Casio Fx 9860Gii Users Manual 9860G Series_fx 9750GII_fx 7400GII_Software Ver. 2.0_Eng
Fx-9750Gii-Soft-E fx-9750gii-soft-e
Fx-7400Gii-Soft-E fx-7400gii-soft-e
User manual fx-7400GII_Soft_E Casio fx-7400GII Calculator User Manuals and Instruction Guides
User manual fx-9750GII_Soft_E Casio fx-9750GII Calculator User Manuals and Instruction Guides
FX-9860GII to the manual 1d51299d-d3aa-4094-a793-8b05f7e7ac00
2015-01-21
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E
fx-9860GII SD
fx-9860GII
fx-9860G AU PLUS
fx-9860G SD (Updated to OS 2.0)
fx-9860G (Updated to OS 2.0)
fx-9860G AU (Updated to OS 2.0)
fx-9750G
fx-7400G
Software Version 2.0
User’s Guide
CASIO Worldwide Education Website
http://edu.casio.com
CASIO EDUCATIONAL FORUM
http://edu.casio.com/forum/
• The contents of this user’s guide are subject to change without notice.
• No part of this user’s guide may be reproduced in any form without the express written
consent of the manufacturer.
• The options described in Chapter 13 of this user’s guide may not be available in certain
geographic areas. For full details on availability in your area, contact your nearest CASIO
dealer or distributor.
• Be sure to keep all user documentation handy for future reference.
i
Contents
Getting Acquainted — Read This First!
Chapter 1 Basic Operation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Keys .............................................................................................................................. 1-1
Display .......................................................................................................................... 1-2
Inputting and Editing Calculations................................................................................. 1-5
Using the Math Input/Output Mode ............................................................................. 1-10
Option (OPTN) Menu .................................................................................................. 1-22
Variable Data (VARS) Menu ....................................................................................... 1-23
Program (PRGM) Menu ............................................................................................. 1-25
Using the Setup Screen .............................................................................................. 1-26
Using Screen Capture................................................................................................. 1-29
When you keep having problems… ........................................................................... 1-30
Chapter 2 Manual Calculations
1.
2.
3.
4.
5.
6.
7.
8.
9.
Basic Calculations......................................................................................................... 2-1
Special Functions.......................................................................................................... 2-6
Specifying the Angle Unit and Display Format............................................................ 2-10
Function Calculations.................................................................................................. 2-11
Numerical Calculations ............................................................................................... 2-21
Complex Number Calculations.................................................................................... 2-30
Binary, Octal, Decimal, and Hexadecimal Calculations with Integers......................... 2-33
Matrix Calculations...................................................................................................... 2-36
Mertic Conversion Calculations................................................................................... 2-48
Chapter 3 List Function
1.
2.
3.
4.
Inputting and Editing a List............................................................................................ 3-1
Manipulating List Data................................................................................................... 3-5
Arithmetic Calculations Using Lists ............................................................................. 3-10
Switching Between List Files....................................................................................... 3-13
Chapter 4 Equation Calculations
1. Simultaneous Linear Equations .................................................................................... 4-1
2. High-order Equations from 2nd to 6th Degree .............................................................. 4-2
3. Solve Calculations......................................................................................................... 4-4
Chapter 5 Graphing
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Sample Graphs ............................................................................................................. 5-1
Controlling What Appears on a Graph Screen.............................................................. 5-2
Drawing a Graph ........................................................................................................... 5-6
Storing a Graph in Picture Memory............................................................................. 5-10
Drawing Two Graphs on the Same Screen................................................................. 5-11
Manual Graphing......................................................................................................... 5-12
Using Tables ............................................................................................................... 5-15
Dynamic Graphing ...................................................................................................... 5-20
Graphing a Recursion Formula ................................................................................... 5-22
Graphing a Conic Section ........................................................................................... 5-27
Changing the Appearance of a Graph ........................................................................ 5-27
Function Analysis ........................................................................................................ 5-29
ii
Chapter 6 Statistical Graphs and Calculations
1.
2.
3.
4.
5.
6.
7.
8.
9.
Before Performing Statistical Calculations .................................................................... 6-1
Calculating and Graphing Single-Variable Statistical Data ........................................... 6-4
Calculating and Graphing Paired-Variable Statistical Data ........................................... 6-9
Performing Statistical Calculations.............................................................................. 6-15
Tests ........................................................................................................................... 6-22
Confidence Interval ..................................................................................................... 6-35
Distribution .................................................................................................................. 6-38
Input and Output Terms of Tests, Confidence Interval, and Distribution .................... 6-50
Statistic Formula ......................................................................................................... 6-53
Chapter 7 Financial Calculation (TVM)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Before Performing Financial Calculations ..................................................................... 7-1
Simple Interest .............................................................................................................. 7-2
Compound Interest........................................................................................................ 7-3
Cash Flow (Investment Appraisal) ................................................................................ 7-5
Amortization .................................................................................................................. 7-7
Interest Rate Conversion .............................................................................................. 7-9
Cost, Selling Price, Margin .......................................................................................... 7-10
Day/Date Calculations................................................................................................. 7-11
Depreciation ................................................................................................................ 7-12
Bond Calculations ....................................................................................................... 7-14
Financial Calculations Using Functions ...................................................................... 7-16
Chapter 8 Programming
1.
2.
3.
4.
5.
6.
7.
8.
Basic Programming Steps............................................................................................. 8-1
PRGM Mode Function Keys.......................................................................................... 8-2
Editing Program Contents ............................................................................................. 8-3
File Management .......................................................................................................... 8-5
Command Reference .................................................................................................... 8-7
Using Calculator Functions in Programs ..................................................................... 8-21
PRGM Mode Command List ....................................................................................... 8-37
Program Library .......................................................................................................... 8-42
Chapter 9 Spreadsheet
1.
2.
3.
4.
Spreadsheet Basics and the Function Menu ................................................................ 9-1
Basic Spreadsheet Operations ..................................................................................... 9-2
Using Special S • SHT Mode Commands .................................................................... 9-14
Drawing Statistical Graphs, and Performing Statistical and Regression
Calculations................................................................................................................. 9-15
5. S • SHT Mode Memory ................................................................................................ 9-20
Chapter 10 eActivity
1.
2.
3.
4.
eActivity Overview ....................................................................................................... 10-1
eActivity Function Menus ............................................................................................ 10-2
eActivity File Operations ............................................................................................. 10-3
Inputting and Editing Data ........................................................................................... 10-4
Chapter 11 Memory Manager
1. Using the Memory Manager ........................................................................................ 11-1
iii
Chapter 12 System Manager
1. Using the System Manager ......................................................................................... 12-1
2. System Settings .......................................................................................................... 12-1
Chapter 13 Data Communications
1.
2.
3.
4.
5.
Connecting Two Units ................................................................................................. 13-1
Connecting the Calculator to a Personal Computer .................................................... 13-1
Performing a Data Communication Operation ............................................................ 13-2
Data Communications Precautions ............................................................................. 13-5
Screen Image Send .................................................................................................. 13-11
Chapter 14 Using SD Cards (fx-9860GⅡ SD only)
1. Using an SD Card ....................................................................................................... 14-1
2. Formatting an SD Card ............................................................................................... 14-3
3. SD Card Precautions during Use ................................................................................ 14-3
Appendix
1. Error Message Table ....................................................................................................A-1
2. Input Ranges ................................................................................................................A-5
E-CON2 Application
1
2
3
4
5
6
7
8
9
10
11
12
E-CON2 Overview
Using the Setup Wizard
Using Advanced Setup
Using a Custom Probe
Using the MULTIMETER Mode
Using Setup Memory
Using Program Converter
Starting a Sampling Operation
Using Sample Data Memory
Using the Graph Analysis Tools to Graph Data
Graph Analysis Tool Graph Screen Operations
Calling E-CON2 Functions from an eActivity
iv
Getting Acquainted — Read This First!
I About this User’s Guide
S Model-specific Function and Screen Differences
This User’s Guide covers multiple different calculator models. Note that some of the functions
described here may not be available on all of the models covered by this User’s Guide. All of
the screen shots in this User’s Guide show the fx-9860Gɉ SD screen, and the appearance of
the screens of other models may be slightly different.
S Math natural input and display
Under its initial default settings, the fx-9860Gɉ SD, fx-9860Gɉ, or fx-9860G AU PLUS
is set up to use the “Math input/output mode”, which enables natural input and display of
math expressions. This means you can input fractions, square roots, differentials, and other
expressions just as they are written. In the “Math input/output mode”, most calculation results
also are displayed using natural display.
You also can select a “Linear input/output mode” if you like, for input and display of
calculation expressions in a single line. The initial default setting of the fx-9860Gɉ SD, fx9860Gɉ, and fx-9860G AU PLUS input/output mode is the Math input/output mode.
The examples shown in this User’s Guide are mainly presented using the Linear input/output
mode. Note the following points if you are using an fx-9860Gɉ SD, fx-9860Gɉ, or fx-9860G
AU PLUS.
• For information about switching between the Math input/output mode and Linear input/
output mode, see the explanation of the “Input/Output” mode setting under “Using the Setup
Screen” (page 1-26).
• For information about input and display using the Math input/output mode, see “Using the
Math Input/Output Mode” (page 1-10).
S For owners of models not equipped with a Math input/output mode
(fx-7400Gɉ, fx-9750Gɉ)...
The fx-7400Gɉ and fx-9750Gɉ do not include a Math input/output mode. When performing
the calculations in this manual on these models, use the linear input mode.
fx-7400Gɉ and fx-9750Gɉ owners should ignore all explanations in this manual concerned
with the Math input/output mode.
S V()
The above indicates you should press and then V, which will input a symbol. All
multiple-key input operations are indicated like this. Key cap markings are shown, followed by
the input character or command in parentheses.
S K EQUA
This indicates you should first press K, use the cursor keys (D, A, B, C) to select
the EQUA mode, and then press U. Operations you need to perform to enter a mode from
the Main Menu are indicated like this.
S Function Keys and Menus
• Many of the operations performed by this calculator can be executed by pressing function
keys through . The operation assigned to each function key changes according to
v
0
the mode the calculator is in, and current operation assignments are indicated by function
menus that appear at the bottom of the display.
• This User’s Guide shows the current operation assigned to a function key in parentheses
following the key cap for that key. (Comp), for example, indicates that pressing
selects {Comp}, which is also indicated in the function menu.
• When (E) is indicated in the function menu for key , it means that pressing displays
the next page or previous page of menu options.
S Menu Titles
• Menu titles in this User’s Guide include the key operation required to display the menu
being explained. The key operation for a menu that is displayed by pressing * and then
{LIST} would be shown as: [OPTN]-[LIST].
• (E) key operations to change to another menu page are not shown in menu title key
operations.
S Command List
The PRGM Mode Command List (page 8-37) provides a graphic flowchart of the various
function key menus and shows how to maneuver to the menu of commands you need.
Example: The following operation displays Xfct: [VARS]-[FACT]-[Xfct]
S E-CON2
This manual does not cover the E-CON2 mode. For more information about the E-CON2
mode, download the E-CON2 manual (English version only) from: http://edu.casio.com.
I Contrast Adjustment
Adjust the contrast whenever objects on the display appear dim or difficult to see.
1. Use the cursor keys (D, A, B, C) to select the SYSTEM icon and press U, then
press (
) to display the contrast adjustment screen.
2. Adjust the contrast.
• The C cursor key makes display contrast darker.
• The B cursor key makes display contrast lighter.
• (INIT) returns display contrast to its initial default.
3. To exit display contrast adjustment, press K.
vi
Chapter 1 Basic Operation
1. Keys
I Key Table
Page
5-29
1-2
2-7
1-2
1
Page
Page
Page
Page
Page
5-5
5-3
5-28
5-30
5-1
5-24
1-22
1-25
1-23
1-26
1-2
2-14
1-18,
2-14
2-14
2-14
2-13
2-30
2-14
1-11
1-12
1-18
2-19
2-13
2-13
2-19
10-11
1-19
2-19
2-1
2-1
10-9
2-6
Page
Page
Page
Page
1-30
1-8
1-9
1-6,1-15
1-16
Page
1-6
1-9
2-1
3-2
2-1
2-41
2-1
2-30
2-13
2-7
2-9
2-1
2-1
Not all of the functions described above are available on all models covered by this manual.
Depending on calculator model, some of the above keys may not be included on your calculator.
1-1
I Key Markings
Many of the calculator’s keys are used to perform more than one function. The functions
marked on the keyboard are color coded to help you find the one you need quickly and easily.
Function
Key Operation
log
J
10x
J
B
?J
The following describes the color coding used for key markings.
Color
•
Key Operation
Yellow
Press and then the key to perform the marked function.
Red
Press ? and then the key to perform the marked function.
Alpha Lock
Normally, once you press ? and then a key to input an alphabetic character, the keyboard
reverts to its primary functions immediately.
If you press and then ?, the keyboard locks in alpha input until you press ? again.
2. Display
I Selecting Icons
This section describes how to select an icon in the Main Menu to enter the mode you want.
S To select an icon
1. Press K to display the Main Menu.
2. Use the cursor keys (B, C, D, A) to move the
highlighting to the icon you want.
1-2
Currently selected icon
3. Press U to display the initial screen of the mode
whose icon you selected. Here we will enter the
STAT mode.
• You can also enter a mode without highlighting an icon in the Main Menu by inputting the
number or letter marked in the lower right corner of the icon.
• Use only the procedures described above to enter a mode. If you use any other procedure,
you may end up in a mode that is different than the one you thought you selected.
The following explains the meaning of each icon.
Icon
Mode Name
RUN
(fx-7400Gɉ only)
RUN • MAT*1
(Run • Matrix)
STAT
(Statistics)
e • ACT*2
(eActivity)
S • SHT*2
(Spreadsheet)
Description
Use this mode for arithmetic calculations and function
calculations, and for calculations involving binary, octal,
decimal, and hexadecimal values.
Use this mode for arithmetic calculations and function
calculations, and for calculations involving binary, octal,
decimal, and hexadecimal values and matrices.
Use this mode to perform single-variable (standard deviation)
and paired-variable (regression) statistical calculations, to
perform tests, to analyze data and to draw statistical graphs.
eActivity lets you input text, math expressions, and other data
in a notebook-like interface. Use this mode when you want to
store text or formulas, or built-in application data in a file.
Use this mode to perform spreadsheet calculations. Each file
contains a 26-column × 999-line spreadsheet. In addition to the
calculator’s built-in commands and S • SHT mode commands,
you can also perform statistical calculations and graph
statistical data using the same procedures that you use in the
STAT mode.
GRAPH
Use this mode to store graph functions and to draw graphs
using the functions.
DYNA*1
Use this mode to store graph functions and to draw multiple
versions of a graph by changing the values assigned to the
variables in a function.
(Dynamic Graph)
TABLE
Use this mode to store functions, to generate a numeric table
of different solutions as the values assigned to variables in a
function change, and to draw graphs.
RECUR*1
(Recursion)
Use this mode to store recursion formulas, to generate a
numeric table of different solutions as the values assigned to
variables in a function change, and to draw graphs.
CONICS*1
Use this mode to draw graphs of conic sections.
EQUA
Use this mode to solve linear equations with two through six
unknowns, and high-order equations from 2nd to 6th degree.
(Equation)
PRGM
(Program)
Use this mode to store programs in the program area and to
run programs.
1-3
Icon
Mode Name
TVM*1
(Financial)
Description
Use this mode to perform financial calculations and to draw
cash flow and other types of graphs.
E-CON2*1
Use this mode to control the optionally available EA-200 Data
Analyzer.
For more information about the E-CON2 mode, download the
E-CON2 manual (English version only) from: http://edu.casio.
com.
LINK
Use this mode to transfer memory contents or back-up data to
another unit or PC.
MEMORY
Use this mode to manage data stored in memory.
SYSTEM
Use this mode to initialize memory, adjust contrast, and to
make other system settings.
*1 Not included on the fx-7400Gɉ.
*2 Not included on the fx-7400Gɉ/fx-9750Gɉ.
I About the Function Menu
Use the function keys ( to ) to access the menus and commands in the menu bar
along the bottom of the display screen. You can tell whether a menu bar item is a menu or a
command by its appearance.
I About Display Screens
This calculator uses two types of display screens: a text screen and a graph screen. The
text screen can show 21 columns and 8 lines of characters, with the bottom line used for the
function key menu. The graph screen uses an area that measures 127 (W) × 63 (H) dots.
Text Screen
Graph Screen
I Normal Display
The calculator normally displays values up to 10 digits long. Values that exceed this limit are
automatically converted to and displayed in exponential format.
S How to interpret exponential format
1.2E+12 indicates that the result is equivalent to 1.2 s 1012. This means that you should move
the decimal point in 1.2 twelve places to the right, because the exponent is positive. This
results in the value 1,200,000,000,000.
1-4
1.2E–03 indicates that the result is equivalent to 1.2 s 10–3. This means that you should move
the decimal point in 1.2 three places to the left, because the exponent is negative. This results
in the value 0.0012.
You can specify one of two different ranges for automatic changeover to normal display.
Norm 1 ................... 10–2 (0.01) > |x|, |x| 1010
Norm 2 ................... 10–9 (0.000000001) > |x|, |x| 1010
All of the examples in this manual show calculation results using Norm 1.
See page 2-11 for details on switching between Norm 1 and Norm 2.
I Special Display Formats
This calculator uses special display formats to indicate fractions, hexadecimal values, and
degrees/minutes/seconds values.
S Fractions
.................... Indicates: 456
12
23
S Hexadecimal Values
................... Indicates: 0ABCDEF1(16), which equals
180150001(10)
S Degrees/Minutes/Seconds
.................... Indicates: 12° 34’ 56.78”
• In addition to the above, this calculator also uses other indicators or symbols, which are
described in each applicable section of this manual as they come up.
3. Inputting and Editing Calculations
I Inputting Calculations
When you are ready to input a calculation, first press
to clear the display. Next, input your
calculation formulas exactly as they are written, from left to right, and press U to obtain the
result.
Example
2 + 3 – 4 + 10 =
A
B C
@?U
1-5
I Editing Calculations
Use the B and C keys to move the cursor to the position you want to change, and then
perform one of the operations described below. After you edit the calculation, you can execute
it by pressing U. Or you can use C to move to the end of the calculation and input more.
• You can select either insert or overwrite for input*1. With overwrite, text you input replaces
the text at the current cursor location. You can toggle between insert and overwrite by
performing the operation: #(INS). The cursor appears as “I” for insert and as “ ” for
overwrite.
*1 With all models except the fx-7400Gɉ/fx-9750Gɉ, insert and overwrite switzng is possible
only when the Linear input/output mode (page 1-29) is selected.
S To change a step
Example
To change cos60 to sin60
AE?
BBB
#
Q
S To delete a step
Example
To change 369 s s 2 to 369 s 2
BEH A
B#
In the insert mode, the # key operates as a backspace key.
S To insert a step
Example
To change 2.362 to sin2.362
A
BEV
BBBBB
Q
1-6
I Using Replay Memory
The last calculation performed is always stored into replay memory. You can recall the
contents of the replay memory by pressing B or C.
If you press C, the calculation appears with the cursor at the beginning. Pressing B causes
the calculation to appear with the cursor at the end. You can make changes in the calculation
as you wish and then execute it again.
• Replay memory is enabled in the Linear input/output mode only. In the Math input/output
mode, the history function is used in place of replay memory. For details, see “History
Function” (page 1-17).
Example 1
To perform the following two calculations
4.12 s 6.4 = 26.368
4.12 s 7.1 = 29.252
C
@A E
CU
BBBB
#(INS)
F
@
U
After you press
, you can press D or A to recall previous calculations, in sequence from
the newest to the oldest (Multi-Replay Function). Once you recall a calculation, you can use
C and B to move the cursor around the calculation and make changes in it to create a new
calculation.
Example 2
@AB
CDEU
ABC DEFU
D (One calculation back)
D (Two calculations back)
• A calculation remains stored in replay memory until you perform another calculation.
• The contents of replay memory are not cleared when you press the
recall a calculation and execute it even after pressing the
key.
I Making Corrections in the Original Calculation
Example
14 w 0 s 2.3 entered by mistake for 14 w 10 s 2.3
@C? A
B
1-7
key, so you can
U
Press ).
Cursor is positioned automatically at the
location of the cause of the error.
Make necessary changes.
B@
Execute again.
U
I Using the Clipboard for Copy and Paste
You can copy (or cut) a function, command, or other input to the clipboard, and then paste the
clipboard contents at another location.
• The procedures described here all use the Linear input/output mode. For details about the
copy and paste operation while the Math input/output mode is selected, see “Using the
Clipboard for Copy and Paste in the Math Input/Output Mode” (page 1-18).
S To specify the copy range
1. Move the cursor (I) to the beginning or end of the range of text you want to copy and then
press G(CLIP). This changes the cursor to “ ”.
2. Use the cursor keys to move the cursor and highlight the range of text you want to copy.
3. Press (COPY) to copy the highlighted text to the clipboard, and exit the copy range
specification mode.
The selected characters are not
changed when you copy them.
To cancel text highlighting without performing a copy operation, press ).
S To cut the text
1. Move the cursor (I) to the beginning or end of the range of text you want to cut and then
press G(CLIP). This changes the cursor to “ ”.
1-8
2. Use the cursor keys to move the cursor and highlight the range of text you want to cut.
3. Press 2(CUT) to cut the highlighted text to the clipboard.
Cutting causes the original
characters to be deleted.
u Pasting Text
Move the cursor to the location where you want to paste the text, and then press
!j(PASTE). The contents of the clipboard are pasted at the cursor position.
A
!j(PASTE)
k Catalog Function
The Catalog is an alphabetic list of all the commands available on this calculator. You can
input a command by calling up the Catalog and then selecting the command you want.
u To use the Catalog to input a command
1. Press !e(CATALOG) to display an alphabetic Catalog of commands.
• The screen that appears first is the last one you used for command input.
2. Press 6(CTGY) to display the category list.
• You can skip this step and go straight to step 5,
if you want.
3. Use the cursor keys (f, c) to highlight the command category you want, and then press
1(EXE) or w.
• This displays a list of commands in the category you selected.
4. Input the first letter of the command you want to input. This will display the first command
that starts with that letter.
5. Use the cursor keys (f, c) to highlight the command you want to input, and then press
1(INPUT) or w.
1-9
Example
To use the Catalog to input the ClrGraph command
A!e(CATALOG)I(C)c~cw
Pressing J or !J(QUIT) closes the Catalog.
4. Using the Math Input/Output Mode
Important!
• The fx-7400GII and fx-9750GII are not equipped with a Math input/output mode.
Selecting “Math” for the “Input/Output” mode setting on the Setup screen (page 1-29) turns on
the Math input/output mode, which allows natural input and display of certain functions, just as
they appear in your textbook.
• The operations in this section all are performed in the Math input/output mode.
- The initial default setting for the fx-9860GII SD/fx-9860GII/fx-9860G AU PLUS is the Math
input/output mode. If you have changed to the Linear input/output mode, switch back to the
Math input/output mode before performing the operations in this section. See “Using the
Setup Screen” (page 1-26) for information about how to switch modes.
- The initial default setting for the fx-9860G SD/fx-9860G/fx-9860G AU is the Linear input/
output mode. Switch to the Math input/output mode before performing the operations in
this section. See “Using the Setup Screen” (page 1-26) for information about how to switch
modes.
• In the Math input/output mode, all input is insert mode (not overwrite mode) input. Note that
the !D(INS) operation (page 1-6) you use in the Linear input/output mode to switch to
insert mode input performs a completely different function in the Math input/output mode. For
more information, see “Using Values and Expressions as Arguments” (page 1-14).
• Unless specifically stated otherwise, all operations in this section are performed in the
RUN • MAT mode.
1-10
k Input Operations in the Math Input/Output Mode
u Math Input/Output Mode Functions and Symbols
The functions and symbols listed below can be used for natural input in the Math input/output
mode. The “Bytes” column shows the number of bytes of memory that are used up by input in
the Math input/output mode.
Function/Symbol
Key Operation
Bytes
Fraction (Improper)
v
9
Mixed Fraction*1
!v(&)
14
Power
M
4
Square
x
4
Negative Power (Reciprocal)
!)(x –1)
5
'
!x(')
6
Cube Root
!((3')
9
Power Root
!M(x')
9
ex
!I(ex)
6
10x
!l(10x)
6
log(a,b)
(Input from MATH menu*2)
7
Abs (Absolute Value)
(Input from MATH menu*2)
6
Linear Differential*3
(Input from MATH menu*2)
7
Quadratic Differential*3
(Input from MATH menu*2)
7
Integral*3
(Input from MATH menu*2)
8
Σ Calculation*4
(Input from MATH menu*2)
11
2
14*5
Matrix
(Input from MATH menu* )
Parentheses
( and )
1
Braces (Used during list input.)
!*( { ) and !/( } )
1
Brackets (Used during matrix input.)
!+( [ ) and !-( ] )
1
*1 Mixed fraction is supported in the Math input/output mode only.
*2 For information about function input from the MATH function menu, see “Using the MATH
Menu” described below.
*3 Tolerance cannot be specified in the Math input/output mode. If you want to specify
tolerance, use the Linear input/output mode.
*4 For Σ calculation in the Math input/output mode, the pitch is always 1. If you want to specify
a different pitch, use the Linear input/output mode.
*5 This is the number of bytes for a 2 × 2 matrix.
1-11
S Using the MATH Menu
In the RUN • MAT mode, pressing (MATH) displays the MATH menu.
You can use this menu for natural input of matrices, differentials, integrals, etc.
• {MAT} ... {displays the MAT submenu, for natural input of matrices}
• {2s2} ... {inputs a 2 × 2 matrix}
• {3s3} ... {inputs a 3 × 3 matrix}
• {msn} ... {inputs a matrix with m lines and n columns (up to 6 × 6)}
• {logab} ... {starts natural input of logarithm logab}
• {Abs} ... {starts natural input of absolute value |X|}
d f(x)
x=a }
dx
d2 f(x)x = a
2
2
• {d /dx } ... {starts natural input of quadratic differential
}
dx2
b
• {°dx} … {starts natural input of integral
f(x)dx }
a
• {d/dx} ... {starts natural input of linear differential
B
• {3(} … {starts natural input of 3 calculation
3 f(x) }
A
x=A
S Math Input/Output Mode Input Examples
This section provides a number of different examples showing how the MATH function menu
and other keys can be used during Math input/output mode natural input. Be sure to pay
attention to the input cursor position as you input values and data.
Example 1
To input 23 + 1
A,
B
C
@
U
Example 2
(
To input 1+
2
5
)
2
@
6
AA
1-12
D
C
V
U
1
Example 3
To input 1+
0
x + 1dx
@
(MATH)(E)(°dx)
T
@
C?
D@
C
U
Example 4
To input 2 ×
1
2
2
2
1
2
A (MATH)(MAT)(2×2)
6@AA
CC
V()AC
1-13
C V()ACC6@AA
U
S When the calculation does not fit within the display window
Arrows appear at the left, right, top, or bottom edge of the
display to let you know when there is more of the
calculation off the screen in the corresponding direction.
When you see an arrow, you can use the cursor keys to
scroll the screen contents and view the part you want.
S Math Input/Output Mode Input Restrictions
Certain types of expressions can cause the vertical width of a calculation formula to be greater
than one display line. The maximum allowable vertical width of a calculation formula is about
two display screens (120 dots). You cannot input any expression that exceeds this limitation.
S Using Values and Expressions as Arguments
A value or an expression that you have already input can be used as the argument of a
function. After you have input “(2+3)”, for example, you can make it the argument of ,
resulting in (2+3).
Example
1. Move the cursor so it is located directly to the left of the part of the expression that you want
to become the argument of the function you will insert.
2. Press #(INS).
• This changes the cursor to an insert cursor ().
3. Press V() to insert the function.
• This inserts the function and makes the parenthetical expression its argument.
As shown above, the value or expression to the right of the cursor after #(INS) are
pressed becomes the argument of the function that is specified next. The range encompassed
as the argument is everything up to the first open parenthesis to the right, if there is one, or
everything up to the first function to the right (sin(30), log2(4), etc.).
1-14
This capability can be used with the following functions.
Function
Key Operation
Improper Fraction
6
Power
,
V()
Cube Root
(3)
Power Root
,(x)
ex
((ex)
10x
J(10x)
log(a,b)
(MATH)(logab)
Absolute Value
(MATH)(Abs)
Linear Differential
(MATH)(d/dx)
Quadratic Differential
(MATH)(d2/dx2)
Integral
(MATH)(E)
(°dx)
3 Calculation
(MATH)(E)
(3( )
Original
Expression
Expression After
Insertion
• In the Linear input/output mode, pressing #(INS) will change to the insert mode. See
page 1-6 for more information.
S Editing Calculations in the Math Input/Output Mode
The procedures for editing calculations in the Math input/output mode are basically the same
as those for the Linear input/output mode. For more information, see “Editing Calculations”
(page 1-6).
Note however, that the following points are different between the Math input/output mode and
the Linear input/output mode.
• Overwrite mode input that is available in the Linear input/output mode is not supported by
the Math input/output mode. In the Math input/output mode, input is always inserted at the
current cursor location.
• In the Math input/output mode, pressing the # key always performs a backspace operation.
• Note the following cursor operations you can use while inputting a calculation with Math
input/output mode.
To do this:
Move the cursor from the end of the calculation to the beginning
Move the cursor from the beginning of the calculation to the end
1-15
Press this key:
C
B
I Using Undoing and Redoing Operations
You can use the following procedures during calculation expression input in the Math input/
output mode (up until you press the U key) to undo the last key operation and to redo the
key operation you have just undone.
- To undo the last key operation, press: ?#(UNDO).
- To redo a key operation you have just undone, press: ?#(UNDO) again.
• You also can use UNDO to cancel an
key operation. After pressing
to clear an
expression you have input, pressing ?#(UNDO) will restore what was on the display
before you pressed
.
• You also can use UNDO to cancel a cursor key operation. If you press C during input and
then press ?#(UNDO), the cursor will return to where it was before you pressed C.
• The UNDO operation is disabled while the keyboard is alpha-locked. Pressing
?#(UNDO) while the keyboard is alpha-locked will perform the same delete operation
as the # key alone.
Example
@
6@C
#
?#(UNDO)
A
?#(UNDO)
I Math Input/Output Mode Calculation Result Display
Fractions, matrices, and lists produced by Math input/output mode calculations are displayed
in natural format, just as they appear in your textbook.
Sample Calculation Result Displays
• Fractions are displayed either as improper fractions or mixed fractions, depending on the
“Frac Result” setting on the Setup screen. For details, see “Using the Setup Screen” (page
1-26).
1-16
• Matrices are displayed in natural format, up to 6 × 6. A matrix that has more than six rows or
columns will be displayed on a MatAns screen, which is the same screen used in the Linear
input/output mode.
• Lists are displayed in natural format for up to 20 elements. A list that has more than 20
elements will be displayed on a ListAns screen, which is the same screen used in the Linear
input/output mode.
• Arrows appear at the left, right, top, or bottom edge of the display to let you know when there
is more data off the screen in the corresponding direction.
You can use the cursor keys to scroll the screen and view the data you want.
• Pressing (DEL)(DEL • L) while a calculation result is selected will delete both the result
and the calculation that produced it.
• The multiplication sign cannot be omitted immediately before an improper fraction or mixed
fraction. Be sure to always input a multiplication sign in this case.
Example: 2× 2
A A6D
5
• A ,, V, or (x–1) key operation cannot be followed immediately by another ,,
V, or (x–1) key operation. In this case, use parentheses to keep the key operations
separate.
BV (x–1)
Example: (32)–1
I History Function
The history function maintains a history of calculation expressions and results in the Math
input/output mode. Up to 30 sets of calculation expressions and results are maintained.
@
AU
AU
You can also edit the calculation expressions that are maintained by the history function and
recalculate. This will recalculate all of the expressions starting from the edited expression.
Example
To change “1+2” to “1+3” and recalculate
Perform the following operation following the sample shown above.
DDDDB#BU
1-17
• The value stored in the answer memory is always dependent on the result produced by
the last calculation performed. If history contents include operations that use the answer
memory, editing a calculation may affect the answer memory value used in subsequent
calculations.
- If you have a series of calculations that use the answer memory to include the result of the
previous calculation in the next calculation, editing a calculation will affect the results of all
the other calculations that come after it.
- When the first calculation of the history includes the answer memory contents, the answer
memory value is “0” because there is no calculation before the first one in history.
I Using the Clipboard for Copy and Paste in the Math Input/Output Mode
You can copy a function, command, or other input to the clipboard, and then paste the
clipboard contents at another location.
• In the Math input/output mode, you can specify only one line as the copy range.
• The CUT operation is supported for the Linear input/output mode only. It is not supported for
the Math input/output mode.
S To copy text
1. Use the cursor keys to move the cursor to the line you want to copy.
2. Press G(CLIP). The cursor will change to “
”.
3. Press (CPY · L) to copy the highlighted text to the clipboard.
S To paste text
Move the cursor to the location where you want to paste the text, and then press
H(PASTE). The contents of the clipboard are pasted at the cursor position.
I Calculation Operations in the Math Input/Output Mode
This section introduces Math input/output mode calculation examples.
• For details about calculation operations, see “Chapter 2 Manual Calculations”.
