Quick Start Guide (fx 991EX/fx570EX)_CASIO All CASIO Fx 991EX 570EX
User Manual:
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Page Count: 48
QUICK START GUIDE
fx-991EX
http://edu.casio.com/
The fx-991EX “ClassWiz” features a high-resolution
display, making it easier to view formulas and symbols.
This remarkable screen can display between 2-6 times
as many characters as other scientic calculators, yet
still runs on solar power.
Use the W key to turn the calculator on, and press
qC(OFF) to power the unit down.
The icon-based menu, accessible via the p key,
allows easy navigation of features using the arrow keys
and the number keys or the Q shortcuts.
The o key can be used like Backspace in a word
processor to delete the character(s) left of the cursor.
The symbols printed on the keys use Natural Textbook
Display™ notation, similar to that found in textbooks.
This makes input of expressions fast and easy.
The n key toggles your calculation results between
Standard (exact) and Decimal forms.
fx-991EX Quick Start Guide2
Icon Menu Name Description
CALCULATE Perform general computations using Natural Textbook Display™ notation, including
absolute value, logs of any base, summation, derivatives, and integrals.
COMPLEX Perform computations with complex numbers, including a + bi form, polar ( )
form, and conversions between the two.
BASE-N Perform binary, octal, and hexadecimal computations, and convert among those number
bases and base-10.
MATRIX Perform operations on matrices up to 4x4, including matrix arithmetic,
determinants, transpositions, and identity matrices.
VECTOR Perform operations on 2- and 3-dimensional vectors, including vector
arithmetic, dot products, angles, and unit vectors.
STATISTICS Calculate 13 different one-variable statistics, and apply linear, quadratic,
logarithmic, exponential, and geometric (power) regressions.
DISTRIBUTION Investigate Normal, Inverse Normal, Binomial, and Poisson probability and
cumulative distributions.
SPREADSHEET Create spreadsheets with up to 5 columns and 45 rows. Spreadsheet
supports Fill, Cut/Copy/Paste, recursive formulas, Mean, and Sum commands.
TABLE Create tables of values to compare up to 2 functions simultaneously.
EQUATION/
FUNCTION
Solve simultaneous (systems of) equations with up to 4 unknowns, and
polynomials of up to degree 4.
INEQUALITY Solve polynomial inequalities of up to degree 4, with the solution set expressed as
a compound inequality.
RATIO Solve proportions of the form A : B = X : D and A : B = C : X.
The following explains the meaning of each icon on the fx-991EX icon menu
fx-991EX Quick Start Guide 3
Below are some examples of the Natural Textbook Display™ input/output notation, as found by selecting the Calculate
icon from the Main Menu of the fx-991EX.
From the Main Menu, use the arrow keys to
highlight the Calculate icon, then press =
or press 1.
Fractions and mixed numbers can be entered using
a and qaA, respectively.
To enter the calculation to the left, press
a7$8$+qaA2$3$
11p.
To change the solution to a decimal format,
press n.
Press qnN to convert the result into
a mixed-number format.
When inputting radical expressions, the radical bar
automatically extends as additional characters are typed.
Press s24=.
The output will be displayed in simplest radical form, but can
be converted into a decimal approximation by pressing n.
CALCULATE
fx-991EX Quick Start Guide4
ClassWiz is capable of recognizing and combining like radicals.
Press s24$+s150=.
It can also calculate unlike radicals. Press
s24$-s98=.
Higher-order radicals can be beautifully expressed using
Natural Textbook Display™ input.
Press q^F5$64=.
Natural Textbook Display™ templates can be stacked
inside one another to allow input of complicated
expressions such as this quotient of rational exponentials.
Press a3^a1$2$$$3^-
2=.
In a trigonometry setting, arithmetic can be performed in
terms of π. Press a3qKC$4$+
2qKC=.
Other useful Natural Textbook Display™ templates that help
overcome typical calculator input frustrations include:
logarithms of any base,
ia1$2$$16=
(Note: the calculator does not generate a Syntax Error when the - key is used to create
a negative sign. Both - and z are acceptable for use.)
CALCULATE
fx-991EX Quick Start Guide 5
...summation (sigma) notation,
qxIxd+1$-3$7=
…derivatives of a function at a specic point (value),
qyY4xd-5x$0.2=
…and denite integrals.
ya1$x$$2$5=.
