.

27.

The correct answer is C. Choice C corrects the
conventional expression to “one and the same.” Choices
A, B, and D are incorrect because they do not reflect the
proper use of this conventional expression.

28.

The correct answer is C. Sentence 5 provides more
information about tamarins’ diurnal activities and thus
should naturally follow sentence 1. The word “however”
also implies that the sentence provides information that
somehow contrasts with the previous sentence and the
idea that tamarins dislike sunlight contrasts with the
notion that they are active during the day. Choices A, B,
and D are incorrect because sentence 5 does not make
sense in those positions.

29.

The correct answer is D. The semicolon in choice D
correctly connects two independent clauses. Choice A is
incorrect because a comma may not be used to
separate independent clauses without the use of a
coordinating conjunction. Choice B is incorrect because
it doesn’t fix the comma splice; it just moves it. Choice C
is incorrect because the sentence requires punctuation
to fix the grammatical error.

30.

The correct answer is C. The graph shows that the
number of tamarins in zoos between 1970 and 1978
ranged from fewer than 100 in 1970 to about 150 in
1978. Choice A is incorrect because it includes incorrect
information from the chart. There were about 140 zoos
participating in 2006, not in the 1970s. Choice B is
incorrect because the graph shows fewer than 100 zoos
participating in the 1970s. Choice D is incorrect because
the graph shows that the number of tamarins in zoos
between 1970 and 1978 ranged from fewer than 100 in
1970 to about 150 in 1978.

31.

The correct answer is B. Choice B clarifies the
ambiguous pronoun “it” by inserting the reference to
“the campaign.” Choice C is incorrect because “it” does
not refer to “the problem.” Choice D is incorrect because
it simply replaces one pronoun with another, which
does nothing to clarify what the pronoun refers to.

32.

The correct answer is B. Choice B accurately states that
tamarin populations have fluctuated in recent years
while the number of zoos participating in the program
has not. Choice A is incorrect because the graph does
not show any decline in the participation of zoos.
Choice C is incorrect because the participation rate of
zoos has not risen substantially in recent years. Choice D
is incorrect because neither the number of participating
zoos nor the population of tamarins has fallen significantly since 2000.

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Answer Keys and Explanations
33.

34.

The correct answer is C. Choice C supports the idea of
“strict” adherence to principles. Choice A is incorrect
because it suggests the adherence is temporary, which
is not supported by the context. Choices B and D are
incorrect because they do not make sense in the
context of the sentence.

35.

The correct answer is C. This information supports the
main idea of the paragraph and provides a logical
conclusion to the paragraph, so it should be placed at
the end. Choice A is incorrect because, although the
information might be interesting, it is out of place and
disrupts the flow of ideas in the paragraph. Choice B is
incorrect because it is a conclusion, not an introduction.
Choice D is incorrect because, although the information
supports the main idea of the paragraph, it is out of
place.

36.

  720

The correct answer is A. Choice A accurately suggests
the efforts have been successful. Choice B is incorrect
because the sentence suggests success rather than a
problem. Choice C is incorrect because the sentence
does not mention making money. Choice D is incorrect
because it suggests their plan is off schedule, but this is
not supported by the sentence.

The correct answer is D. Choice D uses a transition
word and comma to combine the sentences in a
grammatically correct and concise way. Choice A is
incorrect; and suggests additional but equal information, but the second clause modifies the first and is
not equal. Choice B is incorrect because it is syntactically incorrect. Choice C incorrectly separates two
independent clauses with a comma.

37.

The correct answer is B. In choice B, the plural noun
“columns” is in agreement with the second plural noun
“elements,” and the statement contains the plural verb
“are.” Choice A is incorrect because the plural noun
“columns” is not in agreement with the singular noun
“element.” Choice C is incorrect because the singular
noun “column” is not in agreement with the plural noun
“elements.” Choice D is incorrect because the noun
“columns” is plural and the verb “is” is singular.

38.

The correct answer is A. The items in the list need only
be separated by commas. Choice B is incorrect because
the conjunction “and” is incorrectly used in several
places. Choices C and D are incorrect because they
incorrectly and unnecessarily use a semicolon.

www.petersons.com

39.

The correct answer is C. Only choice C maintains
parallel structure by including “the” before each of item
in the series. Choices A, B, and D are incorrect because
they do not provide parallel structure because the
article “the” is not used consistently.

40.

The correct answer is C. Choice C correctly continues
and supports the paragraph’s purpose of providing
examples of how each element is divided into three
parts. The paragraph currently discusses how the
entablature and column are divided into three parts,
and choice C continues that purpose by describing the
three parts of the crepidoma, the third element. Choices
A, B, and D are incorrect because they do not support
the purpose or topic of the paragraph.

41.

The correct answer is D. The antecedent “classical
buildings” is plural, which means the pronoun must also
be plural. Choices A, B, and C are incorrect because they
contain antecedents and pronouns that are not in
agreement.

42.

The correct answer is C. “Its” is a possessive determiner
that refers to the singular noun “building.” Choices A and
B are incorrect because the antecedent is “building,” so
the pronoun should be gender neutral and singular.
Choice D is incorrect because “buildings” should be
singular possessive.

43.

The correct answer is B. “Perceived” means recognized,
which fits with the meaning of the sentence. Choice A is
incorrect because it describes the violations as being
different, which is not what the author intends. Choices
C and D are incorrect because neither makes sense in
the context of the sentence.

44.

The correct answer is D. Choice D follows the paragraph’s focus on the difficulty of following the strict
conventions of classical architecture. Choice A is
incorrect because it focuses on information from a
previous paragraph. Choice B is incorrect because it is a
general statement that is unsupported by the information in the passage. Choice C is incorrect because it
makes a hyperbolic generalization that is not supported
by the paragraph.

Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. A

5. A

9. A

13. A

17. 48

2. D

6. A

10. D

14. C

18. 22

3. A

7. A

11. B

15. D

19. 7

4. B

8. D

12. C

16. 48

20. 15

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is A. Subtract like terms when
simplifying the expression: 4x2 – 3x2 = x2, –5x – (–2x) =
–3x, and 8 – (–5) = 13. Put together, we get the
expression x2 – 3x + 13.

2

−

4
3

=x

y = ( x 2 − 8 x + 16 ) + 9 − 16
y = ( x − 4) 2 − 7

In vertex form, the constants are the coordinates of the
vertex for the parabola. Choices A and C show equations equivalent to the given equation, but in intercept
form and standard form instead of vertex form. Choice
D includes the coordinates of the vertex, but it is not
equivalent to the given equation; it represents only half
of the parabola.

2
3

1

=
=

−

2

x3
1
3

5.

x2

The correct answer is A. Rewrite the expression as a
multiple of a + 4b:
−5−3a + 2 ( 4b + a ) − 12b = −5−3 ( a + 4b ) + 2 ( a + 4b )

The correct answer is A.
2

The correct answer is B. Solve the equation for y, then
complete the square to write it in vertex form.
y = x 2 − 8x + 9

The correct answer is D. To simplify the expression, first
add the exponents, and then use the rule that a
negative exponent is equal to the reciprocal of the
positive exponent of the same number. Finally, rewrite
the rational exponent in radical form:
x3 i x

3.

4.

−2  x (1− 3 x ) + 3 x  = −2  x − 3 x + 3 x 


2

= −5− ( a + 4b)

2

= 5 ( a + 4b)
= 5 (16)

2

= −2  +3 x 2 + 4 x 


4
3
= 2 9 x − 24 x + 16 x 2 


= 18 x 4 + 48 x 3 − 32 x 2

= 80
6.

The correct answer is A. Divide both sides by 2πr to
simplify, then set the equation equal to h:
S=

2πr 2 + 2πrh
2πr 2

S
=r+h
2πr
S
−r =h
2πr

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Answer Keys and Explanations
7.

The correct answer is A. The population will be
reduced by 3.5% each year, so each year the population
is multiplied by (1 – 0.035), or (0.965). The only answer
choice that shows repeated multiplication of (0.965),
through the use of the exponent n, is choice A:
P = P0(0.965)n.

8.

The correct answer is D. Substitute the values 4 and 6
for x and check which equation has the correct function
values for both, or calculate the slope between the
points and substitute one point to find the y-intercept:

(4, 6)

x
Note: Figure not drawn to scale.

From the above figure, we know that point (4, 6) lies on
line q. Therefore, x = 4 and y = 6 must satisfy the
equation of the line. Substitute these values in the
above equation and solve for b, which is the y-intercept:
6 = 4+b
2=b
Therefore, the y-intercept of line q equals 2.

www.petersons.com

The correct answer is B. If the angles of a triangle are
equal to the corresponding angles of another triangle,
the two triangles are similar. Also remember that when
two triangles are similar, their corresponding sides are
proportional.

D

B

2

E

4

C

Note: Figure not drawn to scale.

Since DE is parallel to BC , then ∠ABC = ∠ADE and
∠ACB = ∠AED. Also, the angle at point A is common to
both triangles. Thus, all three angles of triangle ABC are
congruent with the corresponding angles of triangle
ADE.

q
p

  722

5L = 45
L=9

A

The correct answer is A. The standard slope-intercept
form of the equation of a line is y = mx + b, where m is
the slope of the line and b is the y-intercept. Therefore,
the slope of line p equals 1. Since lines p and q are
parallel, their slopes are equal. Therefore, the slope of
line q equals 1. Let line q be represented by the
standard equation of a line, y = mx + b. Since the slope
of line q equals 1, substitute m = 1 in the equation:
y = x + b.

y

The correct answer is D. Write equations based on the
information given; let s = a small cup and L = a large
cup. Multiply the first equation by 4 and the second one
by 3, so that s gets eliminated during the subtraction.
Then solve for L:
4(3s + 2L = 30)
−3(4 s + L = 25)

11.

10 − 2
=4
6−4
y = 4x +b
2 = 4(4) + b
−14 = b
y = 4 x − 14
9.

10.

Therefore, triangle ABC and triangle ADE are similar and
their corresponding sides are proportional.
Now set up a proportion of their corresponding sides
and solve for the length of segment AB:
AB BC
=
AD DE
AB 4
=
3 2
AB
=2
3
AB = 6
Therefore, the length of segment BD is
AB – AD = 6 – 3 = 3.

Answer Keys and Explanations
12.

13.

The correct answer is C. The y-coordinate of the vertex
of a parabola that opens downward, such as the one
described by the function p(x), is the maximum value of
the function.

15.

The correct answer is D. Check each answer choice to
see if the slope between the point (3, 4) and the given
4
coordinates is − . Only choice D gives us this answer:
5
y −4
4
=−
x −3
5
−4 − 4
=
13 − 3
4
−8
=−
10
5

The correct answer is A. You can work backward with
the answer choices to determine the value of x. None of
1
the values works except x = :
2
2

 5
 5
( x + 2 ) 2 + ( x − 3) 2 =   +  − 
 2
 2
25 25
=
−
4
4
=0
14.

2

16.

The correct answer is C.

B

y

The correct answer is 48. Let x be the number of 30
pound bags that Miguel can safely carry. Because his
truck can safely carry only a maximum of 1,500 pounds,
the weight of the bags plus the weight of the wheelbarrow has to be equal to or less than that, which gives
us the inequality 30x + 50 ≤ 1,500. Solve for x to get the
number of bags:
30 x + 50 ≤ 1,500
30 x ≤ 1, 450
x ≤ 48.33

O

Because Miguel can’t take partial bags, he can safely
take 48 bags.
17.

A (0,3)

(0,0)

The correct answer is 48.

6

x

8
The center of this circle is the midpoint of the segment
 −2 + 4 3 + 9 
,
with endpoints (–2, 3) and (4,9): 
 = (1, 6)
 2
2 
. The diameter is the length of the segment with
endpoints (–2, 3) and (4, 9):

( 4 − ( −2))2 + (9 − 3)2

=

72 = 6 2 . So, the radius is

half of the diameter, or 3 2 . Finally, using the standard
form for the equation of the circle, we conclude that its
equation is (x – 1)2 + (y – 6)2 = 18.

We know that each side of the square has length 16
since two triangle sides of length 8 form one side of the
square. From this, we know that the shortest sides of the
hexagonal sign must equal 4: the square side – 2
triangle edges = 16 − 2(6) = 4. Now all we have to do is
find the hypotenuse of one triangle and multiply it by 4.
Use the Pythagorean theorem: a² + b² = c², where c is
the length of the hypotenuse. In this case: 8² + 6² = c²,
64 + 36 = c², 100 = c², and 10 = c.
So the perimeter of the sign is
10(4) + 4(2) = 40 + 8 = 48 inches.

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Answer Keys and Explanations
18.

The correct answer is 22. To solve for b, first multiply
both sides by x – 4 to get 5x +2 = 5x – 20 + b. Then,
subtract 5x – 20 from both sides to get 22 = b.
5 x + 2 5 x − 20 + 22
=
x −4
x −4
5 x − 20 22
=
+
x −4 x −4
22
= 5+
x −4
b = 22

19.

The correct answer is 7.
3x − 4 = 2 x − 5
x = −1
y = 3(−1) − 4 = −7
xy = (−1)(−7) = 7

  724

www.petersons.com

20.

The correct answer is 15.
−3(6 x − 5 y ) = −3(9)
−18 x + 15 y = −27
Multiplying the first equation by –3 will yield an
equivalent equation, so if the second equation actually
had the coefficients of 15 for b, there would be infinitely
many solutions. So, b = 15 is the answer.

Answer Keys and Explanations
Section 4: Math Test—Calculator
1. B

9. B

17. B

25. C

33. 80

2. B

10. C

18. D

26. D

34. 1.5

3. C

11. A

19. B

27. D

35. 24

4. A

12. A

20. A

28. D

36. 51

5. B

13. C

21. C

29. D

37. 2

6. C

14. A

22. D

30. C

38. .225

7. D

15. C

23. A

31. 7/13

8. C

16. D

24. A

32. 40

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B. Let x be the number of nickels
in the collection. Then, there are 3x dimes and 5x
quarters in the collection. Using the value of each coin
yields the following equation. Solve for x:

4.

The correct answer is A. The description can be written
as 18 – 6x = –8 – 4, which is equivalent to 18 – 6x = –12.
Subtracting 18 from both sides gives –6x = –30. Since
–3x is half of –6x, dividing both sides by 2 gives
–3x = –15.

5.

The correct answer is B. The total amount of pain
medication is 24(250)(200) = 1,200,000 milligrams. The
answers are all in kilograms, so convert the measure in
milligrams to kilograms one step at a time:
1,200,000 milligrams = 1,200 grams, and 1,200 grams =
1.2 kilograms.

6.

The correct answer is C. A sample is not equivalent to
the population, and just because a sample is smaller
than the population does not mean that it is not
representative.

7.

The correct answer is D. The slope of the curve is
increasing as the number of years increases. The
population increases from 290 to 425 in the span
between 2010 and 2012. So, the average population for
2011 is 357.50. Similarly, the population increases from
500 to 825 in the span between 2013 and 2015. So, the
average population for 2014 is 662.50. Thus, the
predicted difference in the population between the
years 2014 and 2011 is 305.

0.25(5 x ) + 0.10(3 x ) + 0.05( x ) = 11.20
125 x + 30 x + 5 x = 1,120
160 x = 1,120
x =7

So, there are 3(7) = 21 dimes in the collection.
2.

The correct answer is B.
2 [ −3 − (2 − 4 x )] = −3 + x
2

2 [ −5 + 4 x ] = −9 + x
−10 + 8 x = −9 + x
−1 = −7 x
1
=x
7

 1
So, x −2 =  
 7
3.

−2

= 49.

The correct answer is C. Johnson ran the 400-meter
race in 43.18 seconds. In that time, Halswelle ran at a
rate of 8 meters per second (400 meters/50 seconds =
8 meters/second). So he would have run 43.18 seconds
× 8 meters/second = 345.44 meters. So Halswelle would
have had about 55 more meters to run before reaching
the end of the 400-meter race.

Peterson's SAT® Prep Guide 2017

  725

Answer Keys and Explanations
8.

The correct answer is C. Substitute the points (2009,
250) and (2013, 500) into the equation to obtain two
equations involving A and b:

12.

The correct answer is A. First, find y. To do so, find the
missing angles by extending the line segment BC to a
line:

250 = Ae b(2009)

43° B 137°
37°

500 = Ae b(2013)

l

100°

Solve both equations for A and simplify them to get an
equation involving only b:
250e

− b( 2009 )

A

=A

x°

C

y°

m

500e − b(2013) = A
250e − b(2009 ) = 500e − b(2013)

Since lines l and m are parallel, y must be 137° because
corresponding angles are congruent. Then, using
supplementary angles, the measure of angle ACB is 43°.
Thus, using the triangle sum rule, we have
100 + x + 43 = 180. Therefore, x = 37.

250e − b(2009 )e b(2013) = 500
e 4b = 2
4b = ln 2
1
b = ln 2
4
9.

The correct answer is B. If the mean is significantly
greater than the median, there must be some values
that are much greater than the rest in order to increase
the mean.

10.

The correct answer is C. In the equation
h(t) = –0.5t + 980, 980 represents the height above the
ground of the stuntman when he opens the parachute.

11.

The correct answer is A. Convert 180,000 miles per
second to miles per hour by using the fact that there are
3,600 seconds in one hour:

13.

The correct answer is C. The cost of T memory cards is
xT dollars. The cost after the 15% discount is applied is
0.85xT dollars. The cost after the 6% tax is applied is
0.85xT + 0.06(0.85xT) = 0.901xT dollars. Finally, applying
the 10% discount to that amount yields a total cost for
the purchase of 0.901xT – 0.10(0.901xT) = 0.8109xT
dollars. Without any discount, the cost of T memory
cards is xT + 0.06xT = 1.06xT dollars. So, the savings is
1.06xT – 0.8109xT = 0.2491xT dollars.

14.

The correct answer is A. Multiply both sides of the
equation by z + z2 to clear the fractions:

( z + z ) i 1+1 z = ( z + z ) i  z +4z
z = 4 + (z + z )
2

180,000 miles per second = 180,000 (3,600) miles per hour
= 648,000,000 miles per hour


+ 1


0=4+z2
Since the right side is always positive (in fact, it is never
less than 4), this equation has no solution.
15.

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2

2

Since an object’s speed cannot exceed this value, the
inequality is x ≤ 648,000,000.

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2

The correct answer is C. If $5.95 is the cost per
sandwich, then 5.95x is the revenue from sandwiches,
and y must be the number of beverages sold, since the
number of beverages sold is an unknown value, and z
must be the total revenue.

Answer Keys and Explanations
16.

17.

18.

The correct answer is D. Both coefficients must be
negative to make the system of inequalities true, but
neither must be greater than the other.

22.

+ c = 0 has two complex conjugate solutions when the
radicand in the quadratic formula

The correct answer is B. The number of cookies and
cupcakes that Alex bakes are 18x and 15y respectively.
The number of cookies and cupcakes are x and y
respectively. Since the number of pans of cookies is “at
least” twice as many, the “greater than or equal to”
symbol should be used. Also “no more than 165” means
to use the “less than or equal to” symbol.

equation, keep a as the variable a, then define b = –1,
2
and c = 2. So, the radicand is ( −1) − 4(a) i (2) = 1− 8a . This

expression is negative whenever a >

23.

The correct answer is A. Because the function has
factors (x – 1) and (x + 5), and there are no other linear
factors, the graph of f(x) must have zeros when x – 1 = 0
and x + 5 = 0, and nowhere else. Thus, the only x-intercepts for f(x) are 1 and –5.

24.

The correct answer is A. Only the graphs of choices A
and B have y-intercepts at 8. Only the graphs of choices
A and C have x-intercepts at 4 and –2. Only choice A
offers both the x-intercepts at 4 and –2 and the
y-intercept at 8.

25.

The correct answer is C. The relation between the
number of bacteria and the time in hours should be an
equation like B = A(1.3)h, where A is the initial population of bacteria, h is the number of hours, 0.3 is the
rate of growth, and B is the sample population after h
hours.

26.

The correct answer is D. If k < –1, then the graph must
open downward and be relatively steep.

27.

The correct answer is D. There were 92 juniors, and, of

x =4
x = 16
The correct answer is B. First, solve the system of
equations for S:
G + S = 50
19G + 10.5S = 800
19G + 19 S = 950
19G + 10.5S = 800
8.5S = 150
S = 17.65
S ≈ 18
Then divide the total volume of the crown by 50:
18
= 0.36
50
= 36%

those, 30 students categorized themselves politically as
30

20.

21.

The correct answer is A. The trend of the graph is
positive, and most of the data points are close to a line,
so the association is a strong positive correlation.
The correct answer is C. The trend of the graph is
positive, most of the data points are close to a line, and
the line for y = 20x + 250 goes through the center of the
data. The other graphs don’t go through the center or
don’t follow the trend of data.

1
. The only answer
8

option for which this is true is choice D.

3 x = 12

19.

−b ± b 2 − 4 ac
is
2a

negative. To figure out the radicand for the given

The correct answer is D. Isolate x on one side of the
equation and then square both sides to solve.
3 x + 8 = 20

The correct answer is D. A quadratic equation ax2 + bx

15

conservative: 92 = 46
28.

The correct answer is D. Of the 200 students surveyed,
there were 74 students total who categorized themselves as moderates.
74
× 4, 000 = 1, 480
200

29.

The correct answer is D. The 95% confidence that the
margin of error is ± 3% is important, and choices A and
B ignore the confidence interval. Choice C is not correct
because there are likely people who don’t know or have
no opinion of the job that the U.S. Congress is doing.
Only choice D accurately uses the confidence interval
and the data given in the problem.

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Answer Keys and Explanations
30.

The correct answer is C. First, find the slope of line m
using the points on the line:

34.

−2 − 0 2
=
0−3 3

3(5 − 2 x ) = −4( cx + 4)
4c − 6 = 0
15 − 6 x = −4 cx − 16
4c = 6
  
4 cx − 6 x = −31
c = 1.5

A line that is perpendicular to line m will have a slope
that is the negative reciprocal of that slope, so the slope
3
of line n is − , which means that choice C is correct.
2
31.

The correct answer is

35.

cylinder is π(2h)2h = 4πh3. Since h is the diameter of the
h
sphere, its radius is . So, the volume of the sphere is
2

equals 21. So, there are 21 males and 39 females. Since
21
won’t fit into the grid, you must reduce.
the fraction
39
Divide both the numerator and the denominator by 3 to
7
.
get
13
The correct answer is 40. Write and solve an equation
that represents the home runs hit by batters A and B,
and solve for the desired number.

3

4 h 1 3
π   = πh .
3 2 6
Observe: Volume of the cylinder =
1

4 πh 3 = 24  πh 3  = 24 × volume of the sphere.
6

36.

n – 14 = number of home runs by batter B

33.

37.

2 x − 3 = −3 x 2 + 6 x − 3 + 4
0 = −3 x 2 + 4 x + 4
0 = (3 x + 2)( − x + 2)
2
x=− , 2
3

5(24 hrs.) = 120 hrs.
Then, convert the length of each show to hours:
3
 1 hr. 
90 min. 
=
hrs.
 60 min. 
2

120 hrs.
= 80
3
hrs.
2

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The correct answer is 2. First, combine the equations
by substituting 2x – 3 for y in the second equation. Then
solve for x:
2 x − 3 = −3( x − 1) 2 + 4

The correct answer is 80. First, calculate how many
hours there are in five days:

Finally, divide the number of hours by the length of
each show:

The correct answer is 51.
f ( −2) = 3( −2) 2 − 4( −2) + 8 = 28
g(28 ) = 2(28 ) − 5 = 51
g( f ( −2)) = 51

n = number of home runs by batter A

n + n − 14 = 66
2n − 14 = 66
2n = 80
n = 40

The correct answer is 24. Let h be the height of the
cylinder. Its radius is 2h, and so, the volume of the

7
(7/13). First, determine how
13

many male baboons there are in the troop; 35% of 60

32.

The correct answer is 1.5. First simplify the equation,
and then determine which value of c will make the
equation have no solutions, which is when the coefficient for x = 0.

Negative answers cannot be gridded, so the only
correct answer is 2.
38.

The correct answer is .225. To find the percent of
change, multiply 1.25(1 – 0.3)(1.4) to show the three
years of change as (1.225). This is equivalent to a 22.5%
increase. The equivalent decimal is 0.225. Since there are
only 4 spaces in the grid-in box, ignore the zero (0), and
just grid in the decimal point and 225 so it appears as
.225.

Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
The following is an analysis of the passage by Jessica Smartt Gullion, noting how the writer used evidence, reasoning, and stylistic
or persuasive elements to support her claims, connect the claims and evidence, and add power to the ideas she expressed. Check
to see if you evaluated the passage in a similar way.
Will guns on campus lead to grade inflation?
By Jessica Smartt Gullion, Assistant Professor of Sociology at Texas
Woman’s University
1

Texas college professors may soon face a dilemma
between upholding professional ethics and protecting
their lives.

2

The Texas legislature appears poised to approve a bill that
would allow college students to carry firearms to class.
Called “campus carry,” public universities in Texas will not
be allowed to ban guns on their campuses, once the law
is passed, although private schools could enact their own
prohibitions.

3

1

The writer starts her argument by articulating her central
concern: Texas college professors may soon be forced to put
fear for their safety above professional ethics.

2

The writer states her reason for this concern: a pending Texas
law that permits college students to carry guns on campuses.

Its backers argue that students have the right to protect
themselves on campuses with handguns. The lobbying
extends to sponsoring crash courses such as the NRA
University, a two-hour seminar course for college
students.

3

The writer establishes her credibility and fairness by stating the
reason why some legislators support this bill.

4

With this proposed law, a question coming up for many
academics is whether they would be forced to give As to
undeserving students, just so they can avoid being shot.

4

The writer returns to her central concern, expressing it in more
detail: some instructors might give undeserved high grades to
avoid being shot.

5

This is not as farfetched as it sounds. In my five years
as a college professor, I have had experience with a
number of emotionally distressed students who resort to
intimidation when they receive a lesser grade than what
they feel they deserve.

5

The writer provides facts about herself: she has been a college
professor for five years and has had experience with students
who intimidate instructors. By citing her background, the
writer establishes her credentials as someone qualified to write
about this topic and make this argument.

6

The writer provides a specific example drawn from her own
experience. This makes her argument more personal and
further strengthens her credibility—she truly knows what
she is talking about. In addition, the writer makes this story
extremely vivid using powerful words (screamed; shook in
rage).

7

The writer continues to use evocative words (waving her paper
in my face; heated exchange; sobbing).

Threats on campus
6

Here is an example of one such threatening experience:
One evening in a graduate course, after I handed back
students’ papers, a young woman stood up and pointed
at me. “This is unacceptable!” she screamed as her body
shook in rage.

7

She moved toward the front of the class waving her paper
in my face and screamed again, “unacceptable!” After a
heated exchange, she left the room and stood outside
the door sobbing.

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Answer Keys and Explanations
8

All this was over receiving a B on a completely low-stakes
assignment.

9

What followed was even more startling. The following
week, the student brought along a muscle-bound man to
class. He watched me through the doorway window for
the entire three hours of the class, with his arms folded
across his chest.

10

And if this wasn’t enough, the young woman’s classmates
avoided me on campus because, they said, they were
afraid of getting caught in the crossfire should she decide
to shoot me.

11

After that, every time she turned in a paper I cringed and
prayed that it was good so that I wouldn’t have to give
her anything less than an A.

12

8

The writer underscores the volatility of this student by using
the phrase “all this” and pointing out that she received
a respectable grade (a B) on an assignment that wasn’t
particularly important. The writer is implying that this
woman’s response to the grade was not rational, and she
might have been angrier (and potentially more dangerous) if
this were a major assignment.

9

The writer adds more details to the story, again carefully
choosing words to paint a vivid picture (a muscle-bound man;
the entire three hours; arms folded across his chest). Here,
the writer evokes sympathy for herself and, by extension,
all college teachers who have experienced (or who might
experience) something similar.

Learning from this experience, now I give papers back
only at the end of the class or just “forget” to bring them
with me.

10

The writer points out that the consequence of this experience
went beyond her and one student, extending to her
interactions with her other students.

13

I was lucky that the student didn’t have a gun in my
classroom. Other professors have not been so lucky.

11

14

Last year, a student at Purdue shot his instructor in front
of a classroom of students. In another incident in 2009,
a student at Northern Virginia Community College tried
to shoot his math professor on campus. And, in 2000, a
graduate student at the University of Arkansas shot his
English professor.

The writer concludes the story by relating the effects this
experience had on her, driving home the point that she
is speaking from personal experience and eliciting more
sympathy from the reader. She chooses her words carefully
(cringed; prayed) for maximum impact.

12

The writer makes the reader aware that this experience has
had a lasting effect on her.

13

The writer returns to her central point: students having guns
on campuses.

14

The writer cites three other incidents in which college students
shot or tried to shoot instructors on a college campus.

15

Despite these and other shootings, a new trend has
emerged across the U.S. that supports guns on college
campuses.

The writer points out that in these incidents carrying
handguns on campus was illegal. Thus she implies that things
could get much worse on campuses where carrying handguns
is allowed.

16

Eight states allow firearms onto college campuses and 11
states are now considering similar legislation.

The writer points that even with the issue of students shooting
instructors, there is support for guns on college campuses.

17

The writer uses statistics to support this claim.

18

The writer underscores her point that guns on campus are a
big problem and cites a study to support this claim.

15

In each of these states, carrying handguns on campus
was illegal at the time of the shooting, although a bill was
introduced in Arkansas earlier this year to allow students
to carry guns.
Grade Inflation

16

17

18 We know that some students will carry guns whether it
is legal or not. One study found that close to five percent
of undergraduates had a gun on campus and that almost
two percent had been threatened with a firearm while at
school.
...

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Answer Keys and Explanations
19 Who would want to give a student a low grade and then
get shot for it?

19

The writer asks a rhetorical question to support her argument
that guns on campus could motivate instructors to give
undeserved high grades.

20

Many majors are highly competitive and require certain
GPAs for admission. Students on scholarships and other
forms of financial aid must maintain high grades to keep
their funding. It’s no surprise that some students might
resort to any means necessary to keep up their GPAs.

20

The writer provides reasons why some students are desperate
to maintain good grades, bolstering her claim that students
can become violent if they receive disappointing grades.

21

An international student once cried in my office and
begged me to change his F to an A, as without it, his
country would no longer pay for him to be in the U.S. I
didn’t. He harassed me by posting threatening messages
on Facebook.

21

Citing another example from her past, the writer describes
what a student who was dependent on good grades did to
her. She is again showing that her concern is well-founded
and arousing the reader’s sympathy by relating a personal
experience.

22

So, the question is, will we soon see a new sort of grade
inflation, with students earning a 4.0 GPA with their
firepower rather than brain power? And if so, what sort of
future citizenry will we be building on our campuses?

22

The writer concludes her argument with two rhetorical
questions. She also chooses words that create strong images
(“students earning a 4.0 GPA with their firepower rather than
brain power” and “what sort of future citizenry will we be
building on our campuses”).

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Answer Keys and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Jessica Smartt Gullion.

High-Scoring Essay
The right to bear arms is highly contested in the United States. Rather than entering the national fray, Jessica Smartt Gullion
focuses on only the right of college students to carry guns on campus. To persuade readers that college students should
not be allowed to carry guns, she uses examples from her experience as a college professor to demonstrate the connection
between grades and violence directed at the professors who assign those grades. Examples of violent incidents at other
universities show that her experience is not unique. She brings the examples to life with words that evoke emotion, revealing
the stress and fear that classroom violence creates. Gullion concludes by posing rhetorical questions that ask readers to
consider the effect of guns in the college classroom.
Gullion presents the issue in a single clear sentence. At first, the claim seems extreme—professors might be killed for giving
students poor grades for poor performance. She provides some background information, explaining the “campus carry” bill
that would permit students at public universities in Texas to carry guns on campus. To balance the article’s viewpoint, the
writer briefly explains the opposing view that students should be armed to protect themselves. The article then circles back,
bringing the information together by reminding readers that her concern is that professors who give poor grades for poor
performance put themselves in danger.
To ward off readers’ first impression that her concern is unrealistic, she admits that it may seem farfetched. However, she
states that students have tried to intimidate her into giving better grades a number of times in the five years that she has
been a college professor. In the next section, she uses emotional words that bring a threatening situation to life.
By simply placing the words “threats” and “campus” together, the “Threats on campus” heading brings an immediate sense of
danger to a location where readers expect to feel safe. Gullion recounts a story of a violent event in her classroom. Emotional
words such as “screamed” and “body shook with rage” help readers feel the shock and fear the exchange generated. The writer
points out that the student’s reaction was caused by getting a decent grade on an unimportant assignment. Without actually
saying it, Gullion has made readers wonder what could have happened if the grade had been lower, if the assignment were
more important, or if the student had been armed. The confrontation in the classroom didn’t end there. The tale of the
muscle-bound man watching her silently for three hours increased the “creepiness” rating of the incident and demonstrated
some long-term effects. Even without a “campus carry” law, other students worried about the possibility of a shooting. Gullion
describes how she cringed when the student turned in assignments after that.
Reinforcing the danger by supporting her personal experience with facts, Gullion identifies three separate incidents in which
students shot their teachers. She makes the possibility of being shot for giving bad grades to students seem like it is not
farfetched at all.
Sometimes, Gullion reasons, more is at stake for a student than grades. Poor grades can cause a student to be rejected for
admission to a particular field of study, lose a scholarship, or lose the opportunity to study in the United States. Any of these
results could change a student’s life forever.
The rhetorical questions in the conclusion ask readers what they think about “campus carry” laws after the information she
presented. Using the words “firepower” and “brain power” lays out the two options side by side. Firepower is the physical,
violent option. Brain power is the smart, nonviolent option. She clearly wants readers to choose brain power by voting
against any law that would allow students to carry guns on campus. If readers don’t choose brain power, Gullion fears for the
result.

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Answer Keys and Explanations
Low-Scoring Essay
The Texas legislature thinks it would be safer if people carried guns everywhere they go, including college classes. Jessica
Smartt Gullion disagrees. She has been a college professor for five years. In five years, she has been threatened by students a
number of times. She’s afraid that if students can carry guns, she might be shot.
Jessica Gullion thinks students might shoot her if she gives them bad grades. She tells stories about two times that she was
threatened. One of the students brought a stalker to class with her just to threaten the teacher after getting a bad grade.
The stalker might have shot the teacher if guns were allowed. Later, she talks about another stalker who threatened her on
Facebook before he was forced to leave the country because his grades were bad.
The writer gives some statistics that show that five percent of college students already carry guns on college campuses.
Making it legal, would mean that even more students would carry guns. Although the writer worries about being shot by a
student on purpose, she could also worry about being shot accidentally if students try to shoot each other in the classroom.
At the end of the article, the writer asks if teachers will give better grades to students who are armed. She thinks students
who get good grades by threatening teachers will make worse citizens than students who are smart and study to get good
grades.

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Computing Your Scores
COMPUTING YOUR SCORES
Now that you’ve completed this practice test, it’s time to compute your scores. Simply follow the instructions on the following pages,
and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation as
possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then you’ll calculate the total score. It sounds a little confusing, but we’ll take
you through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test.
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for
wrong answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page 737. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1.  	 Count the number of correct answers you got on the Section 3: Math Test—No Calculator and the Section 4: Math Test—
No Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2.  	 Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—No Calculator.
3.  	 Use the Raw Score Conversion Table 1: Section and Test Scores on page 737 and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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Computing Your Scores
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test that focus on linear equations and inequalities.

• Add up your total correct answers from these sections:
•
•

ºº Math Test—No Calculator: Questions 1–4, 9, 18–20
ºº Math Test—Calculator: Questions 5, 10, 11, 14–17, 30, 34, 36–38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
the interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Question 7
ºº Math Test—Calculator: Questions 1–3, 7, 8, 19–22, 25, 27, 28, 31, 33
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability
to progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations,
and interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 7, 10, 12–14
ºº Math Test—Calculator: Questions 9, 10, 14, 26, 35, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Passport to Advanced Math subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 1, 4, 5, 7, 8, 11, 13, 15, 17, 18, 20, 21, 23, 24, 28, 30–33, 35, 36, 39, 40, 43, 44

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 2, 3, 6, 9, 10, 12, 16, 19, 21, 26, 27, 29, 36–39, 41, 42

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Standard English Conventions
subscore.

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Computing Your Scores
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 5, 9, 18, 22, 38, 42, 51, 52
ºº Writing and Language Test: Questions 6, 8, 14, 17, 33, 34, 43
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts

• Add up your total correct answers from Sections 1 and 2:
•
•

ºº Reading Test: Questions 7, 11, 14, 21, 27, 29, 30, 34, 41, 47, 50
ºº Writing and Language Test: Questions 4, 11, 15, 25, 30, 32, 40
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 738 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 12–32
ºº Writing and Language Test: Questions 3, 4, 11, 15, 22, 35
ºº Math Test—No Calculator: None
ºº Math Test—Calculator: Questions 3, 6–8, 19, 27–29
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 739 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these questions:

•
•

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ºº Reading Test: Questions 1–11, 33–42
ºº Writing and Language Test: Questions 19, 22, 25, 29
ºº Math Test—No Calculator: Questions 7, 12
ºº Math Test—Calculator: Questions 5, 11, 25, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 739 to determine your Analysis in Science cross-test
score.

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Computing Your Scores

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

TOTAL SAT® SCORE
(400–1600)

Peterson's SAT® Prep Guide 2017

  737

Computing Your Scores

  738

www.petersons.com

Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

2

1

1

2

2

5

2

2

3

2

2

3

3

6

3

3

4

3

2

4

4

7

4

4

5

4

3

5

5

8

5

5

6

5

4

6

6

9

6

6

7

6

5

6

7

10

6

7

8

6

6

7

8

11

7

8

9

7

6

8

8

11

8

8

10

7

7

8

9

12

8

9

11

8

7

9

10

12

9

10

12

8

8

9

10

13

9

10

13

9

8

9

11

13

10

11

14

9

9

10

12

14

11

12

15

10

10

10

13

14

12

13

16

10

10

11

14

15

13

14

17

11

11

12

15

14

15

18

11

12

13

15

15

19

12

13

15

20

12

15

21

13

22

14

23

14

24

15

Computing Your Scores
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

1

10

11

19

29

27

2

11

12

20

30

27

3

12

13

21

30

28

4

14

14

22

31

29

5

15

15

23

32

30

6

16

16

24

32

30

7

17

17

25

33

31

8

18

18

26

34

32

9

20

19

27

35

33

10

21

20

28

35

33

11

22

20

29

36

34

12

23

21

30

37

35

13

24

22

31

38

36

14

25

23

32

38

37

15

26

24

33

39

38

16

27

24

34

40

39

17

28

25

35

40

40

Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

Peterson's SAT® Prep Guide 2017

  739

Computing Your Scores
Conversion Equation 3: Cross-Test Scores

ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

RAW SCORE

ANALYSIS IN SCIENCE
QUESTIONS

Reading Test

12–32

1–11, 33–42

Writing and
Language Test

3, 4, 11, 15, 22, 35

19, 22, 25, 29

Math Test—No
Calculator

None

7, 12

Math
Test—Calculator

3, 6–8, 19, 27–29

5, 11, 25, 38

TOTAL

  740

www.petersons.com

ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (10–40)

RAW SCORE

Practice Test 3—Answer Sheet
Section 1: Reading Test
1.

12.

23.

33.

43.

2.

13.

24.

34.

44.

3.

14.

25.

35.

45.

4.

15.

26.

36.

46.

5.

16.

27.

37.

47.

6.

17.

28.

38.

48.

7.

18.

29.

39.

49.

8.

19.

30.

40.

50.

9.

20.

31.

41.

51.

10.

21.

32.

42.

52.

11.

22.

Section 2: Writing and Language Test
1.

10.

19.

28.

37.

2.

11.

20.

29.

38.

3.

12.

21.

30.

39.

4.

13.

22.

31.

40.

5.

14.

23.

32.

41.

6.

15.

24.

33.

42.

7.

16.

25.

34.

43.

8.

17.

26.

35.

44.

9.

18.

27.

36.

Section 3: Math Test—No Calculator
1.

4.

7.

10.

13.

2.

5.

8.

11.

14.

3.

6.

9.

12.

15.

Peterson's SAT® Prep Guide 2017

  741

Practice Test 3—Answer Sheet
Section 3: Math Test—No Calculator
16.

17.

18.

19.

20.

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/
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/
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0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

Section 4: Math Test—Calculator
1.

7.

13.

19.

25.

2.

8.

14.

20.

26.

3.

9.

15.

21.

27.

4.

10.

16.

22.

28.

5.

11.

17.

23.

29.

6.

12.

18.

24.

30.

31.

32.
.

/
.

/
.

.

0

0

0

1

1

2

2

3

.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

7
8

7
8

7
8

9

9

9

34.
.

/
.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

6

7
8

7
8

7
8

7
8

9

9

9

9

36.

  742

33.
/
.

.

/
.

.

.

/
.

/
.

.

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

9

37.

38.

.

/
.

/
.

.

.

/
.

/
.

.

.

/
.

/
.

.

0

0

0

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

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/
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Practice Test 3—Answer Sheet
Section 5: Essay
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Practice Test 3—Answer Sheet

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  744

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Practice Test 3—Answer Sheet

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Peterson's SAT® Prep Guide 2017

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Practice Test 3—Answer Sheet

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  746

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Practice Test 3
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

Questions 1–11 are based on the following passage.
The U.S. Geological Survey (USGS) is a government agency whose
goal is to provide reliable scientific information about the Earth,
including minimizing loss from natural disasters. This excerpt is
from the organization’s website. For the full passage, please visit
http://earthquake.usgs.gov/learn.
Earthquakes, Megaquakes, and the Movies

Line
5

10

15

20

25

30

Throughout the history of Hollywood, disaster films
have been sure-fire winners for moviemakers. … With
amazing special effects, it’s easy to get caught up in the
fantasy disaster epic. What makes a great science fantasy
film often bears no relation to real facts or the hazards
people truly face.
The U.S. Geological Survey is the lead federal
agency responsible for researching, monitoring and
forecasting geologic hazards such as earthquakes,
volcanoes and landslides. . . . Let’s start with some science-based information on earthquakes.
Earthquakes are naturally occurring events
outside the powers of humans to create or stop. An
earthquake is caused by a sudden slip on a fault, much
like what happens when you snap your fingers. Before
the snap, you push your fingers together and sideways.
Because you are pushing them together, friction keeps
them from slipping. When you apply enough stress to
overcome this friction, your fingers move suddenly,
releasing energy. The same “stick-slip” process goes on
in the earth. Stresses in the Earth’s outer layer push the
sides of the fault together. The friction across the surface
of the fault holds the rocks together so they do not slip
immediately when pushed sideways. Eventually enough
stress builds up and the rocks slip suddenly, releasing
energy in waves that travel through the rock to cause
the shaking that we feel during an earthquake.
Earthquakes typically originate several to tens
of miles below the surface of the Earth. It takes
decades to centuries to build up enough stress to make a
large earthquake, and the fault may be tens to hundreds

35

40

45

50

55

60

65

of miles long. People cannot prevent earthquakes
from happening or stop them once they’ve started—
giant nuclear explosions at shallow depths, like those
in some movies, won’t actually stop an earthquake.
It’s well known that California, the Pacific
Northwest, and Alaska all have frequent earthquakes,
some of which are quite damaging. Some areas of the
country are more at risk than others, but, in fact, 42 of
the 50 states could experience damaging ground
shaking from an earthquake in 50 years (which is the
typical lifetime of a building), and 16 states have a
relatively high likelihood of experiencing damaging
ground shaking.
The two most important variables affecting
earthquake damage are the intensity of ground
shaking and the quality of the engineering of
structures in the region. The level of shaking is
controlled by the proximity of the earthquake source
to the affected region and the types of rocks that
seismic waves pass through en route (particularly
those at or near the ground surface). Generally, the
bigger and closer the earthquake, the stronger the
shaking. But there have been large earthquakes with
very little damage because they caused little shaking
or because the buildings were built to withstand that
shaking. In other cases, moderate earthquakes have
caused significant damage because the shaking was
locally amplified, or because the structures were
poorly engineered.
The idea of a “Mega-Quake”—an earthquake of
magnitude 10 or larger—is very unlikely. Earthquake
magnitude is based in part on the length of faults—
the longer the fault, the larger the earthquake. The
simple truth is that there are no known faults
capable of generating a magnitude 10 or larger
“mega-quake.” . . .
Then there’s this business of California falling
off into the ocean. NOT TRUE! The ocean is not a

CONTINUE
Peterson's SAT® Prep Guide 2017

  747

Practice Test 3
70 great hole into which California can fall, but is itself land

75

80

85

90

1

at a somewhat lower elevation with water above it. It’s
impossible that California will be swept out to sea. Instead,
southwestern California is moving slowly (2 inches per
year) towards Alaska. 15 million years (and many earthquakes) from now, Los Angeles and San Francisco will be
next-door neighbors.
Another popular cinematic and literary device is a
fault that opens during an earthquake to swallow up an
inconvenient character. But the ground moves parallel to
a fault during an earthquake, not away from it. If the fault
could open, there would be no friction. Without friction,
there would be no earthquake. Shallow crevasses can form
during earthquake-induced landslides, lateral spreads, or
other types of ground failures. Faults, however, do not
gape open during an earthquake.
So when you see the next big disaster film, rest
assured that movies are just entertainment. Enjoy them!
And then go learn about the real-world science behind
disasters, and if you live in an area where hazards exist,
take the suggested steps to protect you and your family.

B.

  748

4

5

Which of the following best describes the author’s purpose
in writing this article?
A.

2

3

To counter the myths about earthquakes driven by
fictional films
To explain to people the causes and effects of
earthquakes

C.

To show how Hollywood distorts science

D.

To give people advice about what to do if an
earthquake strikes

According to the passage, earthquakes are mainly caused
by
A.

the existence of faults in the Earth’s crust.

B.

stresses in the Earth’s crust that cause a fault to slip.

C.

two faults in the Earth’s crust pressing against each
other.

D.

the quality of the engineering of structures in the
region.

www.petersons.com

6

Who is the target audience of the article?
A.

The general public

B.

Scientists

C.

Filmmakers

D.

Science teachers

How does the article counter the claim that in the future part
of California may fall off into the ocean?
A.

It states that it would be a disaster.

B.

It states that sea level rise will prevent it.

C.

It explains the similarity between California and
Alaska.

D.

It explains how the ocean is just land covered by
water.

Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 69–71 (“The ocean . . . above it.”)

B.

Lines 71–72 (“It’s impossible . . . out to sea.”)

C.

Lines 72–74 (“Instead, southwestern . . . towards
Alaska.”)

D.

Lines 74–76 (“15 million years . . . neighbors.”)

As used in line 25, “stress” most nearly means
A.

anxiety.

B.

weight.

C.

pressure.

D.

emphasis

Practice Test 3
7

8

9

In 1989, an earthquake caused extensive damage to San
Francisco, California. Based only on information in the article,
this most likely occurred because

10 How does the use of the phrase “inconvenient character”
(line 79) affect the tone of the passage?
A.

It reveals a negative attitude about unscientific data.

A.

The earthquake source was very near the affected
region and the buildings were poorly constructed.

B.

It illustrates a mocking tone toward how the
storylines are written.

B.

San Francisco has had earthquakes many times
before, and they were all destructive.

C.

It reveals a scholarly attitude about science.

C.

City officials never thought the city would experience
an earthquake, so they were unprepared.

D.

It communicates a warning about inaccurate
scientific information.

D.

The faults were deep and numerous across the
country.

Which choice provides the best evidence for the answer to
the previous question?

11 How does the author refute the idea that an earthquake
could cause the earth to open up and swallow people and
things?
A.

By pointing out that the idea of the Earth opening up
is portrayed in movies

B.

By noting that there are no known faults capable of
producing a “mega-quake”

A.

Lines 13–22 (“An earthquake is . . . the fault together.”)

B.

Lines 28–32 (“Earthquakes typically . . . miles long.”)

C.

Lines 45–48 (“The two most important . . . in the
region.”)

C.

By explaining that the ground moves parallel to a
fault during an earthquake

D.

Lines 79–81 (“But the ground . . . be no friction.”)

D.

By suggesting that subsequent landslides can cause
crevasses to open up

In line 59, “amplified” most nearly means
A.

lifted.

B.

supplemented.

C.

intensified.

D.

made louder.

CONTINUE
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Practice Test 3
Questions 12–22 are based on the following
passages and supplementary material.
After the Constitution was drafted, it had to be ratified by at least
nine of the thirteen states. The following two passages illustrate the
debate over ratification.
Passage 1 is from Patrick Henry’s speech, made as governor of Virginia
on June 5, 1778, at the state’s convention to ratify the constitution.
Passage 2 is from an essay written by James Madison, which first
appeared in a New York newspaper on June 6, 1788, and later became
part of what is now known as the Federalist Papers.

of our rulers being good or bad? Show me that age and
country where the rights and liberties of the people were
placed on the sole chance of their rulers being good men
35 without a consequent loss of liberty! I say that the loss of
that dearest privilege has ever followed, with absolute
certainty, every such mad attempt.
PASSAGE 2

40

PASSAGE 1

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If you make the citizens of this country agree to
become the subjects of one great consolidated empire
of America, your government will not have sufficient
energy to keep them together. Such a government is
incompatible with the genius of republicanism. There
will be no checks, no real balances, in this government.
What can avail your specious, imaginary balances, your
rope-dancing, chain-rattling ridiculous ideal checks and
contrivances? But, sir, “we are not feared by foreigners;
we do not make nations tremble.” Would this constitute
happiness or secure liberty? I trust, sir, our political hemisphere will ever direct their operations to the security of
those objects.
This Constitution is said to have beautiful features;
but when I come to examine these features, sir, they
appear to me horribly frightful. Among other deformities,
it has an awful squinting; it squints toward monarchy,
and does not this raise indignation in the breast of every
true American? Your president may easily become king.
Your Senate is so imperfectly constructed that your
dearest rights may be sacrificed to what may be a small
minority; and a very small minority may continue for ever
unchangeably this government, altho horridly defective.
Where are your checks in this government? Your strongholds will be in the hands of your enemies. It is on a supposition that your American governors shall be honest
that all the good qualities of this government are founded;
but its defective and imperfect construction puts it in their
power to perpetrate the worst of mischiefs should they
be bad men; and, sir, would not all the world, blame our
distracted folly in resting our rights upon the contingency

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In order to lay a due foundation for that separate and
distinct exercise of the different powers of government,
which to a certain extent is admitted on all hands to be
essential to the preservation of liberty; it is evident that
each department should have a will of its own; and consequently should be so constituted that the members
of each should have as little agency as possible in the
appointment of the members of the others …. It is equally
evident that the members of each department should be
as little dependent as possible on those of the others for
the emoluments annexed to their offices. Were the executive magistrate, or the judges, not independent of the
legislature in this particular, their independence in every
other would be merely nominal. But the great security
against a gradual concentration of the several powers
in the same department, consists in giving to those who
administer each department the necessary constitutional
means and personal motives to resist encroachments of
the others. The provision for defense must in this, as in
all other cases, be made commensurate to the danger of
attack. Ambition must be made to counteract ambition.
The interest of the man must be connected with the
constitutional rights of the place. It may be a reflection
on human nature, that such devices should be necessary
to control the abuses of government. But what is government itself, but the greatest of all reflections on human
nature? If men were angels, no government would be
necessary. If angels were to govern men, neither external
nor internal controls on government would be necessary.
In framing a government which is to be administered by
men over men, the great difficulty lies in this: you must
first enable the government to control the governed; and
in the next place oblige it to control itself. A dependence
on the people is, no doubt, the primary control on the
government; but experience has taught mankind the
necessity of auxiliary precautions.

Practice Test 3
12 Which of the following best represents the differences in
point of view of the authors of the two passages?
A.

Henry was concerned about the balance of power,
and Madison was concerned about concentration of
wealth.

B.

Henry worried about too much power in the hands of
the government, and Madison worried about too
much power in any one branch of government.

C.

Henry was focused on states’ rights, and Madison was
focused on adding the Bill of Rights to the
Constitution.

D.

14 Examine the illustration that shows Patrick Henry delivering
his most famous speech, the one in which he declared,
“Give me liberty or give me death!” Choose the option that
best explains how the artist’s portrayal applies to Henry’s
speech about the Constitution.
A.

The artist shows Henry as an important man with a
message, surrounded by many people who react
strongly his speech. Henry delivers his speech to the
state Assembly as an important figure—governor of
Virginia.

B.

The artist shows Henry as a calm, persuasive speaker,
using logic and reasoning to persuade his listeners.
Henry uses order and reasoning in his speech about
the Constitution. He asks his listeners logical
questions to persuade them that he is right.

C.

The artist shows Henry standing on his feet making
dramatic gestures and speaking with passion. In the
speech about the Constitution, Henry uses dramatic
phrases and figures of speech to try to persuade his
listeners.

D.

The artist shows Henry as an extremist so carried
away by his own emotions that people think he’s a
madman. This view contrasts sharply with Henry’s
speech, in which he slowly builds his argument,
appealing to the listener’s sense of patriotism.

Henry was afraid of a return to monarchy, and
Madison was afraid of government corruption.

13 Which represents the best summary of Patrick Henry’s objection to the drafted Constitution?
A.

It over-emphasizes the need for checks and balances.

B.

It leaves too much power in the hands of the people.

C.

It does not centralize power enough.

D.

It makes government dependent on people who are
flawed.

CONTINUE
Peterson's SAT® Prep Guide 2017

  751

Practice Test 3
15 What was Madison’s strongest counter-argument to those
who were concerned about a strong central government?
A.

Government must reflect human nature.

A.

display their power to Americans.

B.

People are drastically flawed and can never be
trusted.

B.

intimidate other countries.

C.

secure happiness and liberty.

C.

People would have no influence over their
government.

D.

build strong international relationships.

D.

So long as the powers are separated, power will not
be concentrated.

16 Which choice provides the best evidence for the answer to
the previous question?

19 Based on the information in this passage, what kind of government does Henry think is best?
A.

Monarch

B.

Republic

A.

Lines 51–56 (“But the great . . . of the others.”)

C.

Autocracy

B.

Lines 62–64 (“But what is . . . nature?”)

D.

Plutocracy

C.

Lines 64–65 (“If men were . . . would be necessary.”)

D.

Lines 70–73 (“A dependence on . . . auxiliary
precautions.”)

17 What do these two statements show about how their authors
viewed human nature?
Henry, lines 31–35: “Show me that age and country where
the rights and liberties of the people were placed on the sole
chance of their rulers being good men without a consequent
loss of liberty!
Madison, lines 65–66: “If angels were to govern men, neither external nor internal controls on government would
be necessary.”
A.

Henry and Madison both believed that people are
too flawed to be trusted with complete control.

B.

Henry and Madison both believed rulers do not care
about the rights and liberties of the people they
govern.

C.

Henry didn’t trust ordinary people to be rulers, and
Madison believed all people could be trusted to
wield complete control.

D.

  752

18 In lines 9–10, Henry suggests that he believes the framers
of the Constitution felt a need to

Henry believed that government is unnecessary for a
free people, and Madison believed that government
needs to be regulated.

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20 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 2–3 (“one great . . . of America.”)

B.

Line 5 (“the genius . . . republicanism.”)

C.

Line 17 (“it squints . . . monarchcy”)

D.

Line 19 (“Your president . . . become king.”)

21 As it is used in line 42, “department” most nearly means
A.

executive.

B.

territory.

C.

level

D.

branch.

22 As used in line 57, “commensurate” most nearly means
A.

proportional.

B.

provisional.

C.

dependent.

D.

relevant.

Practice Test 3
Questions 23–32 are based on the following
passage and supplementary material.
This article is excerpted from the National Oceanic and Atmospheric
Administration Fisheries website (NOAA). The public agency provides
science news and scientific findings related to the Earth and the Earth’s
atmosphere. This article describes the finding of a tiny, rare shark. For
the full passage, please visit www.nmfs.noaa.gov/stories.
NOAA and Tulane researchers identify second
possible specimen ever found.

Line
5

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25

30

35

A very small and rare species of shark is swimming
its way through scientific literature. But don’t worry, the
chances of this inches-long vertebrate biting through your
swimsuit is extremely slim, because if you ever spotted
one, you’d be the third person to ever do so.
This species common name is the “pocket shark,”
though those in the field of classifying animals refer to it
by its scientific name Mollisquama sp., according to a new
study published in the international journal of taxonomy
Zootaxa. While it is small enough to, yes, fit in your pocket,
it’s dubbed “pocket” because of the distinctive orifice
above the pectoral fin—one of many physiological features scientists hope to better understand.
“The pocket shark we found was only 5 and a half
inches long, and was a recently born male,” said Mark Grace
of NOAA Fisheries’ Pascagoula, Miss., Laboratory, lead
author of the new study, who noted the shark displayed an
unhealed umbilical scar. “Discovering him has us thinking
about where mom and dad may be, and how they got to
the Gulf. The only other known specimen was found very
far away, off Peru, 36 years ago.”
Interestingly, the specimen Grace discovered wasn’t
found in the ocean, per se, but rather in the holdings of
NOAA’s lab in Pascagoula. It was collected in the deep sea
about 190 miles offshore Louisiana during a 2010 mission
by the NOAA Ship Pisces to study sperm whale feeding.
Grace, who was part of that mission after the rare shark
was collected, and upon uncovering the sample at the lab
years later, recruited Tulane University researchers Michael
Doosey and Henry Bart, and NOAA Ocean Service genetics
expert Gavin Naylor, to give the specimen an up-close
examination.
A tissue sample was collected, and by tapping into
the robust specimen collection of Tulane University’s
Biodiversity Research Institute, scientists were able to
place the specimen into the genus Mollisquama. Further
genetic analysis from Naylor indicates that pocket sharks
are closely related to the kitefin and cookie cutter species,
fellow members of the shark family Dalatiidae. Like other

40\ Dalatiidae shark species it is possible that pocket sharks

when hungry may remove an oval plug of flesh from their
prey (various marine mammals, large fishes, and squid).
The specimen is part of the Royal D. Suttkus Fish
Collection at Tulane University’s Biodiversity Research
45 Institute in Belle Chasse, La., and it is hoped that further
study of the specimen will lead to many new discoveries.
Already, the specimen—when compared to the 1979
specimen taxonomic description—is found to have a
series of glands along the abdomen not previously noted.
50 Partners at the Smithsonian National Museum of Natural
History in Washington, D.C., and American Natural History
Museum in New York City have also contributed to the
study of this shark.
“This record of such an unusual and extremely rare
fish
is
exciting, but it’s also an important reminder that we
55
still have much to learn about the species that inhabit our
oceans,” Grace added.
23 What does the article illustrate about how scientific information is gathered?
A.

Multiple scientific institutions are needed to form any
strong scientific conclusion.

B.

Luck plays an essential role whenever scientists work
to gather information.

C.

All scientific research is recorded in journals.

D.

Scientists in different locations often share their
findings.

24 According to the passage, the pocket shark got its name
because of
A.

its small size.

B.

the orifice near its fin.

C.

the way it can be carried in a pocket.

D.

its markings that resemble pockets.

25 The author indicates that the most likely key to determining
how the pocket shark ended up in the Gulf would be
A.

a study of the area around the Gulf.

B.

a comparison between the Gulf and Peru.

C.

a study of sharks native to the Gulf.

D.

the discovery of its parents.

CONTINUE
Peterson's SAT® Prep Guide 2017

  753

Practice Test 3
26 Which choice provides the best evidence for the answer to
the previous question?

28 What information about the “pocket” that is not discussed
in the passage does the diagram provide?

A.

Lines 14–15 (“The pocket . . . born male.”)

A.

The fact that it is a gland

B.

Lines 15–18 (“Mark Grace . . . scar.”)

B.

Its relative position to the pectoral fin

C.

Lines 18–21 (“Discovering . . . ago.”)

C.

That fact that it is used to remove flesh from prey

D.

Lines 22–24 (“Interestingly . . . Pascagoula.”)

D.

Its distinctiveness compared to the shark’s other
features

27 According to the passage, what information was most
important in determining the species of the shark?
A.

The length of the shark

B.

The “pocket” feature that made it unique

C.

Tissue samples to provide genetic information

D.

Its position in the food chain

29 According to the passage, scientists were so excited about
finding a pocket shark because the sharks are
A.

evidence of a new family of sharks.

B.

the only known species that has pockets.

C.

proof that a single breed can live in vastly different
waters.

D.

so unique and so few of them have been found.

Credit: Dr. Mark Grace, Zootaxa 3948 (3): 587–600

  754

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Practice Test 3
Questions 33–42 are based on the following passage.

30 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 20–21 (“The only . . . years ago.”)

B.

Lines 27–28 (“Grace . . . collected”)

C.

Lines 36–39 (“Further genetic . . . Dalatiidae”)

D.

Lines 54–57 (“This record . . . added.”)

31 Based on its use in line 34, “robust” most nearly means

The following passage is excerpted from Mark Twain’s essay, “Fenimore Cooper’s Literary Offenses” (1895). James Fenimore Cooper
(1789–1851) was a popular writer whose works were published in
the first half of the 19th century.

Line
5

A.

typical.

B.

healthy.

C.

varied.

D.

distinguished.

10

32 According to the passage, kitefin sharks
A.

eat oval-shape pieces of flesh.

B.

do not feed on squid.

C.

are identical to pocket sharks.

D.

were discovered after pocket sharks.

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40

[James Fenimore] Cooper’s art has some defects. In
one place in Deerslayer, and in the restricted space of twothirds of a page, Cooper has scored 114 offences against
literary art out of a possible 115.
. . . In his little box of stage properties he kept six
or eight cunning devices. A favorite one was to make a
moccasined person tread in the tracks of the moccasined
enemy, and thus hide his own trail. Cooper wore out
barrels and barrels of moccasins in working that trick.
Another stage-property that he pulled out of his box
pretty frequently was his broken twig. Every time a Cooper
person is in peril, and absolute silence is worth four dollars
a minute, he is sure to step on a dry twig. There may be a
hundred handier things to step on, but . . . Cooper requires
him to turn out and find a dry twig; and if he can’t do it, go
and borrow one. In fact, the Leather Stocking Series ought
to have been called the Broken Twig Series.
If Cooper had any real knowledge of Nature’s ways of
doing things, he had a most delicate art in concealing the
fact. For instance: one of his acute Indian experts, Chingachgook (pronounced Chicago, I think), has lost the trail
of a person he is tracking through the forest. Neither you
nor I could ever have guessed out the way to find it. It was
very different with Chicago. He turned a running stream out
of its course, and there, in the slush in its old bed, were that
person’s moccasin-tracks. The current did not wash them
away, as it would have done in all other like cases—no,
even the eternal laws of Nature have to vacate when Cooper
wants to put up a delicate job of woodcraft on the reader.
. . . In the Deerslayer tale, Cooper has a stream which
is fifty feet wide where it flows out of a lake; it narrows to
twenty as it meanders along for no given reason; and yet
when a stream acts like that it ought to be required to
explain itself. Cooper narrowed it to less than twenty to
accommodate some Indians. He bends a “sapling” to the
form of an arch over this narrow passage, and conceals six
Indians in its foliage. They are “laying” for a settler’s scow or
ark, which is coming up the stream on its way to the lake.
Its rate of progress cannot be more than a mile an hour.
The ark is one hundred and forty feet long; the
dwelling is ninety feet long. The idea of the Indians is to
drop softly and secretly from the arched sapling as the

CONTINUE
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Practice Test 3

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ark creeps along under it. It will take the ark a minute
and a half to pass under. It will take the ninety-foot
dwelling a minute to pass under. Now, then, what did
the six Indians do? It would take you thirty years to
guess. Their chief warily watched the canal-boat as it
squeezed along under him, and when he had got his
calculations fined down to exactly the right shade,
as he judged, he let go and dropped. And missed the
house! He missed the house and landed in the stern of
the scow. It was not much of a fall, yet it knocked him
silly. He lay there unconscious. If the house had been
ninety-seven feet long he would have made the trip.
The fault was Cooper’s, not his. There still remained in
the roost five Indians.
The boat has passed under and is now out of their
reach. Let me explain what the five did—you would not
be able to reason it out for yourself. No. 1 jumped for the
boat, but fell in the water astern of it. Then No. 2 jumped
for the boat, but fell in the water still farther astern of
it. Then No. 3 jumped for the boat and fell a good way
astern of it. Then No. 4 jumped for the boat and fell in
the water away astern. Then even No. 5 made a jump for
the boat—for he was a Cooper Indian. . . .
I may be mistaken, but it does seem to me that
Deerslayer is not a work of art in any sense; it does seem
to me that it is destitute of every detail that goes to the
making of a work of art; in truth, it seems to me that
Deerslayer is just simply a literary delirium tremens.

33 The main purpose of the third paragraph is to

A.

Lines 3–4 (“Cooper has . . . possible 115.”)

B.

Lines 8–9 (“Cooper wore . . . that trick.”)

C.

Line 65 (“for he . . . Cooper Indian”)

D.

Lines 66–67 (“it does seem . . . work of art.”)

36 As used in line 5, “stage properties” most nearly means
A.

literary tricks.

B.

dramatic license.

C.

stage rules.

D.

scripts for a drama.

37 Why did Twain include a pronunciation guide to the Native
American Indian name Chingachgook (lines 20–21)?
A.

To make it easier for people to read his essay

B.

To mock Cooper’s book

C.

To show respect for the Native American tribe

D.

To illustrate that Cooper’s work was about actual
Native American peoples

38 What is Twain’s basic overall criticism of Cooper’s work?

A.

point out flaws in Cooper’s arguments.

A.

Cooper’s books are too complicated.

B.

mock Cooper’s inability to write about nature.

B.

Cooper’s work is too self-serious.

C.

criticize Cooper’s treatment of Native Americans.

C.

Cooper’s plots did not make sense.

D.

explain how Cooper described a stream bed in one
of his stories.

D.

Cooper’s stories are boring.

34 Which of the following words best describes the tone of
Twain’s critique?

  756

35 Which choice provides the best evidence for the answer
to the previous question?

39 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 3–4 (“Cooper has . . . possible 115.”)

A.

Exhausted

B.

Lines 34–35 (“Cooper narrowed . . . some Indians.”)

B.

Scholarly

C.

Lines 58–59 (“Let me . . . for yourself.”)

C.

Cheery

D.

Lines 64–65 (“Then even . . . Cooper Indian.”)

D.

Humorous

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Practice Test 3
Questions 43–52 are based on the following passage.

40 According to Twain’s criticism in the passage, how did
Cooper characterize Native Americans?
A.

They were athletic and smart.

B.

They were cunning and dangerous.

C.

They were sneaky and inept.

D.

They were gentle and respectful.

41 In line 35, Twain most likely puts “sapling” in quotation
marks to emphasize that

Pulitzer prize-winning writer Willa Cather worked as a reporter and
also wrote several novels and short stories. This excerpt is from one
of her more popular short stories, written in 1905.
Paul’s Case: A Study in Temperament

Line
5

A.

the word is not generally used anymore.

B.

Cooper uses the word excessively in his works.

C.

the description of the tree does not sound like a
sapling.

D.

10

sapling is a Latin word used to describe certain
kinds of trees.

42 As used in line 68, “destitute” most nearly means
A.

impoverished.

B.

full.

C.

void.

D.

capable.

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25

30

35

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It was Paul’s afternoon to appear before the faculty
of the Pittsburgh High School to account for his various
misdemeanors. He had been suspended a week ago,
and his father had called at the Principal’s office and
confessed his perplexity about his son. Paul entered
the faculty room suave and smiling. His clothes were
a trifle outgrown, and the tan velvet on the collar of
his open overcoat was frayed and worn; but for all that
there was something of the dandy in him, and he wore
an opal pin in his neatly knotted black four-in-hand, and
a red carnation in his buttonhole. This latter adornment
the faculty somehow felt was not properly significant
of the contrite spirit befitting a boy under the ban of
suspension.
Paul was tall for his age and very thin, with high,
cramped shoulders and a narrow chest. His eyes were
remarkable for a certain hysterical brilliancy, and he continually used them in a conscious, theatrical sort of way,
peculiarly offensive in a boy. The pupils were abnormally
large, as though he was addicted to belladonna, but
there was a glassy glitter about them which that drug
does not produce.
When questioned by the Principal as to why he was
there Paul stated, politely enough, that he wanted to
come back to school. This was a lie, but Paul was quite
accustomed to lying; found it, indeed, indispensable for
overcoming friction. His teachers were asked to state
their respective charges against him, which they did with
such a rancor and aggrievedness as evinced that this
was not a usual case. Disorder and impertinence were
among the offenses named, yet each of his instructors
felt that it was scarcely possible to put into words the
cause of the trouble, which lay in a sort of hysterically
defiant manner of the boy’s; in the contempt which they
all knew he felt for them, and which he seemingly made
not the least effort to conceal. Once, when he had been
making a synopsis of a paragraph at the blackboard, his
English teacher had stepped to his side and attempted
to guide his hand. Paul had started back with a shudder
and thrust his hands violently behind him. The astonished woman could scarcely have been more hurt and
embarrassed had he struck at her. The insult was so

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Practice Test 3

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involuntary and definitely personal as to be unforgettable.
In one way and another he had made all of his teachers,
men and women alike, conscious of the same feeling of
physical aversion. In one class he habitually sat with his
hand shading his eyes; in another he always looked out
the window during the recitation; in another he made
a running commentary on the lecture, with humorous
intention.
His teachers felt this afternoon that his whole attitude
was symbolized by his shrug and his flippantly red carnation flower, and they fell upon him without mercy, his
English teacher leading the pack. He stood through it
smiling, his pale lips parted over his white teeth. (His lips
were constantly twitching, and he had a habit of raising
his eyebrows that was contemptuous and irritating to the
last degree.) Older boys than Paul had broken down and
shed tears under that baptism of fire, but his set smile
did not once desert him, and his only sign of discomfort
was the nervous trembling of the fingers that toyed with
the buttons of his overcoat, and an occasional jerking of
the other hand that held his hat. Paul was always smiling,
always glancing about him, seeming to feel that people
might be watching him and trying to detect something.
This conscious expression, since it was as far as possible
from boyish mirthfulness, was usually attributed to insolence or “smartness.”