S Performing Function Calculations Using Math Input/Output Mode
Example
Operation
6 = 3
4 × 5 10
664 5U
cos = 1 (Angle: Rad)
2
3
A $(P)63CU
log28 = 3
(MATH)(logab) 2C8U
7
,(x) 7C123U
( )
123 = 1.988647795
2 + 3 × 3 64 − 4 = 10
log
3
= 0.1249387366
4
2
3 ,(x) 3C64C 4U
(MATH)(Abs)J364U
1-18
2 + 3 1 = 73
5
4 20
1.5 + 2.3i = 3 + 23 i
2 10
d 3
2
dx ( x + 4x + x − 6 ) x = 3 = 52
5
2x
2
1
6
∑ (k
2
+ 3 x + 4 dx = 404
3
)
− 3k + 5 = 55
k=2
265C
3 6()1C4U
1.5
2.3 ?(i)U,
(MATH)(d/dx)T,3C
4
TV
T 6C3U
(MATH)(E)(°dx) 2TV
3T
4C1
C5U
(MATH)(E)(3)? (K)V 3? (K)
5C? (K)C2C6U
I Performing Matrix Calculations Using Math Input/Output Mode
S To specify the dimensions (size) of a matrix
1. In the RUN • MAT mode, press K(SET UP)(Math)).
2. Press (MATH) to display the MATH menu.
3. Press (MAT) to display the following menu.
• {2s2} … {inputs a 2 × 2 matrix}
• {3s3} … {inputs a 3 × 3 matrix}
• {msn} … {inputs an m-row × n-column matrix (up to 6 × 6)}
Example
To create a 2-row s 3-column matrix
(msn)
Specify the number of rows.
AU
Specify the number of columns.
BU
U
S To input cell values
Example
To perform the calculation shown below
1
1
33
2
×8
13
5
6
4
1-19
The following operation is a continuation of the example calculation on the previous page.
@C@6ACCBBC
@B6CCCDCEC
GU
S To assign a matrix created using Math input/output mode to a MAT mode
matrix
Example
To assign the calculation result to Mat J
A(Mat) (Ans)?
A(Mat)?(J)U
• Pressing the # key while the cursor is located at the top (upper left) of the matrix will delete
the entire matrix.
#
I Using Graph Modes and the EQUA Mode in the Math Input/Output
Mode
Using the Math input/output mode with any of the modes below lets you input numeric
expressions just as they are written in your text book and view calculation results in natural
display format.
Modes that support input of expressions as they are written in textbooks:
RUN • MAT, e • ACT, GRAPH, DYNA, TABLE, RECUR, EQUA (SOLV)
Modes that support natural display format:
RUN • MAT, e • ACT, EQUA
The following explanations show Math input/output mode operations in the GRAPH, DYNA,
TABLE, RECUR and EQUA modes, and natural calculation result display in the EQUA mode.
• See the sections that cover each calculation for details about its operation.
• See “Input Operations in the Math Input/Output Mode” (page 1-11) and “Calculation
Operations in the Math Input/Output Mode” (page 1-18) for details about Math input/output
mode input operations and calculation result displays in the RUN • MAT mode.
• e • ACT mode input operations and result displays are the same as those in the RUN • MAT
mode. For information about e • ACT mode operations, see “Chapter 10 eActivity”.
1-20
Important!
• On a model whose operating system has been updated to OS 2.0 from an older OS version,
Math input/output mode input and result display are not supported in any mode except the
RUN • MAT mode and e • ACT mode.
u Math Input/Output Mode Input in the GRAPH Mode
You can use the Math input/output mode for graph expression input in the GRAPH, DYNA,
TABLE, and RECUR modes.
x
x
In the GRAPH mode, input the function y = 2 − 2 −1 and then graph it.
' '
Make sure that initial default settings are configured on the View
Window.
2
Example 1
mGRAPHvxv!x(')c
ee-vv!x(')cee
-bw
6(DRAW)
Example 2
∫
x 1
In the GRAPH mode, input the function y =
x 2− 1 x −1 dx and then
0 4
2
graph it.
Make sure that initial default settings are configured on the View
Window.
mGRAPHK2(CALC)3(∫dx)
bveevx-bvce
v-beaevw
6(DRAW)
• Math Input/Output Mode Input and Result Display in the EQUA Mode
You can use the Math input/output mode in the EQUA mode for input and display as shown
below.
• In the case of simultaneous equations (1(SIML)) and high-order equations (2(POLY)),
solutions are output in natural display format (fractions, ', π are displayed in natural format)
whenever possible.
• In the case of Solver (3(SOLV)), you can use Math input/output mode natural input.
1-21
Example
To solve the quadratic equation x2 + 3x + 5 = 0 in the EQUA mode
KEQUA K(SET UP)
AAAA(Complex Mode)
(a+bi))
(POLY)(2)@UBUDUU
5. Option (OPTN) Menu
The option menu gives you access to scientific functions and features that are not marked on
the calculator’s keyboard. The contents of the option menu differ according to the mode you
are in when you press the * key.
• The option menu does not appear if you press * while binary, octal, decimal, or
hexadecimal is set as the default number system.
• For details about the commands included on the option (OPTN) menu, see the “* key”
item in the “PRGM Mode Command List” (page 8-37).
• The meanings of the option menu items are described in the sections that cover each mode.
The following list shows the option menu that is displayed when the RUN • MAT (or RUN) or
PRGM mode is selected.
Item names below that are marked with an asterisk (*) are not included on the fx-7400Gɉ.
• {LIST} ... {list function menu}
• {MAT}* ... {matrix operation menu}
• {CPLX} ... {complex number calculation menu}
• {CALC} ... {functional analysis menu}
• {STAT} ... {paired-variable statistical estimated value menu} (fx-7400Gɉ)
{menu for paired-variable statistical estimated value, distribution, standard
deviation, variance, and test functions} (all models except fx-7400Gɉ)
• {CONV} ... {metric conversion menu}
• {HYP} ... {hyperbolic calculation menu}
• {PROB} ... {probability/distribution calculation menu}
• {NUM} ... {numeric calculation menu}
• {ANGL} ... {menu for angle/coordinate conversion, sexagesimal input/conversion}
• {ESYM} ... {engineering symbol menu}
• {PICT} ... {graph save/recall menu}
• {FMEM} ... {function memory menu}
• {LOGIC} ... {logic operator menu}
• {CAPT} ... {screen capture menu}
• {TVM}* ... {financial calculation menu}
• The PICT, FMEM and CAPT items are not displayed when “Math” is selected for the “Input/
Output” mode setting on the Setup screen.
1-22
6. Variable Data (VARS) Menu
To recall variable data, press ) to display the variable data menu.
{V-WIN}/{FACT}/{STAT}/{GRPH}/{DYNA}/{TABL}/{RECR}/{EQUA}/{TVM}/{Str}
• Note that the EQUA and TVM items appear for function keys ( and ) only when you
access the variable data menu from the RUN • MAT (or RUN) or PRGM mode.
• The variable data menu does not appear if you press ) while binary, octal, decimal, or
hexadecimal is set as the default number system.
• Depending on the calculator model, some menu items may not be included.
• For details about the commands included on the variable data (VARS) menu, see the “)
key” item in the “PRGM Mode Command List” (page 8-37).
• Item names below that are marked with an asterisk (*) are not included on the fx-7400Gɉ.
S V-WIN — Recalling V-Window values
• {X}/{Y}/{T,Ƨ} ... {x-axis menu}/{y-axis menu}/{T,Ƨmenu}
• {R-X}/{R-Y}/{R-T,Ƨ} ... {x-axis menu}/{y-axis menu}/{T,Ƨmenu} for right side of Dual
Graph
• {min}/{max}/{scal}/{dot}/{ptch} ... {minimum value}/{maximum value}/{scale}/{dot
value*1}/{pitch}
*1 The dot value indicates the display range (Xmax value – Xmin value) divided by the
screen dot pitch (126). The dot value is normally calculated automatically from the
minimum and maximum values. Changing the dot value causes the maximum to be
calculated automatically.
S FACT — Recalling zoom factors
• {Xfct}/{Yfct} ... {x-axis factor}/{y-axis factor}
S STAT — Recalling statistical data
• {X} … {single-variable, paired-variable x-data}
• {n}/{x
¯ }/{3x}/{3x2}/{Ʊx}/{sx}/{minX}/{maxX} ... {number of data}/{mean}/{sum}/{sum
of squares}/{population standard deviation}/{sample standard deviation}/{minimum
value}/{maximum value}
• {Y} ... {paired-variable y-data}
• {Κ}/{3y}/{3y2}/{3xy}/{Ʊx}/{sy}/{minY}/{maxY} ... {mean}/{sum}/{sum of squares}/{sum
of products of x-data and y-data}/{population standard deviation}/{sample standard
deviation}/{minimum value}/{maximum value}
• {GRPH} ... {graph data menu}
• {a}/{b}/{c}/{d}/{e} ... {regression coefficient and polynomial coefficients}
• {r}/{r2} ... {correlation coefficient}/{coefficient of determination}
• {MSe} ... {mean square error}
• {Q1}/{Q3} ... {first quartile}/{third quartile}
• {Med}/{Mod} ... {median}/{mode} of input data
• {Strt}/{Pitch} ... histogram {start division}/{pitch}
• {PTS} ... {summary point data menu}
• {x1}/{y1}/{x2}/{y2}/{x3}/{y3} ... {coordinates of summary points}
1-23
• {INPT}* ... {statistical calculation input values}
¯ }/{sx}/{n1}/{n2}/{x¯ 1}/{x¯ 2}/{sx1}/{sx2}/{sp} ... {size of sample}/{mean of sample}/{sample
• {n}/{x
standard deviation}/{size of sample 1}/{size of sample 2}/{mean of sample 1}/{mean of
sample 2}/{standard deviation of sample 1}/{standard deviation of sample 2}/{standard
deviation of sample p}
• {RESLT}* ... {statistical calculation output values}
• {TEST} ... {test calculation results}
• {p}/{z}/{t}/{Chi}/{F}/{ p
ˆ }/{ pˆ 1}/{ pˆ 2}/{df}/{se}/{r}/{r 2}/{pa}/{Fa}/{Adf}/{SSa}/{MSa}/{pb}/{Fb}/
{Bdf}/{SSb}/{MSb}/{pab}/{Fab}/{ABdf}/{SSab}/{MSab}/{Edf}/{SSe}/{MSe}
... {p-value}/{z score}/{t score}/{C2 value}/{F value}/{estimated sample proportion}/
{estimated proportion of sample 1}/{estimated proportion of sample 2}/{degrees of
freedom}/{standard error}/{correlation coefficient}/{coefficient of determination}/
{factor A p-value}/{factor A F value}/{factor A degrees of freedom}/{factor A sum of
squares}/{factor A mean squares}/{factor B p-value}/{factor B F value}/{factor B
degrees of freedom}/{factor B sum of squares}/ {factor B mean squares}/{factor AB
p-value}/{factor AB F value}/{factor AB degrees of freedom}/{factor AB sum of
squares}/{factor AB mean squares}/{error degrees of freedom}/{error sum of
squares}/{error mean squares}
• {INTR} ... {confidence interval calculation results}
• {Left}/{Right}/{ p
ˆ }/{ pˆ 1}/{ pˆ 2}/{df} ... {confidence interval lower limit (left edge)}/
{confidence interval upper limit (right edge)}/{estimated sample proportion}/
{estimated proportion of sample 1}/{estimated proportion of sample 2}/{degrees of
freedom}
• {DIST} ... {distribution calculation results}
• {p}/{xInv}/{x1Inv}/{x2Inv}/{zLow}/{zUp}/{tLow}/{tUp} ... {probability distribution
or cumulative distribution calculation result (p-value)}/{inverse Student-t, C2, F,
binomial, Poisson, geometric or hypergeometric cumulative distribution calculation
result}/{inverse normal cumulative distribution upper limit (right edge) or lower limit
(left edge)}/{inverse normal cumulative distribution upper limit (right edge)}/{normal
cumulative distribution lower limit (left edge)}/{normal cumulative distribution upper
limit (right edge)}/{Student-t cumulative distribution lower limit (left edge)}/{Student-t
cumulative distribution upper limit (right edge)}
S GRPH — Recalling graph functions
• {Y}/{r} ... {rectangular coordinate or inequality function}/{polar coordinate function}
• {Xt}/{Yt} ... parametric graph function {Xt}/{Yt}
• {X} ... {X=constant graph function}
• Press these keys before inputting a value to specify a memory area.
S DYNA* — Recalling dynamic graph setup data
• {Strt}/{End}/{Pitch} ... {coefficient range start value}/{coefficient range end value}/
{coefficient value increment}
S TABL — Recalling table setup and content data
• {Strt}/{End}/{Pitch} ... {table range start value}/{table range end value}/{table value
increment}
• {Reslt*1} ... {matrix of table contents}
*1 The Reslt item appears only when the TABL menu is displayed in the RUN • MAT (or
RUN) and PRGM modes.
1-24
S RECR* — Recalling recursion formula*1, table range, and table content data
• {FORM} ... {recursion formula data menu}
• {an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/{cn+1}/{cn+2} ... {an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/
{cn+1}/{cn+2} expressions
• {RANG} ... {table range data menu}
• {Strt}/{End} ... table range {start value}/{end value}
• {a0}/{a1}/{a2}/{b0}/{b1}/{b2}/{c0}/{c1}/{c2} ... {a0}/{a1}/{a2}/{b0}/{b1}/{b2}/{c0}/{c1}/{c2} value
• {anSt}/{bnSt}/{cnSt} ... origin of {an}/{bn}/{cn} recursion formula convergence/divergence
graph (WEB graph)
• {Reslt*2}* ... {matrix of table contents*3}
*1 An error occurs when there is no function or recursion formula numeric table in memory.
*2 “Reslt” is available only in the RUN • MAT and PRGM modes.
*3 Table contents are stored automatically in Matrix Answer Memory (MatAns).
S EQUA* — Recalling equation coefficients and solutions*1 *2
• {S-Rlt}/{S-Cof} ... matrix of {solutions}/{coefficients} for linear equations with two through
six unknowns*3
• {P-Rlt}/{P-Cof} ... matrix of {solution}/{coefficients} for a quadratic or cubic equation
*1 Coefficients and solutions are stored automatically in Matrix Answer Memory (MatAns).
*2 The following conditions cause an error.
- When there are no coefficients input for the equation
- When there are no solutions obtained for the equation
3
* Coefficient and solution memory data for a linear equation cannot be recalled at the same
time.
S TVM* — Recalling financial calculation data
• {n}/{I%}/{PV}/{PMT}/{FV} ... {payment periods (installments)}/{annual interest rate}/
{present value}/{payment}/{future value}
• {P/Y}/{C/Y} ... {installment periods per year}/{compounding periods per year}
S Str — Str command
• {Str} ... {string memory}
7. Program (PRGM) Menu
To display the program (PRGM) menu, first enter the RUN • MAT (or RUN) or PRGM mode
from the Main Menu and then press )(PRGM). The following are the selections
available in the program (PRGM) menu.
• {COM} ...... {program command menu}
• {CTL} ....... {program control command menu}
• {JUMP} ..... {jump command menu}
• {?} ............ {input command}
• {<} .......... {output command}
• {CLR} ....... {clear command menu}
1-25
• {DISP} ...... {display command menu}
• {REL} ....... {conditional jump relational operator menu}
• {I/O} ......... {I/O control/transfer command menu}
• {:} ............. {multi-statement command}
• {STR} ....... {string command}
The following function key menu appears if you press )(PRGM) in the RUN • MAT (or
RUN) mode or the PRGM mode while binary, octal, decimal, or hexadecimal is set as the
default number system.
• {Prog}....... {program recall}
• {JUMP}/{?}/{<}/{REL}/{:}
The functions assigned to the function keys are the same as those in the Comp mode.
For details on the commands that are available in the various menus you can access from the
program menu, see “Chapter 8 Programming”.
8. Using the Setup Screen
The mode’s Setup screen shows the current status of mode settings and lets you make any
changes you want. The following procedure shows how to change a setup.
S To change a mode setup
1. Select the icon you want and press U to enter a mode and display its initial screen. Here
we will enter the RUN • MAT (or RUN) mode.
2. Press K(SET UP) to display the mode’s Setup
screen.
• This Setup screen is just one possible example. Actual
Setup screen contents will differ according to the mode
you are in and that mode’s current settings.
3. Use the D and A cursor keys to move the highlighting to the item whose setting you
want to change.
4. Press the function key ( to ) that is marked with the setting you want to make.
5. After you are finished making any changes you want, press ) to exit the Setup screen.
I Setup Screen Function Key Menus
This section details the settings you can make using the function keys in the Setup screen.
indicates default setting.
Item names below that are marked with an asterisk (*) are not included on the fx-7400Gɉ.
1-26
S Mode (calculation/binary, octal, decimal, hexadecimal mode)
• {Comp} ... {arithmetic calculation mode}
• {Dec}/{Hex}/{Bin}/{Oct} ... {decimal}/{hexadecimal}/{binary}/{octal}
S Frac Result (fraction result display format)
• {d/c}/{ab/c} ... {improper}/{mixed} fraction
S Func Type (graph function type)
Pressing one of the following function keys also switches the function of the T key.
• {Y=}/{r=}/{Parm}/{X=} ... {rectangular coordinate (Y= I(x) type)}/{polar coordinate}/
{parametric}/{rectangular coordinate (X= I(y) type)} graph
• {Y>}/{Y<}/{YP}/{YO} ... {y>f(x)}/{y}/{X<}/{XP}/{XO} ... {x>f(y)}/{x, <, r, b
And (logical operator), and (bitwise operator)
Or, Xor (logical operator), or, xor, xnor (bitwise operator)
*1 You can combine the contents of multiple function memory (fn) locations or graph memory
(Yn, rn, Xtn, Ytn, Xn) locations into composite functions. Specifying fn1(fn2), for example,
results in the composite function fn1°fn2 (see page 5-7). A composite function can consist of
up to five functions.
Example
2 + 3 s (log sin2P2 + 6.8) = 22.07101691 (angle unit = Rad)
1
2
3
4
5
6
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside of a RndFix calculation term.
• When functions with the same priority are used in series, execution is performed from right to
left.
exIn 120 m ex{In( 120)}
Otherwise, execution is from left to right.
• Compound functions are executed from right to left.
• Anything contained within parentheses receives highest priority.
I Calculation Result Irrational Number Display
(fx-9860GII SD/fx-9860GII/fx-9860G AU PLUS only)
You can configure the calculator to display calculation results in irrational number format
(including or P) by selecting “Math” for the “Input/Output” mode setting on the Setup screen.
Example
2+
8 = 3
2
(Input/Output: Math)
V()AC
V()GU
2-3
S Calculation Result Display Range with
Display of a calculation result in format is supported for result with in up to two terms.
Calculation results in format take one of the following forms.
b p d'
e
p a
b, p d p a
b, p a'
c
f
• The following are the ranges for each of the coefficients (a, b, c, d, e, f) can be displayed in
the calculation result format.
1 a < 100, 1 < b < 1000, 1 c < 100
0 d < 100, 0 e < 1000, 1 f < 100
• In the cases shown below, a calculation result may be able to be displayed in format even
if their coefficients (a, c, d) are outside the above ranges.
A format calculation result uses a common denominator.
b + d´'
e
a'
b + d'
e m a´'
c´
c
f
* c´ is the least common multiple of c and f.
Since the calculation result uses a common denominator, calculation result still may be
displayed using the format even when coefficients (a´, c´, d´) are outside the corresponding
range of coefficients (a, c, d).
Example:
3 '
2 10'
3 + 11'
2
'
+
=
11 10
110
Calculation Examples
This calculation:
Produces this type of display:
2 s (3 – 2
5) = 6 – 4
5
format
2)*1
35
2 s 3 = 148.492424 (= 105
Decimal format
150'
2
= 8.485281374*1
25
23 s (5 – 2
3) = 35.32566285 (= 115 – 46
3)*1
Decimal format
2+
3+
8=
3 + 3
2
format
2+'
3+'
6 = 5.595754113*2
'
Decimal format
*1 Decimal format because values are outside of range.
*2 Decimal format because calculation result has three terms.
• The calculation result is displayed using decimal format even if an intermediate result goes
greater than two terms.
Example: (1 +
2+
3) (1 –
2–
3)
(= – 4 – 2
6)
= –8.898979486
• If the calculation formula has a term and a term that cannot be displayed as a fraction,
the calculation result will be displayed in decimal format.
Example: log3 +
2 = 1.891334817
2-4
S Calculation Result Display Range with P
A calculation results is displayed using P format in the following cases.
• When the calculation result can be displayed in the form nP
n is an integer up to |106|.
b
b
P or
P
c
c
However, {number of a digits + number of b digits + number of c digits} must be 9 or less
b
b
when the above a or
is reduced.*1*2 Also, the maximum number of allowable c digits is
c
c
2
• When the calculation result can be displayed in the form a
three.*
*1 When c < b, the number of a, b, and c digits are counted when the fraction is converted
from an improper fraction ( b ) to a mixed fraction (a
c
b
).
c
2
* When “Manual” is specified for the Setup screen “Simplify” setting, the calculation result
may be displayed in decimal format, even if these conditions are met.
Calculation Examples
This calculation:
Produces this type of display:
78P s 2 = 156P
P format
123456P s 9 = 3490636.164 (= 11111104 P)*3
Decimal format
105
2
568
71
P = 105
P
824
103
258
P = 6.533503684
3238
P format
2
129
*4
1619
Decimal format
*3 Decimal format because calculation result integer part is |106| or greater.
*4 Decimal format because number of denominator digits is four or greater for the a
b
P form.
c
I Multiplication Operations without a Multiplication Sign
You can omit the multiplication sign (s) in any of the following operations.
• Before Type A functions ( on page 2-2) and Type C functions ( on page 2-2), except for
negative signs
Example 1
3, 2Pol(5, 12), etc.
2sin30, 10log1.2, 2'
• Before constants, variable names, memory names
Example 2
2P, 2AB, 3Ans, 3Y1, etc.
• Before an open parenthesis
Example 3
3(5 + 6), (A + 1)(B – 1), etc.
2-5
I Overflow and Errors
Exceeding a specified input or calculation range, or attempting an illegal input causes an error
message to appear on the display. Further operation of the calculator is impossible while an
error message is displayed. For details, see the “Error Message Table” on page A-1.
• Most of the calculator’s keys are inoperative while an error message is displayed. Press )
to clear the error and return to normal operation.
I Memory Capacity
Each time you press a key, either one byte or two bytes is used. Some of the functions that
require one byte are: @, A, B, sin, cos, tan, log, In, , and P.
Some of the functions that take up two bytes are d/dx(, Mat, Xmin, If, For, Return, DrawGraph,
SortA(, PxIOn, Sum, and an+1.
• The required number of bytes to input functions and commands is different in the Linear
input/output mode and the Math input/output mode. For details about the number of bytes
required for each function in the Math input/output mode, see page 1-11.
2. Special Functions
I Calculations Using Variables
Example
Operation
Display
193.2??T(A)U
193.2
193.2 ÷ 23 = 8.4
?T(A)23U
8.4
193.2 ÷ 28 = 6.9
?T(A)28U
6.9
I Memory
S Variables (Alpha Memory)
This calculator comes with 28 variables as standard. You can use variables to store values you
want to use inside of calculations. Variables are identified by single-letter names, which are
made up of the 26 letters of the alphabet, plus r and Q. The maximum size of values that you
can assign to variables is 15 digits for the mantissa and 2 digits for the exponent.
• Variable contents are retained even when you turn power off.
S To assign a value to a variable
[value] ? [variable name] U
Example 1
To assign 123 to variable A
@AB??T(A)U
2-6
Example 2
To add 456 to variable A and store the result in variable B
?T(A)
CDE?
?J(B)U
S To assign the same value to more than one variable
[value]? [first variable name]?(~) [last variable name]U
• You cannot use “r” or “Q ” as a variable name.
Example
To assign a value of 10 to variables A through F
@???T(A)
?(~)?R(F)U
S String Memory
You can store up to 20 strings (named Str 1 to Str 20) in string memory. Stored strings can be
output to the display or used inside functions and commands that support the use of strings as
arguments.
For details about string operations, see “Strings” (page 8-18).
Example
To assign string “ABC” to Str 1 and then output Str 1 to the display
?( A -LOCK)$(”)T(A)
J(B)((C)$(”)?(Releases Alpha Lock.)
?)(E)(Str)*@U
(Str)*@U
* fx-7400GII: (Str)
String is displayed justified left.
• Perform the above operation in the Linear input/output mode. It cannot be performed in the
Math input/output mode.
S Function Memory
[OPTN]-[FMEM]
Function memory is convenient for temporary storage of often-used expressions. For longer
term storage, we recommend that you use the GRAPH mode for expressions and the PRGM
mode for programs.
• {STO}/{RCL}/{fn}/{SEE} ... {function store}/{function recall}/{function area specification as a
variable name inside an expression}/{function list}
2-7
S To store a function
Example
To store the function (A+B) (A–B) as function memory number 1
?T(A)
?J(B)
?T(A) ?J(B)
*(E)(E)(FMEM)*
(STO)@U
* fx-7400GII: (FMEM)
)))
• If the function memory number to which you store a function already contains a function, the
previous function is replaced with the new one.
• You can also use ? to store a function in function
memory in a program. In this case, you must enclose the
function inside of double quotation marks.
S To recall a function
Example
To recall the contents of function memory number 1
*(E)(E)(FMEM)*
(RCL)@U
* fx-7400GII: (FMEM)
• The recalled function appears at the current location of the cursor on the display.
S To recall a function as a variable
B??T(A)U
@??J(B)U
*(E)(E)(FMEM)*(fn)
@
AU
* fx-7400GII: (FMEM)
S To display a list of available functions
*(E)(E)(FMEM)*
(SEE)
* fx-7400GII: (FMEM)
2-8
u To delete a function
Example
To delete the contents of function memory number 1
A
K6(g)6(g)3(FMEM)*
1(STO)bw
* fx-7400GII: 2(FMEM)
• Executing the store operation while the display is blank deletes the function in the function
memory you specify.
k Answer Function
The Answer Function automatically stores the last result you calculated by pressing
w (unless the w key operation results in an error). The result is stored in the answer
memory.
• The largest value that the answer memory can hold is 15 digits for the mantissa and 2 digits
for the exponent.
• Answer memory contents are not cleared when you press the A key or when you switch
power off.
u To use the contents of the answer memory in a calculation
Example
123 + 456 = 579
789 – 579 = 210
Abcd+efgw
hij-!-(Ans)w
fx-7400GII, fx-9750GII users...
• The answer memory contents are not changed by an operation that assigns values to Alpha
memory (such as: faal(B)w).
fx-9860GII SD, fx-9860GII, fx-9860G AU PLUS users...
• In the Math input/output mode, the operation to recall answer memory contents is different
from the operation in the Linear input/output mode. For details, see “History Function” (page
1-17).
• Performing an operation that assigns a value to an Alpha memory (such as
faal(B)w), answer memory contents are updated in the Math input/output mode
but not in the Linear input/output mode.
2-9
I Performing Continuous Calculations
Answer memory also lets you use the result of one calculation as one of the arguments in the
next calculation.
Example
1w3=
1w3s3=
@BU
(Continuing) BU
Continuous calculations can also be used with Type B functions (x2, x–1, x!, on page 2-2), +, –,
^(xy), x, ° ’ ”, etc.
3. Specifying the Angle Unit and Display Format
Before performing a calculation for the first time, you should use the Setup screen to specify
the angle unit and display format.
I Setting the Angle Unit
[SET UP]- [Angle]
1. On the Setup screen, highlight “Angle”.
2. Press the function key for the angle unit you want to specify, then press ).
• {Deg}/{Rad}/{Gra} ... {degrees}/{radians}/{grads}
• The relationship between degrees, grads, and radians is shown below.
360° = 2P radians = 400 grads
90° = P/2 radians = 100 grads
I Setting the Display Format
[SET UP]- [Display]
1. On the Setup screen, highlight “Display”.
2. Press the function key for the item you want to set, then press ).
• {Fix}/{Sci}/{Norm}/{Eng} ... {fixed number of decimal places specification}/
{number of significant digits specification}/{normal display}/{Engineering mode}
S To specify the number of decimal places (Fix)
Example
To specify two decimal places
(Fix)AU
Press the number key that corresponds to the number of decimal places you want to specify
(n = 0 to 9).
• Displayed values are rounded off to the number of decimal places you specify.
2-10
S To specify the number of significant digits (Sci)
Example
To specify three significant digits
(Sci)BU
Press the number key that corresponds to the number of significant digits you want to specify
(n = 0 to 9). Specifying 0 makes the number of significant digits 10.
• Displayed values are rounded off to the number of significant digits you specify.
S To specify the normal display (Norm 1/Norm 2)
Press (Norm) to switch between Norm 1 and Norm 2.
Norm 1: 10–2 (0.01) > |x|, |x| 1010
Norm 2: 10–9 (0.000000001) > |x|, |x| 1010
S To specify the engineering notation display (Eng mode)
Press (Eng) to switch between engineering notation and standard notation. The indicator
“/E” is on the display while engineering notation is in effect.
You can use the following symbols to convert values to engineering notation, such as 2,000
(= 2 × 103) m 2k.
E (Exa)
s 1018
m (milli)
s 10–3
P (Peta)
s 1015
M (micro)
s 10–6
T (Tera)
s 1012
n (nano)
s 10–9
G (Giga)
s 109
p (pico)
s 10–12
M (Mega)
s 106
f (femto)
s 10–15
k (kilo)
s 103
• The engineering symbol that makes the mantissa a value from 1 to 1000 is automatically
selected by the calculator when engineering notation is in effect.
4. Function Calculations
I Function Menus
This calculator includes five function menus that give you access to scientific functions not
printed on the key panel.
• The contents of the function menu differ according to the mode you entered from the Main
Menu before you pressed the * key. The following examples show function menus that
appear in the RUN • MAT (or RUN) or PRGM mode.
2-11
S Hyperbolic Calculations (HYP)
[OPTN]-[HYP]
• {sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent}
• {sinh–1}/{cosh–1}/{tanh–1} ... inverse hyperbolic {sine}/{cosine}/{tangent}
S Probability/Distribution Calculations (PROB)
[OPTN]-[PROB]
• {x!} ... {press after inputting a value to obtain the factorial of the value}
• {nPr}/{nCr} ... {permutation}/{combination}
• {RAND} ... {random number generation}
• {Ran#}/{Int}/{Norm}/{Bin}/{List} ... {random number generation (0 to 1)}/{random integer
generation}/{random number generation in accordance with normal distribution based
on mean ƫ and standard deviation Ʊ}/{random number generation in accordance with
binomial distribution based on number of trials n and probability p}/{random number
generation (0 to 1) and storage of result in ListAns}
• {P(}/{Q(}/{R(} ... normal probability {P(t)}/{Q(t)}/{R(t)}
• {t(} ... {value of normalized variate t(x)}
S Numeric Calculations (NUM)
[OPTN]-[NUM]
• {Abs} ... {select this item and input a value to obtain the absolute value of the value}
• {Int}/{Frac} ... select the item and input a value to extract the {integer}/{fraction} part.
• {Rnd} ... {rounds off the value used for internal calculations to 10 significant digits (to match
the value in the answer memory), or to the number of decimal places (Fix) and number
of significant digits (Sci) specified by you}
• {Intg} ... {select this item and input a value to obtain the largest integer that is not greater
than the value}
• {RndFi} ... {rounds off the value used for internal calculations to specified digits (0 to 9) (see
page 2-2).}
• {GCD} ... {greatest common divisor for two values}
• {LCM} ... {least common multiple for two values}
• {MOD} ... {remainder of division (remainder output when n is divided by m)}
• {MOD • E} ... {remainder when division is performed on a power value (remainder output
when n is raised to p power and then divided by m)}
S Angle Units, Coordinate Conversion, Sexagesimal Operations (ANGL)
[OPTN]-[ANGL]
• {°}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value
• {° ’ ”} ... {specifies degrees (hours), minutes, seconds when inputting a degrees/minutes/
seconds value}
• {° ’ ”} ... {converts decimal value to degrees/minutes/seconds value}
• The {° ’ ”} menu operation is available only when there is a calculation result on the display.
• {Pol(}/{Rec(} ... {rectangular-to-polar}/{polar-to-rectangular} coordinate conversion
• {DMS} ... {converts decimal value to sexagesimal value}
2-12
S Engineering Symbol (ESYM)
[OPTN]-[ESYM]
• {m}/{μ}/{n}/{p}/{f} ... {milli (10 )}/{micro (10 )}/{nano (10 )}/{pico (10 )}/{femto (10–15)}
–3
–6
–9
–12
• {k}/{M}/{G}/{T}/{P}/{E} ... {kilo (103)}/{mega (106)}/{giga (109)}/{tera (1012)}/{peta (1015)}/
{exa (1018)}
• {ENG}/{ENG} ... shifts the decimal place of the displayed value three digits to the {left}/{right}
and {decreases}/{increases} the exponent by three.
When you are using engineering notation, the engineering symbol is also changed
accordingly.
• The {ENG} and {ENG} menu operations are available only when there is a calculation result
on the display.
I Angle Units
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
To convert 4.25 rad to degrees:
243.5070629
K(SET UP)AAAAAA*(Deg))
4.25*(E)(ANGL)**(r)U
47.3° + 82.5rad = 4774.20181°
47.3
82.5*(E)(ANGL)**(r)U
2°20´30˝ + 39´30˝ = 3°00´00˝
2*(E)(ANGL)**(° ’ ”) 20(° ’ ”) 30
(° ’ ”)
0(° ’ ”)39(° ’ ”) 30(° ’ ”)U
(° ’ ”)
2.255° = 2°15´18˝
2.255*(E)(ANGL)**(E)(DMS)U
* fx-7400GII, fx-9750GII: AAAAA ** fx-7400GII: (ANGL)
I Trigonometric and Inverse Trigonometric Functions
• Be sure to set the angle unit before performing trigonometric function and inverse
trigonometric function calculations.
radians = 100 grads)
2
• Be sure to specify Comp for Mode in the Setup screen.
(90° =
Example
Operation
cos ( rad) = 0.5
3
K(SET UP)AAAAAA*(Rad))
A $(P)3U
2 • sin 45° s cos 65° = 0.5976724775
K(SET UP)AAAAAA*(Deg))
2 Q45 A65U*1
sin–10.5 = 30°
(x when sinx = 0.5)
Q(sin–1) 0.5*2U
* fx-7400GII, fx-9750GII: AAAAA
*1 can be omitted.
2
* Input of leading zero is not necessary.