Settings for the “Calculate” mode can be accessed by pressing
qp(SET UP).
Press R one or more times to reveal additional Setup options.
Solve x2 + Ax + Bx = 0 for x when A = 5 and B = 6.
Enter the equation by pressing, xd+Qz(A)
x+Qx(B) Qr(=)0.
SOLVE
The fx-991EX can elegantly solve an equation for any unknown using Newton’s method with the SOLVE command. To
use SOLVE, rst input the equation to be solved, then press qr(SOLVE).
CALCULATE
fx-991EX Quick Start Guide6
Input an initial guess for x followed by the values of A and B.
Pressqr(SOLVE) -5p5p6p.
Arrow back up to x= and SOLVE the equation by
pressing p.
To accomplish the same task and solve for A or B, enter a
value for x and a value for one of the other unknowns.
For example, to solve for A when x = 1 and B = 4, press
qr(SOLVE)1p2p4p.
Arrow back up to A= and SOLVE the equation by
pressing p.
The solution also displays L – R = 0. This means that
Newton’s method of approximation is directly on -5. If L – R
is not 0, simply recalculate to get a better approximation.
CALCULATE
fx-991EX Quick Start Guide 7
ENGINEERING CALCULATIONS
There are many menus in the fx-991EX that can handle engineering calculations. The fx-991EX has the power to
handle vectors, matrices, complex numbers and numerically calculates
summation and even denite integrals.
From the Main Menu, use the arrow keys to highlight the
Calculate icon and press p or press 1.
There are many different types of unit conversions that can
be accomplished on this menu. To view the options, press
q8(CONV). Use the down arrow key (R) to see all the
possibilities.
Each one of the choices has a wide range of conversion options
for many different types of unit conversion.
Use the arrow keys to locate the Length conversion and press
1.
To convert 500 inches (in) into centimeters (cm), press C to
return to the initial Calculate screen.
Press 500q8(CONV)1(Length)
1(in : cm)p.
CALCULATE
fx-991EX Quick Start Guide8
To find the difference between one US Gallon and one UK
Gallon, first, convert to a common unit, like a liter (L).
Press 1q8(CONV)3(Volume)
1(gal(US) : L)p.
One US gallon is approximately 3.785 L.
Now, convert the solution to gallons UK.
Press q8(CONV)3(Volume)4
(L : gal(UK))p.
It looks like a US gallon is smaller.
1 US gallon = 0.8326742321 UK gallons.
The same calculation can be accomplished using a
string of conversions.
Press 1q8(CONV)3(Volume)
1(gal(US) : L)q8(CONV)
3(Volume)4(L: gal(UK))p.
Start with a large number like 2.5 X 109.
Press 2.5K9p.
The gap between digits at place value separation can be viewed
by entering Set Up. Press qp(SET UP) and use the arrow
keys to navigate to the third menu.
ENGINEERING NOTATION
Converting large numbers into scientic and engineering notations
can be accomplished through a short series of keystrokes.
CALCULATE
fx-991EX Quick Start Guide 9
Press 4(Digit Separator)1(On) to turn on the Digit Separator
to show separation between place values.
Press p to recalculate the result and display clear place value
separation.
To convert this solution into engineering notation, use the b
key to change the solution into scientic notation. To move the
decimal to the right, press b.
To turn on the engineering symbols in setup, press
qw(SET UP).
Select 4(Engineer Symbol)1(On) to turn on the
Engineering Symbols.
Calculating with engineering symbols has never been easier.
To move the decimal to the left, press qbX.
CALCULATE
fx-991EX Quick Start Guide10
To calculate 500k (kilo) + 10M (Mega), press
500i3(Engineering Symbols)
6(k)+10i3(Engineering Symbols)
7(M)p.
The solution is displayed using the appropriate units.
Now, use the b key to convert between units.
CALCULATE
fx-991EX Quick Start Guide 11
Complex Number calculations can be executed in the Complex Mode.
From the Main Menu, use the arrow keys to highlight the
Complex icon, then press p or press 2.
In Complex Mode, operations can be carried out using
the imaginary unit U. To add complex numbers, press
2+3bU+5-7bUp.
Complex numbers that are multiplied are displayed in
complex format. Press (3-2bU)
(5+6bU)p.