43 Based on the passage, what is the best way to describe the
story?

A.

To show respect for the faculty

B.

To show remorse

C.

To make himself appear wealthy

D.

To defy the faculty

46 The reader can infer from the passage that the feelings of
Paul’s teachers toward him may be described as mostly
A.

frustration and anger.

B.

sadness and confusion.

C.

indifference and coldness.

D.

hope and tenderness.

47 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 3–5 (“He had been . . . about his son.”)

B.

Lines 11–14 (“This latter . . . ban of suspension.”)

C.

Lines 27–30 (“His teachers . . . not a usual case.”)

D.

Lines 44–46 (“In one way . . . physical aversion.”)

48 According to the author, Paul’s English teacher

A.

It’s a character study.

A.

had experience dealing with emotional students.

B.

It’s an account of a real-life character.

B.

took Paul’s dislike of being touched personally.

C.

It’s a psychological story with a complicated plot.

C.

was too impatient to allow Paul to write on his own.

D.

It’s a story that emphasizes the setting.

D.

had to endure hearing Paul make comments on her
lecture.

44 What was the reason that Paul was asked to go to the principal’s office?

  758

45 Why did Paul wear a red carnation?

49 How does Cather show a connection between Paul’s feeling
and his actions?

A.

To explain to the teachers why he wanted to return to
school

A.

B.

To explain to the faculty why he had been
misbehaving

She describes how subtle signals reflect Paul’s mood
or disposition.

B.

C.

To explain to the principal why he was late for class

She describes his reactions compared to how others
would react in similar circumstances.

D.

To explain to his parents why he had been
suspended

C.

She gives details about his physical appearance and
that of the teachers.

D.

She provides details about his behavior and the way
it is interpreted by others.

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Practice Test 3
50 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 54–55 (“He stood . . . white teeth.”)

B.

Lines 55–58 (“His lips were . . . last degree.”)

C.

Lines 58–63 (“Older boys . . . his hat.”)

D.

Lines 66–68 (“This conscious . . . or smartness.”)

52 As in line 9, “dandy” most nearly means someone who
A.

is first-rate in his class.

B.

dresses with elegance and care.

C.

is carefree.

D.

is brilliant.

51 Based on the passage, which meaning of the word “temperament” is used in the title “A Study in Temperament”?
A.

Complexion

B.

Adjustment

C.

Mood

D.

Personality

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

Peterson's SAT® Prep Guide 2017

  759

Practice Test 3
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you will
need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you to
consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).
Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.
After reading each passage, select the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following passage.
Elizabeth Blackwell, the Doctor
On January 23, 1849, in the town of Geneva, New York,

1

Elizabeth Blackwell stepped onto the altar of the Presbyterian
church and received her medical degree from the president of

The writer is considering deleting the underlined
sentence. Should the writer do this?
A.

Yes, because the historical importance of this
event is irrelevant.

B.

Yes, because Blackwell has already been
introduced.

C.

No, because it establishes the importance of
Blackwell’s accomplishment.

D.

No, because it tells us what Blackwell did to
become famous.

A.

NO CHANGE

B.

defied

C.

incited

D.

met

Geneva Medical College. 1 In doing so, she took her place
in history. Blackwell had 2 denounced the expectations of
most of her teachers and classmates to become the country’s
first female doctor.

2

CONTINUE
Peterson's SAT® Prep Guide 2017

  761

Practice Test 3
As a young woman, Blackwell had worked as a school teacher,

3

but she found herself unsatisfied. Once she realized that her
dream was to be a doctor, she faced tremendous obstacles.
There had never before been a female physician in America.
At the time, educating a boy was considered 3 far more
important than a girl. Blackwell’s education did not prepare
her for the challenges of medical school, and she had to work

A.

NO CHANGE

B.

far more important than it was to a girl.

C.

far more important than educating a girl.

D.

far more important than opportunities for girls.

A.

NO CHANGE

B.

A physician’s household, to make up for the gaps in
her education, became her home for the next
several years.

C.

Her home for the next several years, to make up for
the gaps in her education, became a physician’s
household.

D.

To make up for the gaps in her education, she
arranged to live in the household of a physician for
the next several years.

4

hard just to catch up. 4 To make up for the gaps in her
education, the household of a physician became her home for
the next several years. There, she had access to educational
resources and received some medical training.
5 As she prepared to apply to medical school, Blackwell
sought advice from physicians in New York and Philadelphia.
She found that they 6 doubted she would be admitted to
medical school; at least one advisor went so far as to suggest
that she might disguise herself as a man in order to gain
admittance. 7 Their advisors were not far from wrong

5

in their prediction. Blackwell applied to well over a dozen
medical colleges, but she received admission to only one—
Geneva Medical College.

Which choice provides the most logical introduction to
the sentence?
A.

NO CHANGE

B.

After finishing medical school,

C.

While attending university,

D.

Before she applied to be a psychologist.

A.

NO CHANGE

B.

debated

C.

insisted

D.

supposed

A.

NO CHANGE

B.

Her

C.

His

D.

Your

6

7

  762

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Practice Test 3
Gaining admission to the college 8 has become the first in

8

a long line of obstacles for Blackwell. She discovered that her

A.

NO CHANGE

B.

becomes

C.

became

D.

will become

A.

NO CHANGE

Steadily, and with perseverance, Blackwell gained acceptance

B.

students all, of whom, were men had

among the students and faculty. After she completed her

C.

students all of whom, were men had

degree, she continued 10 to face prejudice and biases,

D.

students, all of whom were men, had

unable to establish the private practice she had hoped for.

A.

NO CHANGE

Nevertheless, Blackwell was successful, 11 but when she

B.

to face outright barriers to her career due to
prejudice and biases.

C.

to face a variety of significant barriers to her and
her career.

D.

to face barriers that obstructed her career and
included bias because she was a woman.

fellow 9 students all of whom were men had elected as a
joke to admit her to the medical program and were astonished
when she actually showed up at the college to enroll for
classes. The students were embarrassed by her presence
in lectures on topics—such as human anatomy—that they

9

considered unsuitable for mixed company.

which were real obstacles and challenges against her because
she was a woman, and outright barriers to her career. She was

10

went to study at a hospital in Paris, she was assigned the same
duties as young girls with no education at all.

11 Which choice most effectively maintains support for claims
or points in the text?
A.

NO CHANGE

B.

but she is remembered for having been the first
woman in America to receive a medical degree

C.

and she had a distinguished career as a promoter of
preventative medicine and as a champion of
medical opportunities for women

D.

but she lived an interesting life and had many
opportunities to travel widely and meet new
people

CONTINUE
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  763

Practice Test 3
Questions 12–22 are based on the following
passage and supplementary material.
Rachel Carson, Protector of the Environment
Today, we can hardly imagine a world without websites,
blogs, and articles that express concern for the environment.

12 At this point, the writer is considering adding the following
sentence:
But in 1962, when Rachel Carson’s Silent Spring was published, this was not the case.

12 Carson, a former marine biologist for the Fish and Game
Service, 13 ruffled the feathers of a ton of people who had

Should the writer do this?

a vested interest in maintaining the status quo where the
environment was concerned. Her credibility as a scientist

A.

Yes, because it provides the reader with a date and
historical context.

B.

Yes, because it informs the reader of how old
Carson was when she got published.

C.

No, because it inserts irrelevant information about
an unimportant book.

D.

No, because it divides the paragraph’s focus
between the book and Carson.

A.

NO CHANGE

B.

aggravated a lot of folks

C.

inflamed the outsized egos of those

D.

disturbed many

and her personal courage enabled Carson to withstand the
criticism heaped on her during her lifetime.

13

  764

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Practice Test 3
The 10 most heavily used pesticides active ingredients in 1968 included 5 insecticides and
5 herbicides (percentage total pounds active ingredient applied on 21 selected crops)
16%
Atrazine (H)
Toxaphene (I)

13%

37%

DDT (I)
2, 4-D (H)
Methyl Parathion (I)
Aldrin (I)

11%

Trifluralin (H)
Propachlor (H)
Dinoseb (H)
Chloramben (I)

7%
2%
2%
2%
2%

4%

Other a.i.

4%

Note: H = herbicide, insecticide.
Source: USDA, Economic Research Service using USDA, National Agricultural Statistics Services, and proprietary data.

And what exactly was it that Rachel Carson did that was

14

so 14 disturbing. She pointed out the dangers of 15
pesticides—DDT in particular—to the environment. DDT
was designed to contain insect pests in gardens and on
farmland after World War II. Most people considered it a
“wonder chemical,” 16 and by 1968, they used DDT to cover
approximately 11% of all farmland.

A.

NO CHANGE

B.

disturbing?

C.

disturbing!

D.

disturbing:

A.

NO CHANGE

B.

pesticides—DDT in particular to

C.

pesticides DDT in particular, to

D.

pesticides (DDT) in particular to

15

16 Which choice completes the sentence with accurate data
based on the chart?
A.

NO CHANGE

B.

and in fact, by 1968, DDT accounted for 11% of all
pesticides used.

C.

as it was believed to contain approximately 11% of
all garden pests.

D.

though only about 11% of all farmers and
gardeners actually used it.

CONTINUE
Peterson's SAT® Prep Guide 2017

  765

Practice Test 3
Rachel Carson believed, however, that the pesticides were 17

17

dehydrating the soil and the rivers, and adhering to tree leaves

A.

NO CHANGE

B.

appropriating

C.

transcending

D.

permeating

A.

NO CHANGE

The furor caused by Carson’s writing was mostly felt by

B.

it was

the chemical companies that produced pesticides. Not

C.

the pesticides were

willing to 20 contradict the potential hazards of their

D.

everything was

and branches that were the home for birds and beneficial
insects. She contended that the levels of chemical pesticides
in plants, animals, and humans had already reached alarming
levels. In her view, 18 he was so potent that they were able to
penetrate systems and remain there for years, 19 giving way

18

to possible improvements in general health and well-being.

products, they resisted by seeking to discredit Carson. And
despite her credentials, Carson was discredited for a period
of time. However, in 1970, with the establishment of the

19 Which choice best completes the sentence and remains
consistent with Carson’s argument about pesticides?

Environmental Protection Agency, the nation became more

A.

NO CHANGE

concerned with issues that Carson had raised.

B.

providing a definitive link between cancer and
pesticides.

Since 2001, DDT has been banned for agricultural use

C.

leading to an alarming decrease in local bird
populations.

D.

potentially leading to a breakdown in tissue and
immune systems.

A.

NO CHANGE

B.

acknowledge

C.

propagate

D.

solicit

A.

NO CHANGE

B.

Even though malaria kills 800,000 people every
year, most of them children in Sub-Saharan Africa,
Carson

C.

Coincidentally, malaria kills 800,000 people every
year, most of them children in Sub-Saharan Africa,
Carson

D.

Does malaria kill 800,000 people every year, most of
them children in Sub-Saharan Africa, Carson

worldwide except in small quantities and only as part of a plan
to transition to safer alternatives. The only places in which DDT
is still allowed are those countries in which it is being used to
combat malaria. 21 Since malaria kills more than 800,000

20

people every year, most of them children in Sub-Saharan
Africa, Carson has been blamed for “millions of deaths,” despite
the studies that show that the pesticide can contribute to
cancers, male infertility, miscarriages, developmental delay in
children, and damage to the liver and nervous system.
21

  766

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Practice Test 3
Were it not for those like Rachel Carson, 22 DDT would

22

probably still be seen as “wonder chemicals,” and the only

A.

NO CHANGE

way to combat malaria. Though still controversial, she was a

B.

pesticides with DDT would probably still be seen
as a “wonder chemical,”

C.

DDT would probably still be seen as a “wonder
chemical,”

D.

DDT would probably still be seen as chemicals that
are wondrous.

23 Mexico; Guatemala, Belize, Honduras; and El Salvador.

A.

NO CHANGE

Their rich civilization flourished from the third through the

B.

Mexico, Guatemala, Belize, Honduras, and El
Salvador.

of this society were the Mayan understanding of astronomy,

C.

Mexico, Guatemala, Belize, Honduras; El Salvador.

which was manifest not only in Mayan science but in every

D.

Mexico Guatemala Belize Honduras El Salvador.

A.

NO CHANGE

B.

Among the many notable achievements of this
society are the Mayan understanding of
astronomy,

C.

Among the many notable achievements of this
society will be the Mayan understanding of
astronomy,

D.

Among the many notable achievements of this
society was the Mayan understanding of
astronomy,

scientist of vision and determination who changed the course
of history and brought environmental issues to the world’s
attention.

Questions 23–33 are based on the following passage.
A Mayan Worldview
The ancient Mayans inhabited the area that now consists of

23

ninth centuries. 24 Among the many notable achievements

aspect of the culture.

24

CONTINUE
Peterson's SAT® Prep Guide 2017

  767

Practice Test 3
Ancient Mayans kept meticulous records of 25 the setting

25

Sun, the moving Moon, and the rotation of the planets that

A.

NO CHANGE

were visible to the naked eye. Based on the solar year, they

B.

the setting Sun, the moving Moon, and the rotating
planets

C.

the set sun, the moving moon, and the rotated
planets

D.

the setting Sun, the way the Moon moved, and the
rotation of the planets

A.

NO CHANGE

B.

inept

C.

expected

D.

complicated

created a calendar which they used to keep track of time. So
26 astute were the Mayans’ observations that they could
predict such events as solar and lunar eclipses, and 27 the
movement of the planets.
For the ancient Mayans, astronomy was not just a science; it

26

was a combination of science, religion, and philosophy that
found 28 it’s way into many aspects of their lives, including
architecture. Mayan ceremonial buildings, for example,
were exactly aligned with compass points, so that at the fall
and spring equinoxes, light would flood the interior of the
building. These buildings were designed and built as acts of
worship to the 29 Mayan gods. Science, architecture, and

27 Which choice gives a supporting example that is most
similar to the example already in the sentence?

religion, then, were all intricately and beautifully blended.

A.

NO CHANGE

B.

the migration of birds.

C.

the direction of the winds.

D.

the flow of the tides.

A.

NO CHANGE

B.

its’

C.

its

D.

its’s

28

29 Which choice most effectively combines the two sentences
at the underlined portion?

  768

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A.

Mayan gods: science

B.

Mayan gods; science

C.

Mayan gods, science

D.

Mayan gods, but science

Practice Test 3
Government, too, was 30 inextricably linked with

30

astronomy. The beginning and ending of the reigns of

A.

NO CHANGE

Mayan leaders appear to have been timed to coincide with

B.

bafflingly

astronomical events. Ancient Mayan artwork, carvings and

C.

greedily

murals show royalty wearing 31 symbols: relating to the

D.

embarrassingly

that these gods needed human help to thwart the evil gods

A.

NO CHANGE

who wanted to stop them. Human intervention took the form

B.

symbols, relating to the Sun, Moon, and sky.

of different rituals, including sacrifice. It was considered an

C.

symbols relating to the Sun, Moon, and sky.

honor to die for this cause, and those who were sacrificed

D.

symbols; relating to the Sun, Moon, and sky.

Sun, Moon, and sky. The Mayans believed that the Sun and
Moon were guided across the sky by benevolent gods, and

31

were believed to have gained eternal life.
The planet Venus, which can often be seen by the unaided

32 Which choice provides information that best supports the
focus of this paragraph?

eye, played a large role in Mayan life. The Mayans used the
appearance of Venus in the sky as a means of timing when
they attacked enemies. The night sky, among its other duties,
could then serve as a 32 harvest calendar.
33 In short, the ancient Mayans, in looking to the night sky
for guidance, discovered a natural order around which they
were able to base a rich and textured civilization.

A.

NO CHANGE

B.

reminder of the season

C.

reference point for direction

D.

call to war

A.

NO CHANGE

B.

However,

C.

Moreover,

D.

Incidentally,

33

CONTINUE
Peterson's SAT® Prep Guide 2017

  769

Practice Test 3
Questions 34–44 are based on the following passage.

34

The Real World
Our college employment counseling center recommended
that students have mock interviews before setting out into

A.

NO CHANGE

B.

applying

C.

applied

D.

will apply

A.

NO CHANGE

B.

threw

C.

though

D.

through

A.

NO CHANGE

B.

his

C.

my

D.

their

the world for the real thing. For reasons that I still don’t
understand, I believed that this 34 apply to other people

35

but not to me. Midway 35 thorough my senior year of
college, I sent out resumes to several law firms in the area. I
didn’t consult with anybody about how to begin seeking a job.
My plan was to work at a law firm for a couple of years before
attending law school. I received a couple of responses and was
thrilled to set up 36 our first interview at a prestigious law

36

firm that had offices all over the world. 37

37 Which of the following sentences, if added, would most
effectively conclude this paragraph?
A.

NO CHANGE

B.

I couldn’t imagine enjoying working in this
environment.

C.

I really wish college never ended!

D.

I needed more time to weigh my career options.

A.

NO CHANGE

B.

After happily informing him that I wanted to work
my way up and someday be his boss.

C.

Which is why I happily informed him that I wanted
to work my way up and someday be his boss.

D.

Then I happily informed him that I wanted to work
my way up and someday be his boss.

38

  770

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Practice Test 3
The position for which I was interviewing was a clerical job

39

that, the interviewer made clear from the outset, would
require long hours, late nights, and a great deal of filing and
photocopying. I confidently announced to the interviewer
that I didn’t mind long hours and thankless assignments. 38
And then happily informed him that I wanted to work my way
up and someday be his boss. I figured the surprised look on

A.

NO CHANGE

B.

articulate

C.

conspicuous

D.

incoherent

A.

NO CHANGE

B.

weaknesses’

C.

weaknesses

D.

weakness’

40

his face was because he wasn’t used to seeing young men
as ambitious and 39 enigmatic as I was. I would have kept
going, had he not suggested moving on to another topic.
[1] I’m sorry to say that here I left nothing to the imagination.
[2] I believed that my interviewer would value my stark
honesty when I told him that my greatest 40 weakness’s
included not getting along with other people very well and a

41 For the sake of cohesion, sentence 3 of this paragraph
should be placed

tendency to make more enemies than friends. 41 [3] In the

A.

where it is now.

next phase of the interview, I was asked to list my strengths

B.

before sentence 1.

and weaknesses. [4] The interviewer raised his eyebrows but

C.

before sentence 5.

said nothing, and I was certain that he knew he’d found his

D.

at the beginning of the next paragraph.

along with people to photocopy and file, so I’d hit upon the

A.

NO CHANGE

perfect answer to a tricky question.

B.

I could have cared less

C.

I could of cared less

D.

I couldn’t have cared less

candidate. [5] After all, 42 I could’ve cared less about getting
along with other people and I figured I wouldn’t need to get

42

Peterson's SAT® Prep Guide 2017

  771

Practice Test 3
43 I did not get offered that job, nor the next several for

43 Which of the following would make the most effective
opening sentence for this paragraph?

which I interviewed at other firms. Eventually I paid a 44
deferred trip to the college job counseling office and got a few

A.

After the interview, I waited anxiously to hear back
from the employer.

B.

I never heard back from the employer about the
job.

C.

I met my friends for brunch over the following
weekend.

D.

I got married four years later, after dating for several
years.

A.

NO CHANGE

B.

belated

C.

hastened

D.

disparaged

pointers on my technique. I am happy to say that while I never
did end up going to law school, I have become a high school
guidance counselor who specializes in helping students find
internships in community businesses.

44

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  772

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Practice Test 3
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions
TURN TO SECTION 3 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  773

Practice Test 3
1

2

3

Jared is beginning to track the number of steps he walks
each day. Yesterday he walked 950 steps. He set a goal
of increasing his steps per day by 125, with an eventual
goal of walking at least 3,000 steps per day. Which of the
following functions can be used to determine the number
of steps Jared plans to take d days from yesterday?
A.

f(d) = 3,000 – (950 + 125d)

B.

f(d) = 3,000 – 125d

C.

f(d) = 950 + 125d

D.

f(d) = 950 − 125d

If f(1) = 3, f(3) = –1, g(3) = 1, and g(–1) = 3, what is the value
of f(g(3))?
A.

–3

B.

–1

C.

1

D.

3

The amount of radioactive iodine 131 that remains
in an object after d days is found using the formula
d

y = a(0.5) 8.02 . What does a represent in the formula?

  774

A.

The number of days it takes for the object to lose
half of its radioactive iodine 131

B.

The initial amount of radioactive iodine 131

C.

The amount of radioactive iodine 131 after d days

D.

The amount of radioactive iodine 131 lost each day

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SHOW YOUR WORK HERE

Practice Test 3
4

5

An architect is designing the roof of a house that is to be
symmetric, with two equal sides meeting exactly in the
middle. The house is 30 feet wide. The peak of the roof is
8 feet above the house. If the outside of the roof is separated into two parts, how long is each part from the peak
of the roof to its edge?
A.

15 ft.

B.

17 ft.

C.

23 ft.

D.

31 ft.

SHOW YOUR WORK HERE

y = 2(x – 5)2 – 2
Which equation, where the x-intercepts appear as constants, is equivalent to the equation above?
A.

y = 2x2 – 20x + 48

B.

y = 2(x2 – 10x + 24)

C.

y = 2(x – 4)(x – 6)

D.

y = (2x – 8)(x – 6)

CONTINUE
Peterson's SAT® Prep Guide 2017

  775

Practice Test 3
6

Which of the following graphs represents the equation
3x + y = 4?

4

2

–4

–2

0

2

4

2

4

2

4

2

4

–2

–4

A.

4

2

–4

–2

0

–2

–4

B.

4

2

–4

–2

0

–2

–4

C.

4

2

–4

–2

0

–2

–4

D.

  776

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SHOW YOUR WORK HERE

Practice Test 3
7

8

9

Which of the following is an equation for the line through
the point (2, 3) with a slope of –1?
A.

2x + 3y = –1

B.

3x + 3y = 15

C.

3x + 2y = 10

D.

x + y = –5

SHOW YOUR WORK HERE

A woman can paddle a kayak upstream 10 miles in 2.5
hours, and she can paddle the same distance downstream
in 1.6 hours. Which of the following systems of equations
can be used determine the speed of the current, x, and the
speed at which the woman can kayak in still water, y?
A.

 y + 2.5 x = 0

 y − 1.6 x = 0

B.

 x + y = 10

 x − y = 10

C.

x − y = 4

 x + y = 6.25

D.

10( x − y ) = 2.5

10( x + y ) = 1.6
3

Which of the following is equivalent to
A.

z

B.

z –1

C.

z

D.

−

z

3

z i

z
z

?

2
3

1
5

10 Which of the following is the equation for the graph of
a parabola that has a vertex at (3, –5) and a y-intercept
at 13?
A.

y – 28 = (x – 3)(x + 5)

B.

y = 2(x – 3)2 – 5

C.

y = (x – 3)2 – 13

D.

y = x2 – 6x + 13

CONTINUE
Peterson's SAT® Prep Guide 2017

  777

Practice Test 3
11 The admission cost for a play is $12 for adults and $7 for
children. Which system of equations can be used to determine the number of adults and number of children that
attended if 117 people attended the play and the total
amount collected for admission was $1,079?

12

A.

12 x + 7 y = 117
x + y = 1, 079

B.

12 x + y = 117
x + 7 y = 1, 079

C.

12 x + 7 y = 1, 079
x + y = 117

D.

x + 7 y = 117
12 x + y = 1, 079

4 −i
that can be
3+ i
found by multiplying by the complex conjugate of the
Which of the following is equivalent to

denominator?
A.

1
3

B.

17
11+ 7i

C.

11− 7i
10

D.

13 + i
8

13 What is the solution to the equation –6(t + 1) = 2(1–3t) – 8?

  778

A.

−8

B.

−6

C.

No solution

D.

Infinitely many solutions

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SHOW YOUR WORK HERE

Practice Test 3
14 A small city in Spain grows at an average rate of 1.7%
a year. The population of the city in 1980 was 2,845.
The equation that models the city’s population in 1990
is P = 2,845e(0.017)(10). What does 10 represent in the
equation?

15

A.

The city’s population in 1980

B.

The number of years

C.

The city’s average growth rate

D.

The factor of increase of the city’s population each
year

Assume that p and q are positive and
for n.
A.

p
q −1

B.

p −1
q −1

C.

q +1
p

D.

q −1
p

SHOW YOUR WORK HERE

2 p + 2n
= 2. Solve
qn

CONTINUE
Peterson's SAT® Prep Guide 2017

  779

Practice Test 3
DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
1
7
5.  	 Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
1
1
31
, it will be interpreted as
, not 3 .
If 3 is entered into the grid as
2
2
2
6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

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Decimal
point

0

Answer: 201
Either position is correct.

0
1

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0
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1

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1

2

2

2

2

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3

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4

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4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

  780

www.petersons.com

0

1

.

0

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6

Practice Test 3
16 If

SHOW YOUR WORK HERE

x + 1 − 2 = 3 , what is the value of x?

17 Let b be a real number. For what value of b does the function f(x) = x2 –2bx + (b2 + 2b – 1) have one and only one
x-intercept?

18

3 x 2 − 4 x − 18
21
= 3x − c +
x +3
x +3
What is the value for c that will make the equation above
true?

19

y = 3x +7
4 x − ty = 5
According to the system of equations above, what is the
value of t that makes the system of equations have no
solutions?

20 A spherical scoop of ice cream is placed on top of a hollow
ice cream cone. The scoop and cone have the same radius.
The ice cream melts completely and it fills the cone to the
top. How many times greater is the height of the cone than
the radius of the cone?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

CONTINUE
Peterson's SAT® Prep Guide 2017

  781

Practice Test 3
SECTION 4: MATH TEST—CALCULATOR
55 Minutes—38 Questions
TURN TO SECTION 4 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–30, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 31–38, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 31 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a2 + b2 = c2
Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  783

Practice Test 3
1

2

A certain insect is estimated to travel 1,680 feet per year.
At this rate, about how many months would it take for the
insect to travel 560 feet?
A.

0.75

B.

3

C.

4

D.

5.5

A librarian is tracking the circulation of books at the library.
Out of the books that had been loaned one day, 18 were
renewed, 46 were returned on time, and 11 were returned
late. At this rate, about how many books will be renewed
if the library loans 25,000 books each year?
A.

4,000

B.

6,000

C.

9,000

D.

15,000

3

Smalltown Littletown

Total

Male

175

210

385

Female

195

205

400

Total

370

415

785

Smalltown and Littletown are two towns in Tinytown
County. The table above shows the distribution of population of males and females of the towns. If a person from
the county is selected at random, what is the probability
that the person will be either a male from Littletown or a
female from Smalltown?

  784

A.

39
74

B.

42
83

C.

56
157

D.

81
157

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SHOW YOUR WORK HERE

Practice Test 3
4

5

6

7

A pink dogwood tree has an average growth rate of 0.36
inches per week. Based on the average growth rate, if a
pink dogwood tree was newly planted, what would its
height, in inches, be in 10 years?
A.

43.2 inches

B.

187.2 inches

C.

218 inches

D.

360 inches

SHOW YOUR WORK HERE

Glen earns $10.25 per hour and pays $12.50 per day to
commute to and from work on the bus. He wants to make
sure that he works long enough to earn at least three times
as much as he spends commuting. Which of the following
inequalities best represents this situation?
A.

10.25h ≥ 3(12.50)

B.

3(10.25) ≥ 12.50h

C.

3(10.25h) ≥ 12.50

D.

h ≥ 3(12.50)(10.25)

Nadia spent 7 more hours on math homework last month
than Peter. If they spent a total of 35 hours doing math
homework last month, how many hours did Peter spend
on math homework?
A.

7

B.

14

C.

21

D.

28

If c is 22 percent of e and d is 68 percent of e, what is d – c
in terms of e?
A.

90e

B.

46e

C.

0.9e

D.

0.46e

CONTINUE
Peterson's SAT® Prep Guide 2017

  785

Practice Test 3
8

2 x − 9 y < 12
−3 x + 4 y > 5
Which of the following is a solution to the system of
inequalities shown above?

9

A.

(−4, –4)

B.

(–4, 4)

C.

(4, –4)

D.

(4, 4)

If n = 7, what is 2m(16 – 6n) in terms of m?
A.

−52m

B.

−15m

C.

−14m

D.

32m

10 Tessa wants to raise a total of at least $250 for her favorite
charity. She has already raised $145. Tessa asks for $15 contributions from each person she contacts. Which inequality
best represents this situation?

  786

A.

15x ≥ 250

B.

145(15x) ≥ 250

C.

145 + 15x ≥ 250

D.

145 − 15x ≥ 250

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SHOW YOUR WORK HERE

Practice Test 3
SHOW YOUR WORK HERE

Questions 11 and 12 refer to the
following information.
A class raised money selling t-shirts, and then they began selling
hats. The graph represents the total amount of money in the class
account as the number of hats sold increases.

Amount in Account ($)

600
500
400
300
200
100
0

10

20

30 40 50
Hats Sold

60

70

11 According to the graph, which of the following best approximates the number of hats that must be sold for the class to
have raised a total of $400?
A.

54

B.

58

C.

64

D.

68

12 What does the slope of the line signify?
A.

The amount of money already raised

B.

The amount of money received per hat

C.

The number of hats that are sold

D.

The number of hats that must be sold to meet the
fundraising goal

CONTINUE
Peterson's SAT® Prep Guide 2017

  787

Practice Test 3
13 A survey was conducted to determine whether the voters
in a city of 38,000 would support funding a new park. A
sample of 18 voters randomly selected from the voting
list revealed that 11 voters favored funding the park, 4
voters did not want to fund the park, and 3 voters had no
preference. Which of the following makes it least likely that
a reliable conclusion can be drawn from the data?
A.

The size of the sample population

B.

The size of the city’s population

C.

The number of people with no preference

D.

How the sample population was selected

14 In 2010, a census showed a city had a population of 22,500.
The results of the census also showed that the mean
income of the population was $72,350, and the median
income was $65,580. Which of the following could describe
the difference between the mean income and the median
income of the population?
A.

Most of the income values are between the mean
and median income values.

B.

There are a few income values that are much less
than the other income values.

C.

There are a few income values that are much
greater than the other income values.

D.

The range in income values is greater than the
income value.

15 A group of h neighbors has 1,230 CDs they are selling at a
yard sale. If each neighbor sells on average x CDs per day
for j days of the yard sale, which of the following represents
the total number of CDs that will be left when the yard sale
is over?

  788

A.

1,230 – jhx

B.

1,230 – hx – j

C.

1, 230 −

jx
h

D.

1, 230 +

jx
h

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SHOW YOUR WORK HERE

Practice Test 3
DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
If 3

1
7
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

, it will be interpreted as

31
1
, not 3 .)
2
2

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

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7

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8

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9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

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1

1

1

1

2

2

2

2

2

1

3

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4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

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6

CONTINUE
Peterson's SAT® Prep Guide 2017

  789

Practice Test 3
SHOW YOUR WORK HERE

16 y = –16x2 + 50x + 2
The equation above represents the height y of a ball, in
feet, x seconds after it has been thrown upwards. Which
of the following best describes the meaning of the coefficient 50?
A.

The height of the ball when it is thrown

B.

The height of the ball after x seconds

C.

The initial velocity of the ball when it is thrown

D.

The acceleration of the ball’s upward velocity

Questions 17 and 18 refer to the
following information.
Quinn is moving across the state and needs to rent a moving
truck that will fit her belongings. The table below shows the
mileage rate and daily rental cost for trucks from three different
companies.

Mileage rate, b,
in cents per mile

Rental rate, a, in
dollars per day

Company J

15

19

Company K

10

30

Company L

12

25

The total cost, y, for renting the truck for one day and driving x
miles is found by using the formula y = a + 0.01bx.
17 For which numbers of miles x is the cost of renting from
Company J less than renting from Company K?

18

  790

A.

x < 44

B.

x < 55

C.

x < 220

D.

x < 980

If the relationship between the total cost, y, of renting the
truck from Company L and driving it x miles for one day is
graphed in the xy-plane, what does the slope of the line
represent?
A.

The daily rental cost for the truck

B.

The cost to drive the truck each mile

C.

The total cost for the miles driven

D.

The total cost for renting and driving the truck

www.petersons.com

Practice Test 3
SHOW YOUR WORK HERE

Questions 19 and 20 refer to the
following information.
A sample of the population in two neighborhood towns, Town
A and Town B, was surveyed in order to determine the most
popular types of house styles. The results of the survey are
shown in the table.

House Style
House Style

Town A

Town B

Ranch

75

62

Colonial

25

65

Cape Cod

53

43

Victorian

20

32

19 According to the table above, what is the probability that
a randomly selected house in Town B is a colonial house?
A.

65
202

B.

17
18

C.

31
45

D.

25
62

20 What is the probability that a randomly selected house is
from Town B given that its style is either a Cape Cod or a
Ranch?
A.

105
202

B.

233
375

C.

105
233

D.

7
25

CONTINUE
Peterson's SAT® Prep Guide 2017

  791

Practice Test 3
21

Let a and b be positive real numbers. What is the distance
between the x-coordinates of the points of intersection of
the graphs of f(x) = b2 – (x + a)2 and g(x) = (x + a)2 – b2?
A.

2b

B.

2a

C.

a+b

D.

2(a + b)

22
S

y°
T

y°
x°
P

Q

x°

R

Note: Figure not drawn to scale.

In the figure above, if QP = 11.5, TQ = 15, and QR = 46, what
is the value of SQ?
A.

65

B.

60

C.

49.5

D.

42.5

23
1=

3
4
+
x −4 x –3

Which of the following are the values of x in the equation
above?

  792

A.

7±2 3

B.

7 ± 62

C.

7 ± 86

D.

1, 13

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SHOW YOUR WORK HERE

Practice Test 3
24 A certain type of weather radar, known as a Base Reflectiv-

SHOW YOUR WORK HERE

ity Radar, has a circumference of 572π miles. The central
3π
.
angle of a sector of the circle that the radar makes is
4
What is the area, in square miles, of the sector of the circle?
A.

858π square miles

B.

429 π
square miles
4

C.

61, 347π
square miles
2

D.

81,796π square miles

CONTINUE
Peterson's SAT® Prep Guide 2017

  793

Practice Test 3
25 If w is a negative constant less than 1 and v is a positive
constant greater than 1, which of the following could be
the graph of y = a(x + w)(x + v)?
3
2
1
–8

–7 –6

–5 –4 –3 –2

–1

0

1

2

–1
–2
–3
–4
–5
–6

A.
6
4
2
–10 –8 –6

–4 –2

0

2

4

6

8 10

2

3

4

5

6

1

2

3

4

5

–2
–4
–6
–8

B.

–10
2
1
–4

–3 –2

–1

0

1

–1
–2
–3
–4
–5

C.

4
3
2
1
–5 –4 –3 –2

–1

0
–1
–2

D.

  794

www.petersons.com

–3

SHOW YOUR WORK HERE

Practice Test 3
26

SHOW YOUR WORK HERE

2 x − 5y < 6
x + ay < −3
Which of the following must be true if the system of inequalities has solutions only in quadrants II and III?
A.

a<0

B.

a=0

C.

0 ≤ a ≤ 2.5

D.

a > 2.5

Questions 27 and 28 refer to the
following information.
The graph below shows the results of a study to see how far a
vehicle travels before coming to a complete stop at different
speeds.

Stopping DIstance (m)

140
120
100
80
60
40
20
20

40

60

80 100 120 140

Speed (km/hr)
27 Which equation best models the relationship shown in the
graph between the speed in kilometers per hour, x, and
the stopping distance in meters, y?

B.

1
x
4
y = x – 10

C.

y = 4.82(1.03)x

D.

y = 4.82x1.03

A.

y=

CONTINUE
Peterson's SAT® Prep Guide 2017

  795

Practice Test 3
28 Which of the following best describes the relationship
represented in the graph?
A.

The relationship between the initial speed and the
stopping distance is linear, because the points are
close to a line.

B.

The relationship between the initial speed and the
stopping distance is linear, because the points are
all on a line.

C.

The relationship between the initial speed and the
stopping distance is modeled by exponential
growth, because the slope of the line connecting
any two points increases as the initial speed
increases.

D.

The relationship between the initial speed and the
stopping distance is modeled by exponential
decay, because the slope of the line connecting any
two points increases as the initial speed increases.

29 A recent national poll of adults in the United States found
that 64% favor stricter emissions on power plants. The
margin of error for the poll was ±4% with 95% confidence.
Which of the following statements is a conclusion that can
accurately be drawn from this poll?
A.

The true percentage of people who oppose stricter
emissions of power plants is definitely between
32% and 40%.

B.

The true percentage of people who support stricter
emissions of power plants is definitely between
60% and 68%.

C.

The pollsters are 95% confident that the true
percentage of people who oppose stricter emissions of power plants is between 32% and 40%.

D.

The pollsters are 95% confident that the true
percentage of people who support stricter
emissions of power plants is between 60% and
68%.

30 The equation for the graph of a circle in the xy-plane is
x2 + y2 – 10x + 4y = –20. What are the coordinates of the
center of the circle?

  796

A.

(5, –2)

B.

(–5, 2)

C.

(10, –4)

D.

(–10, 4)

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SHOW YOUR WORK HERE

Practice Test 3
DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 Mark no more than one circle in any column.
4.  	 No question has a negative answer.
5.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
6.  	 Mixed numbers such as 3
		

If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

1
31
, not 3 .
2
2

, it will be interpreted as

7.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

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1

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5

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9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

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3

3

4

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4

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4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

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4

5

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5

5

5

5

7

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9

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9

3

3

3

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7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

CONTINUE
Peterson's SAT® Prep Guide 2017

  797

Practice Test 3
31 A bowling alley charges $4.50 per hour to use a lane. They
also charge $2.50 to rent a pair of bowling shoes. Miguel
and his friend rent a pair of bowling shoes each. The total
cost before taxes is $16.25. How many hours did they bowl?

SHOW YOUR WORK HERE

32 If 4s – 3 < 2 and s is an integer, what is the greatest possible
value of 4s + 5?

33 If 2a – b = 7 and 2a + 2b = 16, what is the value of 3a + 7b?

34 The current population of a certain type of organism is
about 100 million. The population is currently increasing
at an annual rate that will make the population double in
18 years. If this pattern continues, what will the population
be, in millions, 54 years from now?

35 Sally sold pieces of her pottery for x dollars each at an art
show. Paul sold pieces of his pottery for y dollars each at
the same show. Paul sold four pieces of pottery for a total
of $85, and Sally sold five pieces for a total of $40 more
than Paul. How much more, in dollars, did Sally charge for
each piece of her pottery than Paul charged for his? (Ignore
the dollar sign when gridding in your answer.)

36 Carl knitted 4 more scarves this year than last year. If he
knitted 16% more scarves this year than last year, how
many did he knit this year?

37

y = 2x + 5
y = −2( x + 1) 2 + 3

If (x, y) is a solution to the system of equations above, what
is one possible value of y?

38

The average GPA for the girl’s lacrosse team for each year
starting in 2012 and ending in 2016 has been 3.5. What is
the lowest the GPA could be in 2017 so that the average
GPA for all six years is at least 3.47? Round to the nearest
hundredth.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  798

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Practice Test 3
SECTION 5: ESSAY
50 Minutes—1 Essay
DIRECTIONS: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

As you read the passage below, consider how Catherine Anderson uses the following:

• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed.
Adapted from “Michael Graves sought to create joy through superior design” by Catherine Anderson, originally published in
The Conversation on March 25, 2015. Catherine Anderson is Assistant Professor of Interior Architecture and Design at George
Washington University. (This passage was edited for length.)
1

Visit the website of designer Michael Graves, and you’ll be greeted with the words “Humanistic Design = Transformative
Results.” The mantra can double as Graves’ philosophy. For Graves—who passed away at 80 earlier this month—paid no
heed to architectural trends, social movements or the words of his critics. Instead, it was the everyday human being—the
individual—who inspired and informed his work.

2

During a career that spanned over 50 years, Graves held firm to the belief that design could effect tremendous change in
people’s day-to-day lives. From small-scale kitchen products to immense buildings, a thread runs throughout his products:
accessible, aesthetic forms that possess a sense of warmth and appeal.

3

Early in his career, Graves was identified as one of the New York Five, a group of influential architects who whole-heartedly
embraced Modernism, the architectural movement that subscribed to the use of simple, clean lines, forms devoid of
embellishments and modern materials such as steel and glass.

4

However, Graves is best described as a Post-Modernist. He eschewed the austerity of Modernism and its belief that “less is
more,” instead embracing history and references to the past. He rejected the notion that decoration, or ornament, was a
“crime” (as Austrian architect Adolf Loos wrote in 1908); rather, he viewed it as a way for his architecture to convey meaning.

5

As the noted architectural historian Spiro Kostof explains in his book A History of Architecture: Settings and Rituals, “Post
Modernists turn to historical memory . . . to ornament, as a way of enriching the language of architecture.”

6

… Along these lines, Graves loathed the idea of intellectualizing his structures. Instead, he sought to make them accessible,
understandable, and poignant to all passersby. . . .

7

In addition to designing buildings, Graves embarked upon a long and highly successful partnership with the Italian
kitchenware company Alessi. . . . Graves’ most famous Alessi design is his iconic teakettle . . . which had a cheerful red
whistling bird and sky-blue handle. On sale since 1985, the best-selling product is still in production today.

8

In 1999, Minneapolis-based discount retail giant Target approached Graves with an offer to design a line of kitchen
products, ranging from toasters to spatulas.

CONTINUE
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  799

Practice Test 3
9

While some might have shied away from having their work associated with a mega-corporation like Target, Graves wholly
embraced the project. . . .

10

In all, Graves’ collaboration with Target would last 13 years; during this time, the designer would become a household name, with
millions of units of his products appearing in American homes.

11

Many of Graves’ designs for Target—his spatula, can opener, and ice cream scoop—had chunky, sky-blue handles. Other
appliances that were white . . . were sprinkled with touches of color. . . . Black and beige had no place in Graves’ palette.

12

The option to select a better-looking product with a slightly higher price versus the same article but with a less expensive,
nondescript appearance is now the norm for most consumers: good design (and function) are part and parcel of the customer
experience (nowhere is this more evident than in Apple’s rise to dizzying heights as arguably one of the world’s most valuable
brands).

13

It’s an idea that’s democratic in nature, and thinking about design through this lens led Graves to create thoughtful, appealing,
and affordable products for the masses. . . .

14

As Graves’ popularity rose, his critics leveled blistering commentaries about what they deemed a precipitous fall from grace—
from a “trend beyond compare” to a “stale trend,” as architecture critic Herbert Muschamp noted in a 1999 New York Times article.
The notion that he had commodified design—and had somehow “cheapened” it—drew the disdain of those who once lauded
his works.

15

Yet Graves remained true to his beliefs even into the last phase of his life. In 2003, after an illness left him paralyzed below the
waist, he realized that the design of hospitals and equipment . . . could be redesigned and made more functional, comfortable,
and visually appealing. He then went on to improve ubiquitous devices such as wheelchairs and walking canes. . . .

16

Consumers may not have ever known his architecture or what the critics thought of his work (or even realized they were buying
one of his products). Graves didn’t seem to mind. His goal was to provide well-designed items for everyday use rather than
impress his detractors.

17

As he told NPR in 2002, “It’s the kind of thing where you pick something up or use it with a little bit of joy . . . it puts a smile on
your face.”

Write an essay in which you explain how Catherine Anderson builds an argument to persuade her
audience that Michael Graves’ central concern was creating designs that helped “the everyday human
being.” In your essay, analyze how the writer uses one or more of the features listed previously (or
features of your own choice) to strengthen the logic and persuasiveness of her argument. Be sure that
your analysis focuses on the most relevant aspects of the passage.
Your essay should not explain whether you agree with Catherine Anderson’s claims, but rather explain
how she builds an argument to persuade her audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  800

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Answer Keys and Explanations
Section 1: Reading Test

1. A

12. B

23. D

34. D

45. D

2. B

13. D

24. B

35. B

46. A

3. A

14. C

25. D

36. A

47. C

4. D

15. D

26. C

37. B

48. B

5. A

16. A

27. C

38. C

49. A

6. C

17. A

28. A

39. C

50. C

7. A

18. B

29. D

40. C

51. D

8. C

19. B

30. D

41. C

52. B

9. C

20. B

31. C

42. C

10. B

21. D

32. A

43. A

11. C

22. A

33. B

44. B

READING TEST RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is A. The overall main points of the
article are all meant to dispel the myths surrounding
earthquakes: how and why they occur. The article
3.
provides supporting details about the science of
earthquakes, which also counter the Hollywood myths.
Thus, choice A is the correct answer. While the author
does explain the causes and effects of earthquakes, it is
to dispel the myths created by Hollywood, thus choice B
is incorrect. Choice C is incorrect, as the passage applies
to earthquakes only and not to science in general.
Choice D is incorrect as this topic is not covered in the
passage.
The correct answer is B. The main causes of earthquakes are described in paragraph 2, which explains
that “An earthquake is caused by a sudden slip on a
fault” (lines 13–14) before stating that “Stresses in the
Earth’s outer layer push the sides of the fault together”
(lines 21–22). The mere existence of faults is not what
causes earthquakes; it is the actions to which those
faults are subjected that are true causes, so choice A is
not the best answer. An earthquake is caused by the
actions on a single fault, so choice C is incorrect. The
author only mentions the quality of the engineering of
structures in the region in lines 47–48 in relation to the

4.

damage earthquakes cause, not the cause of
earthquakes themselves, so choice D is incorrect.
The correct answer is A. The article is intended to
separate fact from fiction for those who might be
misinformed. Although there are a lot of scientific
facts in the passage, the tone is casual and almost
scolding in its refutation of the myths surrounding
earthquakes, which the author makes clear in lines
86–90 (“So when you see . . . and your family.”).
Choice C is incorrect because filmmakers would not
be particularly interested in being reminded that
the films they make are often not based in reality.
Choices B and D are incorrect as both scientists and
science teachers would already know these facts.
The correct answer is D. The article counters the
myths by pointing out in lines 69–72 that the ocean
isn’t a hole into which a land mass can fall, as the
ocean is itself just land at a lower elevation. Thus,
choice D is the correct answer. Choice A is incorrect
because it accepts the myth as fact rather than
countering it. Choice B is incorrect because while the
author talks about the land mass under the ocean as
being at a lower sea level than California, it is only to
explain the geology of the region. Choice C is

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  801

Answer Keys and Explanations
nevertheless causes “significant damage” in certain
areas. It describes how in certain areas, a moderate
condition is intensified, so choice C is the best answer.
“Lifted” implies an upward movement, and it would not
make sense to suggest that the earthquake’s shaking
was lifted above the surface of the earth, so choice A
cannot be correct in this particular context.
“Supplemented” means “added to,” and it would not
make sense for anything to be added to the shaking, so
choice B is incorrect. While “amplified” can be used to
mean “made louder,” the volume of the earthquake’s
noise is not significant in this context; the intensity of its
shaking and how that shaking started moderately but
caused significant damage is, so choice D is incorrect.

incorrect because the author does not explain that
California and Alaska are similar but rather that southern
California is moving slowly toward Alaska.
5.

The correct answer is A. The author notes in lines
69–72 that California cannot break off, as it is part of the
land that makes up the ocean floor, only at a higher
elevation. Thus, choice A is the correct answer. Choice B
is incorrect, as it is not an explanation as much as a
refutation. Choices C and D are incorrect, as they merely
point out another feature of the geology of California;
they do not clarify why California will not be swept out
into the ocean.

6.

The correct answer is C. In the context of this passage,
“stress” is pressure that builds up in rocks. Only in
human interactions does “stress” describe the pressure
that builds up in people, causing worry and/or anxiety,
so choice A is incorrect. Stress does not imply the idea
of weight in the context of this passage, making choice
B incorrect. It also does not mean “emphasis,” so choice
D is incorrect.

7.

8.

9.

  802

The correct answer is A. The passage makes it clear
that the closer a region is to the earthquake source; the
more that region will be affected. The most likely reason
that San Francisco, or any place, would experience so
much damage is that it lacked buildings that could
withstand the shaking from an earthquake, and the
earthquake was probably very strong. Information in
the passage makes it impossible to know whether or
not choice B is true. The passage implies that earthquakes are a major concern in California, so it is unlikely
that its city officials never thought an earthquake,
would occur in San Francisco. So even though the city
was apparently unprepared for such a strong and
damaging earthquake, choice C is not entirely correct.
Faults across the country are irrelevant to a situation in
one particular city, so choice D is not correct.
The correct answer is C. Lines 45–48 clearly explain
that the effects of an earthquake are dependent on the
proximity of the earthquake source to the affected
region, as well as the quality of the engineering of the
structures that are shaken by the earthquake. Choice B
is incorrect because these lines discuss the creation of
an earthquake but do not mention the affected region
of an earthquake. Similarly, choices A and D both
contain lines that regard the attributes and causes of an
earthquake but fail to address why a region is affected.
Therefore, choices A and D are incorrect.
The correct answer is C. The word “amplified” is used to
describe the shaking of a “moderate” earthquake that

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10.

The correct answer is B. The phrase reveals that
disaster movies are made more dramatic for effect at
the expense of scientific accuracy. Using the word
“inconvenient” mocks the story; it implies that the
earthquake is used as an easy way to write a character
out of the story. Choices A, C, and D are incorrect
because the use of the referenced phrase does not
directly relate to scientific information within the
passages, as stated in these choices.

11.

The correct answer is C. The passage explains that
friction is required for an earthquake (lines 81–82),
making the idea of a gaping fault impossible, as a fault
line could only open up without friction. Choice A is
incorrect because although the concept is portrayed in
movies, as described in lines 77–79, that fact does not
refute the myth. Choice B is incorrect because this
question is about earthquakes causing the ground to
open up and not “mega-quakes.” While the author does
state that earthquakes can cause landslides (lines
82–84), he or she immediately follows this up by stating
“Faults, however, do not gape open during an earthquake.” (lines 84-85), so choice D is incorrect.

12.

The correct answer is B. Patrick Henry lashes out
against concentrated power (Passage 1, lines 1–5).
Madison, on the other hand, explains that power is
essential, but separating the power of the government
into different departments (branches) will act as a check
on that power, ensuring that it cannot get out of control
(Passage 2, sentence 1). Choices A, C, and D are
incorrect because the statements made in them do not
reflect the content of the passages.

13.

The correct answer is D. Henry addresses the issue of
concentrating power and says that it rests “on a
supposition that your American governors shall be
honest” (lines 25–26), which, in his view, is a dangerous

Answer Keys and Explanations
and unnecessarily risky assumption to make. Choice A is
incorrect because Henry actually suggests the opposite
of this conclusion, voicing concern about a lack of check
and balances in lines 5–6 before speculating that a
president who basically operates as a king could be the
result of a lack of checks and balances in line 19. Choices
B and C are both incorrect because neither correlate
with the views of Henry and would therefore not be an
objection of his.
14.

15.

16.

The correct answer is C. The artist portrays Henry as a
passionate speaker. This mirrors the dramatic phases
Henry uses in his speech, such as calling the features of
the Constitution “horribly frightful” and the government
“horridly defective.” Choice A is incorrect because the
reader has no way of knowing how people react to
Henry’s speech. The artist does not portray Henry as
calm; instead Henry appears impassioned, making
choice B incorrect. The artist shows Henry as impassioned, but not necessarily an extremist. Some spectators look excited; some look angry or sullen, but there
is no indication Henry is perceived as a madman. Henry
does appeal to the listener’s patriotism, but his
argument is not built slowly. The structure is logical, but
the pacing is quick and the tone urgent. Therefore,
choice D is also incorrect.
The correct answer is D. Madison argues that a
government whose powers are separated by design will
act as controls, each branch on the other, and avoid
concentration of power. Although Madison describes
government as a reflection of human nature, this is not
a counterargument to those who were concerned about
a strong central government, so choice A does not
make much sense. Choice B is incorrect because it
exaggerates Madison’s simple suggestion that people
are not “angels” and require some monitoring from their
fellow people to ensure that they always act in the
people’s best interests. Choice C is incorrect because
Madison does state that the people should monitor the
government to a certain degree.
The correct answer is A. Lines 51–56 describe how
Madison believes the government should be divided
into branches that would check and balance each other.
This would serve to counteract the idea that the
government is too centralized because the branches
would allow for the power to be divided and would
make it so that one branch would not have too much
power. Choice B makes the mistake of concluding that
choice A was the correct answer to the previous
question and this is not the case. Choice C makes the
mistake that choice B was the correct answer to the

previous question, and it was not. Choice D relates to
people influencing the government, which relates to
choice C in the previous question, but since that answer
choice was incorrect, choice D has no bearing on the
correct answer to this question.
17.

The correct answer is A. Henry and Madison’s statements are both very similar, indicating that both men
believed that even the most seemingly honest person
was too flawed, too human, to be trusted with complete
control of the people she or he ruled. Henry says that
being “good men” is not enough to earn that trust, while
Madison suggests that anyone short of being a
complete “angel” could not be trusted with complete
control. Choice B is too extreme; one does not have to
be completely disinterested in the rights and liberties of
the people they rule to be undeserving of complete
control. Choice C is incorrect because both men are
skeptical of allowing anyone to be trusted with
complete control. Even though its statement about
Madison is true, choice D is incorrect because Henry
does not show that he did not believe government was
necessary.

18.

The correct answer is B. In lines 9–10, Henry voices his
image of the framers of the Constitution with the words
“we are not feared by foreigners; we do not make
nations tremble,” which suggest a desire to intimidate
other countries, so choice B is correct. Since other
countries (“foreigners . . . nations”), and not the
American people, are the targets of these words, choice
A is incorrect. In lines 10–11, Henry questions the idea
that these intimidations would “constitute happiness or
secure liberties” for Americans, so choice C is incorrect.
These words of intimidation would have the opposite
effect of building strong relationships with other
countries, so choice D is incorrect.

19.

The correct answer is B. In line 5 (“the genius of
republicanism”), Henry praises a republican form of
government (i.e., one that has elected representatives
and is not run by a monarchy). Henry indicates that such
a centralized government, as outlined in the
Constitution, cannot work with the goals of forming a
republican government. Choices A, C, and D are
incorrect because Henry is adamant about his opposition to anything similar to a monarchial government,
autocracy and plutocracy included.

20.

The correct answer is B. Line 5 (“the genius of
republicanism”) clearly states that Henry believes that
the ideal form of government is republicanism where all
the people are represented. Choices C and D are similar

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Answer Keys and Explanations
pocket shark was a newborn, so it could not have
transported itself to a place so far from where the only
other pocket shark was discovered near Peru. Locating
the parents, or “mom and dad” (line 19), could provide
clues to how the newborn ended up in the Gulf, so
choice D is the best answer. The author’s mention of the
shark’s parents provides the best clue to this answer,
while the absence of speculation about the area around
the Gulf or whether or not the differences between the
Gulf and Peru had any effect on the pocket shark’s
location make choices A and B less logical conclusions.
The author provides no indication that studying sharks
native to the Gulf would yield any information about
how the pocket shark ended up there.

because they both have to do with the United States
becoming a monarchy. Therefore, these choices are
both incorrect. Choice A is incorrect because it does not
have to do with Henry’s preference in forms of
government.
21.

22.

The correct answer is A. In the context of the sentence,
Madison is referring to how the checks on one
department (or branch) would be in turn proportional
to the checks on another department. One department
would hold another in check to maintain a balance of
power so that power would not get concentrated in one
branch. Choices B, C, and D do not make sense in the
context and are therefore incorrect.

23.

The correct answer is D. The article mentions multiple
scientists and institutions that all worked on identifying
the shark and sharing their information so that it could
be correctly cataloged and understood. The overall
conclusion about methodology, therefore, shows that
science can be a collaborative endeavor. Although the
passage describes multiple institutions working
together, this answer choice assumes that this is
necessary for all examples of scientific information
gathering. This conclusion is too general and baseless
for choice A to be correct. Choice B is too extreme, since
it assumes that the luck that led to the discovery of the
pocket shark in this passage applies to all instances of
scientific information gathering. Choice C also assumes
that the circumstances in this passage will be true for all
other instances of scientific information gathering.

24.

25.

  804

The correct answer is D. Madison’s reference to
“department” refers to the branches of the government
that are outlined in the Constitution (executive,
legislative, judicial), which is apparent from the context.
An executive may be in charge of a department, but a
single person would not constitute an entire government department, so choice A does not make sense.
Choice B is not the best answer since a “territory” would
more likely describe an area of land rather than a
segment of government. Choice C is incorrect because
“level” implies a hierarchy, which does not apply to this
particular context.

The correct answer is B. Lines 10–12 state that while
the shark is small enough to “fit in your pocket,” it
actually gets its name because of the pocket-like “orifice
above the pectoral fin,” which confirms that choice B is
correct and eliminates choices A and C. The author
never suggests that the pocket shark has markings that
resemble pockets, so choice D is incorrect.
The correct answer is D. According to line15, the

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26.

The correct answer is C. Choice C ties all the ideas that
led to the answer to the previous question together. It
mentions the desire to find the shark’s parents, or “mom
and dad,” and learn how those parents got to the Gulf
when the only other discovered pocket shark was
located off Peru. Choice A only establishes that the
pocket shark was a newborn and does not do as strong
a job of establishing the importance of finding its
parents as choice C does. Lines 15–18 only establish
how scientists knew the shark was a newborn (“the
shark displayed an unhealed umbilical scar”), so choice
B is incorrect. Choice D only explains where Mark Grace
found the pocket shark; it provides no insight about the
importance of finding its parents.

27.

The correct answer is C. Paragraph 5 explains that
tissue samples were analyzed to get genetic information that could be compared to other specimens.
Using this data, scientists could then determine how to
classify the pocket shark. Choice A is not the best
answer since other sharks could be the same length as
the pocket shark, and lines 33–36 (A tissue . . .
Mollisquama”) explicitly explain how scientists used
tissue samples to determine the shark’s species. The
author discusses the pocket-like orifice to explain how
the shark got its name but never implies that this
characteristic helped scientists determine its species. In
lines 39–42, the author states that learning its species
may provide clues to the shark’s position on the food
chain, not the other way around, so choice D is
incorrect.

28.

The correct answer is A. The pocket is never described
as a gland in the passage, but the diagram notes that it
is a “pocket gland.” Choice B is incorrect because the
passage does mention that the pocket is located “above
the pectoral fin” (line 12). Although the author mentions
that it is possible that the pocket shark removed oval

Answer Keys and Explanations
plugs of flesh from its prey in lines 41–42, there is no
indication in the diagram that the pocket was used to
remove that flesh, so choice C is incorrect. The conclusion in choice D is a matter of opinion when a fact is
required, and even if an opinion was required, the
pocket shark’s unusual eyes, mouth, and shape are all
features that are arguably more distinctive than its
relatively small pocket slit.
29.

The correct answer is D. The passage explicitly states
that scientists were excited to discover the pocket shark
because it is so unique and so few of them have been
found. Choice A is incorrect because the author actually
places the pocket shark into the Dalatiidae shark family
that existed before the pocket shark was discovered.
While the pocket is “distinctive” (line 11), there is no
evidence that the pocket shark is the only shark with
such an orifice. Even if this is true, an explicit statement
about why scientists are excited about its discovery
renders choice B incorrect. The author mentions that
pocket sharks were found in the Gulf and far away off
Peru but does not offer this detail as the reason why
scientists are so excited about its discovery, so choice C
is incorrect.

30.

The correct answer is D. These lines explicitly state
that it is “exciting” to find a shark that is so “unusual” and
“rare,” so choice D is correct. Choice A seems to make
the mistake that the correct answer to the previous
question was choice C when this is not the case. While
line does indicate that the pocket shark is rare, it does
not indicate that scientists are excited about that fact,
so choice B is not the best answer. Choice C seems to
make the mistake of assuming that choice A was the
correct answer to the previous question when it
was not.

31.

The correct answer is C. “Robust” in this context
describes a collection that has variety. A specimen is a
sample used for testing, so it makes sense for the lab to
have a large, substantial collection of marine animal
samples for testing. Choices A, B, and D are incorrect
because it cannot be inferred, based on the passage,
that the “robust specimen collection” is how these
choices describe it.

32.

The correct answer is A. The kitefish is part of the
Dalatiidae family, which is partially defined by how they
remove oval plugs of flesh from their prey (lines 39–42).
The passage also states that sharks in the Dalatiidae
family eat squid (line 42), so choice B is incorrect. While
the pocket and kitefin sharks are from the same family,
they cannot be identical; otherwise, there would be no

reason to give them distinct names, so choice C does
not make much sense. Whether the pocket shark was
discovered before or after the kitefin shark cannot be
conclusively determined from evidence in the passage,
so choice D is not the best answer.
33.

The correct answer is B. Twain announces his intention
with a mocking turn of phrase (“If Cooper had any real
knowledge of Nature’s ways of doing things, he had a
most delicate art in concealing the fact.”) and goes on to
describe an implausible description of nature in one of
Cooper’s stories, so choice B is the best answer. Cooper
just seems to be telling a story in the tale of
Chingachgook, not making an argument, so choice A is
not the best answer. Although there is a Native
American in the story Twain describes, he is more
focused on criticizing Cooper’s treatment of nature than
his treatment of Native Americans, so choice C is not the
best answer. Twain is making a point about Cooper’s
wider treatment of nature than how the writer specifically described a stream bed, so choice D is not the best
answer choice.

34.

The correct answer is D. For the entirety of the
passage, Twain mocks Cooper’s story, but he does so in
a humorous way. For example, in the first paragraph
Twain makes the humorously absurd suggestion that
there is some way to score committing offenses against
literary art (lines 3–4) and in lines 58–59, he describes
the action of the novel, saying: “Let me explain what the
five did—you would not be able to reason it out for
yourself.” This is sarcasm making mockery of the action
of the characters in the book. It is light-hearted and
expresses incredulity, thus setting a humorous tone.
While Twain might be exhausted with reading Cooper’s
work, Twain’s own writing is so sharp and witty that he
never seems exhausted, himself, in this passage, so
choice A is not the best answer. The voice of the
passage is informal as evidenced by its abundant jokes,
and as a result, not scholarly. This makes choice B
incorrect. The tone of the passage is humorous;
however, it is too biting to accurately be described as
cheery and does not suggest optimism, making choice
C incorrect.

35.

The correct answer is B. Lines 8–9 illustrate the
hyperbole that Twain uses to humorously describe how
Cooper took liberty with his description of the techniques Native Americans used to track footprints to find
and/or attack enemy tribes. In these lines, Twain’s
description of wearing out the moccasins in the process
of following a trail pokes fun at the erroneous nature of

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Answer Keys and Explanations
idea that his stories do not make sense. Choice A is
merely a hyperbolic description of Cooper’s list of
defects and illustrates Twain’s style of satire. Choices B
and D describe instances in which Cooper bent reality
to suit his poor plotting, but neither sends a general
message about the senselessness of Cooper’s writing as
well as choice C does.

Cooper’s characterization. Choices A, C, and D are all
critiques, but they do not express humor.
36.

37.

The correct answer is B. The pronunciation guide is
another way of mocking Cooper’s book. Here, Twain
describes the book and throws in, as an aside, the
pronunciation key to indicate how far Cooper veers
from reality, so much so that the Native Americans he
describes might as well be called Chicago. Choices A
and C are incorrect because Twain is writing satirically
and does not actually intend for the reader to pronounce the Native American’s name correctly. As the
work is satire, Twain only intends to criticize Cooper, and
illustrating that Cooper’s work was about actual Native
Americans would not achieve this goal. Therefore,
choice D is incorrect.

38.

The correct answer is C. The biggest and most
frequent criticism Twain makes in the passage is to
show how unrealistic and senseless the plot and
characters are. For example, in describing the ark
(paragraph 5), he explains how the timing is off for the
entire scene, making its occurrence totally unreasonable. And here he jokes and ridicules the outcome:
“He missed the house and landed in the stern of the
scow. It was not much of a fall, yet it knocked him silly”
(lines 51–53), showing how absurd the storyline is. If
anything, Twain suggests that Cooper had a simplistic
approach to creating stories since his books suffer from
so many lazy plot holes (for example, the incompletely
described passage of the ark in the fifth paragraph), so
choice A is incorrect. While Twain’s tone implies he may
appreciate writing that does not take itself too seriously,
an absence of humor is not one of the criticisms he
lodges against Cooper’s work, so choice B is not the best
answer. Twain describes quite a bit of action in Cooper’s
stories, so “boring” may not be something of which they
are guilty, and Twain certainly never suggests as much
in this particular passage, so choice D can also be
eliminated.

39.

  806

The correct answer is A. Twain refers to Cooper’s use of
various literary devices as “stage properties,” as a way to
mock Cooper. The “barrels and barrels of moccasins” is
one example. Another is his description of “the broken
twig.” The “stage properties” Twain refers to do not have
anything to do with drama or theater, making choices B,
C, and D incorrect.

The correct answer is C. In lines 58–59, Twain
addresses the reader to suggest that there is no way for
the reader to figure out what is happening in a particular sequence in Cooper’s story, which supports the

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40.

The correct answer is C. Twain criticizes Cooper’s
characterization of the Native Americans as sneaky and
inept. From line 30 to line 65, he describes a group of
Native Americans attempting to sneak attack an ark but
completely botching the job. They bumble through
every attempt they make to attack the settlers (for
example, they can’t jump onto a very slow-moving boat,
because they miscalculate the timing). The fact that
they cannot make successful leaps onto the ark
contradicts the notion that Cooper portrays Native
Americans as athletic, and their ineptness indicates that
he does not depict them as very smart either, so choice
A is incorrect. The ineptness of these characters hardly
makes them effectively cunning or dangerous, so choice
B is wrong too. Cooper’s Native American characters
may be unable to plot an attack well, but they still plot
an attack, so it would be wrong to conclude that Cooper
characterizes Native Americans as gentle and respectful,
choice D.

41.

The correct answer is C. Twain notes that Cooper
“conceals six Indians in its (the sapling’s) foliage” (lines
36–37). A sapling is a young, immature tree, so it is
illogical to assume that six people could be hidden in
the foliage of a sapling. Thus, choice C is the correct
answer. Quotation marks are not used to indicate a
word that is not used anymore, and, in any event,
sapling is a word still commonly used today, so choice A
does not make sense. While Twain does criticize Cooper
for overusing certain things, such as the device of
characters stepping on dry twigs (lines 10–13), the word
“sapling” is not something Twain criticizes Cooper of
overusing. A word in another language would be
written in italics, not quotes, and sapling is an English
word, so choice D is incorrect.

42.

The correct answer is C. In the context of the sentence,
“destitute” means that the work is void of the variables
that make a story artful. Although the word can mean
impoverished, that meaning does not fit this context,
making choice A incorrect. Choices B and D are both
incorrect because they do not make sense in this
context.

Answer Keys and Explanations
43.

The correct answer is A. The overall descriptions are of
the character Paul. The passage describes how he looks,
his actions and reactions, and his emotions. Through
the use of a narrator telling the story, it also describes
how others react to him, giving the reader an outside
perspective of the character. Thus, choice A is the
correct answer. Choice B is incorrect because the
passage description notes that it is from a short story
and therefore fiction. Choice C is incorrect because
there is no plot in the passage. Choice D is incorrect
because it is the character of Paul—not any one
setting—that is emphasized.

44.

The correct answer is B. The author notes in lines 1–3
that it “was Paul’s afternoon to appear before the faculty
of the Pittsburgh High School to account for his various
misdemeanors.” Thus, choice B is the correct answer.
Choice A is incorrect because, while the author notes
that Paul does tell the principal that he wants to return
to school, this was not the reason why he was asked to
appear before the faculty. Choice C is incorrect because
tardiness is not mentioned as one of Paul’s infractions.
Choice D is incorrect because, while his father calls the
principal after Paul’s suspension confessing that he is
perplexed by his son’s behavior, there is no mention
that Paul’s parents are in the principal’s office at this
time.

45.

The correct answer is D. The carnation is obvious on
his coat lapel, and it is a contrast to the way he is
dressed in shabby clothes, as if he didn’t care. And yet
the carnation adds a note of frivolity and mockery to
the seriousness of the event. It is a way of subtly
communicating that he will do as he pleases, in
defiance of the wishes of the faculty, thus choice D is
the correct answer. Choice A is incorrect, as Paul does
not wish to show respect to the faculty. Choice B is
incorrect because Paul does not intend to show
remorse. In fact, he intends to show defiance. Choice C
is incorrect because if Paul wanted to appear wealthy,
he would not wear shabby clothes.

46.

The correct answer is A. The author notes in lines
29–30 that his teachers stated their charges against him
with “such a rancor and aggrievedness as evinced that
this was not a usual case,” which indicates extreme
feelings of frustration and anger, so choice A is the
correct answer. While sadness and confusion can often
be felt in conjunction with frustration and anger, the
author’s failure to mention such emotions makes choice
B incorrect. Lines 51–54 indicate extreme emotions that
contradict the conclusion in choice C, and the fact that
these are negative emotions eliminates choice D.

47.

The correct answer is C. In lines 27–30, the author
notes that Paul’s teachers stated their charges with
“rancor and aggrievedness,” words that suggest anger
and frustration. Thus, choice C is the correct answer.
Choice A is incorrect because these lines refer to Paul’s
father’s feelings. Choice B is incorrect because, while it
suggests that the teachers did not feel that Paul was
contrite, it does not support the idea that they were
angry and frustrated. Choice D is incorrect because
these lines explain how the teachers interpreted Paul’s
feelings toward them.

48.

The correct answer is B. When the English teacher took
Paul’s hand to guide him, he reacted by shuddering and
thrusting “his hands violently behind him” (line 40). His
teacher reacts to this with astonishment (lines 41–42)
and “could scarcely have been more hurt and embarrassed had he struck at her,” which supports choice B.
Her astonishment and the fact that she took his reaction
so personally suggest that she may not have much
experience dealing with emotional students, so choice
A is not the best answer. The author merely writes that
she “attempted to guide his hand” (line 39); she does
not suggest that the teacher took his hand because she
was impatient with how slowly Paul was writing, so
choice C is not the best answer. While Paul did make “a
running commentary on the lecture” (line 49) in one of
his classes, the author implies that this class took place
in a different class from the English one, so choice D is
not the best answer.