2-13
I Logarithmic and Exponential Functions
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
log 1.23 (log101.23) = 0.08990511144 J1.23U
log28 = 3
*(CALC)*(E)(logab) 2 8U
(–3)4 = (–3) s (–3) s (–3) s (–3) = 81
7
1
7
3,4U
7 ,(x)123U
123 (= 123 ) = 1.988647795
* fx-7400GII: (CALC)
• The Linear input/output mode and Math input/output mode produce different results when
two or more powers are input in series, like: 2 , 3 , 2.
Linear input/output mode: 2^3^2 = 64
2
Math input/output mode: 23 = 512
This is because the Math input/output mode internally treats the above input as: 2^(3^(2)).
I Hyperbolic and Inverse Hyperbolic Functions
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
sinh 3.6 = 18.28545536
cosh–1
*(E)(HYP)*(sinh) 3.6U
20
= 0.7953654612
15
*(E)(HYP)*(cosh–1)2015U
* fx-7400GII: (HYP)
I Other Functions
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
2 +
5 = 3.65028154
V() 2
V()5U
(–3)2 = (–3) s (–3) = 9
3VU
8! (= 1 s 2 s 3 s .... s 8) = 40320
8*(E)(PROB)*1(x!)U
What is the integer part of – 3.5?
*(E)(NUM)*2(Int) 3.5U
–3
*1 fx-7400GII: (PROB) *2 fx-7400GII: (NUM)
2-14
I Random Number Generation (RAND)
S Random Number Generation (0 to 1) (Ran#, RanList#)
Ran# and RanList# generate 10 digit random numbers randomly or sequentially from 0 to 1.
Ran# returns a single random number, while RanList# returns multiple random numbers in list
form. The following shows the syntaxes of Ran# and RanList#.
Ran# [a]
1a9
RanList# (n [,a])
1 n 999
• n is the number of trials. RanList# generates the number of random numbers that
corresponds to n and displays them on the ListAns screen. A value must be input for n.
• “a” is the randomization sequence. Random numbers are returned if nothing is input for “a”.
Entering an integer of 1 through 9 for a will return the corresponding sequential random
number.
• Executing the function Ran# 0 initializes the sequences of both Ran# and RanList#. The
sequence also is initialized when a sequential random number is generated with a different
sequence of the previous execution using Ran# or RanList#, or when generating a random
number.
Ran# Examples
Example
Operation
Ran#
(Generates a random number.)
*(E)(PROB)*(RAND)
(Ran#)U
(Each press of U generates a new random
number.)
U
U
Ran# 1
(Generates the first random number in
sequence 1.)
*(E)(PROB)*(RAND)
(Ran#)1U
(Generates the second random number in
sequence 1.)
U
Ran# 0
(Initializes the sequence.)
(Ran#)0U
Ran# 1
(Generates the first random number in
sequence 1.)
(Ran#)1U
* fx-7400GII: (PROB)
2-15
RanList# Examples
Example
Operation
RanList# (4)
(Generates four random numbers and
displays the result on the ListAns screen.)
*(E)(PROB)*(RAND)(List)
4U
RanList# (3, 1)
(Generates from the first to the third random
numbers of sequence 1 and displays the
result on the ListAns screen.)
)*(E)(PROB)*(RAND)
(List) 3 1U
(Next, generates from the fourth to the sixth
random number of sequence 1 and displays
the result on the ListAns screen.)
)U
Ran# 0
(Initializes the sequence.)
)(Ran#) 0U
RanList# (3, 1)
(Re-generates from the first to the third
random numbers of sequence 1 and displays
the result on the ListAns screen.)
(List) 3 1U
* fx-7400GII: (PROB)
S Random Integer Generation (RanInt#)
RanInt# generates random integers that fall between two specified integers.
RanInt# (A, B [,n])
A0
1 n 999
• Omitting a value for n returns a generated random number as-is. Specifying a value for n
returns the specified number of random values in list form.
2-16
Example
Operation
RanNorm# (8, 68)
(Randomly produces a body length value
obtained in accordance with the normal
distribution of a group of infants less than
one year old with a mean body length of
68cm and standard deviation of 8.)
*(E)(PROB)*(RAND)(Norm)
8 68U
RanNorm# (8, 68, 5)
(Randomly produces the body lengths of five
infants in the above example, and displays
them in a list.)
*(E)(PROB)*(RAND)(Norm)
8 68 5U
* fx-7400GII: (PROB)
S Random Number Generation in Accordance with Binomial Distribution
(RanBin#)
This function generates random integers in accordance with binomial distribution based on
values specified for the number of trials n and probability p.
RanBin# (n, p [,m])
1 n 100000
1 m 999
0p1
• Omitting a value for m returns a generated random number as-is. Specifying a value for m
returns the specified number of random values in list form.
Example
Operation
RanBin# (5, 0.5)
(Randomly produces the number of heads
that can be expected in accordance with
binomial distribution for five coin tosses
where the probability of heads is 0.5.)
*(E)(PROB)*(RAND)(Bin)
5 0.5U
RanBin# (5, 0.5, 3)
(Performs the same coin toss sequence
described above three times and displays
the results in a list.)
*(E)(PROB)*(RAND)(Bin)
5 0.5 3U
* fx-7400GII: (PROB)
I Coordinate Conversion
S Rectangular Coordinates
S Polar Coordinates
• With polar coordinates, Ƨ can be calculated and displayed within a range of
–180°< Ƨ 180° (radians and grads have same range).
• Be sure to specify Comp for Mode in the Setup screen.
2-17
Example
Operation
Calculate r and Ƨ° when x = 14 and y = 20.7
1
2
24.989
55.928
24.98979792 (r)
55.92839019 ( )
Calculate x and y when r = 25 and Ƨ = 56°
1
2
13.979
20.725
K(SET UP)AAAAAA*
(Deg))
*(E)(ANGL)**(E)(Pol()
14 20.7U)
(Rec() 25 56U
13.97982259 (x)
20.72593931 (y)
* fx-7400GII, fx-9750GII: AAAAA ** fx-7400GII: (ANGL)
I Permutation and Combination
S Permutation
n!
nPr =
(n – r)!
S Combination
n!
nCr =
r! (n – r)!
• Be sure to specify Comp for Mode in the Setup screen.
Example 1
To calculate the possible number of different arrangements using 4
items selected from among 10 items
Formula
10
P4 = 5040
Operation
10*(E)(PROB)*(nPr) 4U
* fx-7400GII: (PROB)
Example 2
To calculate the possible number of different combinations of 4 items
that can be selected from among 10 items
Formula
10
C4 = 210
Operation
10*(E)(PROB)*(nCr) 4U
* fx-7400GII: (PROB)
I Greatest Common Divisor (GCD), Least Common Multiple (LCM)
Example
Operation
To determine the greatest common
divisor of 28 and 35
(GCD (28, 35) = 7)
*(E)(NUM)*(E)(GCD) 28
35U
To determine the least common multiple
of 9 and 15
(LCM (9, 15) = 45)
*(E)(NUM)*(E)(LCM) 9 15
U
* fx-7400GII: (NUM)
2-18
I Division Remainder (MOD), Remainder of Exponential Division (MOD
Exp)
Example
Operation
To determine the remainder when 137 is
divided by 7
(MOD (137, 7) = 4)
*(E)(NUM)*(E)(MOD) 137 7
U
To determine the remainder when 53 is
divided by 3
(MOD • E (5, 3, 3) = 2)
*(E)(NUM)*(E)(MOD • E)
5 3 3U
* fx-7400GII: (NUM)
I Fractions
• In the Math input/output mode, the fraction input method is different from that described
below. For fraction input operations in the Math input/output mode, see page 1-11.
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
2
1
73
–– + 3 –– = –––
5
4
20
= 3.65 (Conversion to decimal)*1
25
314U
1
1
––––– + ––––– = 6.066202547 s 10–4 *2
2578
4572
12578
14572U
1
–– s 0.5 = 0.25*3
2
12 .5U
,
*1 Fractions can be converted to decimal values and vice versa.
*2 When the total number of characters, including integer, numerator, denominator and delimiter
marks exceeds 10, the fraction is automatically displayed in decimal format.
*3 Calculations containing both fractions and decimals are calculated in decimal format.
• Pressing the ,() key toggles the display fraction between mixed fraction and
improper fraction format.
I Engineering Notation Calculations
Input engineering symbols using the engineering notation menu.
• Be sure to specify Comp for Mode in the Setup screen.
Example
Operation
999k (kilo) + 25k (kilo)
= 1.024M (mega)
K(SET UP)DD(Eng))999*(E)(E)
(ESYM)*(E)(k)
25(k)U
9 w 10 = 0.9 = 900m (milli)
= 0.9
910U
*(E)(E)(ESYM)*(E)(E)(ENG)*1
2-19
= 0.0009k (kilo)
= 0.9
= 900m
(ENG)*1
(ENG)*2
(ENG)*2
* fx-7400GII: (ESYM)
*1 Converts the displayed value to the next higher engineering unit, by shifting the decimal
point three places to the right.
*2 Converts the displayed value to the next lower engineering unit, by shifting the decimal point
three places to the left.
I Logical Operators (AND, OR, NOT, XOR)
[OPTN]-[LOGIC]
The logical operator menu provides a selection of logical operators.
• {And}/{Or}/{Not}/{Xor} ... {logical AND}/{logical OR}/{logical NOT}/{logical XOR}
• Be sure to specify Comp for Mode in the Setup screen.
Example
What is the logical AND of A and B when A = 3 and B = 2?
A AND B = 1
Operation
Display
3??T(A)U
2??J(B)U
?T(A)*(E)(E)
(LOGIC)*(And)?J(B)U
1
* fx-7400GII: (LOGIC)
S About Logical Operations
• A logical operation always produces either 0 or 1 as its result.
• The following table shows all of possible results that can be produced by AND, OR and XOR
operations.
Value or Expression A
Value or Expression B
A AND B
A OR B
A XOR B
Ax0
Bx0
1
1
0
Ax0
B=0
0
1
1
A=0
Bx0
0
1
1
A=0
B=0
0
0
0
• The following table shows the results produced by the NOT operation.
Value or Expression A
NOT A
Ax0
0
A=0
1
2-20
5. Numerical Calculations
The following explains the numerical calculation operations included in the function menu
displayed when *(CALC) ((CALC) on the fx-7400GII) is pressed. The following
calculations can be performed.
• {Int÷}/{Rmdr}/{Simp} ... {quotient}/{remainder}/{simplification}
• {Solve}/{d/dx}/{d2/dx2}/{°dx}/{SolvN} ... {equality solution}/{differential}/{quadratic differential}/
{integration}/{f(x) function solution}
• {FMin}/{FMax}/{3(}/{logab} ... {minimum value}/{maximum value}/{summation}/{logarithm
logab}
I Quotient of Integer ÷ Integer
[OPTN]-[CALC]-[Int÷]
The “Int÷” function can be used to determine the quotient when one integer is divided by
another integer.
Example
To calculate the quotient of 107 ÷ 7
@?F*(CALC)*(E)
(E)(Int÷)F
U
* fx-7400GII: (CALC)
I Remainder of Integer ÷ Integer
[OPTN]-[CALC]-[Rmdr]
The “Rmdr” function can be used to determine the remainder when one integer is divided by
another integer.
Example
To calculate the remainder of 107 ÷ 7
@?F*(CALC)*(E)
(E)(Rmdr)F
U
* fx-7400GII: (CALC)
I Simplification
[OPTN]-[CALC]-[Simp]
The “Simp” function can be used to simplify fractions manually. The following operations can
be used to perform simplification when an unsimplified calculation result is on the display.
• {Simp} U ... This function automatically simplifies the displayed calculation result using the
smallest prime number available. The prime number used and the simplified result are
shown on the display.
• {Simp} n U ... This function performs simplification according to the specified divisor n.
2-21
Under initial default settings, this calculator automatically simplifies fraction calculation results
before displaying them. Before performing the following examples, use the Setup screen to
change the “Simplify” setting from “Auto” to “Manual” (page 1-29).
• When “a+bi” or “rQ” is specified for the Setup screen “Complex Mode” setting, fraction
calculation results always are simplified before being displayed, even if the “Simplify” setting
is “Manual”.
• If you want to simplify fractions manually (Simplify: Manual), make sure that the “Real” is
selected for the “Complex Mode” setting.
Example 1
15
60
To simplify
5
1
15
=
=
4
60 20
@DE?U
*(CALC)*(E)(E)(Simp)U
* fx-7400GII: (CALC)
(Simp)U
The “F=” value is the divisor.
Example 2
To simplify
27
specifying a divisor of 9
63
3
27
=
7
63
AFEBU*(CALC)*
(E)(E)(Simp)HU
* fx-7400GII: (CALC)
• An error occurs if simplification cannot be performed using the specified divisor.
• Executing Simp while a value that cannot be simplified is displayed will return the original
value, without displaying “F=”.
I Solve Calculations
[OPTN]-[CALC]-[Solve]
The following is the syntax for using the Solve function in a program.
Solve( f(x), n, a, b)
(a: lower limit, b: upper limit, n: initial estimated value)
There are two different input methods that can be used for Solve calculations: direct
assignment and variable table input.
With the direct assignment method (the one described here), you assign values directly to
variables. This type of input is identical to that used with the Solve command used in the
PRGM mode.
2-22
Variable table input is used with the Solve function in the EQUA mode. This input method is
recommended for most normal Solve function input.
An error (Time Out) occurs when there is no convergence of the solution.
For information about Solve calculations, see page 4-4.
• You cannot use a quadratic differential, 3, maximum/minimum value or Solve calculation
expression inside of any of the above functions.
• Pressing
during calculation of Solve (while the cursor is not shown on the display)
interrupts the calculation.
I Solving an f(x) Function
[OPTN]-[CALC]-[SolvN]
You can use SolvN to solve an f(x) function using numerical analysis. The following is the input
syntax.
SolveN (left side [=right side] [,variable] [, lower limit, upper limit])
• The right side, variable, lower limit and upper limit all can be omitted.
• “left side[=right side]” is the expression to be solved. Supported variables are A through Z, r,
and Q. When the right side is omitted, solution is perform using right side = 0.
• The variable specifies the variable within the expression to be solved for (A through Z, r, Q).
Omitting a variable specification cause X to be used as the variable.
• The lower limit and upper limit specify the range of the solution. You can input a value or an
expression as the range.
• The following functions cannot be used within any of the arguments.
Solve(, d2/dx2, FMin(, FMax(, 3(
Up to 10 calculation results can be displayed simultaneously in ListAns format.
• The message “No Solution” is displayed if no solution exists.
• The message “More solutions may exist.” is displayed when there may be solutions other
than those displayed by SolvN.
Example
To solve x2 – 5x – 6 = 0
*(CALC)*(SolvN)
TV DT EU
* fx-7400GII: (CALC)
)
2-23
I Differential Calculations
[OPTN]-[CALC]-[d/dx]
To perform differential calculations, first display the function analysis menu, and then input the
values using the syntax below.
*(CALC)* (d/dx) f(x) a tol
* fx-7400GII: (CALC)
(a: point for which you want to determine the derivative, tol: tolerance)
d f (a)
d/dx ( f (x), a)
dx
The differentiation for this type of calculation is defined as:
f (a + Ax) – f (a)
f ' (a) = lim –––––––––––––
Ax0
Ax
In this definition, infinitesimal is replaced by a sufficiently small x, with the value in the
neighborhood of f' (a) calculated as:
f (a + Ax) – f (a)
f ' (a) –––––––––––––
Ax
In order to provide the best precision possible, this unit employs central difference to perform
differential calculations.
Example
To determine the derivative at point x = 3 for the function
y = x3 + 4x2 + x – 6, with a tolerance of “tol” = 1E – 5
Input the function f(x).
*(CALC)* (d/dx)T,B
CTV
T E
* fx-7400GII: (CALC)
Input point x = a for which you want to determine the derivative.
B
Input the tolerance value.
@$ DU
Using Differential Calculation in a Graph Function
• Omitting the tolerance (tol) value when using the differential command inside of a graph
function simplifies the calculation for drawing the graph. In such a case, precision is
sacrificed for the sake of faster drawing. The tolerance value is specified, the graph is drawn
with the same precision obtained when you normally perform a differential calculation.
• You can also omit input of the derivative point by using the following format for the differential
graph: Y2=d/dx(Y1). In this case, the value of the X variable is used as the derivative point.
Differential Calculation Precautions
• In the function f(x), only X can be used as a variable in expressions. Other variables
(A through Z excluding X, r, Ƨ) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
• Input of the tolerance (tol) value and the closing parenthesis can be omitted. If you omit
tolerance (tol) value, the calculator automatically uses a value for tol as 1E–10.
• Specify a tolerance (tol) value of 1E–14 or greater. An error (Time Out) occurs whenever no
solution that satisfies the tolerance value can be obtained.
• Pressing
during calculation of a differential (while the cursor is not shown on the display)
interrupts the calculation.
2-24
• Inaccurate results and errors can be caused by the following:
- discontinuous points in x values
- extreme changes in x values
- inclusion of the local maximum point and local minimum point in x values
- inclusion of the inflection point in x values
- inclusion of undifferentiable points in x values
- differential calculation results approaching zero
• Always use radians (Rad mode) as the angle unit when performing trigonometric differentials.
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside a differential calculation term.
• In the Math input/output mode, the tolerance value is fixed at 1E–10 and cannot be changed.
I Quadratic Differential Calculations
[OPTN]-[CALC]-[d2/dx2]
After displaying the function analysis menu, you can input quadratic differentials using the
following syntax.
*(CALC)*(d2/dx2) f(x) a tol
* fx-7400GII: (CALC)
(a: differential coefficient point, tol: tolerance)
d 2 ( f (x), a)
d2
–––
–––2 f (a)
2
dx
dx
Quadratic differential calculations produce an approximate differential value using the following
second order differential formula, which is based on Newton’s polynomial interpretation.
f ''(a) =
2 f(a + 3h) – 27 f(a + 2h) + 270 f(a + h) – 490 f(a) + 270 f(a – h) – 27 f(a –2h) + 2 f(a – 3h)
180h2
In this expression, values for “sufficiently small increments of h” are used to obtain a value that
approximates f"(a).
Example
To determine the quadratic differential coefficient at the point where
x = 3 for the function y = x3 + 4x2 + x – 6
Here we will use a tolerance tol = 1E – 5
Input the function f(x).
*(CALC)* (d2/dx2) T,B
CTV
T E
* fx-7400GII: (CALC)
Input 3 as point a, which is the differential coefficient point.
B
Input the tolerance value.
@$ D
U
Quadratic Differential Calculation Precautions
• In the function f(x), only X can be used as a variable in expressions. Other variables (A
through Z excluding X, r, Ƨ) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
2-25
• Input of the tolerance (tol) value and the closing parenthesis can be omitted.
• Specify a tolerance (tol) value of 1E–14 or greater. An error (Time Out) occurs whenever no
solution that satisfies the tolerance value can be obtained.
• The rules that apply for linear differential also apply when using a quadratic differential
calculation for the graph formula (see page 2-24).
• Inaccurate results and errors can be caused by the following:
- discontinuous points in x values
- extreme changes in x values
- inclusion of the local maximum point and local minimum point in x values
- inclusion of the inflection point in x values
- inclusion of undifferentiable points in x values
- differential calculation results approaching zero
• You can interrupt an ongoing quadratic differential calculation by pressing the
key.
• Always use radians (Rad mode) as the angle unit when performing trigonometric quadratic
differentials.
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside of a quadratic differential calculation
term.
• With quadratic differential calculation, calculation precision is up to five digits for the
mantissa.
• In the Math input/output mode, the tolerance value is fixed at 1E–10 and cannot be changed.
I Integration Calculations
[OPTN]-[CALC]-[°dx]
To perform integration calculations, first display the function analysis menu and then input the
values using the syntax below.
*(CALC)* (°dx) f(x) a b tol
* fx-7400GII: (CALC)
(a: start point, b: end point, tol: tolerance)
b
f(x), a, b, tol) a f(x)dx
Area of
b
f(x)dx is calculated
a
As shown in the illustration above, integration calculations are performed by calculating
integral values from a through b for the function y = f (x) where a x b, and f (x) 0. This in
effect calculates the surface area of the shaded area in the illustration.
2-26
Example
To perform the integration calculation for the function shown below,
with a tolerance of “tol” = 1E – 4
5
1
(2x2 + 3x + 4) dx
Input the function f (x).
*(CALC)* (°dx)ATV
BT
C
* fx-7400GII: (CALC)
Input the start point and end point.
@ D
Input the tolerance value.
@$ CU
Note the following points to ensure correct integration values.
(1) When cyclical functions for integration values become positive or negative for different
divisions, perform the calculation for single cycles, or divide between negative and positive,
and then add the results together.
Positive
part (S )
Negative part (S )
b
c
b
a
a
c
f(x)dx = f(x)dx + (– f(x)dx)
Positive part (S)
Negative part (S)
(2) When minute fluctuations in integration divisions produce large fluctuations in integration
values, calculate the integration divisions separately (divide the large fluctuation areas into
smaller divisions), and then add the results together.
b
f(x)dx =
a
x
1
f(x)dx +
a
x
2
x
1
f(x)dx +.....+
b
x
f(x)dx
4
• Pressing
during calculation of an integral (while the cursor is not shown on the display)
interrupts the calculation.
• Always use radians (Rad mode) as the angle unit when performing trigonometric
integrations.
• An error (Time Out) occurs whenever no solution that satisfies the tolerance value can be
obtained.
2-27
Integration Calculation Precautions
• In the function f(x), only X can be used as a variable in expressions. Other variables (A
through Z excluding X, r, Ƨ) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
• Input of “tol” and closing parenthesis can be omitted. If you omit “tol,” the calculator
automatically uses a default value of 1E–5.
• Integration calculations can take a long time to complete.
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside of an integration calculation term.
• In the Math input/output mode, the tolerance value is fixed at 1E–5 and cannot be changed.
I 3 Calculations
[OPTN]-[CALC]-[3(]
To perform 3 calculations, first display the function analysis menu, and then input the values
using the syntax below.
*(CALC)* (E)(3( ) ak k A B n
* fx-7400GII: (CALC)
(a k, k, , , n) =
a =a
k
+ a +1 +........+ a
k=
(n: distance between partitions)
Example
To calculate the following:
6
(k
2
– 3k + 5)
k=2
Use n = 1 as the distance between partitions.
*(CALC)*(E)(3( )? (K)
V B? (K)
D
? (K) A E @U
* fx-7400GII: (CALC)
3 Calculation Precautions
• The value of the specified variable changes during a 3 calculation. Be sure to keep separate
written records of the specified variable values you might need later before you perform the
calculation.
• You can use only one variable in the function for input sequence ak.
• Input integers only for the initial term (A) of sequence ak and last term (B) of sequence ak.
• Input of n and the closing parentheses can be omitted. If you omit n, the calculator
automatically uses n = 1.
• Make sure that the value used as the final term B is greater than the value used as the initial
term A. Otherwise, an error will occur.
• To interrupt an ongoing 3 calculation (indicated when the cursor is not on the display), press
the
key.
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside of a 3 calculation term.
• In the Math input/output mode, the distance between partitions (n) is fixed at 1 and cannot be
changed.
2-28
I Maximum/Minimum Value Calculations
[OPTN]-[CALC]-[FMin]/[FMax]
After displaying the function analysis menu, you can input maximum/minimum calculations
using the formats below, and solve for the maximum and minimum of a function within interval
a x b.
S Minimum Value
*(CALC)* (E)(FMin) f (x) a b n
* fx-7400GII: (CALC)
(a: start point of interval, b: end point of interval, n: precision (n = 1 to 9))
S Maximum Value
*(CALC)* (E)(FMax) f (x) a b n
* fx-7400GII: (CALC)
(a: start point of interval, b: end point of interval, n: precision (n = 1 to 9))
Example
To determine the minimum value for the interval defined by start
point a = 0 and end point b = 3, with a precision of n = 6 for the function
y = x2 – 4x + 9
Input f (x).
*(CALC)* (E)(FMin)TV CT
H
* fx-7400GII: (CALC)
Input the interval a = 0, b = 3.
? B
Input the precision n = 6.
EU
• In the function f (x), only X can be used as a variable in expressions. Other variables (A
through Z excluding X, r, Ƨ) are treated as constants, and the value currently assigned to
that variable is applied during the calculation.
• Input of n and the closing parenthesis can be omitted.
• Discontinuous points or sections with drastic fluctuation can adversely affect precision or
even cause an error.
• Inputting a larger value for n increases the precision of the calculation, but it also increases
the amount of time required to perform the calculation.
• The value you input for the end point of the interval (b) must be greater than the value you
input for the start point (a). Otherwise an error occurs.
• You can interrupt an ongoing maximum/minimum calculation by pressing the
key.
• You can input an integer in the range of 1 to 9 for the value of n. Using any value outside this
range causes an error.
• You cannot use a differential, quadratic differential, integration, 3, maximum/minimum value,
Solve, RndFix or logab calculation expression inside of a maximum/minimum calculation
term.
2-29
6. Complex Number Calculations
You can perform addition, subtraction, multiplication, division, parentheses calculations,
function calculations, and memory calculations with complex numbers just as you do with the
manual calculations described on pages 2-1 to 2-14.
You can select the complex number calculation mode by changing the Complex Mode item on
the Setup screen to one of the following settings.
• {Real} ... Calculation in the real number range only*1
• {a+bi} ... Performs complex number calculation and displays results in rectangular form
• {rƧ} ... Performs complex number calculation and displays results in polar form*2
*1 When there is an imaginary number in the argument, however, complex number calculation
is performed and the result is displayed using rectangular form.
Examples:
ln 2i
= 0.6931471806 + 1.570796327i
ln 2i + ln (– 2) = (Non-Real ERROR)
*2 The display range of Ƨ depends on the angle unit set for the Angle item on the Setup
screen.
• Deg ... –180 < Ƨ 180
• Rad ... – P < Ƨ P
• Gra ... –200 < Ƨ 200
Press *(CPLX) (*(CPLX) on the fx-7400GII) to display the complex calculation
number menu, which contains the following items.
• {i} ... {imaginary unit i input}
• {Abs}/{Arg} ... obtains {absolute value}/{argument}
• {Conj} ... {obtains conjugate}
• {ReP}/{ImP} ... {real}/{imaginary} part extraction
• {rƧ}/{a+bi} ... converts the result to {polar}/{rectangular} form
• You can also use ?(i) in place of *(CPLX) (*(CPLX) on the fx-7400GII)
(i).
• Solutions obtained by the Real, a+bi and rƧ modes are different for power root (xy)
calculations when x < 0 and y = m/n when n is an odd number.
Example: 3x (– 8) = – 2 (Real)
= 1 + 1.732050808i (a +bi)
= 260 (r Ƨ )
• To input the “ ” operator into the polar coordinate expression (r Ƨ ), press T().
2-30
I Arithmetic Operations
[OPTN]-[CPLX]-[i]
Arithmetic operations are the same as those you use for manual calculations. You can even
use parentheses and memory.
Example
(1 + 2i) + (2 + 3i)
*(CPLX)*
@
A(i)
A
B(i)U
* fx-7400GII: (CPLX)
I Reciprocals, Square Roots, and Squares
Example
(3 + i)
*(CPLX)*
V()B
(i)U
* fx-7400GII: (CPLX)
I Complex Number Format Using Polar Form
Example
230 s 345 = 675
K(SET UP)AAAAAA*
(Deg)A(rƧ))
A T()B? B
T()CDU
* fx-7400GII, fx-9750GII: AAAAA
I Absolute Value and Argument
[OPTN]-[CPLX]-[Abs]/[Arg]
The unit regards a complex number in the form a + bi as a coordinate on a Gaussian plane,
and calculates absolute value²Z ²and argument (arg).
Example
To calculate absolute value (r) and argument (Ƨ) for the complex number
3 + 4i, with the angle unit set for degrees
Imaginary axis
Real axis
2-31
*(CPLX)*(Abs)
B
C(i)U
(Calculation of absolute value)
* fx-7400GII: (CPLX)
*(CPLX)*(Arg)
B
C(i)U
(Calculation of argument)
* fx-7400GII: (CPLX)
• The result of the argument calculation differs in accordance with the current angle unit
setting (degrees, radians, grads).
I Conjugate Complex Numbers
[OPTN]-[CPLX]-[Conj]
A complex number of the form a + bi becomes a conjugate complex number of the form
a – bi.
Example
To calculate the conjugate complex number for the complex number
2 + 4i
*(CPLX)*(Conj)
A
C(i)U
* fx-7400GII: (CPLX)
I Extraction of Real and Imaginary Parts
[OPTN]-[CPLX]-[ReP]/[lmP]
Use the following procedure to extract the real part a and the imaginary part b from a complex
number of the form a + bi.
Example
To extract the real and imaginary parts of the complex number 2 + 5i
*(CPLX)*(E)(ReP)
A
D(E)(i)U
(Real part extraction)
* fx-7400GII: (CPLX)
*(CPLX)*(E)(ImP)
A
D(E)(i)U
(Imaginary part extraction)
* fx-7400GII: (CPLX)
I Polar and Rectangular Form Transformation
[OPTN]-[CPLX]-[rƧ]/[a+bi]
Use the following procedure to transform a complex number displayed in rectangular form to
polar form, and vice versa.
2-32
Example
To transform the rectangular form of complex number 1 +
3 i to its
polar form
K(SET UP)AAAAAA*
(Deg)A(a+bi))
@
V()B
*(CPLX)**(i)(E)(rQ)U
* fx-7400GII, fx-9750GII: AAAAA
** fx-7400GII: (CPLX)
A T()E?
*(CPLX)*(E)(a+bi)U
* fx-7400GII: (CPLX)
• The input/output range of complex numbers is normally 10 digits for the mantissa and two
digits for the exponent.
• When a complex number has more than 21 digits, the real part and imaginary part are
displayed on separate lines.
• The following functions can be used with complex numbers.
, x 2, x –1, ^(x y), 3, x, In, log, logab, 10x, e x, Int, Frac, Rnd, Intg, RndFix(, Fix, Sci, ENG,
ENG, ° ’ ”, ° ’ ”, a b/c, d /c
7. Binary, Octal, Decimal, and Hexadecimal
Calculations with Integers
You can use the RUN • MAT (or RUN) mode and binary, octal, decimal, and hexadecimal
settings to perform calculations that involve binary, octal, decimal and hexadecimal values. You
can also convert between number systems and perform bitwise operations.
• You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations.
• You can use only integers in binary, octal, decimal, and hexadecimal calculations, which
means that fractional values are not allowed. If you input a value that includes a decimal part,
the calculator automatically cuts off the decimal part.
• If you attempt to enter a value that is invalid for the number system (binary, octal, decimal,
hexadecimal) you are using, the calculator displays an error message. The following shows
the numerals that can be used in each number system.
Binary: 0, 1
Octal: 0, 1, 2, 3, 4, 5, 6, 7
Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• Negative binary, octal, and hexadecimal values are produced using the two’s complement of
the original value.
• The following are the display capacities for each of the number systems.
2-33
Number System
Binary
Octal
Decimal
Hexadecimal
Display Capacity
16 digits
11 digits
10 digits
8 digits
• The alphabetic characters used in the hexadecimal number appear differently on the display
to distinguish them from text characters.
Normal Text
A
B
C
D
E
F
Hexadecimal Values
S
T
U
V
W
X
T
J
(
Q
A
R
Keys
• The following are the calculation ranges for each of the number systems.
Binary Values
Positive: 0 x 111111111111111
Negative: 1000000000000000 x 1111111111111111
Octal Values
Positive: 0 x 17777777777
Negative: 20000000000 x 37777777777
Decimal Values
Positive: 0 x 2147483647
Negative: –2147483648 x –1
Hexadecimal Values
Positive: 0 x 7FFFFFFF
Negative: 80000000 x FFFFFFFF
S To perform a binary, octal, decimal, or hexadecimal calculation
[SET UP]-[Mode]-[Dec]/[Hex]/[Bin]/[Oct]
1. In the Main Menu, select RUN • MAT (or RUN).
2. Press K(SET UP). Move the highlighting to “Mode”, and then specify the default
number system by pressing (Dec), (Hex), (Bin), or (Oct) for the Mode setting.
3. Press ) to change to the screen for calculation input. This causes a function menu with
the following items to appear.
• {d~o}/{LOG}/{DISP} ... {number system specification}/{bitwise operation}/
{decimal/hexadecimal/binary/octal conversion} menu
I Selecting a Number System
You can specify decimal, hexadecimal, binary, or octal as the default number system using the
Setup screen.
S To specify a number system for an input value
You can specify a number system for each individual value you input. Press (d~o) to display
a menu of number system symbols. Press the function key that corresponds to the symbol you
want to select and then input the value.
• {d}/{h}/{b}/{o} ... {decimal}/{hexadecimal}/{binary}/{octal}
2-34
S To input values of mixed number systems
Example
To input 12310, when the default number system is hexadecimal
K(SET UP)
Move the highlighting to “Mode”, and then
press (Hex)).
(d~o)(d)@ABU
I Negative Values and Bitwise Operations
Press (LOG) to display a menu of negation and bitwise operators.
• {Neg} ... {negation}*1
• {Not}/{and}/{or}/{xor}/{xnor} ... {NOT}*2/{AND}/{OR}/{XOR}/{XNOR}*3
*1 two’s complement
*2 one’s complement (bitwise complement)
*3 bitwise AND, bitwise OR, bitwise XOR, bitwise XNOR
S Negative Values
Example
To determine the negative of 1100102
K(SET UP)
Move the highlighting to “Mode”, and then
press (Bin)).
(LOG)(Neg)
@@??@?U
• Negative binary, octal, and hexadecimal values are produced by taking the binary two’s
complement and then returning the result to the original number base. With the decimal
number base, negative values are displayed with a minus sign.
S Bitwise Operations
Example
To input and execute “12016 and AD16”
K(SET UP)
Move the highlighting to “Mode”, and then
press (Hex)).
@A?(LOG)
(and)
#U
I Number System Transformation
Press (DISP) to display a menu of number system transformation functions.
• {Dec}/{Hex}/{Bin}/{Oct} ... transformation of displayed value to its {decimal}/
{hexadecimal}/{binary}/{octal} equivalent
2-35
S To convert a displayed value from one number system to another
Example
To convert 2210 (default number system) to its binary or octal value
K(SET UP)
Move the highlighting to “Mode”, and then
press (Dec)).