The argument of the complex number 1+2i, can be found by
taking the arctan (y/x) = 63.4349° or by using the Argument
command.
Press i1(Argument)1+2bU)p.
COMPLEX
fx-991EX Quick Start Guide12
COMPLEX FORM AND POLAR FORM
To convert a complex number into polar form, press
2+5bUiR1(: r∠q)p.
To convert any polar form of a complex number, use the r theta
command or type in the angle in polar form.
Press C2qbZ330iR
2(: a+bi)p.
Alternately, simply type in the angle in polar form by pressing
2qbZ330p.
These calculations can also be accomplished in radian mode.
To change to radian mode, press qp(SET UP)2(Angle
Unit)2(Radian).
COMPLEX
fx-991EX Quick Start Guide 13
Operations with matrices and matrix related calculations are all located in the Matrix Menu.
From the Main Menu, use the arrow keys to highlight the Matrix
icon and press p or press 4.
To enter matrices, rst, dene the matrix.
Press 1(MatA)2(Rows)2(Columns)
1p2pz3p4p.
To enter a second matrix, press i.
From the resulting popup window, press 1(Dene
Matrix)2(MatB).
Select the number of rows, 2(Rows).
Select the number of columns, 2(Columns).
MATRIX
fx-991EX Quick Start Guide14
Enter the matrix values by pressing
3pz6p8p2p.
To perform matrix calculations, like addition, subtraction, and
multiplication, follow these simple commands.
To recall the name of a matrix, press i.
To add A + B, press 3(MatA)+i4(MatB)p.
The solution matrix is displayed in the window and can be viewed
without scrolling.
To calculate the determinant of the matrix, press
iR2(Determinant) i3(MatA))p.
Matrices can be used to solve a system of equations.
Take the following equation with 3 unknowns:
Enter the coefcient matrix as Matrix A and the solution matrix as Matrix B.
MATRIX
To enter Matrix calculation, press C.
fx-991EX Quick Start Guide 15
Redene the matricies by pressing i1
(Dene Matrix).
Press 1(MatA) to dene Matrix A and enter the
3 x 3 coefcient matrix.
Select the number of rows, 3(Rows).
Select the number of columns, 3(Columns).
Enter the values of the coefcients, pressing p after
each one to move to the next value.
Now, enter the 3 x 1 solution matrix as Matrix B.
Press i1(Dene Matrix).
Dene Matrix B 2(MatB) as a 3 x 1, so select 3(Rows)
and 1(Columns) from the next two windows.
MATRIX
fx-991EX Quick Start Guide16
Enter the values of the coefcients, pressing p after each
one to move to the next value.
Press C to return to the Matrix Calculation screen.
The solution can be found by calculating A-1 x B.
Press i3(MatA)uOi4(MatB)p.
The solution represents the following:
This same system can also be solved using the Equation icon.
MATRIX
fx-991EX Quick Start Guide 17
The fx-991EX is capable of handling vector calculations with vectors in 2 or 3 dimensions.
From the Main Menu, use the arrow keys to highlight the
Vector icon and press p or press 5.
Let vectors u and v be dened in the 3-dimensional plane by the
following: u = 2i + 3j – 2k and v = 3i - 4j + 5k
Dene u as Vector A with dimension 3.
Press 1(VctA)3(Dimension).
Enter the components of the vector and press p after each one
to move to the next value.
Dene v as Vector B with dimension 3.
Press i1(Dene Vector).
Press 2(VctB)3(Dimension).
VECTOR
fx-991EX Quick Start Guide18
Enter the components of the vector and press p after each
one to move to the next value.
To execute basic vector operations, press C to enter
Vector calculation.
Recall the names of the vectors and execute the desired
operation by pressing i.
Vector addition, subtractions, and multiplication are all available.
For subtraction, press 3(VctA)-i4(VctB)p.
For multiplication, press
i3(VctA)Oi4(VctB)p.
The sums of the product of the components of a vector
are known as the vector’s dot product. So,
.
Press i3(VctA)iR2(Dot Product)i4(VctB)
p.
VECTOR
fx-991EX Quick Start Guide 19
Even some very complex vector operations like the angle between vectors, which is dened as in
which are easily accomplished on the fx-991EX.
To calculate vector cross product (not vector multiplication),
press iR3(Angle)i3(VctA)q)(,)i
4(VctB))p.