49.

The correct answer is A. Paul’s appearance is described
in great detail, and his outer appearance is often
betrayed by behavior that gives away his true feelings.
For example, he smiles but his fingers tremble and play
with the buttons on his coat (lines 61–62). Choices B, C,
and D are incorrect because they do not describe Paul’s
actions and feelings; rather, they describe contrasts with
others and their appearance and reactions.

50.

The correct answer is C. Cather notes in her
description of Paul playing with the buttons on his coat
that it was the only outward sign of his discomfort, thus
in lines 58–63, she connects his outer actions to his
inner feelings, allowing the reader inside Paul’s
emotional state. Choice C then is the correct answer.
Choices A and B are incorrect, as the lines do not
interpret the meaning of Paul’s facial expression. Choice
D is incorrect, as the interpretation noted here is made
by others and not necessarily reflective of Paul’s
feelings.

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Answer Keys and Explanations
51.

  808

The correct answer is D. The word as used in the title
suggests that the story is focused on the personality
makeup of the protagonist. Thus, choice D is the correct
answer. Choice A is incorrect because the narrator does
not describe Paul’s complexion. Choice B is incorrect, as
the word does not make sense in the context. Choice C
is incorrect, because the story is a description of a boy’s
behavior over a period of time, and mood suggests one
particular moment or feeling.

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52.

The correct answer is B. A dandy is a person who is
meticulous in the way he dresses and takes extreme
care in his appearance. The paragraph in which the
word is used is in the context of Paul’s clothing, and
“dandy” suits the characterization of Paul, so choice B is
the correct answer. Choices A, C, and D are incorrect
because the context is a description of Paul’s dress.

Answer Keys and Explanations
Section 2: Writing and Language Test

1. C

10. B

19. D

28. C

37. A

2. B

11. C

20. B

29. B

38. D

3. C

12. A

21. A

30. A

39. B

4. D

13. D

22. C

31. C

40. C

5. A

14. B

23. B

32. D

41. B

6. A

15. A

24. D

33. A

42. D

7. B

16. B

25. B

34. C

43. A

8. C

17. D

26. A

35. D

44. B

9. D

18. C

27. A

36. C

WRITING AND LANGUAGE TEST RAW SCORE
(Number of correct answers)

1.

2.

3.

The correct answer is C. Choice C is correct because
the sentence provides a transition between sentences
and establishes the historical importance of Blackwell’s
accomplishment. Choice A is incorrect because the
historical importance of this event is relevant to the
paragraph’s main focus. Choice B is incorrect because
the sentence provides new information that has not yet
been introduced. Choice D is incorrect because what
Blackwell did is explained in the previous sentence.
The correct answer is B. The context of the paragraph
makes clear that the expectations of those around her
were that she would fail in becoming a doctor and that
Blackwell had ignored or disregarded those expectations. Choice A is incorrect because her achievement
was not a condemnation or criticism of the expectation
that she would fail; it simply flouted it. Choice C is
incorrect because “incite” means to encourage or
inspire, and the context does not support the idea that
she inspired the expectation that she would fail. Choice
D is incorrect because the context makes clear that in
earning her degree, Blackwell did not meet the
expectations of her peers. Rather, she disregarded and
far surpassed them.
The correct answer is C. The comparison here is
between educating a boy and educating a girl, thus
choice C is the correct answer. Choice A is incorrect

because it illogically compares educating a boy to a girl,
rather than to educating a girl. Choice B is incorrect
because it illogically compares educating a boy to a
girl’s preference for education. Choice D is incorrect
because it illogically compares educating a boy to
opportunities for girls.
4.

The correct answer is D. The phrase, “To make up for
the gaps in her education,” modifies “she” or Blackwell
and should directly precede a reference to Blackwell to
avoid confusion. Choice A is incorrect because the
phrase appears to modify household. Choices B and C
are incorrect because the phrase appears awkwardly in
the middle of the sentence and it is unclear what it
modifies.

5.

The correct answer is A. The first part of the sentence,
“As she prepared to apply to medical school,” correctly
tells the reader when the events of the sentence took
place. Choices B and C incorrectly state when these
events take place. Choice D incorrectly suggests that
Blackwell wanted to be a psychologist.

6.

The correct answer is A. This sentence provides
significant context clues to help you determine the right
word to include. The latter half of the sentence is
building on a specific contention, saying “at least one
advisor went so far as to suggest that she might

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Answer Keys and Explanations
disguise herself as a man in order to gain admittance.”
Such a notion suggests that her advisors felt great doubt
that she would gain direct admittance to medical
school, so choice A is correct. There is no evidence that
there was any debate, insistence, or supposing going
on, so the other answer choices are incorrect.
7.

The correct answer is B. The antecedent of the
pronoun is Blackwell, so the pronoun should be “her,”
making choice B the correct answer. Choices A, C, and D
do not agree with the antecedent “Blackwell.”

8.

The correct answer is C. The sentence should be
written in the simple past tense: became agrees with the
verb tense used in the sentences that follow, thus
choice C is the correct answer. Choice A is incorrect
because it is in the present perfect tense while the
sentence that follows is in the simple past tense. Choice
B is incorrect because it is in the present tense, and all of
the events take place in the distant past. Choice D is
incorrect because it is in the future tense.

9.

10.

11.

  810

The correct answer is D. The phrase, “all of whom were
men,” is nonrestrictive, which means it must be set off
by commas. Only choice D has the commas in the
appropriate place to set off the entire phrase. Choice A
is incorrect, as there are no commas to set off the
nonrestrictive phrase. Choices B and C are incorrect
because the commas are in the wrong place.
The correct answer is B. This choice reduces wordiness
and redundancy, as experiencing prejudice and biases
implies that obstacles and challenges were faced.
Choice A is incorrect because, as stated, experiencing
prejudice and biases implies that real obstacles and
challenges were faced, so there’s no need to restate it.
Choice C is incorrect because it fails to specify that the
challenges faced included prejudice and biases, which is
significant information that should be included. Choice
D is incorrect because the wording is awkward and
would introduce confusion to the sentence.
The correct answer is C. Only choice C supports the
idea that, although she faced barriers, she was successful by distinguishing herself as a promoter of
preventative medicine and medical opportunities for
women. Choice A is incorrect because it does not
support the idea that she was successful, and it does
not refer to her career after she graduated from medical
school. Choice B is incorrect because it does not
describe anything that Blackwell went on to do after
she got her degree. Choice D is incorrect because it
does not describe anything that Blackwell did in her
career.

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12.

The correct answer is A. This choice provides useful
historical context for when Carson’s book was published, informing readers that few people in 1962
expressed concern about the environment. This helps
advance the idea that Carson was brave for speaking
out. Choice B is not correct, as Carson’s age is not a
significant factor here. Choice C is incorrect because this
information is not irrelevant, and the book is indeed an
important publication. Choice D is incorrect because
adding this sentence does not create a division in the
focus of the paragraph.

13.

The correct answer is D. The style of the passage is
formal and objective, and only choice D corresponds
with this style. Choices A and B are incorrect because
they employ an informal style. Choice C is incorrect
because it is not objective in referring to “outsized egos.”

14.

The correct answer is B. The sentence is a question and
requires a question mark at the end. Choices A, C, and D
are incorrect because the sentence is interrogative and
requires a question mark.

15.

The correct answer is A. In this sentence, the phrase
“DDT in particular” represents a sharp break in thought
and should be set off by dashes. The sentence as it is
written is correct. Choice B is incorrect because a dash
must be used at the beginning and end of the phrase to
set it off from the rest of the sentence. Choice C is
incorrect because while commas could be used to
separate the phrase, they must be used before and after
the phrase to be correct. While parenthesis could be
used to set off the phrase, in choice D, they are only
used to set off part of it, making it incorrect.

16.

The correct answer is B. The information above the pie
chart indicates that the chart refers to the most heavily
used pesticides by percentage in 1968. Only choice B
accurately notes this by referencing that DDT accounted
for 11% of all pesticides used in that year. Choice A is
incorrect because the chart does not show the amount
of farmland that was sprayed with DDT. Choice C is
incorrect because the chart does not indicate the
percentage of pests contained by DDT. Choice D is
incorrect because the chart does not show the percentage of farmers and gardeners who used DDT.

17.

The correct answer is D. The context of the paragraph,
as well as the point later in the paragraph that pesticides “were able to penetrate systems and remain there
for years,” indicates that the pesticides were seeping
into, or permeating, the soil and rivers. Choice A is
incorrect because there is no support for the idea that
the pesticides sapped the water from soil and rivers.

Answer Keys and Explanations
Choice B is incorrect because the pesticides could not
seize the soil and rivers. Choice C is not correct because
“transcend” does not make sense in the context.
18.

19.

20.

21.

22.

The correct answer is C. In the original text, the
incorrect pronoun “he” is used, creating confusion as to
what noun it’s replacing. For clarity, the sentence must
restate the antecedent; thus, choice C is the correct
answer. Choice B is incorrect because “it” does not agree
with any antecedent in the preceding sentence. Choice
D is incorrect because “everything” is illogical in the
context.
The correct answer is D. Choice D maintains Carson’s
argument that pesticides are dangerous. Choice A is
incorrect because it suggests that pesticides are
beneficial to health. Choice B is incorrect because
Carson is not making an argument about cancer
specifically, nor does she definitively link the two.
Choice C is incorrect because Carson is not talking
about only bird populations.
The correct answer is B. The context of the paragraph
suggests that the chemical companies were not willing
to accept or admit the potential hazards of their
product; thus, choice B is the correct answer. Choice A is
incorrect because “contradict” suggests that they agreed
with Carson, an idea not supported by the context.
Choice C is incorrect because while it is likely true that
chemical companies were not willing to “propagate” or
communicate the potential hazards of their product, the
fact that they discredited Carson suggests that they
were even stronger in their reaction to her claims.
Choice D is incorrect because “solicit,” or try to obtain,
doesn’t make sense in the context.
The correct answer is A. The first part of the sentence
is a subordinating clause, and the subordinating
conjunction since helps establish the clause’s connection to the rest of the sentence. It explains why
Carson is blamed for the deaths. Therefore, choice A is
the correct answer. The other answer choices are
incorrect because they deploy incorrect subordinating
conjunctions and introduce confusion and awkwardness into the sentences.
The correct answer is C. The noun DDT must agree in
number with “wonder chemical”; thus, choice C is the
correct answer. Choice A is incorrect because DDT does
not agree in number with “wonder chemicals.” Likewise,
choice B is incorrect because “pesticides” does not agree
in number with “wonder chemical.” Choice D is also
incorrect because DDT does not agree in number with
“chemicals.”

23.

The correct answer is B. Because this is a simple list of
countries, the items in the series should be set off by
commas, choice B. Choices A and C are incorrect
because the items are set off by both commas and
semicolons. Choice D is incorrect because the lack of
internal punctuation creates a grammatically incorrect
sentence.

24.

The correct answer is D. The subject and verb in a
sentence must agree in number. In this case, only choice
D reflects agreement of the subject and verb as well as
appropriate verb tense. Choice A is incorrect because
the subject of the sentence, “the Mayan understanding
of astronomy,” is singular and requires a singular verb,
and “were” is plural. Choice B is incorrect because “are” is
plural and is in the present tense rather than the past
tense. Choice C is incorrect because the verb form will
be is in the future tense, while the notable achievements of the Mayans occurred in the past.

25.

The correct answer is B. All of the items in the list
should be in the same form, or parallel. Only choice B
reflects a parallel structure for all of the verbs: setting,
moving, and rotating. The verbs in the other answer
choices do not have parallel structure and are incorrect.

26.

The correct answer is A. The context of the sentence
suggests that the Mayans’ observations were accurate,
as they could predict eclipses and the movement of the
planets. Only “astute” reflects this level of accuracy, so
choice A is correct. Choice B is incorrect, as “inept”
suggests the Mayans weren’t skilled at making observations. Choice C is incorrect, as the observations were not
“expected,” given the time period in which they were
made. Choice D is incorrect, as there’s no evidence or
support within the sentence that refers to the complexity of the Mayan’s observations.

27.

The correct answer is A. This answer (“the movement
of the planets”) provides an example that is related to
astronomy, which is the main focus of the paragraph
and sentence. Choices B, C, and D are incorrect because
they provide examples that are inconsistent with the
topic of astronomy.

28.

The correct answer is C. “Its” is a possessive determiner
and does not require an apostrophe, thus choice C is
the correct answer. Choice A is incorrect because “it’s” is
a contraction of “it is.” Choices B and D are incorrect
because they are not words.

29.

The correct answer is B. A semicolon is used to join
two related sentences that can stand on their own.
Choice A is incorrect because a colon is not used to join

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Answer Keys and Explanations
two independent clauses. Choice C is incorrect because
a comma may only be used to join two independent
clauses if it is followed by a conjunction. Choice D is
incorrect because, while it is followed by a conjunction,
“but” indicates that the second clause is somehow at
odds with the first.
30.

The correct answer is A. The paragraph suggests that
the link between government and astronomy was so
complete that the two were inseparable, so choice A is
the correct answer, as the word “inextricably” means in a
manner that is impossible to separate. There’s nothing
in the passage to suggest that the link was baffling or
embarrassing or that an element of greed was involved,
so the other answer choices are incorrect.

31.

The correct answer is C. No punctuation is required
after “symbols” because the phrase that follows it is
restrictive, or necessary for identifying which symbols.
Only choice C contains no punctuation after “symbols,”
so it is the correct answer. Choice A is incorrect because
the colon is not correct. Choice B is incorrect because
the comma sets the restrictive phrase off from “symbols.”
Choice D is incorrect because a semicolon is used only
to separate two independent clauses, and “relating to
the Sun, Moon, and sky” is not an independent clause.

32.

33.

  812

The correct answer is D. Choice D, call to war, is correct
because it supports the paragraph’s focus on when the
Mayans would attack their enemies. Choices B, C, and D
are incorrect because they provide information that is
inconsistent with the paragraph’s focus.
The correct answer is A. The last paragraph is a short
summary of the rest of the passage, as the phrase “in
short,” suggests. Thus, choice A is the correct answer.
Choice B is incorrect because “however” indicates a
contrast with information that preceded it. Choice C is
incorrect because “moreover” suggests that the
paragraph will include new information, which it does
not. Choice D is also incorrect because “incidentally”
suggests that a digression or side topic will follow.

34.

The correct answer is C. As written, the verb “apply” is
in the wrong tense, that is, in the present tense. The
word “believed” is a clue that this belief occurred in the
past, so for correct parallel construction the past tense
“applied” should be used. The other choices also use
incorrect verb tenses.

35.

The correct answer is D. The narrator has intended to
use the preposition “through” here, and only choice D
reflects the correct spelling. Thus, choice D is the correct
answer. Choice A is incorrect because “thorough” is an
adjective that means complete or exhaustive. Choice B

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is also incorrect because “threw” is the past tense of
“throw.” Choice C is not correct because “though”
functions as either an adverb meaning however or a
conjunction meaning while.
36.

The correct answer is C. Because it is clear that the
narrator is seeking a job, the correct possessive modifier
before a noun must be “my,” as the passage is written in
the first person and the narrator is referring to himself
and no one else. Thus, choice C is the correct answer.
Choice A is incorrect because “our” is plural in number
and refers to the narrator and others, an incorrect
reference. Choice B is not correct because there is no
antecedent for “his” and the interview clearly belongs to
the narrator. Choice D is also incorrect because there is
no antecedent for “their.”

37.

The correct answer is A. The sentence that currently
concludes the paragraph provides an effective summation of the ideas in the paragraph, that the law firm
that will be the location of the narrator’s first interview
is the ideal working environment. It also provides
context for the paragraph that follows, letting readers
know that this job is one that the narrator really wants
to get. Choice B is the opposite of the narrator’s actual
thoughts about the law firm, and there’s no evidence to
suggest that choices C and D represent the narrator’s
actual beliefs.

38.

The correct answer is D. A complete sentence contains
both a subject and a predicate. The sentence as it stands
is a fragment, as it does not contain a subject. Only
choice D contains both a subject (“I”) and a predicate
(“informed”). Choice A is incorrect because, as previously noted, it does not contain a subject. Choice B is
incorrect, as it is a dependent clause, containing neither
a subject nor a predicate. Choice C is incorrect because
it, too, is a dependent clause.

39.

The correct answer is B. The context of the paragraph
suggests that the narrator thinks that he is ambitious
and well-spoken, as he has articulated his goals to the
interviewer. Only choice B fits with the context. Choice
A is incorrect because “enigmatic” means mysterious,
and there is nothing mysterious about the narrator.
Further, the narrator wouldn’t assume that the interviewer thought he was mysterious. Choice C is incorrect
because “conspicuous” means noticeable. While this
could potentially work, it is not usually considered an
admirable trait in a job interview. In this case, “articulate”
is a better fit. Choice D is incorrect because “incoherent”
means unable to be understood, and the narrator
clearly thinks he has made a good impression on the
interviewer.

Answer Keys and Explanations
40.

The correct answer is C. The context requires the plural
form of “weakness,” which is “weaknesses.” Thus, choice
C is the correct answer. Choice A is incorrect because it
is a possessive form of “weakness.” Choice B is incorrect
because it is the possessive form of the plural “weaknesses,” rather than just the plural. Choice D is not
correct because it neither accurately reflects the plural
of “weakness,” nor the possessive of the word.

41.

The correct answer is B. Sentence 3 introduces the
topic of the paragraph, which is the narrator’s listing of
his strengths and weaknesses. Because the sentence
clearly introduces the main point of the paragraph, it
belongs at the beginning of the paragraph. Choice B,
then, is the correct answer, which makes choice A
incorrect. Choice C is incorrect because it makes no
sense to place the sentence after the sentences that tell
the narrator’s response to the interviewer’s question.
Choice D is incorrect, as the existing paragraph is where
information regarding the phases of the interview fits
best.

42.

The correct answer is D. The conventional phrase, “I
couldn’t have cared less,” expresses apathy, as the
speaker cannot care any less. Only choice D reflects the
correct usage. Choice A is incorrect because the narrator
is suggesting that he actually could have cared less than
he already does—the degree of care can be reduced.
Choices B and C are incorrect for the same reason,
though choice C also incorrectly uses “of” instead of
“have.”

43.

The correct answer is A. The previous paragraph ends
following the job interview, and this paragraph begins
with the narrator not getting the job. An effective
transition sentence would chronicle the waiting period
between the interview and the hiring decision, so
choice A is correct. Choice B is incorrect because the
narrator did hear back about the job. Choices C and D
are incorrect because they are outside the scope and
context of the paragraph.

44.

The correct answer is B. The word “eventually,” along
with the narrator’s admission in the first paragraph that
he did not go to the college job counseling office when
first advised to, suggests that the correct term here is
“belated,” or overdue. Thus, choice B is the correct
answer. Choice A is incorrect because “deferred” implies
that he put off the trip with the intention of going at a
later time, and there is no indication that the narrator
did this. Choice C is incorrect because “hastened”
suggests that the narrator made a speedy trip. Choice D
is also incorrect, as “disparaged” means belittled or
criticized, an adjective that doesn’t make sense in the
context of describing his trip to the college job
counseling office.

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Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. C

5. C

9. C

13. D

2. D

6. B

10. B

14. B

3. B

7. B

11. C

15. A

4. B

8. C

12. C

16. 24

1
(1/2)
2
18. 13
4
19.
(4/3)
3
20. 4
17.

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is C. The question asks for Jared’s
goal in steps per day after d days. He increases his goal
by 125 steps each day, so after 1 day it will go up 125(1),
after 2 days it will go up by 125(2), and after d days it
will go up by 125d from his original amount of 950.

2.

The correct answer is D. Use the correct order of
evaluating functions. First evaluate g(3) = 1, then
substitute in f(g(3)) as f(1) to find that f(g(3)) = 3.

3.

The correct answer is B. The formula for exponential
decay is y = a(1 – r)n, where r is the rate of change, n is
the number of times the rate is applied, a is the initial
amount, and y is the amount remaining.

4.

The correct answer is B. First, find half the length of the
horizontal distance, which is 15 ft. Then, use the
Pythagorean theorem to find the length of each of the
slanted sides.
a2 +b2 = c 2
8 2 + 15 2 = c 2
64 + 225 = c 2
289 = c 2
17 = c

5.

The correct answer is C. Since y = 2(x – 4)(x – 6) is
equivalent to the equation, and it is given in the form
y = a(x – b)(x – c), it shows the x-intercepts (4 and 6) as
constants.

6.

The correct answer is B. Find the x- and y-intercepts of
the given equation.
3x + y = 4
3 ( 0) + y = 4
y=4
3x + 0 = 4
4
x=
3
Check the intercepts on the graph of each line to see if
they match the intercepts of the equation in the
problem. Only choice B has intercepts at (0, 4) and
4 
 , 0 .
3 

7.

The correct answer is B. Use the point slope form of a
linear equation to write the slope-intercept form of the
equation:
y − y 1 = m ( x − x 1)
y − 3 = −1( x − 2)
y − 3 = −x + 2
y = −x + 5
Then find the equation that is equivalent to the
slope-intercept form:
3 x + 3 y = 15
3 y = −3 x + 15
y = −x + 5

  814

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Answer Keys and Explanations
8.

The correct answer is C. Using distance = rate × time,
distance
. So, we have
we know that time =
rate

14.

The correct answer is B. The formula for population
growth is P = Po e rt, where P represents the total
population, Po represents the initial population, e
represents the constant value, r represents the rate of
growth, and t represents the time. The “10” in the
problem represents the time, in years, between the two
years of interest—the initial year 1980 and the city’s
population in 1990. There are 10 years between 1980
and 1990.

15.

The correct answer is A. It’s probably easiest to answer
this question by plugging in numbers. We want to select
easy numbers to represent the variables p and q. It is
always a good idea stay away from numbers like 0 and
1, which have special properties; for this question, we
also want to avoid the number 2, since it already
appears in the equation. So, let’s say that p = 4 and q =
3. If we plug these numbers into the original equation,
we get:

10
= 2.5 ⇒ 10 = 2.5( y − x )
y−x
10
= 1.6 ⇒ 10 = 1.6( y + x )
y+x
x − y = 4
This is equivalent to 
 x + y = 6.25
9.

The correct answer is C. Simplify the expression using
the exponent rules:
 1
z = z 2
 

3

3

1

3

1

10.

11.

12.

z

z i

1

=z6
5

1

z =z3 i z2 =z6

z i
3

1
3

z

=

z6
z

5
6

1

=z6

−

5
6

=z

−

2
3

2(4) + 2n
=2
3n
8 + 2n = 6n
8 = 4n
2=n

The correct answer is B. The equation for a parabola
with a vertex at (h, k) is y = a(x – h)2 – k, and if the
y-intercept is 13, then (0, 13) is a point on the parabola,
and 13 = a(0 – h)2 – k. Since 13 = 2(0 – 3)2 – 5, choice B is
correct.

When we plug the numbers 4 and 3 in for the variables
p and q in each of the answer choices, we see that the
expression in choice A works out to be 2; no other
choice works.

The correct answer is C. The amount per each type of
admission is $12 and $17, so the total admission of
$1,079 based upon number of adults and children is
12x + 7y. The total number of people, 117, is represented by x + y.
The correct answer is C.
4 − i 3 − i 11− 7i
×
=
3+ i 3−i
10

p
4
=
=2
q −1 3 −1
16.

The correct answer is 24. To solve this problem, first
isolate x + 1 on one side of the equation. Then, square
both sides:
x +1− 2 = 3

13.

The correct answer is D. Solve the equation:
−6 (t + 1) = 2 (1− 3t ) − 8

x +1 = 5
x + 1= 25
x = 24

−6t − 6 = 2 − 6t − 8
−6 = −6
The equation has infinitely many solutions.

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Answer Keys and Explanations
17.

1
(1/2). Complete the square
2
on the function so that the vertex is readily identifiable:
The correct answer is

19.

The correct answer is

4
(4/3). The equations need to
3

have the same slope but different y-intercepts. The first
equation is already written in slope-intercept form. First,

f ( x ) = x 2 − 2bx + (b 2 + 2b − 1)

rewrite the second equation so that it is in slope-

= ( x 2 − 2bx + b 2 ) + (b 2 + 2b − 1) − b 2

intercept form, then find the value for t that make the

= ( x − b )2 + (2b − 1)

slope 3. This should make the y-intercept different
than 7.

The vertex is (b, 2b – 1), and the parabola opens upward.

4 x − ty = 5
−ty = −4 x + 5
−4 x + 5
y=
−t
−4 x 5
+
y=
−t −t

The graph will have one x-intercept, which coincides
with the vertex, if and only if 2b – 1 = 0. That is, when
1
b= .
2
18.

The correct answer is 13. To find the value of c, divide
the numerator by the denominator using either long
division or synthetic division. Remember that the
remainder can be written as a fraction, with the
remainder as the numerator and the divisor as the
denominator.

So,
−4
=3
−t
−4 = 3t
4
t=
3

3 x − 13R21
3 x 2 − 4 x − 18
= x + 3 3 x 2 − 4 x − 18
x +3

)

To check that the y-intercept is not 7:

Here, the remainder is 21, so the fraction is equal to
21
3 x − 13 +
. Set this equal to the expression in the
x +3
equation to find that c = 13.

5
5
=
−t − 4
3
 3
= 5 − 
 4
15
=−
4

3 x 2 − 4 x − 18
21
= 3 x − 13 +
x +3
x +3
c = 13

20.

The correct answer is 4. Use the formula for the
volume of a sphere and of a cone and set the formulas
equal to each other since their volumes are equal. Then
h
solve for the value of .
r
Vcone = Vscoop
1 2
4
πr h = πr3
3
3
2 
4
3 πr3 
3

h=
π r
h = 4r
h
=4
r

  816

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Answer Keys and Explanations
Section 4: Math Test—Calculator

1. C

9. A

17. C

25. B

33. 36

2. B

10. C

18. B

26. C

34. 800

3. D

11. B

19. A

27. C

35. 3.75

4. B

12. B

20. C

28. C

36. 29

5. A

13. A

21. A

29. D

37. 1 or 3

6. B

14. C

22. B

30. A

38. 3.32

7. D

15. A

23. A

31. 2.5

8. B

16. C

24. C

32. 9

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is C. We must first determine how
many feet the insect travels in an average month. Then
we can determine how many months it will take for the
insect to travel 560 feet. To determine the number of
feet the insect travels per month, we divide the yearly
total by 12:

3.

Littletown is 210, and the number of females in
Smalltown is 195. The probability of choosing a male
210
, and the probability of
who lives in Littletown is
785
195
. The
choosing a woman who lives in Smalltown is
785
probability of choosing one or the other is the sum of

1, 680
= 140
12

The insect travels 140 feet each month. To determine
how many months it would take the insect to travel 560
feet, we divide the total number of feet (560) by the
number of feet that the insect travels in a month (140):
560
=4
140
Traveling at a rate of 140 feet per month, it would take
the insect 4 months to travel 560 feet.
2.

The correct answer is B. The question asks for the
number of books that will be renewed if the library
loans 25,000 books. Use a proportion to solve.
18
x
=
75 25, 000
75 x = 18(25, 000 )
18(25, 000 )
x=
75
x = 6 , 000

The correct answer is D. The number of males in

the individual probabilities:
210 195 405 81
+
=
=
785 785 785 157
4.

The correct answer is B. There are 52 weeks in a year,
so multiplying 0.36 inches by 52 weeks is 18.72 inches. If
the tree grows 18.72 inches in a year, then it will grow
18.72 × 10 = 187.2 inches in 10 years.

5.

The correct answer is A. The total amount that Glen
earns in one day is 10.25h where h is the number of
hours Glen works, and 3(12.50) is three times what he
spends commuting. If he wants to earn at least three
times what he spends commuting, then choice A is the
only answer that represents the situation.

6.

The correct answer is B. If Peter spent x hours, then
Nadia spent x + 7 hours on math homework, and
together they spent x + (x + 7) = 35 hours. Solve for x:
x + ( x + 7) = 35
2 x + 7 = 35
2 x = 28
x = 14

Peterson's SAT® Prep Guide 2017

  817

Answer Keys and Explanations
7.

The correct answer is D. Since c is 22 percent of e, c
equals (e × 0.22), or = 0.22e. Likewise, because d is 68
percent of e, d equals (e × 0.68), or = 0.68e. To find the
value of d – c in terms of e, we can set up an equation:

11.

The correct answer is B. Read the graph and look for
where the line has a vertical coordinate of $400. The
closest approximation is 58 hats.

12.

The correct answer is B. The x-axis of the graph shows
the number of hats sold, and the y-axis shows the
amount of money raised. Consequently, the slope of the
line shows the amount of money received per hat.

13.

The correct answer is A. A sample size of 18 people is
not large enough to make a conclusion for a city of
38,000. The sample population was randomly selected,
the size of the city population alone doesn’t affect the
reliability, and the number of people with no preference
does not affect the reliability.

14.

The correct answer is C. When the mean and median
of a set of data are not the same, outliers tend to affect
the mean more than the median. If some income values
are much greater than the others, the mean will be
greater than the median.

15.

The correct answer is A. The amount of CDs sold would
be equal to the number of days in the sale (j) times the
number of neighbors (h) times the average number of
CDs sold (x), or jhx. To determine the number of CDs
that will be left after the total number of CDs, (jhx), are
sold, we subtract jhx from 1,230. This value can be
expressed as 1,230 – jhx.

16.

The correct answer is C. The formula that is useful for
this problem is the formula for projectile motion:
y = 0.5at2 + vt + h, where a is the acceleration, v is the
upward velocity, h is the initial height, t is the time in
seconds, and y is the height after t seconds. Here, the
coefficient, v, equals 50, so the correct answer must be
choice C.

17.

The correct answer is C. First, write inequalities that
represent the price for each company. Then let the price
from Company J be less than the price for Company K
and solve the inequality.

d − c = ( 0.68e − 0.22e )
d − c = 0.46e
8.

The correct answer is B. Graph the inequalities and
look for where they overlap, or substitute each point
into both inequalities to determine which point satisfies
both inequalities.
4

(–4, 4)

2

–6

–4

–2

0

2

–2

Only choice B is correct:
2 x − 9 y < 12
2(−4) − 9(4) < 12
−8 − 36 < 12 		
9.

−3 x + 4 y > 5
−3(−4) + 4(4) > 5
12 + 16 > 5

The correct answer is A. The question is just asking us
to substitute the value that we are given for n and then
to simplify the expression. We’re asked to provide an
answer in terms of m or, in other words, an answer that
contains the variable m. Let’s see what we get when we
substitute 7 for n:
2m (16 − 6n) = 2m 16 − 6 (7)

Company J = 0.15 x + 19
Company K = 0.10 x + 30
0.15 x + 19 < 0.1x + 30
0.05 x < 11
x < 220

= 2m (16 − 42)
= 2m (−26)
= −52m
10.

  818

The correct answer is C. The total amount that she has
raised is $145. If she gets $15 from each additional
donor, then the total contributions will be equal to
145 + 15x, where x is the number of contributions she
gets from this point forward.

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18.

The correct answer is B. The daily rental cost for the
truck is the y-intercept. The slope of the graph of this
relationship is the per mile cost. The total cost for the
miles driven in the truck is 0.12x. The total cost for
driving the truck the entire distance is 0.12x + 25.

Answer Keys and Explanations
19.

The correct answer is A. To find the conditional

triangle, TQP, is TQ, which measures 15. We also know
that all corresponding sides in the larger triangle, SQR,
are 4 times longer than the ones in the smaller triangle,
TQP, so SQ measures 4 times longer than TQ, or
4 × 15 = 60.

probability that a randomly chosen house in Town B is a
colonial house, first find the total number of houses that
are in Town B: 62 + 65 + 43 + 32 = 202. Then write and
simplify a ratio of colonial houses in Town B to the total
65
.
number of houses in Town B in the survey:
202
20.

23.

The correct answer is C. Reduce the set of outcomes

1=

under consideration to only those houses that are either

x 2 − 14 x + 37 = 0
Now use the quadratic formula with a = 1, b = 14, and
c = 37 to simplify:

The correct answer is A. Set f(x) equal to g(x) and solve
the equation that results to get the x-coordinates of the
points of intersection:

14 ± (−14)2 − 4(37)
2
14 ± 196 − 148
x=
2
x =7±2 3
x=

b 2 − ( x + a) 2 = ( x + a) 2 − b 2
2b 2 = 2( x + a) 2

24.

So, the x-coordinates are –a – b and –a + b. The
difference between these two numbers is:

The correct answer is B. The key to solving this
geometry problem is to recognize that the figure
contains two similar triangles. We know that the
triangles are similar because their corresponding angles
are equal (x = x, y = y, and the two right angles are
equal). Since the triangles have equal corresponding
angles, we know that the sides are in proportion to one
another.
We want to determine the ratio between the corresponding sides in the larger triangle, SQR, and the
smaller triangle, TQP. We can do this by comparing the
two corresponding sides for which we have measures.
We’re given the length of QP in the smaller triangle as
11.5. We’re also given the length of its corresponding
leg from the larger triangle, QR, as 46. How many times
larger is QR than QP? If we divide 46 by 11.5, we see that
QR is 4 times larger than QP.
The question asks us to determine the length of SQ,
which is a side of the larger triangle, SQR. We know that
the measure of its corresponding side in the smaller

The correct answer is C. Use the circumference of the
circle to find the radius.
C = 2π r
572π = 2π r
286 = r

(–a + b) – (–a – b) = –a + b + a + b = 2b.
22.

 3
4 
+
 x − 4 x – 3 

x 2 − 7 x + 12 = 3 x − 9 + 4 x − 16

Of these, 62 + 43 = 105 are from Town B. So, the
105
.
probability is
233

b 2 = ( x + a) 2
±b = x + a
x = −a ± b

3
4
+
x −4 x –3

( x − 3) ( x − 4) = ( x − 3) ( x − 4)

Cape Cod or Ranch; this gives a total of 233 outcomes.

21.

The correct answer is A. First, rewrite the equation as a
quadratic one:

Then use the measure of the central angle and the
radius to find the area of the sector:
3π
2
A = 4 π (r )
2π
3
2
A = π (286)
8
61,347π
A=
2
25.

The correct answer is B. If w < −1 and v > 1, then the
x-intercepts of the graph must be greater than 1 and
less than −1.

26.

The correct answer is C. If a is any value less than 0,
then the border of x + ay < –3 will intersect the y-axis,
and there will be solutions in quadrant I. Eliminate
choice A. If a is greater than 2.5, then there will be
solutions in quadrant IV. Eliminate choice D. If 0 ≤ a ≤
2.5, then there are only solutions in quadrants II and III.
Since a can take on values other than 0, choice B is
incorrect.

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Answer Keys and Explanations
27.

The correct answer is C. The slope increases between
the points, so it is not a linear relationship. Eliminate
choices A and B. An exponential relationship uses the
x-variable for the exponent. Eliminate choice D.
Checking approximate points (32, 13), (80, 54) and
(96, 75) using choice C:

32.

4s − 3 < 2
4s < 5
5
s<
4

y = 4.82 (1.03) → 4.82 (1.03) → y ≈ 12.4
x

32

Since s is an integer, s must be 1, and so 4s + 5 = 4(1) + 5
= 9. The greatest integer value that is less than 10 is 9.

y = 4.82 (1.03) → 4.82 (1.03) → y ≈ 51.3
x

80

y = 4.82 (1.03) → 4.82 (1.03) → y ≈ 82.3
x

96

33.

The equation approximately models the data, so choice
C is correct.
28.

29.

30.

The correct answer is 9. Solve for the expression
requested in the inequality, then interpret the answer in
the context of the question asked:

2a + 2b = 16

The correct answer is C. The relationship between the
initial speed and the stopping distance is modeled by
exponential growth because the slope of the line
connecting any two points increases as the initial speed
increases. While the points are close to a line, an
exponential growth curve better approximates the
relationship.

− (2a − b ) = −(7)
3b = 9
b=3
Insert b = 3 into the first equation:
2 a − ( 3) = 7
2a = 10
a=5

The correct answer is D. The 95% confidence that the
margin of error is ± 4% is important, and choices A and
B ignore the confidence interval. Choice C is not correct
because there are likely people who don’t know or have
no opinion on whether there should be stricter
emissions standards for power plants. Only choice D
accurately uses the confidence interval and the data
given in the problem.
The correct answer is A. Use completing the square to
find the coordinates of the center of the circle. Separate
the equation x- and y-terms:
x 2 + y 2 − 10 x + 4 y = −20
x 2 − 10 x + y 2 + 4 y = −20

( x 2 −10 x + 25) + ( y 2 + 4 y + 4) = −20 + 25 + 4
( x − 5) + ( y + 2)
2

2

=9

The correct answer is 36. Use the method of combination to determine the values of a and b. Start by
subtracting the first equation from the second equation:

Now you are ready to plug both values into the
expression in question:
3a + 7b = 3 (5) + 7 (3)
= 15 + 21
= 36
34.

The correct answer is 800. The formula for population
growth is given in terms of n, the number of years. In
order to solve this problem, plug the value of n, in this
case 54, into the formula and calculate the value of the
n

expression 100(2)18 :
n

Population (in millions) after n years = 100(2)18
54

The center is (5, −2), because the standard form of the
circle is (x – h)2 + (y − k)2 = r2.
31.

The correct answer is 2.5. Write an equation to
represent the situation, and then solve:
16.25 = 2.5 (2) + 4.5 x
11.25 = 4.5 x
2.5 = x

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= 100(2) 18
= 100(2)3
= 800

Answer Keys and Explanations
35.

The correct answer is 3.75. Read the question
carefully; it asks for the difference in the prices of one
object, not the difference between the amounts of
money they made, or any other quantity.

37.

Since Paul sold four pieces of pottery for $85, he made
85
y = = $21.25 per piece. Sally made $40 more than
4
Paul did for all of her pieces, so she made $85 + $40 =

2 x + 5 = −2( x + 1)2 + 3
2 x + 5 = −2 x 2 − 4 x − 2 + 3
0 = −2 x 2 − 6 x − 4
0 = −2( x + 2)( x + 1)
x = −1, −2
y = 2(−1) + 5 = 3
or
y = 2(−2) + 5 = 1

$125 in total. Since she sold five pieces, she made
125
x=
= $25.00 per piece. Per piece, Sally made x – y =
5
$25 – $21.25 = $3.75 more than Paul did. The correct
answer is 3.75.
36.

The correct answer is 29. First, find the original
amount using a percent proportion. Then add 4 to find
the new total.
16 4
=
100 x
16 x = 400
400
x=
16
x = 25
25 + 4 = 29

The correct answer is 1 or 3. First, combine the
equations by substituting 2x + 5 for y in the second
equation. Then solve for x. Next, substitute the x-values
back in and solve for y:

38.

The correct answer is 3.32. Let x be the GPA for the
year 2017. Compute the average of 3.5, 3.5, 3.5, 3.5, 3.5,
and x:

3.5(5) + x
= 3.47
6
17.5 + x = 20.82
x = 3.32

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Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
The following is an analysis of the passage by Catherine Anderson, noting how the writer used evidence, reasoning, and stylistic or
persuasive elements to support her claims, connect the claims and evidence, and add power to the ideas she expressed. Check to
see if you evaluated the passage in a similar way.

  822

1

Visit the website of designer Michael Graves, and
you’ll be greeted with the words “Humanistic Design =
Transformative Results.”

1

Anderson lays the groundwork for the validity of her argument
by referring the reader to an authoritative source on this
subject—the website of Michael Graves.

2

The mantra can double as Graves’ philosophy. For
Graves—who passed away at 80 earlier this month—paid
no heed to architectural trends, social movements or the
words of his critics.

2

The writer uses evocative words and phrases such as “mantra”,
double as, “philosophy,” “paid no heed,” and “trends”.

3

Instead, it was the everyday human being—the
individual—who inspired and informed his work.

3

The writer clearly states her central argument.

4

During a career that spanned over 50 years, Graves held
firm to the belief that design could effect tremendous
change in people’s day-to-day lives. From small-scale
kitchen products to immense buildings, a thread runs
throughout his products: accessible, aesthetic forms that
possess a sense of warmth and appeal.

4

Anderson continues using evocative phrases: “held firm,”
“effect tremendous change,” “immense buildings,” “a thread
runs throughout,” a “sense of warmth and appeal.”

5

Early in his career, Graves was identified as one of the
New York Five, a group of influential architects who
whole-heartedly embraced Modernism, the architectural
movement that subscribed to the use of simple, clean
lines, forms devoid of embellishments and modern
materials such as steel and glass.

5

She provides historical context by discussing Graves’ early
career and establishing his status as a Modernist architect. She
also defines Modernism for the reader.

6

However, Graves is best described as a Post-Modernist.

6

7

He eschewed the austerity of Modernism and its belief
that “less is more,” instead embracing history and
references to the past.

The writer expands her historical context by claiming that
Graves was really a Post-Modernist. She then explains exactly
what this means.

8

He rejected the notion that decoration, or ornament, was
a “crime” (as Austrian architect Adolf Loos wrote in 1908);
rather, he viewed it as a way for his architecture to convey
meaning.

7

The writer uses evocative phrases to paint pictures for the
reader: “eschewed the austerity,” “embracing history,” “rejected
the notion.”

8

Anderson enlivens her writing with a vivid word (crime) used
by an authority and cites her source.

9

Anderson quotes an authoritative source to support her claim
that Graves was a Post-Modernist.

10

The writer builds on this quotation to advance her argument
that Graves was a Post-Modernist.

9

As the noted architectural historian Spiro Kostof
explains in his book A History of Architecture: Settings and
Rituals, “Post Modernists turn to historical memory …
to ornament, as a way of enriching the language of
architecture.”

10

…Along these lines, Graves

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Answer Keys and Explanations
11

loathed the idea of intellectualizing his structures.
Instead, he sought to make them accessible,
understandable and poignant to all passersby. …

11

The writer uses evocative phrases to make her argument vivid:
“loathed the idea,” “intellectualizing his structures,” “poignant
to all passersby.”

12

In addition to designing buildings, Graves embarked
upon a long and highly successful partnership with the
Italian kitchenware company Alessi …

12

Anderson points out that Graves did more than design
buildings, mentioning his partnership with the Italian
kitchenware company Alessi.

13

Graves’ most famous Alessi design is his iconic
teakettle … which had a cheerful red whistling bird and
sky-blue handle. On sale since 1985, the best-selling
product is still in production today.

13

She also mentions one of Graves’ famous creations for Alessi
and points out that it sold extremely well.

14

In 1999, Minneapolis-based discount retail giant Target
approached Graves with an offer to design a line of
kitchen products, ranging from toasters to spatulas.

14

Continuing her discussion of Graves’ non-architectural
creations, the writer refers to his work designing kitchen
products for Target.

15 While some might have shied away from having their
work associated with a mega-corporation like Target,
Graves wholly embraced the project. . . .

15

The writer anticipates a possible negative reaction to this
work, pointing out that Graves “embraced” it.

16

In all, Graves’ collaboration with Target would last 13
years; during this time, the designer would become a
household name, with millions of units of his products
appearing in American homes.

16

Anderson legitimizes Graves’ work with Target, saying
his creations sold millions of units and that he became “a
household name.”

17

Many of Graves’ designs for Target—his spatula, can
opener and ice cream scoop—had chunky, sky-blue
handles. Other appliances that were white . . . were
sprinkled with touches of color. … Black and beige had
no place in Graves’ palette.

17

She gives the reader a strong sense of Graves’ practical,
everyday Target creations, naming specific products and
describing what they looked like.

18 The option to select a better-looking product with a
slightly higher price versus the same article but with a
less expensive, nondescript appearance is now the norm
for most consumers: good design (and function) are part
and parcel of the customer experience

18

Anderson cites the significance of Graves’ work with Target,
pointing out that better design in everyday products has
become the norm.

19

(nowhere is this more evident than in Apple’s rise to
dizzying heights as arguably one of the world’s most
valuable brands).

19

She supports this claim by citing Apple as an example of a
company that routinely offers customers good design in its
products.

20

It’s an idea that’s democratic in nature, and thinking
about design through this lens led Graves to create
thoughtful, appealing and affordable products for the
masses. …

20

The writer reasserts the importance of Graves’ place in the
movement to create “affordable products for the masses.”

21

As Graves’ popularity rose, his critics leveled

21

The writer provides historical context to trace the negative
reaction to Graves’ work with Target.

22

blistering commentaries about what they deemed
a precipitous fall from grace—from a “trend beyond
compare” to a “stale trend,” as

22

She brings this reaction to life using evocative phrases:
“blistering commentaries, precipitous fall from grace,
commodified design, drew the disdain of those who once
lauded his works.”

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Answer Keys and Explanations
architecture critic Herbert Muschamp noted in a
1999 New York Times article. The notion that he had
commodified design—and had somehow “cheapened”
it—drew the disdain of those who once lauded his works.

23

The writer cites a source to support her claim that there was
a negative reaction to Graves’ Target products.

24 Yet Graves remained true to his beliefs even into the last
phase of his life. In 2003, after an illness left him paralyzed
below the waist, he realized that the design of hospitals
and equipment . . . could be redesigned and made
more functional, comfortable and visually appealing.
He then went on to improve ubiquitous devices such as
wheelchairs and walking canes. …

24

Anderson provides additional historical context for
Graves’ later designs for common things and gives specific
examples.

25

Consumers may not have ever known his architecture or
what the critics thought of his work (or even realized they
were buying one of his products). Graves didn’t seem to
mind. His goal was to provide well-designed items for
everyday use rather than impress his detractors.

25

The writer provides psychological insight into Graves’
personality and reasserts his primary goal: “to provide welldesigned items for everyday use.”

26

As he told NPR in 2002, “It’s the kind of thing where you
pick something up or use it with a little bit of joy … it
puts a smile on your face.”

26

The writer concludes her argument with a quotation from
Graves that supports her claim that his primary concern was
quality design for the everyday human being.

23

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Answer Key and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Catherine Anderson.

High-Scoring Essay
Catherine Anderson is clearly a fan of Michael Graves’s architecture and product design. Anderson identifies the everyday
human being as Graves’s inspiration. She gives a history of Graves’ work, explaining how his focus on people inspired him.
Anderson’s word choices and descriptions bring Graves’s products to life. Anderson’s words are as warm and appealing as
the products she describes. Supporting her descriptions with a history of Graves’s designs and biographical details convinces
readers to admire the products he designed and, perhaps, to buy one that fits in their own kitchens.
Anderson tells readers that Graves’s career started as an architect in New York 50 years ago. She provides historical context
by identifying Graves as one of an elite group of Modernist architects who designed simple, plain buildings constructed of
the modern materials steel and glass. Because her description of Modernist architecture sounds cold and empty, Anderson
hastens to say that Graves was actually a Post-Modernist architect whose creations were less plain and more inviting. He
used embellishments in his architectural designs to convey meaning, which sounds more warm and comforting than the
Modernist architectural style she described with the words plain, steel and glass, and austerity.
To support her statements, Anderson cites a well-known architectural expert who describes Post-Modernist architecture as
enriched by ornamentation. She then uses appealing words to attract readers to Graves’s work—accessible, understandable,
and poignant.
Graves didn’t design architecture only. He also designed common items, such as teakettles and spatulas, for common people.
His most famous design is a quirky teakettle that has a sky-blue handle and a bright red bird that whistles when the water is
hot enough to make tea. Just the image Anderson created of the whistling bird on the teakettle makes Graves’s work sound
fun and appealing. The kitchen products Graves designed are sold by Target, a store where the people who inspired Graves
could afford to shop. They must be buying his products because millions of them have been purchased at Target and are still
selling today.
While Graves’s popularity rose among Target shoppers, it dropped among architecture critics. Anderson informs readers of
the critics’ changing attitudes by quoting their comments such as “stale trend” and “cheapened.” Graves, however, heroically
“remained true to his beliefs” by continuing to design attractive products that could be bought by average people.
In 2003 an illness made Graves a paraplegic. Instead of becoming bitter, like many people would have in the same situation,
Graves looked around at the poorly designed medical products and decided that he could make improvements. Even a
hospital environment benefited from his design abilities. He created products, such as wheelchairs and canes, that Anderson
said were “more functional, comfortable and visually attractive.”
Anderson closed the article by quoting Graves’s comment that he hoped his products would make people smile. Anderson
showed that throughout his life, Graves’s main concern was creating designs for the average person. Just as he had hoped, his
products have inspired, and continue to inspire, joy in the people who inspired him—especially when making tea.

Low-Scoring Essay
Catherine Anderson started the article by focusing on Michael Graves’s mantra of “Humanistic Design = Transformative
Results.” This means that focusing on people can make things better.
Michael Graves focused on people to design buildings and things they could use like teakettles and wheelchairs. Because
Michael Graves likes people, he designed things that they would like, things that would make them happy.
Catherine Anderson says his products are warm and appealing. She describes a teakettle that’s fun to use because it whistles.
The buildings he designed have historical meaning because he added a lot of decorations. He said it’s not a crime to build
decorated buildings.

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Answer Key and Explanations
Michael Graves worked with Alessi to design attractive kitchen products that people liked a lot, like the whistling teakettle.
He used warm colors like red to make it more appealing. Catherine Anderson describes his kitchen products as “chunky” and
colorful. This makes them sound like things everyone would want to have. Because millions were sold at Target, he probably
made a lot of money on them. That’s a good reason to ignore the critics who didn’t like his designs. The critics said his kitchen
products were “stale,” which is a clever food-related way to say they were old and boring. Regardless of the critics, his stuff is
popular.
Michael Graves was pretty old when he got sick and couldn’t walk. Because he couldn’t walk, he designed wheelchairs and
canes that he and other people could use. Catherine Anderson says they’re “functional, comfortable and visually appealing.” If
Target sold them, they would probably be as popular as his teakettle.
Michael Graves died in 2015 when he was 80 years old. His buildings and products followed his mantra of “Humanistic Design
= Transformative Results.” He made things better by focusing on people. He improved a lot of things that he designed and
made a lot of people happy. Catherine Anderson proved that the things he made were attractive and made people happy.

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Computing Your Scores
COMPUTING YOUR SCORES
Now that you’ve completed this practice test , it’s time to compute your scores. Simply follow the instructions on the following pages,
and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation as
possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then you’ll calculate the total score. It sounds a little confusing, but we’ll take
you through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test.
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for
wrong answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page 830. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1.  	 Count the number of correct answers you got on the questions in Section 3: Math Test—No Calculator and Section 4:
Math Test—No Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2.  	 Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—No Calculator.
3.  	 Use the Raw Score Conversion Table 1: Section and Test Scores on page 830 and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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Computing Your Scores
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test sections that focus on linear equations and inequalities.

• Add up your total correct answers from these sections:
•
•

ºº Math Test—No Calculator: Questions 1, 6, 7, 11, 13, 14, 17, 19
ºº Math Test—Calculator: Questions 5, 6, 8, 10, 15, 17, 18, 26, 31–33
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: None
ºº Math Test—Calculator: Questions 1–4, 7, 11–14, 19, 20, 27–29, 35, 36, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability to
progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations, and
interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: 2, 3, 5, 8–10, 15, 16, 18
ºº Math Test—Calculator: Questions 9, 16, 21, 23, 25, 34, 37
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Passport to Advanced Math subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 1, 2, 5, 6, 10–13, 17, 19–22, 26, 27, 29, 30, 32, 33, 37, 39, 41, 43, 44

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 3, 4, 7–9, 14, 15, 18, 21–25, 28, 29, 31, 34–36, 38, 40, 42

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Standard English Conventions
subscore.

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Computing Your Scores
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 6, 9, 21, 22, 31, 36, 41, 42, 51, 52
ºº Writing and Language Test: Questions 2, 6, 17, 20, 26, 30, 39, 44
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts.

• Add up your total correct answers from Sections 1 and 2:

•

ºº Reading Test: Questions 5, 8, 16, 20, 26, 30, 35, 39, 47, 50
ºº Writing and Language Test: Questions 1, 5, 11, 12, 19, 27, 32, 43
ºº Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 831 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 12–22, 33–42
ºº Writing and Language Test: Questions 26, 27–30, 32, 33
ºº Math Test—No Calculator: Question 14
ºº Math Test—Calculator: Questions 3, 13, 14, 19, 20, 29, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 832 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 1–11, 23–32
ºº Writing and Language Test: Questions 12, 13, 16, 17, 19, 20
ºº Math Test—No Calculator: Question 3
ºº Math Test—Calculator: Questions 1, 4, 16, 24, 27, 28, 34
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 832 to determine your Analysis in Science cross-test
score.

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Computing Your Scores

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

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TOTAL SAT® SCORE
(400–1600)

Computing Your Scores

Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

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16

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14

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14

24

15

Peterson's SAT® Prep Guide 2017

  831

Computing Your Scores
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

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27

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34

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27

35

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28

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36

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38

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16

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28

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40

  832

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Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

Computing Your Scores
Conversion Equation 3: Cross-Test Scores

ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

ANALYSIS IN SCIENCE

RAW SCORE

QUESTIONS

RAW SCORE

Reading Test

12–22, 33–42

1–11, 23–32

Writing and
Language Test

26, 27–30, 32, 33

12, 13, 16, 17, 19, 20

Math Test—No
Calculator

14

3

Math
Test—Calculator

3, 13, 14, 19, 20,
29, 38

1, 4, 16, 24, 27, 28,
34

TOTAL

ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (10–40)

Peterson's SAT® Prep Guide 2017

  833

Practice Test 4—Answer Sheet
Section 1: Reading Test
1.

12.

23.

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Section 2: Writing and Language Test
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Section 3: Math Test—No Calculator
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Peterson's SAT® Prep Guide 2017

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Practice Test 4—Answer Sheet
Section 3: Math Test—No Calculator
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Section 4: Math Test—Calculator
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Practice Test 4—Answer Sheet
Section 5: Essay
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Practice Test 4—Answer Sheet

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Practice Test 4—Answer Sheet

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Practice Test 4—Answer Sheet

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  840

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Practice Test 4
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

Questions 1–10 are based on the following
passage and supplementary material.
From his humble beginnings, Herbert Hoover made his fortune in
the mining industry. He earned his reputation as a humanitarian
and skilled administrator during and after World War I and later
served as Secretary of Commerce under both Presidents Harding
and Coolidge. In 1928, he was nominated for president by the
Republican Party. The following is an excerpt from a speech he gave
at the end of his campaign against the Democratic nominee, New
York Governor Alfred E. Smith.

Line
5

10

15

20

25

During one hundred and fifty years we have builded
up a form of self government and a social system which
is peculiarly our own. It differs essentially from all others
in the world. It is the American system. . . . It is founded
upon the conception that only through ordered liberty,
freedom and equal opportunity to the individual will his
initiative and enterprise spur on the march of progress.
And in our insistence upon equality of opportunity has
our system advanced beyond all the world.
During [World War I] we necessarily turned to the
government to solve every difficult economic problem.
The government having absorbed every energy of our
people for war, there was no other solution. For the preservation of the state the Federal Government became a
centralized despotism which undertook unprecedented
responsibilities, assumed autocratic powers, and took
over the business of citizens. To a large degree, we
regimented our whole people temporally into a socialistic state. However justified in war time, if continued
in peace-time it would destroy not only our American
system but with it our progress and freedom as well.
When the war closed, the most vital of issues both
in our own country and around the world was whether
government should continue their wartime ownership
and operation of many [instruments] of production
and distribution. We were challenged with a . . . choice
between the American system of rugged individualism
and a European philosophy of diametrically opposed

30

35

40

45

50

55

60

65

doctrines, doctrines of paternalism and state socialism.
The acceptance of these ideas would have meant the
destruction of self-government through centralization
. . . [and] the undermining of the individual initiative
and enterprise through which our people have grown
to unparalleled greatness. . . .
I would like to state to you the effect that . . .
[an interference] of government in business would
have upon our system of self-government and our
economic system. That effect would reach to the daily
life of every man and woman. It would impair the very
basis of liberty and freedom. . . .
Let us first see the effect on self-government.
When the Federal Government undertakes to go
into commercial business it must at once set up the
organization and administration of that business, and
it immediately finds itself in a labyrinth. . . . Commercial
business requires a concentration of responsibility.
Our government to succeed in business would need
to become in effect a despotism. There at once begins
the destruction of self-government. . . .
Liberalism is a force truly of the spirit, a force
proceeding from the deep realization that economic
freedom cannot be sacrificed if political freedom is to
be preserved. [An expansion of the government’s role
in the business world] would cramp and cripple the
mental and spiritual energies of our people. It would
extinguish equality and opportunity. It would dry up
the spirit of liberty and progress. . . . For a hundred
and fifty years liberalism has found its true spirit in
the American system, not in the European systems.
I do not wish to be misunderstood. . . . I am
defining general policy. . . . I have already stated that
where the government is engaged in public works for
purposes of flood control, of navigation, of irrigation,
of scientific research or national defense . . . it will at
times necessarily produce power or commodities as
a by-product.

CONTINUE
Peterson's SAT® Prep Guide 2017

  841

Practice Test 4

70

75

80

85

Nor do I wish to be misinterpreted as believing
that the United States is a free-for-all and devil-takethe-hindmost. The very essence of equality of opportunity and of American individualism is that there shall
be no domination by any group or [monopoly] in this
republic. . . . It is no system of laissez faire. . . .
I have witnessed not only at home but abroad
the many failures of government in business. I have
seen its tyrannies, its injustices, its destructions of
self-government, its undermining of the very instincts
which carry our people forward to progress. I have
witnessed the lack of advance, the lowered standards
of living, the depressed spirits of people working under
such a system. . . .
And what has been the result of the American
system? Our country has become the land of opportunity to those born without inheritance, not merely
because of the wealth of its resources and industry but
because of this freedom of initiative and enterprise.
Russia has natural resources equal to ours. . . . But she has
not had the blessings of one hundred and fifty years of
our form of government and our social system.

7

4

5

4
3

2

4

3

A.

Government involvement in private businesses is
justified during wartime, but not at other times.

B.

Government cannot solve economic problems and
should never be involved in private business.

C.

Government stifles personal liberties and prevents
businesses from making any profit.

D.

Government is responsible for ensuring that private
businesses make a profit.

Why did Hoover believe it was necessary to strengthen the
federal government during wartime?
A.

The United States was fighting despotism and
therefore had to become despotic.

B.

Only a socialistic government can function during
wartime.

C.

Most resources went toward the war effort,
draining them for other uses in the economy.

D.

Businesses acting by themselves could interfere
with the war effort.

12

13

5
13

8
6

13

Based on the excerpt, which statement is true of Hoover’s
ideas about the government’s role in business?

NH 4
6
VT 4

5
3

3

1

10
10
20

18

45

15

24
29 15
8

38
8 12
12
X9

12
9
X 10 X X
12 14
10 X
X

6

X MA 18
RI 4
CT 7
NJ 14
DE 3
MD 8

Smith
Hoover

This map shows the electoral votes for each state in the presidential election of 1928, which Herbert Hoover won in a landslide.

  842

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Practice Test 4
3

4

Which choice provides the best evidence for the answer to
the previous question?
Lines 10–11 (“During . . . problem.”)

A.

Line 50 (“Liberalism . . . spirit”)

B.

Lines 12–13 (“The government . . . other solution.”)

B.

Lines 53–54 (“An expansion . . . world”)

C.

Lines 13–15 (“For the . . . despotism”)

C.

Lines 55–56 (“It would . . . opportunity.”)

D.

Lines 15–17 (“which undertook . . . citizens”)

D.

Lines 58–59 (“liberalism . . . system”)

How does Hoover’s speech change in lines 60–80 (“I do not
wish . . . under such a system.”)?
A.

He changes his position by stating the opposite of all
of the ideas he had stated in the passage previously.

B.

He shows he wants to be understood by repeating
the main points of everything he had discussed in
the passage previously.

D.

6

Which choice provides the best evidence for the answer to
the previous question?

A.

C.

5

7

He shows that his beliefs are the beliefs of all
Americans, and are therefore, moderate and widely
acceptable.
He emphasizes that he wants to clarify his position
and does so by providing details about his
philosophy.

What is the most likely reason that Hoover includes lines
67–69 in his speech?
A.

To appeal to more voters

B.

To ensure his words are not twisted

C.

To soften his position

D.

To provide context for his views

8

9

Based on the map on the previous page, what is a landslide?
A.

A popular vote

B.

A close contest

C.

A hard-won election

D.

A decisive victory

As used in line 45, “labyrinth” most nearly means
A.

maze.

B.

cave.

C.

bind.

D.

landmine.

10 As used in line 18, “regimented” most nearly means
A.

organized.

B.

militarized.

C.

bullied.

D.

established.

According to the passage, Hoover believed liberalism to be
A.

completely exclusive to the American system.

B.

more prevalent in Europe than it is in America.

C.

a defining characteristic of the American system.

D.

a much better philosophy than conservatism.

CONTINUE
Peterson's SAT® Prep Guide 2017

  843

Practice Test 4
Questions 11–21 are based on the following
passages and supplementary material.
Passage 1 is an excerpt from a letter written by Harriet Beecher
Stowe, the abolitionist and author of the best-selling novel Uncle
Tom’s Cabin (1852). The book describes the horrors of slavery and is
said to have helped promote the abolitionists’ cause. The recipient
of the letter, Mrs. Follen, a fellow abolitionist, was also a poet, editor,
and novelist.
Passage 2 is an excerpt from the memoir of Frederick Douglass,
an active abolitionist who had escaped from slavery in 1838. After
gaining his freedom, Douglass published Narrative of the Life of
Frederick Douglass, An American Slave, Written by Himself (1845).
The passage describes how he planned his escape.

every statement in Uncle Tom’s Cabin. I must confess that
till I began the examination of facts in order to write this
30 book, much as I thought I knew before, I had not begun
to measure the depth of the abyss. The law records of
courts and judicial proceedings are so incredible as to fill
me with amazement whenever I think of them. It seems
to me that the book cannot but be felt, and, coming
35 upon the sensibility awaked by the other, do something.
I suffer exquisitely in writing these things. It may be truly
said that I suffer with my heart’s blood. Many times in
writing Uncle Tom’s Cabin I thought my heart would fail
utterly, but I prayed earnestly that God would help me
40 till I got through, and still I am pressed beyond measure
and above strength. . . .
PASSAGE 2

PASSAGE 1

Recollection of Frederick Douglass

Harriet Beecher Stowe, from a letter to Mrs. Follen (1853)

Line
5

10

15

20

25

  844

I had two little curly-headed twin daughters to
begin with, and my stock in this line was gradually
increased, till I have been the mother of seven children,
the most beautiful and the most loved of whom lies
buried near my Cincinnati residence. It was at his dying
bed and at his grave that I learned what a poor slave
mother may feel when her child is torn away from her.
In those depths of sorrow which seemed to me immeasurable, it was my only prayer to God that such anguish
might not be suffered in vain. There were circumstances
about his death of such peculiar bitterness, of what
seemed almost cruel suffering, that I felt that I could
never be consoled for it unless this crushing of my own
heart might enable me to work out some great good
to others . . .
I allude to this here because I have often felt that
much that is in that book (“Uncle Tom”) had its root in
the awful scenes and bitter sorrows of that summer. It
has left now, I trust, no trace on my mind except a deep
compassion for the sorrowful, especially for mothers
who are separated from their children. . . .
I am now writing a work which will contain,
perhaps, an equal amount of matter with Uncle Tom’s
Cabin. It will contain all the facts and documents upon
which that story was founded, and an immense body of
facts, reports of trial, legal documents, and testimony of
people now living South, which will more than confirm

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. . . It is impossible for me to describe my feelings
as the time of my contemplated start grew near. I had a
number of warm-hearted friends in Baltimore,—friends
that I loved almost as I did my life,—and the thought of
being separated from them forever was painful beyond
expression. It is my opinion that thousands would
escape from slavery, who now remain, but for the strong
cords of affection that bind them to their friends. The
thought of leaving my friends was decidedly the most
painful thought with which I had to contend. The love
of them was my tender point, and shook my decision
more than all things else. Besides the pain of separation,
the dread and apprehension of a failure exceeded what
I had experienced at my first attempt. The appalling
defeat I then sustained returned to torment me. I felt
assured that, if I failed in this attempt, my case would be
a hopeless one—it would seal my fate as a slave forever.
I could not hope to get off with anything less than the
severest punishment, and being placed beyond the
means of escape. It required no very vivid imagination to
depict the most frightful scenes through which I would
have to pass, in case I failed. The wretchedness of slavery,
and the blessedness of freedom, were perpetually before
me. It was life and death with me. But I remained firm
and according to my resolution, on the third day of September, 1838, I left my chains, and succeeded in reaching
New York without the slightest interruption of any kind.

Practice Test 4

This map shows population and density of slaves in 1860.
(Credit: Historical Map & Chart Collection, Office of Coast Survey, NOAA)

11 The common thread of the experiences that stimulated the
writing of Stowe and Douglass was that both of them

13 According to the passage, the process of writing Uncle Tom’s
Cabin was

A.

lost close friends to slavery.

A.

artistically satisfying.

B.

experienced deaths in their families.

B.

slow and difficult.

C.

loved their children very deeply.

C.

extremely painful.

D.

lost loved ones in terrible ways.

D.

a positive emotional release.

12 Which choice provides the best partial evidence for the
answer to the previous question?
A.

Lines 1–3 (“I had two . . . children”)

B.

Lines 4–5 (“the most loved . . . residence.”)

C.

Lines 8–9 (“In those depths . . . immeasurable”)

D.

Lines 10–12 (“There were . . . suffering”)

CONTINUE
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Practice Test 4
14 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 28–31 (“I must confess . . . abyss.”)

B.

Lines 31–33 (“The law records . . . of them.”)

C.

Lines 37–39 (“Many times . . . utterly”)

D.

Lines 39–40 (“I prayed . . . got through”)

18 As used in line 36, “exquisitely” most nearly means
A.

beautifully.

B.

exhaustively.

C.

delightfully.

D.

intensely.

19 As used in line 51, “contend” most nearly means
15 The star on the map (on the previous page) indicates the
location of Baltimore. Based on information in the map
and the passage, Frederick Douglass lived in
A.

the city that had the highest slave density in the
entire country.

B.

a city that had extremely few slaves when compared with the rest of the country.

C.

the city that was the first to be liberated when
slavery was abolished.

D.

a city with a medium density of slaves as comparable to the rest of the country.

16 Why might Douglass have given his narrative its title?
A.

He was almost illiterate and liked the way it
sounded.

B.

He wanted people to know that he actually was the
author.

C.

He wanted to make sure no one else could take his
identity.

D.

He wanted to promote the abolitionist cause.

17 What do the passages suggest about the abolitionist
movement in the mid-nineteenth century?

  846

A.

Everyone was too afraid of negative repercussions
to speak up against the evils of slavery.

B.

Some people wrote in order to expose the evils of
slavery in an effort to abolish it.

C.

People in the North were the only ones who were
angry about the evils of slavery.

D.

The conflict over slavery was only just beginning to
heat up when these passages were written.

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A.

struggle.

B.

assert.

C.

debate.

D.

challenge.

20 What evidence suggests that Stowe’s abolitionist activism
was a way to memorialize her lost child?
A.

Lines 5–7 (“It was at . . . mother may feel”)

B.

Lines 12–15 (“that I felt . . . good to others”)

C.

Lines 17–18 (“that book . . . that summer”)

D.

Lines 36–37 (“It may be . . . heart’s blood.”)

21 Why does Stowe believe she needs to do research for her
next book?
A.

Lines 18–20 (“It has left . . . the sorrowful”)

B.

Lines 30–31 (“much as I . . . the abyss.”)

C.

Lines 31–32 (“The law records . . . so incredible”)

D.

Lines 37–39 (“Many times . . . fail utterly”)

Practice Test 4
Questions 22–31 are based on the following
passage and supplementary material.
The following is a news item (May 4, 2015) from the Jet Propulsion
Laboratory at the California Institute of Technology. The lab is part of
NASA and is dedicated to the robotic exploration of space.

40 Design and Navigation Section. “When two spacecraft are

45

Traffic Around Mars Gets Busy

Line
5

10

15

20

25

30

35

NASA has beefed up a process of traffic monitoring,
communication, and maneuver planning to ensure that
Mars orbiters do not approach each other too closely.
Last year’s addition of two new spacecraft orbiting
Mars brought the census of active Mars orbiters to five, the
most ever. NASA’s Mars Atmosphere and Volatile Evolution
(MAVEN) and India’s Mars Orbiter Mission joined the 2003
Mars Express from ESA (the European Space Agency) and
two from NASA: the 2001 Mars Odyssey and the 2006
Mars Reconnaissance Orbiter (MRO). The newly enhanced
collision-avoidance process also tracks the approximate
location of NASA’s Mars Global Surveyor, a 1997 orbiter
that is no longer working.
It’s not just the total number that matters, but also
the types of orbits missions use for achieving their science
goals. MAVEN, which reached Mars on Sept. 21, 2014,
studies the upper atmosphere. It flies an elongated orbit,
sometimes farther from Mars than NASA’s other orbiters
and sometimes closer to Mars, so it crosses altitudes
occupied by those orbiters. For safety, NASA also monitors positions of ESA’s and India’s orbiters, which both fly
elongated orbits.
...
Traffic management at Mars is much less complex
than in Earth orbit, where more than 1,000 active orbiters
plus additional pieces of inactive hardware add to hazards.
As Mars exploration intensifies, though, and will continue
to do so with future missions, precautions are increasing.
The new process was established to manage this growth
as new members are added to the Mars orbital community
in years to come.
All five active Mars orbiters use the communication
and tracking services of NASA’s Deep Space Network,
which is managed at JPL [Jet Propulsion Laboratory]. This
brings trajectory information together, and engineers can
run computer projections of future trajectories out to a
few weeks ahead for comparisons.
“It’s a monitoring function to anticipate when traffic
will get heavy,” said Joseph Guinn, manager of JPL’s Mission

50

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predicted to come too close to one another, we give people
a heads-up in advance so the project teams can start
coordinating about whether any maneuvers are needed.”
The amount of uncertainty in the predicted location
of a Mars orbiter a few days ahead is more than a mile
(more than two kilometers). Calculating projections for
weeks ahead multiplies the uncertainty to dozens of miles,
or kilometers. In most cases when a collision cannot be
ruled out from projections two weeks ahead, improved
precision in the forecasting as the date gets closer will rule
out a collision with no need for avoidance action. Mission
teams for the relevant orbiters are notified in advance
when projections indicate a collision is possible, even if the
possibility will likely disappear in subsequent projections.
This situation occurred on New Year’s weekend, 2015.
On Jan. 3, automated monitoring determined that
two weeks later, MAVEN and MRO could come within
about two miles (three kilometers) of each other, with
large uncertainties remaining in the exact passing distance. Although that was a Saturday, automatic messages
went out to the teams operating the orbiters.
“In this case, before the timeline got short enough to
need to plan an avoidance maneuver, the uncertainties
shrank, and that ruled out the chance of the two spacecraft
coming too near each other,” Guinn said. This is expected
to be the usual pattern, with the advance warning kicking
off higher-level monitoring and initial discussions about
options.
If preparations for an avoidance maneuver were
called for, spacecraft commands would be written, tested,
and approved for readiness, but such commands would
not be sent to a spacecraft unless projections a day or two
ahead showed probability of a hazardous conjunction.
The amount of uncertainty about each spacecraft’s exact
location varies, so the proximity considered unsafe also
varies. For some situations, a day-ahead projection of two
craft coming within about 100 yards (100 meters) of each
other could trigger a maneuver.
The new formal collision-avoidance process for Mars
is part of NASA’s Multi-Mission Automated Deep-Space
Conjunction Assessment Process. A side benefit of it is that
information about when two orbiters will be near each
other—though safely apart—could be used for planning
coordinated science observations. The pair could look at
some part of Mars or its atmosphere from essentially the
same point of view simultaneously with complementary
instruments.