(d~o)(d)AAU
)(DISP)(Bin)U
(Oct)U
8. Matrix Calculations
Important!
• Matrix calculations cannot be performed on the fx-7400GII.
From the Main Menu, enter the RUN • MAT mode, and press (MAT) to perform Matrix
calculations.
26 matrix memories (Mat A through Mat Z) plus a Matrix Answer Memory (MatAns), make it
possible to perform the following matrix operations.
• Addition, subtraction, multiplication, division
• Scalar multiplication calculations
• Determinant calculations
• Matrix transposition
• Matrix inversion
• Matrix squaring
• Raising a matrix to a specific power
• Absolute value, integer part extraction, fractional part extraction, maximum integer
calculations
• Inputting complex numbers in matrix elements and using complex number related functions
• Matrix modification using matrix commands
The maximum number of rows that can be specified for a matrix is 999, and the maximum
number of columns is 999.
About Matrix Answer Memory (MatAns)
• The calculator automatically stores matrix calculation results in Matrix Answer Memory. Note
the following points about Matrix Answer Memory.
• Whenever you perform a matrix calculation, the current Matrix Answer Memory contents are
replaced by the new result. The previous contents are deleted and cannot be recovered.
• Inputting values into a matrix does not affect Matrix Answer Memory contents.
2-36
I Inputting and Editing Matrices
Pressing (MAT) displays the Matrix Editor screen. Use the Matrix Editor to input and edit
matrices.
m s n … m (row) s n (column) matrix
None… no matrix preset
• {DEL}/{DEL•A} ... deletes {a specific matrix}/{all matrices}
• {DIM} ... {specifies the matrix dimensions (number of cells)}
S Creating a Matrix
To create a matrix, you must first define its dimensions (size) in the Matrix Editor. Then you can
input values into the matrix.
S To specify the dimensions (size) of a matrix
Example
To create a 2-row s 3-column matrix in the area named Mat B
Highlight Mat B.
A
(DIM) (This step can be omitted.)
Specify the number of rows.
AU
Specify the number of columns.
BU
U
• All of the cells of a new matrix contain the value 0.
• Changing the dimensions of a matrix deletes its current contents.
• If “Memory ERROR” remains next to the matrix area name after you input the dimensions, it
means there is not enough free memory to create the matrix you want.
S To input cell values
Example
To input the following data into Matrix B:
1 2 3
4 5 6
2-37
The following operation is a continuation of the example calculation on the previous page.
@UAUBU
CUDUEU
(Data is input into the highlighted cell. Each
time you press U, the highlighting moves
to the next cell to the right.)
• Displayed cell values show positive integers up to six digits, and negative integers up to five
digits (one digit used for the negative sign). Exponential values are shown with up to two
digits for the exponent. Fractional values are not displayed.
S Deleting Matrices
You can delete either a specific matrix or all matrices in memory.
S To delete a specific matrix
1. While the Matrix Editor is on the display, use D and A to highlight the matrix you want to
delete.
2. Press (DEL).
3. Press (Yes) to delete the matrix or (No) to abort the operation without deleting
anything.
S To delete all matrices
1. While the Matrix Editor is on the display, press (DEL • A).
2. Press (Yes) to delete all matrices in memory or (No) to abort the operation without
deleting anything.
I Matrix Cell Operations
Use the following procedure to prepare a matrix for cell operations.
1. While the Matrix Editor is on the display, use D and A to highlight the name of the matrix
you want to use.
You can jump to a specific matrix by inputting the letter that corresponds to the matrix name.
Inputting ?G(N), for example, jumps to Mat N.
Pressing (Ans) jumps to the matrix current memory.
2. Press U and the function menu with the following items appears.
• {R-OP} ... {row operation menu}
• {ROW}
• {DEL}/{INS}/{ADD} ... row {delete}/{insert}/{add}
• {COL}
• {DEL}/{INS}/{ADD} ... column {delete}/{insert}/{add}
• {EDIT} ... {cell editing screen}
All of the following examples use Matrix A.
2-38
S Row Calculations
The following menu appears whenever you press (R-OP) while a recalled matrix is on the
display.
• {Swap} ... {row swap}
• {sRw} ... {product of specified row and scalar}
• {sRw+} ... {addition of one row and the product of a specified row with a scalar}
• {Rw+} ... {addition of specified row to another row}
S To swap two rows
Example
To swap rows two and three of the following matrix:
All of the operation examples are performed using the following matrix.
Matrix A =
1
2
3
4
5
6
(R-OP)(Swap)
Input the number of the rows you want to swap.
AUBUU
S To calculate the scalar multiplication of a row
Example
To calculate the product of row 2 and the scalar 4
(R-OP)(sRw)
Input multiplier value.*
CU
Specify row number.
AUU
* A complex number also can be input as multiplier value (k).
S To calculate the scalar multiplication of a row and add the result to another
row
Example
To calculate the product of row 2 and the scalar 4, then add the result to
row 3
(R-OP)(sRw+)
Input multiplier value.*
CU
Specify number of row whose product should be calculated.
AU
Specify number of row where result should be added.
BUU
* A complex number also can be input as multiplier value (k).
2-39
S To add two rows together
Example
To add row 2 to row 3
(R-OP)(Rw+)
Specify number of row to be added.
AU
Specify number of row to be added to.
BUU
S Row Operations
• {DEL} ... {delete row}
• {INS} ... {insert row}
• {ADD} ... {add row}
S To delete a row
Example
To delete row 2
(ROW)A
(DEL)
S To insert a row
Example
To insert a new row between rows one and two
(ROW)A
(INS)
S To add a row
Example
To add a new row below row 3
(ROW)AA
(ADD)
2-40
S Column Operations
• {DEL} ... {delete column}
• {INS} ... {insert column}
• {ADD} ... {add column}
S To delete a column
Example
To delete column 2
(COL)C
(DEL)
I Modifying Matrices Using Matrix Commands
[OPTN]-[MAT]
S To display the matrix commands
1. From the Main Menu, enter the RUN • MAT mode.
2. Press * to display the option menu.
3. Press (MAT) to display the matrix command menu.
The following describes only the matrix command menu items that are used for creating
matrices and inputting matrix data.
• {Mat} ... {Mat command (matrix specification)}
• {MmL} ... {MatmList command (assign contents of selected column to list file)}
• {Aug} ... {Augment command (link two matrices)}
• {Iden} ... {Identity command (identity matrix input)}
• {Dim} ... {Dim command (dimension check)}
• {Fill} ... {Fill command (identical cell values)}
• You can also use A(Mat) in place of *(MAT)(Mat).
S Matrix Data Input Format
[OPTN]-[MAT]-[Mat]
The following shows the format you should use when inputting data to create a matrix using
the Mat command.
a11 a12 ... a1n
...
...
a22 ... a2n
...
a21
am1
am2 ... amn
= [ [a11, a12, ..., a1n] [a21, a22, ..., a2n] .... [am1, am2, ..., amn] ]
m Mat [letter A through Z]
2-41
Example
To input the following data as Matrix A:
1 3 5
2 4 6
( [ )
( [ )@ B D
( ] )
( [ )A C E
( ] ) ( ] )?*(MAT)
(Mat)?T(A)
U
Matrix name
• The maximum value of both m and n is 999.
• An error occurs if memory becomes full as you are inputting data.
• You can also use the above format inside a program that inputs matrix data.
S To input an identity matrix
[OPTN]-[MAT]-[Iden]
Use the Identity command to create an identity matrix.
Example
To create a 3 s 3 identity matrix as Matrix A
*(MAT)(E)(Iden)
B?(E)(Mat)?T(A)U
Number of rows/columns
S To check the dimensions of a matrix
[OPTN]-[MAT]-[Dim]
Use the Dim command to check the dimensions of an existing matrix.
Example 1
To check the dimensions of Matrix A
*(MAT)(E)(Dim)
(E)(Mat)?T(A)U
The display shows that Matrix A consists of two rows and three columns.
Since the result of the Dim command is list type data, it is stored in ListAns Memory.
You can also use {Dim} to specify the dimensions of the matrix.
Example 2
To specify dimensions of 2 rows and 3 columns for Matrix B
( H )A B ( J )?
*(MAT)(E)(Dim)
(E)(Mat)?J(B)U
S Modifying Matrices Using Matrix Commands
You can also use matrix commands to assign values to and recall values from an existing
matrix, to fill in all cells of an existing matrix with the same value, to combine two matrices into
a single matrix, and to assign the contents of a matrix column to a list file.
2-42
S To assign values to and recall values from an existing matrix
[OPTN]-[MAT]-[Mat]
Use the following format with the Mat command to specify a cell for value assignment and
recall.
Mat X [m, n]
X = matrix name (A through Z, or Ans)
m = row number
n = column number
Example 1
To assign 10 to the cell at row 1, column 2 of the following matrix:
1 2
Matrix A =
3
4
5
6
@??*(MAT)(Mat)
?T(A)
( F )@ A
( G )U
Example 2
Multiply the value in the cell at row 2, column 2 of the above matrix by 5
*(MAT)(Mat)
?T(A)
( F )A A
( G ) DU
S To fill a matrix with identical values and to combine two matrices into a
single matrix
[OPTN]-[MAT]-[Fill]/[Aug]
Use the Fill command to fill all the cells of an existing matrix with an identical value and the
Augment command to combine two existing matrices into a single matrix.
Example 1
To fill all of the cells of Matrix A with the value 3
*(MAT)(E)(Fill)
B (E)(Mat)?T(A)U
(Mat)?T(A)U
Example 2
To combine the following two matrices:
1
3
A=
B=
2
4
*(MAT)(Aug)
(Mat)?T(A)
(Mat)?J(B)U
• The two matrices you combine must have the same number of rows. An error occurs if you
try to combine two matrices that have different number of rows.
2-43
• You can use Matrix Answer Memory to assign the results of the above matrix input and edit
operations to a matrix variable. To do so, use the following syntax.
Fill (n, Mat A)
Augment (Mat A, Mat B) m Mat G
In the above, A, B, and G are any variable names A through Z, and n is any value.
The above does not affect the contents of Matrix Answer Memory.
S To assign the contents of a matrix column to a list
[OPTN]-[MAT]-[MmL]
Use the following format with the MatmList command to specify a column and a list.
Mat m List (Mat X, m) m List n
X = matrix name (A through Z)
m = column number
n = list number
Example
To assign the contents of column 2 of the following matrix to list 1:
Matrix A =
1
2
3
4
5
6
*(MAT)(MmL)
(Mat)?T(A) A
?*(LIST)(List)@U
(List)@U
I Matrix Calculations
[OPTN]-[MAT]
Use the matrix command menu to perform matrix calculation operations.
S To display the matrix commands
1. From the Main Menu, enter the RUN • MAT mode.
2. Press * to display the option menu.
3. Press (MAT) to display the matrix command menu.
The following describes only the matrix commands that are used for matrix arithmetic
operations.
• {Mat} ... {Mat command (matrix specification)}
• {Det} ... {Det command (determinant command)}
• {Trn} ... {Trn command (transpose matrix command)}
• {Iden} ... {Identity command (identity matrix input)}
• {Ref} ... {Ref command (row echelon form command)}
• {Rref} ... {Rref command (reduced row echelon form command)}
All of the following examples assume that matrix data is already stored in memory.
2-44
S Matrix Arithmetic Operations
Example 1
[OPTN]-[MAT]-[Mat]/[Iden]
To add the following two matrices (Matrix A + Matrix B):
A=
1
1
2
1
B=
2
3
2
1
*(MAT)(Mat)?T(A)
(Mat)?J(B)U
Example 2
To multiply the two matrices in Example 1 (Matrix A s Matrix B)
*(MAT)(Mat)?T(A)
(Mat)?J(B)U
• The two matrices must have the same dimensions in order to be added or subtracted. An
error occurs if you try to add or subtract matrices of different dimensions.
• For multiplication (Matrix 1 s Matrix 2), the number of columns in Matrix 1 must match the
number of rows in Matrix 2. Otherwise, an error occurs.
S Determinant
Example
[OPTN]-[MAT]-[Det]
Obtain the determinant for the following matrix:
1 2 3
Matrix A =
4
5
6
−1 −2
0
*(MAT)(Det)(Mat)
?T(A)U
• Determinants can be obtained only for square matrices (same number of rows and columns).
Trying to obtain a determinant for a matrix that is not square produces an error.
• The determinant of a 2 s 2 matrix is calculated as shown below.
|A| =
a11 a12
a21 a22
= a11a22 – a12a21
• The determinant of a 3 s 3 matrix is calculated as shown below.
|A| =
a11 a12 a13
a21 a22 a23
a31 a32 a33
= a11a22a33 + a12a23a31 + a13a21a32 – a11a23a32 – a12a21a33 – a13a22a31
S Matrix Transposition
[OPTN]-[MAT]-[Trn]
A matrix is transposed when its rows become columns and its columns become rows.
Example
To transpose the following matrix:
Matrix A =
1
2
3
4
5
6
2-45
*(MAT)(Trn)(Mat)
?T(A)U
S Row Echelon Form
[OPTN]-[MAT]-[Ref]
This command uses the Gaussian elimination algorithm to find the row echelon form of a
matrix.
Example
To find the row echelon form of the following matrix:
Matrix A =
1
2
3
4
5
6
*(MAT)(E)(Ref)
(E)(Mat)?T(A)U
S Reduced Row Echelon Form
[OPTN]-[MAT]-[Rref]
This command finds the reduced row echelon form of a matrix.
Example
To find the reduced row echelon form of the following matrix:
Matrix A =
2
−1
3
19
1
1
−5
−21
0
4
3
0
*(MAT)(E)(Rref)
(E)(Mat)?T(A)U
• The row echelon form and reduced row echelon form operation may not produce accurate
results due to dropped digits.
S Matrix Inversion
Example
[x–1]
To invert the following matrix:
Matrix A =
1
2
3
4
*(MAT)(Mat)
?T(A) (x–1)U
2-46
• Only square matrices (same number of rows and columns) can be inverted. Trying to invert a
matrix that is not square produces an error.
• A matrix with a determinant of zero cannot be inverted. Trying to invert a matrix with
determinant of zero produces an error.
• Calculation precision is affected for matrices whose determinant is near zero.
• A matrix being inverted must satisfy the conditions shown below.
A A–1 = A–1 A = E =
1 0
0 1
The following shows the formula used to invert Matrix A into inverse matrix A–1.
A=
a b
c d
A–1=
1
ad – bc
d –b
–c a
Note that ad – bc x 0.
S Squaring a Matrix
Example
[x2]
To square the following matrix:
Matrix A =
1
2
3
4
*(MAT)(Mat)?T(A)VU
S Raising a Matrix to a Power
Example
[^]
To raise the following matrix to the third power:
Matrix A =
1
2
3
4
*(MAT)(Mat)?T(A)
,BU
• For matrix power calculations, calculation is possible up to a power of 32766.
S Determining the Absolute Value, Integer Part, Fraction Part, and Maximum
[OPTN]-[NUM]-[Abs]/[Frac]/[Int]/[Intg]
Integer of a Matrix
Example
To determine the absolute value of the following matrix:
Matrix A =
1
–2
–3
4
*(E)(NUM)(Abs)
*(MAT)(Mat)?T(A)U
2-47
S Complex Number Calculations with a Matrix
Example
To determine the absolute value of a matrix with the following complex
number elements:
–1 + i
Matrix D =
1+i
1+i
–2 + 2i
*(E)(NUM)(Abs)
*(MAT)(Mat)?Q(D)U
• The following complex number functions are supported in matrices.
i, Abs, Arg, Conjg, ReP, ImP, a+bi, rQ
Note, however, that “a+bi” and “rQ” cannot be used in the Linear input/output mode.
Matrix Calculation Precautions
• Determinants and inverse matrices are subject to error due to dropped digits.
• Matrix operations are performed individually on each cell, so calculations may require
considerable time to complete.
• The calculation precision of displayed results for matrix calculations is p1 at the least
significant digit.
• If a matrix calculation result is too large to fit into Matrix Answer Memory, an error occurs.
• You can use the following operation to transfer Matrix Answer Memory contents to another
matrix (or when Matrix Answer Memory contains a determinant to a variable).
MatAns m Mat A
In the above, A is any variable name A through Z. The above does not affect the contents of
Matrix Answer Memory.
9. Metric Conversion Calculations
You can convert values from one unit of measurement to another. Measurement units are
classified according to the following 11 categories. The indicators in the “Display Name”
column show the text that appears in the calculator’s function menu.
Display Name
Category
Display Name
Category
Display Name
Category
LENG
Length
TMPR
Temperature
PRES
Pressure
AREA
Area
VELO
Velocity
ENGY
Energy/Work
VLUM
Volume
MASS
Mass
PWR
Power
TIME
Time
FORC
Force/Weight
2-48
You can convert from any unit in a category to any other unit in the same category.
• Attempting to convert from a unit in one category (such as “AREA”) to a unit in another
category (such as “TIME”) results in a Conversion ERROR.
• See the “Unit Conversion Command List” (page 2-50) for information about the units included
in each category.
I Performing a Unit Conversion Calculation
[OPTN]-[CONV]
Input the value you are converting from and the conversion commands using the syntax shown
below to perform a unit conversion calculation.
{value converting from}{conversion command 1} {conversion command 2}
• Use {conversion command 1} to specify the unit being converted from and {conversion
command 2} to specify the unit being converted to.
• is a command that links the two conversion commands. This command is always available
at () of the Conversion menu.
• Real numbers or a list that contains real number elements only can be used as the value
being converted from. When values being converted from are input into a list (or when list
memory is specified), conversion calculation is performed for each element in the list and
calculation results are returned in list format (ListAns screen).
• A complex number cannot be used as a value to be converted from. An error occurs if even
a single element of a list being used as the value being converted from contains a complex
number.
Example 1
To convert 50cm to inches
D?*(E)(CONV)*(LENG)
D(cm)()(LENG)CA(in)U
* fx-7400GII: (CONV)
Example 2
To convert {175, 162, 180} centimeters to feet
({)@FD @EA
@G? (})
*(E)(CONV)*(AREA)A(m2)
()(AREA)B(ha)U
* fx-7400GII: (CONV)
2-49
I Unit Conversion Command List
Display Name
Cat.
Display Name
Unit
fm
fermi
cm3
cubic centimeter
Å
angstrom
mL
milliliter
Mm
micrometer
mm
millimeter
m3
cubic meter
cm
centimeter
in3
cubic inch
m
meter
ft3
cubic foot
km
kilometer
AU
astronomical unit
l.y.
light year
pc
parsec
Mil
1/1000 inch
pt
pint
in
inch
qt
quart
ft
foot
tsp
teaspoon
yd
yard
tbsp
tablespoon
fath
fathom
cup
cup
rd
rod
ns
nanosecond
mile
mile
Ms
microsecond
nautical mile
ms
millisecond
n mile
Area
Unit
Volume
L
liter
fl_oz(UK)
ounce
fl_oz(US)
fluid ounce (U.S.)
gal(US)
gallon
gal(UK)
UK gallon
cm2
square centimeter
m2
square meter
ha
hectare
km2
square kilometer
in2
square inch
week
week
ft2
square foot
yr
year
yd2
square yard
s-yr
sidereal year
acre
acre
t-yr
tropical year
mile2
square mile
Time
Length
Cat.
2-50
s
second
min
minute
h
hour
day
day
Temperature
°C
degrees Celsius
Pa
Pascal
K
Kelvin
kPa
Kilo Pascal
°F
degrees Fahrenheit
mmH2O
millimeter of water
°R
degrees Rankine
mmHg
millimeter of Mercury
m/s
meter per second
atm
atmosphere
km/h
kilometer per hour
inH2O
inch of water
knot
knot
inHg
inch of Mercury
ft/s
foot per second
lbf/in2
pound per square
inch
mile/h
u
mile per hour
Display Name
bar
kgf/cm2
atomic mass unit
eV
milligram
bar
kilogram force per
square centimeter
electron Volt
kg
kilogram
calth
calorieth
metric ton
cal15
calorie (15°C)
oz
avoirdupois ounce
calIT
calorieIT
lb
pound mass
kcalth
kilocalorieth
kcal15
kilocalorie (15°C)
kcalIT
kilocalorieIT
l-atm
liter atmosphere
slug
ton(short)
ton, short (2000lbm)
ton(long)
ton, long (2240lbm)
Energy/Work
gram
mton
J
Unit
g
slug
Force/Weight
Cat.
Joule
N
newton
kW•h
kilowatt hour
lbf
pound of force
ft•lbf
foot-pound
tonf
ton of force
Btu
British thermal unit
dyne
dyne
erg
erg
kgf
kilogram of force
kgf•m
W
calth/s
Power
Mass
mg
Unit
Pressure
Display Name
Velocity
Cat.
hp
ft•lbf/s
Btu/min
kilogram force meter
watt
calorie per second
horsepower
foot-pound per
second
British thermal unit
per minute
Source: NIST Special Publication 811 (1995)
2-51
Chapter 3 List Function
A list is a storage place for multiple data items.
This calculator lets you store up to 26 lists in a single file, and you can store up to six files in
memory. Stored lists can be used in arithmetic and statistical calculations, and for graphing.
Element number
List 1
SUB
1
2
3
4
5
6
7
8
•
•
•
•
56
37
21
69
40
48
93
30
Display range
Cell
List 2
List 3
1
2
4
8
16
32
64
128
107
75
122
87
298
48
338
49
•
•
•
•
•
•
•
•
•
•
•
•
Column
List 4
List 5
3.5
6
2.1
4.4
3
6.8
2
8.7
4
0
0
2
0
3
9
0
•
•
•
•
•
•
•
•
List 26
0
0
0
0
0
0
0
0
List name
Sub name
Row
•
•
•
•
1. Inputting and Editing a List
When you enter the STAT mode, the “List Editor” will appear first. You can use the List Editor to
input data into a list and to perform a variety of other list data operations.
S To input values one-by-one
Use the cursor keys to move the highlighting to the list
name, sub name or cell you want to select. Note that A
does not move the highlighting to a cell that does not
contain a value.
The screen automatically scrolls when the highlighting is located at either edge of the screen.
The following example is performed starting with the highlighting located at Cell 1 of List 1.
1. Input a value and press U to store it in the list.
BU
• The highlighting automatically moves down to the next
cell for input.
2. Input the value 4 in the second cell, and then input the
result of 2 + 3 in the next cell.
CUA
BU
• You can also input the result of an expression or a complex number into a cell.
• You can input values up to 999 cells in a single list.
3-1
3
S To batch input a series of values
1. Use the cursor keys to move the highlighting to another
list.
2. Press ( { ), and then input the values you want,
pressing between each one. Press ( } ) after
inputting the final value.
( { )E F G ( } )
3. Press U to store all of the values in your list.
U
• Remember that a comma separates values, so you should not input a comma after the final
value of the set you are inputting.
Right: {34, 53, 78}
Wrong: {34, 53, 78,}
You can also use list names inside of a mathematical expression to input values into another
cell. The following example shows how to add the values in each row in List 1 and List 2, and
input the result into List 3.
1. Use the cursor keys to move the highlighting to the name
of the list where you want the calculation results to be
input.
2. Press * and input the expression.
*(LIST)(List)@
*(LIST)(List)AU
• You can also use @(List) in place of *(LIST)(List).
I Editing List Values
S To change a cell value
Use the cursor keys to move the highlighting to the cell whose value you want to change. Input
the new value and press U to replace the old data with the new one.
S To edit the contents of a cell
1. Use the cursor keys to move the highlighting to the cell whose contents you want to edit.
2. Press (E)(EDIT).
3. Make any changes in the data you want.
3-2
S To delete a cell
1. Use the cursor keys to move the highlighting to the cell you want to delete.
2. Press (E)(DEL) to delete the selected cell and cause everything below it to be shifted
up.
• The cell delete operation does not affect cells in other lists. If the data in the list whose cell
you delete is somehow related to the data in neighboring lists, deleting a cell can cause
related values to become misaligned.
S To delete all cells in a list
Use the following procedure to delete all the data in a list.
1. Use the cursor key to move the highlighting to any cell of the list whose data you want to
delete.
2. Pressing (E)(DEL • A) causes a confirmation message to appear.
3. Press (Yes) to delete all the cells in the selected list or (No) to abort the delete
operation without deleting anything.
S To insert a new cell
1. Use the cursor keys to move the highlighting to the location where you want to insert the
new cell.
2. Press (E)(INS) to insert a new cell, which contains a value of 0, causing everything
below it to be shifted down.
• The cell insert operation does not affect cells in other lists. If the data in the list where you
insert a cell is somehow related to the data in neighboring lists, inserting a cell can cause
related values to become misaligned.
I Naming a List
You can assign List 1 through List 26 “sub names” of up to eight bytes each.
S To name a list
1. On the Setup screen, highlight “Sub Name” and then press (On)).
2. Use the cursor keys to move the highlighting to the SUB cell of the list you want to name.
3-3
3. Type in the name and then press U.
• To type in a name using alpha characters, press ? to enter the ALPHA-LOCK
mode.
Example: YEAR
(Y)A(E)T(A)E(R)U
• The following operation displays a sub name in the RUN • MAT (or RUN) mode.
@(List) n
( [ )? ( ] )U
(n = list number from 1 to 26)
• Though you can input up to 8 bytes for the sub name, only the characters that can fit within
the List Editor cell will be displayed.
• The List Editor SUB cell is not displayed when “Off” is selected for “Sub Name” on the Setup
screen.
I Sorting List Values
You can sort lists into either ascending or descending order. The highlighting can be located in
any cell of the list.
S To sort a single list
Ascending order
1. While the lists are on the screen, press (E)(TOOL)(SRT • A).
2. The prompt “How Many Lists?:” appears to ask how many lists you want to sort. Here we will
input 1 to indicate we want to sort only one list.
@U
3. In response to the “Select List List No:” prompt, input the number of the list you want to sort.
@U
Descending order
Use the same procedure as that for the ascending order sort. The only difference is that you
should press (SRT • D) in place of (SRT • A).
S To sort multiple lists
You can link multiple lists together for a sort so that all of their cells are rearranged in
accordance with the sorting of a base list. The base list is sorted into either ascending
order or descending order, while the cells of the linked lists are arranged so that the relative
relationship of all the rows is maintained.
3-4
Ascending order
1. While the lists are on the screen, press (E)(TOOL)(SRT • A).
2. The prompt “How Many Lists?:” appears to ask how many lists you want to sort. Here we will
sort one base list linked to one other list, so we should input 2.
AU
3. In response to the “Select Base List List No:” prompt, input the number of the list you want
to sort into ascending order. Here we will specify List 1.
@U
4. In response to the “Select Second List List No:” prompt, input the number of the list you
want to link to the base list. Here we will specify List 2.
AU
Descending order
Use the same procedure as that for the ascending order sort. The only difference is that you
should press (SRT • D) in place of (SRT • A).
• You can specify a value from 1 to 6 as the number of lists for sorting.
• If you specify a list more than once for a single sort operation, an error occurs.
An error also occurs if lists specified for sorting do not have the same number of values
(rows).
2. Manipulating List Data
List data can be used in arithmetic and function calculations. In addition, various list data
manipulation functions make manipulation of list data quick and easy.
You can use list data manipulation functions in the RUN • MAT (or RUN), STAT, TABLE,
EQUA and PRGM modes.
I Accessing the List Data Manipulation Function Menu
All of the following examples are performed after entering the RUN • MAT (or RUN) mode.
Press * and then (LIST) to display the list data manipulation menu, which contains the
following items.
• {List}/{LmM}/{Dim}/{Fill}/{Seq}/{Min}/{Max}/{Mean}/{Med}/{Aug}/{Sum}/{Prod}/{Cuml}/
{%}/{ }
Note that all closing parentheses at the end of the following operations can be omitted.
S To transfer list contents to Matrix Answer Memory
(Not included on the fx-7400GII)
[OPTN]-[LIST]-[LmM]
*(LIST)(LmM)(List) (List) ...
(List) U
• You can skip input (List) in the part of the above operation.
• All the lists must contain the same number of data items. If they don’t, an error occurs.
Example: List m Mat (1, 2)U
3-5
Example
To transfer the contents of List 1 (2, 3, 6, 5, 4) to column 1, and the
contents of List 2 (11, 12, 13, 14, 15) to column 2 of Matrix Answer
Memory
*(LIST)(LmM)
(List)@ (List)AU
S To count the number of data items in a list
[OPTN]-[LIST]-[Dim]
*(LIST)(Dim)(List) U
• The number of cells a list contains is its “dimension.”
Example
To count the number of values in List 1 (36, 16, 58, 46, 56)
*(LIST)(Dim)
(List)@U
S To create a list by specifying the number of data items
[OPTN]-[LIST]-[Dim]
Use the following procedure to specify the number of data in the assignment statement and
create a list.
?*(LIST)(Dim)(List) U (n = 1 - 999)
Example
To create five data items (each of which contains 0) in List 1
D?*(LIST)(Dim)
(List)@U
You can view the newly created list by entering the STAT
mode.
S To replace all data items with the same value
*(LIST)(Fill) (List) U
Example
To replace all data items in List 1 with the number 3
*(LIST)(Fill)
B (List)@U
The following shows the new contents of List 1.
3-6
[OPTN]-[LIST]-[Fill]
S To generate a sequence of numbers
[OPTN]-[LIST]-[Seq]
*(LIST)(Seq)
U
• The result of this operation is stored in ListAns Memory.
Example
To input the number sequence 12, 62, 112, into a list, using the function
f(x) = X2. Use a starting value of 1, an ending value of 11, and an
increment of 5.
*(LIST)(Seq)TV
T @ @@ DU
Specifying an ending value of 12, 13, 14, or 15 produces the same result as shown above
since they are less than the value produced by the next increment (16).
S To find the minimum value in a list
[OPTN]-[LIST]-[Min]
*(LIST)(E)(Min)(E)(E)(List) U
Example
To find the minimum value in List 1 (36, 16, 58, 46, 56)
*(LIST)(E)(Min)
(E)(E)(List)@U
S To find which of two lists contains the greatest value
[OPTN]-[LIST]-[Max]
*(LIST)(E)(Max)(E)(E)(List) (List)
U
• The two lists must contain the same number of data items. If they don’t, an error occurs.
• The result of this operation is stored in ListAns Memory.
Example
To find whether List 1 (75, 16, 98, 46, 56) or List 2 (35, 59, 58, 72, 67)
contains the greatest value
*(LIST)(E)(Max)
(E)(E)(List)@
(List)AU
S To calculate the mean of data items
[OPTN]-[LIST]-[Mean]
*(LIST)(E)(Mean)(E)(E)(List) U
Example
To calculate the mean of data items in List 1 (36, 16, 58, 46, 56)
*(LIST)(E)(Mean)
(E)(E)(List)@U
3-7
S To calculate the median of data items of specified frequency
[OPTN]-[LIST]-[Med]
This procedure uses two lists: one that contains values and one that indicates the frequency
(number of occurrences) of each value. The frequency of the data in Cell 1 of the first list is
indicated by the value in Cell 1 of the second list, etc.
• The two lists must contain the same number of data items. If they don’t, an error occurs.
*(LIST)(E)(Med)(E)(E)(List) (List)
U
Example
To calculate the median of values in List 1 (36, 16, 58, 46, 56), whose
frequency is indicated by List 2 (75, 89, 98, 72, 67)
*(LIST)(E)(Med)
(E)(E)(List)@
(List)AU
S To combine lists
[OPTN]-[LIST]-[Aug]
• You can combine two different lists into a single list. The result of a list combination operation
is stored in ListAns memory.
*(LIST)(E)(Aug)(E)(E)(List) (List)
U
Example
To combine the List 1 (–3, –2) and List 2 (1, 9, 10)
*(LIST)(E)(Aug)
(E)(E)(List)@
(List)AU
S To calculate the sum of data items in a list
[OPTN]-[LIST]-[Sum]
*(LIST)(E)(E)(Sum)(E)(List) U
Example
To calculate the sum of data items in List 1 (36, 16, 58, 46, 56)
*(LIST)(E)(E)(Sum)
(E)(List)@U
S To calculate the product of values in a list
[OPTN]-[LIST]-[Prod]
*(LIST)(E)(E)(Prod)(E)(List) U
Example
To calculate the product of values in List 1 (2, 3, 6, 5, 4)
*(LIST)(E)(E)(Prod)
(E)(List)@U
3-8
S To calculate the cumulative frequency of each data item [OPTN]-[LIST]-[Cuml]
*(LIST)(E)(E)(Cuml)(E)(List) U
• The result of this operation is stored in ListAns Memory.
Example
To calculate the cumulative frequency of each data item in List 1
(2, 3, 6, 5, 4)
*(LIST)(E)(E)(Cuml)
(E)(List)@U
2+3=
2+3+6=
2+3+6+5=
2+3+6+5+4=
S To calculate the percentage represented by each data item
[OPTN]-[LIST]-[%]
*(LIST)(E)(E)(%)(E)(List) U
• The above operation calculates what percentage of the list total is represented by each data
item.
• The result of this operation is stored in ListAns Memory.
Example
To calculate the percentage represented by each data item in List 1
(2, 3, 6, 5, 4)
*(LIST)(E)(E)(%)
(E)(List)@U
2/(2+3+6+5+4) × 100 =
3/(2+3+6+5+4) × 100 =
6/(2+3+6+5+4) × 100 =
5/(2+3+6+5+4) × 100 =
4/(2+3+6+5+4) × 100 =
S To calculate the differences between neighboring data inside a list
[OPTN]-[LIST]-[ ]
*(LIST)(E)(E)( ) U
• The result of this operation is stored in ListAns Memory.
Example
To calculate the difference between the data items in List 1 (1, 3, 8, 5, 4)
*(LIST)(E)(E)( )
@U
3–1=
8–3=
5–8=
4–5=
3-9
• You can specify the storage location in list memory for a calculation result produced by a list
calculation whose result is stored in ListAns memory. For example, specifying “ List 1 m List
2” will store the result of List 1 in List 2.
• The number of cells in the new List is one less than the number of cells in the original list.