VECTOR
fx-991EX Quick Start Guide20
The fx-991EX can calculate several one-variable statistics, and also analyze relationships between two data sets
using various regression models.
From the Main Menu, use the arrow keys to highlight the
Statistics icon, then press p or press 6.
On the resulting menu, select 1 for “1-Variable” statistics.
A data entry screen appears.
This example uses the following list of some students’ heights,
given in inches: 70.5, 74, 67, 71, 71, 72, 73.5, 72, 69, 71.
Enter data by typing in each value one at a time, with each
followed by the p key.
70.5p, 74p, etc.
To calculate the 1-Variable statistics for this data set,
press i3(1-Variable Calc).
STATISTICS
fx-991EX Quick Start Guide 21
Press C to return to the data entry screen.
Enter the Option menu by pressing i.
Select item 4(Statistics Calc) to enter the Statistics
calculation area.
Press i, and then the down arrow (R) once to reveal the
different categories of statistical variables.
For instance, to calculate the interquartile range (IQR), press
3(Min/Max)4(Q3)-iR3(Min/Max)2(Q1)p.
13 different 1-variable statistics have been calculated, 6 of which appear on the rst screen. Press R one or more
times to reveal additional statistics:
These statistics have each been stored inside the fx-991EX as variables, in case you should wish to use them in
further calculations.
STATISTICS
fx-991EX Quick Start Guide22
FREQUENCY TABLES
If the data comes from a frequency table, ClassWiz can be set up to input the data values in one column, and the
frequencies in another.
To access the set-up menu, press qp(SET UP).
Press the down arrow (R) to reach the second page and 3
to select the Statistics settings.
Press 1 to turn the Frequency option On.
The Statistics Calculation area appears again. Even though
nothing appears to have happened, the setting has indeed
changed.
To access the Data entry area, press i3(Data).
Notice a second column for frequencies now appears and
the previous data set has been erased.
STATISTICS
fx-991EX Quick Start Guide 23
To calculate a linear regression, press
i i1(Select Type).
Select option 2(y=a+bx).
A reminder that changing the type of statistics will clear previous
data appears.
Press p to conrm and Clear memory.
(Notice, the statistics are identical to those previously found.)
Enter the same 10 students’ height used previously making
use of the Frequency column. As each data point is inputted,
ClassWiz automatically assigns a default Frequency of 1. Edit a
Frequency by using the arrow keys to highlight it, then typing a
new Frequency followed by p.
Once all of the data points (x) and frequencies (Freq) have been
entered, press i3(1-Variable Calc) again to display the
1-Variable statistics.
REGRESSIONS
STATISTICS
fx-991EX Quick Start Guide24
The 2-Variable statistics display calculation results for both x and y:
Two columns for pairwise data (ordered pairs) now appears.
Note, the Frequency (Freq) column still appears; press
qp(SET UP)R3(Statistics)2(Off)
to remove it.
Input the ordered pairs (1, 1), (2, 4), (3, 9), and (4, 16). Use the
arrow keys to navigate to the “y” column as necessary.
To view 2-Variable statistics or the linear regression results,
press i3.
Other regressions, including quadratic, logarithmic, exponential,
and geometric, can be accessed via i1(Select Type).
Press Ci4(Regression Calc) to display the linear
regression results.
STATISTICS
fx-991EX Quick Start Guide 25
The fx-991EX can quickly generate probability distribution tables, covering the Normal, Inverse Normal, Binomial, and
Poisson distributions.
From the Main Menu, use the arrow keys to highlight the
Distribution icon, then press por press 7.
Select 1(Binomial CD) from the second page to analyze the
following Binomial Distribution problem: “A fair 6-sided die is
rolled six times. Find P(6 comes up at least twice).”
After pressing p to input the value of p, ClassWiz
automatically converts the fraction into a decimal for its
own purposes.
Press p again to calculate the probability.
To enter the values of x (number of successes), N (number of
trials), and p (probability of success), press 2(Variable). Input
the values as shown, using a to create the fraction separator.
Several distribution choices appear. Use R to access the second page.
DISTRIBUTION
fx-991EX Quick Start Guide26
A probability of 73.7% is displayed.
Because x = 1 was entered, the calculator calculated P(≤ 1 six is
rolled). This provides a great opportunity to use the complement
of an event: P = 1 – 0.737 = 0.263 = 26.3%.