CONTINUE
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Practice Test 4

MOM

MRO

Mars Express
Phobos

Mars Odyssey
Demios

Maven

This graphic depicts the relative shapes and distances from Mars for five active orbiter missions plus the
planet’s two natural satellites. It illustrates the potential for intersections of the spacecraft orbits.

22 Which of the following is the best summary of the passage?
A.
B.

Gathering information from space requires careful
and complex monitoring of spacecraft satellites.
The satellites orbiting Mars could collide, so
monitoring and collision avoidance measures are
necessary.

C.

Planning for space satellites around other planets
takes skilled teamwork.

D.

Monitoring traffic around the Earth is more
complex than monitoring the traffic around Mars.

23 Which areas are involved in monitoring Mars’ satellites?

A.

Lines 16–17 (“MAVEN . . . atmosphere.”)

B.

Lines 57–58 (“MAVEN . . . each other”)

C.

Lines 60–61 (“Although that . . . orbiters.”)

D.

Lines 63–65 (“the uncertainties . . . other”)

26 Based on information given in the passage, the distances
between satellites are
A.

related to the degree of danger they pose.

B.

impossible to calculate before it is too late.

A.

The United States, Russia, and India

C.

minor details in satellite collision warning reports.

B.

Europe and the United States

D.

C.

India, Europe, and the United States

extremely constant without even a minimum of
variation.

D.

The United States, China, and Russia

24 According to information in the passage, what happened
on New Year’s weekend 2015?

  848

25 Which choice provides the best evidence for the answer
to the previous question?

A.

Data indicated that there could be a collision.

B.

Data gave scientists new information about the
orbit of the satellites.

C.

Scientists failed to react to a collision alert.

D.

Two satellites experienced a devastating collision.

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27 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 51–53 (“Mission teams . . . is possible”)

B.

Lines 57–58 (“MAVEN and . . . each other”)

C.

Lines 74–75 (“The amount . . . also varies”)

D.

Lines 79–81 (“The new formal . . . Assessment
Process.”)

Practice Test 4
Questions 32–42 are based on the following passage.

28 Based on information in the passage and the graphic (on
the previous page), a natural satellite of Mars is most likely
A.

Mars Odyssey.

B.

MAVEN.

C.

MRO.

D.

Phobos.

29 Based on the graphic, which satellite is least likely to collide
with Mars?
A.

Phobos

B.

MRO

C.

Deimos

D.

MAVEN

Potatoes were first cultivated in Peru by the Incas between 8000 and
5000 BCE. Today, potatoes make up the fourth-largest food crop in
the world. In a ground-breaking agreement between the International
Potato Center (known by its Spanish acronym CIP), the nonprofit
organization ANDES, and the Association of the Potato Park communities, scientists are helping Peruvian farmers test and monitor
many varieties of potatoes. One of their goals is to ensure continued
diversity in potatoes—an action that could prevent disasters such as
the Irish Potato Famine.

Line
5

30 As used in line 73, “conjunction” most nearly means
A.

rejection.

B.

combination.

C.

contention.

D.

connection.

10

15

31 As used in line 36, “projections” most nearly means
A.

use of trajectory information.

B.

reference to future trajectories.

C.

comparisons to other trajectories.

D.

engineers can make comparisons.

20

25

30

35

As world leaders gather in Lima to negotiate a new
global climate deal at the UN Climate conference, this
innovative, inclusive work shows the importance of new
kinds of partnerships between scientists and farmers for
adaptation to climate change.
In the Peruvian highlands near Cusco, climate change
has already impacted farmers in a fundamental way.
Rising temperatures are correlated with increased pests
and diseases, making it difficult to grow potatoes, their
staple food.
The effects of these temperature changes are very
pronounced in the Potato Park, a valley outside of Cusco,
where just 30 years ago, cultivation of native potato was
routinely done at 3,800 meters.
Now, native potato cultivation starts at around 4,000
meters. In just 30 years, challenges associated with a
warming climate have pushed potato cultivation up by
200 meters. The speed of this change in planting zones
due to a warming climate is unprecedented as it is pushing
the farmers to the top of the mountain, beyond which
there is no more soil or land.
In addition to moving to higher elevation for potato
cultivation, Quechua farmers in the Potato Park are also
responding to this challenge by stewarding over 1,440
cultivars of native potato. These include their own varieties
plus cultivars that different entities have provided to the
Park, 410 of which have come from CIP.
The five communities that make up the Potato Park
are also working with CIP scientists in the characterization
of potato diversity, monitoring changes in potato varieties
used over time and testing of varieties in different parts of
the landscape, a combined territory of over 9,000 hectares.
Planting a diversity of potatoes provides a vital safeguard against crop failure—if disaster strikes, the farmers
will always have food. This strategy to reduce risk comes
from their ancestors.

CONTINUE
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  849

Practice Test 4

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55

60

65

70

75

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The agreement with CIP has brought back varieties
which had been collected from the communities in
the 1960s but had since been lost. The resulting landscape-based gene bank is actively managed by the five
Potato Park communities.
It provides a critical source of climate-resilient crops
for adaptation, both locally and globally. Although gene
banks conserve many food crops, they cannot safeguard
them all, and their collections are no longer evolving in
response to climatic changes or accessible to farmers.
Alejandro Argumedo, Director of Programs of
the Peruvian NGO ANDES explained: “The landmark
agreement between CIP and the Potato Park for repatriation and monitoring of native potatoes represents
a fundamental shift in approach. Rather than only
collecting crops from farmers, scientists have also
given farmers crops from their gene bank in return. The
disease-free seeds and scientific knowledge gained
have boosted food security, and the new varieties have
enhanced income, enabling the communities to develop
novel food products.”
Head of the CIP Genetic Resources-Genebank
David Ellis said: “Through the agreement, first signed in
2004, CIP is increasing its understanding of how climate
change is affecting potato diversity and agro-ecosystems, and through collaborative and mutually
beneficial research with the farmers, it has continued to
enhance knowledge, adaptation to climate change and
capacity development for sustaining potato production
and traditional knowledge.
In Asia and Africa, hardy local landraces and livestock breeds are also proving a vital resource in the
struggle to cope with more extreme weather such as
droughts.
Krystyna Swiderska, Principal Researcher at IIED
[International Institute for Environment and Development] said: “From China to Kenya, farmers have
improved both resilience and productivity by crossing
resilient landraces with high-yielding modern varieties.”

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32 What is the relationship between plant diversity and climate change?
A.

Plant diversity can provide some protection from
crop failure due to climate change.

B.

Increasing plant diversity with ancient varieties of
potatoes may be more resilient to the higher
temperatures associated with climate change.

C.

In general, no variety of potato is adaptable to
changes in climate.

D.

The potato gene bank tries to ensure plant diversity
but cannot save them from extinction.

33 According to the passage, how are potato farmers trying
to combat climate change?
A.

They will be attending the UN summit on climate
change.

B.

They are inventing new ways to exterminate pests.

C.

They are planting more diverse seeds and plants.

D.

They are experimenting with a different kind of
staple food.

34 What kind of climate is best suited for potatoes?
A.

Tropical

B.

Cool

C.

Hot

D.

Moist

35 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 8–10 (“Rising temperatures . . . staple food”)

B.

Lines 33–34 (“Planting a . . . crop failure”)

C.

Lines 43–46 (“Although gene . . . climatic changes”)

D.

Lines 60–63 (“CIP is . . . the farmers”)

Practice Test 4
36 Which of the following is the best summary of the passage?
A.

New farming techniques are helping Peruvian
farmers adapt to a changing climate.

B.

Peruvian farmers are part of an international group
trying to fight the effects of climate change.

C.

Ancestral growing techniques combined with new
scientific methods are proving to be useful in
combating the effects of climate change on
Peruvian farmers.

D.

Extreme weather conditions are proving difficult
challenges for farmers all over the world.

37 What are the implications of climate change on world
hunger?

39 What evidence in the passage illustrates the effects of
climate change in Peru?
A.

Lines 64–66 (“adaptation . . . knowledge”)

B.

Lines 67–68 (“hardy local . . . resource”)

C.

Lines 68–70 (“in the struggle . . . droughts.”)

D.

Lines 73–75 (“farmers have . . . varieties.”)

40 As used in line 12, “pronounced” most nearly means
A.

articulated.

B.

official.

C.

well-known.

D.

noticeable.

A.

It won’t be affected.

B.

It may enable the development of new crops to
feed the world.

C.

With the right scientific intervention, it could
alleviate hunger.

A.

Lines 25–27 (“These include . . . the Park”)

B.

Lines 28–31 (“Potato Park . . . over time”)

It may get worse.

C.

Lines 35–36 (“This strategy . . . their ancestors”)

D.

Lines 37–39 (“The agreement . . . been lost”)

D.

38 According to the passage, some farmers are dealing with
the effects of climate change by
A.

studying how to stop droughts.

B.

focusing on raising meat.

C.

only growing modern potato varieties.

D.

abandoning their farming careers.

41 What evidence does the text provide to show that potatoes
were eaten by Peruvian people for a very long time?

42 As used in line 24, “stewarding” most nearly means
A.

managing.

B.

controlling.

C.

regulating.

D.

developing.

CONTINUE
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Practice Test 4
Questions 43–52 are based on the following passage.

turned the plough aside, showing plainly that he was no
45 madman, and after that could no longer refuse to fulfill

In his leisure time, Thomas Bulfinch (1796–1867) enjoyed writing
condensed summaries of classical literature. Written for the general
reader, “to popularize mythology and extend the enjoyment of
elegant literature,” his three volumes of classics were published
under the title Bulfinch’s Mythology. This passage is an excerpt
from chapter XXVII, The Trojan War.

Line
5

10

15

20

25

30

35

40

  852

Minerva was the goddess of wisdom, but on one
occasion she did a very foolish thing; she entered into
competition with Juno and Venus for the prize of beauty.
It happened thus: At the nuptials of Peleus and Thetis
all the gods were invited with the exception of Eris, or
Discord. Enraged at her exclusion, the goddess threw a
golden apple among the guests, with the inscription,
“For the fairest.” Thereupon Juno, Venus, and Minerva
each claimed the apple. Jupiter, not willing to decide
in so delicate a matter, sent the goddesses to Mount
Ida, where the beautiful shepherd Paris was tending
his flocks, and to him was committed the decision.
The goddesses accordingly appeared before him. Juno
promised him power and riches, Minerva glory and
renown in war, and Venus the fairest of women for his
wife, each attempting to bias his decision in her own
favor. Paris decided in favour of Venus and gave her the
golden apple, thus making the two other goddesses his
enemies. Under the protection of Venus, Paris sailed to
Greece, and was hospitably received by Menelaus, king
of Sparta. Now Helen, the wife of Menelaus, was the very
woman whom Venus had destined for Paris, the fairest
of her sex. She had been sought as a bride by numerous
suitors, and before her decision was made known, they
all, at the suggestion of Ulysses, one of their number,
took an oath that they would defend her from all injury
and avenge her cause if necessary. She chose Menelaus,
and was living with him happily when Paris became their
guest. Paris, aided by Venus, persuaded her to elope with
him, and carried her to Troy, whence arose the famous
Trojan war, the theme of the greatest poems of antiquity,
those of Homer and Virgil.
Menelaus called upon his brother chieftains of
Greece to fulfill their pledge, and join him in his efforts
to recover his wife. They generally came forward, but
Ulysses, who had married Penelope, and was very happy
in his wife and child, had no disposition to embark in
such a troublesome affair. He therefore hung back and
Palamedes was sent to urge him. When Palamedes
arrived at Ithaca, Ulysses pretended to be mad. He yoked
an ass and an ox together to the plough and began
to sow salt. Palamedes, to try him, placed the infant
Telemachus before the plough, whereupon the father

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his promise. Being now himself gained for the undertaking, he lent his aid to bring in other reluctant chiefs,
especially Achilles. This hero was the son of that Thetis at
whose marriage the apple of Discord had been thrown
50 among the goddesses. Thetis was herself one of the
immortals, a sea-nymph, and knowing that her son was
fated to perish before Troy if he went on the expedition,
she endeavoured to prevent his going. She sent him
away to the court of King Lycomedes, and induced him
55 to conceal himself in the disguise of a maiden among
the daughters of the king. Ulysses, hearing he was there,
went disguised as a merchant to the palace and offered
for sale female ornaments, among which he had placed
some arms. While the king’s daughters were engrossed
60 with the other contents of the merchant’s pack, Achilles
handled the weapons and thereby betrayed himself to
the keen eye of Ulysses, who found no great difficulty
in persuading him to disregard his mother’s prudent
counsels and join his countrymen in the war.
43 Which of the following is a theme used in this myth?
A.

Humans use deception to achieve goals.

B.

The gods have special powers of to control events.

C.

The bonds of marriage tie people’s loyalties to one
another.

D.

War is a dangerous undertaking that threaten
human life.

44 According to the passage, Ulysses’s reasons for not participating in the war were
A.

courageous.

B.

loyal.

C.

hypocritical.

D.

cowardly.

45 It can reasonably be inferred that Discord tossed the apple
at the nuptials to
A.

find out how the fairest goddesses truly was.

B.

reduce the ceremony to chaos and disharmony.

C.

get the three goddesses ejected from the nuptials.

D.

present a ceremonial gift to the three goddesses.

Practice Test 4
46 Why did Thetis try to prevent Achilles from going to Troy?
A.

She thought his presence might start a war.

B.

She didn’t want him to marry Helen.

C.

She wanted him to ask King Lycomedes for his help.

D.

She didn’t want her son to be killed in battle.

50 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 40–44 (“Ulysses . . . aside”)

B.

Lines 46–48 (“Being . . . Achilles.”)

C.

Lines 50–52 (“Thetis . . . Troy.”)

D.

Lines 53–55 (“She sent . . . maiden”)

47 Based on the myth, what started the Trojan War?
51 As used in line 35, “recover” most nearly means
A.

A fight over an apple

B.

A fight for the hand of Helen

C.

A test of Ulysses’ loyalty

D.

The marriage of Peleus and Thetis

48 Which choice provides the best evidence for the answer to
the previous question?

A.

retrieve.

B.

balance.

C.

salvage.

D.

repair.

52 As used in line 63, “prudent” most nearly means

A.

Lines 19–21 (“Under . . . Sparta.”)

A.

fierce.

B.

Lines 27–31 (“She chose . . . war”)

B.

cautious.

C.

Lines 31–32 (“the theme . . . Virgil”)

C.

legal.

D.

Lines 33–34 (“Menelaus . . . pledge”)

D.

indifferent.

49 What is the relationship between Telemachus and Ulysses?
A.

Telemachus was Ulysses’ son.

B.

Telemachus was a god and Ulysses human.

C.

Telemachus was a prince and Ulysses was king of
Sparta.

D.

Telemachus was an old man and Ulysses was his son.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

Peterson's SAT® Prep Guide 2017

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Practice Test 4
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you will
need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you to
consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).
Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.
After reading each passage, select the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following
passages and supplementary material.
The struggle of African Americans to make economic and political
progress within the socioeconomic structure of the United States
has been long and filled with setbacks. The following passages
document some of the events in that long struggle and seek to
explain why it has been so difficult.
PASSAGE 1
The Fight for African American Progress:
The Economic Picture
Slavery—which lasted until 1865—and 1 comprehensive
education guaranteed that African Americans remained
socioeconomically disadvantaged until well into the twentieth
century. Segregated schools were rarely on par with schools
for whites; consequently, African Americans often found they
could not compete with whites for jobs.

1

Which choice provides the most relevant detail?
A.

NO CHANGE

B.

inadequate

C.

spacious

D.

superior

CONTINUE
Peterson's SAT® Prep Guide 2017

  855

Practice Test 4
Increased opportunities for African Americans followed in the
wake of

2

2 the civil rights movement, African Americans

A.

NO CHANGE

B.

the civil rights movement and African Americans

C.

the civil rights movement African Americans

D.

the civil rights movement. African Americans

between low-income African Americans and those who

A.

NO CHANGE

were able to improve their socioeconomic status. By 2010,

B.

Moreover,

the economic status of many African American households

C.

To begin with,

had declined, 4 with the median net worth in 2009

D.

Irrelevantly,

were finally able to gain higher levels of education and
achieve better positions in a variety of professions. In the
1980s, large numbers of African Americans moved into the
upper middle class.
3 However, by the 1990s, there was a noticeable gap

3

less than half of what it had been in 2005. Today, many
low-income African Americans do not have a place in the

4

class structure because of poverty and underlying racial

Which choice most effectively reflects information in the
chart?

prejudice, particularly in urban areas. 5 Too often, urban

A.

NO CHANGE

neighborhoods become a place of high crime, poor schools,

B.

though the median net worth in 2009 was several
times more than what it had been in 2005.

C.

whereas the median net worth of white households
grew by 50% from 2005 to 2009.

D.

while the median net worth of white and Hispanic
households grew modestly.

A.

NO CHANGE

B.

Too often, urban neighborhoods become places of
high crime, poor schools, and substandard housing.

C.

Too often, urban neighborhoods become a
high-crime place with poor schools and substandard housing.

D.

Too often, an urban neighborhood becomes places
of high crime, poor schools, and substandard
housing.

and substandard housing.

Median Net Worth of Households, 2005 and 2009
in 2009 dollars
5

2009
Whites

$113,149

Hispanics

$6,325

Blacks

$5,677

2005
Whites

Hispanics

Blacks

$134,992
$18,359
$12,124

Source: Pew Research Center tabulation of Survey of Income
and Program Particpation data

  856

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Practice Test 4
PASSAGE 2

6

The Fight for African American Progress:
The Political Picture

A.

NO CHANGE

B.

Only with the enforcement of the Reconstruction
Act of 1867, and the ratification of the Fifteenth
Amendment,

C.

Only with the enforcement of the Reconstruction
Act of 1867 and the ratification of the Fifteenth
Amendment

D.

Only with the enforcement of the Reconstruction
Act of 1867, and the ratification of the Fifteenth
Amendment

A.

NO CHANGE

B.

he

C.

we

D.

it

A.

NO CHANGE

B.

evinced

C.

championed

D.

disputed

6 Only, with the enforcement of the Reconstruction Act
of 1867 and the ratification of the Fifteenth Amendment did
African Americans first win seats in Congress. On February
25, 1870, Hiram Revels of Mississippi became the first African
American Senator. Later that same year, Joseph Rainey of
South Carolina became the first African American member of
the House of Representatives.
7
African Americans throughout the South became politically
active soon after the close of the Civil War. A generation
of African American leaders emerged, almost all of whom
supported the Republican Party because 7 they had
8 discerned their rights.
8

CONTINUE
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  857

Practice Test 4
During the 1890s and early 1900s, however, no African

9

American won election to Congress, in part because of
9 restrictive state election codes in some southern states.
During World War I and in the following decade, African
Americans who migrated to northern cities created the
foundations for political organization in urban centers. Over
the next three decades, African Americans won congressional
seats in New York City, Detroit, and Philadelphia. In the wake

A.

NO CHANGE

B.

favorable

C.

irrelevant

D.

progressive

10 The writer is considering deleting the underlined sentence.
Should the writer do this?

of the civil rights movement, African Americans regained seats

A.

No, because it provides relevant details about the
main topic of the paragraph.

B.

No, because it provides context for the following
paragraph.

C.

Yes, because it introduces a detail that is not
directly related to the topic of the paragraph.

D.

Yes, because it creates a transition to the next
paragraph.

opportunities and land grants for freed slaves. In the mid-

A.

NO CHANGE

twentieth century, they focused on urban communities

B.

The Congressional Black Caucus demonstrated a
special concern for the protection of civil rights; the
guarantee of equal opportunity in education,
employment, and housing; and a broad array of
foreign and domestic policy issues.

C.

The Congressional Black Caucus demonstrated a
special concern for the protection of civil rights the
guarantee of equal opportunity in education
employment and housing and a broad array of
foreign and domestic policy issues.

D.

The Congressional Black Caucus demonstrated a
special concern for the protection of civil rights. The
guarantee of equal opportunity in education.
Employment and housing. And a broad array of
foreign and domestic policy issues.

in the South. 10 The South is a beautiful part of the country,
and you should seriously consider visiting it for your next
vacation.
These members of Congress have traditionally served
as advocates for all African Americans, not just their
constituencies. During Reconstruction and the late nineteenth
century, they worked to protect the voting rights of African
Americans. They also called for expanded educational

11

and urged federal programs for improved housing and job
training. 11 The Congressional Black Caucus demonstrated a
special concern for the protection of civil rights, the guarantee
of equal opportunity in education, employment, and housing,
and a broad array of foreign and domestic policy issues.

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Practice Test 4
Questions 12–22 are based on the following passage.

12

Morocco's Musical Traditions
Morocco has many rich musical traditions stemming from
12 their unique geographical conditions and a long history

A.

NO CHANGE

B.

our

C.

its

D.

your

of intermingled cultures. For the past century, Morocco has
attracted musicians and other artists from the west who
wanted to learn from the country’s creative and hospitable

13 Which choice most effectively maintains the paragraph’s
focus on relevant information and ideas?

people. For instance, Jimi Hendrix’s style of guitar playing was

A.

NO CHANGE

influenced by his travels to Marrakesh and Essaouira, where

B.

Jazz musicians such as Pharaoh Sanders and
Ornette Coleman have also made pilgrimages, in
search of Morocco’s earthy, trance-inducing
rhythms, and complex melodies.

C.

The band once made a trip to Morocco in the late
1960s while waiting for the verdict on drug charges
made against them in Great Britain.

D.

Today, raj, a type of music from Algeria, is popular
among young Moroccans for the way it mixes
western rock with Jamaican reggae and Moroccan
pop.

A.

NO CHANGE

B.

This area covered with farmland and several large
cities and towns, is the most prosperous part of the
country.

C.

This area, covered with farmland and several large
cities and towns, is the most prosperous part of the
country.

D.

This area, covered with farmland and several large
cities and towns is the most prosperous part of the
country.

he discovered the rhythmic music of the Ganawa tribe. The
Rolling Stones were fascinated with Morocco’s music and
made several trips there to hear it. During one of the Stones’
stays, Brian Jones recorded an album of village folk music.
13 The Rolling Stones have also been influenced by such
legendary African American musicians as Muddy Waters,
Chuck Berry, and James Brown.
Morocco is located on the northeastern corner of Africa, only
a few miles from the southern tip of Spain across the Strait
of Gibraltar. Mountain ranges form the “backbone” of the
country, running from the northeast to the southwest. Fertile
plains stretch from the northern side of these mountains to

14

the Mediterranean Sea and Atlantic Ocean. 14 This area
covered with farmland and several large cities and towns
is the most prosperous part of the country. Although the
mountains themselves are quite rugged and rocky, there is
plenty of water to support fruit orchards and isolated villages
of goatherds. The southern side of the mountains is more arid,
with rocky plateaus and several fertile river valleys descending
gradually into the Sahara Desert. The river valleys are dotted
with towns and villages that get smaller as the rivers dry up
along the desert’s edge. Several nomadic tribes travel among
the villages and desert oases.

CONTINUE
Peterson's SAT® Prep Guide 2017

  859

Practice Test 4
15 Berbers could be found in dense population clusters
throughout the country. 16 There ancestors lived all along

15 Which of the following would make the most effective
opening sentence for this paragraph?

the North African coast until frequent invasions brought

A.

Foreign invaders found it impossible to conquer the
Berbers.

B.

The Berbers have long been the largest ethnic
group in Morocco.

C.

Ancestors of the Berbers lived in rugged, isolated
mountain ranges.

D.

Berbers are hospitable people, despite the origins
of their name.

A.

NO CHANGE

B.

They’re

C.

Theyre

D.

Their

musical influence is found in their lyrics, which often praise

A.

NO CHANGE

Allah or refer to the Qur’an.

B.

euphemism

C.

locution

D.

reflection

A.

NO CHANGE

B.

autonomous

C.

indigenous

D.

illustrious

foreign rulers to many of the countries, including Morocco.
However, invading Greeks, Romans, Vandals, and Turks found
it all but impossible to control the Berbers who lived in the
rugged and isolated mountain ranges. Despite ruling the
country, foreigners could not conquer the stubborn Berber
spirit. The Romans gave them their name, which eventually
evolved into the term barbarian, although this is a 17
misnomer for such gracious and hospitable people.

16

Beginning in the seventh century, Arab legions invaded
Morocco on several occasions. These invasions began to
affect the region not only politically, but religiously as well.
Eventually the Berbers and most of the other 18 notorious
tribes became Islamic and adopted some elements of Arabic

17

culture, including classical Arabic music. The strongest Arabic

18

  860

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Practice Test 4
Despite these additional influences, the Berbers were still

19

able to maintain most of their own beliefs and traditions.
Traditional Berber music was performed solo or in larger
ensembles, sometimes accompanied by dancers. Musicians

A.

NO CHANGE

B.

drum skins, that had been, heated over lanterns
were thumped a few chords, on a flute or a lute,
were played some castanets were clacked or a few,
dance steps were stomped out.

C.

drum skins. That had been heated over lanterns.
Were thumped, a few chords on a flute or a lute
were played. Some castanets were clacked, or a few
dance steps were stomped out.

D.

drum skins that had been heated over lanterns
were thumped, a few chords on a flute or a lute
were played, some castanets were clacked, or a few
dance steps were stomped out.

A.

NO CHANGE

B.

Our family

C.

This music

D.

Everything

could be found performing in the medina marketplaces in the
older parts of towns. The musicians often got a performance
started with improvisational banter, referring to one another
and to people in the gathering crowd. Then they began to
warm up their instruments as they continued jesting: 19
drum skins that had been heated over lanterns were thumped
someone played a few chords on a flute or a lute some
castanets clacked or a few dance steps were stomped out. This
buildup set the dramatic tone for the frenzied music about to
be played; it also encouraged the audience to toss out a few
more coins.
Tribes of Saharan nomads, such as the Ganawa and the Tuareg,
brought the music and musical traditions of West Africa to
Morocco. 20 It traveled with the gold and salt caravans

20

through Timbuktu and up to Marrakesh just across the Atlas
Mountains. The most notable instruments were large, metal,
double-castanets clapped between the fingers to make
a galloping rhythm. Hand clapping, fast drumming, and
harmonized chanting were also common elements of these
southern Moroccan tribes.

CONTINUE
Peterson's SAT® Prep Guide 2017

  861

Practice Test 4
Morocco’s musical traditions were additionally influenced by
the country’s northern neighbor, Spain. Arabs had lived in
southern Spain for several centuries before they were driven

21 Which choice gives a second supporting example that is
most similar to the example that precedes it in the paragraph?

out during the Spanish Inquisition. Arab musicians from the

A.

NO CHANGE

Spanish region of Andalusia brought a sophisticated and

B.

The rebec, a predecessor of the violin, was also an
instrument in Andalusian musical traditions.

C.

Today, there are two basic types of ouds: Arabic and
Turkish.

D.

Folk traditions of Andalusia were embedded in the
music of the region.

intricate style of music back to North Africa. Much of this
Andalusian music was played on the oud, an Arabian lute
with a pear-shaped body, three rounded sound holes, a short,
fretless neck, and five pairs of strings. 21 Some researchers
believe that Andalusian music found its way into the poetry
of the troubadours. Andalusian music, with its distinctly
western classic sound, had in fact influenced the troubadours
who played in the medieval courts of Europe. A good deal

A.

similar they

of southern European folk music, such as Flamenco, was

B.

similar they,

influenced by Andalusian music.

C.

similar: they

D.

similar they—

Today many Moroccan musicians adeptly blend these various
musical styles, perhaps playing an Andalusian melody over
a Ganawa rhythm while chanting in praise of Allah. Their
lively mixes are as naturally eclectic as the rest of Moroccan
culture. A few musicians, such as Nouamane Lahlou, have
taken practically the reverse path of Jimi Hendrix and Ornette
Coleman, blending their Moroccan musical traditions with
modern styles. 22 Yet the result is similar. They have created
popular songs that have a more international appeal.

  862

22 Which choice most effectively combines the two sentences
at the underlined portion?

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Practice Test 4
Questions 23–33 are based on the following passage.

23 At this point, the writer is considering adding the following
sentence:

Mildred Dresselhaus
Heralded as “The Queen of Carbon,” Mildred Dresselhaus is a

With all the honors Dresselhaus has received, she has never
forgotten those who helped her, and she continues to help
others pursue the field she loves.

pioneer for women in science, especially physics and electrical

Should the writer make this addition here?

engineering. 23 Born into a poor household in the Bronx,

A.

Yes, because it provides a detail to reinforce the
passage’s main idea.

B.

Yes, because it serves as an introduction to her
childhood.

she became 25 cognizant of the fact that there were schools

C.

No, because it detracts from the main idea.

within the city that could offer her a better education. She

D.

No, because it should be included later in the
passage.

A.

NO CHANGE

B.

stroke and luck

C.

stroke of luck

D.

stroke of lucky

A.

NO CHANGE

B.

apprehensive

C.

dismayed

D.

astute

New York, Dresselhaus had 24 a stroke in luck when her
brother won a scholarship to attend a music school in New
York City. Dresselhaus soon joined him, and through music

secured a place at Hunter College High School—a school open
only to girls.

24

25

CONTINUE
Peterson's SAT® Prep Guide 2017

  863

Practice Test 4
After high school, she attended Hunter College with the
goal of becoming a teacher. 26 This was a common career

26 Which choice best supports the statement made in the
previous sentence?

path for women in this era. Fortunately, during her second

A.

NO CHANGE

year at Hunter, 27 Dresselhaus met the celebrated Rosalyn

B.

Hunter College was established in 1870 and is
located in New York City.

C.

Dresselhaus later received her master’s degree from
Radcliffe College.

D.

By this point, she was not as interested in music.

into a graduate program for math. To her delight, she won a

A.

NO CHANGE

scholarship.

B.

Dresselhaus met Rosalyn Yalow—a woman who
would eventually win the Nobel Prize in Medicine.

C.

Dresselhaus met Rosalyn Yalow—a woman who
would, a little later in her career, win one of the
most prestigious awards in her field—the Nobel
Prize in Medicine.

D.

Dresselhaus met Rosalyn Yalow—a woman who
would eventually, but later, win the Nobel Prize in
Medicine.

A.

NO CHANGE

B.

Yalows’

C.

Yalow

D.

Yalow’s

Yalow—a woman who would eventually gain recognition
for winning the Nobel Prize in Medicine. With 28 Yalows
encouragement, Dresselhaus began to explore science and
became passionate about physics. After seeing a notice
on a bulletin board, Dresselhaus applied for a Fulbright
Scholarship in physics, despite having already been accepted

27

28

  864

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Practice Test 4
[1] The Fulbright Scholarship sent her to the Cavendish

29

Laboratory in Cambridge, England. [2] In 1958, Dresselhaus
received her Ph.D. in physics from the University of Chicago.
29 [3] There, only she had often been the woman in
her classes. [4] Dresselhaus continued her research on

A.

NO CHANGE

B.

There, she had often been the only woman in her
classes.

C.

There, she had often only been the woman in her
classes.

D.

Only there, she had often been the woman in her
classes.

the microwave properties of superconductors at Cornell
University—after winning a two-year NSF post-doctoral
fellowship. 30 [5] After Dresselhaus returned to the United
States, her mentor Yalow persuaded her to continue her
research.

30 For the sake of cohesion, sentence 5 of this paragraph
should be placed

After her two years at Cornell, Dresselhaus accepted a position

A.

where it is now.

at MIT. She first worked as a researcher for Lincoln Laboratories

B.

before sentence 1.

and later as a visiting professor of electrical engineering

C.

before sentence 2.

and computer science. While at MIT, Dresselhaus shifted her

D.

before sentence 3.

A.

NO CHANGE

B.

immanent

C.

imminent

D.

emigrant

A.

NO CHANGE

we drive, the energy we generate, the electronic devices that

B.

students: about 20 percent of them women.

power our lives.”

C.

students; about 20 percent of them women.

d.

students—about 20 percent of them: women.

A.

NO CHANGE

B.

indifference

C.

ignorance

D.

fascination

research from semiconductors to the structure of semimetals,
especially graphite.

31

In 1968, she became a full professor, teaching condensed
matter physics to engineering students, while continuing her
research. Shortly thereafter, Dresselhaus began to achieve
recognition for her work, recognition that has continued up
to the present. She is celebrated as an 31 eminent scientist.

32

In 2014, when President Obama awarded her the Medal of
Freedom, he said, “Her influence is all around us, in the cars

Although Dresselhaus is pleased to be recognized for her
work in physics, perhaps her greatest enjoyment comes from
her mentoring of numerous Ph.D. 32 students—about 20
percent of them women. Despite her age, Dresselhaus’s 33
complacency with physics has not diminished. She says, “I am
excited by my present research and am not yet anxious to stop
working.”

33

CONTINUE
Peterson's SAT® Prep Guide 2017

  865

Practice Test 4
Questions 34–44 are based on the following passage.

34 Which choice most effectively sets up the examples given
in this sentence?

Sense of Smell

A.

NO CHANGE

Smell is considered to be the most delicate of our five senses.

B.

Dogs have a stronger sense of smell;

It has many practical functions—allowing us, for example, to

C.

Our sense of smell offers a variety of helpful
functions;

D.

Other senses are more acute than smell.

memories. Smells can remind us of our aunt’s cooking or

A.

NO CHANGE

our second-grade classroom, just as an infant identifies the

B.

The nose even plays a complementary role in
tasting:

C.

The nose even played a complementary role in
tasting:

D.

The nose has played a complementary role in
tasting:

determine whether food has gone bad or to detect smoke
when something is burning. 34 Some things smell good
to us, and some things don’t; our noses are powerful tools
for recognizing familiar people and places or recalling old

35

individual scents of its mother and father. Smell also factors
into romance, which is why the perfume industry labors to
extract and mix pleasure-provoking aromas. 35 The nose
will even play a complementary role in tasting: if you plug
your nose while eating, you will find that your food seems to
lose some of its taste. It is certainly true that we can perceive
much more subtle olfactory variations than visual or auditory
ones.

  866

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Practice Test 4
Despite all of these known applications, our knowledge of

36

just how the nose knows 36 is less than the knowledge

A.

NO CHANGE

B.

is less than our other senses.

C.

is less than that of how our other senses operate.

D.

is less than how our other senses operate.

A.

NO CHANGE

have been classified by scientists into 10 groups, each of

B.

distinct

which is characterized by its volatile compounds.

C.

expansive

D.

elusive

of our other senses. First of all, it’s often difficult to describe
how something smells. It’s relatively easy to identify a
D major chord or paint a verbal picture of something that
is silvery-blue, but the fragrance of a rose is more 37
concordant. The scent of one rose might be “flowery and

37

sweet, with a touch of citrus,” while that of another might be
more “like honey and freshly-cut grass.” 38 Therefore, scents

38 Which choice most effectively maintains support for claims
or points in the text?
A.

NO CHANGE

B.

Even those employed in the perfume and food
industries often have trouble agreeing on how to
describe and categorize particular scents.

C.

Yet many studies of scents attempt to classify new
and interesting fragrance mediums.

D.

Even wine aromas have been assigned to twelve
different categories, each represented by a section
of a wine aroma wheel.

CONTINUE
Peterson's SAT® Prep Guide 2017

  867

Practice Test 4
Sights and sounds are measured in terms of their wavelengths,
39 allowing us to make better art and music, which can

39 The writer is considering deleting the underlined part of
the sentence. Should the writer do this?

be assessed with scientific instruments. Scent molecules are

A.

No, because it provides scientific details about the
measurement of two of the senses.

B.

No, because it provides comparative data about
perception.

C.

Yes, because it should be placed later in the
passage.

D.

Yes, because it adds irrelevant details.

A.

NO CHANGE

B.

We know that molecules up to a certain mass have
scents because there are

C.

Since we know that molecules up to a certain mass
have scents, there are

D.

We know that molecules up to a certain mass have
scents, and there are

versa. For example, two differently shaped compounds will

A.

NO CHANGE

still 41 stink like rotten eggs if they both contain sulfur.

B.

smell like rotten eggs

C.

emit a disgusting odor like rotten eggs

D.

have a nasty smell like rotten eggs

not as easy to quantify. 40 We know that molecules up to a
certain mass have scents, but there are conflicting theories as
to what determines their smell and how the nose records and
transmits this information to the brain. Until recently, most
experts believed us able to recognize a certain smell based on
a molecule’s shape. Such a theory asserts that when a scent
molecule of a certain shape enters the nose and touches a

40

receptor, like a key, it unlocks and triggers a particular smell,
which is then sent to the brain. Likewise, a variety of different
scent molecules can open a combination of locks, sending a
mixture of scent signals to the brain (“smells like this spaghetti
sauce has basil and garlic in it”). This “lock-and-key” theory
does hold true for the shape and smell of many molecules.
For instance, most molecules that contain an amine group
will have a fishy smell. There are, however, many instances
of similarly shaped molecules with different smells, and vice

  868

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41

Practice Test 4
Luca Turin, a biophysicist and perfume enthusiast, questioned

42

these discrepancies and resolved to form a new theory of

A.

NO CHANGE

B.

sanction

C.

instigate

D.

refute

A.

NO CHANGE

Decaborane resembles camphane structurally, except that

B.

factor?

it has boron atoms where camphane has carbon atoms.

C.

factor.

According to the lock-and-key theory, both compounds

D.

factor!

sulfur). This example proves that molecular shape is not always

A.

NO CHANGE

the determining factor of smell.

B.

The number of atoms and electrons within a
molecule determines

Then what exactly is the determining 43 factor—Turin

C.

The number of atoms and electrons within a
molecule have determined

D.

The number of atoms and electrons within a
molecule will have determined

his own. Turin has performed many experiments that 42
invade the lock-and-key theory. He believes that out of
literally millions of different smells, there are too many cases
in which the shape does not determine the smell. He once
demonstrated this assertion by comparing a hydrocarbon

43

called camphane (the main component of camphor,
sometimes used in cold medicines) with decaborane.

should smell like camphor. However, the decaborane instead
smells like rotten eggs (which is surprising, as it contains no

44

theorizes that the vibration of a molecule’s atoms provides
its signature smell. 44 The number of atoms and electrons
connected within a molecule determine that molecule’s
particular vibration. The result of these minute shakes and
quivers can be recorded as a particular frequency. The
receptors in the nose, therefore, actually record the vibration
of the molecules and transmit that information to the brain as
a scent. This theory puts smell in the same category as sight
and sound. Colors can be measured along a spectrum of light
according to their wavelengths; tones can be measured along
a spectrum of octaves according to their wavelengths. Turin
claims that the same types of measurements can be taken
with smells. Although the frequencies of scents are much
more complicated to measure, measuring them is exactly
what Turin has set out to do.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

Peterson's SAT® Prep Guide 2017

  869

Practice Test 4
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions
TURN TO SECTION 3 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  871

Practice Test 4
1

2

If 3x –2[1 – 2(x + 4)] = 5x, what is the value of x?
A.

–14

B.

–7

C.

7

D.

12

Which expression shows the simplified form of
(3x2 – 7x + 5) – (–6x2 + 5x – 4)?

3

A.

–3x2 – 2x + 1

B.

–3x2 – 12x + 9

C.

9x2 – 2x + 1

D.

9x2 – 12x + 9

y ≤ 3x − 4
5x + 4 y ≥ 6
Which point is a solution to the system of inequalities?

4

5

  872

A.

(0, 0)

B.

(–1, 5)

C.

(2, –3)

D.

(3, 4)

Angie took 3x hours to make it on time for her brother’s
birthday party in another state, and she drove the route at
an average of z miles per hour. If b is the number of hours
Angie spent at rest stops, when she was NOT traveling,
which of the following represents the total distance Angie
traveled to get to her brother’s party?
A.

z(b – 3x)

B.

b – 3x

C.

z(3x – b)

D.

3xz – b

If 3s – r = 9 and 6s = 36, what is the value of r?
A.

3

B.

6

C.

9

D.

12

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Practice Test 4
6

7

8

9

Gary deposits $50 into an existing savings account. Each
month he plans to increase the amount he deposits by $7.
Using y = 50 + 7(x – 1) to represent this situation, what is
the meaning of y in the equation?
A.

The total amount that Gary has in the account after
x months

B.

The number of months that Gary has been making
deposits

C.

The amount that Gary deposits into his account in
month x

D.

The increase in the monthly amount of Gary’s
deposits

If f ( x ) = cx −
A.

1 – cd

B.

1 + cd

C.

c2 −

D.

d 2
−c
c

SHOW YOUR WORK HERE

 1
d
, which of the following represents f   ?
c 
x

d
c

Let a and b be positive real numbers. Consider the function
g(x) = (x2 – a2)(x2 + b2). Which of the following statements
concerning g(x) are is true?
A.

The graph of g(x) crosses the x-axis twice.

B.

g(–b) = 0

C.

The graph of g(x) never extends below the x-axis.

D.

The graph of g(x) does not have a y-intercept.

The x-intercepts of the function g(x) are –2, 3, and 5. Which
of the following is a factor of g(x)?
A.

x+2

B.

x+3

C.

x – 15

D.

x – 30

CONTINUE
Peterson's SAT® Prep Guide 2017

  873

Practice Test 4
10 The ratio of marbles in each package of marbles is 2 red:
3 green: 4 blue. How many green and blue marbles does
Ina have if she bought 108 marbles?

11

A.

12

B.

36

C.

48

D.

84
1

4

What is the value of a, if x 5 • x 5 = x − a ?
A.

−5

B.

−1

C.

1

D.

5

12

y

(0,4)
(2, 2)
p
O

x
q

In the figure above, lines p and q are parallel. If point
(x, y) lies on line q, which of the following represents the
relationship between x and y?

  874

A.

x+y=0

B.

x–y=0

C.

x+y=1

D.

x – y = –1

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Practice Test 4
13

14

15

2
and m∠E = 90°. Which of
3
the following statements is true?
In a right triangle DEF, sinF =

SHOW YOUR WORK HERE

1
3

A.

cos F =

B.

tanF = 2

C.

cos D =

D.

sin D =

2
3

1
3

A circle is drawn on an xy-plane. The diameter of the circle
has endpoints at (–9, 7) and (15, –3). Which of the following
is an equation for the graph of the circle?
A.

(x – 3)2 + (y – 2)2 = 169

B.

(x – 3)2 + (y – 2)2 = 676

C.

(x – 6)2 + (y – 4)2 = 169

D.

(x – 6)2 + (y – 4)2 = 676

3x 2 − 5x + 9
x −3
Which expression is equivalent to the expression above?
A.

3x + 4 +

21
x −3

B.

3x − 5 −

6
x −3

C.

3x + 9 +

36
x −3

D.

3 x − 14 +

51
x −3

CONTINUE
Peterson's SAT® Prep Guide 2017

  875

Practice Test 4

DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the
answer sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
1
7
5.  	 Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
1
1
31
If 3 is entered into the grid as
, it will be interpreted as
, not 3 .)
2
2
2
6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

1

1

2

2

2

1

1

3

3

3

3

3

4

4

4

4

4

5

5

5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

  876

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0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

7

7

7

8

8

8

8

8

9

9

9

9

9

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

7

7

7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

Practice Test 4
16

A ball is tossed into the air from 6 meters off of the ground,
with a velocity of 13 meters per second. The equation that
represents the height of the ball (h, in meters) at time (t,
in seconds) is h = 6 + 13t – 5t2. How many seconds will it
take for the ball to hit the ground?

17

If b = 6 is a solution to the equation 6b + m = 270, where
m is a constant, what is the value of m?

18

C

SHOW YOUR WORK HERE

E

10
A

6
B

D

In the figure above, ACED is a rectangle and B is the midpoint of AD . What is the value of AD ?

19

20

What is the value of x, if

x + 10 − 2 x − 5 = 0?

fx + gy = −16
3 x − 8 y = 32
In the system of equations above, f and g are constants.
If the system has infinitely many solutions, what is the
g
value of − ?
f

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

CONTINUE
Peterson's SAT® Prep Guide 2017

  877

Practice Test 4
SECTION 4: MATH TEST—CALCULATOR
55 Minutes—38 Questions
TURN TO SECTION 4 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–30, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 31–38, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 31 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  879

Practice Test 4
1

2

  880

The North American X-15 is the fastest aircraft in the world,
with a speed of 4,474 miles per hour. The second fastest,
the Lockheed SR-71 Blackbird, has a top speed of 2,193
miles per hour. If 1 Mach is equivalent to approximately
0.213 miles per second, what is the difference in their
speeds in Machs?
A.

2.859

B.

2.977

C.

4.474

D.

5.836

A major city performed a recent study to see the effect that
snowfall totals have on the number of drivers on the road.
The results of the study are represented in the scatterplot,
where the x-axis represents the amount of snowfall and the
y-axis represents the number of drivers. Which statement
best describes the results of the study?

A.

There is no correlation between the amount of
snowfall and the number of drivers on the road.

B.

There is a positive correlation between the amount
of snowfall and the number of drivers on the road.

C.

There is a negative correlation between the amount
of snowfall and the number of drivers on the road.

D.

The scatterplot does not display enough data to
interpret a correlation between the amount of
snowfall and the number of drivers on the road.

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Practice Test 4
3

A rectangular practice field is to be enclosed using 600
yards of fencing material. It takes 2.5 times longer to install
a yard of fence used for the short sides of the field than
for the longer sides, due to the additional supporting
beams that must be installed on these ends. If x represents
the length of the shorter side of the field (in yards) and t
denotes the time (in minutes) to install one yard of fence
along the shorter side of the field, which of the following
expresses the total time (in minutes) it takes to install the
entire fence?
A.

4

5

600xt

C.

3
300t + xt
2
1,500 − 3xt

D.

600t + 3xt

B.

SHOW YOUR WORK HERE

Martina earns $480 per week plus 15% commission on all
of her sales. Which shows the amount she earns each week
as a function of her total sales, x?
A.

f(x) = 480(0.15x)

B.

f(x) = 480 + 0.15x

C.

f(x) = 480(15x)

D.

f(x) = 480 + 15x

The city of Smallville had an increase of 8% in its tax revenues from last year to this year. For next year, the mayor
projects the city’s tax revenues to increase by 10% from
this year. What will be the total percent increase from last
year to next year’s projection?
A.

18%

B.

18.8%

C.

19%

D.

19.8%

CONTINUE
Peterson's SAT® Prep Guide 2017

  881

Practice Test 4
6

7

8

  882

A random sample of people in a county were asked whether or not they drive more when gas prices decrease. Of the
682 people who responded, 471 of them said they do not
drive more when gas prices decrease. If there are about
898,000 people living in the county, about how many
people would be expected to not drive more when gas
prices decrease?
A.

280,000

B.

320,000

C.

580,000

D.

620,000

A scale model drawing of the Moon shows its diameter
as 6 inches. The scale of the drawing is 1 inch = 360 miles.
What is the approximate diameter of the actual Moon?
A.

2,160 miles

B.

2,260 miles

C.

3,060 miles

D.

3,360 miles

There are 380 seats in a movie theater. The theater must
collect at least $600 in admission per movie screening in
order to make a profit. The prices for admission are $6.50
for children and $8.25 for adults. Solving which of the following systems of inequalities yields the number of child
tickets, x, and the number of adult tickets, y, sold?

A.

x + y ≥ 380
6.5 x + 8.25 y ≤ 600

B.

x + y < 380
6.5 x + 8.25 y > 600

C.

x + y ≤ 380
6.5 x + 8.25 y ≤ 600

D.

x + y ≤ 380
6.5 x + 8.25 y ≥ 600

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Practice Test 4
9

A couch is on sale for 15% off the retail price r. A 6% sales
tax is added to the sale price. Which expression represents
the total cost of the couch, including the sales tax?
A.

0.15r + 1.06

B.

0.85r + 1.06r

C.

0.85r × 1.06

D.

0.15r × 1.06r

SHOW YOUR WORK HERE

10 Which of the following equations could be used to determine the number of ounces of a 26% fertilizer solution
should be mixed with 80 ounces of a 12% fertilizer solution
to make a 20% fertilizer solution?

11

A.

0.26x + 0.12(80) = 0.20(80 + x)

B.

0.38(80 + x) = 0.20

C.

0.26(80 – x) + 0.12x = 0.20(80)

D.

0.26(80) + 0.12x = 0.20(x + 80)

3
, which of the following expressions is
b
a−3
?
equivalent to
3b − 3
If b ≠ 1 and a =

A.
B.
C.
D.

–b
1
−
b
–a
1
a

12 Which of the following is equivalent to 34 x 3 ?
4

A.

3x 3

B.

3x 4

C.

3 x3

3

D.

( )
3( x )

4

1
4 3

CONTINUE
Peterson's SAT® Prep Guide 2017

  883

Practice Test 4
13 Aaron earns $9 per hour working part-time at the pool and
$11 per hour working part-time at the bakery. He needs
to make at least $215 each week, but he cannot work
more than a total of 25 hours each week. Which system
of inequalities represents this situation, where x is the
number of hours at the pool and y is the number of hours
at the bakery?
A.

9 x + 11y ≥ 215
x + y ≤ 25

B.

9 x + 11y < 215
x + y < 25

C.

9 x + 11y < 215
x + y > 25

D.

9 x + 11y > 215
x + y ≤ 25

14 A car and an antique truck depart from the rest area at
the base of a mountain at noon, both heading up the
mountain. The average speed of the car is 15 miles per
hour slower than twice the speed of the truck. In 3 hours,
the car is 21 miles ahead of the truck. How fast is the car
traveling?
A.

11 miles per hour

B.

22 miles per hour

C.

25 miles per hour

D.

29 miles per hour

15 What is the y-intercept of the line whose equation is
3x + 4y = 16?

  884

A.

3 
 , 0
4 

B.

(4, 0)

C.

 3
 0, 
 4

D.

(0, 4)

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Practice Test 4
Questions 16 and 17 refer to the following information.

SHOW YOUR WORK HERE

Amount of Radioactive Material (in grams)

The graph below shows the amount of radioactive material in y
grams that remains after x days in a container. Each point shows a
measured amount that remains, and the best fit relation between
those points is drawn to connect those points.

18

y

16
14
12
10
8
6
4
2
0

2

4

6

8

10

x
12 14 16 18

Days
16 Which of the following equations would describe the
relationship between the amount of radioactive material
and the number of days that have passed?
A.

f(x) = 3x + 18

B.

g(x) = 18 – 2.5x

C.

h(x) = 18e0.5x

D.

j(x) = 18e–0.4x

17 If 2 grams were left, how many days had radioactive
material been in the container?
A.

4

B.

5.5

C.

6.5

D.

8.5

CONTINUE
Peterson's SAT® Prep Guide 2017

  885

Practice Test 4
18

H

I
3a

4a

47°

b
F

G
Note: Figure not drawn to scale.

In the rectangle FGHI above, what is the value of ∠b?
A.

17°

B.

20°

C.

33°

D.

45°

19 The population of a country has been growing at an annual
rate of about 2.5%. The population in the year 2014 was
estimated at 339,800. Which of the following equations
shows the projected population of the country x years
after 2010?
A.

y = 339,800(1.025)x

B.

y = 339,800(1.025)x – 4

C.

y = 339,800(2.5)x

D.

y = 339,800(2.5)x – 4

20 A city newspaper randomly surveyed 250 subscribers
about their support for the mayor. Of the respondents,
27% said they supported the mayor, and the results had a
margin of error of 3%. The newspaper ran a headline that
less than 30% of city residents support the mayor. Which
of the following statements best explains why the results
do not support the conclusion stated in the headline?

  886

A.

The sample size is too small.

B.

The percent of supporters could be exactly 30.

C.

The margin of error is too large to make any
conclusions.

D.

The sample is likely biased and not representative
of the city.

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Practice Test 4
21
Identify the value if a, if a > 0 and
A.

3 3

B.

3 2

C.

2 3

D.

2 2

2
3 −a 3

( )

 1
= 9 a
 

SHOW YOUR WORK HERE

−6

.

Questions 22 and 23 refer to the following information.
The tables below give the number of days of rain per month for
one year in Town A and Town B.

Frequency

Days of Rain
Per Month

Frequency

Town B

Days of Rain
Per Month

Town A

5

1

1

1

6

3

3

3

7

2

5

2

8

1

9

1

9

2

12

2

10

1

15

1

11

2

19

2

22 Which of the following is true about the data shown in the
table?
A.

The median number of days of rain is greater in
Town A.

B.

The median number of days of rain is greater in
Town B.

C.

The median number of days of rain is the same in
both towns.

D.

There is not enough information to compare the
mean, median, or mode.

CONTINUE
Peterson's SAT® Prep Guide 2017

  887

Practice Test 4
23 Which of the following is true about the standard deviation
of the data shown in the tables?
A.

The standard deviation of days of rain per month in
Town A is greater.

B.

The standard deviation of days of rain per month in
Town B is greater.

C.

The standard deviation of days of rain per month is
the same in both towns.

D.

There isn’t enough information to calculate the
standard deviations.

24 The graph of a linear function has intercepts at (a, 0) and
(0, a). Which of the following is true about the slope of the
graph of the function?
A.

It is positive.

B.

It is negative.

C.

It is zero.

D.

It is undefined.

25 What is the value of x in the diagram below?
(x–25.5)

36°

38°

Note: Figure not drawn to scale.
Note:
Figure not drawn to scale.

  888

A.

16

B.

41.5

C.

54

D.

79.5

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Practice Test 4
Questions 26 and 27 refer to the following information.

SHOW YOUR WORK HERE

A poll surveyed 300 randomly selected voters for an upcoming
city election. Of the respondents, 31% said that they will vote for
Candidate A. The margin of error for the results was ±4% with
95% confidence.
26 Which of the following statements is best supported by
the data?
A.

The sample size is too small to make an inference
about the election.

B.

The margin of error is too large to make an
inference about the election.

C.

The sample is likely biased, so an inference about
the election cannot be made.

D.

The sample is likely unbiased and large enough to
make an inference about the election.

27 Which of the following statements can be best drawn from
this data?
A.

The actual percentage of voters who will vote for
Candidate A is 27%.

B.

The actual percentage of voters who will vote for
Candidate A is 35%.

C.

The actual percentage of voters who will vote for
Candidate A is most likely between 27% and 35%.

D.

The actual percentage of voters who will vote for
Candidate A is most likely between 91% and 99%.

CONTINUE
Peterson's SAT® Prep Guide 2017

  889

Practice Test 4
28 The diameter of Pluto’s largest moon Charon is about
750 miles. The diameter of Pluto is about 2 times greater
than the diameter of Charon. Which of the following best
describes the volume of Pluto?

29

A.

The volume of Pluto is about two times as great as
the volume of Charon.

B.

The volume of Pluto is about four times as great as
the volume of Charon.

C.

The volume of Pluto is about six times as great as
the volume of Charon.

D.

The volume of Pluto is about eight times as great as
the volume of Charon.

y = −2
y = ax 2 − b
Which of the following values for a and b will make the
system of equations have one solution?
A.

a = 3, b = –3

B.

a = –2, b = –2

C.

a = –2, b = 2

D.

a = 3, b = 3

30 h(x) = –(x – 8)(x + 2)
Which of the following is an equivalent form of the function h above in which the maximum value of h appears as
a constant or coefficient?

  890

A.

h(x) = –x2 + 16

B.

h(x) = –x2 + 6x + 16

C.

h(x) = –(x + 3)2 – 7

D.

h(x) = –(x – 3)2 + 25

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SHOW YOUR WORK HERE

Practice Test 4

DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the
answer sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
1
7
5.  	 Mixed numbers such as 3 must be gridded as 3.5 or .
2
2
1
1
31
If 3 is entered into the grid as
, it will be interpreted as
, not 3 .)
2
2
2
6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

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5

5

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6

6

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9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

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4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

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0

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1

1

1

1

1

1

1

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2

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3

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3

3

3

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8

9

9

9

9

9

9

9

6

6

CONTINUE
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  891

Practice Test 4
31 Sorin rents a car for $49, plus mileage, for the weekend.
The car rental company charges a fee for every mile over
100 miles driven. The equation y = 49 + 0.24(x – 100) shows
the total cost to rent the car and drive x miles. What is the
fee per mile if driving in excess of 100 miles?

32 Amber has $25 to spend. She wants to buy a book that
costs $12 and pens that cost $2.75 each. What is the greatest number of pens she can buy?

33 A team scored 74 points in a basketball game, not including foul shots. They scored on a total of 33 attempted shots,
which are broken down into 2-point shots and 3-point
shots, depending on where the shooter is standing on the
court. How many 2-point shots did the team score in the
game?

  892

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Practice Test 4
Questions 34 and 35 refer to the following information:
The data provided in the table shows the results of a 2010 census showing the estimated population of four countries, in millions of
people, divided into males and females in each country.

Canada

China

Mexico

United
States

Total

Males

16.9

696.3

55.9

153.1

922.2

Females

17.1

645.0

57.5

157.2

876.8

Total

34

1,341.3

113.4

310.3

1,799.0

34 If a person is chosen at random, what is the probability that
the person is a female from China? Express your answer as
a decimal rounded to the nearest hundredth.

SHOW YOUR WORK HERE

35 If a person is chosen at random, what is the probability
that the person is from Mexico or the United States, given
that the person is male? Express your answer as a decimal
rounded to the nearest hundredth.

36

g( x ) =

1
( x − 6) + 2( x − 6) + 1
2

For what value of x is the function g above undefined?

Questions 37 and 38 refer to the following information.
A famous painting last sold for $300,000 ten years ago. Similar
paintings have increased by about 14% annually in that time. The
current owner of the painting is using the equation V = 300(r)t
to model the value, V, in thousands of dollars t years after it was
last sold.
37 What value should the current owner use for r?

38 What is the estimated value, to the nearest whole thousands
of dollars, of the painting today? (Disregard the dollar sign
and any commas when gridding your answer. For instance,
if your answer is $2,359,000, enter 2359 in the grid.)

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
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  893

Practice Test 4
SECTION 5: ESSAY
50 Minutes—1 Essay
Directions: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

As you read the passage below, consider how the writer, Marc de Rosnay, uses the following:
• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed.

Adapted from “Milestones: what is the ‘right’ age for kids to travel alone, surf the web, learn about war?” by Marc de Rosnay,
originally published by The Conversation on January 4, 2015. Marc de Rosnay is a Professor and Head of Early Start at the School
of Education at University of Wollongong, Australia. (This passage was edited for length.)
1

Being a parent presents some problems. Irrespective of what you want, your children are going to take actions or be
exposed to things that you may not relish. There is the ever-present possibility that they will experience things that you
want to actively protect them from. The web provides some salient examples, like pornography. I really don’t want my
eight-year-old seeing pornography.

2

However, when my eight-year-old asks me an important Dungeons & Dragons question like, “Dad, can a paladin do magic
and wear armour?” or he wants to know how solar panels operate, I always encourage him to look on the web. I’ve taught
him to search on Google, to follow his curiosity, and I sometimes do it with him.

3

Ultimately, I want him to be able to seek answers to the questions that are interesting to him independently. He is
guaranteed to run into something dodgy on the web, and my wife and I can take ordinary precautions.

4

To our way of thinking, however, more extreme precautions—prohibiting unsupervised internet use and high-level
parental control—start to present their own risks.

5

One might ask, at what age should I allow my child to use the web unsupervised?

6

From the perspective of developmental and educational psychology, this is a slightly odd question. Let me explain. Most
parents are familiar with the idea that certain developmental achievements happen at specific ages. Thus, infants become
more wary of strangers at about nine months of age (stranger wariness), and they start to point communicatively by about
12 months of age (declarative pointing). These kinds of developments in the child’s capacity are to be expected in all
children given a typical environment; we call them developmental milestones.
…

CONTINUE
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  895

Practice Test 4
7

I spoke recently to a friend who wanted her ten-year-old daughter to be able to get to school, in the city, on public transport
from the inner-west by herself. This particular young girl is very intelligent and responsible, I’m sure that she could have gotten
herself to school at seven years of age. But there is no way her parents would have felt comfortable about that.

8

Why? For her parents to give her the independence to travel to school alone, they need to be satisfied not just that she can
present her ticket, change trains, and get on the right bus, they need to be confident that she understands the importance of
staying on the path, like Little Red Riding Hood.

9

This understanding is largely derived from countless conversations in which the parents have been able to convey important
information about the world and the risks it presents to their daughter.

10

We know that children seek information from the people they trust, and from people who have a good record at providing useful
information; actually, these two things are not unconnected. Between early childhood and mid-adolescence children have to
understand all sort of things for which they need information from people they trust.

11

The information we convey to our children, and the manner in which we do it, helps prepare them for life. For most things, like
knowledge about their bodies and sexuality, there is no particular moment at which children are ready for specific knowledge or
experience, and much of this we can’t control anyway.

12

But what we can do is answer their questions honestly in a manner that is appropriate for their age and conveys our values. The
risks of overprotection are simple: children will grow up anyway but they won’t have access to good information from people
that they trust.
So what age is a good age?

13

It is very difficult to put an age on when a child should or shouldn’t be able to grasp a new domain of independence. Your
decisions will depend on specific circumstances . . . Managing risk is critical.

14

The web provides a salient example. By year five or six, today’s children should have some freedom to search for the information
they need independently. They can do this in a family space rather than in their bedroom. Talk to them honestly about the
unsavoury content on the web; this will give them a framework for managing troubling or embarrassing content with you.

15

Independent action is also very important for children. Think back to your own childhood, there is a good chance that some of
your fondest memories don’t involve adults. Sometimes, children can walk to the shops before they are 12 years old, and around
this time, they should be able to stay in the house for a little while as well.
…

16

Independence is linked to responsibility and much can be done to build responsibility in children before they undertake fully
independent actions. But when you give your children independence you provide them with evidence that you trust them, and
that trust fortifies responsibility in a way that supervised activity cannot.

Write an essay in which you explain how Marc de Rosnay builds an argument to persuade his audience
that being overly protective of children can be as risky as not protecting them enough. In your essay,
analyze how the writer uses one or more of the features previously listed (or features of your own
choice) to strengthen the logic and persuasiveness of his argument. Be sure that your analysis focuses
on the most relevant aspects of the passage.
Your essay should not explain whether you agree with Marc de Rosnay 's claims, but rather explain how
he builds an argument to persuade his audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  896

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Answer Keys and Explanations
Section 1: Reading Test

1. A

12. D

23. C

34. B

45. B

2. C

13. C

24. A

35. A

46. D

3. B

14. C

25. B

36. C

47. B

4. D

15. D

26. A

37. D

48. B

5. B

16. B

27. C

38. B

49. A

6. C

17. B

28. D

39. B

50. A

7. D

18. D

29. C

40. D

51. A

8. D

19. A

30. D

41. C

52. B

9. A

20. B

31. B

42. A

10. A

21. B

32. A

43. A

11. D

22. B

33. C

44. C

READING TEST RAW SCORE
(Number of correct answers)

1.

2.

The correct answer is A. Hoover spends paragraph 2
explaining how the government’s involvement in
businesses was necessary to solve economic problems
during World War I before concluding that although
government involvement in businesses is “justified in
war time, if continued in peace-time it would destroy
not only our American system but with it our progress
and freedom as well” (lines 19–21). Therefore, the best
answer is choice A. The fact that Hoover defends
government involvement in private businesses during
wartime eliminates choice B, which argues that the
government should never be involved in private
businesses. Choice C is incorrect because it draws an
extreme conclusion (“prevents businesses from making
any profit”) that Hoover never draws in the passage.
Choice D is too simplistic, failing to take into account
the role that government should play in business during
wartime and not play during peacetime.
The correct answer is C. Hoover supports the idea that
the government needed to take over businesses during
World War I because the entire country was mainly
focused on the war effort, so choice C is correct.
Although Hoover does describe the government as
having been despotic during World War I, he does not
draw the more philosophical conclusion that despotism
is required to fight despotism in general, so choice A is

not the best answer. Although Hoover says the
government became more socialistic during the
war, and this is generally acceptable only during
wartime, he does not make the extreme conclusion
that only a socialistic government can function
during wartime, so choice B is not the best answer.
He only discusses government takeover of businesses in terms of how it helps the economy and
the war effort; he does not imply the more negative
concept that businesses would actually hurt the
war effort by continuing to run privately during
wartime, so choice D is not the best answer choice.
3.

The correct answer is B. In lines 12–13, Hoover
explains that “The government having absorbed
every energy of our people for war, there was no
other solution,” which supports the idea that the
government needed to take over businesses during
World War I because the entire country was mainly
focused on the war effort. Choice A merely
introduces the idea of the government becoming
more involved in the economy; it does not get into
why this was necessary, so it is inadequate evidence
to support the previous correct answer. Choice C
seems to make the mistake that choice A was the
correct answer to the previous question since both
that choice and these lines refer to despotism.

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  897

Answer Keys and Explanations
Choice D just goes on to define how the government
became despotic, and that does not support the
previous correct answer.
4.

5.

6.

  898

The correct answer is D. In these two paragraphs,
Hoover explains that his general statements are not to
be interpreted as extreme positions, and in doing so, he
provides some details to clarify his position, beginning
his clarification with the explicit introductory phrase “I
do not wish to be misunderstood” (line 60). Hoover is
merely clarifying his position in these paragraphs; he is
not changing his position at all, so choice A is incorrect.
Although Hoover does summarize a few of his previously made points in these paragraphs (“I have already
stated . . . by-product” lines 61–66), he does not repeat
every point he had made in the passage up until this
point, so choice B is incorrect. While Hoover does feel
strongly about his position, he does not assume that his
position is that of all Americans, which would be too
extreme and too unrealistic since different individuals
often have different ideas, so choice C is incorrect.
The correct answer is B. Hoover begins this line by
stating “Nor do I wish to be misinterpreted,” because a
misinterpretation of his words could lead someone to
twist them into believing that he is saying something he
does not intend to say, such as the belief that the United
States should be a “free-for-all,” which would be an
extreme interpretation of his position. Hoover is making
a general statement about the government’s role in
private business in this passage; there is no evidence that
he is trying to drum up votes for himself or anyone else,
so choice A is incorrect. Hoover is only clarifying his
position in these lines; he is not changing or softening his
position, so choice C is incorrect. There is establishment
of context in these lines, so choice D is also incorrect.
The correct answer is C. In the passage, Hoover
suggests that liberalism is a defining characteristic of
the American system, so choice C is the best answer.
Although Hoover believes that liberalism is a defining
characteristic of the American system, he does not
make the extreme judgment that America is the only
liberal country, so choice A is incorrect. However,
Hoover does say that liberalism is more important to
the American system than the European system (lines
58–60), which is the opposite of the conclusion in
choice B. Hoover never makes any comparison between
liberalism and conservatism, which he does not
mention at all in this passage, so choice D cannot be
correct.

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7.

The correct answer is D. By defining liberalism as “the
true spirit in the American system,” Hoover is distinguishing it as the defining characteristic of that system,
so choice D is correct. Choices A and B simply make
general statements about liberalism, neither of which
connect it to the American system specifically, so these
are not the best answer choices. Choice C only mentions
an effect of expanding the government’s role in
business; it does not define the role of liberalism in the
American system, so it is incorrect.

8.

The correct answer is D. The map shows the electoral
votes being wildly in Hoover’s favor, with Smith only
winning seven states for a total of 82 votes. The
description of Hoover’s victory as a “landslide” in the
caption supports the idea that a “landslide” is a decisive
victory, so choice D is the best answer. This conclusion
also eliminates choice B, which is the opposite of the
correct answer. Electoral votes and popular votes are
not the same thing, and there is no mention of popular
votes in this map, so choice A is incorrect. How hard the
campaign was is not something that can be determined
from this map, so choice C is incorrect.

9.

The correct answer is A. A labyrinth is a maze or a
puzzle, which in the context of the sentence shows that
Hoover is referring to the problems that will ensue if
government gets into business. The result, he says, will
be a tangled mess of bureaucracy rather than a smooth
operation.

10.

The correct answer is A. In the context of this sentence, the word “regimented” refers to the organization
of people or government. Although the context is
military, the regiment here refers to the civilian
population.

11.

The correct answer is D. Stowe recalls how she was
deeply affected by the loss of her young child, while
Douglass describes escaping from slavery. However, the
fact that he left behind friends who remained slaves is
certainly terrible too, so choice D is the best answer.
Only Douglass discusses the loss of friends to slavery, so
choice A is incorrect. Only Stowe discusses the death of
a family member and the fact that she had children
whom she loved deeply, so choices B and C can be
eliminated.