• An error occurs if you execute List for a list that has no data or only one data item.
3. Arithmetic Calculations Using Lists
You can perform arithmetic calculations using two lists or one list and a numeric value.
List
Numeric Value
+
−
×
÷
ListAns Memory
List
=
Numeric Value
List
Calculation results are stored in
ListAns Memory.
I Error Messages
• A calculation involving two lists performs the operation between corresponding cells.
Because of this, an error occurs if the two lists do not have the same number of values
(which means they have different “dimensions”).
• An error occurs whenever an operation involving any two cells generates a mathematical
error.
I Inputting a List into a Calculation
There are three methods you can use to input a list into a calculation.
• Specification of the list number of a list created with List Editor.
• Specification of the sub name of a list created with List Editor.
• Direct input of a list of values.
S To specify the list number of a list created with List Editor
1. In the RUN • MAT (or RUN) mode, perform the following key operation.
*(LIST)(List)
• Enter the “List” command.
2. Enter the list number (integer from 1 to 26) you want to specify.
S To specify the sub name of a list created with List Editor
1. In the RUN • MAT (or RUN) mode, perform the following key operation.
*(LIST)(List)
• Enter the “List” command.
2. Enter the sub name of the list you want to specify, enclosed in double quotes (" ").
Example: "QTY"
3-10
S To directly input a list of values
You can also directly input a list of values using {, }, and .
Example
To input the list: 56, 82, 64
( { )DE GA
EC ( } )
S To assign the contents of one list to another list
Use ? to assign the contents of one list to another list.
Example
To assign the contents of List 3 (41, 65, 22) to List 1
*(LIST)(List)B?(List)@U
In place of (LIST)(List)B operation in the above procedure, you could input
( { )C@ ED AA ( } ).
S To recall the value in a specific list cell
You can recall the value in a specific list cell and use it in a calculation. Specify the cell number
by enclosing it inside square brackets.
Example
To calculate the sine of the value stored in Cell 3 of List 2
Q*(LIST)(List)A
( [ )B ( ] )U
S To input a value into a specific list cell
You can input a value into a specific list cell inside a list. When you do, the value that was
previously stored in the cell is replaced with the new value you input.
Example
To input the value 25 into Cell 2 of List 3
AD?*(LIST)(List)B
( [ )A ( ] )U
I Recalling List Contents
Example
To recall the contents of List 1
*(LIST)(List)@U
• The above operation displays the contents of the list you specify and also stores them in
ListAns Memory. You can then use the ListAns Memory contents in a calculation.
3-11
S To use list contents in ListAns Memory in a calculation
Example
To multiply the list contents in ListAns Memory by 36
*(LIST)(List) (Ans) BEU
• The operation *(LIST)(List) (Ans) recalls ListAns Memory contents.
• This operation replaces current ListAns Memory contents with the result of the above
calculation.
I Graphing a Function Using a List
When using the graphing functions of this calculator, you can input a function such as Y1 =
List 1X. If List 1 contains the values 1, 2, 3, this function will produces three graphs: Y = X,
Y = 2X, Y = 3X.
There are certain limitations on using lists with graphing functions.
I Inputting Scientific Calculations into a List
You can use the numeric table generation functions in the TABLE mode to input values that
result from certain scientific function calculations into a list. To do this, first generate a table
and then use the list copy function to copy the values from the table to the list.
Example
To use the TABLE mode to create a number table for the formula (Y1 = x2
–1), and then copy the table to List 1 in the STAT mode
1. In the TABLE mode, input the formula Y1 = x2 –1.
2. Create the number table.
3. Use C to move the highlighting to the Y1 column.
4. Press *(LMEM).
5. Press @U.
6. Enter the STAT mode to confirm that TABLE mode column Y1 has been copied to List 1.
3-12
I Performing Scientific Function Calculations Using a List
Lists can be used just as numeric values are in scientific function calculations. When the
calculation produces a list as a result, the list is stored in ListAns Memory.
Example
To use List 3
41
65
22
to perform sin (List 3)
Use radians as the angle unit.
Q*(LIST)(List)BU
4. Switching Between List Files
You can store up to 26 lists (List 1 to List 26) in each file (File 1 to File 6). A simple operation
lets you switch between list files.
S To switch between list files
1. From the Main Menu, enter the STAT mode.
Press K(SET UP) to display the STAT mode Setup screen.
2. Use A to highlight “List File”.
3. Press (FILE) and then input the number of the list file you want to use.
Example
To select File 3
(FILE)B
U
All subsequent list operations are applied to the lists contained in the file you select (List File 3
in the above example).
3-13
Chapter 4 Equation Calculations
From the Main Menu, enter the EQUA mode.
• {SIML} ... {linear equation with 2 to 6 unknowns}
• {POLY} ... {degree 2 to 6 equation}
• {SOLV} ... {solve calculation}
1. Simultaneous Linear Equations
You can solve simultaneous linear equations with two to six unknowns.
• Simultaneous Linear Equation with Two Unknowns:
a1x + b1y = c1
a2x + b2y = c2
• Simultaneous Linear Equation with Three Unknowns:
…
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3
1. From the Main Menu, enter the EQUA mode.
2. Select the SIML (Simultaneous) mode, and specify the number of unknowns (variables).
You can specify from 2 to 6 unknowns.
3. Sequentially input the coefficients.
• The cell that is currently selected for input is highlighted. Each time you input a coefficient,
the highlighting shifts in the sequence:
a1 m b1 m c1 m … an m bn m cn m (n = 2 to 6)
• You can also input fractions and values assigned to variables as coefficients.
• You can cancel the value you are inputting for the current coefficient by pressing ) at
any time before you press U to store the coefficient value. This returns to the coefficient
to what it was before you input anything. You can then input another value if you want.
• To change the value of a coefficient that you already stored by pressing U, move the
cursor to the coefficient you want to edit. Next, input the value you want to change to.
• Pressing (CLR) clears all coefficients to zero.
4. Solve the equations.
Example
To solve the following simultaneous linear equations for x, y, and z
4 x + y – 2z = – 1
x + 6y + 3z = 1
– 5x + 4y + z = – 7
4-1
4
K EQUA
(SIML)
(3)
CU@U AU @U
@UEUBU@U
DUCU@U FU
(SOLV)
• Internal calculations are performed using a 15-digit mantissa, but results are displayed using
a 10-digit mantissa and a 2-digit exponent.
• Simultaneous linear equations are solved by inverting the matrix containing the coefficients
of the equations. For example, the following shows the solution (x, y, z) of a simultaneous
linear equation with three unknowns.
a1 b1 c1 –1 d1
x
y
d2
= a2 b2 c2
z
a3 b3 c3
d3
Because of this, precision is reduced as the value of the determinant approaches zero. Also,
simultaneous equations with three or more unknowns may take a very long time to solve.
• An error occurs if the calculator is unable to find a solution.
• After calculation is complete, you can press (REPT), change coefficient values, and then
re-calculate.
2. High-order Equations from 2nd to 6th Degree
Your calculator can be used to solve high-order equations from 2nd to 6th degree.
• Quadratic Equation: ax2 + bx + c = 0 (a p 0)
• Cubic Equation:
…
• Quartic Equation:
ax3 + bx2 + cx + d = 0 (a p 0)
ax4 + bx3 + cx2 + dx + e = 0 (a p 0)
1. From the Main Menu, enter the EQUA mode.
2. Select the POLY (Polynomial) mode, and specify the degree of the equation.
You can specify a degree 2 to 6.
3. Sequentially input the coefficients.
• The cell that is currently selected for input is highlighted. Each time you input a coefficient,
the highlighting shifts in the sequence:
ambmcm…
• You can also input fractions and values assigned to variables as coefficients.
• You can cancel the value you are inputting for the current coefficient by pressing ) at
any time before you press U to store the coefficient value. This returns to the coefficient
to what it was before you input anything. You can then input another value if you want.
4-2
• To change the value of a coefficient that you already stored by pressing U, move the
cursor to the coefficient you want to edit. Next, input the value you want to change to.
• Pressing (CLR) clears all coefficients to zero.
4. Solve the equations.
Example
To solve the cubic equation (Angle unit = Rad)
x3 – 2x2 – x + 2 = 0
K EQUA
(POLY)
(3)
@U AU @UAU
(SOLV)
Multiple Solutions (Example: x3 + 3x2 + 3x + 1 = 0)
Complex Number Solution (Example: x3 + 2x2 + 3x + 2 = 0)
Complex Mode: Real (page 1-27)
Complex Mode: a + bi
Complex Mode: rQ
• Internal calculations are performed using a 15-digit mantissa, but results are displayed
using a 10-digit mantissa and a 2-digit exponent.
• It may take considerable time for the calculation result of a high-order equation of 3rd degree
or higher to appear on the display.
• An error occurs if the calculator is unable to find a solution.
• High-order equation calculations may not produce accurate results when the equation has
multiple solutions.
• After calculation is complete, you can press (REPT), change coefficient values, and then
re-calculate.
4-3
3. Solve Calculations
The Solve Calculation mode lets you determine the value of any variable in a formula without
having to solve the equation.
1. From the Main Menu, enter the EQUA mode.
2. Select the SOLV (Solver) mode, and input the equation as it is written.
• If you do not input an equals sign, the calculator assumes that the expression is to the left
of the equals sign, and there is a zero to the right.
• An error occurs if you input more than one equals sign.
3. In the table of variables that appears on the display, input values for each variable.
• You can also specify values for Upper and Lower to define the upper and lower limits of
the range of solutions.
• An error occurs if the solution falls outside the range you specify.
4. Select the variable for which you want to solve to obtain the solution.
“Lft” and “Rgt” indicate the left and right sides that are calculated using the solution.*1
*1 Solutions are approximated using Newton’s method. Lft and Rgt values are displayed for
confirmation, because Newton’s method may produce results that are the real solution.
The closer the difference between the Lft and Rgt values is to zero, the lower degree of
error in the result.
Example
An object thrown into the air at initial velocity V takes time T to reach
height H. Use the following formula to solve for initial velocity V when
H = 14 (meters), T = 2 (seconds) and gravitational acceleration is G =
9.8 (m/s2).
H = VT – 1/2 GT2
K EQUA
(SOLV)
?,(H)
(=)?A(V)?(T) \
@A?(G)?(T)VU
@CU(H = 14)
?U(V = 0)
AU(T = 2)
H
GU(G = 9.8)
Press DDD to highlight V = 0, and then press
(SOLV).
• The message “Retry” appears on the display when the calculator judges that convergence is
not sufficient for the displayed results.
• A Solve operation will produce a single solution. Use POLY when you want to obtain multiple
solutions for a high-order equation (such as ax2 + bx + c = 0).
4-4
Chapter 5 Graphing
Select the icon in the Main Menu that suits the type of graph you want to draw or the type of table
you want to generate.
• GRAPH … General function graphing
• RUN • MAT (or RUN) … Manual graphing (pages 5-12 to 5-15)
• TABLE … Number table generation (pages 5-15 to 5-19)
• DYNA* … Dynamic graphing (pages 5-20 to 5-22)
• RECUR* … Recursion graphing or number table generation (pages 5-22 to 5-26)
• CONICS* … Conic section graphing (page 5-27)
* Not included on the fx-7400Gɉ.
1. Sample Graphs
5
I How to draw a simple graph (1)
To draw a graph, simply input the applicable function.
1. From the Main Menu, enter the GRAPH mode.
2. Input the function you want to graph.
Here you would use the V-Window to specify the range and other parameters of the graph.
See page 5-2.
3. Draw the graph.
Example
To graph y = 3x2
K GRAPH
BTVU
(DRAW) (or U)
• Press
to return to the screen in step 2 (Graph relation list). After drawing a graph, you
can toggle between the Graph relation list and graph screen by pressing (GjT).
I How to draw a simple graph (2)
You can store up to 20 functions in memory and then select the one you want for graphing.
1. From the Main Menu, enter the GRAPH mode.
2. Specify the function type and input the function whose graph you want to draw.
You can use the GRAPH mode to draw a graph for the following types of expressions:
rectangular coordinate expression (Y=f(x)), polar coordinate expression, parametric
function, rectangular coordinate expression (X=f(y)), inequality.
(TYPE)(Y=) ... rectangular coordinates (Y=f(x) type)
(r=) ... polar coordinates
(Parm) ... parametric function
(X=) ... rectangular coordinates (X=f(y) type)
5-1
(CONV)(Y=) to (Yb)
(E)(X=) to (Xb) ... changes the function type
(E)(Y>) to (Yb) .... Y inequality on left side
(E)(E)(X>) to (Xb) .... X inequality on left side
Repeat this step as many times as required to input all of the functions you want.
Next you should specify which of the functions among those that are stored in memory
you want to graph (see page 5-6). If you do not select specific functions here, the graph
operation will draw graphs of all the functions currently stored in memory.
3. Draw the graph.
• You can use the function menu that appears when you press (STYL) in step 2 of the
above procedure to select one of the following line styles for each graph.
(
) ... Normal (initial default)
(
) … Thick (twice the thickness of Normal)
(
) … Broken (thick broken)
(
) … Dot (dotted)
• When simultaneously graphing multiple inequalities, you can use the “Ineq Type” setting
on the Setup screen ( K(SETUP)) to specify either of two fill ranges.
(AND) ... Fills areas only where the conditions of
all of the graphed inequalities are satisfied.
This is the initial default.
(OR) ..... Fills all areas where the conditions of the
graphed inequalities are satisfied.
Example
Input the functions shown below and draw their graphs.
Y1 = 2x2 – 3, r2 = 3sin2Q
K GRAPH
(TYPE)(Y=)ATV BU
(TYPE)(r=)BQATU
(DRAW)
2. Controlling What Appears on a Graph Screen
I V-Window (View Window) Settings
Use the View Window to specify the range of the x- and y-axes, and to set the spacing
between the increments on each axis. You should always set the V-Window parameters you
want to use before graphing.
5-2
S To make V-Window settings
1. From the Main Menu, enter the GRAPH mode.
2. Press (V-WIN) to display the V-Window setting screen.
Rectangular coordinate parameter
Xmin/Xmax … Minimum/maximum x-axis value
Xscale … Spacing of x-axis increments
Xdot … Value that corresponds to one x-axis dot
Ymin/Ymax … Minimum/maximum y-axis value
Yscale … Spacing of y-axis increments
Polar coordinate parameter
TQ min/TQ max ... Minimum/maximum T, Q values
TQ ptch ... T, Q pitch
3. Press A to move the highlighting and input an appropriate value for each parameter,
pressing U after each.
• {INIT}/{TRIG}/{STD} … V-Window {initial settings}/{initial settings using specified angle
unit}/{standardized settings}
• {STO}/{RCL} … V-Window setting {store}/{recall}
After settings are the way you want them, press ) or )(QUIT) to exit the V-Window
setting screen.
• Pressing U without inputting anything while I (busy indicator) is displayed exits the
V-Window setting screen.
S V-Window Setting Precautions
• Inputting zero for TQ ptch causes an error.
• Any illegal input (out of range value, negative sign without a value, etc.) causes an error.
• When TQ max is less than TQ min, TQ ptch becomes negative.
• You can input expressions (such as 2P) as V-Window parameters.
• When the V-Window setting produces an axis that does not fit on the display, the scale of
the axis is indicated on the edge of the display closest to the origin.
• Changing the V-Window settings clears the graph currently on the display and replaces it
with the new axes only.
• Changing the Xmin or Xmax value causes the Xdot value to be adjusted automatically.
Changing the Xdot value causes the Xmax value to be adjusted automatically.
• A polar coordinate (r =) or parametric graph will appear coarse if the settings you make in
the V-Window cause the TQ ptch value to be too large, relative to the differential between
the TQ min and TQ max settings. If the settings you make cause the TQ ptch value to be
too small relative to the differential between the TQ min and TQ max settings, on the other
hand, the graph will take a very long time to draw.
• The following is the input range for V-Window parameters.
–9.999999999E 97 to 9.999999999E 97
5-3
I V-Window Memory
You can store up to six sets of V-Window settings in V-Window memory for recall when you
need them.
S To store V-Window settings
1. From the Main Menu, enter the GRAPH mode.
2. Press (V-WIN) to display the V-Window setting screen, and input the values you
want.
3. Press (STO) to display the pop-up window.
4. Press a number key to specify the V-Window memory where you want to save the settings,
and then press U. Pressing @U stores the settings in V-Window Memory 1 (V-Win1).
S To recall V-Window memory settings
1. From the Main Menu, enter the GRAPH mode.
2. Press (V-WIN) to display the V-Window setting screen.
3. Press (RCL) to display the pop-up window.
4. Press a number key to specify the V-Window memory number for the settings you want to
recall, and then press U. Pressing @U recalls the settings in V-Window Memory 1
(V-Win1).
I Specifying the Graph Range
You can define a range (start point, end point) for a function before graphing it.
1. From the Main Menu, enter the GRAPH mode.
2. Make V-Window settings.
3. Specify the function type and input the function. The following is the syntax for function
input.
Function
( [ ) Start Point End Point ( ] )
4. Draw the graph.
Example
Graph y = x2 + 3x – 2 within the range – 2 x 4.
Use the following V-Window settings.
Xmin = –3,
Xmax = 5,
Xscale = 1
Ymin = –10,
Ymax = 30,
Yscale = 5
K GRAPH
(V-WIN) BUDU@UA
@?UB?UDU)
(TYPE)(Y=)TV
BT A
( [ ) A C ( ] )U
(DRAW)
• You can specify a range when graphing rectangular expressions, polar expressions,
parametric functions, and inequalities.
5-4
I Zoom
This function lets you enlarge and reduce the graph on the screen.
1. Draw the graph.
2. Specify the zoom type.
(ZOOM)(BOX) ... Box zoom
Draw a box around a display area, and that area is enlarged to
fill the entire screen.
(FACT)
Specifies the x-axis and y-axis zoom factors for factor zoom.
(IN)/(OUT) ... Factor zoom
The graph is enlarged or reduced in accordance with the factor
you specify, centered on the current pointer location.
(AUTO) ... Auto zoom
V-Window y-axis settings are automatically adjusted so the
graph fills the screen along the y-axis.
(E)(ORIG) ... Original size
Returns the graph to its original size following a zoom operation.
(E)(SQR) ... Graph correction
V-Window x-axis values are corrected so they are identical to
the y-axis values.
(E)(RND) ... Coordinate rounding
Rounds the coordinate values at the current pointer location.
(E)(INTG) ... Integer
Each dot is given a width of 1, which makes coordinate values
integers.
(E)(PRE) ... Previous
V-Window parameters are returned to what they were prior to
the last zoom operation.
Box zoom range specification
3. Use the cursor keys to move the pointer ( ) in the center of the screen to the location
where you want one corner of the box to be, and then press U.
4. Use the cursor keys to move the pointer. This causes a box to appear on the screen. Move
the cursor until the area you want to enlarge is enclosed in the box, and then press U to
enlarge it.
Example
Graph y = (x + 5)(x + 4)(x + 3), and then perform a box zoom.
Use the following V-Window settings.
Xmin = –8,
Xmax = 8,
Xscale = 2
Ymin = –4,
Ymax = 2,
Yscale = 1
K GRAPH
(V-WIN) GUGUAUA
CUAU@U)
(TYPE)(Y=)T
DT
C
T
BU
(DRAW)
5-5
(ZOOM)(BOX)
B~BU
B~B,D~DU
• You must specify two different points for box zoom, and the two points cannot be on a
straight line vertically or horizontally from each other.
3. Drawing a Graph
You can store up to 20 functions in memory. Functions in memory can be edited, recalled, and
graphed.
I Specifying the Graph Type
Before you can store a graph function in memory, you must first specify its graph type.
1. While the Graph relation list is on the display, press (TYPE) to display the graph type
menu, which contains the following items.
• {Y=}/{r=}/{Parm}/{X=} ... {rectangular coordinate (Y=f(x) type)}/{polar coordinate}/
{parametric}/{rectangular coordinate (X=f(y) type)} graph
• {Y>}/{Y<}/{YP}/{YO} ... {Y>f (x)}/{Y}/{X<}/{XP}/{XO} ... {X>f(y)}/{X}/{Y<}/{YP}/{YO}/{X=}/{X>}/{X<}/{XP}/{XO}
... {changes the function type of the selected expression}
2. Press the function key that corresponds to the graph type you want to specify.
I Storing Graph Functions
S To store a rectangular coordinate function (Y=)
Example
To store the following expression in memory area Y1: y = 2x2 – 5
(TYPE)(Y=) (Specifies rectangular coordinate expression.)
ATV D(Inputs expression.)
U (Stores expression.)
• A function cannot be stored into a memory area that already contains a function of a different
type from the one you are trying to store. Select a memory area that contains a function that
is the same type as the one you are storing, or delete the function in the memory area to
which you are trying to store.
5-6
S To store a parametric function
Example
To store the following expressions in memory areas Xt3 and Yt3:
x = 3 sinT
y = 3 cosT
(TYPE)(Parm) (Specifies parametric expression.)
BQTU(Inputs and stores x expression.)
BATU(Inputs and stores y expression.)
S To create a composite function
Example
To use relations in Y1 and Y2 to create composite functions for Y3
and Y4
Y1 = (X + 1), Y2 = X2 + 3
Assign Y1°Y2 to Y3, and Y2°Y1 to Y4.
(Y1°Y2 = ((x2 + 3) +1) = (x2 + 4) Y2°Y1 = ( (X + 1))2 + 3 = X + 4 (X −1))
Input relations into Y3 and Y4.
(TYPE)(Y=))(GRPH)
(Y)@(Y)AU
)(GRPH)(Y)A
(Y)@U
• A composite function can consist of up to five functions.
S To assign values to the coefficients and variables of a graph function
Example
To assign the values −1, 0, and 1 to variable A in Y = AX2−1, and draw a
graph for each value
(TYPE)(Y=)
?T(A)TV @U
)(GRPH)(Y)@?T(A)
(=) @U
)(GRPH)(Y)@?T(A)
(=)?U
)(GRPH)(Y)@?T(A)
(=)@U
DDDD(SEL)
(DRAW)
5-7
The above three screens are produced using the Trace function.
See “Function Analysis” (page 5-29) for more information.
I Editing and Deleting Functions
S To edit a function in memory
Example
To change the expression in memory area Y1 from y = 2x2 – 5 to
y = 2 x2 – 3
C (Displays cursor.)
CCCCC#B(Changes contents.)
U(Stores new graph function.)
S To change the line style of a graph function
1. On the Graph relation list screen, use D and A to highlight the relation whose line style
you want to change.
2. Press (STYL).
3. Select the line style.
Example
To change the line style of y = 2x2 – 3, which is stored in area Y1, to
“Broken”
(STYL)(
) (Selects “Broken”.)
S To change the type of a function *1
1. While the Graph relation list is on the display, press D or A to move the highlighting to
the area that contains the function whose type you want to change.
2. Press (TYPE)(CONV).
3. Select the function type you want to change to.
Example
To change the function in memory area Y1 from y = 2x2 – 3 to
y < 2 x2 – 3
(TYPE)(CONV)(Y<) (Changes the function type to “Y<”.)
1
* The function type can be changed for rectangular coordinate functions and inequalities only.
S To delete a function
1. While the Graph relation list is on the display, press D or A to move the highlighting to
the area that contains the function you want to delete.
2. Press (DEL) or #.
5-8
3. Press (Yes) to delete the function or (No) to abort the procedure without deleting
anything.
• Using the above procedure to delete one line of a parametric function (such as Xt2) also
will delete the applicable paired line (Yt2, in the case of Xt2).
I Selecting Functions for Graphing
S To specify the draw/non-draw status of a graph
1. On the Graph relation list, use D and A to highlight the relation you do not want to graph.
2. Press (SEL).
• Each press of (SEL) toggles graphing on and off.
3. Press (DRAW).
Example
To select the following functions for drawing:
Y1 = 2x2 – 5, r2 = 5 sin3Q
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –5,
Ymax = 5,
Yscale = 1
TQ min = 0,
TQ max = P ,
TQ ptch = 2P / 60
AD (Select a memory area that contains a
function for which you want to specify non-draw.)
(SEL) (Specifies non-draw.)
(DRAW) or U (Draws the graphs.)
• You can use the Setup screen settings to alter the appearance of the graph screen as shown
below.
• Grid: On (Axes: On Label: Off)
This setting causes dots to appear at the grid intersects
on the display.
• Axes: Off (Label: Off Grid: Off)
This setting clears the axis lines from the display.
• Label: On (Axes: On Grid: Off)
This setting displays labels for the x- and y-axes.
5-9
I Graph Memory
Graph memory lets you store up to 20 sets of graph function data and recall it later when you
need it.
A single save operation saves the following data in graph memory.
• All graph functions in the currently displayed Graph relation list (up to 20)
• Graph types
• Function graph line information
• Draw/non-draw status
• V-Window settings (1 set)
S To store graph functions in graph memory
1. Press (GMEM)(STO) to display the pop-up window.
2. Press a number key to specify the Graph memory where you want to save the graph
function, and then press U. Pressing @U stores the graph function to Graph Memory 1
(G-Mem1).
• There are 20 graph memories numbered G-Mem1 to G-Mem20.
• Storing a function in a memory area that already contains a function replaces the existing
function with the new one.
• If the data exceeds the calculator’s remaining memory capacity, an error occurs.
S To recall a graph function
1. Press (GMEM)(RCL) to display the pop-up window.
2. Press a number key to specify the Graph memory for the function you want to recall, and
then press U. Pressing @U recalls the graph function in Graph Memory 1 (G-Mem1).
• Recalling data from graph memory causes any data currently on the Graph relation list to
be deleted.
4. Storing a Graph in Picture Memory
You can save up to 20 graphic images in picture memory for later recall. You can overdraw
the graph on the screen with another graph stored in picture memory.
S To store a graph in picture memory
1. After graphing in GRAPH mode, press *(PICT)(STO) to display the pop-up
window.
2. Press a number key to specify the Picture memory where you want to save the picture, and
then press U. Pressing @U stores the picture function to Picture Memory 1 (Pict 1).
• There are 20 picture memories numbered Pict 1 to Pict 20.
• Storing a graphic image in a memory area that already contains a graphic image replaces
the existing graphic image with the new one.
• A dual graph screen or any other type of graph that uses a split screen cannot be saved in
picture memory.
5-10
S To recall a stored graph
1. After graphing in GRAPH mode, press *(PICT)(RCL) to display the pop-up
window.
2. Press a number key to specify the Picture memory for the picture you want to recall, and
then press U. Pressing @U recalls the picture function in Picture Memory 1 (Pict 1).
• Recalling picture memory contents causes the currently displayed graph to be overwritten.
• Use the sketch Cls function (page 5-28) to clear a graph that was recalled from picture
memory.
5. Drawing Two Graphs on the Same Screen
I Copying the Graph to the Sub-screen
Dual Graph lets you split the screen into two parts. Then you can graph two different functions
in each for comparison, or draw a normal size graph on one side and its enlarged version on
the other side. This makes Dual Graph a powerful graph analysis tool.
With Dual Graph, the left side of the screen is called the “main screen”, while the right side is
called the “sub-screen”.
S Main Screen
The graph in the main screen is actually drawn from a function.
S Sub-screen
The graph on the sub-screen is produced by copying or zooming the main screen graph.
You can even make different V-Window settings for the sub-screen and main screen.
S To copy the graph to the sub-screen
1. From the Main Menu, enter the GRAPH mode.
2. On the Setup screen, select “G + G” for Dual Screen.
3. Make V-Window settings for the main screen.
Press (RIGHT) to display the sub-graph settings screen. Pressing (LEFT) returns to
the main screen setting screen.
4. Store the function, and draw the graph in the main screen.
5. Perform the Dual Graph operation you want.
*(COPY) ... Duplicates the main screen graph in the sub-screen
*(SWAP) ... Swaps the main screen contents and sub-screen contents
• Indicators appear to the right of the formulas in the Graph relation list to tell where graphs
are drawn with Dual Graph.
Indicates sub-screen graph (on right side of display)
Indicates graph drawn on both sides of display
Performing a draw operation with the function marked “ R ” in the above example screen
causes the graph to be drawn on the right side on the display. The function marked “ B ” is
drawn on both sides of the graph.
5-11
Pressing (SEL) while one of the function’s is highlighted would causes its “ R ” or “ B ”
indicator to be cleared. A function without an indicator is drawn as the main screen graph
(on the left side of the display).
Graph y = x(x + 1)(x – 1) in the main screen and sub-screen.
Example
Use the following V-Window settings.
(Main Screen) Xmin = –2,
Xmax = 2,
Xscale = 0.5
Ymin = –2,
Ymax = 2,
Yscale = 1
Xmin = –4,
Xmax = 4,
Xscale = 1
Ymin = –3,
Ymax = 3,
Yscale = 1
(Sub-screen)
K GRAPH
K(SET UP)_
AAAA*(G + G))
*fx-7400Gɉ, fx-9750Gɉ: AAA
(V-WIN) AUAU?
DUA
AUAU@U
(RIGHT) CUCU@UA
BUBU@U)
(TYPE)(Y=)TT
@
T @U
(DRAW)
*(COPY)
• Pressing
while a graph is on the display will return to the screen in step 4.
6. Manual Graphing
I Rectangular Coordinate Graph
Inputting the Graph command in the RUN • MAT (or RUN) mode enables drawing of
rectangular coordinate graphs.
1. From the Main Menu, enter the RUN • MAT (or RUN) mode.
2. Make V-Window settings.
3. Input the commands for drawing the rectangular coordinate graph.
4. Input the function.
Example
Graph y = 2x2 + 3x – 4.
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 2
Ymin = –10,
Ymax = 10,
Yscale = 5
K RUN • MAT (or RUN)
5-12
(V-WIN) DUDUAUA
@?U@?UDU)
(SKTCH)(Cls)U
(GRPH)(Y=)
ATV
BT CU
• Certain functions can be graphed easily using built-in function graphs.
• You can draw graphs of the following built-in scientific functions.
Rectangular Coordinate Graph
• sin x
• cos–1 x
• tanh x
•
x
• 10x
d (x)
•
dx
• cos x
• tan–1 x
• sinh–1 x
• x2
• ex
d2
• 2 (x)
dx
• tan x
• sinh x
• cosh–1 x
• log x
• x–1
• xdx
Polar Coordinate Graph
• sin–1 x
• cosh x
• tanh–1 x
• lnx
• 3
x
• sin Q
• cos–1 Q
• tanh Q
•
Q
• 10Q
• cos Q
• tan–1 Q
• sinh–1 Q
• Q2
• eQ
• tan Q
• sinh Q
• cosh–1 Q
• log Q
• Q–1
• sin–1 Q
• cosh Q
• tanh–1 Q
• lnQ
• 3
Q
- Input for x and Q variables is not required for a built-in function.
- When inputting a built-in function, other operators or values cannot be input.
I Drawing Multiple Graphs on the Same Screen
Use the following procedure to assign various values to a variable contained in an expression
and overwrite the resulting graphs on the screen.
1. From the Main Menu, enter the GRAPH mode.
2. On the Setup screen, change the “Dual Screen” setting to “Off”.
3. Make V-Window settings.
4. Specify the function type and input the function. The following is the syntax for function
input.
Expression containing one variable
( [ ) variable
(=)
value value ... value ( ] )
5. Draw the graph.
Example
To graph y = Ax2 – 3 as the value of A changes in the sequence 3, 1, –1
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 1
Ymin = –10,
Ymax = 10,
Yscale = 2
K GRAPH
K(SET UP)_
AAAA*(Off))
*fx-7400Gɉ, fx-9750Gɉ: AAA
(V-WIN) DUDU@UA
@?U@?UAU)
5-13
(TYPE)(Y=)?T(A)TV B
( [ )?T(A)
(=)B @ @
( ] )U
(DRAW)
• The value of only one of the variables in the expression can change.
• Any of the following cannot be used for the variable name: X, Y, r, Q, T.
• You cannot assign a variable to the variable inside the function.
• When Simul Graph is turned on, all of the graphs for the specified variable values are drawn
simultaneously.
• Overwrite can be used when graphing rectangular expressions, polar expressions,
parametric functions, and inequalities.
I Using Copy and Paste to Graph a Function
You can graph a function by copying it to the clipboard, and then pasting it into the graph
screen.
There are two types of functions you can paste into the graph screen.
Type 1 (Y= expression)
A function with the Y variable to the left of the equal sign is graphed as Y=
expression.
Example: To paste Y=X and graph it
• Any spaces to the left of Y are ignored.
Type 2 (expression)
Pasting this type of expression graphs Y= expression.
Example: To paste X and graph Y=X
• Any spaces to the left of the expression are ignored.
S To graph a function using copy and paste
1. Copy the function you want to graph to the clipboard.
2. From the Main Menu, enter the GRAPH mode.
3. On the Setup screen, change the “Dual Screen” setting to “Off”.
4. Make V-Window settings.
5. Draw the graph.
6. Paste the expression.
Example
While the graph of y = 2x2 + 3x – 4 is currently displayed, to paste the
previously copied function Y=X from the clipboard
Use the following V-Window settings.
Xmin = –5,
Xmax = 5,
Xscale = 2
Ymin = –10,
Ymax = 10,
Yscale = 5
5-14
K RUN • MAT (or RUN)
? (Y)
(=)T
G(CLIP)BBB(COPY)
KGRAPH
K(SET UP)_
AAAA*(Off))
*fx-7400Gɉ, fx-9750Gɉ: AAA
(V-WIN) DUDUAUA
@?U@?UDU)
(TYPE)(Y=)ATV
BT CU
(DRAW)
H(PASTE)
• Paste is supported only when “Off” is selected for the “Dual Screen” setting on the Setup
screen.
• Though there is no limit on the number of graphs you can draw by pasting a function, the
total number of graphs supported by trace and other functions is 30 (number of graphs
drawn using expression number 1 to 20, plus graphs drawn using pasted functions).
• For the graph of a pasted function, the graph expression that appears when using trace or
other functions is displayed in the format: Y= expression.
• Re-executing a draw without clearing graph screen memory will redraw all the graphs,
including those produced by pasting functions.