To display the probabilities of obtaining any number of sixes in 6
rolls, press i1(Select Type).
This time, choose 4(Binomial PD).
Once the nal value has been entered, press p again to end
the data entry process.
Notice, the values of N and p are preserved from the cumulative
probability calculation.(N and p are global calculator variables.)
Enter the values 0, 1, 2, 3, 4, 5, and 6 into the “x” column (which
represents number of successes). Press p after each input.
Because the calculation is for probabilities for several different
numbers of successes, select 1(List).
DISTRIBUTION
fx-991EX Quick Start Guide 27
Press p one more time to calculate the probability
distribution table.
Notice how the small probabilities are expressed in proper
scientic notation!
INVERSE NORMAL
To calculate an Inverse Normal Distribution, press
i1(Select Type).
(“Editor” edits the previous PD’s data list.)
Select 3(Inverse Normal).
Input the values as shown to answer the question: “If the heights
of U.S. males are normally distributed with a mean of 70 inches
and a standard deviation of 4 inches, what range denes the
tallest 10% of U.S. males?”
Press p once more to reveal the result. To be in the top 10%
of U.S. males by height, a man must be over 75 inches (6’3”) tall.
DISTRIBUTION
fx-991EX Quick Start Guide28
From the Main Menu, use the arrow keys to highlight the
Spreadsheet icon, then press por press 8.
The ClassWiz spreadsheet looks and acts similarly to many
popular software spreadsheet applications.
Investigate the mass of different common sizes of laundry
detergent bottles, when the average density of liquid laundry
detergent is 0.885 g/mL. Type 0.885p in
cell A1.
Use the arrow keys to move over to cell B1, and input
40p to represent a 40 fl oz. (1 fl oz. = 29.5735 mL)
bottle of laundry detergent.
Move to cell C1, and press Qr(=) to create an equals
sign. Like in other spreadsheet programs, this is the rst step
necessary when entering a formula.
To “grab” the value within a cell, press i2(Grab).
The Spreadsheet mode is useful for studying the statistics of data that require more than two lists. It also supports
recursive formulas, sequences, and series.
SPREADSHEET
fx-991EX Quick Start Guide 29
Navigate to cell B1, and press p (Set) to Grab the value in that
cell.
This places a reference to cell B1 within the formula.
To create a conversion from uid ounces ( oz.) to milliliters (mL),
type O29.5735p.
The formula has correctly calculated that a 40 oz. bottle of
laundry detergent has a volume of 1182.9 mL.
Formulas can also be typed directly, without using the Grab
command.
Navigate to cell D1 and input Qr(=)
Qz(A)1OQu(C)1p.
A 40 fl oz. (1182.9 mL) bottle of laundry detergent
has a mass of 1046.9 grams.
Now, let’s use the power of relational formulas to check some
other bottle sizes:
To populate many different cells with the same value, press
i2(Fill Value).
SPREADSHEET
fx-991EX Quick Start Guide30
Input the density of laundry detergent as the Value and
A2:A6 as the cell Range. Press Qz(A)2Qy(:)
Qz(A)6pp.
Column A is now lled with the density value.
Next populate column B with additional bottle sizes.
Navigate to cell B2, and input the value 75 by pressing
75p.
To populate many different cells with the same formula,
press i1(Fill Formula).
Input the formula Qx(B)2+25p.
Notice, the cell Range is pre-populated with the currently
highlighted cell (B3).
Use the right arrow to edit only the end cell by pressing
$$$$$$o6pp.
Scroll down to cell B6 to make sure that the formula has been
adjusted relative to each cell’s position, so that cells B2 to B6 now
display bottle sizes from 75 to 175 fl oz. (1 fl oz. = 29.5735 mL).
SPREADSHEET
fx-991EX Quick Start Guide 31
Navigate to cell C1, which still displays the formula used to
convert uid ounces to milliliters.
The ClassWiz has a “copy and paste” option that can be used
instead of retyping the same formula repeatedly.
Press iR2(Copy & Paste).
The formula from the currently highlighted cell (C1) has now
been copied.
Scroll down one cell at a time (Rp) to Paste this formula
into cells C2 through C6.
Column C now contains the volumes, in milliliters, of the different
sizes of laundry detergent bottles.
To exit Copy & Paste mode, press C.