12.

The correct answer is D. In lines 10–12, Stowe explains
how her son’s death involved “cruel suffering,” which
partially supports the previous answer about how she
and Douglass lost loved ones in terrible ways. Choice A
merely introduces the idea that she had children. By
dealing with how much Stowe loved her children,

Answer Keys and Explanations
attitudes about slavery in the north and south in either
passage, and since there were many people in the
south, such as slaves, who were terribly angry about the
evils of slavery, choice C does not makes sense. Neither
passage indicates when the conflict over slavery started
heating up in relation to when these passages were
written, so choice D is incorrect.

choice B seems to make the mistake that choice C was
the correct answer to the previous question. Choice C
establishes that she felt terrible about her son’s death,
but it does not indicate that the circumstances of his
death were especially terrible.
13.

14.

15.

The correct answer is C. Stowe describes the process of
writing Uncle Tom’s Cabin in terms that emphasize how
extremely painful it was to recount the terrible experiences of the slavery era, so choice C is the best answer.
She does not indicate that it was artistically satisfying,
so choice A is incorrect, nor does she get into the actual
work involved in writing it, so choice B is incorrect as
well. While writing the book was extremely emotional,
she describes it in negative terms, so choice D is not the
most logical answer.
The correct answer is C. In lines 37–39, Stowe uses the
phrase “I thought my heart would fail utterly” to
illustrate how extremely painful it was to write Uncle
Tom’s Cabin, so choice C is the best answer. Choice A
alludes to how terrible the circumstances of slavery
were, which she illustrates by referring to “the depth of
the abyss,” but she doesn’t explain how that affected her
emotions, so it is not the best answer. Similarly, choice B
deals with the law records and not Stowe’s emotions, so
it is also incorrect. Choice D explains how Stowe got
through the extremely painful experience of writing
Uncle Tom’s Cabin; it does not establish the idea that
writing the book was extremely painful.
The correct answer is D. According to the key on the
map, the darkest areas had the most slaves and the
lightest ones had the fewest. Since the star indicating
Baltimore, the city in which Douglass lived as a slave
(line 44), is a medium-dark grey, choice D is the best
answer. Since black indicates extremely high slave
density, choice A is incorrect. Since a very light color,
such as white, indicates an area with extremely few
slaves, choice B is incorrect too. There is no way to reach
the conclusion in choice C from information in this
particular passage/map pair.

16.

The correct answer is B. The addition of “An American
Slave, Written by Himself” reinforces the idea that it was
unusual for a slave to write anything, no less a complete
book. We can infer from the inclusion of this information
in the title that Douglass wanted to make sure no one
thought someone else had written the work.

17.

The correct answer is B. Both passages are written
documents of the evils of slavery created in the effort to
abolish the vile practice, which supports choice B and
eliminates choice A. There is no comparison between

18.

The correct answer is D. The only meaning of the word
that makes sense in the sentence is choice D. Here
Stowe is talking about the intense pain she felt when
discovering that the slave experience was even worse
than she had thought. Although “exquisite” can mean
beautiful or delightful, in this context its meaning is
intensely.

19.

The correct answer is A. In this part of the narrative,
Douglass describes his feelings about leaving his friends
when he escapes. These feelings are part of his struggle
to make the final decision to attempt the escape, so in
this context, he is contending with his feelings of pain
about the decision.

20.

The correct answer is B. In this part of the passage,
Stowe expresses her deep sorrow and says that what
would make her feel better would be knowing that she
could use her loss for some greater purpose. Her belief
in the evil of slavery and acting on that belief through
the abolitionist movement was one way she used to
come to terms with her child’s death.

21.

The correct answer is B. The fact that Stowe felt she
had to document what she wrote in the book indicates
that some people questioned the validity of the premise
of Uncle Tom’s Cabin. Her research lead her to discover,
not that the book got it wrong, but that the treatment
of slaves was even worse than she had imagined when
writing Uncle Tom’s Cabin. Choice B suggests that
whatever ideas Stowe recorded in the book were
incomplete, and she needed more work to further the
truth.

22.

The correct answer is B. The main idea of the passage
is how NASA and its partners monitor the satellites
orbiting around Mars to make sure they don’t collide. A
summary must include the main idea along with some
other information that provides an overview of the
entire text. Choice B includes both the main idea and
the detail that explains the reason the satellites need
monitoring. The passage doesn’t discuss gathering
information, choice A, and choice D is a detail.

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  899

Answer Keys and Explanations
23.

The correct answer is C. The passage details the
various spacecraft currently in orbit around Mars and
their sponsoring areas. Four belong to the United
States, one to India, and one to the European Union.

24.

The correct answer is A. The passage describes a close
call in which a collision alert was sounded because two
satellites came within a close distance of each other,
triggering the plans put in place for such an event. The
alarms are set so that the orbits can be closely monitored and steps taken to prevent a collision should they
be needed. Over that weekend, the alarms went off, but
no action was needed because it was determined that
the satellites were not that close to each other after all,
a fact the scientists could not predict earlier. While the
passage does not go into great detail about how the
scientists reacted to the alert, it certainly does not
indicate that they failed to respond to the alert
completely, so choice C is incorrect. There was only a
danger of collision during this period; the collision
never actually occurred, so choice D is incorrect.

25.

  900

The correct answer is B. These lines explain how the
satellites MAVEN and MRO came within collision
distance of each other, which provides evidence to
support the correct answer to the previous question.
Choice A merely introduces one of those satellites; it
does not describe the circumstances in which it was
involved on New Year’s weekend 2015. Choice C
explains how the message went out, not the more
important details of what was in the message, so it is
not the best answer. Choice D explains the resolution of
the incident, not what that incident was, so it is not the
best answer either.

26.

The correct answer is A. According to the passage, the
closer satellites come toward each other, the greater
danger to human life and each other they pose, so
choice A is the best answer. This fact also eliminates
choice C. If it were impossible to calculate the distance
between satellites was impossible to calculate until it
was too late, there would be no preventative point in
calculating at all, so choice B does not make sense. Also,
if the distance never varied, there would be no point in
reporting on satellites’ distance from each other, so
choice D is incorrect.

27.

The correct answer is C. A satellite could collide if its
orbital path crosses the orbital path of another satellite
at the same time. Choice C explains this relationship.
None of the other choices describes this relationship.

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28.

The correct answer is D. According to the first
paragraph of the passage, Mars Odyssey, MAVEN, and
MRO are all human-made satellites of Mars. Therefore,
choices A, B, and C can all be eliminated. That leaves
Phobos, choice D, as the only satellite in the graphic
(and this particular question) that could be a natural
one of Mars.

29.

The correct answer is C. The graphic depicts how
Deimos makes the widest orbit around Mars and does
not come nearly as close to the planet as the other
orbits do. Based on that, it is reasonable to conclude
that it is the satellite least likely to collide with the
planet, making choice C the best answer and choices A,
B, and D incorrect.

30.

The correct answer is D. “Conjunction” here is used to
describe the “connection” of satellites, causing a
collision, so choice D is the best answer. Choice A can be
eliminated because “rejection” has the opposite
meaning of “connection.” While “combination” can be
used as a synonym for “conjunction” in other contexts, it
does not make sense in this particular context, so choice
B can be eliminated. Choice C means “argument,” and
while there would certainly be conflict between two
satellites involved in a dangerous conjunction, they
cannot actually argue as humans do.

31.

The correct answer is B. In line 36, the word “future,” in
“projections of future trajectories” explains when the
data will be used, from which it can be inferred that
“projection” is something forecast for later or at a future
time. In this case the data consists of forecasts about the
paths of the satellites in the future as they travel in their
orbits.

32.

The correct answer is A. Because climate change is
already affecting the potato crops in Peru, especially
those at high altitudes, diversity of crops can help
determine which varieties are better suited for the
higher altitudes and warmer temperatures. Some
ancient varieties could be resilient to warmer temperatures, but the statement does not explain how diversity
of crops can be resilient to the effects of climate
change—choice B. According to the passage, it is
possible to help potatoes adapt to changes in the
climate (lines 63–66), so choice C is incorrect. Choice D
is incorrect because lines 58–66 indicate that the gene
bank could help save varieties of potatoes from
extinction.

33.

The correct answer is C. Diversity of crops can help
alleviate disease and enhance adaptation to different
environments, and the farmers are using more diverse

Answer Keys and Explanations
plants and seedlings. This tactic will help fight crop
failure and also help the crops to adapt to changing
conditions as the farmers experiment with breeds of
plants and seeds. Lines 1–2 only mention that world
leaders attend the UN summit on climate change, not
farmers, so choice A is incorrect. According to the
passage, climate change is causing a rise in pests that
devastate crops (lines 6–10), but it never suggests that
scientists are working to invent new kinds of pesticides,
so choice B is not the best answer. The passage does not
suggest that the farmers are trying out a different kind
of staple food, choice D.
34.

35.

The correct answer is B. The author explains that rising
temperatures are making it difficult to grow potatoes,
so it is logical to conclude that relatively cool temperatures are best for growing potatoes. This confirms
choice B as the best answer and eliminates choices A
and C. A climate can be cool and moist, but since
moisture level is not discussed in this passage, there is
no evidence to support choice D.
The correct answer is A. These are the lines that
explain how rising temperatures are bad for potato
farming, confirming that relatively cool temperatures
are ideal. Choice B is about the benefits of planting
diverse potato species, not the effect of temperature on
potatoes. Choice C is about the limitations of gene
banks, so it is irrelevant to the correct answer to the
previous question. Choice D is about how genetic
researchers are working with farmers to solve the
potato-farming problem.

36.

The correct answer is C. Choice C is best because it
includes the main idea of the passage—Peruvian
farmers are working to combat the effects of climate
change—and the idea that the strategies include both
the old and the new. Choice A includes only one facet of
this concept, and choices B and D are details that are
not needed in a summary.

37.

The correct answer is D. The passage describes the
effects of farming the potato, a staple crop for thousands of people, and how climate change is reducing
output of the crop. Although farmers and scientists are
working together in Peru and other places, it will be
challenging to stay ahead of the changes already
occurring. These changes, as described in the passage,
for example, having to move crops to higher altitudes,
may have limited use; as the article states, the land at
higher altitudes is scarce and rockier. The passage also
states that efforts to maintain a gene bank to increase
crop diversity are limited, and sometimes the crops

don’t respond well and/or not all farmers have access to
the gene banks. These factors suggest that the problem
could grow worse.
38.

The correct answer is B. According to the author, some
farmers are dealing with the devastating effects of
climate change on vegetable growing by raising
animals for meat instead. According to the passage,
droughts are a major problem for farmers, but it never
suggests that these farmers are dealing with that issue
by studying how to stop droughts themselves, so choice
A is incorrect. It also indicates that some farmers are
working with modern varieties in reaction to climate
change, but they are crossing them with other varieties,
so choice C is incorrect since it indicates that farmers are
only growing modern varieties. While choice D is
possible, it is not mentioned in the passage, so it cannot
be deduced with information in the passage as this
question requires.

39.

The correct answer is B. Lines 67–68 explain that
farmers are dealing with climate change by raising
“hardy . . . livestock breeds,” so choice B supports the
previous answer well. Choice A only suggests that
farmers are adapting to climate change; it does not
explain how they are adapting. Choice C seems to make
the mistake that choice A was the correct answer to the
previous question since it references droughts. Choice D
makes the same mistake with choice C from the
previous question since these lines reference modern
varieties.

40.

The correct answer is D. In some contexts, the word
“pronounced” can mean “to articulate,” choice A, but
here it is used to refer to how “noticeable” the temperature changes are in the Potato Valley; in fact, the
entire passage describes the effects of climate change
on crops in the Potato Valley, so those effects must be
noticeable enough there to warrant such a discussion.
Therefore, choice D is the best answer. Choices B and C
do not make sense in this particular context.

41.

The correct answer is C. The word “ancestors” suggests
someone who existed hundreds of generations ago, so
the sentence in choice C indicates that the potato is a
food that was grown for food a very long time ago.
Choice D refers to the past, but one would not refer to
relatives past as “ancestors” if they lived as recently as
the 1960s. Choices A and B do not refer to past events
at all.

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Answer Keys and Explanations
42.

43.

  902

The correct answer is A. This sentence refers to how
the farmers care for their native plants; they are
“managing” them as they try to find breeds that are
hardier at higher altitudes and withstand some of the
effects of higher temperatures. None of the other words
conveys this exact meaning—the farmers can’t control
the seedlings, choice B; nor can they regulate them,
choice C. The farmers are not developing the crops,
choice D; scientists are working on that aspect.
The correct answer is A. The myth includes two
examples of deception to achieve goals: one when
Thetis sends Achilles to the court of King Lycomedes
disguised as a young girl and the other when Ulysses
disguises himself as a merchant to gain access to the
royal palace. Both acts show people trying to deceive
others to get what they want. The gods aren’t shown to
control events so much as cleverly intervene in human
endeavors, so choice B is wrong. Marriage loyalties are
shown as bonds that can be broken (Helen willingly
went off with Paris though she was married to
Menelaus), making choice C incorrect. There are several
references to the dangers of war, choice D, but the men
are encouraged to join the war efforts.

44.

The correct answer is C. Ulysses had urged others to
swear to defend Helen, but when he was called upon to
do the same, he opted out because he didn’t want to
upset his happy life. This decision was hypocritical,
choice C. While refusing to participate in a war can be
very courageous under certain circumstances, Ulysses’s
reasons were personal, selfish, and a violation of his
own oath to protect Helen, so choice A can be eliminated. Choice B can be eliminated too since breaking an
oath is a betrayal of loyalty. While it is possible that
Ulysses was afraid, the passage never makes that clear,
and the correct answer must be “according to the
passage,” so choice D is not the best answer.

45.

The correct answer is B. The author states that Discord
was “Enraged at her exclusion” (line 6) from the nuptials,
and tossing the apple among the guests caused a
disagreement among the goddesses Juno, Venus, and
Minerva at the nuptials. Therefore, it is reasonable to
conclude that she was trying to ruin the ceremony by
reducing it to chaos and disharmony, so choice B is the
best answer. There is no reason to believe Discord was
actually interested in finding out who the fairest woman
was; she just knew that introducing such a question
would cause trouble, so choice A is not the best answer.
There is no evidence that the three goddesses were in
danger of being ejected from the nuptials, so choice C is

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not as strong an answer as choice B is. Since Discord
was angry and her goal was to cause trouble, a
motivation as sincere as the desire to present a gift is
unlikely, so choice D is incorrect.
46.

The correct answer is D. Lines 52–53 state that Thetis
was afraid that Achilles might perish if he went to war.
The battle was already beginning, so choice A is
incorrect. Her objections were based on her fear for his
safety, not any ideas about his future marriage plans,
making choice B incorrect. Her plan for Achilles to go to
King Lycomedes was not to ask for help, choice D, but
rather so he could avoid being drafted to fight by
concealing his true identity.

47.

The correct answer is B. According to the passage, the
main cause of the Trojan War was the fight between
Paris and Menelaus for Helen. It was the goddesses
Juno, Venus, and Minerva who fought over the apple, so
choice A is incorrect. The war did prove that Ulysses was
disloyal, since he refused to fight in it even though he
had sworn an oath to fight, but these circumstances did
not start the war, so choice C is incorrect. The marriage
of Paris and Helen, not the marriage of Peleus and
Thetis, started the war, so choice D is incorrect.

48.

The correct answer is B. Lines 27–31 explain how Paris
wanted the much-prized Helen for his wife even though
she was married to Menelaus, and after he persuaded
her to go with him, the Trojan War broke out. The men
set out to bring Helen back to her rightful husband.
Choice A only discusses the first meeting of Paris and
Menelaus and says nothing about the conflict between
the two men that led to the Trojan War. Choice C only
mentions the legacy of the war; it does not explain the
war’s cause. Choice D explains how Menelaus began
gathering soldiers to fight the war; it fails to mention
how the war started, so it is incorrect.

49.

The correct answer is A. The passage reveals that
Telemachus is Ulysses’ son when the young child is put
in danger, and Ulysses had to drop his guise as a
madman to save him. The fact that Telemachus was
Ulysses’ son, and not the other way around, eliminates
choice D. Both Telemachus and Ulysses were humans,
but neither was royalty, making choices B and C
incorrect.

Answer Keys and Explanations
50.

The correct answer is A. In lines 40–44, Palamades
intended to find out if Ulysses was actually mad or just
pretending, and he tests Ulysses by putting the infant
Telemachus in danger. Referring to how the “father”
(line 43) failed the test by saving the infant reveals the
relationship in choice A. Choice B just discusses the
aftermath of the test and reveals nothing about the
relationship between Ulysses and Telemachus. Choices C
and D are about Thetis and her son, not Ulysses and his.

51.

The correct answer is A. In line 35, the word “recover”
refers to what Menelaus wants to do to his wife, whom
Paris has taken. Therefore, the most sensible definition
of the word in this context is “retrieve,” which means “get
back.” Choices B, C, and D are all synonyms of “recover,”
but none make sense in this particular context. Paris
needed to retrieve his wife, not “balance” her, which
probably would not make sense in any context, so
choice B is wrong. One salvages wrecked objects, not
healthy human beings, so choice C is incorrect. Helen is
not damaged, she is just missing, so choice D does not
make sense either.

52.

The correct answer is B. The context of the sentence
indicates that “prudent counsels” is associated with
something told to Achilles by his mother. His mother
had advised Achilles to adopt the disguise to avoid
participating in the war, which reveals the cautiousness
of her advice, so choice B is the best answer. Had his
mother’s advice been “fierce,” she likely would have
impelled Achilles to fight rather than hide, so choice A
does not make sense. There is no evidence that there
was some legal component to Achilles’s mother’s
advice, so choice C does not make sense either. The
cautiousness of her advice shows that Achilles’s mother
cared about her son very much, yet choice D is the
opposite of caring.

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  903

Answer Keys and Explanations
Section 2: Writing and Language Test
1. B

11. B

21. B

31. A

41. B

2. D

12. C

22. C

32. A

42. D

3. A

13. B

23. D

33. D

43. B

4. A

14. C

24. C

34. C

44. B

5. B

15. B

25. A

35. B

6. C

16. D

26. A

36. C

7. D

17. A

27. B

37. D

8. C

18. C

28. D

38. B

9. A

19. D

29. B

39. D

10. C

20. C

30. C

40. A

WRITING AND LANGUAGE TEST RAW SCORE
(Number of correct answers)

1.

2.

3.

  904

The correct answer is B. This sentence provides key
context clues to help you determine if the underlined
word is correct. The sentence requires an adjective to
describe the type of education that would guarantee
“that African Americans remained socioeconomically
disadvantaged until well into the twentieth century.”
Clearly, this describes an inferior education. What word
among the answer choices best fits this description?
Choice B, inadequate, is correct. Choices A and D
describe an opposite type of education. Choice C
doesn’t make sense; “spacious” isn’t an appropriate
adjective to describe an education.
The correct answer is D. This sentence contains two
independent clauses that are neither separated by
appropriate punctuation nor connected with a
coordinating conjunction, making it a run-on sentence.
Only choice D provides the appropriate punctuation in
the form of a period, and thus it is correct. Choice A is
incorrect, as a comma alone is inadequate to separate
two independent clauses. Choice B is incorrect, as a
coordinating conjunction like “and” must be preceded
by a comma. Choice C is incorrect because it includes
no punctuation at all.
The correct answer is A. The third paragraph contains
information that contrasts with information presented
in the second paragraph. The introductory word
“however” is the best choice to connect these two

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contrasting ideas. Thus, choice A is the correct answer.
Choice B is incorrect because “moreover” is used to
introduce additional information to support the
preceding idea. Choice C is incorrect because “to begin
with” does not generally connect two ideas. Choice D is
also incorrect because it suggests a disconnected,
unimportant piece of information, which is not the case
here.
4.

The correct answer is A. The chart shows the median
net worth of households dropped from 2005 to 2009,
with Black households showing a drop from $12,124 to
$5,677. Thus, choice A is the correct answer, as the
median net worth of Black households did drop to less
than half of what it had been in 2005. Choice B is
incorrect, as the median net worth dropped, not rose.
Choices C and D are not correct because the median net
worth of all households fell in the same time period.

5.

The correct answer is B. In this sentence “urban
neighborhoods” must agree in number with “places,” so
choice B is the correct answer as both are plural. Choices
A and C are incorrect because “place” is singular. Choice
D is also incorrect because while “places” is plural,
“neighborhood” is singular.

6.

The correct answer is C. The first part of this sentence
requires no punctuation, so choice C is correct. Choice A
is incorrect because “only” should not be set off by a

Answer Keys and Explanations
correct answer, as the semicolons help to avoid
confusion by linking lists of items that already contain
commas. Choice A is incorrect, as there is no way to
discern the lists. Choice C is incorrect because the lack
of internal punctuation creates a run-on sentence.
Choice D is incorrect, as using periods in this way
creates a bunch of grammatically incorrect sentence
fragments.

comma. Choice B is incorrect because “and the ratification of the Fifteenth Amendment” should not be
separated by a comma from the preposition “with” as it
is part of the prepositional phrase. Choice D is incorrect,
as the entire phrase is an adverbial phrase that modifies
“did win” and should not be separated by a comma.
7.

8.

9.

The correct answer is D. The pronoun antecedent is
“Republican Party,” so the pronoun that refers to it
should be singular and gender neutral. Thus, choice D is
correct. Choice A is incorrect because “they” does not
agree with the antecedent in number. Choice B is
incorrect, as “he” is an incorrect shift in pronoun person.
Choice C is also incorrect, as “we” is an incorrect shift in
both person and number.
The correct answer is C. The context in this paragraph
suggests that African Americans supported the
Republican Party because the party somehow aided
them in gaining rights. The best choice, then, is
“championed”, choice C, as it implies that the
Republican Party fought for the rights of African
Americans. Choice A is incorrect because “discern“
means “to perceive,” which doesn’t suggest a good
enough reason for African Americans to support the
party. Choice B is incorrect, as “evinced” means “reveal”
and that, too, is not a strong enough reason for African
Americans to support the party. Choice D is incorrect
because African Americans would not support the
Republican Party if the party disputed or argued against
their rights.
The correct answer is A. The context suggests that the
state election codes were somehow limiting for African
American candidates, as they were not elected because
of the codes. Thus, choice A, “restrictive,” is the correct
answer. Choices B and D are incorrect, because
“favorable” and “progressive” would be used to describe
an opposite type of state election codes. Choice D is
incorrect, as “expansive” suggests that the codes
allowed a greater number of people to compete in the
elections.

10.

The correct answer is C. The writer should delete the
sentence because it introduces a detail that is not
directly related to the topic of the paragraph. Choice A
is incorrect because its details are irrelevant. Choice B is
incorrect because the scenic aspect of the South is not
necessary context for the following paragraph. Choice D
is incorrect because the sentence does not provide a
transition for the paragraph that follows.

11.

The correct answer is B. A semicolon is used to link lists
of items in which commas are used. Thus, choice B is the

12.

The correct answer is C. The antecedent in this
sentence is Morocco, so the pronoun “its” must be used
for agreement. Thus, choice C is the correct answer.
Choice A is incorrect because “they” does not correctly
refer to Morocco but rather to Moroccans, a noun that is
not used in this sentence. Choices B and D are incorrect,
as there are no logical antecedents to which “our” and
“your” might refer.

13.

The correct answer is B. The paragraph is about the
influence that Moroccan music has had on non-Moroccan musicians, and only choice B maintains this focus
by pointing out how some jazz musicians were
influenced by Moroccan music. Choices A and C are
incorrect because the sentences take the focus off
Moroccan music and on the people who influenced the
Rolling Stones. Choice D is incorrect because it talks
about how other types of music have influenced
Moroccan music.

14.

The correct answer is C. The clause “covered with
farmland and several large cities and towns” is a
nonrestrictive phrase, which means that it is not
necessary for understanding the sentence; thus it
should be set off with commas, choice C. Choice A is
incorrect, as commas are necessary to indicate that the
information contained within them is additional and
nonessential. Choices B and D are incorrect because
other commas are necessary in the sentences.

15.

The correct answer is B. The existing initial sentence of
the paragraph describes the “dense population clusters”
of Berbers throughout Morocco. Which of the sentences
among the answer choices would serve to introduce
and support this fact? Choice B would make the most
effective lead-in sentence. The other answer choices
don’t serve to introduce the initial contention of this
paragraph. Choice A is incorrect because, although the
author mentions foreign invaders, the main topic is to
explain who the Berbers are. Choice C is incorrect
because the author’s focus is on who the Berbers are,
not where their ancestors lived. Choice D is incorrect
because this is a minor point in the paragraph.

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Answer Keys and Explanations
16.

17.

18.

19.

20.

  906

The correct answer is D. Here, the possessive determiner “their,” choice D, is correct, as the word describes
ancestors belonging to the Berbers. Choice A is
incorrect because “there” is an adverb telling where.
Choice B is incorrect because “they’re” is a contraction of
“they are.” Similarly, choice C is incorrect because
“theyre” is the contraction of “they are” spelled
incorrectly.
The correct answer is A. The context suggests that the
word “barbarian” does not fit the Berber people, and
“misnomer”means “inaccurate name.” Thus, choice A is
the correct answer. Choice B is incorrect, as
“euphemism” means “a milder word for one considered
too harsh,” which is not what the context suggests.
Choice C is incorrect, as “locution” refers to the way a
word is pronounced. Choice D is incorrect because the
context, that the Berbers are gracious and hospitable
people, is not a reflection of the term “barbarian”, which
suggests the opposite of gracious and hospitable.
The correct answer is C. The author explains that the
Berbers and most of the other tribes became Islamic.
The context, then, suggests that the other tribes were
like the Berbers, which means they were indigenous, or
native to the area. Choice C is the correct answer. Choice
A is incorrect because “notorious” means “famous”,
usually for something bad, and there is no indication
that this was so. Choice B is incorrect because “autonomous” means “independent”, and the idea of
autonomy, for the Berbers or any tribe, is not noted
anywhere else. Choice D is incorrect because “illustrious”
means “distinguished” and this, too, is not supported by
the context.
The correct answer is D. This sentence requires proper
internal punctuation to ensure clarity and appropriate
grammatical construction. Choice D deploys appropriate internal punctuation to produce a clear, grammatically correct sentence. Choice A is incorrect; the
sentence is a run-on as written. Choice B is also
incorrect; the commas are place inappropriately and
create confusion. Choice C uses end punctuation
(periods) inappropriately and creates sentence
fragments.
The correct answer is C. It is unclear what the pronoun
here refers to. For clarity, the sentence must restate the
antecedent, thus choice C is correct. Choice A is
incorrect because it is unclear whether “it” refers to the
music, the traditions, or Morocco. Choice B is incorrect,
as it doesn’t make sense in this context. Choice D is
incorrect because the rest of the paragraph focuses on

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the music and musical traditions, not everything that
the caravans carried.
21.

The correct answer is B. This answer provides another
example of the instruments used in Andalusian music.
Choice A is not an example; it describes another aspect
of Andalusian traditions. Choice C gives a detail about
the example given rather than a second example.
Choice D provides further information about
Andalusian culture and is not a further example of the
types of instruments used.

22.

The correct answer is C. As the second sentence is an
explanation of the first, a colon would be an effective
way to combine these two independent clauses. Choice
A is incorrect because it creates a run-on sentence.
Choices B and D use incorrect internal punctuation for
this sentence.

23.

The correct answer is D. The sentence would work
better later in the passage, after Dresselhaus’s honors
have been described and before her mentoring is
discussed. Choice A is incorrect because the sentence is
not a detail that supports the main idea. Choice B is
incorrect because the sentence is about her work later
in life, not her childhood. Choice C is incorrect because
the sentence does not detract from the main idea.

24.

The correct answer is C. The conventional expression
used here is “stroke of luck,” which means a fortunate
occurrence. Only choice C is an accurate representation
of this expression. Choices A, B, and D are incorrect
because they are inaccurate expressions.

25.

The correct answer is A. The context suggests that
Dresselhaus became aware that there were better
schools in the area, as she later got into a school for
girls. Choice A means the same as “aware”, thus it is
correct. Choice B is incorrect, as “apprehensive” means
“worried,” and there is no indication that Dresselhaus
was worried. Choice C is incorrect, as “dismayed” means
“alarmed,” and there is no sense that she was alarmed.
Choice D is incorrect, as “astute” doesn’t fit the context.

26.

The correct answer is A. The statement in the passage
provides more information about why Dresselhaus’s
original goal was to become a teacher, so choice A is
correct. Choice B is incorrect because it offers more
information about Hunter College, rather than
Dresselhaus’s goals. Choice C is incorrect because it
would fit better later in the passage. Choice D is
incorrect because it does not relate to why Dresselhaus
wanted to be a teacher.

Answer Keys and Explanations
27.

The correct answer is B. Only choice B avoids wordiness and redundancy, making it the correct answer.
Choice A is incorrect because “celebrated” and “gain
recognition” make the sentence unnecessarily wordy.
Choice C is incorrect because it is also wordy: “a little
later in her career” could easily be substituted for
“eventually,” and “one of the most prestigious awards in
her field” is unnecessary. Choice D is incorrect because
“but later” is redundant.

28.

The correct answer is D. In this sentence, “Yalow” is
possessive, and thus must be followed by ’s. Only choice
D reflects the correct spelling of this possessive noun.
Choice A is incorrect because there is no apostrophe
before the s. Choice B incorrectly places the apostrophe
after the s instead of before it. Choice C is incorrect
because it contains no apostrophe or s.

29.

30.

31.

32.

The correct answer is B. The context of the paragraph
makes clear that often, there were no other women in
the classes Dresselhau attended. The modifier “only”
must appear directly before the word it modifies, in this
case “woman.” Thus, choice B is the correct answer.
Choice A is incorrect because placing the modifier
before “she” makes the sentence unclear. Choice C is
incorrect because “only” modifies the verb “had been,”
again making the sentence unclear. Choice D is
incorrect because “only” modifies “there,” suggesting
that “there” was the only place she had been a woman.
The correct answer is C. The first sentence of the
paragraph notes that Dresselhaus studied in
Cambridge, England. And the second sentence notes
that she received her Ph.D. from the University of
Chicago. Since sentence 5 is about Dresselhaus
returning to the United States to continue her research,
it most logically fits between sentences 1 and 2. Thus,
choice C is the correct answer. Choices A, B, and D are
incorrect because they do not reflect a logical sequence
of events.
The correct answer is A. The author’s intention is to
point out that Dresselhaus is a distinguished scientist,
and only choice A reflects the correct spelling of the
word eminent. Choices B and C are incorrect, as
immanent means “inherent or within,” and imminent
means “impending or close at hand.” Choice D is
incorrect, as an emigrant is someone who leaves his or
her own country to settle in another.
The correct answer is A. In this sentence, the phrase
“about 20 percent of them women” represents a sharp
break in thought, and it should be set off by a dash. The

sentence as it is written is correct, so choice A is the
correct answer. Choice B is incorrect because a colon is
used before a list or explanation, and the phrase “about
20 percent of them women” is neither a list nor an
explanation. Instead, it is additional information. A dash
is more appropriate in this case. Choice C is incorrect
because a semicolon is used to separate items in a series
or two independent clauses. Although it employs a dash
correctly, Choice D includes a colon before “women,” an
addition that is unnecessary and incorrect.
33.

The correct answer is D. The context makes clear that
Dresselhaus enjoys her work and is interested in it. Only
“fascination” conveys this idea, thus choice D is the
correct answer. Choice A is incorrect, as “complacency”
means “self-satisfied,” but the word is usually used in the
context of being stuck in a position and unwilling to
move forward. Choice B is incorrect, as ”indifference”
would suggest that Dresselhaus had absolutely no
interest in physics, which is incorrect. Choice C is
incorrect, as “ignorance” suggests that Dresselhaus did
not have a solid understanding of physics, which is
incorrect.

34.

The correct answer is C. Choice C correctly introduces
the variety of useful functions that our sense of smell
provides us. Choice A is incorrect because it does not
effectively set up the information in the rest of the
sentence—namely, the variety of functions our sense of
smell provides. Choice B is incorrect because the focus
is on humans rather than dogs. Choice D is incorrect
because it focuses on other senses rather than on smell.

35.

The correct answer is B. The paragraph is written in the
present tense, as is the conditional clause that follows
the colon. Thus, this clause must be written in the
present tense, making choice B the correct answer.
Choice A is incorrect, as the clause makes an inappropriate shift to the future tense. Choice C is incorrect
because the clause makes an inappropriate shift to the
past tense. Choice D is incorrect because the clause
makes an inappropriate shift to the present perfect
tense.

36.

The correct answer is C. The comparison here is
between our knowledge of how the nose works and our
knowledge of how other senses work, thus choice C is
the correct answer. Choice A is incorrect because it
illogically compares our knowledge of how the nose
works to our general knowledge about the other
senses. Choice B is incorrect because it illogically
compares our knowledge of how the nose works to our
other senses, without specifying any particular thing

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Answer Keys and Explanations
about the other senses. Choice D is incorrect because it
illogically compares our knowledge of how the nose
works to how our other senses work, without mentioning the word knowledge.
37.

38.

39.

  908

The correct answer is D. The context of the paragraph
suggests that the fragrance of a rose is difficult to pin
down, as the author contrasts it with identifying a
D major chord or describing something that is silvery-blue. The word “elusive” best captures this sense, as
it means “difficult to capture or pin down.” Thus, choice
D is the correct answer. Choice A is incorrect because
“concordant” means “consistent,” which is not what the
author is trying to convey. Choice B is incorrect because
“distinct” means “recognizably different or distinguishable,” and the author’s point is that a rose’s scent,
while recognizable, is difficult to describe. Choice C is
also incorrect, as expansive means “covering a large
space or area” and does not fit within the context of this
sentence.
The correct answer is B. The paragraph makes the
point that our knowledge of how the nose differentiates
odors and our ability to categorize those odors is
limited. Only choice B supports this point by noting that
people who make scent their job have a hard time
agreeing on how to classify or categorize scents. Choice
A is incorrect because the fact that scientists have
classified scents into 10 groups directly contradicts the
point the author is making in the paragraph that our
ability to categorize scents is limited. Choice C is
incorrect because while it doesn’t contradict the
author’s main point, it also doesn’t support it. Choice D
is incorrect because it also contradicts the author’s main
point that scents are hard to categorize, as wine aromas
have been assigned to twelve different categories.
The correct answer is D. The writer should delete the
underlined part of the sentence because it adds
irrelevant details that are not related to the rest of the
passage. Choices A and B are incorrect because they
suggest adding irrelevant or erroneous information.
Choice C is incorrect because it is irrelevant and
shouldn’t be included at all.

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40.

The correct answer is A. The context of the paragraph
makes clear two points: We know that molecules up to a
certain mass have scents and that there are conflicting
theories as to what determines their smell and how the
nose records and transmits this information to the brain.
The second independent clause contrasts with the first,
as it presents uncertainty while the first points out what
we know. Thus, the coordinating conjunction “but” is
the best way to join these two clauses. Choice A is the
correct answer. Choices B and C are incorrect as they set
up a causal relationship that is inaccurate. Choice D is
incorrect as it doesn’t accurately establish the contrast
information presented in the two clauses.

41.

The correct answer is B. The style of the passage is
formal and objective, and only choice B corresponds
with this style. Choices A, B, and C are incorrect because
they employ an informal and subjective style, using
words like “stink,” “disgusting,” and “nasty.”

42.

The correct answer is D. Turin’s questioning of the
lock-and-key theory along with the results of his
experiments suggest that he has disproved the theory,
which makes choice D the correct answer. Choice A is
incorrect, as “invade” means to “enter and take control
by force” and does not fit within the context of this.
Choice B is incorrect, as “sanction” means “to support,”
and Turin’s experiments did not support the theory.
Choice C is incorrect, as “instigate” means “to bring
about or induce,” which doesn’t make sense in the
context.

43.

The correct answer is B. The sentence is clearly
interrogative and thus requires a question mark at the
end. Choice B, then, is the correct answer. Choice A is
incorrect, as a dash is not used as end-of-sentence
punctuation. Choice C is incorrect, as a period is used
for a declarative sentence, and this sentence is interrogative. Choice D is incorrect because an exclamation
point is used for an exclamatory statement, and this one
is not.

44.

The correct answer is B. The subject of the sentence is
“number,” which is singular, so the verb should agree in
number. Only “determines” agrees in number with the
subject, so choice B is the correct answer. Choice A is
incorrect, as “determine” is a plural verb. Choices C and
D are incorrect because both contain plural verbs as
well as shifts in tense.

Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. B

5. C

9. A

13. C

17. 234

2. D

6. C

10. D

14. A

18. 16

3. D

7. A

11. B

15. A

4. C

8. A

12. A

16. 3

19. 15
8
20.
(8/3) or
3
2.66 or 2.67

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B.

4.

3 x − 2 [1− 2( x + 4)] = 5 x
3 x − 2 [−2 x − 7] = 5 x
3 x + 4 x + 14 = 5 x
7 x + 14 = 5 x
2 x = −14
x = −7
2.

The correct answer is D. Subtract the two polynomials
by combining like terms:

30(3 × 1 – 1) = 30(3 – 1) = 30(2) = 60

(3 x − 7 x + 5) − (−6 x + 5 x − 4)
= (3 x − ( −6 x )) + ( −7 x − 5 x ) + (5 − ( −4 ))
2

2

2

It is the correct answer.

2

You can also solve this problem by thinking it through.
You are looking for a distance, and distance = rate ×
time. The rate is z miles per hour. The time is the amount
of time it took Angie to arrive at the party (3x) minus
any time she stopped during the trip B. So the time is 3x
– b. If you multiply the rate by the time to find the
distance, you get z(3x – b), which is choice C.

= 9 x 2 −12 x + 9
3.

The correct answer is D. To determine which point is
correct, substitute each value into each inequality:
A.

0 ≤ 3(0) − 4
5(0) + 4(0) ≥ 6

Wrong

B.

5 ≤ 3(−1) − 4
5(−1) + 4(5) ≥ 6

Wrong

C.

−3 ≤ 3(2) − 4
5(2) + 4(−3) ≥ 6

Wrong

D.

4 ≤ 3(3) − 4
5(3) + 4(4) ≥ 6

Correct

The correct answer is C. Pick values for the numbers.
Suppose x = 1. That means Angie took 3 × 1, or 3, hours
to get to the party. If it took her 3 hours to get to the
party, she could have stopped for 1 hour (b = 1) and
driven 30 miles per hour (z = 30). If she took 3 hours to
get to the party and she stopped for 1 hour, then she
was only driving for 2 hours. That means that she must
have driven 30 × 2, or 60, miles total. Now try the
answer choices. Plug in x = 1, b = 1, and z = 30. The
answer choice that is correct will also total 60. Choice C
results in:

5.

The correct answer is C. First, solve for s: 6s = 36; s = 6.
Now plug in 6 for s to solve for r: 3s – r = 9; 3(6) – r = 9;
18 – r = 9; –r = –9; r = 9.
Another way you could solve this is to work backwards.
After finding the value of s to be 6, plug in each answer
choice as a value for r. For example, if you started with
choice A: 3(6) – 3 = 18 – 3 = 15, which is not 9, so
eliminate choice A. You could try out each answer
choice until you reached choice C and found that: 3(6)
– 9 = 18 – 9 = 9, so C is correct.

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Answer Keys and Explanations
6.

7.

The correct answer is C. The value of y is dependent on
the number of x months of increasing deposits, so y
represents the amount that Gary deposits into his
account in month x, making choice C the correct
answer. Choice A incorrectly assumes that the equation
is totaling the amounts added each month, when it is
only calculating the amount deposited each month
based on the previous month. Choice B is incorrect
because the formula is calculating a total amount; the
variable x represents the number of months. Choice D is
incorrect because calculating the increase would
involve a comparison of the previous month(s).

12.

Slope of p =

2−4
2−0
−2
=
2
= −1

Since lines p and q are parallel, their slopes must be
equal. This means that the slope of q is also equal to −1.

 1
1
f   plug x = into the given function and simplify:
c 
c

8.

9.

Since you know that line q passes through points (0, 0)
and (x, y) and the slope is −1, you can write an equation
representing the relationship between x and y:

1
 1 d
= c   − = 1− cd
 c 1
c
c

Slope of q =

The correct answer is A. g(x) = 0 when either (x2 – a2) =
0 or (x2 + b2) = 0. The first of these has solutions x = a
and x = –a. The second one has only imaginary solutions, which do not yield x-intercepts. Therefore, the
graph of g(x) crosses the x-axis twice.

y −0
x −0
y
=
x
y
= −1
x
y = −x
x+y =0

Therefore, the relationship between x and y can be
represented by the equation x + y = 0.

x = –2, x = 3, x = 5

g(x) = f(x)(x + 2)(x – 3)(x – 5)
10.

11.

The correct answer is D. The total per package is 9
marbles, and 108 marbles is 9 × 12 = 108. So the
number of each color needs to be multiplied by 12; 3 ×
12 = 36, 4 × 12 = 48. 36 + 48 = 84.
The correct answer is B. When multiplying exponential
terms with the same base, exponents are added:
x

1
5

x

i x

4
5

1 4
+
5 5

=x

−a

= x −a

5
5

x = x −a
x 1 = x −a
−a = 1
a = −1

  910

www.petersons.com

y 2 − y1
x 2 − x1

=

The correct answer is A. The factors of a function can
be found from its x-intercepts through a process like
below:

x + 2 = 0, x – 3 = 0, x – 5 = 0

y 2 − y1
x 2 − x1

=

The correct answer is A. In order to find the value of

f

The correct answer is A. When two lines are parallel,
their slopes are equal. Since you know that line p passes
through points (0, 4) and (2, 2), you can use this
information to find the slope of p:

13.

The correct answer is C. In any right triangle the sine of
one acute angle is equal to the cosine of the other acute
angle.

D
e

f
E

d
opposite
hypotenuse
f 2
= =
e 3

sin F =

adjacent
hypotenuse
f 2
= =
e 3

cos D =

F

Answer Keys and Explanations
14.

The correct answer is A. First, find the center of the
circle by finding the midpoint of its diameter.

18.

 −9 + 15 7 + (−3)   6 4 
,

 →  ,  → (3,2)
2  2 2 
 2
Next, find the radius of the circle by finding half the
length of the diameter:

Using the Pythagorean theorem: a² + b² = c²; 6² + b² =
10²; 36 + b² = 100; b² = 64; b = 8. So now you know that
AB = 8 . You know that B is the midpoint of AD and that
the midpoint divides a segment in half. That means that
AB = BD . Since AB = 8 , BD also equals 8. That means that
the length of AD = 8 + 8 = 16.

( −9 − 15) 2 + (7 − ( −3)) 2
= 13
2
Then, plug the center and the radius into the standard
form for the equation of a circle and simplify:
( x − h) 2 + ( y − k ) 2 = r 2
( x − 3) 2 + ( y − 2) 2 = 13 2
( x − 3) 2 + ( y − 2) 2 = 169

15.

19.

The correct answer is A. Divide the two expressions
using either long division or synthetic division:

The correct answer is 15. Transfer the radical expressions on the opposite sides of the equation and then
square both sides:
x + 10 − 2 x − 5 = 0

3x + 4
x − 3 3x 2 − 5x + 9

)

The correct answer is 16. You know that opposite sides
of a rectangle are equal, so since ED = 6, CA must also
equal 6. You know from the diagram that CB = 10 . Since
ΔABC is a right triangle, you can use the Pythagorean
theorem or what you know about 3-4-5 triangles to find
the length of AB .

x + 10 = 2 x − 5

(

−(3 x 2 − 9 x )

x + 10

0 x 2 + 0 x + 21

3(3)2 – 5(3) + 9 = 27 – 15 + 9 = 21
16.

The correct answer is 3. To find a solution, first set the
equation equal to 0, since the height of the ball when it
hits the ground is 0. Then, solve the equation for t using
factoring.
0 = 6 + 13t − 5t 2
0 = 5t 2 − 13t − 6
0 = (5t + 2)(t − 3)

2

2x − 5

)

2

x + 10 = 2 x − 5
10 + 5 = 2 x − x
x = 15

0x 2 + 4x + 9
−( 4 x − 12)

Alternatively, you can use the remainder theorem to
solve. Substitute 3 for x in the numerator, and the value
should be the remainder:

) =(

20.

8
(8/3) or 2.66 or 2.67. For a
3
system of linear equations to have infinitely many
The correct answer is

solutions, the equations must be equivalent. To make
the first equation equivalent to the second equation, we
must multiply by –2:
−2( fx + gy = −16) = −2fx − 2 gy = 32
−2fx − 2 gy = 32
3 x − 8 y = 32
2
−2f = 3 → f = −
3
2g = 8 → g = 4

5t + 2 = 0; t = 3
2
t= − ;t=3
5
Since the time cannot be negative, the solution is t = 3.
The ball will hit the ground in 3 seconds.
17.

The correct answer is 234. Since m is a constant, that
means that m must always have the same value. So use
b = 6 to solve for m.
6b + m = 270
6 ( 6) + m = 270
36 + m = 270

Then write and simplify the ratio that is asked for in the
problem:
3
f =− , g=4
2
4
4 8
g
− =−
= =
3 3 3
f
−
2 2
8
, which you would grid as 8/3.
3
Also correct would be the decimal equivalent, 2.66 or
2.67.
The correct answer is

After subtracting 36 from both sides of the equation,
you will get m = 234.

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Answer Keys and Explanations
Section 4: Math Test—Calculator
1. B

9. C

17. B

25. D

33. 25

2. C

10. A

18. C

26. D

34. 0.36

3. D

11. B

19. B

27. C

35. 0.23

4. B

12. B

20. D

28. D

36. 5

5. B

13. A

21. B

29. C

37. 1.14

6. D

14. D

22. A

30. D

38. 1112

7. A

15. D

23. B

31. 24

8. D

16. D

24. B

32. 4

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B. Convert each speed to Machs,
as follows:

3.

Since the perimeter is 600, we have 2x + (2)length =

4 , 474 miles
1 hour
i
≈ 1.243 miles per second
3, 600 seconds
1 hour

600, so length = 300 – x. The time needed to install the
length portions of the fence is 2(300 – x )(t). The time

2,193 miles
1 hour
i
≈ 0.609 miles per second
3, 600 seconds
1 hour

needed to install the width portions of the fence is
5 
2(x)  t  . So, the total time needed to construct the
2 
entire fence is
5 
2 (300 − x )(t ) + 2 ( x )  t  = 600t + 3 xt minutes.
2 

Now, convert each to Machs, as follows:
1.243 miles per second
≈ 5.836
0.213 miles per second
0.609 miles per second
≈ 2.859
0.213 miles per second
Therefore, the difference in speeds of these two aircraft
in Machs is 2.977.
2.

  912

The correct answer is C. A negative correlation is a
relationship between two variables such that when one
variable increases, the other variable decreases. The
points on the scatterplot show that as the amount of
snowfall increases, the number of drivers on the road
decreases. Therefore, the scatterplot shows a negative
correlation.

www.petersons.com

The correct answer is D. The width of the field is x.

4.

The correct answer is B. The amount of $480 is
constant, and the amount she makes in commission
depends on her total sales. The term that represents her
commission should include the variable, and since she
makes 15% of her total sales x, the term 0.15x represents the amount of commission. Adding both of
these amounts together results in f(x) = 480 + 0.15x.

5.

The correct answer is B. Choose an initial amount for
the tax revenue for the town of $100,000. An increase of
8% would be an increase of $8,000 to $108,000. An
additional 10% increase the next year would be another
$10,800, for total revenue of $118,800. This is 18.8%
more than the original $100,000.

Answer Keys and Explanations
6.

The correct answer is D. 471 of the 682 respondents is
471
≈ 0.69 = 69% . To estimate the number of
about
682
people in the county who will not drive more if gas

11.

The correct answer is B. You know that b cannot equal
1. Pick values for a and b. For example, suppose b = 6.
That would mean that a = 0.5, because ab = 3. Plug in
these values for the expression given:

prices drop, multiply the entire population by the

a−3
0.5 − 3
=
3b − 3 3 ( 6) − 3

percent in the random sample.

−2.5
15
5 1
=− ×
2 15
1
=−
6

898,000(0.69) = 619,620
The answer that comes closest to this calculation is
choice D.

10.

The correct answer is C. The discount is 15%, or
1 – 0.15 = 0.85 of the retail price, which is 0.85r. The 6%
sales tax is added to this discounted cost, which is the
same as multiplying by 1.06. The expression combining
those two is 0.85r × 1.06.

12.

1
1
Since b = 6, − = − , which matches choice B.
6
b
The correct answer is B. Simplify the expression:

26%
solution

0.26

x

0.26x

12%
solution

0.12

80

0.12(80)

End result
20%
solution

0.20

80 + x

0.20(80 + x)

Therefore, the equation is 0.26x + 0.12(80) = 0.20(x + 80).

3

1

3 4 x 3 = 3( x 3 ) 4 = 3 x 4
13.

The correct answer is A. The amount earned per hour
is 9x for the pool and 11x for the bakery, and needs to
be at least $215, so 9x + 11y ≥ 215 represents this. The
total number of hours needs to be at most 25, so
x + y ≤ 25 represents this. Only choice A shows both of
these inequalities.

14.

The correct answer is D.

Car
Truck

The correct answer is A.

Number of ounces
of pure fertilizer

9.

The correct answer is D. There are 380 seats in the
theater, so the total number of tickets that can be sold is
at most 380. The theater will sell x child tickets and y
adult tickets for a maximum of 380 tickets, or
x + y ≤ 380 . The income from the tickets will be $6.50
per child, or 6.5x, and $8.25 per adult, or 8.25y. The total
amount the theater collects, 6.5x + 8.25y, has to be at
least $600, or 6.5x + 8.25y ≥ 600. Only choice D shows
both of these inequalities.

Number of ounces

8.

The correct answer is A. The model drawing of the
Moon’s diameter is 6 inches. To find the diameter of the
actual Moon, use the scale: 6 × 360 = 2,160. Therefore,
the approximate diameter of the actual Moon is 2,160
miles.

% fertilizer

7.

=

Distance
(in miles)

Rate
(in mph)

Time
(in hours)

d + 21

2r – 15

3

d

r

3

Using distance equals rate times time, we get the
following system of equations:
d + 21= 3(2r − 15)

d = 3r

To solve this system, substitute the expression for d
given by the second equation in for d in the first
equation to get an equation involving only r. Solve the
equation as follows:
3r + 21= 3(2r − 15)
3r + 21= 6r − 45
3r = 66
r = 22
So, the car is traveling at the rate of 2(22) – 15 = 29 miles
per hour.

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Answer Keys and Explanations
15.

The correct answer is D. The slope-intercept form of
the equation of a line is y = mx + b, where m is the slope
of the line and b is the y-intercept. The coordinates of
the y-intercept are (0, b).

19.

The formula for exponential growth is y = a(1 + r)n,
where a is the initial amount, r is the rate at which the
amount is increasing, and n is the number of times that
the amount increases at that rate. In this question a =
339,800, r = 0.025, and n = x – 4. Plugging these values
into the formula, we get y = 339,800(1 + 0.025)x–4, which
is choice B.

In order to solve this problem, transform the given
equation into the slope-intercept form:
3 x + 4 y = 16
4 y = −3 x + 16
3
y =− x+4
4
Comparing the above equation with the slope-intercept
equation, y = mx + b, you can see that b = 4.

20.

The correct answer is D. The sample is likely biased
since they only asked subscribers of their newspaper.
Also, subscribers of the newspaper may not live in the
city.

21.

The correct answer is B. To solve this problem, first
convert 9 into an exponential term with base 3, so that
both sides have the same base. Then equate powers on
both sides. Also remember that when raising an
exponential term with another power, exponents are
multiplied, thus (xm)n = xm×n.

Therefore, the coordinates of the y-intercept are (0, 4).
16.

The correct answer is D. The graph is that of a
decreasing exponential function. These are of the form
E(x) = A • b-cx, where A, b, and c are positive constants.
The function in choice D is the only one of this form.

17.

The correct answer is B. Use the curve to draw a
horizontal line at y = 2. Connect that intersection point
vertically to the x-axis. This corresponds to 5.5 days,
since the x-axis scale is 0.5 days.

18.


=  32



−2a
3

( )

=3

−6

1  −6
a




−12
a

−2a 2 = −36



a 2 = 18

a = 19 

a = 18
a = li 9 × 2

If a = 19°, then 3a = 3(19°) = 57°. Angle I and the angles
labeled b and 3a form a triangle. The sum of the angles
of a triangle is 180°. Since FGHI is a rectangle, you know
that angle I = 90°. So:

a= 9 × 2
a=3 2
22.

The correct answer is A. The median for Town A is 7.5
and for Town B is 7, so the median is greater for Town A.
This is the only statement among the answer choices
that is true.

23.

The correct answer is B. The numbers of days of rain
have a much greater variation in Town B than in Town A.
Since standard deviation is a measure of variation,
choice B is correct.

180  = 147 + b
33  = b

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2
3 −a 3

3

7a + 47  = 180 

  914

 1
= 9 a
 

( )

3a + 4 a + 47  = 180 

180  = 57  + 90  + b

2
3 −a 3

( )

The correct answer is C. You know that the angles
labeled 3a, 4a, and 47° all lie on the same line. You know
that a straight line measures 180°, so you can find the
value of a by adding:

7a = 133

The correct answer is B. Note that in the question it
asks for the projected population x years after 2010, but
it gives the population in 2014. The equation must take
into account this difference.

Answer Keys and Explanations
24.

The correct answer is B. Consider an example that
would make the statement in the question true. If the
intercepts of a function are at (a, 0) and (0, a), then they
could be at (3, 0) and (0, 3). The slope of the line through
those points is:
3−0 3
= = −1
0 − 3 −3

29.

The correct answer is C. For the system to have exactly
one real solution, the graph of the system will be a line
and a parabola that is tangent to the line. For the
parabola to be tangent to the line, it must have its
vertex along that line. Since the graph of y = ax2 has its
vertex along the line y = 0, then y = ax2 – 2 has its vertex
along the line y = –2.

30.

The correct answer is D. Remember that the vertex
form of a quadratic equation is h(x) = a(x – h)2 + k, where
k is the minimum or maximum value of the function.
Since in this question h is the equation for a parabola
that opens down, it will have a maximum at k when
written in vertex form. Choices C and D are both in
vertex form, but only choice D is equivalent to the
original function. Check by writing both in standard
form:

OR
a−0 a
=
= −1
0 − a −a
−a − 0 −a
The same is true when a is negative: 0 − −a = a = −1
( )
25.

26.

27.

28.

The correct answer is D. An inscribed triangle that
passes through the center forms a right triangle. So the
missing angle measure is 90 – 36 = 54. Using the given
expression x – 25.5 = 54, x = 79.5.
The correct answer is D. There is nothing to indicate
that the sample is biased or too small, or that the
margin of error is too large, so choice D is best supported by the data.

−( x − 8 )( x + 2) = −( x − 3) 2 + 25
−( x 2 − 6 x − 16 ) = −( x 2 − 6 x + 9 ) + 25
− x 2 + 6 x + 16 = − x 2 + 6 x + 16
31.

The correct answer is C. The 95% confidence that the
margin of error is ±4% means that there is a high
probability that the actual percent of the voters that will
vote for Candidate A is most likely 31%, ±4%, or
between 27% and 35%.
The correct answer is D. We can calculate and compare
their actual volumes or the ratio of their volumes.
4
4 3
V Charon = πr 3
πr
3
3
3
4
3
4  750 
= π (750)
= π

3
3  2 
≈ 1, 766 , 250 , 000
≈ 220 , 781, 250

V Pluto =

1,766,250,000
=8
220,781,250

The correct answer is 24. To use the formula to find the
answer, find the total cost for driving one additional
mile, or 101 miles.
y = 49 + 0.24 ( x –100)
y = 49 + 0.24(101− 100)
y = 49 + 0.24
y = 49.24

32.

The correct answer is 4. Write and solve an inequality
to find the number of pens she can buy, and then
interpret the answer, including the remainder.
2.75 x + 12 ≤ 25
2.75 x ≤ 13
x ≤ 4.72
Since she can’t buy fractions of a pen, the greatest
number of pens that Amber can buy is 4.

OR
4
π(2r ) 3
V Pluto
3
=
4 3
V Charon
πr
3
=

8r 3

r3
=8
The volume comparison of any two spheres where the
diameter of one sphere is twice the diameter of the
other sphere is always 8 to 1.

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Answer Keys and Explanations
33.

The correct answer is 25. Write and solve a system of
equations. Let x = the number of 2-point shots made
and y = the number of 3-point shots made.

36.

x + y = 33
2 x + 3 y = 74

The correct answer is 5. A function like g is undefined
when the denominator is equal to 0, so set the denominator equal to 0 and solve for x:
( x − 6 )2 + 2( x − 6 ) + 1 = 0
x − 12 x + 36 + 2 x − 12 + 1 = 0
2

x 2 − 10 x + 25 = 0

Multiply the first equation by 2:

( x − 5)2 = 0
x −5= 0

2 ( x + y ) = 2 × 33

x =5

2 x + 2 y = 66
Now subtract the second equation from this new one:

37.

The correct answer is 1.14. Substitute 1.14 for r
because there is an increase of 14%, so r should be 1 +
0.14, or 1.14, in order to match the standard form for
exponential growth.

38.

The correct answer is 1112. Substitute 1.14 for r to
represent a 14% increase and 10 for t to represent 10
years after it was last sold:

2 x + 2 y = 66
−(2 x + 3 y ) = 74
− y = −8
y =8
Substitute y = 8 into the initial equation:
x + y = 33
x + 8 = 33
x = 25
34.

The correct answer is 0.36. The number of females in
China is 645 million. The total number of people
represented in the table is 1,799 million. The probability
that a random person chosen in this census is a female
in China is:
645
= 0.358 = 0.36
1,799

35.

The correct answer is 0.23. Reduce the set of outcomes that you use to the first row because you are told
that the person is male. Thus, we use 922.2 outcomes
instead of 1,799.0. Now, the probability that the person
from this group is Mexican or from the United States is
55.9 + 153.1
= 0.23.
922.2

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V = 300(1.14 ) 10
= 1,112.166

This is rounded to 1,112, which is 1,112 thousands of
dollars.

Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
The following is an analysis of the passage by Marc de Rosnay, noting how the writer used evidence, reasoning, and stylistic or persuasive elements to support his claims, connect the claims and evidence, and add power to the ideas he expressed. Check to see if
you evaluated the passage in a similar way.
1

The writer begins his argument by pointing out that there
are problems inherent in raising a child and names the issue
that is central to his essay: children are going to do things or
be exposed to things a parent will not like.

1

Being a parent presents some problems. Irrespective of
what you want, your children are going to take actions or
be exposed to things that you may not relish. There is the
ever-present possibility that they will experience things
that you want to actively protect them from.

2

The web provides some salient examples, like
pornography. I really don’t want my eight-year-old seeing
pornography.

3

However, when my eight-year-old asks me an important
Dungeons & Dragons question like, “Dad, can a paladin
do magic and wear armour?” or he wants to know how
solar panels operate, I always encourage him to look on
the web.

3

The writer establishes his legitimacy to write about this topic
by mentioning that he is the parent of an eight-year-old boy.

4

I’ve taught him to search on Google, to follow his
curiosity, and I sometimes do it with him.

4

Using his relationship with his son as an example, the writer
describes a situation in which a parent gives a child free
access to the web.

5

Ultimately, I want him to be able to seek answers to the
questions that are interesting to him independently.

5

The writer states why he believes he is right to give his child
free access to the web.

6

He is guaranteed to run into something dodgy on the
web, and my wife and I can take ordinary precautions.

6

De Rosnay returns to the issue of children being exposed
to things a parent will not like, admitting that his son “is
guaranteed” to encounter something objectionable on the
web. He then raises the possibility of taking precautions
against this situation. However, these precautions are
“ordinary,” or reasonable.

7

To our way of thinking, however, more extreme
precautions—prohibiting unsupervised internet use and
high-level parental control—start to present their own
risks.

7

The writer states his central argument: extreme precautions
can present their own risks.

8

One might ask, at what age should I allow my child to use
the web unsupervised?

8

Proceeding with his argument, the writer asks a rhetorical
question.

9

From the perspective of developmental and educational
psychology, this is a slightly odd question. Let me explain.
Most parents are familiar with the idea that certain
developmental achievements happen at specific ages.
Thus, infants become more wary of strangers at about
nine months of age (stranger wariness), and they start
to point communicatively by about 12 months of age
(declarative pointing). These kinds of developments in

9

The writer answers his question by explaining that some
developmental achievements (developmental milestones)
occur at specific ages.

2

The writer then cites a specific example: the web.

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Answer Keys and Explanations
the child’s capacity are to be expected in all children
given a typical environment; we call them developmental
milestones.
10

I spoke recently to a friend who wanted her ten-year-old
daughter to be able to get to school, in the city, on public
transport from the inner-west by herself. This particular
young girl is very intelligent and responsible, I’m sure that
she could have gotten herself to school at seven years
of age. But there is no way her parents would have felt
comfortable about that.

10

Again referring to his personal experience, the writer cites a
specific example of a parent wrestling with the question of
how much freedom to give her child.

11

Why? For her parents to give her the independence to
travel to school alone, they need to be satisfied not just
that she can present her ticket, change trains, and get
on the right bus, they need to be confident that she
understands the importance of staying on the path, like
Little Red Riding Hood.

11

The writer explores the problems this question raises, citing
some of the specific issues a parent must address.

12 We know that children seek information from the people
they trust, and from people who have a good record at
providing useful information; actually, these two things
are not unconnected. Between early childhood and
mid-adolescence children have to understand all sort of
things for which they need information from people they
trust.

12

The writer changes perspective from the personal to
the objective to discuss how children seek and acquire
information.

13 The information we convey to our children, and the
manner in which we do it, helps prepare them for life.

13

The writer lays the foundation for his argument by talking
about the importance of parents allowing children to
acquire information: it helps prepare them for life.

14

For most things, like knowledge about their bodies and
sexuality, there is no particular moment at which children
are ready for specific knowledge or experience, and much
of this we can’t control anyway.

14

De Rosnay strengthens his argument by pointing out that
often there is no ideal moment to communicate “specific
knowledge or experience.” He also points out that parents
have little or no control over when their children acquire
specific knowledge or experience.

15

But what we can do is answer their questions honestly in
a manner that is appropriate for their age and conveys
our values.

15

The writer supports his central argument by stating what
parents do have control over: answering children’s questions
honestly and appropriately.

16

The risks of overprotection are simple: children will
grow up anyway but they won’t have access to good
information from people that they trust.

16

The writer strengthens his central argument by citing
the risks of overprotection: children will not gain good
information from people they trust.

This understanding is largely derived from countless
conversations in which the parents have been able to
convey important information about the world and the
risks it presents to their daughter.

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Answer Keys and Explanations
So what age is a good age?
17

It is very difficult to put an age on when a child
should or shouldn’t be able to grasp a new domain of
independence. Your decisions will depend on specific
circumstances . . . Managing risk is critical.

17

De Rosnay returns to the essay’s central question (the ideal
age to let a child acquire new independence), stressing the
crucial role played by the different factors in each situation.

18 The web provides a salient example.

18

The writer returns to his first specific example: the web.

19

19

The writer suggests an age at which a child should have
“some freedom” to use the web independently.

20

The writer suggests some precautions parents can take as
they give children this freedom.

21

The writer concludes his argument by summing up his
reasoning: giving children independence shows that you
trust them, which in turn teaches children to be responsible;
denying children independence by overprotecting them
does not give them the same trust-fosters-responsibility
experience.

By year five or six, today’s children should have some
freedom to search for the information they need
independently.

20 They can do this in a family space rather than in their
bedroom. Talk to them honestly about the unsavoury
content on the web; this will give them a framework for
managing troubling or embarrassing content with you.
Independent action is also very important for children.
Think back to your own childhood, there is a good chance
that some of your fondest memories don’t involve adults.
Sometimes, children can walk to the shops before they
are 12 years old, and around this time, they should be
able to stay in the house for a little while as well.
...
21

Independence is linked to responsibility and much can
be done to build responsibility in children before they
undertake fully independent actions. But when you give
your children independence you provide them with
evidence that you trust them, and that trust fortifies
responsibility in a way that supervised activity cannot.

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Answer Keys and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Marc de Rosnay.

High-Scoring Essay
The central argument in this article is that parents have to give their children a certain amount of freedom to help them grow
up to be responsible, independent adults. Marc de Rosnay says that children will be exposed to things that parents won’t like,
but a good parent gives a child freedom and support. If a parent teaches the child how to handle things that are unpleasant
or dangerous, the child learns to be independent and stay safe. Overprotecting children can pose risks because these
children may not learn to protect themselves. To convince us of his viewpoint, de Rosnay uses knowledge about childhood
development, examples from his experience as a parent, and logic.
As they grow up, children will be exposed to things that parents won’t like, such as Internet pornography. De Rosnay
establishes his qualification to write about this topic by revealing that he has an eight-year-old son and he’s encouraged
him to search for information on the Internet. This gives us an example of a danger—pornography on the Internet—and de
Rosnay’s response—allowing his son to use the Internet. He explains that he taught his son to use Google and he sometimes
uses the Internet with him.
De Rosnay uses logic to explain this decision. (1) He wants his son to be able to use the Internet without his help. (2) He
takes precautions (which he calls “ordinary”) to protect his son from objectionable material. (3) Forms of overprotection,
like forbidding his son to use the Internet without supervision or setting up a high level of parental control, can also cause
problems.
The author poses a rhetorical question to ask how old a child should be to use the Internet without supervision. This
question is really about how a parent determines when a child is old enough to do anything, and de Rosnay uses logic to
answer it. He uses the term “developmental milestone” to discuss the age at which most children acquire a skill, such as
declarative pointing at the age of 12 months. More complex skills aren’t acquired at a particular age because the skill is more
complicated and factors like the environment and the child’s maturity are different.
De Rosnay provides an example of a complex skill. His friend wanted her ten-year-old daughter to be able to use public
transportation to go to school. However, the girl would have to change trains and take a bus to get from home to school.
More importantly, she had to understand the dangers she could face and how to avoid them, which meant her parents had
to prepare her.
Using this example, the author connects to how parents can prepare their children for life—where children will face all kinds
of new experiences, including some that are dangerous. He argues that the best a parent can do is answer questions in a way
that is honest and appropriate for the child’s age, and conveys good values. Children taught this way will trust their parents
and go to their parents for information and help when they need it. He contrasts this with overprotected children who have
not learned that they can get good information from their parents, and so won’t turn to their parents for help.
The author acknowledges that it is difficult to say how much independence a child should have at a specific age. He cites
differences in parents, children, and the amount of risk in a situation (like a bad neighborhood). He does say that children
should have some independence on the Internet by the age of five or six, but also suggests that parents take the precaution
of making access available in a family space (as opposed to the child’s bedroom). He also gives milestones for other
independent activities like staying home alone.
To wrap up his argument, de Rosnay uses logic to link responsibility, independence, and trust. He believes that trusting
children makes them more responsible. Responsibility leads to giving a child more independence. Giving more
independence shows more trust. The cycle starts with trusting the child. As the cycle continues, the child eventually grows up
and becomes an independent, responsible adult. De Rosnay’s examples and logic create a solid argument for giving a child as
much independence as the child can handle while providing a framework to help the child mature.

  920

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Answer Keys and Explanations
Low-Scoring Essay
In his article called “Milestones: what is the ‘right’ age for kids to travel alone, surf the web, learn about war?” Marc de Rosnay
looks at what ages kids should be allowed to do certain things like surfing the Internet, walking to school, and watching the
news.
Marc de Rosnay is the head of a school in Australia, which is why he knows about child development. In his own life, Marc
determined that his eight-year-old son was old enough to use the Internet alone. He thinks his son would probably use the
Internet alone anyway, so trying to keep him from using it would cause problems.
Marc de Rosnay asks when children should be allowed to do other things like riding a bike. He says that Dutch people start
riding bikes at 2 because riding bikes is really popular there. They learn how to ride by watching other people do it and then
imitating them.
Marc de Rosnay gives ages when children should be able to do certain things. They should go to the store alone at 10-14
years, surf the Internet at 5-6 years old, stay home alone at 11 years old, visit a war memorial at 6-8 years old, and watch the
news or read the newspaper at 7-9 years old.
In conclusion, Marc de Rosnay says it’s hard to know when children can do some things alone. Parents just have to trust their
children.

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Computing Your Score
COMPUTING YOUR SCORES
Now that you’ve completed this practice test , it’s time to compute your scores. Simply follow the instructions on the following pages,
and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation as
possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then you’ll calculate the total score. It sounds a little confusing, but we’ll take
you through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test.
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for
wrong answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page 925. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1.  	 Count the number of correct answers you got on the Section 3: Math Test—No Calculator and the Section 4: Math Test—
No Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2.  	 Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—No Calculator.
3.  	 Use the Raw Score Conversion Table 1: Section and Test Scores on page 925. and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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Computing Your Score
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test that focus on linear equations and inequalities.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 1, 3–6, 12, 17, 20
ºº Math Test—Calculator: Questions 3, 4, 8–10, 13, 15, 24, 31–33
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: 10
ºº Math Test—Calculator: Questions 1, 2, 5–7, 14, 16, 17, 20, 22, 23, 26, 27, 34, 35, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability
to progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations,
and interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 2, 7–9, 11, 15, 16, 19
ºº Math Test—Calculator: Questions 11, 12, 19, 21, 29, 30, 36, 37
Your Raw score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Passport to Advanced Math subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test.
ºº Questions 1, 3, 4, 8–10, 13, 15, 17, 18, 21–23, 25–27, 30, 33, 34, 37–39, 41, 43

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test.
ºº Questions 2, 5–7, 11, 12, 14, 16, 19, 20, 24, 28, 29, 31, 32, 35, 36, 40, 43, 44

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Standard English Conventions
subscore.