7. Using Tables
To enter the TABLE mode, select the TABLE icon on the Main Menu.
I Storing a Function and Generating a Number Table
S To store a function
Example
To store the function y = 3x2 – 2 in memory area Y1
Use D and A to move the highlighting in the Table relation list to the memory area where
you want to store the function. Next, input the function and press U to store it.
S Variable Specifications
There are two methods you can use to specify value for the variable x when generating a
numeric table.
• Table range method
With this method, you specify the conditions for the change in value of the variable.
• List
With this method, the data in the list you specify is substituted for the x-variable to
generate a number table.
5-15
S To generate a table using a table range
Example
To generate a table as the value of variable x changes from –3 to 3, in
increments of 1
K TABLE
(SET)
BUBU@U
The numeric table range defines the conditions under which the value of variable x changes
during function calculation.
Start ............ Variable x start value
End ............. Variable x end value
Step ............ Variable x value change (interval)
After specifying the table range, press ) to return to the Table relation list.
S To generate a table using a list
1. While the Table relation list is on the screen, display the Setup screen.
2. Highlight Variable and then press (LIST) to display the pop-up window.
3. Select the list whose values you want to assign for the x-variable.
• To select List 6, for example, press EU. This causes the setting of the Variable
item of the Setup screen to change to List 6.
4. After specifying the list you want to use, press ) to return to the previous screen.
S Generating a Table
Example
To generate a table of values for the functions stored in memory areas
Y1 and Y3 of the Table relation list
Use D and A to move the highlighting to the
function you want to select for table generation and
press (SEL) to select it.
The “=” sign of selected functions is highlighted on
the screen. To deselect a function, move the cursor
to it and press (SEL) again.
Press (TABL) to generate a number table using
the functions you selected. The value of variable x
changes according to the range or the contents
of the list you specified.
The example screen shown here shows the results based
on the contents of List 6 (–3, –2, –1, 0, 1, 2, 3).
Each cell can contain up to six digits, including negative sign.
5-16
S To generate a differential number table
Changing the setting of Setup screen’s Derivative item to On causes a number table that
includes the derivative to be displayed whenever you generate a number table.
Locating the cursor at a differential
coefficient displays “dy/dx” in the top line,
which indicates differential.
• An error occurs if a graph for which a range is specified
or an overwrite graph is included among the graph
expressions.
S Specifying the Function Type
You can specify a function as being one of three types.
• Rectangular coordinate (Y=)
• Polar coordinate (r=)
• Parametric (Parm)
1. Press (TYPE) while the relation list is on the screen.
2. Press the number key that corresponds to the function type you want to specify.
• The number table is generated only for the function type specified on the relation list (Table
Func). You cannot generate a number table for a mixture of different function types.
I Editing Tables
You can use the table menu to perform any of the following operations once you generate a
table.
• Change the values of variable x
• Edit (delete, insert, and append) rows
• Delete a table
• Draw a connect type graph
• Draw a plot type graph
• {FORM} ... {return to Table relation list}
• {DEL} ... {delete table}
• {ROW}
• {DEL}/{INS}/{ADD} ... {delete}/{insert}/{add} row
• {G • CON}/{G • PLT} ... {connected type}/{draw plot type} graph draw
• If you try to replace a value with an illegal operation (such as division by zero), an error
occurs and the original value remains unchanged.
• You cannot directly change any values in the other (non-x) columns of the table.
5-17
I Copying a Table Column to a List
A simple operation lets you copy the contents of a numeric table column into a list.
Use B and C to move the cursor to the column you want to copy. The cursor can be in any
row.
S To copy a table to a list
Example
To copy the contents of Column x into List 1
*(LMEM)
Input the number of the list you want to copy and then press U.
@U
I Drawing a Graph from a Number Table
Use the following procedure to generate a number table and then draw a graph based on the
values in the table.
1. From the Main Menu, enter the TABLE mode.
2. Make V-Window settings.
3. Store the functions.
4. Specify the table range.
5. Generate the table.
6. Select the graph type and draw it.
(G • CON) ... line graph
(G • PLT) ... plot type graph
• After drawing the graph, pressing (G j T) or
Example
returns to the number table screen.
Store the two functions below, generate a number table, and then draw
a line graph. Specify a range of –3 to 3, and an increment of 1.
Y1 = 3x2 – 2, Y2 = x2
Use the following V-Window settings.
Xmin = 0,
Xmax = 6,
Xscale = 1
Ymin = –2,
Ymax = 10,
Yscale = 2
K TABLE
(V-WIN)?UEU@UA
AU@?UAU)
5-18
(TYPE)(Y=)BTV AU
TVU
(SET) BUBU@U)
(TABL)
(G • CON)
• You can use Trace, Zoom, or Sketch after drawing a graph.
I Simultaneously Displaying a Number Table and Graph
Specifying T+G for Dual Screen on the Setup screen makes it possible to display a number
table and graph at the same time.
1. From the Main Menu, enter the TABLE mode.
2. Make V-Window settings.
3. On the Setup screen, select T+G for Dual Screen.
4. Input the function.
5. Specify the table range.
6. The number table is displayed in the sub-screen on the right.
7. Specify the graph type and draw the graph.
(G • CON) ... line graph
(G • PLT) ... plot type graph
Example
Store the function Y1 = 3x2 – 2 and simultaneously display its number
table and line graph. Use a table range of –3 to 3 with an increment of 1.
Use the following V-Window settings.
Xmin = 0,
Xmax = 6,
Xscale = 1
Ymin = –2,
Ymax = 10,
Yscale = 2
K TABLE
(V-WIN)?UEU@UA
AU@?UAU)
K(SET UP)AAA*(T+G))_
*fx-7400Gɉ, fx-9750Gɉ: AA
(TYPE)(Y=)BTV AU
(SET)
BUBU@U)
(TABL)
(G • CON)
• The Setup screen’s “Dual Screen” setting is applied in the TABLE mode and the RECUR
mode.
• You can make the number table active by pressing *(CHNG) or
5-19
.
8. Dynamic Graphing
Important!
• The fx-7400Gɉ is not equipped with the DYNA mode.
I Using Dynamic Graph
Dynamic Graph lets you define a range of values for the coefficients in a function, and then
observe how a graph is affected by changes in the value of a coefficient. It helps to see how
the coefficients and terms that make up a function influence the shape and position of a graph.
1. From the Main Menu, enter the DYNA mode.
2. Make V-Window settings.
3. On the Setup screen, specify the Dynamic Type.
(Cnt) ... Continuous
(Stop) ... Automatic stop after 10 draws
4. Use the cursor keys to select the function type on the built-in function type list.*1
5. Input values for coefficients, and specify which coefficient will be the dynamic variable.*2
6. Specify the start value, end value, and increment.
7. Specify the drawing speed.
(SPEED) ( ).... Pause after each draw (Stop&Go)
( ) ...... Half normal speed (Slow)
( ) ...... Normal speed (Normal)
( )..... Twice normal speed (Fast)
8. Draw the Dynamic Graph.
*1 The following are the seven built-in function types.
• Y=AX+B
• Y=A(X+B)2+C
• Y=AX2+BX+C
• Y=Asin(BX+C)
• Y=Acos(BX+C)
• Y=Atan(BX+C)
• Y=AX^3+BX2+CX+D
After you press (TYPE) and select the function type you want, you can then input the
actual function.
*2 You could also press U here and display the parameter setting menu.
• The message “Too Many Functions” appears when more than one function is selected for
Dynamic Graphing.
Example
Use Dynamic Graph to graph y = A (x – 1)2 – 1, in which the value of
coefficient A changes from 2 through 5 in increments of 1. The graph is
drawn 10 times.
K DYNA
(V-WIN)(INIT))
K(SET UP)A*(Stop))
*fx-9750Gɉ: K(SET UP)
(B-IN)A(SEL)
(VAR)AU @U @U
(SET)AUDU@U)
(SPEED)( ))
(DYNA)
5-20
Repeats from through .
1
2
4
3
I Drawing a Dynamic Graph Locus
Turning on the Dynamic Graph locus setting on the Setup screen lets you overlay a graph
drawn by changing the coefficient values.
1. From the Main Menu, enter the DYNA mode.
2. Make V-Window settings.
3. On the Setup screen, select “On” for “Locus”.
4. Use the cursor keys to select the function type on the built-in function type list.
5. Input values for coefficients, and specify which coefficient will be the dynamic variable.
6. Specify the start value, end value, and increment.
7. Specify Normal for the draw speed.
8. Draw the Dynamic Graph.
Example
Use Dynamic Graph to graph y = Ax, in which the value of coefficient
A changes from 1 through 4 in increments of 1. The Graph is drawn 10
times.
K DYNA
(V-WIN)(INIT))
K(SET UP)_
AA*(On))_
*fx-9750Gɉ: A
(B-IN)(SEL)
(VAR)@U?U
(SET)@UCU@U)
(SPEED)( ))
(DYNA)
····
····
5-21
I Graph Calculation DOT Switching Function
Use this function to specify drawing of all the dots on the Dynamic Graph X-axis, or every
other dot. This setting is value for Dynamic Func Y= graphic only.
1. Press K(SET UP) to display the Setup screen.
2. Press \
AAA* to select Y=Draw Speed.
*fx-9750Gɉ: AA
3. Select the graphing method.
(Norm) … Draws all X-axis dots. (initial default)
(High) … Draws every other X-axis dot. (faster drawing than Normal)
4. Press ).
I Using Dynamic Graph Memory
You can store Dynamic Graph conditions and screen data in Dynamic Graph memory for
later recall when you need it. This lets you save time, because you can recall the data and
immediately begin a Dynamic Graph draw operation. Note that you can store one set of data
in memory at any one time.
S To save data in Dynamic Graph memory
1. While a Dynamic Graph draw operation is being performed, press
speed adjustment menu.
to change to the
2. Press (STO). In response to the confirmation dialog that appears, press (Yes) to
save the data.
S To recall data from Dynamic Graph memory
1. Display the Dynamic Graph relation list.
2. Pressing (RCL) recalls Dynamic Graph memory contents and draws the graph.
9. Graphing a Recursion Formula
Important!
• The fx-7400Gɉ is not equipped with the RECUR mode.
I Generating a Number Table from a Recursion Formula
You can input up to three of the following types of recursion formulas and generate a number
table.
• General term of sequence {an}, composed of an, n
• Linear two-term recursion composed of an+1, an, n
• Linear three-term recursion composed of an+2, an+1, an, n
1. From the Main Menu, enter the RECUR mode.
5-22
2. Specify the recursion type.
(TYPE)(an) ... {general term of sequence an}
(an+1) ... {linear two-term recursion}
(an+2) ... {linear three-term recursion}
3. Input the recursion formula.
4. Specify the table range. Specify a start point and end point for n. If necessary, specify a
value for the initial term, and a pointer start point value if you plan to graph the formula.
5. Display the recursion formula number table.
Example
Generate a number table from recursion between three terms as
expressed by an+2 = an+1 + an, with initial terms of a1 = 1, a2 = 1 (Fibonacci
sequence), as n changes in value from 1 to 6.
K RECUR
(TYPE)(an+2)
(n.an ··)(an+1)
(an)U
(SET)(a1)@UEU@U@U)
(TABL)
* The first two values correspond
to a1 = 1 and a2 = 1.
• Pressing (FORM) will return to the screen for storing recursion formulas.
• Specifying “On” for the “3Display” of the Setup screen causes the sum of each term to be
included in the table.
I Graphing a Recursion Formula
After generating a number table from a recursion formula, you can graph the values on a line
graph or plot type graph.
1. From the Main Menu, enter the RECUR mode.
2. Make V-Window settings.
3. Specify the recursion formula type and input the formula.
4. Specify the table range, and start and ending values for n. If necessary, specify the initial
term value and pointer start point.
5. Select the line style for the graph.
6. Display the recursion formula number table.
7. Specify the graph type and draw the graph.
(G • CON) ... line graph
(G • PLT) ... plot type graph
Example
Generate a number table from recursion between two terms as
expressed by an+1 = 2an + 1, with an initial term of a1 = 1, as n changes in
value from 1 to 6. Use the table values to draw a line graph.
Use the following V-Window settings.
Xmin = 0,
Xmax = 6,
Xscale = 1
Ymin = –15,
Ymax = 65,
Yscale = 5
5-23
K RECUR
(V-WIN)?UEU@UA\
@DUEDUDU)
(TYPE)(an+1)A(an)
@U
(SET)(a1)@UEU@U)
(SEL+S)D(
))
(TABL)
(G • CON)
• After drawing a graph, you can use Trace, Zoom, and Sketch.
• Press
to return to the number table screen. After drawing a graph, you can toggle
between the number table screen and graph screen by pressing (GjT).
I Graphing a Phase Plot from Two Numeric Sequences
You can draw the phase plot for numeric sequences generated by two expressions input in the
RECUR mode with one value on the horizontal axis and the other value on the vertical axis.
For an (an+1, an+2), bn (bn+1, bn+2), cn (cn+1, cn+2), the numeric sequence of the alphabetically first
expression is on the horizontal axis while the following numeric sequence is on the vertical
axis.
1. From the Main Menu, enter the RECUR mode.
2. Configure V-Window settings.
3. Enter two recursion formulas and select both of them for table generation.
4. Configure table generation settings.
Specify the start and end values for variable n and the initial term for each recursion
formula.
5. Display the recursion formula number table.
6. Draw the phase plot.
Example
To input the two sequence formulas for regression between two terms
an+1 = 0.9an and bn+1 = bn + 0.1n − 0.2, and specify initial terms a1 = 1 and
b1 = 1 for each. Generate a number table as the value of the n variable
goes from 1 to 10 and use it to draw a phase plot.
Use the following V-Window settings.
Xmin = 0,
Xmax = 2,
Xscale = 1
Ymin = 0,
Ymax = 4,
Yscale = 1
K RECUR
(V-WIN)?UAU@UA
?UCU@U)
(TYPE)(an+1)?
H(an)U
(n.an ··)(bn)
?
@(n) ?
AU
(SET)(a1)@U@?U@U@U)
5-24
(TABL)
(PHAS)
• If you enter three expressions on the RECUR mode screen and select all of them for table
creation, you will need to specify which two of the three expressions you want to use to draw
the phase plot. To do so, use the function menu that appears when you press (PHAS) on
the table screen.
(a • b).......... Graph using an (an+1, an+2) and bn (bn+1, bn+2).
(b • c).......... Graph using bn (bn+1, bn+2) and cn (cn+1, cn+2).
(a • c).......... Graph using an (an+1, an+2) and cn (cn+1, cn+2).
• Specifying “On” for the “3Display” of the Setup screen causes the sum of each term to be
included in the table. At this time you can select use of the two numeric sequences as-is to
draw the plot graph, or use of the sums of each of the two numeric sequences. To do so, use
the function menu that appears when you press (PHAS) on the table screen.
(an) ............ Use numeric sequence for graphing.
(3 an).......... Use numeric sequence sums for graphing.
• When “On” is selected “3Display” on the Setup screen and all three of the expressions
you input in the RECUR mode are selected for table creation, use the function menu
that appears when you press (PHAS) on the table screen to specify which two of the
expressions you want to use, and to specify whether you want to use numeric sequence
data or numeric sequence sum data.
(a • b).......... Graph using number sequences an
(an+1, an+2) and bn (bn+1, bn+2)
(b • c).......... Graph using number sequences bn
(bn+1, bn+2) and cn (cn+1, cn+2)
(a • c).......... Graph using number sequences an
(an+1, an+2) and cn (cn+1, cn+2)
(3 a • b) ....... Graph using the sums of number
sequences an (an+1, an+2) and bn (bn+1, bn+2)
(3 b • c) ....... Graph using the sums of number
sequences bn (bn+1, bn+2) and cn (cn+1, cn+2)
(3 a • c) ....... Graph using the sums of number
sequences an (an+1, an+2) and cn (cn+1, cn+2)
5-25
I WEB Graph (Convergence, Divergence)
y = f(x) is graphed by presuming an+1 = y, an = x for linear two-term regression an+1 = f(an)
composed of an+1, an. Next, it can be determined whether the function is convergent or
divergent.
1. From the Main Menu, enter the RECUR mode.
2. Make V-Window settings.
3. Select 2-term recursion as the recursion formula type, and input the formula.
4. Specify the table range, n start and end points, initial term value, and pointer start point.
5. Display the recursion formula number table.
6. Draw the graph.
7. Press U, and the pointer appears at the start point you specified.
Press U several times.
If convergence exists, lines that resemble a spider web are drawn on the display. Failure
of the web lines to appear indicates either divergence or that the graph is outside the
boundaries of the display screen. When this happens, change to larger V-Window values
and try again.
You can use DA to select the graph.
Example
To draw the WEB graph for the recursion formula an+1 = –3(an)2 + 3an, bn+1
= 3bn + 0.2, and check for divergence or convergence. Use the following
table range: Start = 0, End = 6, a0 = 0.01, anStr = 0.01, b0 = 0.11, bnStr
= 0.11
K RECUR
(V-WIN)?U@U@UA
?U@U@U)
(TYPE)(an+1) B(an)V
B(an)U
B(bn)
?
AU
(SET)(a0)
?UEU?
?@U?
@@UA
?
?@U?
@@U)
(TABL)
(WEB)
U~U(an is convergence)
AU~U(bn is divergence)
• To change the graph line style, press (SEL+S) after step 4.
• With WEB Graph, you can specify the line type for a y = f(x) graph. The line type setting is
valid only when “Connect” is selected for “Draw Type” on the Setup screen.
5-26
10. Graphing a Conic Section
Important!
• The fx-7400Gɉ is not equipped with the CONICS mode.
I Graphing a Conic Section
You can use the CONICS mode to graph parabolas, circles, ellipses, and hyperbolas. You can
input a rectangular coordinate function, polar coordinate function, or parametric function for
graphing.
1. From the Main Menu, enter the CONICS mode.
2. Select the function type.
(RECT).... {rectangular coordinate}
(POL).... {polar coordinate}
(PARM).... {parametric}
3. Select the pattern of the function in accordance with the type of graph you want to draw.
1
U
4. Enter the coefficients of the function and draw the graph.
Example
To input the rectangular coordinate function x = 2y2 + y − 1 and graph a
parabola open on the right, and then input the polar coordinate function
r = 4cosQ and draw a circle graph.
KCONICS
(RECT)A(X=AY2+BY+C)U
AU@U @U(DRAW)
))
(POL)AAAA(R=2AcosQ)U
AU(DRAW)
11. Changing the Appearance of a Graph
I Drawing a Line
The sketch function lets you draw points and lines inside of graphs.
You can select one of four different line styles for drawing with the sketch function.
5-27
1. From the Main Menu, enter the GRAPH mode.
2. Make V-Window settings.
3. On the Setup screen, use the “Sketch Line” setting to specify the line style you want.
(
) … Normal (initial default)
(
) … Thick (twice the thickness of Normal)
(
) … Broken (thick broken)
(
) … Dot (dotted)
4. Input the function of the graph.
5. Draw the graph.
6. Select the sketch function you want to use.*1
(SKTCH)(Cls) ... Screen clear
(Tang) ... Tangent line
(Norm) ... Line normal to a curve
(Inv) ... Inverse function*2
_
(E)(PLOT)
{Plot}/{Pl • On}/{Pl • Off}/{Pl • Chg} ... Point {Plot}/{On}/{Off}/{Change}
_
(E)(LINE)
{Line}/{F • Line} ... {connects 2 points plotted by (E)(PLOT) with
a line}/{for drawing a line between any 2 points}
(E)(Crcl) ... Circle
(E)(Vert) ... Vertical line
(E)(Hztl) ... Horizontal line
(E)(E)(PEN) ... Freehand
(E)(E)(Text) ... Text input
7. Use the cursor keys to move the pointer (
press U.*3
) to the location where you want to draw, and
*1 The above shows the function menu that appears in the GRAPH mode. Menu items may
differ somewhat in other modes.
*2 In the case of an inverse function graph, drawing starts immediately after you select this
option.
*3 Some sketch functions require specification of two points. After you press U to specify the
first point, use the cursor keys to move the pointer to the location of the second point and
press U.
• You can specify line type for the following sketch functions: Tangent, Normal, Inverse, Line,
F • Line, Circle, Vertical, Horizontal, Pen
Example
Draw a line that is tangent to point (2, 0) on the graph for y = x (x + 2)
(x – 2).
K GRAPH
(V-WIN)(INIT))
K_
(SET UP)AAAAAAAA*(
))_
*fx-7400Gɉ, fx-9750Gɉ: AAAAAAA
5-28
(TYPE)(Y=)TT
AT_
AU
(DRAW)
(SKTCH)(Tang)
C~CU*1
*1 You can draw a tangent line in succession by moving the “
” pointer and pressing U.
12. Function Analysis
I Reading Coordinates on a Graph Line
Trace lets you move a pointer along a graph and read out coordinates on the display.
1. From the Main Menu, enter the GRAPH mode.
2. Draw the graph.
3. Press (TRCE), and a pointer appears in the center of the graph.*1
4. Use B and C to move the pointer along the graph to
the point at which you want to display the derivative.
When there are multiple graphs on the display, press \
D and A to move between them along the x-axis of
the current pointer location.
5. You can also move the pointer by pressing T to display the pop-up window, and then
inputting coordinates.
The pop-up window appears even when you input coordinates directly.
To exit a trace operation, press (TRCE).
*1 The pointer is not visible on the graph when it is located at a point outside the graph display
area or when an error of no value occurs.
• You can turn off display of the coordinates at the pointer location by specifying “Off” for the
“Coord” item on the Setup screen.
• The following shows how coordinates are displayed for each function type.
Polar Coordinate Graph
Parametric Graph
Inequality Graph
I Displaying the Derivative
In addition to using Trace to display coordinates, you can also display the derivative at the
current pointer location.
5-29
1. From the Main Menu, enter the GRAPH mode.
2. On the Setup screen, specify On for Derivative.
3. Draw the graph.
4. Press (TRCE), and the pointer appears at the
center of the graph. The current coordinates and the
derivative also appear on the display at this time.
I Graph to Table
You can use trace to read the coordinates of a graph and store them in a number table. You
can also use Dual Graph to simultaneously store the graph and number table, making this an
important graph analysis tool.
1. From the Main Menu, enter the GRAPH mode.
2. On the Setup screen, specify GtoT for Dual Screen.
3. Make V-Window settings.
4. Save the function and draw the graph on the
main (left) screen.
5. Activate Trace. When there are multiple graphs on
the display, press D and A to select the graph you
want.
6. Use B and C to move the pointer and press U
to store coordinates into the number table. Repeat
this step to store as many values as you want.
7. Press *(CHNG) to make the number table active.
I Coordinate Rounding
This function rounds off coordinate values displayed by Trace.
1. From the Main Menu, enter the GRAPH mode.
2. Draw the graph.
3. Press (ZOOM)(E)(RND). This causes
the V-Window settings to be changed automatically
in accordance with the Rnd value.
4. Press (TRCE), and then use the cursor keys
to move the pointer along the graph. The coordinates
that now appear are rounded.
I Calculating the Root
This feature provides a number of different methods for analyzing graphs.
1. From the Main Menu, enter the GRAPH mode.
2. Draw the graphs.
3. Select the analysis function.
(G-SLV)(ROOT) ... Calculation of root
(MAX) ... Local maximum value
(MIN) ... Local minimum value
5-30
(Y-ICPT) ... y-intercept
(ISCT) ... Intersection of two graphs
(E)(Y-CAL) ... y-coordinate for given x-coordinate
(E)(X-CAL) ... x-coordinate for given y-coordinate
(E)(°dx) ... Integral value for a given range
4. When there are multiple graphs on the screen, the selection cursor (I) is located at the
lowest numbered graph. Press D and A to move the cursor to the graph you want to
select.
5. Press U to select the graph where the cursor is located and display the value produced by
the analysis.
When an analysis produces multiple values, press C to calculate the next value.
Pressing B returns to the previous value.
• Either of the following can cause poor accuracy or even make it impossible to obtain
solutions.
- When the graph of the solution obtained is a point of tangency with the x-axis
- When a solution is an inflection point
I Calculating the Point of Intersection of Two Graphs
Use the following procedure to calculate the point of intersection of two graphs.
1. Draw the graphs.
2. Press (G-SLV)(ISCT). When there are three or more graphs, the selection cursor
(I) appears at the lowest numbered graph.
3. Press D and A to move the cursor to the graph you want to select.
4. Press U to select the first graph, which changes the shape of the cursor from I to R.
5. Press D and A to move the cursor to the second graph.
6. Press U to calculate the point of intersection for the two graphs.
When an analysis produces multiple values, press C to calculate the next value.
Pressing B returns to the previous value.
Example
Graph the two functions shown below, and determine the point of
intersection between Y1 and Y2.
Y1 = x + 1, Y2 = x2
5-31
• You can calculate the point of intersection for rectangular coordinate graphs (Y=f(x) type)
and inequality graphs (Y f(x), Y f(x), Y P f(x) or Y O f(x)) only.
• Either of the following can cause poor accuracy or even make it impossible to obtain
solutions.
- When a solution is a point of tangency between two graphs
- When a solution is an inflection point
I Determining the Coordinates for Given Points
The following procedure describes how to determine the y-coordinate for a given x, and the
x-coordinate for a given y.
1. Draw the graph.
2. Select the function you want to perform. When there are multiple graphs, the selection
cursor (I) appears at the lowest numbered graph.
(G-SLV)(E)(Y-CAL) ... y-coordinate for given x
(E)(X-CAL) ... x-coordinate for given y
3. Use DA to move the cursor (I) to the graph you want, and then press U to select it.
4. Input the given x-coordinate value or y-coordinate value.
Press U to calculate the corresponding y-coordinate value or x-coordinate value.
Example
Graph the two functions shown below and then determine the ycoordinate for x = 0.5 and the x-coordinate for y = 2.2 on graph Y2.
Y1 = x + 1, Y2 = x(x + 2)(x – 2)
• When there are multiple results for the above procedure, press C to calculate the next
value. Pressing B returns to the previous value.
• The X-CAL value cannot be obtained for a parametric function graph.
I Calculating the lntegral Value for a Given Range
Use the following procedure to obtain integration values for a given range.
1. Draw the graph.
2. Press (G-SLV)(E)(°dx). When there are multiple graphs, this causes the
selection cursor (I) to appear at the lowest numbered graph.
3. Use DA to move the cursor (I) to the graph you want, and then press U to select it.
4. Use BC to move the lower limit pointer to the location you want, and then press U.
5. Use C to move the upper limit pointer to the location you want.
6. Press U to calculate the integral value.
5-32
Example
Graph the function shown below, and then determine the integral value
at (–2, 0).
Y1 = x(x + 2)(x – 2)
• You can also specify the lower limit and upper limit by inputting them on the 10-key pad.
• When setting the range, make sure that the lower limit is less than the upper limit.
• Integral values can be calculated for rectangular coordinate graphs only.
I Conic Section Graph Analysis
Important!
• The fx-7400Gɉ is not equipped with the CONICS mode.
You can determine approximations of the following analytical results using conic section
graphs.
1. From the Main Menu, enter the CONICS mode.
2. Select the function type.
(RECT).... {rectangular coordinate}
(POL).... {polar coordinate}
(PARM).... {parametric}
3. Use D and A to select the conic section you want to analyze.
4. Input the conic section constants.
5. Draw the Graph.
After graphing a conic section, press (G-SLV) to display the following graph analysis
menus.
S Parabolic Graph Analysis
• {FOCS}/{VTX}/{LEN}/{e} ... {focus}/{vertex}/{length of latus rectum}/{eccentricity}
• {DIR}/{SYM} ... {directrix}/{axis of symmetry}
• {X-IN}/{Y-IN} ... {x-intercept}/{y-intercept}
S Circular Graph Analysis
• {CNTR}/{RADS} ... {center}/{radius}
• {X-IN}/{Y-IN} ... {x-intercept}/{y-intercept}
S Elliptical Graph Analysis
• {FOCS}/{VTX}/{CNTR}/{e} ... {focus}/{vertex}/{center}/{eccentricity}
• {X-IN}/{Y-IN} ... {x-intercept}/{y-intercept}
S Hyperbolic Graph Analysis
• {FOCS}/{VTX}/{CNTR}/{e} ... {focus}/{vertex}/{center}/{eccentricity}
• {ASYM} ... {asymptote}
• {X-IN}/{Y-IN} ... {x-intercept}/{y-intercept}
5-33
S To calculate the focus and length of latus rectum
Example
[G-SLV]-[FOCS]/[LEN]
To determine the focus and length of latus rectum for the parabola X =
(Y – 2)2 + 3
Use the following V-Window settings.
Xmin = –1,
Xmax = 10,
Xscale = 1
Ymin = –5,
Ymax = 5,
Yscale = 1
K CONICS
U
@UAUBU(DRAW)
(G-SLV)
(FOCS)
(Calculates the focus.)
(G-SLV)
(LEN)
(Calculates the length of latus rectum.)
• When calculating two foci for an ellipse or hyperbolic graph, press C to calculate the
second focus. Pressing B returns to the first focus.
• When calculating two vertexes for a hyperbolic graph, press C to calculate the second
vertex. Pressing B returns to the first vertex.
• Pressing C when calculating the vertices of an ellipse will calculate the next value.
Pressing B will scroll back through previous values. An ellipse has four vertices.
S To calculate the center
Example
[G-SLV]-[CNTR]
To determine the center for the circle
(X + 2)2 + (Y + 1)2 = 22
K CONICS
AAAAU
AU @UAU(DRAW)
(G-SLV)
(CNTR)
(Calculates the center.)
5-34
Chapter 6 Statistical Graphs and
Calculations
Important!
This chapter contains a number of graph screen shots. In each case, new data values were input in
order to highlight the particular characteristics of the graph being drawn. Note that when you try to
draw a similar graph, the unit uses data values that you have input using the List function. Because
of this, the graphs that appear on the screen when you perform a graphing operation will probably
differ somewhat from those shown in this manual.
1. Before Performing Statistical Calculations
Entering the STAT mode from the Main Menu displays the List Editor screen.
You can use the List Editor screen to input statistical data and perform statistical calculations.
Use D, A, B and C to move the
highlighting around the lists.
Once you input data, you can use it to produce a graph and
check for tendencies. You can also use a variety of different
regression calculations to analyze the data.
• For information about using the statistical data lists, see
“Chapter 3 List Function”.
I Changing Graph Parameters
Use the following procedures to specify the graph draw/non-draw status, the graph type, and
other general settings for each of the graphs in the graph menu (GPH1, GPH2, GPH3).
While the statistical data list is on the display, press (GRPH) to display the graph menu,
which contains the following items.
• {GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3} drawing*1
• {SEL} ... {simultaneous graph (GPH1, GPH2, GPH3) selection}
You can specify the multiple graphs.
• {SET} ... {graph settings (graph type, list assignments)}
*1 The initial default graph type setting for all the graphs (Graph 1 through Graph 3) is scatter
diagram, but you can change to one of a number of other graph types.
1. General graph settings
[GRPH]-[SET]
This section describes how to use the general graph settings screen to make the following
settings for each graph (GPH1, GPH2, GPH3).
• Graph Type
The initial default graph type setting for all the graphs is scatter graph. You can select one of a
variety of other statistical graph types for each graph.
6-1
6
• List
The initial default statistical data is List 1 for single-variable data, and List 1 and List 2 for
paired-variable data. You can specify which statistical data list you want to use for x-data and
y-data.
• Frequency
Normally, each data item or data pair in the statistical data list is represented on a graph as
a point. When you are working with a large number of data items however, this can cause
problems because of the number of plot points on the graph. When this happens, you can
specify a frequency list that contains values indicating the number of instances (the frequency)
of the data items in the corresponding cells of the lists you are using for x-data and y-data.
Once you do this, only one point is plotted for the multiple data items, which makes the graph
easier to read.
• Mark Type
This setting lets you specify the shape of the plot points on the graph.
S To display the general graph settings screen
[GRPH]-[SET]
Pressing (GRPH)(SET) displays the general graph
settings screen.
• StatGraph (statistical graph specification)
• {GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3}
• Graph Type (graph type specification)
• {Scat}/{xy}/{NPP}/{Pie} ... {scatter diagram}/{xy line graph}/{normal probability plot}/{pie
graph}
• {Hist}/{Box}/{Bar}/{N·Dis}/{Brkn} ... {histogram}/{med-box graph}/{bar graph}/{normal
distribution curve}/{broken line graph}
• {X}/{Med}/{X^2}/{X^3}/{X^4} ... {linear regression graph}/{Med-Med graph}/{quadratic
regression graph}/{cubic regression graph}/{quartic regression graph}
• {Log}/{Exp}/{Pwr}/{Sin}/{Lgst} ... {logarithmic regression graph}/{exponential regression
graph}/{power regression graph}/{sinusoidal regression graph}/{logistic regression
graph}
• XList (x-axis data list)/YList (y-axis data list)
• {List} ... {List 1 to 26}
• Frequency (number of times a value occurs)
• {1} ... {1-to-1 plot}
• {List} ... {List 1 to 26}
• Mark Type (plot mark type)
• {U}/{s}/{•} ... scatter diagram plot points
When “Pie” (pie graph) is selected as the Graph Type:
• Data (Specifies the list to be used as graph data.)
• {LIST} ... {List 1 to List 26}
6-2
• Display (pie graph value display setting)
• {%}/{Data} ... For each data element {display as percentage}/{display as value}
• % Sto Mem (Specifies storage of percentage values to a list.)
• {None}/{List} ... For percentage values: {Do not store to list}/{Specify List 1 to 26 and store}
When “Box” (med-box graph) is selected as the Graph Type:
• Outliers (outliers specification)
• {On}/{Off} ... {display}/{do not display} Med-Box outliers
When “Bar” (bar graph) is selected as the Graph Type:
• Data1 (first stick data list)
• {LIST} ... {List 1 to 26}
• Data2 (second stick data list)/Data3 (third stick data list)
• {None}/{LIST} ... {none}/{List 1 to 26}
• Stick Style (stick style specification)
• {Leng}/{HZtl} ... {length}/{horizontal}
2. Graph draw/non-draw status
[GRPH]-[SEL]
The following procedure can be used to specify the draw (On)/non-draw (Off) status of each of
the graphs in the graph menu.