Time to practice! Use the same technique to Copy & Paste the
mass calculation formula from cell D1 into cells D2 through D6.
If done correctly, Column D should show masses (in grams) as
shown.
So, for example, a 175 fl oz. (5175.3 mL) bottle of laundry
detergent has a mass of about 4.5 kg.
A decent amount of data has been entered now. To check
how much free space remains in ClassWiz’s memory, press
i4(Free Space).
SPREADSHEET
fx-991EX Quick Start Guide32
1318 Bytes of memory remain as free space.
Numerical values require 10 Bytes each, while formulas require
17+ Bytes each.
Determine the average capacity of the different bottles of laundry
detergent.
Navigate to cell B7, and press i.
Scroll down three pages (RRR), and select 3(Mean).
Type in the cell range of the average Qx(B)1Qy(:)
Qx(B)6)p.
The average capacity is 110.83 uid ounces.
If one of each of these bottles was purchased, what is the total
weight of laundry detergent purchased that would be placed in
a car?
Navigate to cell D7, and press i.
Return again to the summary statistics calculation screen
(RRR) and select 4(Sum).
SPREADSHEET
fx-991EX Quick Start Guide 33
Use the Grab command rather than typing the locations of the
cells in the cell range.
Press i2(Grab).
Scroll up to cell D1, and Set it as the object to be Grabbed by
pressing p.
Use Qy(:) to type a colon.
Grab cell D6 as the ending cell in the cell range by pressing
i2Ep.
Close the parentheses ()), and press p to calculate the sum
of the masses in cells D1 through D6.
The bottles would have a total mass of 17404 grams, or about
17.4 kilograms.
But this is a mass, not a weight!
SPREADSHEET
fx-991EX Quick Start Guide34
This is one example of the powerful ways in which various
features of the fx-991EX can be combined.
Begin entering the formula as shown into cell D8 by pressing
Qr(=)Qj(D)7.
Press q8(CONV) to access the Conversion menu.
Select 4(Mass).
Choose mass conversion 4(kg:lb).
This will convert the mass from cell D7, which is currently in
kilograms, into pounds.
Press p, and Voila!
Even ClassWiz’s powerful Conversion feature can be used within
the Spreadsheet module. But wait… 38 thousand pounds?!?
17404 grams needs to be converted into kilograms.
With cell D8 highlighted, press i3(Edit Cell).
A cursor appears in the previously entered formula, allowing it to
be edited.
SPREADSHEET
fx-991EX Quick Start Guide 35
Use the right arrow key ($) to move within the formula,
inserting parentheses and a factor-of-1000 adjustment as
shown. Press $($$P1000)p.
Phew! That’s better. The car is no longer carrying 19+ tons of
laundry detergent home. The actual total weight is a much more
reasonable 38 pounds.
SPREADSHEET
fx-991EX Quick Start Guide36
The function that represents the volume of the box is
f(x)= x(20-x)(15-x).
To enter this function, press x(20-x)
(15-x)p.
From the Main Menu, use the arrow keys to highlight the Table
icon and press p or press 9.
To change the setup of the table to generate a table with only one
function, press qp(SET UP).
Use the down arrow key to view the menu option for Table; it
will be the 3rd screen.
Press 2(Table) to choose the number of functions used in
the table.
Press 1(f(x)) to generate a table with only one function as
an input.
The Table feature on the fx-991EX is a powerful way to solve a single function or two functions simultaneously.
The table range and step is easily customizable.
Consider the classic volume of a box problem. What is the maximum volume of a box made from a 20x15 sheet of
cardboard by removing squares from each corner?
TABLE
fx-991EX Quick Start Guide 37
To set the range from 1 to 7 and the step at 1, press
1p7p1p.
Press p to view the table.
Use the arrow keys to scroll through the values.
The maximum value appears to be between 5 and 6.
To rene the search, enter a new value in any place in the table.
For example, at line 8, press 6.5p.
To enter a value one-step greater than the previous value,
press +.
To enter a value one-step less than the previous value,
press -.
To change the step value or change the start and end values of
the table, press Cp.
Enter the new values and press p to view the table.
Use the arrow keys to scroll to the value that gives the
maximum volume.
TABLE
fx-991EX Quick Start Guide38
The maximum volume calculated to one decimal place appears
at 5.7 inches.