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Computing Your Score
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 9, 10, 18, 19, 30, 31, 40, 42, 51, 52
ºº Writing and Language Test: Questions 8, 9, 17, 18, 25, 33, 37, 42
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 3, 7, 8, 12, 14, 15, 20, 21, 25–29, 35, 39, 48, 50
ºº Writing and Language Test: Questions 1, 10, 15, 21, 23, 26, 34, 39
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 926 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these sections:
• Reading Test: Questions 1–10, 11–21
• Writing and Language Test: Questions 13, 15, 17, 18, 21, 22
• Math Test—No Calculator: None
• Math Test—Calculator: Questions 5, 6, 19, 20, 26, 27, 34, 35
• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 3: Cross-Test Scores on page 927 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these sections:

•
•

  924

ºº Reading Test: Questions 22–31, 32–42
ºº Writing and Language Test: Questions 34, 37–39, 41, 42
ºº Math Test—No Calculator: Question 16
ºº Math Test—Calculator: Questions 2, 7, 16, 17, 22, 23, 28
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 927 to determine your Analysis in Science cross-test
score.

www.petersons.com

Computing Your Score

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

TOTAL SAT® SCORE
(400–1600)

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Computing Your Score

  926

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Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

2

1

1

2

2

5

2

2

3

2

2

3

3

6

3

3

4

3

2

4

4

7

4

4

5

4

3

5

5

8

5

5

6

5

4

6

6

9

6

6

7

6

5

6

7

10

6

7

8

6

6

7

8

11

7

8

9

7

6

8

8

11

8

8

10

7

7

8

9

12

8

9

11

8

7

9

10

12

9

10

12

8

8

9

10

13

9

10

13

9

8

9

11

13

10

11

14

9

9

10

12

14

11

12

15

10

10

10

13

14

12

13

16

10

10

11

14

15

13

14

17

11

11

12

15

14

15

18

11

12

13

15

15

19

12

13

15

20

12

15

21

13

22

14

23

14

24

15

Computing Your Score
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

1

10

11

19

29

27

2

11

12

20

30

27

3

12

13

21

30

28

4

14

14

22

31

29

5

15

15

23

32

30

6

16

16

24

32

30

7

17

17

25

33

31

8

18

18

26

34

32

9

20

19

27

35

33

10

21

20

28

35

33

11

22

20

29

36

34

12

23

21

30

37

35

13

24

22

31

38

36

14

25

23

32

38

37

15

26

24

33

39

38

16

27

24

34

40

39

17

28

25

35

40

40

Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

Peterson's SAT® Prep Guide 2017

  927

Computing Your Score
Conversion Equation 3: Cross-Test Scores
ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

RAW SCORE

ANALYSIS IN SCIENCE
QUESTIONS

Reading Test

1–10, 11–20

22–31, 32–42

Writing and
Language Test

13, 15, 17, 18, 21,
22

34, 37–39, 41, 42

Math Test—No
Calculator

None

16

Math Test—
Calculator

5, 6, 19, 20, 26, 27,
34, 35

2, 7, 16, 17, 22,
23, 28

TOTAL

  928

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ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (1–40)

RAW SCORE

Practice Test 5—Answer Sheet
Section 1: Reading Test
1.

12.

23.

33.

43.

2.

13.

24.

34.

44.

3.

14.

25.

35.

45.

4.

15.

26.

36.

46.

5.

16.

27.

37.

47.

6.

17.

28.

38.

48.

7.

18.

29.

39.

49.

8.

19.

30.

40.

50.

9.

20.

31.

41.

51.

10.

21.

32.

42.

52.

11.

22.

Section 2: Writing and Language Test
1.

10.

19.

28.

37.

2.

11.

20.

29.

38.

3.

12.

21.

30.

39.

4.

13.

22.

31.

40.

5.

14.

23.

32.

41.

6.

15.

24.

33.

42.

7.

16.

25.

34.

43.

8.

17.

26.

35.

44.

9.

18.

27.

36.

Section 3: Math Test—No Calculator
1.

4.

7.

10.

13.

2.

5.

8.

11.

14.

3.

6.

9.

12.

15.

Peterson's SAT® Prep Guide 2017

  929

Practice Test 5—Answer Sheet
Section 3: Math Test—No Calculator
16.

17.

18.

19.

20.

.

/
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/
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/
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/
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.

.

/
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/
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/
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0

0

0

0

0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

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6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

Section 4: Math Test—Calculator
1.

7.

13.

19.

25.

2.

8.

14.

20.

26.

3.

9.

15.

21.

27.

4.

10.

16.

22.

28.

5.

11.

17.

23.

29.

6.

12.

18.

24.

30.

31.

32.
.

/
.

/
.

.

0

0

0

1

1

2

2

3

.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

7
8

7
8

7
8

9

9

9

34.
.

/
.

/
.

.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4
5

4
5

4
5

4
5

6

6

6

6

7
8

7
8

7
8

7
8

9

9

9

9

36.

  930

33.
/
.

.

/
.

.

.

/
.

/
.

.

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

9

37.

38.

.

/
.

/
.

.

.

/
.

/
.

.

.

/
.

/
.

.

0

0

0

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

4
5

6

6

6

6

6

6

6

6

6

6

6

6

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

7
8

9

9

9

9

9

9

9

9

9

9

9

9

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35.
/
.

Practice Test 5—Answer Sheet
Section 5: Essay
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  932

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Practice Test 5—Answer Sheet

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Practice Test 5—Answer Sheet

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  934

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Practice Test 5
SECTION 1: READING TEST
65 Minutes—52 Questions
TURN TO SECTION 1 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage (or pair of passages) in this section is followed by a number of multiple-choice questions. After
reading each passage, select the best answer to each question based on what is stated or implied in the passage or passages
and in any supplementary material, such as a table, graph, chart, or photograph.

Questions 1–11 are based on the following passage.

Previously, staff from the Galapagos Agency

Snail-Sniffing Dogs in the Galapagos
The Galapagos Islands, which belong to Ecuador, are located
approximately 906 km (563 mi.) west of the mainland. Because of
their isolation, these volcanic islands are home to a variety of unique
species, such as gigantic land tortoises and marine iguanas. As more
people have visited and settled on the islands, however, it has become
increasingly difficult to protect the native plants and animals.
The following text has been adapted from Ecosystem Restoration:
Invasive Snail Detection Dogs, which was originally published by
Galapagos Conservancy (www.galapagos.org). Galapagos Conservancy is a conservation group that collaborates with scientists
worldwide to ensure protection of the Galapagos Islands. (For the
complete article, see http://galapagos.org/conservation.)

Line
5

10

15

20

In Galapagos, native species are threatened
by introduced, invasive species such as goats, rats,
pigs, and cats, among many others. While much has
been accomplished in the management of existing
invasive species, the islands are constantly at risk of
new unwanted species arriving each day. The Giant
African Land Snail (GALS)—the largest species of snail
found on land, growing to nearly 8 inches in length—is
one such new invasive that has taken up residence in
Galapagos. Known to consume at least 500 different
types of plants, scientists consider the GALS to be one
of the most destructive snail species in the world. It now
poses a serious threat to the native snails and plants of
Galapagos.
Invasive Giant African Land Snails were first
detected on Santa Cruz Island in 2010, and currently less
than 20 hectares (50 acres) are infested—but the snails
are expanding their range every wet season. Experience
has shown that once an invasive species becomes established, it is almost impossible to remove. At this point
in time, it is still possible to eradicate the GALS from
Galapagos if additional management techniques are
integrated into current activities.

30

35

40

45

50

55

60

Quarantine (ABG) had to search for and collect GALS
on rainy nights using headlamps—an extremely
challenging and unsustainable solution to the permanent eradication of the snails. Dogs, on the other
hand, have an incredible sense of smell and can be
trained to detect scents imperceptible to the human
nose, making them ideal for the detection of the
GALS. Detection dogs have been used for finding
contraband drugs and shark fins in Galapagos, but not
for other purposes. This project entails utilizing two
scent detection dogs to detect GALS in order to help
clear currently affected areas and search for previously
undetected populations in the islands.
During the first phase of the project, which
took place in the fall of 2014, two detection dogs
were trained by Dogs for Conservation (DFC) in the
United States to specifically detect GALS. Darwin, a
golden Labrador retriever, was rescued after he was
unable to successfully complete a service dog training
program, and Neville, a black Labrador retriever, was
saved from a shelter. Darwin and Neville were selected
for this project based on their detection abilities and
temperament for working with multiple handlers, in
preparation for work with new handlers in Galapagos.
In December of 2014, the dogs were brought to Galapagos where six ABG staff were trained as handlers for
this and future detection projects. Many had never
worked with dogs before and had to learn the basics of
canine behavior, learning theory, scent theory, training
methods, and handling skills. New kennels were built
by ABG personnel with materials funded through this
project in order to house the dogs.
Both dogs required a period of acclimation to
Galapagos and to their new roles. The dogs could only
be trained on dead snails in the U.S. due to biosecurity
risks for this highly invasive species, so additional

Practice Test 5 — reading

25 for the Regulation and Control of Biosecurity and

CONTINUE
Peterson's SAT® Prep Guide 2017

  935

Practice Test 5
training was needed upon their arrival in Galapagos
to transition them to live snails and snail eggs. Darwin
and Neville have now been fully trained to detect the
65 invasive snails, and the dogs will be regularly assisting
with GALS eradication and monitoring on Santa Cruz.
DFC continues to provide guidance and support
to the GALS K9 team, with whom they are in weekly
communication. Future updates to the project will be
70 posted … as they occur. This project is also serving as a
pilot to establish a permanent canine detection program
in the Galapagos. Expertly trained dogs and experienced
handlers will be a highly cost-effective detection tool
for ongoing biosecurity programs aimed at eliminating
75 targeted invasive species that threaten the unique and
fragile ecosystems of Galapagos.
1

A.

To bring tourists to the Galapagos

B.

To raise money for the organization

C.

To inform the public about the problems of invasive
species

7

Which best describes the threat of GALS to the Galapagos
Islands?
A.

Their growth patterns

B.

Their eating habits

C.

Their ability to hide from detection

D.

Their ability to survive in hot climates

According to the passage, the GALS problem on the Galapagos Islands
A.

has been solved by hunting dogs.

B.

has been exaggerated by the media.

C.

is steadily growing worse every year.

D.

is the biggest problem affecting the islands.

Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 10–12 (“Known to . . . the world.”)

B.

Lines 17–18 (“the snails . . . season.”)

C.

Lines 24–29 (“Previously, staff . . . the snails.”)

D.

Lines 59–61 (“The dogs . . . biosecurity risks”)

Why did the scientists decide to try using dogs to find the
GALS?

Dogs can help reduce invasive species in the
Galapagos.

A.

Scientists have found no way to reduce invasive
species in the Galapagos.

Dogs are friendly animals that are easy to work
with.

B.

Dogs can also be trained to find illicit drugs.

C.

Galapagos ecosystems include unique species.

C.

Dogs are trainable and able to find GALS by smell.

D.

Organizations are working together to rid the
Galapagos of invasive species.

D.

Dogs can go into the small spaces in which GALS
hide.

B.

  936

6

To persuade people that it is important to keep
species of animals and plants from becoming
extinct

Which statement best represents the main idea of the
passage?
A.

3

5

What is the purpose of this article?

D.

2

4

Why do the Galapagos have a unique ecosystem?
A.

Islands can only support certain kinds of species.

B.

There were no mammals there until humans
brought them.

C.

Only certain types of animals and plants can live
there because of the climate.

D.

It was isolated for a long time, so humans did not
interfere with the natural ecosystems.

www.petersons.com

8

Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 29–32 (“Dogs, on . . . human nose”)

B.

Lines 33–34 (“Detection . . . drugs”)

C.

Lines 35–37 (“This project . . . areas”)

D.

Lines 39–40 (“During the . . . 2014”)

Practice Test 5
9

Questions 12–22 are based on the following passage.

As used in line 60, “biosecurity” most nearly means
A.

safe handling of animals.

B.

safety from dangerous animals and plants.

C.

protection to keep wildlife from extinction.

D.

protection of an ecosystem from invasive species.

The following is an excerpt from a speech given by President Jimmy
Carter, spoken and broadcast from the White House library two weeks
after he took office. Prior to Carter’s election, the country had faced
a severe oil shortage and rising prices for oil and related products.
Report to the American People (February 2, 1977)

10 As used in line 58, “acclimation” is best defined as
A.

adjusting to changes in the environment.

B.

conforming to one’s surroundings.

C.

adaptation of a species.

D.

modification of behavior.

11 Why are dogs considered an invasive species to the Galapagos?
A.

The dogs’ sense of smell helps them find native
species and use them for food.

B.

The dogs required time to get acclimated to the
environment.

C.

The dogs did not inhabit the Galapagos until brought
by humans.

D.

The dogs once thrived on the Galapagos, but they
had depleted their limited food sources.

Line
5

10

15

20

25

30

35

40

The extremely cold weather this winter has dangerously depleted our supplies of natural gas and fuel oil
and forced hundreds of thousands of workers off the job.
I congratulate the Congress for its quick action on the
Emergency Natural Gas Act, which was passed today and
signed just a few minutes ago. But the real problem—our
failure to plan for the future or to take energy conservation
seriously—started long before this winter, and it will take
much longer to solve.
I realize that many of you have not believed that we
really have an energy problem. But this winter has made
all of us realize that we have to act.
Our program will emphasize conservation. The
amount of energy being wasted which could be saved is
greater than the total energy that we are importing from
foreign countries. We will also stress development of our
rich coal reserves in an environmentally sound way; we will
emphasize research on solar energy and other renewable
energy sources; and we will maintain strict safeguards on
necessary atomic energy production.
The responsibility for setting energy policy is now
split among more than 50 different agencies, departments,
and bureaus in the Federal Government. Later this month,
I will ask the Congress for its help in combining many of
these agencies in a new energy department to bring order
out of chaos. Congressional leaders have already been
working on this for quite a while.
We must face the fact that the energy shortage is
permanent. There is no way we can solve it quickly. But
if we all cooperate and make modest sacrifices, if we
learn to live thriftily and remember the importance of
helping our neighbors, then we can find ways to adjust
and to make our society more efficient and our own
lives more enjoyable and productive. Utility companies
must promote conservation and not consumption. Oil
and natural gas companies must be honest with all of
us about their reserves and profits. We will find out the
difference between real shortages and artificial ones.
We will ask private companies to sacrifice, just as private
citizens must do.

CONTINUE
Peterson's SAT® Prep Guide 2017

  937

Practice Test 5

45

50

55

60

65

All of us must learn to waste less energy. Simply by
keeping our thermostats, for instance, at 65 degrees in
the daytime and 55 degrees at night we could save half
the current shortage of natural gas.
There is no way that I, or anyone else in the Government, can solve our energy problems if you are not
willing to help. I know that we can meet this energy
challenge if the burden is borne fairly among all our
people—and if we realize that in order to solve our
energy problems we need not sacrifice the quality of
our lives.
The Congress has made great progress toward
responsible strip-mining legislation, so that we can
produce more energy without unnecessary destruction
of our beautiful lands. My administration will support
these efforts this year. We will also ask Congress for its
help with legislation which will reduce the risk of future
oil tanker spills and help deal with those that do occur.
I would like to tell you now about one of the things
that I have already learned in my brief time in office. I
have learned that there are many things that a President
cannot do. There is no energy policy that we can develop
that would do more good than voluntary conservation.
There is no economic policy that will do as much as
shared faith in hard work, efficiency, and in the future
of our system.

B.

A.

Lowering the thermostats

B.

Forming a new energy department

C.

Developing coal reserves

D.

Protecting the environment from oil spills

15 Which of the following best represents the belief system
illustrated in Carter’s speech?
A.

The idea that the United States should be energy
independent

B.

The concept of shared sacrifice

C.

The idea that the environment needs to be
protected by volunteers

D.

The concept of equal powers among the three
branches of government

16 What does Carter think should be the foundation for conserving energy?
A.

The responsible use of strip mining to produce
more energy

B.

He wanted to reassure people that he was going to
make the United States energy independent.

The reduction of indoor temperatures to conserve
fuel

C.

As a new president, he wanted to start a dialogue
with the people.

The use of solar and other renewable energy
sources

D.

A voluntary policy in which people share in
creating efficiency

12 What is the most likely reason that Carter gave this speech?
A.

14 Which of the following actions does Carter propose that
the government take to help solve the problem?

C.

He wanted to explain the severity of the energy
crisis and what needed to be done to address it.

D.

He wanted people to understand the limitations of
the president.

17 How does Carter try to convince the public that everyone
needs to participate to solve the problem?
A.

He describes how utility companies are also
promoting conservation, not consumption.

B.

He explains that all people waste a lot of energy.

C.

He tells the public to lower the thermostats in their
homes, which can save natural gas.

D.

He explains that the energy crisis requires some
major sacrifices.

13 What is the theme of the speech?

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A.

The United States has a long-term energy problem.

B.

There are many ways to conserve energy.

C.

People need to use less energy in their homes.

D.

The government cannot solve environmental
problems.

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Practice Test 5
18 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 34–35 (“Utility companies . . . consumption.”)

B.

Lines 37–38 (“We will . . . ones.”)

C.

Line 41 (“All of . . . energy.”)

D.

Lines 41–43 (“Simply . . . at night”)

22 Explain how the word “reserves” is used in line 17 and
line 37.
A.

In the first use, “reserves” refers to something
protected in order to prevent easy access to it; in the
second use, it refers to something that is difficult to
obtain.

B.

In the first use, “reserves” refers to something
discarded; in the second use; it refers to something
set aside in case of emergencies.

C.

In the first use, “reserves” refers to something saved in
case of future needs; in the second use, it refers to
being set aside in order to raise prices.

D.

In the first use, “reserves” refers to something not
used because there is an excess; in the second use, it
refers to something that belongs to someone else.

19 Which of the following best explains the tone of the speech?
A.

Carter speaks bluntly about the problem but also
tries to be persuasive and optimistic in order to
encourage everyone to work together.

B.

Carter is speaking on national television and wants
his audience to keep listening to him, so his tone is
light and informal, even though the topic is a serious
one.

C.

Carter is deeply concerned over the energy problem,
so the tone of the speech is stern and authoritative
because he wants people to follow his requests.

D.

Carter wants to be taken seriously, so he avoids
persuasive language; instead, he speaks with
informative, matter-of-fact neutrality.

20 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 45–48 (“There is no . . . challenge”)

B.

Lines 52–53 (“The Congress . . . legislation”)

C.

Lines 55–56 (“My administration . . . year.”)

D.

Lines 59–60 (“I would . . . office.”)

21 As used in line 2, “depleted” most nearly means
A.

consumed.

B.

replaced.

C.

weakened.

D.

wasted.

CONTINUE
Peterson's SAT® Prep Guide 2017

  939

Practice Test 5
Questions 23–32 are based on the following passage.
Rudyard Kipling (1865–1936) was one of the most popular English
writers of his era, authoring stories, novels, and poems, many of
which take place in colonial India, where he was born and lived
as a young child and returned to as a young adult. “The Arrest of
Lieutenant Golightly,” one of his earliest stories, was first published
in an English-language newspaper in India where Kipling worked
as a journalist. The following is an excerpt from that story.

Line
5

10

15

20

25

30

35

40

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If there was one thing on which Golightly prided
himself more than another, it was looking like “an Officer
and a gentleman.” He said it was for the honor of the
Service that he attired himself so elaborately; but those
who knew him best said that it was just personal vanity.
There was no harm about Golightly. … He recognized a
horse when he saw one, … he played a very fair game
at billiards, and was a sound man at the whist-table.
Everyone liked him; and nobody ever dreamed of seeing
him handcuffed on a station platform as a deserter. But
this sad thing happened.
He was going down from Dalhousie, at the end of
his leave—riding down. He had cut his leave as fine as
he dared, and wanted to come down in a hurry.
It was fairly warm at Dalhousie [a town in India in
the hills, used as a summer retreat for British personnel]
and knowing what to expect below, he descended in a
new khaki suit—tight fitting—of a delicate olive-green;
a peacock-blue tie, white collar, and a snowy white solah
[a plant made into fabric used in hat-making] helmet. He
prided himself on looking neat even when he was riding
post. He did look neat, and he was so deeply concerned
about his appearance before he started that he quite
forgot to take anything but some small change with
him. He left all his notes at the hotel. His servants had
gone down the road before him, to be ready in waiting
at Pathankote with a change of gear.
Twenty-two miles out of Dalhousie it began to
rain—not a mere hill-shower, but a good, tepid monsoonish downpour. Golightly bustled on, wishing that
he had brought an umbrella. The dust on the roads
turned into mud, and the pony mired a good deal. So
did Golightly’s khaki gaiters. But he kept on steadily and
tried to think how pleasant the coolth was.
His next pony was rather a brute at starting, and
Golightly’s hands being slippery with the rain, contrived to get rid of Golightly at a corner. He chased the
animal, caught it, and went ahead briskly. The spill had
not improved his clothes or his temper, and he had
lost one spur. He kept the other one employed. By the
time that stage was ended, the pony had had as much
exercise as he wanted, and, in spite of the rain, Golightly

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was sweating freely. At the end of another miserable
half-hour, Golightly found the world disappear before
his eyes in clammy pulp. The rain had turned the pith
of his huge and snowy solah-topee into an evil-smelling
dough, and it had closed on his head like a half-opened
mushroom. Also the green lining was beginning to run.
Golightly did not say anything worth recording
here. He tore off and squeezed up as much of the brim
as was in his eyes and ploughed on. The back of the
helmet was flapping on his neck and the sides stuck
to his ears, but the leather band and green lining kept
things roughly together, so that the hat did not actually
melt away where it flapped.
Presently, the pulp and the green stuff made a
sort of slimy mildew which ran over Golightly in several
directions—down his back and bosom for choice. The
khaki color ran too … and sections of Golightly were
brown, and patches were violet, and contours were
ochre, and streaks were ruddy red, and blotches were
nearly white, according to the nature and peculiarities
of the dye. When he took out his handkerchief to wipe
his face and the green of the hat-lining and the purple
stuff that had soaked through on to his neck from the
tie became thoroughly mixed, the effect was amazing.
He went to the Station-Master to negotiate for a
first-class ticket to Khasa, where he was stationed. The
booking-clerk said something to the Station-Master, the
Station-Master said something to the Telegraph Clerk,
and the three looked at him with curiosity. They asked
him to wait for half-an-hour, while they telegraphed to
Umritsar for authority. So he waited, and four constables
came and grouped themselves picturesquely round him.
Just as he was preparing to ask them to go away, the
Station-Master said that he would give the Sahib [term
of respect; like calling someone “sir” in English] a ticket
to Umritsar, if the Sahib would kindly come inside the
booking-office. Golightly stepped inside, and the next
thing he knew was that a constable was attached to each
of his legs and arms, while the Station-Master was trying
to cram a mailbag over his head.

23 Which of the following best describes the tone of the story?
A.

Disgust

B.

Mocking

C.

Ironic

D.

Proud

Practice Test 5
24 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 1–3 (“If there . . . gentleman.”)

B.

Lines 6–7 (“There was . . . saw one”)

C.

Lines 7–8 (“he played . . . whist-table”)

D.

Line 9 (“Everyone . . . him”)

25 Even though the author says “this sad thing happened,”
which detail from the passage shows that Kipling considers
Golightly to be responsible for what happened to him?
A.

28 How does Kipling make fun of his character Golightly?
A.

His explanation of Golightly’s vanity is satiric.

B.

His description of Golightly’s experience shows how
he has trouble coping with the severe rainstorms in
India.

C.

He gives a detailed description of how silly Golightly
looks.

D.

He shows that Golightly had difficulty riding the horse.

29 Why did Kipling provide such detail about Golightly’s looks?

He did look neat, and he was so deeply concerned
about his appearance before he started that he quite
forgot to take anything but some small change with
him.

A.

To make fun of his vanity and usual appearance

B.

To show how intense the climate is in India

C.

To help the reader understand the setting

B.

He prided himself on looking neat even when he was
riding post.

D.

To describe the problems of the British military in India

C.

Golightly bustled on, wishing that he had brought an
umbrella.

D.

His next pony was rather a brute at starting, and
Golightly’s hands being slippery with the rain,
contrived to get rid of Golightly at a corner.

26 Which of the following best explains the identity and actions
of the main character, Golightly?
A.

He’s a proper military man leaving his post.

B.

He’s a British soldier trying to escape capture by the
Indian government.

C.

He’s an outlaw trying to escape capture.

D.

He’s a British businessman on a trip overseas.

27 Which choice provides the best evidence for the answer to
the previous question?
A.

Lines 9–11 (“nobody ever . . . happened.”)

B.

Lines 12–13 (“He was going . . . his leave”)

C.

Lines 15–16 (“It was fairly . . . personnel”)

D.

Lines 17–20 (“he descended . . . helmet.”)

30 How are lines 50–51 (“He tore off . . . ploughed on.”) distinguished from the rest of the text in the passage?
A.

Kipling describes the character’s verbal response to
the situation.

B.

The narrator interjects his own viewpoint.

C.

It adds internal dialogue to the story.

D.

The narrator describes Golightly’s thoughts rather
than his appearance.

31 What is the meaning of the sentence: “He had cut his leave
as fine as he dared.” (lines 13–14)?
A.

He dared to take leave without telling the authorities.

B.

He arranged to take as much time as he could
without getting in trouble.

C.

He was daring in leaving the military post because it
was dangerous.

D.

He wanted to leave, but was afraid he’d get caught.

32 As used in line 32, “mired” most nearly means
A.

sped.

B.

slowed.

C.

pooled.

D.

ate.

CONTINUE
Peterson's SAT® Prep Guide 2017

  941

Practice Test 5
Questions 33–42 are based on the following
passages and supplementary material.
Passage 1 is an excerpt from a speech modeled on the Declaration
of Independence, written and read by Elizabeth Cady Stanton at
the Woman’s Rights Convention, held in Seneca Falls, New York,
July 19, 1848. About 300 people attended the event and about a
third (68 women and 32 men) signed the declaration.
Passage 2 is excerpted from The Narrative of Sojourner Truth, the
memoir of a slave in pre-Civil War New York. Born into slavery as
Isabella, after being freed in 1827, she took the name Sojourner
Truth to express her strong faith. Because Truth was illiterate, she
dictated her story to the writer Olive Gilbert, whom she had met in
Massachusetts. The book was published in 1850 and was widely
distributed by Abolitionists to help further their cause.

as to be wholly regardless of the happiness of women—
the law, in all cases, going upon a false supposition of the
supremacy of man, and giving all power into his hands.
35
After depriving her of all rights as a married woman,
if single, and the owner of property, he has taxed her to
support a government which recognizes her only when
her property can be made profitable to it. …
He has endeavored, in every way that he could, to
40 destroy her confidence in her own powers, to lessen her
self-respect, and to make her willing to lead a dependent
and abject life. . . .

PASSAGE 1
Declaration of Sentiments

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The history of mankind is a history of repeated
injuries and usurpations on the part of man toward
woman, having in direct object the establishment of
an absolute tyranny over her. To prove this, let facts be
submitted to a candid world.
He has never permitted her to exercise her
inalienable right to the elective franchise.
He has compelled her to submit to laws, in the
formation of which she had no voice.
He has withheld from her rights which are given
to the most ignorant and degraded men—both natives
and foreigners.
Having deprived her of this first right of a citizen,
the elective franchise, thereby leaving her without representation in the halls of legislation, he has oppressed
her on all sides.
He has made her, if married, in the eye of the law,
civilly dead.
He has taken from her all right in property, even to
the wages she earns.
He has made her, morally, an irresponsible being,
as she can commit many crimes with impunity, provided they be done in the presence of her husband.
In the covenant of marriage, she is compelled to
promise obedience to her husband, he becoming, to all
intents and purposes, her master—the law giving him
power to deprive her of her liberty, and to administer
chastisement.
He has so framed the laws of divorce, as to what
shall be the proper causes, and in the case of separation,
to whom the guardianship of the children shall be given,

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(Credit: Women’s Political Union, 1911. Library of Congress)

PASSAGE 2
From: The Narrative of Sojourner Truth
After emancipation had been decreed by the State,
some years before the time fixed for its consummation,
45 Isabella’s master told her if she would do well, and be
faithful, he would give her “free papers,” one year before
she was legally free by statute. In the year 1826, she had
a badly diseased hand, which greatly diminished her
usefulness; but on the arrival of July 4, 1827, the time
50 specified for her receiving her “free papers,” she claimed
the fulfillment of her master’s promise; but he refused

Practice Test 5

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60

65

70

75

granting it, on account (as he alleged) of the loss he had
sustained by her hand. She plead that she had worked all
the time, and done many things she was not wholly able
to do, although she knew she had been less useful than
formerly; but her master remained inflexible. Her very
faithfulness probably operated against her now, and he
found it less easy than he thought to give up the profits of
his faithful Bell, who had so long done him efficient service.
But Isabella inwardly determined that she would
remain quietly with him only until she had spun his wool—
about one hundred pounds—and then she would leave
him, taking the rest of the time to herself. “Ah!” she says,
with emphasis that cannot be written, “the slaveholders
are TERRIBLE for promising to give you this or that, or such
and such a privilege, if you will do thus and so; and when
the time of fulfillment comes, and one claims the promise,
they, forsooth, recollect nothing of the kind; and you are,
like as not, taunted with being a LIAR; or, at best, the slave
is accused of not having performed his part or condition of
the contract.”“Oh!” said she, “I have felt as if I could not live
through the operation sometimes. Just think of us! so eager
for our pleasures, and just foolish enough to keep feeding
and feeding ourselves up with the idea that we should get
what had been thus fairly promised; and when we think
it is almost in our hands, find ourselves flatly denied! Just
think! how could we bear it?”

33 What was Stanton’s purpose in writing and speaking the
Declaration of Sentiments?

35 Which lines in the text are best illustrated by the graphic?
A.

Lines 10–12: (“He has withheld . . . and foreigners”)

B.

Lines 17–18: (“He has made . . . civilly dead.”)

C.

Lines 33–34: (“going upon a . . . into his hands.”)

D.

Lines 36–38: (“he has taxed . . . profitable to it”)

36 How does Stanton support her argument that women have
been forced into obedience?
A.

She explains that women can’t work outside the
home.

B.

She expresses anger at the idea that women are not
allowed to vote.

C.

She expresses dismay at how children can be taken
from mothers in cases of divorce or separation.

D.

She explains how marriage legally compels women
to obey their husbands.

37 What does Stanton mean by “elective franchise” as used in
line 14?
A.

The sport of elections

B.

The business of elections

C.

The team needed for elections

D.

The right to vote

A.

She wanted to show that women could write
important documents.

B.

She wanted to shock the audience in upstate New
York.

C.

She wanted to show why women needed rights.

A.

D.

She wanted to gain support for equal protection of
minorities.

Neither women nor slaves could get paid for their
work.

B.

Both women and slaves had to take care of the
children in a family.

C.

Women had to obey their husbands; slaves had to
obey their masters.

D.

Men made and broke promises to both women and
slaves.

34 What is the effect of repeating the phrase “He has”?
A.

It shows how strongly she feels about how women
were treated.

B.

It emphasizes the transgressions of men against
women.

C.

It makes the speech dull because it repeats the same
words.

D.

It makes the speech more like the Declaration of
Independence.

38 What do the two passages suggest about what women and
slaves had in common?

CONTINUE
Peterson's SAT® Prep Guide 2017

  943

Practice Test 5
Questions 43–52 are based on the following
passage and supplementary material.

39 Which of the following statements is true about the two
passages?
A.

They both display a tone of anger at their lack of
freedom.

B.

Stanton’s tone is angry and Truth’s tone is sad.

C.

Truth’s tone is bitter; Stanton’s tone is outrage.

D.

They both show a tone of frustration.

The following passage has been adapted from “New Dinosaur’s Keen
Nose Made It a Formidable Predator, Penn Study Finds” by Katherine
Unger Baillie, originally published by the University of Pennsylvania,
May 11, 2015. (This passage was edited for length.)
New Dinosaur’s Keen Nose Made It a Formidable Predator

40 What set Isabella’s master apart from other slaveholders?
A.

He didn’t mistreat her as much.

B.

He allowed her to learn to read and write.

C.

He finally did set her free before he had to.

D.

He made promises he didn’t keep.

41 Which choice provides the best evidence for the answer
to the previous question?
A.

Lines 45–47 (“Isabella’s . . . by statute.”)

B.

Lines 47–49 (“In the year . . . usefulness”)

C.

Lines 50–51 (“she claimed . . . promise.”)

D.

Lines 53–55 (“She plead . . . able to do”)

42 In line 57, Truth says that her “faithfulness probably operated against her.” What does she mean by this phrase?
A.

Her faith in God would help her through the
difficulties operating against her.

B.

Her loyalty made her more important and valuable
to her master.

C.

She needed to be faithful to her God so that her
master would not break his promises.

D.

She needed to be faithful in the face of her master’s
inflexibility.

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A researcher from the University of Pennsylvania
has identified a species of dinosaur closely related to
Velociraptor, the group of creatures made infamous by
the movie Jurassic Park. The newly named species likely
possessed a keen sense of smell that would have made
it a formidable predator.
Steven Jasinski, a doctoral student in the School of
Arts & Science’s Department of Earth and Environmental
Science at Penn, and acting curator of paleontology
and geology at the State Museum of Pennsylvania, discovered the new species while investigating a specimen
originally assigned to a previously known species. His
analysis suggests the fossil—part of the dinosaur’s
skull—actually represents a brand new species, which
Jasinski has named Saurornitholestes sullivani. The
creature’s genus name Saurornitholestes, which means
“lizard bird thief,” gives a sense of what the prehistoric
predator would have looked like. These animals were
lightly built with long legs and jaws lined with teeth,
and they are believed to be very distant relatives of
today’s birds.
...
The specimen, roughly 75 million years old, was
discovered by paleontologist Robert Sullivan in the
Bisti/De-Na-Zin Wilderness Area of New Mexico in 1999.
When first described, scientists believed it was a member
of Saurornitholestes langstoni, a species of theropod
dinosaurs in the Dromaeosauridae family that had been
found in present-day Alberta, Canada.
But when Jasinski … began a comparative analysis
of the specimen to other S. langstoni specimens, he
found subtle differences. Notably, he observed that
the surface of the skull corresponding with the brain’s
olfactory bulb was unusually large. This finding implies
a powerful sense of smell.
“This feature means that Saurornitholestes sullivani had a relatively better sense of smell than other
dromaeosaurid dinosaurs, including Velociraptor, Dromaeosaurus, and Bambiraptor,” Jasinski said. “This keen
olfaction may have made S. sullivani an intimidating
predator as well.”

Practice Test 5

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50

55

60

65

S. sullivani comes from the end of the time of dinosaurs, or the Late Cretaceous, and represents the only
named dromaeosaur from this period in North America
south of Montana.
At the time S. sullivani lived, North America was
split into two continents separated by an inland sea.
This dinosaur lived on the western shores in an area
called Laramidia. Numerous dromaeosaurs, which
are commonly called raptors, are known from more
northern areas in Laramidia, including Alberta, Canada,
and Montana. However, S. sullivani represents the only
named dromaeosaur from the Late Cretaceous of
southern Laramidia.
S. sullivani shared its world with numerous other
dinosaurs. . . . Though a distinct species, S. sullivani
appears to be closely related to S. langstoni. Finding the
two as distinct species further shows that differences
existed between dinosaurs between the northern and
southern parts of North America.
At less than 3 feet at its hip and roughly 6 feet in
length, S. sullivani was not a large dinosaur. However,
previous findings of related species suggest the animal
would have been agile and fast, perhaps hunting in
packs and using its acute sense of smell to track down
prey.
“Although it was not large, this was not a dinosaur
you would want to mess with,” Jasinski said.

43 Which of the following is the best statement of the main
idea of the article?
A.

The S. sullivani was a predator aided by its keen
sense of smell.

B.

The new species resembled today’s birds.

C.

Scientific discoveries make important contributions
to our knowledge of prehistoric animals.

D.

Recent fossil evidence identified a new species of
dinosaur.

44 What conclusion can you draw from the way the S. sullivani
species was discovered?
A.

Students can sometimes make amazing
discoveries.

B.

Scientific investigations can yield surprising results.

C.

Students do important work with academics in
their field of studies.

D.

Some discoveries are attributable to chance.

A pair of S. sullivani attack a young hadrosaur. (Illustration by Mary P. Williams)

CONTINUE
Peterson's SAT® Prep Guide 2017

  945

Practice Test 5
45 According to the passage, a strong sense of smell helps a
predator because it
A.

would help a predator find food.

B.

could help a predator sense danger.

C.

would make up for poor eyesight.

D.

could help a predator find a mate.

49 How did scientists recognize that the fossil they found was
a new species?

46 What does the name of the new species tell us about this
dinosaur?
A.

Dinosaurs are named after real people.

B.

The name tells us where the dinosaur fossils were
found.

C.

Dinosaurs are given names based on where they
lived.

D.

The name suggests what it might have looked like.

A.

The fossil was larger than others that they had
found previously.

B.

By comparing it to other fossils, they noticed
differences in the skull.

C.

By looking at its closest relatives, they realized this
was a different species.

D.

The fossil had different markings than other
species.

50 Which choice provides the best evidence for the answer
to the previous question?

47 Which choice provides the best evidence for the answer
to the previous question?

A.

Lines 7–9 (“Steven Jasiniski . . . at Penn”)

B.

Lines 30–32 (“But when . . . differences.”)

C.

Lines 34–35 (“This finding . . . smell.”)

D.

Lines 42–43 (“S. sullivani . . . Cretaceous”)

51 As used in line 6, “formidable” most nearly means
A.

Lines 14–15 (“brand new . . . sullivani”)

B.

Lines 18–21 (“These animals . . . birds.”)

C.

Lines 23–24 (“The specimen . . . Robert Sullivan”)

D.

Lines 26–27 (“When first . . . langstoni”)

48 How is the information in the passage supported by the
graphic?
A.

It shows that S. sullivani lived about 75 million years
ago.

B.

It shows that S. sullivani stood less than 3 feet at its
hip and about 6 feet in length.

C.

It shows that S. sullivani had a very keen sense of
smell, which helped it hunt other dinosaurs.

D.

It shows that S. sullivani had legs and feet that
resemble those of birds, and in fact may be
distantly related to birds.

A.

frightened.

B.

inspiring.

C.

impressive.

D.

difficult.

52 As used in line 34, “olfactory” most nearly means
A.

bulb.

B.

sense of smell.

C.

surface of the skull.

D.

unusually large.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  946

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Practice Test 5
SECTION 2: WRITING AND LANGUAGE TEST
35 Minutes—44 Questions
TURN TO SECTION 2 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: Each passage below is accompanied by a number of multiple-choice questions. For some questions, you will
need to consider how the passage might be revised to improve the expression of ideas. Other questions will ask you to
consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage may
be accompanied by one or more graphics—such as a chart, table, or graph—that you will need to refer to in order to best
answer the question(s).
Some questions will direct you to an underlined portion of a passage—it could be one word, a portion of a sentence, or the full
sentence itself. Other questions will direct you to a particular paragraph or to certain sentences within a paragraph, or you’ll
be asked to think about the passage as a whole. Each question number refers to the corresponding number in the passage.
After reading each passage, select the answer to each question that most effectively improves the quality of writing in
the passage or that makes the passage follow the conventions of Standard Written English. Many questions include a “NO
CHANGE” option. Select that option if you think the best choice is to leave that specific portion of the passage as it is.

Questions 1–11 are based on the following passage.

1

The Glass Ceiling

The writer is considering deleting the underlined sentence. Should the writer do this?
No, because it provides a detail that supports
the main topic of the paragraph.

B.

No, because it acts as a transition to the next
paragraph.

C.

Yes, because it repeats information that has
been provided.

D.

Yes, because it is a detail that is irrelevant to the
main topic of the paragraph.

A.

NO CHANGE

B.

America.

C.

America?

D.

America...

“The Glass Ceiling” is a metaphor that refers to the
imperceptible and subversive forms of discrimination women
in the workforce encounter when pursuing upper-level
management positions. A popular phrase in the 1980s, it has
become less widely used over the ensuing years. 1 Other
phrases from past decades are still in frequent use. However,
as recent data make clear, “The Glass Ceiling” remains a solid
barrier to women working in 2 America!

2

— writing and language

A.

CONTINUE
Peterson's SAT® Prep Guide 2017

  947

Practice Test 5
According to data from the U.S. Bureau of Labor Statistics

3

and the Pew Research Center, women make up 57.2% of the
nation’s workforce 3 but hold 5% of CEO only positions in
Fortune 500 companies. Women also account for only 17% of
board membership at Fortune 500 companies. While these

A.

NO CHANGE

B.

but hold only 5% of CEO positions in Fortune 500
companies

C.

but hold 5% of only CEO positions in Fortune 500
companies

D.

but hold 5% of CEO positions only in Fortune 500
companies

A.

NO CHANGE

B.

passing

C.

passive

D.

past

A.

NO CHANGE

B.

In 1995, a bipartisan Federal Glass Ceiling
Commission, was formed to determine the root of
gender discrimination within corporate America.

C.

In 1995, a bipartisan Federal Glass Ceiling
Commission was formed to determine the root of
gender discrimination within corporate America.

D.

In 1995 a bipartisan Federal Glass Ceiling
Commission was formed to determine the root of
gender discrimination; within corporate America.

A.

NO CHANGE

B.

affect

C.

effective

D.

affection

percentages note a minimal increase in female leadership over
the 4 passed thirty years, barriers still seem to exist.
5 In 1995, a bipartisan Federal Glass Ceiling Commission
was formed; to determine the root of gender discrimination

4

within corporate America. The committee, headed by
Secretary of Labor Robert Reich, noted that “At the highest
levels of corporations the promise of reward for preparation
and pursuit of excellence is not equally available to members
of all groups.” Two barriers that contributed most to “The
Glass Ceiling” 6 effect were “supply barriers” and “internal

5

business barriers.”

6

  948

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Practice Test 5
“Supply barriers” represent the lack of leadership, education,

7

and experience women are given access to during high school

A.

NO CHANGE

B.

their

C.

his

D.

your

A.

NO CHANGE

leaders. This includes creating more mentoring programs and

B.

providers

school-to-work initiatives and 8 provide more educational

C.

provided

scholarships.

D.

providing

A.

NO CHANGE

B.

The difference between what corporate executives
say they want to do; in regard to discrimination,
and

C.

The difference between what corporate executives
say they want to do and in regard to discrimination

D.

The difference between what corporate executives
say they want to do in regard to discrimination and

and college. Corporations have viewed this lack of access as an
educational reform issue, not a business issue, and they do not
think it’s 7 her responsibility to fix it. However, corporations
are equipped with both financial and educational resources
to overcome this “supply barrier.” If corporations are serious

8

about ending discrimination in the workplace, they need to
invest in educational programs that train women to be future

9 The difference between what corporate executives say
they want to do. In regard to discrimination, and efforts being
made (or not made) to end discriminatory practices is another

9

issue. Talking the talk and not walking the walk is what the
“internal business barrier” is all about. The reason for this
discrepancy is that many white males working in the highly
competitive corporate America believe they are “losing the
corporate game, losing control, and losing opportunity.” In
essence, white men in corporate leadership feel threatened by
including women in their ranks.

CONTINUE
Peterson's SAT® Prep Guide 2017

  949

Practice Test 5
10 While many efforts have been made to prevent overt

10

discriminatory practices, 65% of women still see gender bias
as a barrier they have to overcome. 11 Until women can be

Which of the following sentences would make an effective
opening sentence to this paragraph?
A.

Ending discrimination against women in the
workforce is a relatively easy problem to fix.

B.

Ending discrimination against women in the
workforce is an involved, complicated process.

C.

There are plenty of opportunities for women to find
fulfillment and success.

D.

Technology is helping modern societies overcome
issues involving gender bias.

A.

NO CHANGE

B.

Until women can be accepted as equals in the
corporate sphere, “The Glass Ceiling” will remain
firmly intact.

C.

Until women can be accepted as equally in the
corporate sphere, “The Glass Ceiling” will remain
firmly intact.

D.

Until women can be accepted in the corporate
sphere as equally, “The Glass Ceiling” will remain
firmly intact.

as equals accepted in the corporate sphere, “The Glass Ceiling”
will remain firmly intact.

11

  950

www.petersons.com

Practice Test 5
Questions 12–22 are based on the following
passage and supplementary material.

12
A.

NO CHANGE

B.

It is difficult to maintain such a vast collection—

C.

Among the collections of

D.

Already collections number

A.

NO CHANGE

B.

The Library’s services extend not only to members
and committees of Congress, but also to the
executive and judicial branches of government; to
libraries throughout the nation and the world; and
to scholars researchers, artists, and scientists

C.

The Library’s services extend not only to members
and committees of Congress, but also to the
executive and judicial branches, of government, to
libraries throughout the nation, and the world and
to scholars, researchers, artists, and scientists

D.

The Library’s services, extend not only to members
and committees of Congress, but also to the
executive and judicial branches of government to
libraries, throughout the nation and the world, and
to scholars, researchers, artists, and scientists

books as may be necessary for the use of Congress—and for

A.

NO CHANGE

putting up a suitable apartment for containing them therein. . . .”

B.

A little history is in order here.

C.

Nevertheless, John Adams signed a bill to create
the library.

D.

We’re lucky we have this institution.

considered to be one of the finest in the United States.

A.

NO CHANGE

Congress accepted Jefferson’s offer. Thus the foundation was

B.

replacement

C.

stand-in

D.

copy

The Library of Congress
The Library of Congress is the world’s largest and most open
library. 12 With collections numbering more than 158
million items on 838 miles of shelving, it includes materials

13

in 470 languages; the basic manuscript collections of 23
Presidents of the United States; maps and atlases that have
aided explorers and navigators in charting both the world
and outer space; and the earliest motion pictures and
examples of recorded sound, as well as the latest databases
and software packages. 13 The Library’s services extend,
not only to members and committees of Congress, but also
to the executive, and judicial branches of government, to
libraries throughout the nation and the world, and to scholars,
researchers, artists, and scientists who use its resources.
14 This was not always the case. When President John
Adams signed the bill that provided for the removal of the
seat of government to the new capital city of Washington in
1800, he created a reference library for Congress only. The bill
provided, among other items, $5,000 “for the purchase of such

14

After this small congressional library was destroyed by fire
along with the Capitol building in 1814, former President
Thomas Jefferson offered as a 15 substitute his personal
library, accumulated over a span of fifty years.” It was

laid for a great national library.

15

CONTINUE
Peterson's SAT® Prep Guide 2017

  951

Practice Test 5
By the close of the Civil War, the collections of the Library

16

of Congress had grown to 82,000 volumes and were still

A.

NO CHANGE

B.

it collections

C.

its collections

D.

its’ collections

A.

NO CHANGE

B.

Library would receive two free copies of every
book, map, chart, dramatic or musical composition
engraving, cut, print, or photograph, submitted for
copyright.

C.

Library would receive two, free copies of every
book, map, chart, dramatic or musical composition;
engraving, cut, print, or photograph submitted for
copyright

D.

Library would receive two free copies of every
book, map, chart, dramatic or musical composition,
engraving, cut, print, or photograph submitted for
copyright.

He quickly realized that the Library had to get control of

A.

NO CHANGE

the collections that had been overflowing the rooms in

B.

ever-existing

the Capitol. Young set up organizational units and devised

C.

ever-expending

programs that changed the Library. 19 Instead of being

D.

ever-expounding

principally used by members of Congress and committees.
In 1864, President Lincoln appointed as Librarian of Congress
a man who was to transform the Library: Ainsworth Rand
Spofford, who opened the Library to the public and greatly
expanded 16 it’s collections. Spofford successfully

17

advocated a change in the copyright law so that the 17
Library would receive two, free copies of every book, map,
chart, dramatic, or musical composition, engraving, cut, print,
or photograph submitted for copyright. Predictably, Spofford
soon filled all the Capitol’s library rooms, attics, and hallways.
In 1873, he then won another lobbying effort, for a new
building to permanently house the nation’s growing collection
and reading rooms to serve scholars and the reading public.
The result was the Thomas Jefferson Building, completed in
1897. Since then, two more buildings have been constructed
to house the Library’s 18 ever-expanding collection.
The first librarian in the new building was a newspaperman
with no previous library experience, John Russell Young.

essentially an acquisitions operation, it became an efficient
processing factory that organized the materials and made

18

19 Which choice most effectively sets up the information that
follows?

them useful.

  952

www.petersons.com

A.

NO CHANGE

B.

In spite of being essentially an acquisitions
operation,

C.

Once it was essentially an acquisitions operation,

D.

In addition to it being essentially an acquisitions
operation,

Practice Test 5
20 Formerly head of the Boston Public Library, Herbert

20

Putnam succeeded Young. Putnam served as Librarian of
Congress for 40 years. While Librarian, Spofford had collected
the materials, Young had organized them, and Putnam set out
to ensure that they would be used. 21 They took the Library

A.

NO CHANGE

B.

Young was succeeded. Herbert Putnam had
formerly been head of the Boston Public Library.

C.

Young was succeeded by someone else—Herbert
Putnam, former head of the Boston Public Library.

D.

Young was succeeded after only two years by
Herbert Putnam, formerly the head of the Boston
Public Library.

A.

NO CHANGE

B.

Them

C.

He

D.

We

of Congress directly into the national library scene and made
its holdings known and available to the smallest community
library in the most distant part of the country.

21

CONTINUE
Peterson's SAT® Prep Guide 2017

  953

Practice Test 5
In about 1912, both Librarian Putnam and members of

22 Which choice best describes a conclusion that can be
drawn from the chart?

Congress became concerned about the distance that was
widening between the Library and its employer, the Congress.

A.

There are more public university than private
university libraries that are similar in scope and
scale to the Library of Congress.

B.

University libraries of the same scope and scale as
the Library of Congress are more common than one
would expect.

C.

When it comes to university libraries of the same
scope and scale as the Library of Congress, the
private sector is doing more to create them than
the public sector.

D.

As the years go on, university libraries of the same
scope and scale as the Library of Congress are
rapidly increasing.

Various states had begun to set up “legislative reference
bureaus,” which brought together skilled teams of librarians,
economists, and political scientists whose purpose was to
respond quickly to questions that arose in the legislative
process. Congress wanted the same kind of service for itself,
so Putnam designed such a unit for the Library of Congress.
Called the Legislative Reference Service, it went into operation
in 1914 to prepare indexes, digests, and compilations of
law that the Congress might need, but it quickly became
a specialized reference unit for information transfer and
research. This service was the forerunner of the Library’s
current Congressional Research Service. 22

Public
Private
Total 4-year and above
Doctor’s
Master’s
Bachelor’s
Less than 4-year
Less than 1,500
1,500 to 4,999
5,000 or more

www.petersons.com

1,000,000 or more

500,000–999,999

158

241

450

450

691

747

275

153

160

43
277

57
101

77
136

145
96

297
153

362
329

231
516

146
129

106
47

109
51

48
6
19
23
110

90
8
24
58
123

89
5
22
61
152

155
14
39
102
295

361
35
177
148
330

673
131
378
164
74

273
83
151
39
2

151
93
51
7
2

160
151
9
0
0

193
47
1

257
185
8

352
249
90

363
297
87

36
135
104

4
36
113

1
7
152

0
0
3
26
317
82
2

0
0
47
178
328
116
22

1
10
211
292
74
126
33

1
20
164
66
2
21
1

10
44
76
17
1
3
2

113
35
9
3
0
0
0

Control
Level
115
12
35
68
205

Size (FTE enrollment)
138
20
0

186
26
1

Carnegie classification (1994)
0
1
1
1
150
50
117

0
0
0
5
75
33
45

0
0
3
5
85
67
53

0
0
4
6
150
60
21

Source: U.S. Department of Education, National Center for Education Statistics, 1996 Integrated
Postsecondary Education Data System, “Academic Libraries Survey” (IPEDS-L: 1996).

  954

250,000–499,999

100,000–249,999

50,000–99,999

30,000–49,999

20,000–29,999

10,000–19,999

320

309
9
2

Research I and II
Doctoral I and II
Master’s I and II
Baccalaureate I and II
Associate of Arts
Specialized
Not classified

5,000–9,999

Institutional characteristic
All higher education institutions

Less than 5,000

Number of Libraries in Volume Category

Practice Test 5
Questions 23–33 are based on the following passage.

23
A.

NO CHANGE

B.

Emily’s now forever empty bedroom, Lavinia
recalled some verses

Lavinia Dickinson had become all too accustomed to. Looking

C.

Emily’s bedroom, Lavinia recalled some verses

around her sister 23 Emily’s now forever empty bedroom

D.

Emily’s now forever empty bedroom, Lavinia
recalled some verses and poetry

Lavinia & Emily
The Homestead was quiet and still, a preternatural quiet

that contained nothing, Lavinia recalled some verses penned
by Emily many years ago:
The bustle in a house
The morning after death
Is solemnest of industries
Enacted upon earth, —

24 Which of the following sentences does NOT add a relevant
detail to this paragraph?

The sweeping up the heart,
And putting love away
We shall not want to use again
Until eternity.

A.

Some people wondered at Emily’s seeming
preoccupation with death.

B.

Emily had always had a curious mind and a
voracious appetite for learning.

C.

She also greatly enjoyed being in nature.

D.

For Emily, faith was more than rote belief.

A.

NO CHANGE

B.

sister’s

C.

sisters’

D.

sister

24 Some people wondered at Emily’s seeming
preoccupation with death. But Lavinia found it natural for her
25 sisters inquisitive mind to be drawn to exploring this final
journey in the cycle of life, especially since Emily had seen so
many loved ones pass into eternal slumber. Emily had always
had a curious mind, and a voracious appetite for learning. She

25

also greatly enjoyed being in nature. Faith was something
she refused to accept blindly, without thought, much to the
chagrin of the Calvinist community around her. For Emily, faith
was more than rote belief.
Faith is a fine invention
For gentlemen who see;
But microscopes are prudent
In an emergency!

CONTINUE
Peterson's SAT® Prep Guide 2017

  955

Practice Test 5
26 Emily had felt very fully her isolation as one “standing
alone in rebellion” of faith. Reading 27 through her letters

26 Which of the following sentences would make an effective
addition to this paragraph?

and the poems Emily had hidden away, Lavinia realized just

A.

One reason for Emily’s sense of isolation was her
resistance to common ideas of her time.

B.

One reason for Emily’s sense of isolation was her
refusal to take part in social events.

C.

One reason for Emily’s sense of isolation was her
need to be alone to write poetry.

D.

One reason for Emily’s sense of isolation was her
house’s remote location.

A.

NO CHANGE

B.

tough

C.

though

D.

thought

how isolated her beloved sister had felt. Perhaps that was why
the self-professed “belle of Amherst” had withdrawn so much
from the public sphere.
Emily felt, quite keenly, the limitations of womanhood. Lavinia
still remembered the indignation Emily had expressed during
the Whig Convention of 1852 when women were not allowed
to be delegates. “Why can’t I be a Delegate? ...don’t I know all
about Daniel Webster, and the Tariff and the Law?” 28

27

28 At this point, the writer is considering adding the following
sentence:
But Lavinia also knew that her sister was not cut out for
politics and all the socializing and public display it would
entail.
Should the writer make this addition here?

  956

www.petersons.com

A.

Yes, because it adds more information about Emily’s
personality.

B.

Yes, because it explains the contrast between
Emily’s words and actions.

C.

No, because it detracts from the point about
women’s issues.

D.

No, because it is not relevant to Emily’s life.

Practice Test 5
Yes, it seemed to Lavinia that her sister had most decidedly felt

29

the trappings of being a woman. And, as much as 29 they
tried to eschew them 30 by not becoming a wife or mother,
she still felt trapped by society’s strict bonds.
I Never Hear the Word “Escape”
I never hear the word “escape”
Without a quicker blood,
A sudden expectation,
A flying attitude.

31 given?

NO CHANGE

B.

we

C.

she

D.

her

30 Which choice best fits with the style and tone of the passage?

I never hear of prisons broad
By soldiers battered down,
But I tug childish at my bars, —
Only to fail again!
Emily never understood the power of the gift she had been

A.

A.

NO CHANGE

B.

by never being a wife or mother

C.

by postponing choosing to be a wife or mother

D.

by refusing the role of wife or mother

31
A.

NO CHANGE

The Duel

B.

given!

I took my power in my hand.
And went against the world;
‘T was not so much as David had,
But I was twice as bold.

C.

given.

D.

given;

A.

NO CHANGE

B.

decider

C.

decided

D.

decide

32
I aimed my pebble, but myself
Was all the one that fell.
Was it Goliath was too large,
Or only I too small?
Sitting in the stillness of Emily’s room, surrounded by her
internal monologue expressed through thousands of poems,
32 it was deciding by Lavinia that it was time the world
knew the full treasure her sister was. 33

33 Which of the following would make an effective concluding sentence for this paragraph and passage?
A.

The world will never know this unique treasure.

B.

The world was about to receive a gift it would long
cherish.

C.

The world already had enough special voices.

D.

The world is approximately 4.5 billion years old.

CONTINUE
Peterson's SAT® Prep Guide 2017

  957

Practice Test 5
Questions 34–44 are based on the following passage.
What Is Sleep?
Scientists have known for some years that sleep is important
to human health. In fact, cases of long-term sleep deprivation
have even led to death. 34 Yet, scientists are still studying
this unique state in which humans spend a third of their lives.
35 [1] It isn’t only current scientists who are intrigued with
sleep. [2] Throughout history, people have attempted to
understand this remarkable experience. [3] Many centuries
ago, for example, sleep was regarded as a type of anemia of
the brain. [4] Alcmaeon, a Greek scientist, believed that blood
retreated into the blood vessels, and the partially starved
brain went to sleep. [5] Plato supported the idea that the soul
left the body during sleep, wandered through the world, and
woke up the body when it returned. [6] During the twentieth
century, great strides were made in the study of sleep.

34
A.

NO CHANGE

B.

Scientists are yet studying

C.

Scientists are studying yet

D.

Yet, scientists study still

35 Which sentence in this paragraph is the BEST choice to
move to the fourth paragraph to create a more logical
sequence?
A.

Sentence 1

B.

Sentence 2

C.

Sentence 4

D.

Sentence 6

36 Which choice most effectively sets up the information that
follows?

Recently, more scientific explanations of sleep have been
proposed. Looking at them, we see a variety of ideas about
the nature of sleep. 36 Research may be able to help people
who have sleep disorders. According to one theory, the brain
is put to sleep by a chemical agent that accumulates in the
body when it is awake. Another theory is that weary branches
of certain nerve cells break connections with neighboring
cells. The flow of impulses required for staying awake is then
disrupted. These more recent theories have to be subjected to
laboratory research.

  958

www.petersons.com

A.

NO CHANGE

B.

Some of the newer ideas may yield important data
about the science of sleep.

C.

Although science has not yet solved the mysteries
of sleep, breakthroughs are imminent.

D.

However, some of the old ideas may prove to be
correct.

Practice Test 5
Why do we sleep? Why do we dream? Modern sleep

37

research is said to have begun in the 1920s with the 37

A.

NO CHANGE

B.

invention

C.

idea

D.

suggestion

A.

NO CHANGE

B.

when

sleep, the subjects rarely could recall their dreams. Aserinsky

C.

or

and Kleitman used EEGs and other machines in an attempt to

D.

so

A.

NO CHANGE

B.

Even so,

C.

As predicted,

D.

On the other hand,

discovery of a machine that could measure brain waves, the
electroencephalograph (EEG). The study of sleep was further
enhanced in the 1950s, 38 and Eugene Aserinsky, a graduate
student at the University of Chicago, and Nathaniel Kleitman,
his professor, observed periods of rapid eye movements

38

(REMs) in sleeping subjects. When awakened during these
REM periods, subjects almost always remembered dreaming.
39 Nevertheless, when awakened during non-REM phases of

learn more about REMs and sleep patterns.

39

40 Guided by REMs, it became possible for investigators to
“spot” dreaming from outside and then 41 awakening the
sleeper to collect dream stories. They could also
42 altar the dreamers’ experiences with noises, drugs, or
other stimuli before or during sleep. Thankfully, it appears the
body takes care of itself by temporarily paralyzing muscles
during REM sleep, preventing the dreamer from “acting out”

40 Which choice sets up the most logical introduction to the
sentence?

dream activities.

A.

NO CHANGE

B.

Regardless of REMs,

C.

No longer hampered by REMs,

D.

Nevertheless, with REMs,

A.

NO CHANGE

B.

quickly awakening

C.

awakened

D.

awaken

A.

NO CHANGE

B.

alter

C.

alternate

D.

alternative

41

42

CONTINUE
Peterson's SAT® Prep Guide 2017

  959

Practice Test 5
Since the mid-1950s researchers 43 has been drawn into

43

sleep laboratories. There, bedrooms adjoin other rooms that
contain EEGs and other equipment. The EEG amplifies signals
from sensors on the face, head, and other parts of the body,
which together yield tracings of respiration, pulse, muscle
tension, and changes of electrical potential in the brain that
are sometimes called brain waves. These recordings supply

A.

NO CHANGE

B.

were been drawn

C.

have been drawn

D.

was drawn

A.

NO CHANGE

B.

sleep—they

C.

sleep; they

D.

sleep, they

44

clues to the changes of the sleeping person’s activities.
These sleep studies have changed long-held beliefs that
sleep was an inactive, or passive, state only used for rest and
recuperation. As scientists have learned more about the
purpose of sleep and dreams during REM 44 sleep. They
are now turning to the study of sleep disorders to learn more
about problems during sleep.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  960

www.petersons.com

Practice Test 5
SECTION 3: MATH TEST—NO CALCULATOR
25 Minutes—20 Questions
TURN TO SECTION 3 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–15, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 16–20, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 16 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is not permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  961

Practice Test 5
1

2

3

4

  962

If

x +2
= m and m = –3, what is the value of x?
5

A.

−17

B.

−15

C.

−5

D.

−1

50
, and m is a positive number, then as m inm
creases in value, d

If d = m −

A.

increases in value.

B.

decreases in value.

C.

increases, then decreases.

D.

decreases, then increases.

Pieces of wire are soldered together so as to form the edges
of a cube whose volume is 64 cubic inches. The number of
inches of wire used is
A.

24.

B.

48.

C.

64.

D.

96.

Myra baked 6 sheets of cookies with r cookies on each
sheet. Neil baked 7 sheets of cookies with p cookies on
each sheet. Which of the following represents the total
number t of cookies baked by Myra and Neil?
A.

t = 13pr

B.

t = 42pr

C.

t = 6r + 7p

D.

t = 7r + 6p

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Practice Test 5
5

6

1
1
=
If 2 y = , then
4
y
3
A.

3
2

B.

3
4

C.

1
5

D.

4
3

y=

SHOW YOUR WORK HERE

( x − 3)3
4

Which expression is equivalent to x?

7

8

A.

4y +3

B.

4y +3

C.

3

4y +3

D.

3

4y +3

Hannah recently purchased a plant that grows 4.5 centimeters each week. The height of Hannah’s plant can be found
using the equation h = 4.5w + 6, where h is the height of
the plant in centimeters, and w is the number of weeks.
What is the meaning of the 6 in the equation?
A.

Hannah’s plant will be 6 centimeters tall after 4.5
weeks.

B.

Hannah’s plant grows 6 centimeters each week.

C.

Hannah’s plant will grow for 6 weeks.

D.

Hannah’s plant was initially 6 centimeters tall.

(x)6 + (2x2)3 + (3x3)2 =
A.

5x5 + x6

B.

17x5 + x6

C.

6x6

D.

18x6

CONTINUE
Peterson's SAT® Prep Guide 2017

  963

Practice Test 5
Question 9 refers to the following graph.
200

Number of Trout

160

120

80

40

0

2

4

Number of Days
9

10

  964

Stephen was studying the population of a certain trout
pond. When he started his study, there were 55 trout in
the pond. He observed the pond each day for 10 days and
observed that there were 12 new trout each day. The graph
above represents the relationship between the number of
trout in the pond and the number of days. Which of the
following is an equation for the graph?
A.

y = 12x + 55

B.

y = 10x + 12

C.

y = 55x + 12

D.

y = 12x + 10

27
Which of the following is equal to  − 
 8
A.

−

3
2

B.

−

2
3

C.

2
3

D.

3
2

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−

1
3

?

6

8

10

Practice Test 5
11 The area of a square is 49x2. What is the length of a diagonal
of the square?
A.

7x

B.

7x 2

C.

14x

D.

SHOW YOUR WORK HERE

7x
2

12 The distance, s, in feet that an object falls in t seconds when
dropped from a height is obtained by use of the formula
s = 16t2. When graphed, what is the meaning of the slope
between any two points in the graph?

13

A.

The height in feet from where the object falls

B.

The speed, in feet per second, of the object as it
falls

C.

The time in seconds it takes for the object to fall to
the ground

D.

The acceleration, in feet per second squared, of the
object as it falls

D + B = 24
4 D + 2B = 84
In this system of equations, the first equation represents
the total number of dogs, D, and birds, B, in a pet store.
The second equation represents the number of legs a dog
has, 4D, and the number of legs a bird has, 2B. How many
dogs and birds are in the pet store?
A.

D = 6; B = 18

B.

D = 18; B = 6

C.

D = 24; B = 84

D.

D = 60; B = 24

14 f(x) = x2 – 4x – 21
Which of the following is an equivalent equation that
shows the zeros of the function as coefficients or constants?
A.

f(x) = (x – (–7))(x – 3)

B.

f(x) = (x – 7)(x – (–3))

C.

f(x) = (x – 2)2 – 21

D.

f(x) = (x – 2)2 – 25

CONTINUE
Peterson's SAT® Prep Guide 2017

  965

Practice Test 5
15 Which equation represents the equation of a line perpendicular to y = 3x – 2 that goes through the point (1, 3)?

  966

A.

y = –3x + 6

B.

1 10
y =− x+
3
3

C.

1
9
y =− x+
3
3

D.

y = 3x

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SHOW YOUR WORK HERE

Practice Test 5

DIRECTIONS: For Questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.

1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

, it will be interpreted as

31
1
, not 3 .
2
2

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either roundedor
truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

1

1

2

2

2

1

1

3

3

3

3

3

4

4

4

4

4

5

5

5

5

6

6

6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

0

0

0

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

7

7

7

8

8

8

8

8

9

9

9

9

9

3

3

3

4

4

4

5

5

5

6

6

6

6

6

7

7

7

7

7

7

7

7

8

8

8

8

8

8

8

9

9

9

9

9

9

9

6

6

CONTINUE
Peterson's SAT® Prep Guide 2017

  967

Practice Test 5
16

SHOW YOUR WORK HERE

70°

x°

120°

In the figure above, x =

17 The only linear factors of the function f are (x + 3)2 and
(3x – 2). What is the product of its three zeroes?

18 What value of a ensures that the function g(x) = ax2 + 20x
+ 25 has exactly one x-intercept?

19
4 − x 2 = 3x
What is one solution to the equation?

20

2 x + 3y = 7
ax − 12 y = b
According to the system of equations above, what is the
value of ab that will make the system of equations have
an infinite number of solutions?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.

  968

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Practice Test 5
SECTION 4: MATH TEST—CALCULATOR
55 Minutes—38 Questions
TURN TO SECTION 4 OF YOUR ANSWER SHEET TO ANSWER THE QUESTIONS IN THIS SECTION.
DIRECTIONS: For Questions 1–30, solve each problem, select the best answer from the choices provided, and fill in the
corresponding circle on your answer sheet. For Questions 31–38, solve the problem and enter your answer in the grid on
the answer sheet. The directions before Question 31 will provide information on how to enter your answers in the grid.

ADDITIONAL INFORMATION:
1.  	 The use of a calculator in this section is permitted.
2.  	 All variables and expressions used represent real numbers unless otherwise indicated.
3.  	 Figures provided in this test are drawn to scale unless otherwise indicated.
4.  	 All figures lie in a plane unless otherwise indicated.
5.  	 Unless otherwise specified, the domain of a given function f is the set of all real numbers x for which f(x) is a real number.

Circle:

Rectangle:

r
C = 2�r
A = �r2

l
A = lw

r

c

a
b

x 2

x

b

1
A = bh
2

Cylinder:

w
V = lwh

h

w

Rectangular
Solid:

l

Triangle:

x

x

Special Right Triangles

a + b2 = c2
2

Sphere:

2x

x 3

Cone:

Rectangular-Based
Pyramid:

h
r

V = �r2h

h

h
r

4
V = �r3
3

The number of degrees of arc in a circle is 360.
The number of radians in the arc of a circle is 2 .
The sum of the measures in degrees of the angles of a triangle is 180.

1
V = �r2h
3

l

w
1
3

V = lwh

CONTINUE
Peterson's SAT® Prep Guide 2017

  969

Practice Test 5
1

2

3

4

  970

If 9x + 5 = 23, what is the numerical value of 18x + 5?
A.

46

B.

41

C.

36

D.

32

A pickup truck has maximum load capacity of 1,500
pounds. Bruce is going to load small radiators, each weighing 150 pounds, and large radiators, each weighing 250
pounds, into the truck. There are 15 radiators to choose
from. Which system of linear inequalities represents this
situation?

A.

x + y < 15
150 x + 250 y < 1, 500

B.

x + y ≥ 15
150 x + 250 y ≥ 1, 500

C.

x + y > 15
150 x + 250 y > 1, 500

D.

x + y ≤ 15
150 x + 250 y ≤ 1, 500

If 15 cans of food are needed for 7 adults for two days, how
many cans are needed to feed 4 adults for seven days?
A.

15

B.

20

C.

25

D.

30

Fiona earns $28 per hour working for herself. She saves
25% of her income to pay taxes. Which function can be
used to determine the non-taxed amount Fiona earns for
working x hours?
A.

f(x) = 28(0.25x)

B.

f(x) = 28 + 0.25x

C.

f(x) = 28(0.75x)

D.

f(x) = 28 + 0.75x

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Practice Test 5
SHOW YOUR WORK HERE

Questions 5 and 6 refer to the following information.
Total Annual Sales

8

Total Sales ($ millions)

6

4

2

0

2

4

6

8

Years after 2005

The graph above represents the sales for a company after 2005.
5

6

Which phrase best describes the correlation between the
years after 2005 and the total sales?
A.