S To specify the draw/non-draw status of a graph
1. Pressing (GRPH)(SEL) displays the graph On/Off
screen.
• Note that the StatGraph1 setting is for Graph 1 (GPH1 of the graph menu), StatGraph2 is
for Graph 2, and StatGraph3 is for Graph 3.
2. Use the cursor keys to move the highlighting to the graph whose status you want to change,
and press the applicable function key to change the status.
• {On}/{Off} ... {On (draw)}/{Off (non-draw)}
• {DRAW} ... {draws all On graphs}
3. To return to the graph menu, press ).
• V-Window parameters are normally set automatically for statistical graphing. If you want to
set V-Window parameters manually, you must change the Stat Wind item to “Manual”.
While the statistical data list is on the display, perform the following procedure.
K(SET UP)(Man)
)(Returns to previous menu.)
Note that V-Window parameters are set automatically for the following types of graphs
regardless of whether or not the Stat Wind item is set to “Manual”.
Pie, 1-Sample Z Test, 2-Sample Z Test, 1-Prop Z Test, 2-Prop Z Test, 1-Sample t Test, 2Sample t Test, C2 GOF Test, C2 2-way Test, 2-Sample F Test (x-axis only disregarded).
• The default setting automatically uses List 1 data as x-axis (horizontal) values and List 2 data
as y-axis (vertical) values. Each set of x/y data is a point on the scatter diagram.
6-3
2. Calculating and Graphing Single-Variable
Statistical Data
Single-variable data is data with only a single variable. If you are calculating the average height
of the members of a class for example, there is only one variable (height).
Single-variable statistics include distribution and sum. The following types of graphs are
available for single-variable statistics.
You can also use the procedures under “Changing Graph Parameters” on page 6-1 to make
the settings you want before drawing each graph.
I Normal Probability Plot
This plot compares the data accumulated ratio with a normal distribution accumulated ratio.
XList specifies the list where data is input, and Mark Type is used to select from among the
marks {U / s / • } you want to plot.
Press
, ) or )(QUIT) to return to the statistical data list.
I Pie Graph
You can draw a pie graph based on the data in a specific list. The maximum number of graph
data items (list lines) is 20. The graph is labeled A, B, C, and so on, corresponding to lines 1,
2, 3, and so on of the list used for the graph data.
When “%” is selected for the “Display” setting on the general graph settings screen (page 6-3),
a value showing the percentage is displayed for each of the alphabetic label letters.
I Histogram
XList specifies the list where the data is input, while Freq specifies the list where the data
frequency is input. 1 is specified for Freq when frequency is not specified.
U(DRAW)
6-4
The display screen appears as shown above before the graph is drawn. At this point, you can
change the Start and Width values.
I Med-box Graph
This type of graph lets you see how a large number of
data items are grouped within specific ranges. A box
minX
encloses all the data in an area from the first quartile
(Q1) to the third quartile (Q3), with a line drawn at the
median (Med). Lines (called whiskers) extend from
either end of the box up to the minimum (minX) and
maximum (maxX) of the data.
From the statistical data list, press (GRPH) to display the
graph menu, press (SET), and then change the graph
type of the graph you want to use (GPH1, GPH2, GPH3) to
med-box graph.
Q1 Med Q3
maxX
To plot the data that falls outside the box, first specify
“MedBox” as the Graph Type. Then, on the same screen you
use to specify the graph type, turn the Outliers item “On”,
and draw the graph.
• Changing the “Q1Q3 Type” setting on the Setup screen can cause the Q1 and Q3 positions
to change, even when a Med-box graph is drawn based on a single list.
I Bar Graph
You can specify up to three lists for drawing a bar graph. The graph is labeled [1], [2], [3], and
so on, corresponding to lines 1, 2, 3, and so on of the list used for the graph data.
• Any of the following causes an error and cancels bar graph drawing.
- A Condition ERROR occurs when drawing of multiple graphs is specified using the graph
On/Off screen (page 6-3), and bar graph is specified for one of the graphs and a different
graph type is specified for another graph.
- A Dimension ERROR occurs when you draw a graph with two or three lists specified and
the specified lists have a different number of list elements.
- A Condition ERROR occurs when lists are assigned for Data1 and Data3, while “None” is
specified for Data2.
6-5
I Normal Distribution Curve
The normal distribution curve is graphed using the normal
distribution function.
XList specifies the list where the data is input, while Freq
specifies the list where the data frequency is input. 1 is
specified for Freq when frequency is not specified.
I Broken Line Graph
Lines connect center points of a histogram bar.
XList specifies the list where the data is input, while Freq specifies the list where the data
frequency is input. 1 is specified for Freq when frequency is not specified.
U(DRAW)
The display screen appears as shown above before the graph is drawn. At this point, you can
change the Start and Width values.
I Displaying the Calculation Results of a Drawn Single-Variable Graph
Single-variable statistics can be expressed as both graphs
and parameter values. When these graphs are displayed,
the single-variable calculation results appear as shown to
the right when you press (1VAR).
• Use A to scroll the list so you can view the items that run off the bottom of the screen.
The following describes the meaning of each of the parameters.
x¯ ..................mean
3x ................sum
3x2 ...............sum of squares
Q1 ................first quartile
Sx .................population standard
deviation
maxX............maximum
sx .................sample standard
deviation
Mod:n ..........number of data mode items
Med ..............median
Q3 ................third quartile
Mod ..............mode
Mod:F ..........data mode frequency
n ..................number of data items
minX.............minimum
6-6
• Press (DRAW) to return to the original single-variable statistical graph.
• When Mod has multiple solutions, they are all displayed.
• You can use the Setup screen’s “Q1Q3 Type” setting to select either “Std” (standard
calculation) or “OnData” (French calculation) for the Q1 and Q3 calculation mode.
For details about calculation methods while “Std” or “OnData” is selected, see “Calculation
Methods for the Std and OnData Settings” below.
I Calculation Methods for the Std and OnData Settings
Q1 and Q3 can be calculated in accordance with the Setup screen’s “Q1Q3 Type” setting as
described below.
S Std
With this calculation method, processing depends on whether the number of elements n in the
population is an even number or odd number.
When the number of elements n is an even number:
Using the center point of the total population as the reference, the population elements are
divided into two groups: a lower half group and an upper half group. Q1 and Q3 then become
the values described below.
Q1 = {median of the group of
Q3 = {median of the group of
n
2
n
2
Center Point
1
2
3
items from the bottom of the population}
items from the top of the population}
Center Point
4
5
Center Point
6
7
8
4+5
= Median
2
2+3
= Q1
2
6+7
= Q3
2
When the number of elements n is an odd number:
Using the median of the total population as the reference, the population elements are divided
into two groups: a lower half group (values less than the median) and an upper half group
(values greater than the median). The median value is excluded. Q1 and Q3 then become the
values described below.
n–1
Q1 = {median of the group of
items from the bottom of the population}
2
n–1
Q3 = {median of the group of
items from the top of the population}
2
• When n = 1, Q1 = Q3 = population center point.
6-7
Center Point
1
2
Center Point
3
4
5
6
7
8
9
Median
2+3
= Q1
2
7+8
= Q3
2
S OnData
The Q1 and Q3 values for this calculation method are described below.
Q1 = {value of element whose cumulative frequency ratio is greater than 1/4 and nearest to
1/4}
Q3 = {value of element whose cumulative frequency ratio is greater than 3/4 and nearest to
3/4}
The following shows an actual example of the above.
(Number of Elements: 10)
Data Value
Frequency
Cumulative
Frequency
Cumulative
Frequency Ratio
1
1
1
1/10 = 0.1
2
1
2
2/10 = 0.2
3
2
4
4/10 = 0.4
4
3
7
7/10 = 0.7
5
1
8
8/10 = 0.8
6
1
9
9/10 = 0.9
7
1
10
10/10 = 1.0
• 3 is the value of whose cumulative frequency ratio is greater than 1/4 and nearest to 1/4, so
Q1 = 3.
• 5 is the value of whose cumulative frequency ratio is greater than 3/4 and nearest to 3/4, so
Q3 = 5.
Reference Point (0.25)
0.1
0.2
1
2
Reference Point (0.75)
0.4
3
3
4
4
Q1
0.7
0.8
0.9
1.0
4
5
6
7
Q3
6-8
3. Calculating and Graphing Paired-Variable
Statistical Data
I Drawing a Scatter Diagram and xy Line Graph
The following procedure plots a scatter diagram and connects the dots to produce an xy line
graph.
1. From the Main Menu, enter the STAT mode.
2. Input the data into a list.
3. Specify Scat (scatter diagram) or xy (xy line graph) as the graph type, and then execute the
graph operation.
Press
, ) or )(QUIT) to return to the statistical data list.
Example
Input the two sets of data shown below. Next, plot the data on a scatter
diagram and connect the dots to produce an xy line graph.
0.5, 1.2, 2.4, 4.0, 5.2 (xList)
–2.1, 0.3, 1.5, 2.0, 2.4 (yList)
K STAT
?
DU@
AUA
CUCUD
AUC
A
@U?
BU@
DUAUA
CU
(Scatter diagram) (GRPH)(SET)A(Scat))(GPH1)
(xy line graph) (GRPH)(SET)A(xy))(GPH1)
(xy line graph)
(Scatter diagram)
I Drawing a Regression Graph
Use the following procedure to input paired-variable statistical data, perform a regression
calculation using the data, and then graph the results.
1. From the Main Menu, enter the STAT mode.
2. Input the data into a list, and plot the scatter diagram.
3. Select the regression type, execute the calculation, and display the regression parameters.
4. Draw the regression graph.
6-9
Example
Input the two sets of data shown below and plot the data on a scatter
diagram. Next, perform logarithmic regression on the data to display the
regression parameters, and then draw the corresponding regression
graph.
0.5, 1.2, 2.4, 4.0, 5.2 (xList)
–2.1, 0.3, 1.5, 2.0, 2.4 (yList)
K STAT
?
DU@
AUA
CUCUD
AUC
A
@U?
BU@
DUAUA
CU
(GRPH)(SET)A(Scat))(GPH1)
(CALC)(E)(Log)
(DRAW)
• You can perform trace on a regression graph. You cannot perform trace scroll.
• Input a positive integer for frequency data. Other types of values (decimals, etc.) cause an
error.
I Selecting the Regression Type
After you graph paired-variable statistical data, you can use the function menu at the bottom of
the display to select from a variety of different types of regression.
• {ax+b}/{a+bx}/{Med}/{X^2}/{X^3}/{X^4}/{Log}/{ae^bx}/{ab^x}/{Pwr}/{Sin}/{Lgst} ...
{linear regression (ax+b form)}/{linear regression (a+bx form)}/{Med-Med}/{quadratic
regression}/{cubic regression}/{quartic regression}/{logarithmic regression}/{exponential
regression (aebx form)}/{exponential regression (abx form)}/{power regression}/
{sinusoidal regression}/{logistic regression} calculation and graphing
• {2VAR}... {paired-variable statistical results}
I Displaying Regression Calculation Results
Whenever you perform a regression calculation, the regression formula parameter (such as a
and b in the linear regression y = ax + b) calculation results appear on the display. You can use
these to obtain statistical calculation results.
Regression parameters are calculated as soon as you press a function key to select a
regression type, while a graph is on the display.
The following parameters are used by linear regression, logarithmic regression, exponential
regression, and power regression.
r .............. correlation coefficient
r2 ............. coefficient of determination
MSe......... mean square error
6-10
I Graphing Statistical Calculation Results
While the parameter calculation result is on the display, you can graph the displayed
regression formula by pressing (DRAW).
I Linear Regression Graph
Linear regression uses the method of least squares to plot a straight line that passes close to
as many data points as possible, and returns values for the slope and y-intercept (y-coordinate
when x = 0) of the line.
The graphic representation of this relationship is a linear regression graph.
(CALC)(X)
(ax+b) or (a+bx)
(DRAW)
The following is the linear regression model formula.
y = ax + b
a ............. regression coefficient (slope)
b ............. regression constant term (y-intercept)
y = a + bx
a ............. regression constant term (y-intercept)
b ............. regression coefficient (slope)
I Med-Med Graph
When it is suspected that there are a number of extreme values, a Med-Med graph can be
used in place of the least squares method. This is similar to linear regression, but it minimizes
the effects of extreme values.
(CALC)(Med)
(DRAW)
The following is the Med-Med graph model formula.
y = ax + b
a .............. Med-Med graph slope
b .............. Med-Med graph y-intercept
I Quadratic/Cubic/Quartic Regression Graph
A quadratic/cubic/quartic regression graph represents connection of the data points of a
scatter diagram. It uses the method of least squares to draw a curve that passes close to
as many data points as possible. The formula that represents this is quadratic/cubic/quartic
regression.
Ex. Quadratic regression
(CALC)(X^2)
(DRAW)
6-11
Quadratic regression
Cubic regression
Model formula....... y = ax2 + bx + c
Model formula....... y = ax3 + bx2 + cx + d
a .......... regression second coefficient
b .......... regression first coefficient
c .......... regression constant term
(y-intercept)
a .......... regression third coefficient
b .......... regression second coefficient
c .......... regression first coefficient
d .......... regression constant term
(y-intercept)
Quartic regression
Model formula....... y = ax4 + bx3 + cx2 + dx + e
a .......... regression fourth coefficient
b .......... regression third coefficient
c .......... regression second coefficient
d .......... regression first coefficient
e .......... regression constant term (y-intercept)
I Logarithmic Regression Graph
Logarithmic regression expresses y as a logarithmic function of x. The standard logarithmic
regression formula is y = a + b × In x, so if we say that X = In x, the formula corresponds to
linear regression formula y = a + bX.
(CALC)(E)(Log)
(DRAW)
The following is the logarithmic regression model formula.
y = a + b·ln x
a .............. regression constant term
b .............. regression coefficient
I Exponential Regression Graph
Exponential regression expresses y as a proportion of the exponential function of x. The
standard exponential regression formula is y = a × ebx, so if we take the logarithms of both
sides we get In y = In a + bx. Next, if we say Y = In y, and A = In a, the formula corresponds to
linear regression formula Y = A + bx.
(CALC)(E)(Exp)
(aeˆbx) or (abˆx)
(DRAW)
The following is the exponential regression model formula.
y = a·ebx
a .............. regression coefficient
b .............. regression constant term
y = a·bx
a .............. regression constant term
b .............. regression coefficient
6-12
I Power Regression Graph
Power regression expresses y as a proportion of the power of x. The standard power
regression formula is y = a × xb, so if we take the logarithm of both sides we get In
y = In a + b × In x. Next, if we say X = In x, Y = In y, and A = In a, the formula corresponds to
linear regression formula Y = A + bX.
(CALC)(E)(Pwr)
(DRAW)
The following is the power regression model formula.
y = a·xb
a .............. regression coefficient
b .............. regression power
I Sinusoidal Regression Graph
Sinusoidal regression is best applied for cyclical data.
The following is the sinusoidal regression model formula.
y = a·sin(bx + c) + d
(CALC)(E)(Sin)
(DRAW)
Drawing a sine regression graph causes the angle unit setting of the calculator to automatically
change to Rad (radians). The angle unit does not change when you perform a sine regression
calculation without drawing a graph.
• Certain types of data may take a long time to calculate. This does not indicate malfunction.
I Logistic Regression Graph
Logistic regression is best applied for time-based phenomena in which there is a continual
increase until a saturation point is reached.
The following is the logistic regression model formula.
y=
c
1 + ae–bx
(CALC)(E)(E)(Lgst)
(DRAW)
• Certain types of data may take a long time to calculate. This does not indicate malfunction.
I Residual Calculation
Actual plot points (y-coordinates) and regression model distance can be calculated during
regression calculations.
6-13
While the statistical data list is on the display, recall the Setup screen to specify a LIST (“List 1”
through “List 26”) for “Resid List”. Calculated residual data is stored in the specified list.
The vertical distance from the plots to the regression model will be stored in the list.
Plots that are higher than the regression model are positive, while those that are lower are
negative.
Residual calculation can be performed and saved for all regression models.
Any data already existing in the selected list is cleared. The residual of each plot is stored in
the same precedence as the data used as the model.
I Displaying the Calculation Results of a Drawn Paired-Variable Graph
Paired-variable statistics can be expressed as both graphs and parameter values. When these
graphs are displayed, the paired-variable calculation results appear as shown below when you
press (CALC)(2VAR).
• Use A to scroll the list so you can view the items that run off the bottom of the screen.
M ........... mean of data stored in xList
3y2 ........ sum of squares of data stored in yList
3x ......... sum of data stored in xList
Sy .......... population standard deviation of data
stored in yList
3x2 ........ sum of squares of data stored in
xList
Sx .......... population standard deviation of
data stored in xList
sy .......... sample standard deviation of data
stored in yList
3xy ........ sum of the product of data stored in
xList and yList
sx .......... sample standard deviation of
data stored in xList
minX...... minimum of data stored in xList
n ........... number of data
maxX..... maximum of data stored in xList
N ............ mean of data stored in yList
minY...... minimum of data stored in yList
3y ......... sum of data stored in yList
maxY..... maximum of data stored in yList
I Copying a Regression Graph Formula to the GRAPH Mode
You can copy regression formula calculation results to the GRAPH mode Graph relation list,
and store and compare.
1. While a regression calculation result is on the display (see “Displaying Regression
Calculation Results” on page 6-10), press (COPY).
• This will display the GRAPH mode Graph relation list.*1
2. Use D and A to highlight the area to which you want to copy the regression formula of
the displayed result.
3. Press U to save the copied graph formula and return to the previous regression calculation
result display.
*1 You cannot edit regression formulas for graph formulas in the GRAPH mode.
6-14
4. Performing Statistical Calculations
All of the statistical calculations up to this point were performed after displaying a graph. The
following procedures can be used to perform statistical calculations alone.
S To specify statistical calculation data lists
You have to input the statistical data for the calculation you want to perform and specify
where it is located before you start a calculation. Display the statistical data and then press
(CALC)(SET).
The following is the meaning for each item.
1Var XList ....... location of single-variable statistic x values (XList)
1Var Freq........ location of single-variable frequency values (Frequency)
2Var XList ....... location of paired-variable statistic x values (XList)
2Var YList ....... location of paired-variable statistic y values (YList)
2Var Freq........ location of paired-variable frequency values (Frequency)
• Calculations in this section are performed based on the above specifications.
I Single-Variable Statistical Calculations
In the previous example under “Displaying the Calculation Results of a Drawn Single-Variable
Graph”, statistical calculation results were displayed after the graph was drawn. These were
numeric expressions of the characteristics of variables used in the graphic display.
These values can also be directly obtained by displaying the
statistical data list and pressing (CALC)(1VAR).
After this, pressing D or A scrolls the statistical calculation result display so you can view
variable characteristics.
For details on the meanings of these statistical values, see “Displaying the Calculation Results
of a Drawn Single-Variable Graph” (page 6-6).
I Paired-Variable Statistical Calculations
In the previous example under “Displaying the Calculation Results of a Drawn Paired-Variable
Graph”, statistical calculation results were displayed after the graph was drawn. These were
numeric expressions of the characteristics of variables used in the graphic display.
6-15
These values can also be directly obtained by displaying the
statistical data list and pressing (CALC)(2VAR).
After this, pressing D or A scrolls the statistical calculation result display so you can view
variable characteristics.
For details on the meanings of these statistical values, see “Displaying the Calculation Results
of a Drawn Paired-Variable Graph” (page 6-14).
I Regression Calculation
In the explanations from “Linear Regression Graph” to “Logistic Regression Graph”, regression
calculation results were displayed after the graph was drawn. Here, each coefficient value of
the regression line or regression curve is expressed as a number.
You can directly determine the same expression from the data input screen.
Pressing (CALC)(REG) displays a function menu, which contains the following items.
• {ax+b}/{a+bx}/{Med}/{X^2}/{X^3}/{X^4}/{Log}/{ae^bx}/{ab^x}/{Pwr}/{Sin}/{Lgst} ...
{linear regression (ax+b form)}/{linear regression (a+bx form)}/{Med-Med}/{quadratic
regression}/{cubic regression}/{quartic regression}/{logarithmic regression}/{exponential
regression (aebx form)}/{exponential regression (abx form)}/{power regression}/
{sinusoidal regression}/{logistic regression} parameters
Example
To display single-variable regression parameters
(CALC)(REG)(X)(ax+b)
The meanings of the parameters that appear on this screen are the same as those for “Linear
Regression Graph” to “Logistic Regression Graph”.
S Calculation of the Coefficient of Determination (r2) and MSe
You can use the STAT mode to calculate the coefficient of determination (r2) for quadratic
regression, cubic regression, and quartic regression. The following types of MSe calculations
are also available for each type of regression.
6-16
• Linear Regression (ax + b)............. MSe =
(a + bx)............. MSe =
• Quadratic Regression..................... MSe =
• Cubic Regression ........................... MSe =
• Quartic Regression ........................ MSe =
• Logarithmic Regression.................. MSe =
• Exponential Repression (a·ebx) ....... MSe =
(a·bx)........ MSe =
• Power Regression .......................... MSe =
• Sin Regression ............................... MSe =
• Logistic Regression ........................ MSe =
1
n–2
n
(y – (ax + b))
i
1
n–4
n
(y – (a + bx ))
i
n
(y – (ax
i
1
n–2
+ bxi + c))2
n
(y – (ax + bx + cx + d ))
3
i
i
i
2
i
2
i=1
n
(y – (ax + bx
4
i
i
3
i
+ cxi2 + dxi + e))2
i=1
n
(y – (a + b ln x ))
i
2
i
i=1
n
(ln y – (ln a + bx ))
i
i
2
i=1
n
1
n–2
1
n–2
2
i
i=1
1
n–2
1
n–2
2
i
i=1
1
n–5
1
n–2
2
i=1
1
n–2
1
n–3
i
(ln y – (ln a + (ln b) · x ))
i
2
i
i=1
n
(ln y – (ln a + b ln x ))
i
i
2
i=1
n
(y – (a sin (bx + c) + d ))
i
2
i
i=1
n
yi –
i=1
C
1 + ae–bxi
2
S Estimated Value Calculation for Regression Graphs
The STAT mode also includes a Y-CAL function that uses regression to calculate the estimated
y-value for a particular x-value after graphing a paired-variable statistical
regression.
The following is the general procedure for using the Y-CAL function.
1. After drawing a regression graph, press (G-SLV)(Y-CAL) to enter the graph
selection mode, and then press U.
If there are multiple graphs on the display, use D and A to select the graph you want,
and then press U.
• This causes an x-value input dialog box to appear.
2. Input the value you want for x and then press U.
• This causes the coordinates for x and y to appear at
the bottom of the display, and moves the pointer to the
corresponding point on the graph.
6-17
3. Pressing T or a number key at this time causes the x-value input dialog box to reappear
so you can perform another estimated value calculation if you want.
• The pointer does not appear if the calculated coordinates are not within the display range.
• The coordinates do not appear if “Off” is specified for the “Coord” item of the Setup screen.
• The Y-CAL function can also be used with a graph drawn by using DefG feature.
S Regression Formula Copy Function from a Regression Calculation Result
Screen
In addition to the normal regression formula copy function that lets you copy the regression
calculation result screen after drawing a statistical graph (such as Scatter Plot), the STAT
mode also has a function that lets you copy the regression formula obtained as the result of a
regression calculation. To copy a resulting regression formula, press (COPY).
I Estimated Value Calculation ( , )
After drawing a regression graph with the STAT mode, you can use the RUN • MAT (or RUN)
mode to calculate estimated values for the regression graph’s x and y parameters.
Example
To perform a linear regression using the nearby data and estimate the
values of ţ and [ů when xi = 20 and yi = 1000
xi
yi
10
15
20
25
30
1003
1005
1010
1011
1014
1. From the Main Menu, enter the STAT mode.
2. Input data into the list and draw the linear regression graph.
3. From the Main Menu, enter the RUN • MAT (or RUN) mode.
4. Press the keys as follows.
A?(value of xi)
*(STAT)*(ţ)U
* fx-7400GII: (STAT)
The estimated value ţ is displayed for xi = 20.
@???(value of yi)
(xˆ )U
The estimated value xˆ is displayed for yi = 1000.
• You cannot obtain estimated values for a Med-Med, quadratic regression, cubic regression,
quartic regression, sinusoidal regression, or logistic regression graph.
6-18
I Normal Probability Distribution Calculation
You can calculate normal probability distributions for single-variable statistics with the
RUN • MAT (or RUN) mode.
Press *(E)(PROB) ((PROB) on the fx-7400GII) (E) to display a function
menu, which contains the following items.
• {P(}/{Q(}/{R(} ... obtains normal probability {P(t)}/{Q(t)}/{R(t)} value
• {t(} ... {obtains normalized variate t(x) value}
• Normal probability P(t), Q(t), and R(t), and normalized variate t(x) are calculated using the
following formulas.
Standard Normal Distribution
P (t)
Q (t)
0 t
R (t)
0 t
0 t
x
Example
The following table shows the results of measurements of the height of
20 college students. Determine what percentage of the students fall in
the range 160.5 cm to 175.5 cm. Also, in what percentile does the 175.5
cm tall student fall?
Class no. Height (cm) Frequency
Class no. Height (cm) Frequency
1
158.5
1
6
173.3
4
2
160.5
1
7
175.5
2
3
163.3
2
8
178.6
2
4
167.5
2
9
180.4
2
5
170.2
3
10
186.7
1
1. From the Main Menu, enter the STAT mode.
2. Input the height data into List 1 and the frequency data into List 2.
3. Perform the single-variable statistical calculations.
You can obtain the normalized variate immediately after
performing single-variable statistical calculations only.
(CALC)(SET)
(LIST)@U
A(LIST)AU )(QUIT)
(CALC)(1VAR)
6-19
4. Press K, select the RUN • MAT (or RUN) mode, press *(E)(PROB)
((PROB) on the fx-7400GII) to recall the probability calculation (PROB) menu.
(PROB)*(E)(t() @E?
DU
* fx-7400GII: (PROB)
(Normalized variate t for 160.5 cm)
Result: –1.633855948
( –1.634)
(t() @FD
DU
(Normalized variate t for 175.5 cm)
Result: 0.4963343361
( 0.496)
(P()?
CHE
(P() @
EBCU
(Percentage of total)
Result:
0.638921
(63.9% of total)
(R()?
CHEU
(Percentile)
Result:
0.30995
(31.0 percentile)
I Drawing a Normal Probability Distribution Graph
You can draw a normal probability distribution graph using manual graphing with the
RUN • MAT (or RUN) mode.
1. From the Main Menu, enter the RUN • MAT (or RUN) mode.
2. Input the commands to draw a rectangular coordinate graph.
3. Input the probability value.
Example
To draw a normal probability P (0.5) graph.
K RUN • MAT (or RUN)
(SKTCH)(Cls)U
(GRPH)(Y=)
*(E)(PROB)*(E)(P()?
DU
* fx-7400GII: (PROB)
I Calculations Using the Distribution Function
Important!
• The following operations cannot be performed on the fx-7400GII.
You can use special functions in the RUN • MAT mode or PRGM mode to perform calculations
that are the same as the STAT mode distribution function calculation (page 6-38).
Example
To calculate normal probability distribution in the RUN • MAT mode for
the data {1, 2, 3}, when the population standard deviation is S = 1.5 and
the population mean is ƫ = 2.
6-20
1. From the Main Menu, enter the RUN • MAT mode.
2. Press the keys as follows.
*(STAT)(DIST)(NORM)
(NPd) ( { )@ A B
( } ) @
D AU
• For details about what you can do with the distribution function and its syntax, see
“Performing Distribution Calculations in a Program” (page 8-29).
I Determining Standard Deviation and Variance from List Data
You can use functions to determine standard deviation and variance for specified list data. This
calculation is performed in the RUN • MAT (or RUN) mode. You can perform calculations using
data you saved to a list (List 1 to List 26) with the STAT mode List Editor or list data you input
directly on the RUN • MAT (or RUN) mode screen.
Syntax
StdDev(List n [,List m])
Variance(List n [,List m])
List n........Sample data
List m.......Frequency data
Example
To store the x-data below in List 1, the frequency values in List 2, and
determine the standard deviation and variance
x
60
70
80
90
Frequency
3
5
4
1
1. From the Main Menu, enter the STAT mode.
2. Use the List Editor to store the above data.
3. From the Main Menu, enter the RUN • MAT (or RUN) mode.
4. Press the keys as follows.
*(STAT)(S • Dev)*)
(LIST)(List)@ (List)AU
* fx-7400GII: (STAT)(S • Dev)
)(STAT)(Var)*)
(LIST)(List)@ (List)AU
* fx-7400GII: (STAT)(Var)
6-21
I Calculations Using the TEST Command
Important!
• The following operations cannot be performed on the fx-7400GII.
You can use special functions in the RUN • MAT mode or PRGM mode to perform calculations
that are the same as the STAT mode Z Test, t Test, and other test calculations (page 6-22).
Example
To determine the z score and p-value when a one-sample Z test is
performed under the conditions below:
test condition (ƫcondition) x ƫ0*, assumed population mean ƫ0 = 0,
population standard deviation Ʊ = 1, sample mean M = 1, number of
samples n = 2
* “ƫ condition x ƫ0” can be specified by entering 0 as the initial argument of
the one-sample Z test command “OneSampleZTest”.
1. From the Main Menu, enter the RUN • MAT mode.
2. Perform the following key operation.
*(STAT)(E)(TEST)(Z)
(1-S)? ? @ @ A
U
)))
(LIST)(List) (Ans)U
The following calculation results are displayed as ListAns elements 1 through 4.
1: z score
2: p-value
3: M
4: n
• For details about the function of the supported TEST command and their syntax, see “Using
the TEST Command to Execute a Command in a Program” (page 8-32).
5. Tests
Important!
• Test calculations cannot be performed on the fx-7400GII.
The Z Test provides a variety of different standardization-based tests. They make it possible to
test whether or not a sample accurately represents the population when the standard deviation
of a population (such as the entire population of a country) is known from previous tests. Z
testing is used for market research and public opinion research, that need to be performed
repeatedly.
6-22
1-Sample Z Test tests for the unknown population mean when the population standard
deviation is known.
2-Sample Z Test tests the equality of the means of two populations based on independent
samples when both population standard deviations are known.
1-Prop Z Test tests for an unknown proportion of successes.
2-Prop Z Test tests to compare the proportion of successes from two populations.
The t Test tests the hypothesis when the population standard deviation is unknown. The
hypothesis that is the opposite of the hypothesis being proven is called the null hypothesis,
while the hypothesis being proved is called the alternative hypothesis. The t Test is normally
applied to test the null hypothesis. Then a determination is made whether the null hypothesis
or alternative hypothesis will be adopted.
1-Sample t Test tests the hypothesis for a single unknown population mean when the
population standard deviation is unknown.
2-Sample t Test compares the population means when the population standard deviations are
unknown.
LinearReg t Test calculates the strength of the linear association of paired data.
With the C2 test, a number of independent groups are provided and a hypothesis is tested
relative to the probability of samples being included in each group.
The C2 GOF test (C2 one-way Test) tests whether the observed count of sample data fits
a certain distribution. For example, it can be used to determine conformance with normal
distribution or binomial distribution.
The C2 two-way test creates a cross-tabulation table that structures mainly two qualitative
variables (such as “Yes” and “No”), and evaluates the independence of the variables.
2-Sample F Test tests the hypothesis for the ratio of sample variances. It could be used, for
example, to test the carcinogenic effects of multiple suspected factors such as tobacco use,
alcohol, vitamin deficiency, high coffee intake, inactivity, poor living habits, etc.
ANOVA tests the hypothesis that the population means of the samples are equal when
there are multiple samples. It could be used, for example, to test whether or not different
combinations of materials have an effect on the quality and life of a final product.
One-Way ANOVA is used when there is one independent variable and one dependent
variable.
Two-Way ANOVA is used when there are two independent variables and one dependent
variable.
The following pages explain various statistical calculation methods based on the principles
described above. Details concerning statistical principles and terminology can be found in any
standard statistics textbook.
On the initial STAT mode screen, press (TEST) to display the test menu, which contains
the following items.
• (TEST)(Z) ... Z Tests (page 6-24)
(t) ... t Tests (page 6-26)
(CHI) ... C2 Test (page 6-29)
(F) ... 2-Sample F Test (page 6-30)
(ANOV) ... ANOVA (page 6-31)
6-23
After setting all the parameters, use A to move the highlighting to “Execute” and then press
one of the function keys shown below to perform the calculation or draw the graph.
• (CALC) ... Performs the calculation.
• (DRAW) ... Draws the graph.
• V-Window settings are automatically optimized for drawing the graph.
I Z Tests
S Z Test Common Functions
You can use the following graph analysis functions after drawing a Z Test result output graph.
• (Z) ... Displays z score.
Pressing (Z) displays the z score at the bottom of the display, and displays the pointer at
the corresponding location in the graph (unless the location is off the graph screen).
Two points are displayed in the case of a two-tail test. Use B and C to move the pointer.
• (P) ... Displays p-value.
Pressing (P) displays the p-value at the bottom of the display without displaying the pointer.
• Executing an analysis function automatically stores the z and p values in alpha variables Z
and P, respectively.
S 1-Sample Z Test
This test is used when the population standard deviation is known to test the hypothesis. The
1-Sample Z Test is applied to the normal distribution.
Perform the following key operations from the statistical data list.
(TEST)
(Z)
(1-S)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
Mx11.4 .......... direction of test
sx .................. Displayed only for Data: List setting.
6-24
• [Save Res] does not save the M condition in line 2.
S 2-Sample Z Test
This test is used when the standard deviations for two populations are known to test the
hypothesis. The 2-Sample Z Test is applied to the normal distribution.
Perform the following key operations from the statistical data list.
(TEST)
(Z)
(2-S)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
M1xM2 ............ direction of test
sx1 ................ Displayed only for Data: List setting.
sx2 ................ Displayed only for Data: List setting.
• [Save Res] does not save the M1 condition in line 2.