Consider the following two functions .
Find the roots of the equations and points of intersection, as well as
the end behavior of each function.
Press qp(SET UP) and use the down arrow key to view
the menu option for Table. Press 2(Table) to choose the
number of functions used in the table.
Press 2(f(x),g(x)) to generate a table with two function as
inputs.
Enter the rst function as f(x) by pressing x^3$-
7x+6p.
If there is already a function present, press C
to clear the previous function.
Enter the second function as g(x) by pressing xd-
3x+2p.
Create a table that has a domain of -5 to 5 with step of 1.
TABLE
fx-991EX Quick Start Guide 39
Press p to view the table.
Based on the information from the table, it appears f(x) goes to
negative innity to the left and g(x) goes to positive innity to the
left.
There appears to be roots of 1 and 2 for both functions.
To determine the behavior between roots, type in a number
between 1 and 2, like 1.5.
The right end behavior for both functions appears to be
increasing towards positive innity.
TABLE
fx-991EX Quick Start Guide40
The fx-991EX numerically solves equations elegantly. It is accomplished with the help of the Natural Textbook
Display™ in the Equation/Func mode. The Equation/Func mode uses Newton’s method to nd solutions to equations.
The fx-991EX has the power to handle Simultaneous Equations with up to 4 unknowns and Polynomial Equations up
to the 4th degree.
SIMULTANEOUS EQUATIONS
From the Main Menu, use the arrow keys to highlight the
Equation/Func icon and press p or press z(A).
To solve the following system of simultaneous equations
,
select 1(Simul Equation).
Choose the number of Unknowns. For this example,
press 2(Unknowns).
A 2x2 system of equations template is displayed. The template is
in Ax + BY = C form in which A, B and C can be any value. For
fractional values, use the a key.
Type in each value followed by the p key.
Press 2p1p, etc.
EQUATION/FUNC
fx-991EX Quick Start Guide 41
To solve, press p and use the arrow keys (RE) to toggle
between solutions.
The solutions are shown in natural display format. For decimal
approximations, press n.
To change the values in the system of equations without
changing the type of equation or system, press C.
The fx-991EX also solves inconsistent systems, both
independent and dependent. Enter the displayed inconsistent
and independent system
Press p to see the solution.
To change the type of equation or system size, press i and select from the on-screen menus.
EQUATION/FUNC
fx-991EX Quick Start Guide42
Enter the displayed inconsistent dependent system.
Press p to see the solution.
To input a larger system of simultaneous equation
,
press i1(Simul Equation)3(Unknowns).
Enter the coefcents for each equation and press p to solve.
EQUATION/FUNC
fx-991EX Quick Start Guide 43
POLYNOMIAL EQUATIONS
The fx-991EX has the computing power to solve polynomial equations up to 4th degree.
To start solving polynomial equations, in the Equation/Func icon,
press i2(Polynomial).
Select the degree of the polynomial. For this example, use a
3rd degree polynomial. Press 3(Degree).
Fill out the template for a 3rd degree polynomial. Type in each
coefcient followed by the p key.
x3 + 4x2 +x – 6 = 0
Press p to solve the equation.
Use the arrow keys (ER) to toggle through the solutions.
EQUATION/FUNC
fx-991EX Quick Start Guide44
The fx-991EX has the power to solve polynomials in the complex plane.
Press i and change the type of polynomial to
quadratic (2).
Enter the coefcients that appear in the displayed screen into
the quadratic template, and press p.
The solutions are displayed in simplied radical form including
the imaginary unit.
Press R to see the second imaginary solution.
EQUATION/FUNC
fx-991EX Quick Start Guide 45
Solving polynomial inequalities has never been easier.
From the Main Menu, use the arrow keys to highlight the
Inequality icon and press por press x(B).
Enter the degree of the polynomial inequality, in this case,
3(Degree).
Choose the form of the inequality. Press 2
( ).
Enter the coefcients of the polynomial, as shown.
Press 1p4p1pz6p.
Press p to see the solutions.
Notice, the form of the inequality is written
as x < a, b < x < c.
If the solution runs off the screen, use the left and right (!$)
arrow keys to see the entire solution.
INEQUALITY
fx-991EX Quick Start Guide46
NOTES
fx-991EX Quick Start Guide 47
NOTES
fx-991EX Quick Start Guide
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