Weak negative

B.

Strong negative

C.

Weak positive

D.

Strong positive

Which equation best models the data shown in the graph?
A.

y = 0.4x + 1

B.

y = x + 0.5

C.

y = 1.5x

D.

y = 0.5x

CONTINUE
Peterson's SAT® Prep Guide 2017

  971

Practice Test 5
7

8

9

  972

If a box of notepaper costs $4.20 after a 40% discount, what
was its original price?
A.

$2.52

B.

$5.88

C.

$7.00

D.

$10.50

The average attendance at basketball games at a local
university over the last 10 years can be modeled by the
equation y = 329x + 6,489, where y represents the average attendance at basketball games x years after 2004.
Which of the following describes the meaning of 329 in
the equation?
A.

The average attendance at basketball games in
2004.

B.

The total attendance at basketball games in 2004.

C.

The annual increase in average attendance at
basketball games.

D.

The total increase in average attendance at
basketball games for the last 10 years.

One supercomputer can process a job 1.5 times faster than
another supercomputer. When both supercomputers are
used simultaneously to complete a job, the job is completed in 3 hours. Which of the following equations can
be used to determine the time it takes the faster supercomputer to complete the job alone? (Here, h represents
the time it takes the slower supercomputer to complete
the job alone.)
A.

h 1.5h
+
=1
3
3

B.

3
h+ h = 3
2

C.

1 2 1
+ =
h 3h 3

D.

3 2
+ =1
h h

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Practice Test 5
10

A local library had 25,825 books at the beginning of 2010.
Since then, it has added 375 books each year. The library
can fit a maximum of 35,000 books. If x represents the
number of years after the start of 2010, which inequality
shows the number of years that the library can continue
adding books at this pace without adding space?
A.

35,000 − 375 ≤ x

B.

35,000 ≤ 375x

C.

35,000 ≥ 375x − 25,825

D.

35,000 ≥ 375x + 25,825

SHOW YOUR WORK HERE

11 If d , d , and d represent the three solutions of the equa1 2
3
tion (2 – 3x)(x2 – 2x + 3) = 0, compute d 1 i d 2 i d 3 .

A.

−

B.

1

C.

2
9
2

D.

2
3

12 A study was performed to determine if a new medication,
Z, helps people who suffer from a certain affliction. A group
of 500 randomly selected people who have the affliction
were included in the study. Of the group, 200 people
were given Z, 200 people were given an old medication,
Y, and another 100 people received no treatment. The
data showed that people who received Z had significantly
decreased effects of the affliction, more than people who
received no treatment or who were given medicine Y.
Based on the design and results of the study, which of the
following is an appropriate conclusion?
A.

Z is likely to lessen the effects of the affliction in
people who suffer from the affliction.

B.

Z is likely to lessen the effects of the affliction better
than any other medication.

C.

Z is likely to lessen the effects of the affliction for
anyone who takes the medication.

D.

Z is likely to lessen the effects of the affliction for
those who received no treatment.

CONTINUE
Peterson's SAT® Prep Guide 2017

  973

Practice Test 5
13 A group of 27 people visit a city. The people rent either a
bicycle or rollerblades. They pay $7 to rent a bicycle or $5
to rent rollerblades for the day. If the total cost for rentals
is $171, how many more people rented bicycles than roller
blades?
A.

0

B.

9

C.

12

D.

18

14 After installing a circular pond with diameter 12 feet, Kosi
decided to install an 18-inch walkway around the entire
pond. The stone costs $7.25 per square foot. What is the
total cost of the stone for the walkway?

15

A.

$130.50

B.

$461.23

C.

$819.96

D.

$1,281.18

y = 2x −5
y = ( x − 2) − 9
2

If (x, y) and (v, w) are the two solutions of the system, what
is v + w + x + y?

  974

A.

–10

B.

4

C.

8

D.

18

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SHOW YOUR WORK HERE

Practice Test 5
Questions 16 and 17 refer to the following information.
The graph provided shows the population of California, in millions, from the years 1860 to 1980. Each point represents the population
at a particular year. The best fit relation between the points is drawn to connect them.

Population of California
24

Population (in Millions)

21

18

15

12

9

6

3

1830

1860

1890

1920

1950

1980

16 Which phrase describes the relationship between the
population and the number of years?
A.

Linear increasing

B.

Linear decreasing

C.

Exponential growth

D.

Exponential decay

17 Based on the graph, which of the following would be the
best prediction of the population of California in 1990?
A.

20 million

B.

23 million

C.

25 million

D.

30 million

CONTINUE
Peterson's SAT® Prep Guide 2017

  975

Practice Test 5
18 A rectangular sign is cut down by 10% of its height and 30%
of its width. What percent of the original area remains?
A.

37%

B.

57%

C.

63%

D.

70%

19 A recent report states that if you were to eat each meal in
a different restaurant in New York City, it would take you
more than 19 years to cover all of New York City’s eating
places, assuming that you eat three meals a day. On the
basis of this information, the number of restaurants in New
York City
A.

exceeds 20,500.

B.

is fewer than 20,000.

C.

exceeds 21,000 but does not exceed 21,500.

D.

exceeds 21,500.

20 If a cubic inch of gold weighs 0.70 pounds, how much does
a cubic foot of gold weigh?

21

A.

700 pounds

B.

1,210 pounds

C.

1,296 pounds

D.

1,728 pounds

3 x −1 2 x + 3
−
2 x + 3 3 x −1
Which of the following is equivalent to the expression
above?

  976

A.

5 x 2 − 18 x − 8
6x2 +7x −3

B.

x −4
6x +7x −3

C.

5 x 2 + 10
6x2 +7x −3

D.

5 x 2 − 12 x − 8
6x2 +7x −3

2

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Practice Test 5
SHOW YOUR WORK HERE

22

8
6
4
2

–8

–6

–4

–2

0

2

4

6

8

–2
–4
–6
–8

Which of the following is an equation for the graph?

23

A.

y=

6
−1
x +3

B.

y=

6
−1
x −3

C.

y=

1
−1
x +3

D.

y=

1
−1
x −3

3
x −1
g( x ) = ( x − 4)2

f (x) =

What is the value of g(f(4))?
A.

–3

B.

0

C.

1

D.

9

CONTINUE
Peterson's SAT® Prep Guide 2017

  977

Practice Test 5
24 The number of people living in a certain city has been
growing at a constant rate of about 3.8% each year since
1980. The population in 2000 was 38,500. If y is the population of the city x years after 1980, which equation best
represents this situation?
A.

y = 18,260(1.038)x

B.

y = 38,500(1.38)x

C.

y = 38,500(1.038)x

D.

y = 81,172(1.38)x

25 If f(x) = x2 − 2x − 8, for which value(s) of x does f(x) = 0?
A.

x = −4, 2

B.

x = 2, 4

C.

x = −4, −2

D.

x = −2, 4

Questions 26 and 27 refer to the following information.
A recent poll surveyed a random selection of 850 likely voters in
a state election. Of the sample, 31% say that they favor candidate
A, and 18% say that they favor candidate B. The margin of error
reported for this was ±3.4% with 95% confidence.
26 Which of the following statements can accurately be drawn
from this data?

  978

A.

The margin of error is too large to make any
conclusions.

B.

The sample of likely voters doesn’t represent all
voters.

C.

The sample size is too small to represent the voters
across the entire state.

D.

The sample was randomly selected and is large
enough to make conclusions.

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Practice Test 5
27 Which of the following statements can accurately be drawn
from this data?
A.

The true percentage of likely voters who will vote
for candidate A is 31%.

B.

The true percentage of likely voters who will vote
for candidate A is most likely between 27.6% and
34.4%.

C.

The true percentage of likely voters who will vote
for candidate B is 18%.

D.

The true percentage of likely voters who will vote
for someone other than candidate A or candidate B
is most likely between 45.6% and 52.4%.

SHOW YOUR WORK HERE

28 In a certain course, a student takes eight tests, all of which
count equally. When figuring out the final grade, the instructor drops the best and the worst grades and averages
the other six. The student calculates that his average for all
eight tests is 84%. After dropping the best and the worst
grades, the student averages 86%. What was the average
of the best and the worst grades?
A.

68

B.

73

C.

78

D.

88

CONTINUE
Peterson's SAT® Prep Guide 2017

  979

Practice Test 5
29 x2 + y2 – 8x + 12y = 144
What is the length of the radius of the circle with the
equation above?
A.

6

B.

12

C.

14

D.

24

30 If a represents a real number, what condition must a satisfy so that the graph of f(x) = 2(3a – x) – (5 + ax) does not
intersect Quadrant III?

  980

5
6

A.

a<

B.

−2 ≤ a <

C.

a>

D.

a ≤ −2

5
6

5
6

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SHOW YOUR WORK HERE

Practice Test 5
DIRECTIONS: For Questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer
sheet.
1.  	 Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in
the circles accurately. You will receive credit only if the circles are filled in correctly.
2.  	 Mark no more than one circle in any column.
3.  	 No question has a negative answer.
4.  	 Some problems may have more than one correct answer. In such cases, grid only one answer.
5.  	 Mixed numbers such as 3
		

If 3

7
1
must be gridded as 3.5 or .
2
2

1
is entered into the grid as
2

, it will be interpreted as

1
31
, not 3 .
2
2

6.  	 Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded
or truncated, but it must fill the entire grid.
7
12

Answer:

Answer: 2.5

Write answer
in boxes.

.

Fraction
line
0

Grid in
result.

0

0

0

0
1

1

2

2

3

3

3

4

4

4

5

5

5

6

6

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9

9

1

1

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2

1

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3

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5

5

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6

7

7

8

8

9

9

1

2

Decimal
point

0

Answer: 201
Either position is correct.

0
1

1

0
2

2

0

0

1

1

1

1

2

2

2

2

2

1

3

3

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3

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4

Acceptable ways to grid

2
are:
3

.

1

0

0

0

1

1

1

2

2

2

0

1

.

0

0

0

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1

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1

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3

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9

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9

9

9

6

6

Peterson's SAT® Prep Guide 2017

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Practice Test 5
31 The 50 members of a governing body of an organization
have held office for the following number of complete
terms. (Note that a zero means that the member is currently in the process of serving his or her first term.)

Number of
Complete Terms
Served

Number of Members

0

6

1

13

2

21

3

4

4

5

5

1

What is the mean number of terms served by the members
of this governing body?

32

If

x x
+ = 1 , what is the value of x?
12 18

33 An African elephant can lift a total of approximately
660 pounds with its trunk. A small bundle of twigs weighs
12 pounds. If an African elephant lifts a small log that
weighs 50 pounds, what is the greatest number of small
twig bundles that it could theoretically lift in addition to
the log?

  982

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SHOW YOUR WORK HERE

Practice Test 5
Questions 34 and 35 refer to the following information.

Population of United States by Gender and Age in 2010 (in millions)
0–24 years

25–49 years

50–74 years

75–100 years

Total

Males

53.6

52.2

38.6

7.3

151.7

Females

51.2

52.6

41.8

11.2

156.8

Total

104.8

104.8

80.4

18.5

308.5

34 What percent of males were 49 years or younger in 2010?
Round your answer to the nearest tenth.

SHOW YOUR WORK HERE

35 What is the probability that a randomly selected female
is between the ages of 25 and 74? Write your answer as a
decimal to the nearest hundredth.

36

5 x + 4 y = 11
6 x − 8 y = 10
In the system of equations above, what is the value of y?

37 A car travels from town A to town B, a distance of 360
miles, in 9 hours. How many hours would the same trip
have taken had the car traveled 5 mph faster?

38
2
3
4 x +7
+
=
x + 2 x − 5 x 2 − 3 x − 10
What is the solution to the equation shown above?

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
Peterson's SAT® Prep Guide 2017

  983

Practice Test 5
SECTION 5: ESSAY
50 Minutes—1 Essay
DIRECTIONS: The essay gives you an opportunity to show how effectively you can read and comprehend
a passage and write an essay analyzing the passage. In your essay, you should demonstrate that you
have read the passage carefully, present a clear and logical analysis, and use language precisely.
Your essay will need to be written on the lines provided in your answer booklet. You will have enough
space if you write on every line and keep your handwriting to an average size. Try to print or write
clearly so that your writing will be legible to the readers scoring your essay.

As you read the passage below, consider how the writers, Alex Jensen and Susan M. McHale, use the
following:
• Evidence, such as facts, statistics, or examples, to support claims.
• Reasoning to develop ideas and to connect claims and evidence.
• Stylistic or persuasive elements, such as word choice or appeals to emotion, to add power
to the ideas expressed.

Adapted from “What makes siblings from the same family so different? Parents” by Alex Jensen and Susan M. McHale, originally published in The Conversation, July 6, 2015. Alex Jensen is an Assistant Professor of Human Development at Brigham Young University.
Susan M. McHale is a Professor of Human Development and Family Studies at Pennsylvania State University.
What makes siblings from the same family so different? Parents
1

A colleague related the following story: while running errands with her 11- and 7-year-old daughters, a back seat battle
began to rage. My colleague’s attempts to defuse the situation only led to a shouting match about who was to blame for
the skirmish. Finally the 11-year-old proclaimed to her sister, “You started it the day you were born and took away Mom’s
love!”

2

This pair of sisters fight frequently, and from their mother’s perspective, part of the reason is that the two have little in
common. As it turns out, their situation is not unique.

3

Despite the fact that siblings are, on average, 50% genetically similar, are often raised in the same home by the same
parents, attend the same schools and have many other shared experiences, siblings are often only as similar to each other
as they are to children who are growing up across town or even across the country.

4

So, what is it that makes two siblings from the same family so different?
What makes the difference?

5

As researchers of sibling and family relationships, we knew that at least one answer to this question comes from theory and
data showing that, at least in some families, siblings try to be different from one another and seek to establish a unique
identity and position in their family.

6

From a child’s perspective, if an older brother excels at school, it may be easier to attract her parents’ attention and praise
by becoming a star athlete than by competing with her brother to get the best grades. In this way, even small differences
between siblings can become substantial differences over time.

7

But parents may also play a role. For instance, when parents notice differences between their children, children may pick up
on parents’ perceptions and beliefs about those differences. This, in turn, can increase sibling differences.

CONTINUE
Peterson's SAT® Prep Guide 2017

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Practice Test 5
8

We wanted to test these ideas to see what makes siblings different. So, we used data from first- and second-born teenage
siblings from 388 two-parent families to examine sibling differences in school performance.

9

We asked mothers and fathers to report on whether they thought the two siblings differed in their academic abilities, and if so,
which sibling was more capable. We also collected school grades from both siblings’ report cards.
Preference for the firstborn

10

Our analyses showed some interesting results: parents tended to believe that the older sibling was better in school. This was
even when older siblings did not actually receive better grades, on average.

11

This may be a product of parents having greater expectations for firstborns or that, at any given time, the older sibling is
undertaking more advanced school work.

12

There was, however, an exception to this pattern: in families with older brothers and younger sisters, parents rated the younger
sibling as being more capable. In fact, in those families, younger sisters received better grades than their older brothers.

13

Our findings also showed that it was not sibling differences in school grades that predicted parents’ ratings of their children’s
abilities. Rather, parents’ beliefs about differences in their children’s abilities predicted later sibling differences in school grades.

14

In other words, when parents believed one child was more capable than the other, that child’s school grades improved more over
time than their sibling’s.
Sustaining beliefs

15

Although we expected that children’s school grades and parents’ beliefs about their children’s relative abilities would be mutually
influential, it turned out that parents’ beliefs did not change much over their children’s teenage years.

16

Instead, sibling differences in school grades did change and were predicted by parents’ beliefs. In this way, parents’ beliefs about
differences between their children may encourage the development of actual sibling difference.

17

The above comment by an 11-year-old highlights that children are sensitive to their place and value in the family—relative
to those of their siblings. Parents may strive to show their love for their children, but they also should be aware that small
differences in how they treat their children can have large effects—including on their children’s development and adjustment
and also on the sibling relationship.

18

Indeed, some research suggests that sibling conflict arises when children try to be different from their siblings.

19

My colleague may be correct that her daughters fight frequently because they have nothing in common. But their conflicts may
also be motivated by her daughter’s perception that their differences started on the day her sister was born “and took away
Mom’s love.”

Write an essay in which you explain how the writers build an argument to persuade their audience
that parents are the reason why siblings from the same family behave differently. In your essay, analyze
how Alex Jensen and Susan M. McHale use one or more of the features previously listed (or features
of your own choice) to strengthen the logic and persuasiveness of their argument. Be sure that your
analysis focuses on the most relevant aspects of the passage.
Your essay should not explain whether you agree with the writers’ claims but rather explain how they
build an argument to persuade their audience.

STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
  986

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Answer Keys and Explanations
Section 1: Reading Test

1. C

12. C

23. B

34. B

45. A

2. A

13. A

24. B

35. A

46. D

3. D

14. C

25. A

36. D

47. B

4. B

15. B

26. A

37. D

48. D

5. C

16. D

27. A

38. C

49. B

6. B

17. B

28. C

39. D

50. B

7. C

18. C

29. A

40. C

51. C

8. A

19. A

30. B

41. A

52. B

9. D

20. A

31. B

42. B

10. A

21. A

32. B

43. D

11. C

22. C

33. C

44. C

READING TEST RAW SCORE
(Number of correct answers)

5

1.

The correct answer is C. The overall idea of the article
emphasizes the problem of GALS, an invasive species
that threatens the ecosystems of the islands. The article
is informational and does not attempt to persuade
readers, choice D, or encourage them to visit, choice A,
or raise money, choice B.

2.

The correct answer is A. The main discussion of the
article is about how scientists are trying to contain and
eliminate GALS by using trained dogs to detect them.
Choice B is incorrect because it states the opposite of
the correct answer. Choice C is a true statement, but it is
not the main idea of the article. Choice D is also true,
but the article does not focus on how organizations are
collaborating; rather its emphasis is on training dogs to
help solve the specific problem of one invasive species.

3.

The correct answer is D. The article mentions the
location of the islands, which are quite a distance from
any mainland. This fact of geography likely kept people
from settling there for a long time. This meant that the
natural ecosystems were in balance.

4.

The correct answer is B. The article explains that
the GALS is very destructive because it eats so
many different types of plants. Once this snail
enters a population, it takes over by reproducing
quickly and eating plant species that keep the
ecosystems in balance. While their ability to hide,
choice C, makes them difficult to find, the threat
comes from their eating habits.

5.

The correct answer is C. According to the passage,
GALS only affected 50 acres of land as of its writing,
but they are covering more ground every year, and
since they will destroy much needed plant life on
that ground, choice C is the best answer. Although
dogs are being used in an effort to solve the GALS
problem, that problem has not been solved yet, so
choice A is not the best answer. There is no
discussion of media treatment of the problem in
this passage, so choice B is incorrect, nor is the
GALS problem compared to other invasive species
problems on the island, so choice D cannot be
determined.

Peterson's SAT® Prep Guide 2017

  987

Answer Keys and Explanations
6.

The correct answer is B. Choice B explains how GALS
are covering more ground “every wet season,” and since
they will destroy the plant life on that ground, this
proves that the problem is getting worse with each
passing season or year. Choice A introduces the
problem; it does not explain how it is getting worse,
which is what the correct answer to the previous
question states. Choices C and D only explain efforts to
solve the problem; they are not evidence that shows
how the problem is steadily growing worse every year.

7.

The correct answer is C. Dogs have a very highly
developed sense of smell and can be trained to follow a
scent that humans cannot detect, so choice C is the best
answer. Dogs were not chosen based on their ease of
interaction with people or for their ability to find drugs,
so choice A and choice B are incorrect. The passage
never indicates that GALS hide in small spaces or that
dogs track them in such spaces, so choice D is incorrect.

8.

The correct answer is A. These lines reveal that dogs
“have an incredible sense of smell and can be trained to
detect scents,” which is basically a rewording of the
correct answer to the previous question, so choice A is
best. Choice B seems to have mistaken choice B for the
correct answer to the previous question, since it
references how dogs can detect drugs. Choice C
describes how dogs are used in the project, not why
they are ideal for the project. Choice D just explains
when the first phase of the project began.

9.

The correct answer is D. “Biosecurity” is a combined
form of the prefix bio- (meaning life) and security. As
used in the passage, the word refers to security from
harmful biological species. The word is not related to
handling of plants or animals, choices A and B. The
article does not mention extinction, choice C. Here,
“biosecurity” is protection of the ecosystems, choice D.

10.

  988

The correct answer is A. “Acclimation,” as used in the
context provided, describes how the dogs had to adjust
to the Galapagos, which was not their native environment. “Conforming,” choice B, suggests blending in
rather than adjusting. “Adaptation,” choice C, is a process
that takes many years, not a few days or weeks. Training
is a type of behavior modification, choice D, but it is
unrelated to acclimation.

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11.

The correct answer is C. Dogs are not native to the
Galapagos, which are islands far from any mainland,
inhabited mostly by species unique to the islands, such
as giant tortoises and iguanas. Dogs were brought to
the islands by people to help them find the invasive
species that are upsetting the balance found on the
islands. The dogs’ sense of smell makes them good
hunters for the invasive species on the islands, but that
does not explain why they are invasive, so choice A is
incorrect. The text explains that the dogs had to be
acclimated both to the islands and their trainers, but
their adjustment was so that they could be trained
properly for their role as hunters. This acclimation does
not explain why they would be considered invasive, so
choice B is incorrect. Choice D is incorrect because the
text does not say that dogs ever thrived on the islands
or were predators of any native species; it only stated
that the dogs brought by the project helped in finding a
particular invasive species so that it could be eradicated.

12.

The correct answer is C. In lines 6–12, Carter explains
how important it is for people to grasp the severity of
the energy problem. In lines 13–28, he explains how he
plans to address the problem. Although energy
independence was cited as a goal, it was not a reason
for his speech, so choice A is incorrect. This passage has
a very specific and important purpose: addressing the
energy crisis; choice B incorrectly concludes that merely
engaging with the public was its main purpose. Carter
does mention at the end of his speech how he understands the limitations of the office, but that idea is not
the reason for addressing the public, so choice D is
incorrect.

13.

The correct answer is A. The overriding idea that
Carter emphasizes is that the energy problem is not
new; it is complex; it will take a long time to fix it; and
many people, the public included, will have to work
together to change it. There are many ways to conserve
energy, choice B, but this is not the specific focus of the
passage. Carter’s urging people to use less energy in
their homes, choice C, is a detail. Carter never claims
that government cannot solve environmental problems,
choice D.

Answer Keys and Explanations
14.

The correct answer is C. Developing coal reserves is an
example of how the United States could decrease its
dependence on foreign sources of energy. Carter
proposes that people lower their thermostats, choice A,
but that is not a government action. He also proposes
consolidating different agencies to form a new
cabinet-level department, but that is not an action that
would solve the energy problem, so choice B is
incorrect. Protection from oil spills, choice D, would help
mitigate pollution and stop the waste of energy, but it is
not mentioned as a way to solve the problem.

18.

The correct answer is C. In line 41, President Carter
makes a very simple and direct statement about how
everyone must participate in energy conservation to
solve the crisis, so choice C is the best answer. Choice A
seems to have mistaken choice A for the correct answer
to the previous question since it mentions utility
companies. Carter is not yet talking about what the
citizens he is addressing need to do in lines 37–38, so
choice B is not the best answer. Choice D describes one
thing people can do to conserve energy; it is not a plea
for them to conserve.

15.

The correct answer is B. Throughout his speech, Carter
references the public and its role in addressing the
problem. He emphasizes that the problem affects
everyone and that everyone needs to participate to
help solve it. He says that the sacrifices needed to be
made by the public should be “borne fairly among all
our people” (lines 48–49). Choice A is true, but it is not a
belief system. Choice D is referenced when he explains
the limitations of presidential power, but that is not a
belief system; it is a part of the Constitution.

19.

16.

The correct answer is D. Carter explains how he
believes that if everyone cooperates and contributes to
conservation, the problem will get solved more easily
and quickly. Although he mentions all of the other
choices as actions that can be taken, his main thrust is
to appeal to people acting together as a nation to be
more energy efficient.

The correct answer is A. Because Carter is addressing
the public, he makes suggestions that people can easily
do and tries to encourage conservation. He speaks
directly and plainly to the people in an effort to get
them on board. The fact that he is on television, choice
B, is irrelevant. The speech is not authoritarian, choice
C—it is the opposite: an effort to enlist the citizenry in
solving a national problem. Because he recognizes the
depth of the problem and needs to persuade the
citizenry about participating, his tone is not merely
informational, so choice D is incorrect.

20.

The correct answer is A. In lines 45–48, Carter speaks
bluntly about the energy crisis in a way that shows how
the public needs to be involved in solving it (“There is
no way that I, or anyone else in the Government, can
solve our energy problems if you are not willing to
help.”). However, he also shows his optimism by stating,
“I know that we can meet this energy challenge . . .”
Therefore, choice A is the best answer. Choice B is
optimistic, but it fails to capture the blunt and persuasive tone of the rest of the passage. Choice C is
matter of fact about the Carter administration’s plans; it
is not blunt, persuasive, or optimistic. Choice D merely
introduces a new topic, and does not serve as evidence
of the passage’s overall tone.

21.

The correct answer is A. In the context of this sentence, depleted means “consumed” or used up. Carter is
speaking about the overall supplies, not individual
waste. The supplies were used during the cold winter
months. The energy sources were not “weakened”,
choice C, or “wasted,“ choice D, or “replaced,” choice B.

17.

The correct answer is B. By explaining various sources
of waste, Carter shows people that it won’t be all that
difficult to conserve energy; simple, small changes can
make a difference if enough people participate. Choices
A and C are ideas that he mentions, but they are not
statements that support his argument that people can
make a difference by conserving the energy they now
waste. People generally are not willing to make
sacrifices for the sake of making sacrifices; they need a
reason to convince them to make such sacrifices, so
choice D is not the best answer.

Peterson's SAT® Prep Guide 2017

  989

Answer Keys and Explanations
22.

The correct answer is C. In both of these sentences, the
word reserves refers to something that is saved for
future use. In the first use (“We will also stress development of our rich coal reserves in an environmentally
sound way…”), the reserves are lands that contain coal
that has not yet been mined; they are reserved for
future use. In the second use (“Oil and natural gas
companies must be honest with all of us about their
reserves and profits.”), the reserves are oil and gas
supplies that are set aside in order to raise prices.

23.

The correct answer is B. The attention to detail is
designed to show how ridiculous Golightly looked. The
descriptions show the character to be helpless in the
face of a normal event—a rainstorm. Contrasted with
his vanity, the picture Kipling paints is mocking, choice
B. Disgust, irony, and pride are not shown, so choices A,
C, and D are incorrect.

24.

25.

26.

  990

The correct answer is B. These lines offer Golightly’s
ability to recognize a horse as one of his virtues; since
this is something almost anyone can do, it is hardly a
virtue of any significance and can be interpreted as an
instance of the author mocking Golightly. Choice A
makes a statement about Golightly’s desires, but those
desires are not ridiculous enough to reveal the passage’s overall mocking tone. Choice C reveals that
Golightly had some abilities when it came to playing
games, and does not mock him for those abilities.
Choice D seems to express genuine sympathy for
Golightly, so it is hardly mocking.
The correct answer is A. In the passage, Kipling states
that Golightly’s focus on his appearance led him to not
take enough money with him. This results in him
negotiating with the Station Master for a first-class
ticket and his subsequent arrest. His pride, lack of an
umbrella, and fall from his horse may have been
contributing factors to his arrest, but none is the best
answer: It was not pride alone that led to the arrest;
even with an umbrella, Golightly would still have had no
money for a ticket; and Golightly was not responsible
for the fall, as it was an accident.
The correct answer is A. Golightly is described as an
officer. We are told he was taking a leave of his post,
which would indicate a military post. There is no
indication that he was trying to escape capture by the
Indian government, so choice A is incorrect. Golightly
was not an outlaw, so choice C is incorrect, nor was he a
businessman on an overseas trip, choice D.

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27.

The correct answer is A. The previous correct answer
classifies Golightly as a proper military man leaving his
post. In lines 9–10, “nobody ever dreamed of seeing him
handcuffed” because he was so proper, and the
description of him as a “deserter” shows that he left his
post, because that is the crime of which deserters are
guilty. Choice B merely shows the direction in which
Golightly was heading when things went wrong for
him. Choice C helps to establish setting; it says nothing
about Golightly, himself. Choice D describes what
Golightly was wearing; it does not say what he does.

28.

The correct answer is C. Kipling piles on the missteps
Golightly makes, each one adding to the other, making
Golightly look silly and inept. For a person whose title is
“officer,” Golightly does not show professionalism or skill
at handling a relatively minor problem. The rainstorm,
choice B, is a backdrop for the setting in which he falters
and is not in itself a way to make fun of the character.
There is no satire shown, so choice A is incorrect.
Golightly’s trouble with the horse, choice D, went
beyond “difficulty.”

29.

The correct answer is A. It is the detail of the descriptions that give the story its mocking tone and attitude.
Kipling sets up the character by describing his intense
vanity, which contrasts with the way he looks when
caught in the rainstorm. The details are not relevant to
any of the other choices.

30.

The correct answer is B. Throughout the excerpt,
Kipling uses an omniscient narrator to tell the story. But
in this line, the narrator editorializes and injects his own
opinion. Instead of describing the character’s response,
the narrator judges it and then continues to describe
Golightly’s behavior. The narrator does not report the
character’s verbal response or add dialogue.

31.

The correct answer is B. This sentence from the
passage is an idiomatic way of saying that Golightly was
pushing the envelope to the greatest extent possible
without ruffling feathers in the line of command. His
capture by the authorities was a result of misidentification because he was so unrecognizable from being
out in the rainstorm and falling off the horse. He was
doing what was expected, so there was nothing to get
caught doing, choice D, except that he looked suspicious to others in his disheveled state. Choice A is
contrary to the meaning of the text; he had told his
superiors. The sentence is about how much leave he
could take, not about leaving without permission.

Answer Keys and Explanations
32.

The correct answer is B. Lines 31–32 explain that the
pony was walking through mud, which would logically
slow down its pace, so choice B is the best answer and
choice A can be eliminated. A mire is a muddy pool, but
it makes no sense to say that a pony “pooled,” so choice
C can be eliminated. Indicating that the pony started
eating at this point in line 32 would not flow naturally
from the previous statement about how the path had
turned into mud, so choice D is not the best answer.

37.

The correct answer is D. “Franchise” is another word for
the right to vote. By pairing the word with elective, the
focus is on the right to vote in elections. Stanton
emphasizes how women are deprived of this basic right.
A more modern meaning of franchise is in sports,
indicating a team that is a member of a larger group or
league. At the time of the speech, there were no such
sports leagues, and the word was commonly used to
refer to the right to vote.

33.

The correct answer is C. The content of the speech
shows Stanton’s concern about how women were
treated unfairly, with few rights. Although some people
at the time may have been shocked by her speech, her
purpose was not shock value, choice B, but to inform
and persuade. Although she was sympathetic to the
plight of minorities/African Americans, this speech was
focused on women’s issues, so choice D is incorrect.

38.

34.

The correct answer is B. Stanton repeats the phrase
“He has” to list each of the transgressions of men against
women’s rights. The repetition emphasizes and
magnifies these transgressions and makes the point
that they can’t be ignored. Stanton did feel strongly,
choice A, but the use of repetition does not indicate
strength of feeling, it shows strength of her argument.
Although Stanton did use the Declaration of
Independence as a model, choice D, the repetition is not
part of that model.

The correct answer is C. The commonality is in the
necessity for obedience. For women, obedience to their
husbands was the rule of law; for slaves, it was a given
that they had to obey their masters. In some cases,
women did get paid for their work, choice A, and
women, whether or not they were slaves, were generally in charge of children, whether their own or others’,
choice B. While some men may break promises, only the
Sojourner text discusses how her master continually
broke his promises to her, so choice D is incorrect.

39.

The correct answer is D. Stanton’s list of grievances
shows her frustration and resulting anger at the system
that has denied women basic rights. Truth’s narrative
expresses her feelings of frustration at being promised
her freedom only to have it denied. Truth doesn’t show
anger, choice A; sadness, choice B; or bitterness, Choice
C. She shows resolve and determination to get her
freedom.

35.

The correct answer is A. The graphic is a cover from an
old newspaper that was published by a women’s group.
The drawing shows a policeman holding back the
women from voting while he points to the ballot box for
the inmates, who are shown by their stereotypical
striped prison clothes. The message is clear: criminals
can vote but women can’t, which is the sentiment
reflected in choice A: “He has withheld from her rights
which are given to the most ignorant and degraded
men—both natives and foreigners.”

40.

The correct answer is C. He was willing to give her
freedom before he had to and the introduction tells us
that she was granted her freedom in 1827, before it was
legally mandated. Forcing her to work longer than he
had originally said was a form of mistreatment. He did
not allow her to learn to read and write, which was why
her narrative is told through someone else’s voice,
choice B. Although he did make promises that he didn’t
keep, choice D, Truth suggests that all slaveholders used
this tactic to get more work out of their slaves.

36.

The correct answer is D. In lines 24–28, Stanton shows
how women have been enslaved by the legal system
and by men, who are considered superior. Some women
did have jobs outside the home, as is implied by lines
19–20, choice A, but Stanton explains that they were
not allowed to keep their wages. Women were not
allowed to vote, and Stanton includes this in her list of
grievances, but voting rights is not directly related to
obedience. Choice C is implied by lines 29–32, but this
issue is not directly related to obedience.

41.

The correct answer is A. Lines 45–47 convey the
relative good treatment of Isabella’s master as he set her
free before she was legally required to go free. Choice B
makes a statement about Isabella’s physical condition; it
does not reveal anything about her master, so it cannot
serve as evidence to support the previous correct
answer. Choice C simply says that Isabella’s master
honored a promise he made to her, but one can make a
promise to mistreat someone else, so this is not the best
piece of evidence to support the previous correct
answer. Choice D makes a statement about the work
Isabella did, and if anything, it shows that her master
was inconsiderate by making her do work “she was not
wholly able to do.”

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Answer Keys and Explanations
42.

The correct answer is B. Although Truth had great
religious faith, the faithfulness referred to here is not
about religion, choices A and C; it is about loyalty,
choice B. Truth reminisces here about her service to her
master. He had asked that she be a faithful servant (lines
45–46), which she was, but then she recognizes that,
ironically, this is exactly why she has become so
valuable to her master.

43.

The correct answer is D. The overall main idea
encompasses the discovery and its meaning (a new
species). Choices A and B are details that support the
main idea. Choice C is a general statement that could be
a conclusion, but it is not the main idea.

44.

The correct answer is C. The article describes how the
discovery was made by a student and other researchers.
The discovery was important because it identified a new
species and will help scientists and researchers continue
to add to our body of knowledge about prehistoric
mammals. The discovery wasn’t totally by chance
because Jasinski was conducting related research,
choice D. Choices A and B are general statements that
could have general application, but they are not
conclusions based on facts in the article.

45.

46.

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The correct answer is A. Lines 65–66 explicitly state
how its sense of smell made the S. sullivani an effective
predator as it used “its acute sense of smell to track
down prey.” Choices B, C, and D could all be correct in
another context, but this question specifies that the
answer must be determined “according to the passage,”
which does not provide evidence for any answer except
for choice A.
The correct answer is D. The meaning of the genus
name Saurornitholestes provides clues about the
dinosaur’s appearance. None of the Latin names
indicates where the fossils were found, choice B, or
where the dinosaurs lived, choice C. The discovered
species was named after a human, as are others on
occasion, but the name does not reveal anything about
the dinosaur.

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47.

The correct answer is B. The first part of the dinosaur’s
name, Saurornitholestes, means “lizard bird thief,” and
lines 19–21 reveal that it had physical characteristics
similar to those of birds (it was “lightly built with long
legs”) and lizards (it had “jaws lined with teeth”). Choice
A merely states the Latin name without explaining what
it means, so unless the reader speaks Latin, there is little
way to use this information to learn anything about
how the dinosaur looked. The fact that Robert Sullivan
discovered the dinosaur explains why the second part
of its name is sullivani, but it says nothing about how
the dinosaur looked. Choice D merely mentions a
mistake in classifying the dinosaur; it provides no clue
to what its name says about its appearance.

48.

The correct answer is D. Looking at the drawing, the
traits shown on the S. sullivani are as described in the
text. The drawing is made to reflect what scientists think
this dinosaur looked like based on the fossil evidence
and research. Choices A and C are facts in the text that
are unrelated to the drawing. Choice B describes its size,
but the drawing displays only relative size.

49.

The correct answer is B. The passage explains the
process by which Jasinski noticed that the species he
was examining differed from the description of what
was expected. He didn’t recognize this because of either
the size of the fossil, choice A, or its markings, choice D.
Scientists did not know what its closest relatives were
because they had not yet realized that it was a different
species, so choice C is incorrect.

50.

The correct answer is B. The author states that Jasinski
realized that the fossil actually had “subtle differences”
(line 32) from the one to which he compared it and was,
therefore, a different species. Choice A merely introduces Jasinski; it says nothing about how he figured out
he had found a new species. Choice C explains one of
the things Jasinski discovered about the dinosaur; it
does not suggest that the dinosaur’s sense of smell is
how he knew he was dealing with a new species. Choice
D only explains when the dinosaur lived.

Answer Keys and Explanations
51.

The correct answer is C. “Formidable” can mean
“impressive” in the sense of its size or power, and in this
context, the predator—the newly discovered species—
would have been threatening to other species. The
predator might have even been frightened at times, but
this is not a defining characteristic of predators, which
are generally thought to inspire fear more than feel it, so
choice A is not the best answer. Choice B would be an
odd description of the effectiveness of a predator, so it
is not a very good answer either. While “difficult” can be
used as a synonym for “formidable,” it would be better
used to describe an opponent in a contest, not a
predator that presents more of a danger than a
challenge, so choice D is not the best answer choice.

52.

The correct answer is B. Lines 34–35 provide context
clues that the olfactory bulb is related to the sense of
smell. The organs that are used for smell are contained
in that part of the skull, which was unusually large, but
the clue is in the next sentence that defines “olfactory.”
These clues eliminate choices A, C, and D, which are not
supported by the passage. Choice A would create a
redundancy, translating “olfactory bulb” as “bulb bulb.”

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Answer Keys and Explanations
Section 2: Writing and Language Test
1. D

11. B

21. C

31. C

41. D

2. B

12. A

22. A

32. C

42. B

3. B

13. B

23. B

33. B

43. C

4. D

14. A

24. C

34. A

44. D

5. C

15. B

25. B

35. D

6. A

16. C

26. A

36. B

7. B

17. D

27. A

37. B

8. D

18. A

28. C

38. B

9. D

19. A

29. C

39. D

10. B

20. D

30. D

40. A

WRITING AND LANGUAGE TEST RAW SCORE
(Number of correct answers)
1.

  994

The correct answer is D. The underlined sentence
should be deleted because other phrases from the 1980s
are not related to the Glass Ceiling. Choices A and B are
incorrect because the sentence should not be kept. It
does not support the main topic nor does it act as a
transition. Choice C is incorrect because it is not information that has already been provided.

2.

The correct answer is B. The proper end punctuation for
this sentence is a period. Any other punctuation will be
grammatically incorrect or inappropriately change the
tone or intent of the sentence. Thus, choice B is the
correct answer. Choice A is incorrect because ending the
sentence with an exclamation point injects emotion that
is missing from the rest of the passage. It is like shouting
at the reader. Choice C is incorrect because this sentence
is not a question. Choice D is incorrect because ending
the sentence with an ellipsis suggests the thought isn’t
finished, which is not the case.

3.

The correct answer is B. As written, the text has a syntax
error. The intention of the writer is to say that the number
of women in CEO positions in Fortune 500 companies is
just 5% of the total. To convey this, the modifier only has
to be placed correctly in the sentence—before 5%.
Choice B does this, so that’s the correct answer. Choices A
and C are incorrect because they say women hold 5% of
CEO positions (but may or may not hold that percentage
of any other positions), and they take the emphasis off
the low figure of 5% and place it on CEO positions; this is
not what the writer means to say. Choice D is incorrect

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because it says women hold 5% of CEO positions in
Fortune 500 companies (but may or may not hold that
percentage in other kinds of companies), and it takes the
emphasis off the low figure of 5% and places it on Fortune
500 companies; this is not what the writer means to say.
4.

The correct answer is D. This sentence requires a word
that means “having existed or taken place in a period
before the present,” which is what “past” means.
Therefore, choice D is the correct answer. Choice A is
incorrect because “passed “is the past tense of “pass”.
(“Past” and “passed” are commonly confused words.)
Choice B is incorrect because “passing” doesn’t have the
right meaning for this sentence. While it refers to time
going by, it changes the sense of the sentence by
referring to passing years rather than events that have
taken place. Choice C is incorrect because the word
“passive” doesn’t make sense in this sentence.

5.

The correct answer is C. The only internal punctuation
this sentence requires is a comma after the introductory
phrase “In 1995,” making choice C the correct answer.
Choice A is incorrect because it includes a semicolon
after “formed”, which makes the rest of the sentence a
fragment. Choice B is incorrect because, while it removes
the incorrect semicolon, it introduces a new error by
including a second comma after “Commission.” Choice D
is not correct because, while it removes the incorrect
semicolon, it introduces two new errors by removing the
comma after 1995 and by placing a semicolon after
“discrimination”, which creates a sentence fragment.

Answer Keys and Explanations
6.

7.

The correct answer is A. This sentence requires a word
that means “result,” or “something caused by something
else,” which is the meaning of effect—a noun that
means “the result of something.” Therefore, choice A is
the correct answer. Choice B is incorrect because “affect”
is the wrong word for this sentence. It is a verb that
means “to bring about a result.” (Effect and affect are
commonly confused words. One way to know the
difference between them is to remember that after you
affect something, there is an effect.) Choice C is incorrect
because the word “effective” doesn’t make sense in this
sentence. Choice D is incorrect because the word
“affection” doesn’t make sense in this sentence.
The correct answer is B. The sentence uses the plural
pronoun form they earlier in the sentence, which
provides a clue that another plural pronoun is needed
here to replace the plural noun “corporations.” Therefore,
choice B is correct. The pronouns among the other
answer choices are singular, and are incorrect.

8.

The correct answer is D. As written, the verbs in the
sentence do not have correct parallel structure. Choice
D fixes the problem, and offers appropriate parallel
structure: creating and providing. The other answer
choices do not fix this error in parallel structure and are,
therefore, incorrect.

9.

The correct answer is D. The original punctuation
creates a sentence fragment. Combining the text
eliminates the fragment, so choice D is the correct
answer. Choice A is incorrect because the period after
do creates a sentence fragment. Choice B is incorrect
because, while it eliminates the incorrect period, it
introduces a new error by replacing the period with a
semicolon to separate the two dependent clauses.
Choice C is not correct because, although it removes the
incorrect period, it introduces a new error by including
the conjunction and. With this addition, the sentence no
longer makes sense.

10.

The correct answer is B. This paragraph discusses some
of the obstacles and challenges that persist regarding
gender discrimination and bias that have proven
difficult to overcome. A good opening sentence would
support this notion, which choice B does. Choices A and
C provide direct opposition to this point of view, and are
incorrect. Choice D is out of context and unsupported
by this paragraph and passage. Therefore, it is incorrect.

11.

The correct answer is B. The writer is saying that
women must be accepted “as equals” in the corporate
sphere. Only choice B places this modifier after
“accepted,” the correct position in the sentence.

Therefore, choice B is the correct answer. Choice A is
incorrect because the modifying phrase “as equals” is
not placed in the right part of the sentence, creating a
syntax error. Choice C is incorrect because, while it
repositions the modifying phrase, it introduces a new
error by using the adverb form of equally. Choice D is
incorrect because, while it repositions the modifying
phrase (which could be correct in this part of the
sentence), it, too, uses the adverb form of equally.
12.

The correct answer is A. The sentence as is introduces
details that describe the entire collection. Choice B adds
information not supported by the passage. Choice C
implies the examples are not inclusive. Choice D is
incorrect because “Already” has no meaning in the
context of the sentence.

13.

The correct answer is B. Semicolons are needed when
items in a series already contain commas. Choice B
correctly shows the proper separation of items in a
series with semicolons and commas. Choice A incorrectly places commas after “extend” and “executive.”
Choice C incorrectly places a comma after “branches”
and incorrectly eliminates the comma after “world.”
Choice D incorrectly places a comma after ”services” and
incorrectly eliminates the comma after “government.”

14.

The correct answer is A. The author is introducing a
new topic (going from an overview of the modern
Library of Congress to its beginnings), and pointing out
that the Library did not start out as large as it is today.
The sentence in the original text is the best transition
phrase for cohesion, so choice A is the correct answer.
Choice B might sound correct, but it changes the tone
of the passage from formal to informal, so it is not the
best answer. Choice C is incorrect because it changes
the sense and meaning of the text and creates a
sentence that does not support the main idea of the
paragraph. Choice D might appear to be correct, but
like choice B, it changes the tone of the passage from
formal to informal, so it is not the best answer.

15.

The correct answer is B. After the original Library of
Congress was destroyed, the nation needed a new,
similar institution. In other words, the library had to be
replaced. Therefore, choice B is the correct answer.
Choice A is incorrect because while it suggests a new
library, it also suggests the continued presence of the
original library, which was not the case. Choice B is the
better answer because it is a more precise word in this
context. Choice C also indicates a new library, but like
choice A, it suggests the continued presence of the
original library. Choice D is not correct because the new

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Answer Keys and Explanations
library was a replacement as opposed to a copy of the
old library.

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16.

The correct answer is C. “Its” is a possessive determiner
and does not require an apostrophe. Thus, choice C is
the correct answer. Choice A is incorrect because it’s is a
contraction of “it is.” Choice B is incorrect because it
makes no sense. Choice D is incorrect because its’ is not
a word.

17.

The correct answer is D. This text requires seven
commas, and only choice D has all the necessary
commas in the right places. Choice A incorrectly places
commas after “two” and “dramatic.” Choice B incorrectly
leaves out a comma after “composition” and incorrectly
places a comma after “photograph.” Choice C incorrectly
places a comma after “two” and a semicolon after
“composition.”

18.

The correct answer is A. The library’s collection keeps
growing—it is ever-expanding. Thus, choice A is the
correct answer. Choice B is incorrect because it changes
the meaning of the sentence to say that the library’s
collection always exists. This is not what the author
means. Choice C is incorrect because it makes no sense.
Choice D is incorrect because it also makes no sense.

19.

The correct answer is A. Choice A best expresses the
idea that Young instigated the change. Choice B is
incorrect because it implies that there was opposition
to the change. Choice C implies that it had to be an
acquisitions library first before making the change.
Choice D is incorrect because the introductory phrase
implies that there was an addition to the operation
rather than a replacement of one system for another.

20.

The correct answer is D. In this paragraph the author is
shifting from John Russell Young to Herbert Putnam.
Choice D adds the phrase “after only two years,” a detail
with additional information that gives the reader a fuller
sense of this story and creates a smoother transition.
Therefore, choice D is the correct answer. Choices A, B,
and C make the shift from Young to Putnam, but none of
them has the additional information or makes as
smooth a transition as choice D, so none of them is the
best answer.

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21.

The correct answer is C. This paragraph is mainly about
Herbert Putnam, and Putnam (in the previous sentence)
is the antecedent of the pronoun that starts this
sentence. Putnam is one person, so the singular
pronoun he is required. Therefore, choice C is the correct
answer. Choice A is incorrect because if “they” is used,
the meaning of the sentence changes—it means
Spofford, Young, and Putnam “took the Library of
Congress directly into the national library scene.” Choice
B is incorrect because them is the objective case, and
this sentence requires a pronoun in the subjective case.
Choice D is incorrect because the antecedent of the
pronoun that starts this sentence is Putnam, so a
singular pronoun is required.

22.

The correct answer is A. The last column of the chart
shows information for the largest libraries (the category
of the Library of Congress). According to the chart, there
are 109 of these in the private sector and 51 in the
private sector. So there are more public than private
libraries similar in scope and scale to the Library of
Congress, making choice A correct. Choices B, C, and D
are incorrect because the chart does not support these
conclusions.

23.

The correct answer is B. As written, this sentence
contains a redundancy—empty and contained nothing
mean the same thing. Choice B eliminates this redundancy. Choice C is not the best answer because, while it
eliminates the redundancy, it changes the sense and
intent of the sentence, taking away the weight and
urgency of the bedroom being “forever empty.” Choice D
is incorrect because, although it eliminates the original
redundancy, it adds a new one: verses and poetry are the
same thing.

24.

The correct answer is C. The paragraph is mainly about
Emily’s independence and keen intellect. Choice C tells
readers that she also liked being in nature, which is a
facet of her personality unrelated to her intellectual
pursuits. This isn’t relevant to the main topic of the
paragraph, so choice C is the correct answer. Choice A is
relevant because it introduces Lavinia’s musings on
Emily’s “inquisitive mind.” Choice B is relevant because it
refers to Emily’s “curious mind” and “voracious appetite
for learning.” Choice D is relevant because it refers to
Emily’s intellectual independence.

Answer Keys and Explanations
25.

The correct answer is B. Emily is the sister in question, so
this sentence calls for a singular possessive pronoun.
Choice B is the possessive pronoun for sister, so it is the
correct answer. Choice A is incorrect because it is the
plural of sister, not the possessive pronoun for the word.
Choice C is incorrect because it is a plural possessive
pronoun (for “sisters”), not a singular possessive pronoun
(for sister). Choice D is incorrect because it is not a
possessive pronoun.

26.

The correct answer is A. The paragraph is mainly about
Emily’s isolation and the reason for it. In Emily’s own
words, she was “one ‘standing alone in rebellion’ of faith”
as she resisted ideas common to her time. Only choice A
refers to this, which makes it the correct answer. Choice
B might seem like a good answer, but Emily’s refusal to
take part in social events stemmed from her sense of
isolation rather than acting as the cause of it. The
passage does not say she became isolated after refusing
to participate in social events; it implies her refusal to be
social was a decision she made because she felt so
isolated. Choices C and D are incorrect because they are
not supported by the passage. The author does not say
either of these reasons caused Emily’s sense of isolation.

27.

28.

The correct answer is A. Choice A is the only choice
that supplies the correct word “through” for this
sentence. Choices B, C, and D are all incorrect because
none of these words makes sense in the sentence.
The correct answer is C. The writer should not add the
sentence because it detracts from the point about
women’s issues. The added sentence focuses on the
idea of Emily being involved in politics, which is not the
point Lavinia is making. Choices A and B are incorrect
because the information is not directly related to the
point being made by Lavinia. Choice D is incorrect
because, although the statement is about Emily’s life, it
is misplaced in the midst of Lavinia’s thoughts about
how Emily viewed the limitations society imposed on
women.

29.

The correct answer is C. Because it is clear that it was
Emily who felt “the trappings of being a woman,” the
required word is the singular subjective pronoun she.
Thus, choice C is the correct answer. Choice A is
incorrect because they is plural. If they is used, the
sentence appears to be saying that both Emily and
Lavinia “tried to eschew” the trappings of being a
woman, which is not supported by the passage; in
addition, the rest of the sentence will make no sense
because her is used toward the end of the sentence.
Choice B is incorrect because there is no antecedent for
we. Choice D is incorrect because the sentence calls for
a subjective pronoun; her is a possessive or an objective
pronoun.

30.

The correct answer is D. The passage is written in a
formal style and has a literary tone. Instead of saying
Emily did not accept the role of women, the author
writes she “eschewed” “the trappings of being a woman.”
Only choice D matches this style and tone, so it is the
correct answer. Choices A, B, and C are incorrect
because while each conveys this same thought, the
uninspired word choice in each answer does not match
the style or tone of the passage. Choice C is also
unnecessarily wordy.

31.

The correct answer is C. The proper end punctuation
for this sentence is a period. Most other punctuation
will be grammatically incorrect or inappropriately
change the tone or intent of the sentence. Thus, choice
C is the correct answer. Choice A is incorrect because
this sentence is not a question. Choice B is incorrect
because ending the sentence with an exclamation point
injects emotion that is missing from the rest of the
passage and is inappropriate here. Choice D is not
correct because it is incorrect to end a sentence with a
semicolon.

32.

The correct answer is C. The correct form of the verb
“to decide” is the past tense “decided”—the preceding
word “was” provides a helpful context clue to make this
determination. Choices A and D feature incorrect verb
tenses for this sentence. Choice B is a noun, and is not
appropriate given the context of this sentence.

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Answer Keys and Explanations
33.

34.

The correct answer is A. The point of this opening
paragraph is to establish the fact that even though
scientists have long known that sleep is important to
human health, they continue to study sleep. The “even
though” part of this idea is conveyed by the word yet,
which must be placed in the right part of the sentence if
the sentence is to make sense. Only choice A does this,
making it the correct answer. Choices B and C are
incorrect because they change the meaning of the
sentence by eliminating the “even though” element that
the writer wants to convey, and they demonstrate
clumsy syntax. Choice D is incorrect because while it
places yet correctly in the sentence, the rest of this
answer demonstrates clumsy syntax.

35.

The correct answer is D. This passage is mainly
concerned with past theories about sleep. The fourth
paragraph addresses sleep study in the twentieth
century. Sentence 6, choice D, refers to advances in the
study of sleep that were made during the twentieth
century, so the passage would have a more logical
sequence if this sentence were moved to the fourth
paragraph. Thus, choice D is the correct answer. Choices
A and B are incorrect because the first two sentences
serve as transitions to the topic of past theories about
sleep and should remain in this paragraph. Choice C,
sentence 4, is incorrect because it describes one of
these past theories about sleep. Therefore, it, too,
should remain in this paragraph.

36.

  998

The correct answer is B. This passage chronicles the
early years of the famous writer Emily Dickinson, whom
the world would eventually get to know and cherish,
and the preceding sentence provides an important
context clue to answer this question: “…it was time the
world knew the full treasure her sister was.” Choice B
makes the best sense to follow and build upon this
notion and is the correct answer. Choices A, C, and D are
incorrect and don’t make sense given the context of the
passage.

The correct answer is B. The sentence in choice B leads
to the introduction of the theories that follow. Choice A
is incorrect because it is irrelevant to this part of the
passage. Choices C and D are incorrect because the text
does not imply either statement.

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37.

The correct answer is B. This sentence tells the reader
that modern sleep research began with a machine.
Machines are created, or invented, and only choice B
conveys this idea. Choices A, C, and D are incorrect
because each conveys a different idea. A machine isn’t
discovered, choice A, though a new use for a machine
may be discovered. The passage makes it clear that
sleep study went beyond the idea, choice C, or suggestion, choice D, of a machine.

38.

The correct answer is B. The second part of the
sentence is a subordinate clause, and a subordinating
conjunction is necessary to establish the clause’s
connection to the beginning of the sentence: The study
of sleep was enhanced as a result of Aserinsky and
Kleitman’s work. Choice B is the only answer with a
subordinating conjunction. Therefore, choice B is the
correct answer. Choices A, C, and D are not correct
because they are all coordinating conjunctions that, if
used, change the meaning of the sentence. Choice A
makes the enhancement of sleep study and Aserinsky
and Kleitman’s work separate and equal things rather
than one being the result of the other. Choice C creates
a sentence that does not make sense. Choice D changes
the cause and effect: it means that Aserinsky and
Kleitman did their work because the study of sleep was
enhanced.

39.

The correct answer is D. The link between the ideas in
this sentence and the previous sentence is contradiction. Subjects awakened during REM sleep almost
always remembered dreaming; but subjects awakened
during non-REM sleep could rarely recall dreams. To
convey this idea, a contradictory transition word or
phrase is required. Only choice D provides the right
phrase. Choices A and B are incorrect because, while
these phrases can indicate contradiction, in this case
each creates a sentence that does not make sense.
Choice C is incorrect because the passage does not say
any predictions were made about what would happen
during this study.

40.

The correct answer is A. The underlined phrase leads
directly to the idea presented in the second part of the
sentence. Choice B is incorrect because this part of the
passage links to REMs; it is not regardless of them.
Choice C is incorrect because it contains an erroneous
implication. Choice D is incorrect because the adverb
used implies that there is contradictory text preceding
it, which there is not.

Answer Keys and Explanations
41.

The correct answer is D. As written, this sentence lacks
parallel construction. Choice D makes the verbs “spot,”
“awaken,” and “collect” parallel in tense and form, so it is
the correct answer. Choices A, B, and C are incorrect
because they don’t correct the lack of parallel construction, and they are incorrect verb-tense or
verb-form changes.

42.

The correct answer is B. The intent of this sentence is
to talk about changing dreamers’ experiences. Only
choice B is the correct word to communicate this (“alter”
means “to change”), so choice B is the correct answer.
Choice A is incorrect because the definition of “altar “is
“a usually raised structure or place on which sacrifices
are offered or incense is burned in worship.” (“Alter” and
“altar” are frequently confused words.) Choice C is
incorrect because it creates a sentence that means
scientists could switch dreamers’ various experiences for
one another. Choice D is incorrect because it creates a
sentence that does not make sense. (“Alternate” and
“alternative” are frequently confused words.)

43.

The correct answer is C. The subject and verb in a
sentence must agree in number. The subject of this
sentence (researchers) is plural, so a plural verb in the
right tense is required. Only choice C reflects agreement
between the subject and verb, as well as appropriate
verb tense. Choice A is incorrect because the subject of
the sentence (researchers) is plural, and “has been
drawn” is singular. Choice B is plural but there is no such
verb as “were been drawn”. Choice D is incorrect
because “was drawn” is singular.

44.

The correct answer is D. The original punctuation
creates a sentence fragment. Combining the text in a
grammatically correct way eliminates the fragment, and
only choice D does this. Choice A is incorrect because
the period after sleep creates the sentence fragment.
Choice B is incorrect because, while it eliminates the
incorrect period after sleep, replacing the period with a
dash creates a sentence that does not make sense.
Choice C is not correct because, although it removes the
incorrect period, it introduces a different error by
replacing it with a semicolon. Semicolons are used with
complete thoughts. The first part of this sentence is not
a complete thought, so choice C does not correct the
original fragment.

Peterson's SAT® Prep Guide 2017

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Answer Keys and Explanations
Section 3: Math Test—No Calculator

1. A

5. A

9. A

13. B

17. 6

2. A

6. C

10. B

14. B

18. 2

3. B

7. D

11. B

15. B

19. 1

4. C

8. D

12. B

16. 50

20. 224

MATH TEST—NO CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is A. Substitute the value for m and
solve for x:

5.

1
3
6y =1
1
y=
6
1
1
1 3
= =
=
 1 2 2
4y
4 
6 3
2y =

x +2
=m
5
x +2
= −3
5
x + 2 = −15
x = −17
2.

3.

The correct answer is A. If h is any positive quantity,
50
, we can see that dh is
then letting dh = ( m + h) −
m+ h
50
is
greater than d, since h is greater than zero, and
m
50
. Therefore, d increases as m does.
greater than
m+ h

6.

The correct answer is C.
( x − 3)3
4
4 y = ( x − 3)3
y=

3

The correct answer is B. The volume of a cube is V = s3.
A side of this cube is

3

3

64 in. Since there are 12 edges

to a cube, the amount of wire needed is 12 × 4 in., or
48 inches.
4.

The correct answer is A.

The correct answer is C. The total number of cookies is
equal to the sum of the cookies that Myra baked plus
the cookies Neil baked. Myra baked 6 sheets of r
cookies, or 6r cookies, and Neil baked 7 sheets of p
cookies, or 7p cookies. The total number of cookies
must be 6r + 7p.

4y = x −3

4y +3 = x

7.

The correct answer is D. The plant grows 4.5 centimeters a week, and that is represented by the 4.5w in
the equation. Since the 6 is a constant in the equation,
this represents the initial height of the plant. Therefore,
the plant must have been 6 centimeters tall when
Hannah bought it.

8.

The correct answer is D.
x6 + (2x2)3 + (3x3)2 = x6 + 8x6 + 9x6 = 18x6

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Answer Keys and Explanations
9.

10.

The correct answer is A. The graph shows that the
y-intercept is approximately at the point (0, 55). The
equation that shows a y-intercept of 55 is in choice A. To
further verify, substitute points in for the number of
days to find the corresponding number of trout. For
example, substitute 10 in for x: y = 12(10) + 55 =
120 + 55 = 175. The point (10,175) is on the graph.

−

1
3

the slope of the first line. So the slope of the new line
1
must be − . The only equations with that slope are
3
choices B and C. Check which equation is correct by
substituting the given point. Using choice B, you will see
that it is correct:

1

 8 3
2
= −  = −
 27 
3

11.

The correct answer is B. If the area is 49x2, the side of
the square is 7x. Therefore, the diagonal of the square
must be the hypotenuse of a right isosceles triangle of
leg 7x. Hence the diagonal = 7 x 2 .

12.

The correct answer is B. The slope of the graph of a
function is its vertical variable divided by its horizontal
variable. In this case, the slope is feet divided by
seconds, so the answer must be choice B.

1 10
y =− x+
3
3
1
10
3 = − (1) +
3
3
9
3=
3
16.

Then, substitute B = 6 into the other equation, and solve
for D:
D + 6 = 24
D = 18

The correct answer is 50.
70°
70°
x°

The correct answer is B. Solve the system of equations
by solving for one of the variables in the first equation,
and then substituting that expression into the second
equation:
D = 24 − B
4(24 − B ) + 2B = 84
96 − 4 B + 2B = 84
96 − 2B = 84
−2B = −12
B=6

14.

The correct answer is B. The slope of a line perpendicular to another line will be the negative reciprocal of

The correct answer is B.

 27 
− 
 8

13.

15.

x°

120°

120 = 70 + x
x = 50

17.

The correct answer is 6. The factor (x + 3) occurs twice.

18.

So, the zero –3 should be counted twice. Also, (3x – 2) is
2
a zero. Therefore, the product of the
a factor, making
3
2
three zeros is (−3)(−3)   = 6.
3
The correct answer is 2. In order for g(x) to have
precisely one x-intercept, the expression ax2 + 20x + 25
must factor as (Ax + B)2. Expanding this squared
binomial yields A2x2 + 2ABx + B2. Equate this to
ax2 + 20x + 25 and identify corresponding coefficients:

Therefore, the number of dogs in the pet store is 18, and
the number of birds in the pet store is 6.

First, B2 = 25, so B = 5. It cannot be –5 because the
middle term, 20x, has a positive coefficient.

The correct answer is B. Both choices B and D are
equivalent to the original function. This can be shown
by multiplying the binomial factors and simplifying the
product. The form of the equation in choice D gives
coordinates of the vertex as its coefficients, and choice B
is in intercept form, where 7 and –3 are the x-intercepts
of the function.

Next, 2AB = 20, so 2A(5) = 20; therefore, A = 2.
Finally, A2 = 4, so a = 2.

Peterson's SAT® Prep Guide 2017

  1001

Answer Keys and Explanations
19.

The correct answer is 1.
4 − x 2 = 3x
4 − x 2 = 3x
0 = x 2 + 3x − 4
0 = ( x + 4)( x − 1)
x = −4, x = 1

20.

The correct answer is 224. The system will have an
infinite number of solutions when the two equations
are equivalent, so multiply each term in the first
equation by –4 to find the values for a and b, then find
their product:
−4(2 x + 3 y ) = −4(7)
−8 x − 12 y = −28

Only 1 works because, although
4 − (−4)2 = 3(−4)
−12 = −12 ,
negative numbers cannot be gridded.

  1002

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For the two equations to be equivalent, a must be –8
and b must be –28.
−8 x − 12 y = −28
ax − 12 y = b
a = −8
b = −28
ab = −8(−28) = 224

Answer Keys and Explanations
Section 4: Math Test—Calculator
1. B

9. C

17. D

25. D

33. 50

2. D

10. D

18. C

26. D

34. 69.7

3. D

11. C

19. A

27. B

35. 0.60

4. C

12. A

20. B

28. C

5. D

13. B

21. A

29. C

36. 1/4 or
.025

6. A

14. B

22. A

30. C

7. C

15. C

23. D

31. 1.84

8. C

16. C

24. A

32. 36/5 or
7.2

37. 8
38. 11

MATH TEST—CALCULATOR RAW SCORE
(Number of correct answers)

1.

The correct answer is B. If 9x + 5 = 23, 9x = 18, and
x = 2. Thus, 18x + 5 = 36 + 5 = 41.

2.

The correct answer is D. There can be at most 15
radiators, so x + y ≤ 15. Each small radiator weighs 150
pounds, represented by 150x. Each large radiator
weighs 250 pounds, represented by 250y. The maximum
load can be equal to but not exceed 1,500 pounds:
150x + 250y ≤ 1,500.

3.

6.

The correct answer is A. Using a line that passes
through (2, 1.9) and (6, 3.5), the slope is
3.5 − 1.9 1.6
=
= 0.4
6−2
4
The line passes through (0, 1), making the equation
y = 0.4x + 1.

7.

The correct answer is C. Let x = original price. Then:

The correct answer is D. Each adult needs 15 cans/7
15
adults = cans in two days, or  1  15  = 15 cans per
7
 2  7  14
adult per day. Multiply this by the number of adults and
by the number of days:
15
(4 adults)(7days) = 30 cans of food
14
.

4.

The correct answer is C. Fiona’s non-taxed amount is
75% of what she earns each hour, or 0.75x. This can be
multiplied by the hourly rate, which in this case is $28,
leading to the expression 28(0.75x).

5.

The correct answer is D. The data are increasing and
stay relatively close to a line of best fit that would pass
through the center of the points. This means that the
company has strong positive sales numbers.

or

8.

0.60 x = $4.20
6 x = $42.00
x = $7.00

The correct answer is C. The number 329 represents
the slope of the graph of the equation, which is the rate
of increase in attendance.

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Answer Keys and Explanations
9.

The correct answer is C. The various times (in hours) it
takes the supercomputers, alone or together, to
complete the job are:

12.

The correct answer is A. Choice C is incorrect because
we cannot say with certainty that a medication will help
all people who need it. Choice D doesn’t make sense;
the medication cannot help people who don’t take it.
Choice B is incorrect because we only compared Z
against one other medication, Y. The inference can be
applied only to the given medications and populations.

13.

The correct answer is B. Write equations to represent
the situation. Let x be the number of bicycles rented
and y be the number of pairs of rollerblades rented.
Then solve the system using elimination:

Slower supercomputer: h hours
Faster supercomputer: 1.5 hours
Together: 3 hours
The portion of a single job that the supercomputers
(working alone or together) contributes:
1
h

Faster supercomputer:
Slower supercomputer:
Together:

1
3

1
2
=
1.5h 3h

This leads to the equation:
10.

11.

x + y = 27
7 x + 5 y = 171
Multiply x + y = 27 by −5 to solve by elimination:

1 2 1
+ =
h 3h 3

−5 x − 5 y = −135
7 x + 5 y = 171
2 x = 36
x = 18

The correct answer is D. The number of books that the
library adds is 375x, or 375 times the number of years.
The total number of books must be the sum of 375x and
25,825 (the number they already have), not to exceed
35,000.

Substitute the value for x into the first equation.
18 + y = 27
y =9

The correct answer is C. Set each factor equal to zero
and solve for x:
2 − 3x = 0 ⇒ x =

2
3

x2 −2x +3 = 0 ⇒
x=

So, 18 – 9 = 9 more people rented bicycles than roller
blades.
14.

−(−2) ± (−2) − 4(1) ⋅ (3)
2(1)

The correct answer is B. Draw the following diagram:

2

2 ± 4 − 12
2
2 ± 2i 2
=
2
= 1± i 2
=

2
1− i 2
3
2
= 1− i 2
3
2
= [1+ 2]
3
=2

(

18 in = 1.5 ft
12 ft

So,
d1 ⋅ d2 ⋅ d3 =

18 in = 1.5 ft

)(1+ i 2 )

( ) 
2

The area of the pond plus the walkway:
2
 15  225π
The diameter is 15 feet, so the area is π   =
2
4
square feet.
The area of the pond only:

2

 12 
The diameter is 12 feet, so the area is π   = 36π
2
square feet
So, the area of the walkway is the difference of these
225π
81
− 36π = π square feet. Therefore, the
two areas:
4
4
 81 
cost is ($7.25)  π  ≈ $461.23.
4 

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Answer Keys and Explanations
15.

The correct answer is C. If x = 0, then y = 2(0) – 5 = –5.
If x = 6, then y = 2(6) – 5 = 7.

22.

So, v + w + x + y = 0 + (–5) + 6 + 7 = 8.
16.

17.

18.

The correct answer is C. The graph shows points
connected by a curve with an increasing positive slope
that approximates an exponential graph, so this is
exponential growth.
The correct answer is D. The graph shows an exponential growth curve, and the population of California in
1980 is approximately 24 million. Therefore, choices A
and B can be eliminated, because based on the
exponential growth, the population in 1990 would be
more than the population in 1980. And because it is
exponential growth, 30 million, choice D, would be the
best prediction.

determine whether choice A or C is the correct
equation, locate points on the graph and check against
both equations. (0, 1) is a point on the graph.
1
−1
x +3
6
y=
−1
1
x +3
−1
1=
0+3
6
1=
−1
2
0+3
1≠ −
   
3
1= 2 − 1
y=

Only answer choice A works.
23.

The correct answer is C. Let the original sign be 10
by 10.

 3 
= g
 4 − 1
= g(1)

9
Area = 100

= (1− 4 ) 2
=9

7 Area = 63

Then, the new sign is 7 by 9.

24.

63
= 63%
100
19.

20.

21.

So, the correct answer is choice A.
25.

3 x − 1 2 x + 3 (3 x − 1)(3 x − 1) (2 x + 3)(2 x + 3)
−
=
−
2 x + 3 3 x − 1 (2 x + 3)(3 x − 1) (3 x − 1)(2 x + 3)
(3 x − 1)2 − (2 x + 3)2
(2 x + 3)(3 x − 1)

=

5 x 2 − 18 x − 8
6x2 +7x −3

The correct answer is D. In order to determine when
f(x) = 0, solve the equation x2 − 2x − 8 = 0.
x 2 − 2 x − 8 = 0 Factor the left-hand side.
( x − 4)( x + 2) = 0 Set each factor equal to 0.
x − 4 = 0, x + 2 = 0 Solve each equation.
x = 4, −2

The correct answer is A. Subtract by writing using a
common denominator, and then simplify:

=

The correct answer is A. To write an exponential
equation for this situation, you need to find the
population in 1980:
38 , 500 = P(1+ 0.038 ) 20
38 , 500
=P
(1.038 ) 20
18 , 260 ≈ P

The correct answer is A. Three meals a day times 365
days per year means there are 3 × 365 = 1,095 meals in
one year. Over 19 years, there are 1,095 × 19 = 20,805
meals. Therefore, the number of restaurants in New York
City exceeds 20,500.
The correct answer is B. One cubic foot equals 123, or
1,728 cubic inches. One cubic foot of gold weighs
1,728 × 0.70 = 1,210 pounds.

The correct answer is D.
g(f ( x )) = g(f ( 4 ))

10
10

The correct answer is A. The graph is a hyperbola,
a
+ c . There are
which is of the general form y =
x −b
asymptotes at x = –3 and y = –1, b = –3 and c = –1. To

26.

The correct answer is D. The sample size leads to the
margin of error that is given with the data. As long as
the margin of error is considered when making
conclusions, those conclusions are reasonable.

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  1005

Answer Keys and Explanations
27.

28.

29.

The correct answer is B. The 95% confidence that the
margin of error is ±3.4% is important, and choices A and
C ignore the confidence interval. Choice D is not correct,
because this interval is centered on 49%, instead of
51%, which is the number of people who support a
different candidate or no candidate at this time. Only
choice B accurately uses the confidence interval and the
data given in the problem.
The correct answer is C. If the average for the eight
tests is 84%, then the sum of the eight tests must be 8
times 84, or 672. For the six tests, the sum must be 6
times 86, or 516. The two dropped tests must have
accounted for 156 points. 156 divided by 2 is 78.

32.

x
x
36   + 36   = 1(36)
 12 
 18 
3 x + 2 x = 36
5 x = 36
36
1
2
x = = 7 = 7 = 7.2
5
5 10
33.

x 2 + y 2 − 8 x + 12 y = 144

Since the elephant cannot lift part of a bundle, the
greatest number of bundles it can lift is 50.

x 2 − 8 x + y 2 + 12 y = 144
2

) (

)

− 8 x + 16 + y 2 + 12 y + 36 = 144 + 16 + 36

( x − 4)

2

+ ( y + 6) = 196
2

34.

Since 196 is 142, the radius is 14.
30.

105.8
= 0.697
151.7
= 69.7%

f ( x ) = 2(3a − x ) − (5 + ax )
= 6a − 2 x − 5 − ax
= −(2 + a ) x + (6a − 5)
35.
(2 + a) must be nonnegative AND the y-intercept (6a
– 5) must be positive. This gives two conditions: −(2 + a)

31.

≤ 0 AND 6a – 5 0. Solving these inequalities yields a ≥
5
−2 AND a > . Both conditions must hold. So, it must
6
5
be the case that a > .
6
The correct answer is 1.84. Compute the mean as
follows:
0(7) + 1(13) + 2(21) + 3(4) + 4(5) + 5(1)
= 1.84
50

  1006

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The correct answer is 69.7. The males who are 49 years
old or younger are in the 0–24 range and the 25–49
range. First, find this sum: 53.6 + 52.2 = 105.8.
Then, divide it by the total number of males, which is
151.7 million:

The correct answer is C. First, put the function into
slope-intercept form:

In order for the graph to not intersect Quadrant III,

The correct answer is 50. Write and solve an inequality
that represents the situation. Then interpret the
solution:
50 + 12 x ≤ 660
12 x ≤ 610
x ≤ 50.8

The correct answer is C. Complete the square to write
the equation in standard form for a circle:

(x

The correct answer is 36/5 or 7.2. Begin by multiplying
all terms of the equation by the LCD of 36:

The correct answer is 0.60. The probability is the
number of females who are in the age range of 25 to 74
(52.6 + 41.8 = 94.4) divided by the total number of
females, which is 156.8 million:
94.4
= 0.602
156.8
≈ 0.60

Answer Keys and Explanations
36.

The correct answer is 1/4 or 0.25. Solve using
elimination so that the x-terms are eliminated:
−6(5 x + 4 y ) = −6(11)
5(6 x − 8 y ) = 5(10)

−30 x − 24 y = −66
+ 30 x − 40 y = 50
− 64 y = −16
16
64
1
=
4

38.

The correct answer is 11. Solve using a common
denominator, and check your answer:
2
3
4 x +7
+
=
x + 2 x − 5 x 2 − 3 x − 10
2( x − 5)
3( x + 2)
4 x +7
+
=
( x + 2)( x − 5) ( x − 5)( x + 2) x 2 − 3 x − 10
2 x − 10 + 3 x + 6
4 x +7
= 2
2
x − 3 x − 10
x − 3 x − 10
5x − 4 = 4 x +7
x = 11

y=

37.

The correct answer is 8. Distance = rate × time:
360 = r (9)
40 = r

2
3
4(11) + 7
+
=
11+ 2 11− 5 (11)2 − 3(11) − 10
2 3 51
+ =
13 6 78
2(6) 3(13) 51
+
=
13(6) 6(13) 78
51 51
=
78 78

If r were 40 + 5 = 45
d = rt
360 = 45t
t =8

Peterson's SAT® Prep Guide 2017

  1007

Answer Keys and Explanations
Section 5: Essay
Analysis of Passage
The following is an analysis of the passage by Alex Jensen and Susan M. McHale, noting how the writers used evidence, reasoning,
and stylistic or persuasive elements to support their claims, connect the claims and evidence, and add power to the ideas the writers
expressed. Check to see if you evaluated the passage in a similar way.
What makes siblings from the same
family so different? Parents
1

A colleague related the following story: while running
errands with her 11- and 7-year-old daughters, a back
seat battle began to rage. My colleague’s attempts to
defuse the situation only led to a shouting match about
who was to blame for the skirmish. Finally the 11-year-old
proclaimed to her sister, “You started it the day you were
born and took away Mom’s love!”

1

The writers begin the essay with an anecdote drawn from
personal experience. This story (which includes the evocative
statement “You... took away Mom’s love!”) immediately makes
the essay more personal and prepares the reader to engage
with the writers’ argument.

2

This pair of sisters fight frequently, and from their
mother’s perspective, part of the reason is that the two
have little in common. As it turns out, their situation is not
unique.

2

The writers broaden their point of view from the personal to
the objective and give the reader more perspective on the
topic.

3

Despite the fact that siblings are, on average, 50%
genetically similar, are often raised in the same home
by the same parents, attend the same schools and have
many other shared experiences,

3

The writers use statistics and factual information to provide
context for and lay the foundation of their argument.

4

siblings are often only as similar to each other as they
are to children who are growing up across town or even
across the country.

4

5

So, what is it that makes two siblings from the same
family so different?

Jensen and McHale clearly state a key premise of their
argument — siblings are rarely similar. Having said this, they
now have to support the rest of their argument: parents are
the reason for these differences.

5

The writers pose a rhetorical question to introduce support for
their argument.

6

The writers provide their backgrounds, which show why
they’re qualified to be making this argument: they are
researchers of sibling and family relationships.

7

The writers refer to theory and data that support their
argument: “some siblings try to be different from one another,
and seek to establish a unique identity and position in their
family.”

8

The writers go into more detail about this information,
presenting a concrete example that is easily understood by the
reader.

What makes the difference?
6

As researchers of sibling and family relationships, we
knew that at least one answer to this question comes
from

7

theory and data showing that, at least in some families,
siblings try to be different from one another and seek to
establish a unique identity and position in their family.

8

  1008

From a child’s perspective, if an older brother excels at
school, it may be easier to attract her parents’ attention
and praise by becoming a star athlete than by competing
with her brother to get the best grades. In this way,
even small differences between siblings can become
substantial differences over time.

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Answer Keys and Explanations
9

But parents may also play a role. For instance, when
parents notice differences between their children,
children may pick up on parents’ perceptions and beliefs
about those differences. This, in turn, can increase sibling
differences.

9

The writers now discuss the role of parents in sibling
differences, paving the way to support the central point
in their argument: parents are a major force in sibling
differences.

10 We wanted to test these ideas to see what makes siblings
different. So, we used data from first- and second-born
teenage siblings from 388 two-parent families to examine
sibling differences in school performance.

10

The writers explain how they tested the validity of their
argument.

11

11

The writers provide more detailed information about the study
they conducted to test the validity of their argument.

12

The writers provide results of their study that revealed parents’
perceptions of and ideas about older siblings. Specifically,
parents tended to believe that the older sibling was better in
school (whether this was true or not).

13 This may be a product of parents having greater
expectations for firstborns or that, at any given time, the
older sibling is undertaking more advanced school work.

13

The writers go into more detail about parents’ perceptions of
and ideas about older siblings.

14 There was, however, an exception to this pattern: in
families with older brothers and younger sisters, parents
rated the younger sibling as being more capable. In fact,
in those families, younger sisters received better grades
than their older brothers.

14

The writers go into further detail about results of their study.
This detail shows a difference in how parents regarded their
children, apparently favoring girls over boys in the area of
academic capability.

15

Our findings also showed that it was not sibling
differences in school grades that predicted parents’
ratings of their children’s abilities. Rather, parents’ beliefs
about differences in their children’s abilities predicted
later sibling differences in school grades.

15

The writers provide additional details from their study,
showing parental beliefs and attitudes toward their children’s
abilities greatly affected sibling differences regarding
academic performance.

16

In other words, when parents believed one child was
more capable than the other, that child’s school grades
improved more over time than their sibling’s.

16

Jensen and McHale explain these details and show how they
support their argument: When parents believed one child was
more academically capable than the other, that child’s school
grades improved more over time than their sibling’s.

17

The writers provide information showing that once parents
form perceptions and beliefs about their children’s academic
abilities, these attitudes and ideas do not greatly change.

We asked mothers and fathers to report on whether
they thought the two siblings differed in their academic
abilities, and if so, which sibling was more capable. We
also collected school grades from both siblings’ report
cards.
Preference for the firstborn

12

Our analyses showed some interesting results: parents
tended to believe that the older sibling was better in
school. This was even when older siblings did not actually
receive better grades, on average.

Sustaining beliefs
17

Although we expected that children’s school grades and
parents’ beliefs about their children’s relative abilities
would be mutually influential, it turned out that parents’
beliefs did not change much over their children’s teenage
years.

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Answer Keys and Explanations
18

  1010

Instead, sibling differences in school grades did change
and were predicted by parents’ beliefs. In this way,
parents’ beliefs about differences between their children
may encourage the development of actual sibling
difference.

18

Jensen and McHale use the information revealed by their
study to prove their argument: While parents’ beliefs about
their children’s academic abilities did not change, sibling
differences in school grades did. Thus, “parents’ beliefs
about differences between their children may encourage the
development of actual sibling difference.”

19 The above comment by an 11-year-old highlights that
children are sensitive to their place and value in the
family—relative to those of their siblings. Parents may
strive to show their love for their children, but they also
should be aware that small differences in how they treat
their children can have large effects—including on their
children’s development and adjustment and also on the
sibling relationship.

19

The writers strengthen their argument by returning to their
introductory anecdote and summing up what their study
revealed: “Children are sensitive to their place and value in the
family,” and differences in how parents treat their children can
have “large effects” on them.

20

Indeed, some research suggests that sibling conflict arises
when children try to be different from their siblings.

20

The writers conclude the essay by referring to research that
supports the mother’s statement in the introductory anecdote:
sibling conflict can be created “when children try to be
different from their siblings.”

21

My colleague may be correct that her daughters fight
frequently because they have nothing in common.

21

While this may seem like the writers are giving up on their
argument, acknowledging their colleague might be right
about the cause of her daughters’ conflicts demonstrates the
writers’ honesty and objectivity.

22

But their conflicts may also be motivated by her
daughter’s perception that their differences started on
the day her sister was born “and took away Mom’s love.”

22

Jensen and McHale then end the essay by offering additional
insight about their colleague’s daughters. Here, they provide
an alternative explanation for the girls’ differences, restating
their argument and repeating the 11-year-old girl’s evocative
remark: the conflict between these two siblings may also be
motivated by the girl’s belief that the birth of her younger sister
changed their mother’s behavior toward the older girl because
the younger sister “took away Mom’s love.”

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Answer Keys and Explanations
Sample Essays
The following are examples of a high-scoring and low-scoring essay, based on the passage by Alex Jenson and Susan M. McHale.

High-Scoring Essay
No two siblings are alike. Alex Jensen and Susan M. McHale are two university professors who investigated the reasons for
the differences between siblings. They concluded that parents cause the differences. To explain their conclusion, they use
professional authority, personal experience, statistics, results of a study they conducted, and references to other research.
Professional authority is established immediately—both authors are identified as university professors in the area of human
development. In the second section, they reinforce their authority by stating that they are researchers of sibling and family
relationships. This demonstrates their knowledge specifically in the area of siblings. Readers can trust their conclusions.
The article begins with a personal story of two young siblings who constantly fight. During a particular fight, the 11-year-old
girl accuses her 7-year-old sister of starting the fight when she was born and “took away mom’s love.” This harsh accusation
hooks readers into wondering about the real cause of sibling differences.
A quick look at statistics provided by the authors reveals many reasons for siblings to be similar rather that different. Siblings
are 50% genetically similar and share the same parents, schools, and other experiences. Again, this makes the reader wonder
about the cause of sibling differences.
The answer comes from theory and data, reinforcing their role as authorities in the subject. One cause, the authors state, is
that siblings try to be different from each other to be unique in the family. They support this with an example of how one
sibling can choose to excel at athletic pursuits because an older sibling already excels in academics. Over time, one small
choice made to be different, such as joining a soccer team, causes other, bigger differences. One sibling becomes an athlete
while the other becomes a scholar.
Finally, the authors address the role of parents in sibling differences. They theorize that parents notice small differences
between children and children react to their parents’ perceptions by becoming even more different. To confirm their theory,
the authors conducted a study of the first and second siblings in 388 two-parent homes. Readers can easily see the study as a
reasonable approach to determining the cause of the differences. The authors asked parents about their perceptions of their
children’s academic abilities and compared the perceptions to the children’s report cards. In effect, they compared parents’
perceptions to actual performance.
The authors present the analysis of the study results. Parents seem to expect the oldest sibling to perform better than the
younger child, even though it wasn’t always true. They describe an exception: If the older sibling is male and the younger
sibling is female, the parents expect the girl to perform better academically, and the girl does get better grades than her
brother.
The authors present their findings. Overall, the authors determined that parents’ perception caused siblings’ academic
performance. If the parents believed that Suzy would perform better that Sally, Suzy’s grades would improve until they were
better than Sally’s. Over time, parents’ perceptions caused behaviors to change; behaviors did not cause parents’ perceptions
to change.
Parents have a large role in shaping their children and the relationship between their children. The authors briefly cite other
research that points to differences between siblings as the cause of conflict between siblings.
At the end of the article, the authors return to the personal story told at the beginning of the article. The authors’ colleague
says that the conflict between her daughters is caused by the differences between the daughters. After reading the authors’
findings though, readers can conclude that the differences are caused by the parents. Hence, the conflict between the
siblings is actually caused by the parents. The authors have successfully presented their theory and their results to convince
readers that parents should be more aware of the effect they have on their children.

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Answer Keys and Explanations
Low-Scoring Essay
Alex Jensen and Susan M. McHale are two professors who researched the cause of sibling rivalry. They start the article with
a story about two sisters having a fight in the backseat of a car. One of the girls accuses the other of stealing Mom’s love. It
refers to the age-old argument that “Mom loves you best.”
The researchers look at some of the reasons that siblings fight even though they share so many of the same things, including
genes, parents, schools, and probably clothes. They conclude that siblings try to be different on purpose so they can have a
unique place in the family. The differences might start as things their parents notice like, “You’re better at math than Mike,”
or “You run faster than Jake.” Eventually, the small differences that parents notice become big things. Jake becomes an
accountant because he’s better at math. Mike becomes a gym teacher and coaches at the local high school because he’s a
better athlete.
The authors talk about a study they did about sibling rivalry. The differences between the siblings are caused by the way that
parents expect the children to act. Children act the way they do to get attention.
The authors tell us that parents should be careful about the characteristics they encourage in their children and the
perceptions they talk about. The “Mom loves you best” argument can shape children’s lives. Parents should be careful to say
good things about their children and interact evenly with both children. Then, no one will win the “Mom loves you best”
argument and siblings will fight less.

  1012

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Computing Your Scores
COMPUTING YOUR SCORES
Now that you’ve completed this practice test , it’s time to compute your scores. Simply follow the instructions on the following pages,
and use the conversion tables provided to calculate your scores. The formulas provided will give you as close an approximation as
possible on how you might score on the actual SAT® exam.

To Determine Your Practice Test Scores
1. After you go through each of the test sections (Reading, Writing and Language, Math—No Calculator, and Math—Calculator)
and determine which answers you got right, be sure to enter the number of correct answers in the box below the answer
key for each of the sections.
2. Your total score on the practice test is the sum of your Evidence-Based Reading and Writing Section score and your Math
Section score. To get your total score, convert the raw score—the number of questions you got right in a particular section—
into the “scaled score” for that section, and then you’ll calculate the total score. It sounds a little confusing, but we’ll take
you through the steps.

To Calculate Your Evidence-Based Reading and Writing Section Score
Your Evidence-Based Reading and Writing Section score is on a scale of 200–800. First determine your Reading Test score, and then
determind your score on the Writing and Language Test.
1. Count the number of correct answers you got on the Section 1: Reading Test. Remember that there is no penalty for
wrong answers. The number of correct answers is your raw score.
2. Go to Raw Score Conversion Table 1: Section and Test Scores on page 1016. Look in the “Raw Score” column for your raw
score, and match it to the number in the “Reading Test Score” column.
3. Do the same with Section 2: Writing and Language Test to determine that score.
4. Add your Reading Test score to your Writing and Language Test score.
5. Multiply that number by 10. This is your Evidence-Based Reading and Writing Section score.

To Calculate Your Math Section Score
Your Math score is also on a scale of 200–800.
1.  	 Count the number of correct answers you got on the Section 3: Math Test—No Calculator and the Section 4: Math Test—
No Calculator. Again, there is no penalty for wrong answers. The number of correct answers is your raw score.
2.  	 Add the number of correct answers on the Section 3: Math Test—No Calculator and the Section 4: Math Test—Calculator.
3.  	 Use the Raw Score Conversion Table 1: Section and Test Scores on page 1016 and convert your raw score into your Math
Section score.

To Obtain Your Total Score
Add your score on the Evidence-Based Reading and Writing Section to the Math Section score. This is your total score on this SAT®
Practice Test, on a scale of 400–1600.

Subscores Provide Additional Information
Subscores offer you greater details about your strengths in certain areas within literacy and math. The subscores are reported on
a scale of 1–15 and include Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, Expression of Ideas,
Standard English Conventions, Words in Context, and Command of Evidence.

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  1013

Computing Your Scores
Heart of Algebra
The Heart of Algebra subscore is based on questions from the Math Test that focus on linear equations and inequalities.

• Add up your total correct answers from these sections:
•
•

ºº Math Test—No Calculator: Questions 1, 4, 7, 9, 13, 15, 18, 20
ºº Math Test—Calculator: Questions 1, 2, 4, 8–10, 13, 21, 32, 33, 36
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Heart of Algebra subscore.

Problem Solving and Data Analysis
The Problem Solving and Data Analysis subscore is based on questions from the Math Test that focus on quantitative reasoning,
interpretation and synthesis of data, and solving problems in rich and varied contexts.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: None
ºº Math Test—Calculator: Questions 3, 5–7, 12, 16–20, 26–28, 31, 34, 35, 37
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Problem Solving and Data Analysis
subscore.

Passport to Advanced Math
The Passport to Advanced Math subscore is based on questions from the Math Test that focus on topics central to your ability
to progress to more advanced math, such as understanding the structure of expressions, reasoning with more complex equations,
and interpreting and building functions.

• Add up your total correct answers from these questions:
•
•

ºº Math Test—No Calculator: Questions 2, 5, 6, 8, 10, 12, 14, 17, 19
ºº Math Test—Calculator: Questions 15, 22–25, 30, 38
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Passport to Advanced Math
subscore.

Expression of Ideas
The Expression of Ideas subscore is based on questions from the Writing and Language Test that focus on topic development,
organization, and rhetorically effective use of language.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
ºº Questions 1, 3, 4, 10, 12, 14, 15, 19, 20, 23, 24, 26, 28, 30, 33–37, 39, 40

• Your Raw Score = the total number of correct answers from all of these questions.
• Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Expression of Ideas subscore.

Standard English Conventions
The Standard English Conventions subscore is based on questions from the Writing and Language Test that focus on sentence
structure, usage, and punctuation.

• Add up your total correct answers from these questions in Section 2: Writing and Language Test:
•
•
  1014

ºº Questions 2, 3, 5–9, 11, 13, 16–18, 21 25, 27, 29, 31, 32, 38, 41, 42–44
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Standard English Conventions
subscore.

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Computing Your Scores
Words in Context
The Words in Context subscore is based on questions from the Reading Test and the Writing and Language Test that address
word/phrase meaning in context and rhetorical word choice.

• Add up your total correct answers from these questions in Sections 1 and 2:
•
•

ºº Reading Test: Questions 9, 10, 22, 23, 31, 32, 37, 42, 51, 52
ºº Writing and Language Test: Questions 4, 6, 15, 18, 27, 37, 39, 42
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Words in Context subscore.

Command of Evidence
The Command of Evidence subscore is based on questions from the Reading Test and the Writing and Language Test that ask
you to interpret and use evidence found in a wide range of passages and informational graphics, such as graphs, tables, and charts.

• Add up your total correct answers from Sections 1 and 2:
•
•

ºº Reading Test: Questions 6, 8, 18, 20, 21, 24, 27, 30, 35, 41, 47, 50
ºº Writing and Language Test: Questions 1, 12, 19, 24, 26, 28, 36, 40
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 2: Subscores on page 1017 to determine your Command of Evidence subscore.

Cross-Test Scores
The SAT® exam also reports two cross-test scores: Analysis in History/Social Studies and Analysis in Science. These scores are based
on questions in the Reading Test, Writing and Language Test, and both Math Tests that ask you to think analytically about texts and
questions in these subject areas. Cross-test scores are reported on a scale of 10–40.

Analysis in History/Social Studies
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 12–22, 33–42
ºº Writing and Language Test: Questions 12–22
ºº Math Test—No Calculator: None
ºº Math Test—Calculator: Questions16, 17, 24, 26, 27, 31, 34, 35
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 1018 to determine your Analysis in History/Social
Studies cross-test score.

Analysis in Science
• Add up your total correct answers from these questions:

•
•

ºº Reading Test: Questions 1–11, 43–52
ºº Writing and Language Test: Questions 34–44
ºº Math Test—No Calculator: Questions 7, 9, 12, 13
ºº Math Test—Calculator: Questions 12, 20, 33
Your Raw Score = the total number of correct answers from all of these questions.
Use the Raw Score Conversion Table 3: Cross-Test Scores on page 1018 to determine your Analysis in Science cross-test
score.

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  1015

Computing Your Scores

Raw Score

Math Section Score

Reading Test Score

Writing and Language
Test Score

10
10
10
10
11
12
13
13
14
15
16
16
17
18
19
19
20
21
21
22

20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

450
460
470
480
480
490
500
510
520
520
530
540
550
560
560
570
580
590
600
600

22
23
23
24
24
25
25
26
26
27
28
28
29
29
30
30
31
31
32
32

23
23
24
25
25
26
26
27
28
28
29
30
30
31
32
32
33
34
34
35

40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

610
620
630
640
650
660
670
670
680
690
700
710
730
740
750
760
780
790
800

33
33
34
35
35
36
37
37
38
38
39
40
40

Writing and Language
Test Score

Writing and Language
Test Score

10
10
10
11
12
13
14
15
15
16
17
17
18
19
19
20
20
21
21
22

Reading Test Score

Reading Test Score

200
200
210
230
240
260
280
290
310
320
330
340
360
370
380
390
410
420
430
440

Math Section Score

Math Section Score

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Raw Score

Raw Score

Raw Score Conversion Table 1: Section and Test Scores

36
37
38
39
40

Conversion Equation 1 Section and Test Scores
READING TEST
RAW SCORE (0–52)

WRITING AND LANGUAGE TEST
RAW SCORE (0–44)

CONVERT

CONVERT

10
READING
TEST SCORE (10–40)

WRITING AND LANGUAGE
TEST SCORE (10–40)

READING AND WRITING
TEST SCORE (20–80)
MATH TEST
RAW SCORE
(0–58)

MATH TEST—NO CALCULATOR
RAW SCORE (0–20)

MATH TEST—CALCULATOR
RAW SCORE (0–38)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

EVIDENCE-BASED
READING AND WRITING
SECTION SCORE (200–800)

CONVERT
MATH SECTION
SCORE (200–800)
MATH SECTION
SCORE (200–800)

  1016

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TOTAL SAT® SCORE
(400–1600)

Computing Your Scores

Raw Score
(# of correct answers)

Expression of Ideas

Standard English Conventions

Heart of Algebra

Problem Solving
and Data Analysis

Passport to Advanced Math

Words in Context

Command of Evidence

Raw Score Conversion Table 2: Subscores

0

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

2

1

1

2

2

5

2

2

3

2

2

3

3

6

3

3

4

3

2

4

4

7

4

4

5

4

3

5

5

8

5

5

6

5

4

6

6

9

6

6

7

6

5

6

7

10

6

7

8

6

6

7

8

11

7

8

9

7

6

8

8

11

8

8

10

7

7

8

9

12

8

9

11

8

7

9

10

12

9

10

12

8

8

9

10

13

9

10

13

9

8

9

11

13

10

11

14

9

9

10

12

14

11

12

15

10

10

10

13

14

12

13

16

10

10

11

14

15

13

14

17

11

11

12

15

14

15

18

11

12

13

15

15

19

12

13

15

20

12

15

21

13

22

14

23

14

24

15

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  1017

Computing Your Scores
Conversion Equation 2 Subscores
HEART OF ALGEBRA
RAW SCORE (0–19)

EXPRESSION OF IDEAS
RAW SCORE (0–24)

COMMAND OF EVIDENCE
RAW SCORE (0–18)

PROBLEM SOLVING AND DATA
ANALYSIS RAW SCORE (0–17)

CONVERT

CONVERT

CONVERT

CONVERT

HEART OF ALGEBRA
SUBSCORE (1–15)

EXPRESSION OF IDEAS
SUBSCORE (1–15)

COMMAND OF EVIDENCE
SUBSCORE (1–15)

PROBLEM SOLVING AND DATA
ANALYSIS SUBSCORE (1–15)

STANDARD ENGLISH CONVENTIONS
RAW SCORE (0–20)

WORDS IN CONTEXT
RAW SCORE (0–18)

PASSPORT TO ADVANCED
MATH RAW SCORE (0–16)

CONVERT

CONVERT

CONVERT

STANDARD ENGLISH CONVENTIONS
SUBSCORE (1–15)

WORDS IN CONTEXT
SUBSCORE (1–15)

PASSPORT TO ADVANCED
MATH SUBSCORE (1–15)

Analysis in History/Social
Studies Cross-Test Score

Analysis in Science
Cross-Test Score

10

10

18

28

26

1

10

11

19

29

27

2

11

12

20

30

27

3

12

13

21

30

28

4

14

14

22

31

29

5

15

15

23

32

30

6

16

16

24

32

30

7

17

17

25

33

31

8

18

18

26

34

32

9

20

19

27

35

33

10

21

20

28

35

33

11

22

20

29

36

34

12

23

21

30

37

35

13

24

22

31

38

36

14

25

23

32

38

37

15

26

24

33

39

38

16

27

24

34

40

39

17

28

25

35

40

40

  1018

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Raw Score
(# of correct answers)

Analysis in Science
Cross-Test Score

0

Raw Score
(# of correct answers)

Analysis in History/Social
Studies Cross-Test Score

Raw Score Conversion Table 3: Cross-Test Scores

Computing Your Scores
Conversion Equation 3: Cross-Test Scores

ANALYSIS IN
HISTORY/SOCIAL STUDIES
TEST

QUESTIONS

RAW SCORE

ANALYSIS IN SCIENCE
QUESTIONS

Reading Test

12–22, 33–42

1–11, 43–52

Writing and
Language Test

12–22

34–44

Math Test—No
Calculator

None

7, 9, 12, 13

Math
Test—Calculator

16, 17, 24, 26, 27,
31, 34, 35

12, 20, 33

RAW SCORE

TOTAL

ANALYSIS IN HISTORY/
SOCIAL STUDIES
RAW SCORE (0–35)

ANALYSIS IN SCIENCE
RAW SCORE (0–35)

CONVERT

CONVERT

ANALYSIS IN HISTORY/
SOCIAL STUDIES
CROSS-TEST SCORE (10–40)

ANALYSIS IN SCIENCE
CROSS-TEST SCORE (10–40)

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  1019

PART VIII: APPENDIX

Parents’ Guide to College Admission Testing

Parents’ Guide to College Admission Testing
GETTING INVOLVED
The first step in creating a plan to help your teen prepare for college-admissions tests is to define your role. As a parent, you
already play a variety of roles in raising your children, wearing different hats at different times. You may find yourself acting as
mentor, chauffeur, cook, coach, mediator, or even prison warden. All of these roles require different time commitments and often
even require you to acquire new skills.
When it comes to helping your teen tackle the SAT®, you might feel confused about which role to take. Many parents find becoming
involved with their teen’s education a bit challenging. Teenagers can have a hard time accepting their parents as teachers.
Sometimes, when parents try to teach their teen, their efforts lead to the three “Fs”: failure, friction, and frustration. When these
experiences arise, parents may conclude that they have no role to play in their child’s education.
Of course, nothing could be further from the truth. In fact, there are many roles parents should choose to play in helping their
teens prepare for college-admissions tests.

ROLES FOR PARENTS
You can play a variety of roles in helping your teen prepare for college-admissions tests. In guiding your teen, you may choose
to be one, or any combination, of the following:

• Buyer
• Advocate
• Supporter

• Helper
• Organizer

1023

• Manager
• Tutor

Appendix
Parents’
Guide to
College
Admission
Testing

The Buyer
“Here’s the money for the SAT® books you want to buy.”
This parent feels that it is the teenager’s job to prepare for college-admissions tests, and the parent’s job is to offer financial
support. The teenager is the main decision maker and is responsible for obtaining the necessary materials and services. This
parental role is supportive and not too time-consuming, although it may present problems for parents who are on a tight budget.

The Advocate
“How does your school help juniors prepare for the SAT®?”
This parent believes that it is the school’s job to prepare students for the test. The parent starts the ball rolling and requests
information from school personnel about what services are available. The teenager may or may not be involved in this information-gathering process. Most parents feel comfortable in this role, as it requires little time and is accepted by both school
personnel and teachers.

Peterson’s SAT® Prep Guide 2017

The Supporter
“I know it’s a tough test. I see you’re working hard and spending a lot of time studying for it.”
This parent believes that the teenager has the major responsibility in preparing for the test. The teenager is the decision maker, and
the parent offers suggestions and support. The parent is understanding, empathetic, and non-critical. This can be a comfortable
parental role since it is non-threatening to the teenager, is positive, and requires a minimal amount of time.

The Helper
“I picked up this SAT® practice book and made a list of some tutoring courses for you.”
This parent believes that it is the parent’s job to help the teenager with his plans, but that it is up to the teenager to make the
final decisions. This parent only helps when asked and follows the teen’s timetable when possible. This is a comfortable role since
it is supportive, non-threatening, and not time-consuming. However, this role might pose problems for working parents who do
not have flexible schedules.

The Organizer
“I’ve signed you up to take a test-prep course.”

1024
Appendix
Parents’
Guide to
College
Admission
Testing

This parent feels that the teenager should not be responsible for the arrangements involved in test preparation. The parent
assumes a major role in establishing a timetable, finding out about resources, arranging for services, and purchasing materials.
The teenager’s responsibility is to follow the parent’s game plan. In short, the parent provides the framework so that the teenager
can spend her time preparing effectively. This role is time-consuming and parent-directed.

The Manager
“After you study your vocabulary words for 30 minutes, you can use the car.”
This parent believes that good intentions are not enough to make her child perform well on the SAT® exam. She believes in
the rule “work first, then play.” Firm guidelines and consequences are established to keep the ball rolling. The degree to which
the teenager is involved in planning and implementing this approach depends on a number of factors, such as the teenager’s
maturity and motivation.

NOTE: Educators and legislators recognize the importance of having parents involved in their children’s education.
Research shows that parents can successfully teach their teens, when they have been taught how to do it.

Your comfort with this role is related to the extent to which you believe in the “work first, then play” philosophy. If you already
ascribe to this rule in raising your children, extending it to SAT® exam preparation will be an easy task. Patience and willingness
to check on study behavior are also important factors to consider when thinking about the role of manager.

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The Tutor
“I’ll explain the algebra problem to you.”
Parents who take on the role of tutor believe that they can work effectively with their teenager on academic subjects. These
parents offer direct instruction in one or more of the test areas, such as vocabulary, reading comprehension, geometry, or algebra.

Remember, no single role is superior to the other. Find roles that are best
suited to you and your teenager’s needs.

WHICH ROLE IS FOR YOU?
Defining your role requires two steps:
1. Collecting information about yourself
2. Using this information systematically, as you decide which role you want to take on and when
To collect information about yourself, take the following “Parent Survey.”

PARENT SURVEY
LOW

MEDIUM

HIGH

1. How much money is
available for test
preparation, tutoring
books, etc.?

Up to $25 for books

$25–$150 for books and
tutoring

More than $150 for
courses, books, etc.

2. Do you question
school personnel?

Never. I feel
uncomfortable.

Sometimes, if it is
important.

Usually. It’s my right.

3. Do you make
supportive statements
about academic
achievements?

Not usually. I don’t want
to spoil my child.

Sometimes, if grades
are good.

Frequently, especially about trying
hard.

4. What resources are
available in your school
or community?

I don’t have the faintest
idea!

I thought I saw an
advertisement for an
SAT® course,

I know a tutor and
saw an SAT® book in
the store.

5. How involved do you
feel?

I don’t know if I should
be involved.

I’ll do what I can if I’m
asked.

This is important!
I’ll help whenever
I can.

6. How much time are
you willing to devote to

1–3 hours total

1–2 hours per week

3 or more hours per
week

7. How efficient is your
decision making?

It’s either too slow or too
hasty.

Sometimes good, but
it’s a tiresome process.

Usually good. I
consider options
and select one.

8. Who should be
the primary decision
maker?

Not me. It’s not my job!

I’ll make decisions
sometimes.

Me. I have more
experience.

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SAT® exam preparation?

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LOW

MEDIUM

HIGH

9. How organized are
you?

I lose papers, forget
dates, and am often
late.

I write schedules but
forget to follow them.

A place for everything and everything in its place!

10. How comfortable
are you with your
teenager?

It’s tough being around
my child.

Some days are good,
others aren’t.

Minor problems, but
we get along.

11. How firm or consistent are your limits?

No one listens to me. I
nag and yell.

My children know the
rules, but I forget to
enforce them.

My children follow
the rules.

12. Do you have reading
and math skills?

Minimal skills; low
confidence.

Some skills; average
confidence.

Strong skills; high
confidence.

13. How effective are
you as your teenager’s
teacher?

We always end up
fighting.

Sometimes it works,
sometimes it doesn’t.

It’s not easy, but we
work together.

Choosing Your Role by Interpreting Your Survey Responses
While there are no hard and fast rules to use in choosing a role, your answers to the survey questions will help you select your role in a
systematic way. Using your survey responses, you can use the following guidelines to identify which roles to try first. Remember that any
combination of roles is good. To help clarify:

• The roles of buyer, advocate, and supporter are appropriate if a majority of your answers fall in the low or medium
columns. These roles demand the least amount of direct parent-as-teacher involvement, yet they are an important part
of test preparation. Most parents can assume these roles.

• The roles of helper, organizer, and manager require that the majority of your answers fall in the medium or high

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columns. These roles involve more constant and direct interaction with your teen. Some parents can assume these roles.

• The role of tutor is the most demanding role and requires that at least eleven out of thirteen responses fall in the
medium or high columns. There are few parents who can comfortably and successfully assume this role.
Depending on your time and resources, you may, for example, want to begin in the advocate and supporter roles, followed by that of
a buyer. If necessary, you could find someone else to act as a manager and tutor. Or, alternatively, you might find yourself best suited to
being an organizer, manager, helper, and supporter right away.

BECOMING ACTIVE
Parents entrust their most valuable assets—their children—to the schools. As an investor in your child’s education, you have the same
concerns as any other person investing in the future. Unfortunately, sometimes parents are made to feel that the school is the “expert.” In
some schools, parents are viewed as meddlers if they ask for, or insist upon, information about their children’s progress. As a parent, you
can, and should, be involved in your teen’s education, even at the secondary level. Don’t be afraid to pursue information on your teen’s
behalf—you need to be informed, ask questions, offer suggestions, and reject suggestions if they aren’t the right solutions to the problems!

HOW TO APPROACH YOUR TEENAGER
For the first time, your teen may be striving for independence and questioning himself or herself and the future. These changes
may make your role as a parent additionally tough, and you may find it hard to help your teen prepare for college-admissions
tests. The key to reaching your teen is to focus on where he or she is academically and personally.

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GETTING INFORMATION FROM DIFFERENT SOURCES
To design your SAT® exam preparation plan, you’ll need to get up-to-date information about your teenager from several sources,
including yourself, your teenager, and the school. Your child’s guidance counselor is a primary source of information, since he or
she can provide information from classroom teachers and across various subject areas.

You and Your Teen
The first source of information is you. Parents must neither overestimate nor underestimate the importance of their own information about their teenager. You can be most effective if you know which questions to ask and whom to ask. You need to know
about your teenager’s concerns, goals, attitudes, academics, work habits, general behavior, and special strengths and weaknesses.
To initiate this step, ask your teen to meet with you for an hour to discuss college plans and how he or she feels about preparing
for the SAT®. You can begin by asking your teen for his or her opinions on matters concerning his or her education and future goals.
In this first conversation, you can ask about colleges he or she is considering. Because many colleges suggest that its applicants’
test scores fall within a certain range, information about the college’s requirements is important. The required scores may affect
the amount of time and the kind of commitment required for the test preparation.
You may also want to ask your teen to evaluate his or her study skills and the kind of study skills needed to prepare for the SAT®.
Some teenagers work effectively in groups. Others are uncomfortable or distracted when studying in a group. Students’ work
habits and interactions with other people also influence their attitudes toward college-admissions tests and their scores. Your
teenager’s reaction to tests in general is an important factor to take into consideration.
Don’t feel rejected if your teen says, “I don’t want to meet. I know what to do.” Don’t push it; just try again later. The timing may
be right on the second go-around.

NOTE: Taking the SAT® exam can create a lot of stress. Excessive anxiety interferes with test performance. Collecting information from your teenager will help identify his or her problems and concerns,
so you can help reduce test-prep stress.

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The School
Another important source of information is the school. Guidance counselors, teachers, and others, such as coaches or band directors,
can tell you about your teenager’s attitudes and interactions with peers and adults outside the home. These attitudes may influence
your teen’s college selection and in turn lead you to the most appropriate type of preparation for the college-admissions tests.
Your teen’s guidance counselor can review previous standardized test scores with you and discuss differences in performance
between tests and grades. Reviewing standardized test scores and grades can help you establish realistic guidelines for SAT®
preparation.
Teachers and counselors can also describe specific weaknesses that might block an otherwise solid test performance. In addition,
they can offer information about your child’s work habits, such as whether homework is submitted on time or how well-organized
his or her papers are.

Peterson’s SAT® Prep Guide 2017

Additional Options
Independent school counselors, or educational consultants, are another alternative to consider. These types of counselors are not
affiliated with a school and work as private consultants. If you lack confidence in your teen’s counselor or feel that the counselor
is too busy to provide the extensive work necessary for appropriate college planning, you may want to work with an educational
consultant.
A private consultant may work with students from all over the United States and foreign countries. This broader perspective can
provide more diverse options for your child. Many independent counselors also have firsthand experience as college-admissions
officers and therefore are aware of the kind of information that should be collected and ways of presenting such information to
colleges.

WHAT TO ASK
The following is a list of questions you’ll want to ask yourself, your teen, and school personnel or educational consultants.

Goals
• What career choices is your teen considering?
• Are there specific colleges your teen wants to attend?
• What range of SAT® exam scores do those colleges require? (Or are these scores optional?)

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Attitudes
• How confident is your teen about his or her ability to succeed?

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• What attitude does your teen have toward school and school personnel?

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• Are your teen’s friends a good influence in terms of future plans?
• How helpful is the family in terms of school success?
• What is your teen’s attitude toward college-admissions tests?

Academics
• How has your teen done on other standardized tests?
• Do standardized test scores accurately reflect your teen’s skills or abilities?
• Do your teen’s grades accurately reflect his or her skills or abilities?
• What are your teen’s areas of strength?
• What are your teen’s areas of weakness?

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Work Habits
• How effective are your teen’s organizational and

• Are there obstacles that might interfere with

study skills?

• Does your teen the student do better with certain
study procedures (e.g., in a group or listening to
recorded lectures)?

effective test preparation (e.g., a job or extracurricular activities)?

• Are there barriers to effective test-taking; (e.g.,

• How effective are your teen’s test-taking skills?

struggles with long reading passages or not liking
multiple-choice tests)?

Behavior
• To what degree does your teen need or accept help?
• To what degree is your teen a good decision maker?
• How good is your teen at self-managing or being a self-starter?
• To what degree does your teen test limits or rules?
• How well does your teen cope with stress or adversity?
• How well does your teen relate to school personnel and teachers?
• How well does your teen relate to peers and classmates?
• How well does your teen relate to family members?

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• With whom will your teen talk about problems (e.g., a sibling or a neighbor)?

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Special Issues

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• Does your teen have special talents or abilities?
• Does your teen have special challenges or obstacles?
• Have special challenges or obstacles been addressed previously?
• In what way will any of these issues affect preparation for the college-admissions tests?

SAT Exam
• How do students in your school perform on the test?
• How did your teen perform on other college-admissions tests?
• How do your teen’s test scores compare with others in the class?
• What services do school personnel provide for SAT® exam preparation?
By asking these questions, you can really focus on your teenager. By answering these questions now, you’ll reveal information
gaps, identify consistencies or inconsistencies in opinions or behaviors, highlight strengths and weaknesses, and begin your
systematic plan for helping your teen.

Peterson’s SAT® Prep Guide 2017

HOW TO USE THE INFORMATION
To get the most out of the information you have collected, pay particular attention to the following issues:

• Consistency of answers provided by each of the sources—for example, whether the counselor’s answers conflict
with your teenager’s answers

• Trends that emerge—such as better work this year or more anxiety than last year
• Gaps in information—such as no previous standardized test scores available
• Strengths and weaknesses—such as being well organized or having poor reading comprehension

YOUR TEEN’S STRENGTHS
All teenagers have strengths. However, some teenagers’ strengths are more obvious than others. Your job as a parent includes:

• Identifying, highlighting, maintaining, and increasing existing strengths
• Providing opportunities for new strengths to develop
Strengths may be grouped into several broad categories—knowledge, work habits, attitude, behavior, and special. To help clarify:

• Strengths in the knowledge area include mastering basic skills, achieving good grades, and having a potential for
learning.

• Strengths in the area of work habits include applying skills and knowledge in an organized and effective way and

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achieving desired goals.

• Strengths in the area of attitude include having clear goals, optimism, motivation, and self-confidence.
• Strengths in the behavior category refer to the teenager’s ability to cope, follow rules, and get along with peers and
adults.

• Special strengths may include talents in areas such as music, art, writing, or science.
Too frequently, both parents and teachers forget to accent the positive. They zero in on the weaknesses rather than on the
strengths. To avoid this common mistake, review the information you have collected and list your teen’s strengths and special
talents in the following chart. We’ll come back to filling in the problem areas later.

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SOURCE

KNOWLEDGE WORK HABITS

ATTITUDE

BEHAVIOR

SPECIAL

Strength
Parent

Problem
Strength

Teenager

Problem
Strength

School

Problem

Remember to discuss these strengths with your teenager, especially if he or she does not recognize his or her own strengths or
talents. Building your teen’s confidence is important and will pay off enormously.

IDENTIFYING SPECIFIC PROBLEM AREAS
Several kinds of problems may become obvious as you collect information about your teenager. These problem areas may be
grouped into the same five categories we used to identify strengths.

Knowledge Problems
Students with knowledge problems may make statements such as: “I’m not even sure about getting all the ratio and proportion
problems right,” or “I hate reading,” or “I never do those grammar parts—I skip most of them.”
Knowledge problems include:

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• Lack of mastery of basic skills, such as arithmetic.

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• Lack of understanding of rules and concepts in more advanced areas, such as geometry.

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• Lack of experience, which leaves gaps in some areas covered on the SAT® exam.
• Difficulties in one or more of the following: remembering previously learned material, analyzing material, or putting
information together (e.g., as in a report).
Your teenager may have a knowledge problem in only one area, which may or may not have an effect on any other area. For
example, Marcus, a 10th-grader, had a reading problem, and testing showed that he read two years below his present grade level.
His computation skills were good, and he did well in algebra. However, word problems were his downfall. In this case, a knowledge
problem in one area had an effect on another area.

Peterson’s SAT® Prep Guide 2017

Work-Habits Problems
Statements such as “I can’t find my notes,” “I think I left my books at school,” or “I’ll study later, after my favorite TV show” signal
work-habits problems.
Work-habits problems include:

• Poor study habits

• Lack of organization

• Test anxiety

• Difficulty estimating how long a task will take

• Ineffective test-taking skills
Teenagers with work-habit problems lack the skills necessary to study effectively or to apply the knowledge they have during
a testing situation. These teenagers may work too slowly and be unable to complete portions of the test, or they may work too
quickly and inadvertently skip questions and make careless errors.

Attitude Problems
Students with attitude problems may make statements such as: “It doesn’t matter how much I study, I’ll never be able to do it,”
or “I don’t care—the SAT® doesn’t matter anyway.”
Attitude problems involve:

• Unrealistic self-image and academic goals

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• Over- or under-estimation of the importance of the SAT®
On the one hand, teenagers may be overly optimistic in thinking that they are smart, do not need to prepare for the SAT®, and
can get into any college on the basis of grades alone. On the other hand, teenagers may have an overly negative view of their
ability and therefore avoid school, worry about grades, panic on tests, and can be difficult or quarrelsome.
Attitude problems can influence the degree to which teenagers are willing to spend time and energy preparing for the SAT®.

Behavior Problems
Teenagers with behavior problems are likely to make statements such as: “I don’t have to study just because you say so,” or “I know
I should study, but I just can’t make myself do it,” or “I keep getting headaches when I think about the SAT®.”
Behavior problems include:

• Poor self-control

• Drug and/or alcohol abuse

• Lack of responsible behavior

• Inability or unwillingness to follow rules and maintain

• Inability to get along with peers, adults, or family

commitments in school and in the community

Teenagers with behavior problems usually use ineffective ways of coping with stress, are overly dependent or rebellious, are
unable to control anger, and are unwilling to face or discuss problems with adults.

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Special Problems
Teenagers with special problems may make statements such as: “I’ve always had trouble with spelling and reading,” or “I know I
have physical problems, but I want to try to go to college,” or “I can do those questions; I just need more time.”
Special problems include:

• Specific learning disabilities
• Severe physical, sensory, or emotional limitations
• Language barriers
• Disadvantaged backgrounds that may result in a lack of culturally enriching experiences
Special problems may prevent or affect your teen’s ability to take the test. If your teenager is eligible, he or she may be able to
take the SAT® with certain accommodations, such as extended time. Be sure to review the options and eligibility requirements
and submit an accommodations request well in advance, as it can take several weeks to be approved.
To begin designing an SAT® plan, you need to review your teenager’s problems. List these problems on the same chart where
you have already listed the teenager’s strengths. When discussing these problems with your teenager, remember to talk about
his or her strengths as well.

HOW TO USE THE INFORMATION ABOUT YOUR TEEN
After collecting information about your teenager, you should summarize the information by reviewing the chart you completed.
Remember that strengths, along with weaknesses, may exist in each area. Keep the following in mind as you evaluate and summarize the information you have gathered:

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• The number of sources that agree or disagree
Appendix

• The number of objective measures that agree or disagree, such as tests, grades, or reports
• The number of times you are aware of the strength or problem—for example, your teenager always seems to be studying
or is always complaining

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WORKING WITH YOUR TEEN’S GUIDANCE COUNSELOR
Relative to college-admissions tests, the counselor’s role is to help students understand the nature of these tests, the benefits of
study and coaching, what test to take and when, and whether to retake a test in order to achieve a higher score.
The counselor can help you and your teen summarize information about how prepared your teen is for the SAT® and can discuss
strengths and weaknesses in light of current and past test results and grades. Making an appointment with your teen’s guidance
counselor now will enable you to make reasonable decisions about a course of action.

DEVELOPING EFFECTIVE WORK HABITS
In addition to assessing knowledge of English, math, and other content areas, the SAT® exam tests how well your teen takes
standardized tests. Part of becoming a successful test-taker involves developing effective work habits. Developing these habits
now will save your teen lots of frustration, time, and energy and will inevitably improve his or her test scores.

Peterson’s SAT® Prep Guide 2017

MANAGING TIME
Consider the following example. John is a fairly good student and earns Bs and Cs in his high school courses. He is concerned
about the SAT® and wants to do well. During a practice SAT® test, he plods through each section and spends extra time on some
of the more difficult questions. He doesn’t finish parts of the test. His practice SAT® scores are unnecessarily low because he didn’t
have time to answer all of the questions he could have easily handled. John’s test behavior indicates that he needs help in work
habits, especially in learning to manage his time and pace himself during the test.
When people work in factories or offices, they are usually told how much time should be spent on different tasks. This process
ensures productivity, allowing workers to know what is expected of them and helping them pace themselves so that they get
the most done in the least amount of time. Similarly, your teen will also benefit from learning how to manage the time he has to
take the SAT®. Before taking the tests, he or she should know the following:

• How many questions are on each section of the test
• How much time is provided for each section
• Approximately how much time can be given to each question if he or she is to complete the test and if all of the questions are of equal difficulty

• The kinds of questions that he or she can’t do and should skip until completing those questions he or she can definitely
answer correctly
With test-taking, managing time means that your teen can predict what he or she has to do, how long it should take, how to pace
himself or herself to get the job done, and how to leave time to check his or her work. Although most testing centers have clocks,
your teen should wear a watch during the test (and practice tests) to keep track of time and check his or her pacing.

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GETTING ORGANIZED AND STICKING TO TASKS
Now consider the case of another test-taker, Emma. The following takes place in her parents’ kitchen after dinner:

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7:05 p.m. “Mom, did you see my SAT® practice book?”
7:10 p.m. “Mom, I found some paper. Where are some pencils?”
7:15 p.m. “Oh, I’d better text Liam to see if I have a ride tomorrow!”
7:20 p.m. “What time is it?”
7:22 p.m. “I need to get on the computer.”
7:25 p.m. “That’s enough math! I think I’ll do some vocabulary.”
7:40 p.m. “I hate vocabulary! I’ll go back to math.”
Emma displays several work-habits problems. One problem is that she hasn’t recognized what she can’t do during study time—
for example, disrupting herself by sending a text message. Another problem is that Emma jumps from task to task, breaking her
own concentration.
Good work habits entail being organized. Teenagers need to learn how to organize materials, list what has to be done, and specify
how much time might be needed to complete each job. Study styles may differ, but teenagers must find the most effective ways
to use their time and follow their own plans.

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Students like Emma benefit from guidelines to follow during study time, such as:

• Spend at least 20–30 minutes on each activity, maintaining concentration, and building up skills.
• Stick to some basic study rules, including not avoiding work because it is too difficult or boring.
• Invoke the rule: “Work first and then play.” For example, text, go online, or make phone calls only after work is
completed.
Sticking to a task is an essential work habit. Unless she changes her habits, Emma will not reach the critical test-related goal:
accurately completing the greatest number of problems she can within specific time limits. Emma is also operating under some
misconceptions. She really believes that she is working hard and that her fatigue is a result of studying. She may also begin to think
that she is not so bright as her friends because they are getting better results on practice tests. All of these potential problems
can be resolved by changing her work habits.

IF IT WORKS, DON’T CHANGE IT
Another 10th-grader, Caleb, likes his comforts. He loads up on soda and chips before he settles down to work. The radio is an
essential part of his lifestyle. When his mother and sisters pass by his room, they see him sprawled on his bed with a small light
turned on and papers and books all over the floor. Sometimes he’s sound asleep. Because he seems so casual, everybody stops
by and talks to him.
Some parents might assume that the manner in which Caleb goes about studying is totally ineffective. It doesn’t appear that any
teenager could concentrate and maintain attention curled up in bed with music blaring, people walking in and out, poor lighting,
and a nap now and then. Most parents would be right. Caleb’s parents had been concerned and were annoyed by his work habits.
However, Caleb earns high grades in school, and on the first SAT® he took, he scored more than 600 on the reading and writing
sections. He has also shown his parents how his speed is increasing on certain practice SAT® exercises. In this case, the parents
have specific information and assurance that their son’s work habits work for him, despite appearing inefficient.
Your objective here is to check the effectiveness of your teenager’s work habits. Consider what effect these habits have on
classroom or college-admissions test performance. Remember to have your teen take a practice test under actual SAT® conditions
to see how his or her work habits hold up.

TAMING THE PROCRASTINATOR

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Procrastination is a common problem for teens. Leslie is an 11th-grader having a conversation with her father, Mr. Rand.
Mr. Rand: “Did you start to study for the SAT®?”
Leslie: “No, it’s in two months.”
Mr. Rand: “Shouldn’t you start now?”
Leslie: “I wish you would stop nagging me. I can take care of myself.”
Here’s another scenario, between Mrs. Sanchez and her 11th-grader, Ricky:
Mrs. Sanchez: “I haven’t seen that SAT® book around. Are you studying in school?”
Ricky: “I started looking at it, but it’s so long I’ll never get through it.”
Putting off work occurs when people feel overwhelmed, don’t know where to begin, feel pressured to get other things done, or
are distracted by other things they would rather do. Parents who recognize this work-habit problem in their teenagers may have
similar habits themselves.

Peterson’s SAT® Prep Guide 2017

Procrastination becomes a particular problem because:

• Time is limited; when time is limited, people feel pressure.
• There can be a penalty for delay—for example, you might miss the SAT® because your payment was not received
on time.

• Avoiding work increases the load, rather than decreases it.
By taking into account the time available before the SAT® and the preparation that has to be done, you can help your teenager
create a sensible plan that divides one seemingly overwhelming task into smaller and more manageable ones. Predicting what
has to be done, and doing those tasks one by one, gives teenagers control over feelings of being swamped and unable to cope.

A WORK-HABITS CHECKLIST
To help your teenager develop effective work habits, ask him or her questions regarding time management, materials, atmosphere,
and space. You may want to use the following checklist.

Time Management
Are there signals to others that this is a study time (e.g., a “Do Not Disturb” sign)?
Are there rules set up for the study time (e.g., no phone calls or no visitors)?
Is a time schedule agreed upon and posted?
Are study breaks scheduled?

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Materials
Is a clock or kitchen timer available?

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Are supplies handy (e.g., pencils, eraser, computer)?
Does the seating encourage attention and alert behavior (e.g., a chair and a desk rather than a bed)?

Atmosphere
Is the lighting adequate?
Is the noise level low?
Is the area visually nondistracting?
Is the area well-ventilated and does it have a moderate temperature?

Space
Is there a special place designated (e.g., desk, room, or area) for studying?
Is this space away from the main traffic of the home?
Is the space large enough to allow for writing?
Is there space available for storing or filing materials?

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HOW TO HELP YOUR TEEN WITH WORK HABITS
Teenagers have difficulty finding time to do homework or household chores, but they usually seem to have a lot of time to text
or talk on the phone, go online, or hang out with friends. Managing time comes down to establishing priorities. Here are some
guidelines that you can use to help your teenager use his or her time more effectively:

• Set a realistic study schedule that doesn’t interfere too much with normal activities.
• Divide the task into small and manageable parts—for example, instead of trying to memorize 2,000 vocabulary words
in two weeks, have your teen learn and use five new words a day, three times a week.

• Use what has just been learned whenever possible—for example, talk about, joke about, and use new vocabulary words.
• Find times that are best for concentration and, if possible, have your teen avoid studying at times when he or she is
tired, hungry, or irritable.

• Plan a variety of study breaks, such as music or jogging, to revive concentration.
• Encourage your teenager to get a group of friends together to practice taking the exam, review test items, compare
answers, and/or discuss the ways they used to solve the problems. Such a group can range in size from two to six
students.

WHY CREATE A PLAN?
It takes more than good intentions to do well on a college-admissions test. It takes time, organization, and hard work. A test-prep
plan provides the means for converting good intentions into meaningful test preparation. An effective plan specifies:

• Goals

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• Responsibilities of parent and teenager
• Available resources

Appendix

• Schedules

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• Budgets
• Instruction
• Possible problems or concerns
By clearly establishing who is responsible for what, a test-prep plan removes many sources of conflict between parent and teenager
and allows each person to channel all of his or her efforts toward the goal of improving test scores.

CREATING TEST-PREP PLANS
Let’s look at some step-by-step ways of creating test-prep plans and what to expect as you create a plan for your teen.

Make Time to Plan
Family life is hectic. Finding time to sit down and talk together is frequently a problem. Like a well-managed business, families
with educational concerns and goals also need to have planning meetings. They need to find the time and place that will allow
for discussion and working together.

Peterson’s SAT® Prep Guide 2017

Setting up a time to talk about a plan with your teen will work best if you approach him or her when he or she is most apt to be
receptive. How you proceed is as important as what you do. A first step in developing a plan is to set goals.

Some teenagers need to review a specific skill or subject; others have
problems that require intensive instruction and practice. Since each
teenager is unique, each test-prep plan must be individually tailored to
fit specific needs.

List Goals
Goals help identify in a concrete way what you want to happen, such as your teen raising his or her verbal score by 40 to 60 points.
Sometimes teenagers choose goals that are too general, such as doing geometry problems more accurately or completing the
reading section more rapidly. Goals should be specific to the SAT® even when they include study skills. For example, just having
a goal of studying for 30 minutes a night does not guarantee improvement. The following list contains some sample goals.

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For accuracy:
		

Increase the number of correct math and vocabulary
test answers.

For speed:
		
		

Decrease the time needed to read comprehension
exercises while maintaining an understanding of
what is read.

For speed and accuracy:
		

Decrease the time needed to read comprehension
exercises and increase understanding of what is read.

For quantity:

Increase the number of problems tried or completed.

For frequency:
		
		

Study vocabulary words and do essay writing
practice exercises for about 30 minutes at least three
times per week.

For duration:
		

Increase study sessions to 1 hour, adding additional
practice math problems.

After outlining the goals, the next step in planning is to prepare a schedule.

Remember to take action in a way that is sensitive to your teen’s needs
and schedules.

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Make a Schedule
A test-preparation schedule should include a timetable and weekly or daily activity lists. First make the timetable. You can use a
regular calendar that covers the time between the current date and the date of the SAT®. To make your timetable, write down all
activities related to preparing for the test and the test date on the calendar.
You should also keep weekly and/or daily lists to identify specific tasks, such as the type or number of practice exercises to be
completed. Such scheduling spells out the tasks ahead of time, reduces unnecessary worrying, and allows for more realistic
planning. Often, teenagers become overwhelmed by the thought of all that has to be done and end up doing nothing. Writing
a list and assigning times to each task tends to make these jobs more doable and more realistic.

Talk About Costs
Although you want to do everything possible for your teen’s college-admissions test preparation, cost is an important consideration.
Most families’ budgets are already strained without adding the expenses of materials, tutors, or commercial courses—especially
since test preparation comes at a time when parents are trying to save money for college tuition.
Regardless of who pays the bill—the parent, the teenager, or both—budgets should be discussed. The estimated costs of various
alternatives should also be outlined. Any budget limits and expected responsibilities should be proposed. By discussing these
issues up front, you clarify problems and provide a realistic basis for decision making.

Find Out About Resources
Your community may have a variety of resources to help teenagers prepare for college-admissions tests. However, it may take
a little detective work to find them. For example, many religious groups and local organizations, such as your department of
recreation, senior center, or the town library, sponsor young-adult activities. These groups usually know skilled people within
the community who would be willing to help teenagers study for the SAT®. In addition, parent or community groups may also
be willing to sponsor special activities if they are aware of teenagers’ needs.

Match Materials to Your Teen’s Goals
You and your teen should now select which books, equipment, and/or specialized materials will be used. You should match these
materials to your teenager’s goals. Consider drawing on information from teachers or counselors, previous standardized tests,
and test-prep books that analyze the SAT®. Material can be purchased, borrowed, or shared by several teenagers.

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Locate a Tutor
In finding a tutor, you should consider someone who has experience with the college-admissions tests. You may actually hire
more than one tutor, since instruction may be provided by volunteers, peers, schoolteachers, or professional tutors. Discuss
various tutoring options with your teen.

Peterson’s SAT® Prep Guide 2017

Find a Place to Practice and Study
Regardless of your plan’s specifics, your teen needs a suitable place in which to study. Teenagers who register for courses or who
receive tutoring have to practice test-taking at home, too. It is important to select a quiet study place at home or at school for
SAT® homework assignments or for sessions with the tutor. It is also smart to turn off phones, the TV, and computers to reduce
interruptions and distractions while your teen is preparing for the test. Some students do well working in a library or another
area set aside for quiet study.

ANTICIPATE POSSIBLE HURDLES
Some common problems that arise during the test-prep process include:

• The teenager doesn’t work well with the tutor.
• The instructor gets sick.
• The study group falls apart.
• One of the parents loses a job, so money is no longer available for a commercial course.
More subtle problems can occur when:

• Teenagers set unrealistic goals and then feel tired, frustrated, and angry.
• Parents become worried that their teenager isn’t making enough progress.
• Parents feel angry and disappointed when things don’t work out exactly as planned.

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When managing a plan, you must assume that problems will arise and that plans have to be changed to deal with these problems.
Helping your teenager shift gears and learn how to make adjustments is vital preparation for the real world and a valuable skill
for him or her to learn now.

WAYS TO TRACK PROGRESS
Here are some ways you can check on your teen’s performance progress:

• Keep records for each study session.
• Keep track of the number of problems completed correctly.
• Keep track of how much time it takes to complete the work.
• Review the records to see if changes to the plan need to be made.
• Make sure your teen is focused on the specific test sections or questions that need special attention.
Teenagers can check on their progress in several ways. These methods include calendars, checklists, charts, and graphs. The best
method is the one that your teen will regularly use.

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Timing Your Comments
You should comment on performance when the progress has occurred, not a week or two later. Teenagers usually do not want
anyone to know that they are studying for the tests, so it’s best to comment when no one else is around. You should also be
especially sensitive to how your teenager will receive any comments about his or her work. Teenagers often view these helpful
hints as criticism, even when they are offered in a positive way. You may find it easier to use notes or humor as a way of making
a point that can be accepted by your teen. For example, Anne’s father wrote her the following note:
Dear Anne:
I see that you’re keeping track of the number of problems you complete for the SAT. Looks as if you’re doing at least 2–3 more
problems each time—HOORAY!

Research suggests that tracking progress can positively influence a
student’s performance. Remember the days when you hung your
children’s drawings on the refrigerator? Recognition still goes a long way.
Post progress charts where they can be seen and acknowledged.

FIXING PROBLEMS
When teenagers are not progressing as anticipated, parents frequently jump to conclusions and think that the teenager has
done something wrong. It may appear that the teenager is lazy. In fact, he or she may just be feeling overwhelmed, confused,
and exhausted. When you become aware of problems, you may need to take a second look at the situation, looking for specific
performance obstacles.
Rather than blaming your teenager, or labeling his or her behavior as right or wrong, you might consider behavior in terms of its
being efficient or inefficient. To help you pinpoint what’s going on, you may want to ask your teenager two questions:

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• How is your study schedule working?
• Are you learning what you thought you would?
Your teen can give you the information to zero in on the specific problem. Some common problems teenagers face stem from
unrealistic goals, unsuitable materials, and inefficient organization.

Parents’
Guide to
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Admission
Testing

Applying Solutions
Usually there is more than one solution for every identified problem. Here are some common SAT® test-prep problems and a
variety of possible solutions.

Peterson’s SAT® Prep Guide 2017

Problem:
The teen seems to give up because it appears to him or her that the material is too complicated.
Solution:
 emind the teen that habits are like muscles. The first time someone goes for a run, it may seem very difficult, but
R
it gets easier each time the person does it. Incorporating regular study time for the SAT® into the day will become
easier the more the teen does it. If necessary, have the teen start small so she or he will be energized by
successes.
Problem:
Progress is slower than anticipated and there isn’t enough time left to reach the original goal.
Solutions:
Lower the expectations about the scores.
Rearrange the study schedule.
Provide more intensive instruction.
Schedule the test at a later date.
Shoot for a later college-admissions date.

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Problem:
The teenager is studying, but he or she does not remember anything the next day.
Solutions:
Change from group to individual tutoring.
Change from reading the information to listening to some of the information.
Practice aloud before doing the test exercises.
Study in a different place.
 heck that the teaching materials match the required skills. Also try to determine how the teen learns best and
C
use the information to leverage those strengths. For example, some students remember better if they write things
down by hand rather than if they type them. Other students benefit from talking out loud as they work through
the steps of a difficult concept.

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Problem:
The teenager is studying, but he or she seems to lose things and waste time.
Solution:
Give him or her information and techniques that will help him or her to become better organized.
Problem:
The teenager seems frantic and appears to be spending too much time studying.
Solution:
Provide some written material that will help him or her rank what has to be done in order of importance.
Review the goals, costs, and benefits, but keep in mind that the test is part of a larger picture.

NOTE: Keep in mind that the idea is to study more effectively, not necessarily longer.

MOTIVATING YOUR TEENAGER
Studying for the test usually isn’t fun. It is hard work and teenagers need encouragement to keep going.
Sometimes teenagers are motivated because they immediately taste success. For example, Rico studied for a chemistry test and
received an A. It is highly likely that he will study for the next test because he saw that his work paid off.
Checking on progress on the SAT® practice tests is important. Doing so gives your teenager the opportunity to realize that his or
her work does pay off and progress is being made.
Sometimes parents need to boost motivation when they see signs of fatigue or signals that their teenager is being turned off to
studying. If you are trying to find ways to encourage your teenager, consider the following:

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• Make positive statements, such as “I know you’re working hard.”
• Provide extra treats, such as a special dinner or extra use of the car.
• Leave a small, humorous gift in their room, such as a giant pencil or a silly figurine.
• Organize some special event, such as going to the movies, a concert, or out to eat with another family whose teenager
is also taking the test.

• Do some chore for your teenager so that your teen has more time to study.
Regardless of the system of rewards, remember to be positive, low-key, and avoid
negative or punishing situations. The goal is to encourage and support effective
studying, not to control your teenager. By establishing realistic goals and rewards,
you help your teenager do his or her best and show him or her that you really care.

Peterson’s SAT® Prep Guide 2017

Setting Up Rewards
Like everyone else, not all teenagers are motivated the same way. This is why it’s helpful to know as much as possible about your
teen’s personality. Some teens feel very comfortable with a lot of structure and being held accountable by a tutor, parent, or
teacher. Others are fine with a lot of structure as long as the purpose behind it makes sense to them. Highly independent teens
may perceive it as “being told what to do,” however. Challenge teens for whom choice is essential to come up with their own plan
for test preparation. These teens can be very good at “thinking outside the box” and may be more motivated by proving they can
succeed doing things their way than by any other reward.
Sometimes, you need to put into practice methodical and consistent ways to make sure that plans are followed. In other words,
you may need to make sure that certain events occur after, and only after, a task is completed. The following examples show how
you can build in rewards for work accomplished.

• Ron tends to be forgetful. For a month, he had not done the vocabulary exercises he agreed to do. He and his parents
worked out a plan so that if a certain number of exercises were completed on Tuesday and Thursday nights, he could
have the car on Fridays.

• Diana, on the other hand, did not want the car—she loved talking on the phone. Her family devised a plan that required
her to work on her writing exercises for 30 minutes, three nights a week, before she could talk on the phone.

• You can also set up a tracking system using counters such as paper clips, to record short blocks of study time—a half
hour, for example. Each counter can represent something the student can use as he or she wishes. For example, each
paper clip might represent a half hour that can be spent with friends or playing sports.

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Research also shows that linking habits—also called anchoring or stacking habits—makes a person more likely to accomplish
them. Have the student choose an activity he or she performs every day, then link a desired new habit to an existing one. For
example, if Rose takes 5 minutes every night before she brushes her teeth to be sure that she’s written out her study plan for the
next day and gathered all the materials she will need, she’s more likely to do so. The new habit, writing the study plan, is linked
to an established habit, brushing her teeth.
This final list of questions is provided to help you check on your teen’s progress and iron out problems. When plans are wellmanaged, trouble spots are easily identified and changes can usually be made without anyone feeling that he or she has failed,
especially the teenager.

Managing Your Plan: A Checklist
Is progress being checked using charts, checklists, graphs, or other means?
Do charts or graphs show any problems?
What adjustments are necessary?
Have alternative solutions been considered?
Are any additional resources or checklists necessary?
Has progress been made toward the goals?

Originally published in a slightly different form in Parent’s Guide to the SAT® & ACT® (Lawrenceville, NJ: Peterson’s, 2005), 27–133. Reprinted
by permission of the authors.

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