S 1-Prop Z Test
This test is used to test for an unknown proportion of successes. The 1-Prop Z Test is applied
to the normal distribution.
Perform the following key operations from the statistical data list.
(TEST)
(Z)
(1-P)
6-25
Calculation Result Output Example
Propx0.5 ....... direction of test
• [Save Res] does not save the Prop condition in line 2.
S 2-Prop Z Test
This test is used to compare the proportion of successes. The 2-Prop Z Test is applied to the
normal distribution.
Perform the following key operation from the statistical data list.
(TEST)
(Z)
(2-P)
Calculation Result Output Example
p1>p2 ............ direction of test
• [Save Res] does not save the p1 condition in line 2.
I t Tests
S t Test Common Functions
You can use the following graph analysis functions after drawing a t Test result output graph.
• (T) ... Displays t score.
Pressing (T) displays the t score at the bottom of the display, and displays the pointer at the
corresponding location in the graph (unless the location is off the graph screen).
Two points are displayed in the case of a two-tail test. Use B and C to move the pointer.
• (P) ... Displays p-value.
6-26
Pressing (P) displays the p-value at the bottom of the display without displaying the pointer.
• Executing an analysis function automatically stores the t and p values in alpha variables T
and P, respectively.
S 1-Sample t Test
This test uses the hypothesis test for a single unknown population mean when the population
standard deviation is unknown. The 1-Sample t Test is applied to t distribution.
Perform the following key operations from the statistical data list.
(TEST)
(t)
(1-S)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
Mx11.3 .......... direction of test
• [Save Res] does not save the M condition in line 2.
S 2-Sample t Test
2-Sample t Test compares the population means when the population standard deviations are
unknown. The 2-Sample t Test is applied to t distribution.
Perform the following key operations from the statistical data list.
(TEST)
(t)
(2-S)
6-27
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
M1xM2 ............ direction of test
sp ................. Displayed only when Pooled: On setting.
• [Save Res] does not save the M1 condition in line 2.
S LinearReg t Test
LinearReg t Test treats paired-variable data sets as (x, y) pairs, and uses the method of least
squares to determine the most appropriate a, b coefficients of the data for the regression
formula y = a + bx. It also determines the correlation coefficient and t score, and calculates the
extent of the relationship between x and y.
Perform the following key operations from the statistical data list.
(TEST)
(t)
(REG)
Calculation Result Output Example
Bx0 & Rx0 ......... direction of test
Pressing (COPY) while a calculation result is on the display copies the regression formula
to the Graph relation list.
6-28
When there is a list specified for the [Resid List] item on the Setup screen, regression formula
residual data is automatically saved to the specified list after the calculation is finished.
• You cannot draw a graph for LinearReg t Test.
• [Save Res] does not save the B & R conditions in line 2.
• When the list specified by [Save Res] is the same list specified by the [Resid List] item on the
Setup screen, only [Resid List] data is saved in the list.
I Ƶ2 Test
• Ƶ2 Test Common Functions
You can use the following graph analysis functions after drawing a graph.
• (CHI) ... Displays C2 value.
Pressing (CHI) displays the C2 value at the bottom of the display, and displays the pointer at
the corresponding location in the graph (unless the location is off the graph screen).
• (P) ... Displays p-value.
Pressing (P) displays the p-value at the bottom of the display without displaying the pointer.
• Executing an analysis function automatically stores the C2 and p values in alpha variables C
and P, respectively.
• Ƶ2 GOF Test (Ƶ2 one-way Test)
The C2 GOF Test (Ƶ2 one-way test) tests whether the frequency of sample data fits a certain
distribution. For example, it can be used to determine conformance with normal distribution or
binomial distribution.
Perform the following key operations from the statistical data list.
(TEST)
(CHI)
(GOF)
Next, specify the lists that contain the data. The following shows the meaning of the above
items.
Observed ...... name of List (1 to 26) that contains observed counts (all cells positive
integers)
Expected....... name of List (1 to 26) that is for saving expected frequency
CNTRB ......... Specifies a list (List 1 to List 26) as the storage location of the contribution
of each observed count obtained as calculation results.
6-29
Calculation Result Output Examples
CNTRB ......... list for output of contribution values
• Ƶ2 two-way Test
C2 two-way Test sets up a number of independent groups and tests hypothesis related to
the proportion of the sample included in each group. The C2 Test is applied to dichotomous
variables (variable with two possible values, such as yes/no).
Perform the following key operations from the statistical data list.
(TEST)
(CHI)
(2WAY)
Next, specify the matrix that contains the data. The following shows the meaning of the above
items.
Observed ...... name of matrix (A to Z) that contains observed counts (all cells positive
integers)
Expected....... name of matrix (A to Z) that is for saving expected frequency
Calculation Result Output Example
• The matrix must be at least two lines by two columns. An error occurs if the matrix has only
one line or one column.
• Pressing (Mat) while the “Observed” and “Expected” parameter settings are highlighted
will display the Matrix (A to Z) setting screen.
• Pressing (MAT) while setting parameters enters the Matrix Editor, which you can use to
edit and view the contents of matrices.
• Pressing (MAT) while a calculation result is displayed enters the Matrix Editor, which
you can use to edit and view the contents of matrices.
I 2-Sample F Test
2-Sample F Test tests the hypothesis for the ratio of sample variances. The F Test is applied
to the F distribution.
6-30
Perform the following key operations from the statistical data list.
(TEST)
(F)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
S1xS2 ............ direction of test
x¯ 1 .................. Displayed only for Data: List setting.
x¯ 2 .................. Displayed only for Data: List setting.
You can use the following graph analysis functions after drawing a graph.
• (F) ... Displays F value.
Pressing (F) displays the F value at the bottom of the display, and displays the pointer at
the corresponding location in the graph (unless the location is off the graph screen).
Two points are displayed in the case of a two-tail test. Use B and C to move the pointer.
• (P) ... Displays p-value.
Pressing (P) displays the p-value at the bottom of the display without displaying the pointer.
• Executing an analysis function automatically stores the F and p values in alpha variables F
and P, respectively.
• [Save Res] does not save the S1 condition in line 2.
I ANOVA
ANOVA tests the hypothesis that the population means of the samples are equal when there
are multiple samples.
One-Way ANOVA is used when there is one independent variable and one dependent
variable.
Two-Way ANOVA is used when there are two independent variables and one dependent
variable.
6-31
Perform the following key operations from the statistical data list.
(TEST)
(ANOV)
The following is the meaning of each item in the case of list data specification.
How Many..... selects One-Way ANOVA or Two-Way ANOVA (number of levels)
Factor A ........ category list (List 1 to 26)
Dependnt ...... list to be used for sample data (List 1 to 26)
Save Res ...... first list for storage of calculation results (None or List 1 to 22)*1
Execute......... executes a calculation or draws a graph (Two-Way ANOVA only)
*1 [Save Res] saves each vertical column of the table into its own list. The leftmost column
is saved in the specified list, and each subsequent column to the right is saved in the next
sequentially numbered list. Up to five lists can be used for storing columns. You can specify
an first list number in the range of 1 to 22.
The following item appears in the case of Two-Way ANOVA only.
Factor B ........ category list (List 1 to 26)
After setting all the parameters, use A to move the highlighting to “Execute” and then press
one of the function keys shown below to perform the calculation or draw the graph.
• (CALC) ... Performs the calculation.
• (DRAW) ... Draws the graph (Two-Way ANOVA only).
Calculation results are displayed in table form, just as they appear in science books.
Calculation Result Output Example
One-Way ANOVA
Line 1 (A) .......... Factor A df value, SS value, MS value, F value, p-value
Line 2 (ERR) ..... Error df value, SS value, MS value
Two-Way ANOVA
Line 1 (A) .......... Factor A df value, SS value, MS value, F value, p-value
Line 2 (B) .......... Factor B df value, SS value, MS value, F value, p-value
Line 3 (AB)........ Factor A s Factor B df value, SS value, MS value, F value, p-value
* Line 3 does not appear when there is only one observation in each
cell.
Line 4 (ERR) ..... Error df value, SS value, MS value
F ...................... F value
6-32
p ....................... p-value
df ..................... degrees of freedom
SS ..................... sum of squares
MS ................... mean squares
With Two-Way ANOVA, you can draw Interaction Plot graphs. The number of graphs depends
on Factor B, while the number of X-axis data depends on the Factor A. The Y-axis is the
average value of each category.
You can use the following graph analysis function after drawing a graph.
• (Trace) or (TRCE) ... Trace function
Pressing B or C moves the pointer on the graph in the corresponding direction. When there
are multiple graphs, you can move between graphs by pressing D and A.
• Graphing is available with Two-Way ANOVA only. V-Window settings are performed
automatically, regardless of Setup screen settings.
• Using the Trace function automatically stores the number of conditions to alpha variable A
and the mean value to variable M, respectively.
I ANOVA (Two-Way)
S Description
The nearby table shows measurement results for a metal product produced by a heat
treatment process based on two treatment levels: time (A) and temperature (B). The
experiments were repeated twice each under identical conditions.
B (Heat Treatment Temperature)
A (Time)
B1
B2
A1
113 ,
116 139 ,
132
A2
133 ,
131 126 ,
122
Perform analysis of variance on the following null hypothesis, using a significance level of 5%.
Ho : No change in strength due to time
Ho : No change in strength due to heat treatment temperature
Ho : No change in strength due to interaction of time and heat treatment temperature
S Solution
Use Two-Way ANOVA to test the above hypothesis.
Input the above data as shown below.
List1={1,1,1,1,2,2,2,2}
List2={1,1,2,2,1,1,2,2}
List3={113,116,139,132,133,131,126,122}
6-33
Define List 3 (the data for each group) as Dependent. Define List 1 and List 2 (the factor
numbers for each data item in List 3) as Factor A and Factor B respectively.
Executing the test produces the following results.
• Time differential (A) level of significance P = 0.2458019517
The level of significance (p = 0.2458019517) is greater than the significance level (0.05), so
the hypothesis is not rejected.
• Temperature differential (B) level of significance P = 0.04222398836
The level of significance (p = 0.04222398836) is less than the significance level (0.05), so the
hypothesis is rejected.
• Interaction (A s B) level of significance P = 2.78169946e-3
The level of significance (p = 2.78169946e-3) is less than the significance level (0.05), so the
hypothesis is rejected.
The above test indicates that the time differential is not significant, the temperature differential
is significant, and interaction is highly significant.
S Input Example
S Results
6-34
6. Confidence Interval
Important!
• Confidence interval calculations cannot be performed on the fx-7400GII.
A confidence interval is a range (interval) that includes a statistical value, usually the
population mean.
A confidence interval that is too broad makes it difficult to get an idea of where the population
value (true value) is located. A narrow confidence interval, on the other hand, limits the
population value and makes it difficult to obtain reliable results. The most commonly used
confidence levels are 95% and 99%. Raising the confidence level broadens the confidence
interval, while lowering the confidence level narrows the confidence level, but it also
increases the chance of accidently overlooking the population value. With a 95% confidence
interval, for example, the population value is not included within the resulting intervals 5% of
the time.
When you plan to conduct a survey and then t test and Z test the data, you must also consider
the sample size, confidence interval width, and confidence level. The confidence level changes
in accordance with the application.
1-Sample Z Interval calculates the confidence interval for an unknown population mean when
the population standard deviation is known.
2-Sample Z Interval calculates the confidence interval for the difference between two
population means when the population standard deviations of two samples are known.
1-Prop Z Interval calculates the confidence interval for an unknown proportion of successes.
2-Prop Z Interval calculates the confidence interval for the difference between the proportion
of successes in two populations.
1-Sample t Interval calculates the confidence interval for an unknown population mean when
the population standard deviation is unknown.
2-Sample t Interval calculates the confidence interval for the difference between two
population means when both population standard deviations are unknown.
On the initial STAT mode screen, press (INTR) to display the confidence interval menu,
which contains the following items.
• (INTR)(Z) ... Z intervals (page 6-36)
(t) ... t intervals (page 6-37)
After setting all the parameters, use A to move the highlighting to “Execute” and then press
the function key shown below to perform the calculation.
• (CALC) ... Performs the calculation.
• There is no graphing for confidence interval functions.
S General Confidence Interval Precaution
Inputting a value in the range of 0 C-Level < 1 for the C-Level setting sets a value you input.
Inputting a value in the range of 1 C-Level < 100 sets a value equivalent to your input divided
by 100.
6-35
I Z Interval
S 1-Sample Z Interval
1-Sample Z Interval calculates the confidence interval for an unknown population mean when
the population standard deviation is known.
Perform the following key operations from the statistical data list.
(INTR)
(Z)
(1-S)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
S 2-Sample Z Interval
2-Sample Z Interval calculates the confidence interval for the difference between two
population means when the population standard deviations of two samples are known.
Perform the following key operations from the statistical data list.
(INTR)
(Z)
(2-S)
S 1-Prop Z Interval
1-Prop Z Interval uses the number of data to calculate the confidence interval for an unknown
proportion of successes.
Perform the following key operations from the statistical data list.
(INTR)
(Z)
(1-P)
6-36
Data is specified using parameter specification.
Calculation Result Output Example
S 2-Prop Z Interval
2-Prop Z Interval uses the number of data items to calculate the confidence interval for the
defference between the proportion of successes in two populations.
Perform the following key operations from the statistical data list.
(INTR)
(Z)
(2-P)
I t Interval
S 1-Sample t Interval
1-Sample t Interval calculates the confidence interval for an unknown population mean when
the population standard deviation is unknown.
Perform the following key operations from the statistical data list.
(INTR)
(t)
(1-S)
The following shows the parameter data specification items that are different from list data
specification.
Calculation Result Output Example
6-37
S 2-Sample t Interval
2-Sample t Interval calculates the confidence interval for the difference between two
population means when both population standard deviations are unknown. The t interval is
applied to t distribution.
Perform the following key operations from the statistical data list.
(INTR)
(t)
(2-S)
7. Distribution
Important!
• Distribution calculations cannot be performed on the fx-7400GII.
There is a variety of different types of distribution, but the most well-known is “normal
distribution”, which is essential for performing statistical calculations. Normal distribution
is a symmetrical distribution centered on the greatest occurrences of mean data (highest
frequency), with the frequency decreasing as you move away from the center. Poisson
distribution, geometric distribution, and various other distribution shapes are also used,
depending on the data type.
Certain trends can be determined once the distribution shape is determined. You can calculate
the probability of data taken from a distribution being less than a specific value.
For example, distribution can be used to calculate the yield rate when manufacturing some
product. Once a value is established as the criteria, you can calculate normal probability when
estimating what percent of the products meet the criteria. Conversely, a success rate target
(80% for example) is set up as the hypothesis, and normal distribution is used to estimate the
proportion of the products will reach this value.
Normal probability density calculates the probability density of normal distribution from a
specified x value.
Normal cumulative distribution calculates the probability of normal distribution data falling
between two specific values.
Inverse normal cumulative distribution calculates a value that represents the location within
a normal distribution for a specific cumulative probability.
Student-t probability density calculates t probability density from a specified x value.
Student-t cumulative distribution calculates the probability of t distribution data falling
between two specific values.
Inverse Student-t cumulative distribution calculates the lower bound value of a Student-t
cumulative probability density for a specified percentage.
Like t distribution, probability density (or probability), cumulative distribution and inverse
cumulative distribution can also be calculated for C2, F, Binomial, Poisson, Geometric and
Hypergeometric distributions.
On the initial STAT mode screen, press (DIST) to display the distribution menu, which
contains the following items.
6-38
• (DIST)(NORM) ... Normal distribution (page 6-39)
(t) ... Student-t distribution (page 6-41)
(CHI) ... C2 distribution (page 6-42)
(F) ... F distribution (page 6-43)
(BINM) ... Binomial distribution (page 6-44)
(E)(POISN) ... Poisson distribution (page 6-46)
(E)(GEO) ... Geometric distribution (page 6-47)
(E)(H.GEO) ... Hypergeometric distribution (page 6-49)
After setting all the parameters, use A to move the highlighting to “Execute” and then press
one of the function keys shown below to perform the calculation or draw the graph.
• (CALC) ... Performs the calculation.
• (DRAW) ... Draws the graph.
I Common Distribution Functions
• V-Window settings for graph drawing are set automatically when the Setup screen’s “Stat
Wind” setting is “Auto”. Current V-Window settings are used for graph drawing when the “Stat
Wind” setting is “Manual”.
• After drawing a graph, you can use the P-CAL function to calculate an estimated p-value for
a particular x value. The P-CAL function can be used only after a Normal Probability Density,
Student-t Probability Density, Ƶ2 Probability Density, or F Probability Density graph is drawn.
The following is the general procedure for using the P-CAL function.
1. After drawing a distribution graph, press (G-SLV) (P-CAL) to display the x value
input dialog box.
2. Input the value you want for x and then press U.
• This causes the x and p values to appear at the bottom of the display, and moves the
pointer to the corresponding point on the graph.
3. Pressing T or a number key at this time causes the x value input dialog box to reappear
so you can perform another estimated value calculation if you want.
4. After you are finished, press ) to clear the coordinate values and the pointer from the
display.
• Executing an analysis function automatically stores the x and p values in alpha variables X
and P, respectively.
I Normal Distribution
• Normal Probability Density
(DIST)(NORM)(NPd)
Normal Probability Density calculates the probability
density (p) for a specified single x-value or a list. When a
list is specified, calculation results for each list element are
displayed in list form.
6-39
• Normal probability density is applied to standard normal distribution.
• Specifying Ʊ = 1 and ƫ = 0 specifies standard normal distribution.
Calculation Result Output Examples
When a list is specified
Graph when an x-value is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Normal Cumulative Distribution
(DIST)(NORM)(NCd)
Normal Cumulative Distribution calculates the normal
cumulative probability of a normal distribution between a
lower bound and an upper bound.
Calculation Result Output Examples
When a list is specified
Graph when an x-value is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Inverse Normal Cumulative Distribution
(DIST)(NORM)(InvN)
Inverse Normal Cumulative Distribution calculates the
boundary value(s) of a normal cumulative distribution
probability for specified values.
Area: probability value
(0 Area 1)
Inverse cumulative normal distribution calculates a value that represents the location within a
normal distribution for a specific cumulative probability.
6-40
Upper
f (x)dx = p
Tail: Left
upper boundary
of integration
interval
f (x)dx = p
Lower
Tail: Right
lower boundary
of integration
interval
Upper
f (x)dx = p
Lower
Tail: Central
upper and lower
boundaries of
integration interval
Specify the probability and use this formula to obtain the integration interval.
• This calculator performs the above calculation using the following: d = 1E99, –d = –1E99
• There is no graphing for Inverse Normal Cumulative Distribution.
I Student-t Distribution
• Student-t Probability Density
(DIST)(t)(tPd)
Student-t Probability Density calculates the probability
density (p) for a specified single x-value or a list. When a
list is specified, calculation results for each list element are
displayed in list form.
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Student-t Cumulative Distribution
(DIST)(t)(tCd)
Student-t Cumulative Distribution calculates the Student-t
cumulative probability of a Student-t distribution between a
lower bound and an upper bound.
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
6-41
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Inverse Student-t Cumulative Distribution
(DIST)(t)(InvN)
Inverse Student-t Cumulative Distribution calculates the
lower bound value of a Student-t cumulative distribution for
a specified df (degrees of freedom) value.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Student-t Cumulative Distribution.
I Ƶ2 Distribution
• Ƶ2 Probability Density
(DIST)(CHI)(CPd)
Ƶ2 Probability Density calculates the Ƶ2 probability density
(p) for a specified single x-value or a list. When a list is
specified, calculation results for each list element are
displayed in list form.
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Ƶ2 Cumulative Distribution
(DIST)(CHI)(CCd)
Ƶ Cumulative Distribution calculates the cumulative
probability of a Ƶ2 distribution between a lower bound and
2
an upper bound.
6-42
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Inverse Ƶ2 Cumulative Distribution
(DIST)(CHI)(InvC)
Inverse Ƶ Cumulative Distribution calculates the lower
bound value of a Ƶ2 cumulative distribution probability for a
specified df (degrees of freedom) value.
2
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Ƶ2 Cumulative Distribution.
I F Distribution
• F Probability Density
(DIST)(F)(FPd)
F Probability Density calculates the F probability density
(p) for a specified single x-value or a list. When a list is
specified, calculation results for each list element are
displayed in list form.
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
6-43
• F Cumulative Distribution
(DIST)(F)(FCd)
F Cumulative Distribution calculates the cumulative
probability of an F distribution between a lower bound and
an upper bound.
Calculation Result Output Examples
When a list is specified
Graph when variable (x) is specified
• Graphing is supported only when a variable is specified and a single x-value is entered as
data.
• Inverse F Cumulative Distribution
(DIST)(F)(InvF)
Inverse F Cumulative Distribution calculates the lower
bound value of an F cumulative distribution probability for
specified n:df and d:df (degrees of freedom of numerator
and denominator) values.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse F Cumulative Distribution.
I Binomial Distribution
• Binomial Probability
(DIST)(BINM)(BPd)
Binomial Probability calculates a probability at a specific
single x-value or each list element for the discrete binomial
distribution with the specified number of trials and
probability of success on each trial. When a list is specified,
calculation results for each list element are displayed in list
form.
6-44
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Binomial Probability.
• Binomial Cumulative Distribution
(DIST)(BINM)(BCd)
Binomial Cumulative Distribution calculates the cumulative
probability in a binomial distribution that the success will
occur on or before a specified trial.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Binomial Cumulative Distribution.
• Inverse Binomial Cumulative Distribution
(DIST)(BINM)(InvB)
Inverse Binomial Cumulative Distribution calculates
the minimum number of trials of a binomial cumulative
distribution for specified values.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Binomial Cumulative Distribution.
6-45
Important!
When executing the Inverse Binomial Cumulative Distribution calculation, the calculator uses
the specified Area value and the value that is one less than the Area value minimum number
of significant digits (>Area value) to calculate minimum number of trials values.
The results are assigned to system variables xInv (calculation result using Area) and >xInv
(calculation result using >Area). The calculator always displays the xInv value only. However,
when the xInv and >xInv values are different, the message shown below will appear with both
values.
The calculation results of Inverse Binomial Cumulative Distribution are integers. Accuracy may
be reduced when the first argument has 10 or more digits. Note that even a slight difference
in calculation accuracy affects calculation results. If a warning message appears, check the
displayed values.
I Poisson Distribution
(DIST)(E)(POISN)(PPd)
• Poisson Probability
Poisson Probability calculates a probability at a specific
single x-value or each list element for the discrete Poisson
distribution with the specified mean.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Poisson Probability.
(DIST)(E)(POISN)(PCd)
• Poisson Cumulative Distribution
Poisson Cumulative Distribution calculates the cumulative
probability in a Poisson distribution that the success will
occur on or before a specified trial.
6-46
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Poisson Cumulative Distribution.
• Inverse Poisson Cumulative Distribution
(DIST)(E)(POISN)(InvP)
Inverse Poisson Cumulative Distribution calculates
the minimum number of trials of a Poisson cumulative
probability distribution for specified values.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Poisson Cumulative Distribution.
Important!
When executing the Inverse Poisson Cumulative Distribution calculation, the calculator uses
the specified Area value and the value that is one less than the Area value minimum number
of significant digits (>Area value) to calculate minimum number of trials values.
The results are assigned to system variables xInv (calculation result using Area) and >xInv
(calculation result using >Area). The calculator always displays the xInv value only. However,
when the xInv and >xInv values are different, the message will appear with both values.
The calculation results of Inverse Poisson Cumulative Distribution are integers. Accuracy may
be reduced when the first argument has 10 or more digits. Note that even a slight difference
in calculation accuracy affects calculation results. If a warning message appears, check the
displayed values.
I Geometric Distribution
(DIST)(E)(GEO)(GPd)
• Geometric Probability
Geometric Probability calculates the probability at a specific
single x-value or each list element, and the number of the
trial on which the first success occurs, for the geometric
distribution with a specified probability of success.
6-47
Calculation Result Output Examples
When variable (x) is specified
When a list is specified
• There is no graphing for Geometric Probability.
(DIST)(E)(GEO)(GCd)
• Geometric Cumulative Distribution
Geometric Cumulative Distribution calculates the cumulative
probability in a geometric distribution that the success will
occur on or before a specified trial.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Geometric Cumulative Distribution.
• Inverse Geometric Cumulative Distribution
(DIST)(E)(GEO)(InvG)
Inverse Geometric Cumulative Distribution calculates
the minimum number of trials of a geometric cumulative
probability distribution for specified values.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Geometric Cumulative Distribution.
6-48
Important!
When executing the Inverse Geometric Cumulative Distribution calculation, the calculator uses
the specified Area value and the value that is one less than the Area value minimum number
of significant digits (>Area value) to calculate minimum number of trials values.
The results are assigned to system variables xInv (calculation result using Area) and >xInv
(calculation result using >Area). The calculator always displays the xInv value only. However,
when the xInv and >xInv values are different, the message will appear with both values.
The calculation results of Inverse Geometric Cumulative Distribution are integers. Accuracy
may be reduced when the first argument has 10 or more digits. Note that even a slight
difference in calculation accuracy affects calculation results. If a warning message appears,
check the displayed values.
I Hypergeometric Distribution
(DIST)(E)(H.GEO)(HPd)
• Hypergeometric Probability
Hypergeometric Probability calculates the probability at
a specific single x-value or each list element, and the
number of the trial on which the first success occurs, for the
hypergeometric distribution with a specified probability of
success.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Hypergeometric Probability.
• Hypergeometric Cumulative Distribution
(DIST)(E)(H.GEO)(HCd)
Hypergeometric Cumulative Distribution calculates the
cumulative probability in a hypergeometric distribution that
the success will occur on or before a specified trial.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Hypergeometric Cumulative Distribution.
6-49
• Inverse Hypergeometric Cumulative Distribution
(DIST)(E)(H.GEO)(InvH)
Inverse Hypergeometric Cumulative Distribution calculates
the minimum number of trials of a hypergeometric
cumulative probability distribution for specified values.
Calculation Result Output Examples
When a list is specified
When variable (x) is specified
• There is no graphing for Inverse Hypergeometric Cumulative Distribution.
Important!
When executing the Inverse Hypergeometric Cumulative Distribution calculation, the calculator
uses the specified Area value and the value that is one less than the Area value minimum
number of significant digits (>Area value) to calculate minimum number of trials values.
The results are assigned to system variables xInv (calculation result using Area) and >xInv
(calculation result using >Area). The calculator always displays the xInv value only. However,
when the xInv and >xInv values are different, the message will appear with both values.
The calculation results of Inverse Hypergeometric Cumulative Distribution are integers.
Accuracy may be reduced when the first argument has 10 or more digits. Note that even
a slight difference in calculation accuracy affects calculation results. If a warning message
appears, check the displayed values.
8. Input and Output Terms of Tests, Confidence
Interval, and Distribution
(All models except fx-7400GII)
The following explains the input and output terms that are used by tests, confidence interval,
and distribution.
I Input Terms
Data ...................................data type
ƫ (1-Sample Z Test) ...........population mean value test conditions (“x ƫ0” specifies two-tail test,
“< ƫ0” specifies lower one-tail test, “> ƫ0” specifies upper one-tail
test.)
ƫ1 (2-Sample Z Test) ..........population mean value test conditions (“x ƫ2” specifies two-tail test,
“< ƫ2” specifies one-tail test where sample 1 is smaller than sample
2, “> ƫ2” specifies one-tail test where sample 1 is greater than
sample 2.)
6-50
Prop (1-Prop Z Test) ..........sample proportion test conditions (“x p0” specifies two-tail test,
“< p0” specifies lower one-tail test, “> p0” specifies upper one-tail
test.)
p1 (2-Prop Z Test)...............sample proportion test conditions (“x p2” specifies two-tail test,
“< p2” specifies one-tail test where sample 1 is smaller than sample
2, “> p2” specifies one-tail test where sample 1 is greater than
sample 2.)
ƫ (1-Sample t Test) ............population mean value test conditions (“x ƫ0” specifies two-tail test,
“< ƫ0” specifies lower one-tail test, “> ƫ0” specifies upper one-tail
test.)
ƫ1 (2-Sample t Test) ...........sample mean value test conditions (“x ƫ2” specifies two-tail test,
“< ƫ2” specifies one-tail test where sample 1 is smaller than sample
2, “> ƫ2” specifies one-tail test where sample 1 is greater than
sample 2.)
B & R (LinearReg t Test) .....R-value test conditions (“x 0” specifies two-tail test, “< 0” specifies
lower one-tail test, “> 0” specifies upper one-tail test.)
Ʊ1 (2-Sample F Test)..........population standard deviation test conditions (“x Ʊ2” specifies
two-tail test, “< Ʊ2” specifies one-tail test where sample 1 is smaller
than sample 2, “> Ʊ2” specifies one-tail test where sample 1 is
greater than sample 2.)
ƫ0 .......................................assumed population mean
Ʊ.........................................population standard deviation (Ʊ > 0)
Ʊ1 .......................................population standard deviation of sample 1 (Ʊ1 > 0)
Ʊ2 .......................................population standard deviation of sample 2 (Ʊ2 > 0)
List .....................................list whose contents you want to use as data (List 1 to 26)
List1 ...................................list whose contents you want to use as sample 1 data (List 1 to 26)
List 2...................................list whose contents you want to use as sample 2 data (List 1 to 26)
Freq....................................frequency (1 or List 1 to 26)
Freq1..................................frequency of sample 1 (1 or List 1 to 26)
Freq2..................................frequency of sample 2 (1 or List 1 to 26)
Execute ..............................executes a calculation or draws a graph
M .........................................mean of sample
M1 .......................................mean of sample 1
M2 ........................................mean of sample 2
n .........................................size of sample (positive integer)
n1........................................size of sample 1 (positive integer)
n2........................................size of sample 2 (positive integer)
p0........................................expected sample proportion (0 < p0 < 1)
p1........................................sample proportion test conditions
x (1-Prop Z Test) ................sample value (x > 0 integer)
x (1-Prop Z Interval)...........data (0 or positive integer)
x1 ........................................data value of sample 1 (x1 > 0 integer)
x2 ........................................data value of sample 2 (x2 > 0 integer)
sx ........................................sample standard deviation (sx > 0)
sx1 .......................................standard deviation of sample 1 (sx1 > 0)
sx2 .......................................standard deviation of sample 2 (sx2 > 0)
6-51
XList...................................list for x-axis data (List 1 to 6)
YList...................................list for y-axis data (List 1 to 6)
C-Level...............................confidence level (0 C-Level < 1)
Pooled................................pooling On (in effect) or Off (not in effect)
x (Distribution)....................data
Ʊ (Distribution) ...................standard deviation (Ʊ > 0)
ƫ (Distribution) ...................mean
Lower (Distribution)............lower boundary
Upper (Distribution)............upper boundary
df (Distribution) ..................degrees of freedom (df > 0)
n:df (Distribution) ...............numerator degrees of freedom (positive integer)
d:df (Distribution) ...............denominator degrees of freedom (positive integer)
Numtrial (Distribution) ........number of trials
p (Distribution)....................success probability (0 p 1)
I Output Terms
z .........................................z score
p .........................................p-value
t ..........................................t score
Ƶ2 ........................................Ƶ2 value
F ........................................F value
ˆ..........................................estimated sample proportion
p
ˆ 1 ........................................estimated proportion of sample 1
p
ˆ 2 ........................................estimated proportion of sample 2
p
M .........................................mean of sample
M1 ........................................mean of sample 1
M2 ........................................mean of sample 2
sx ........................................sample standard deviation
sx1 .......................................standard deviation of sample 1
sx2 .......................................standard deviation of sample 2
sp ........................................pooled sample standard deviation
n ........................................size of sample
n1........................................size of sample 1
n2........................................size of sample 2
df ........................................degrees of freedom
a .........................................constant term
b .........................................coefficient
se ........................................standard error
r .........................................correlation coefficient
r2 ........................................coefficient of determination
Left.....................................confidence interval lower limit (left edge)
Right...................................confidence interval upper limit (right edge)
6-52
9. Statistic Formula
I Test
Test
1-Sample Z Test
= (o – 0)/(/'
)
2-Sample Z Test
= (o1 – o2)/ (12/1) + (22/2)
1-Prop Z Test
z = (x/n – p0)/ p0(1 – p0)/n
2-Prop Z Test
z = (x1/n1 – x2/n2)/ pˆ (1 – pˆ )(1/n1 + 1/n2)
1-Sample t Test
= (o – 0)/(s/'
)
t = (o1 – o2)/ sp2(1/n1 + 1/n2)
2-Sample t Test (pooled)
sp = ((n1 – 1)sx12 + (n2 – 1)sx22)/(n1 + n2 – 2)
df = n1 + n2 − 2
t = (o1 – o2)/ sx12/n1 + sx22/n2
2-Sample t Test (not pooled) df = 1/(C 2/(n1 – 1) + (1 – C )2/(n2 – 1))
C = (sx12/n1)/(sx12/n1 + sx22/n2)
LinearReg t Test
n
n
i=1
i=1
b = (xi – o)(yi – p)/(xi – o)2
a = p – bo
t = r (n – 2)/(1 – r 2)
Oi: The i-th element of the observed
k
C2 GOF Test
2 = ( Oi − Ei)2 /Ei
i
list
Ei: The i-th element of the expected
list
k R
2 = ( Oij − Eij)2 /Eij
C2 two-way Test
2-Sample F Test
i
j
k
R
i=1
j=1
Eij = xij • xij / n
the observed matrix
Eij: The element at row i, column j of
the expected matrix
F = sx12/sx22
F = MS/MSe
MS = SS/Fdf
k
ANOVA Test
Oij: The element at row i, column j of
MSe = SSe/Edf
k
SS = ni (oi − o)2
SSe = ( ni – 1)sxi2
Fdf = k − 1
Edf = ( ni – 1)
i=1
i=1
k
i=1
6-53
I Confidence Interval
Confidence Interval
Left: confidence interval lower limit (left edge)
Right: confidence interval upper limit (right edge)
1-Sample Z Interval
= o + (α /2) · /'
2-Sample Z Interval
= (o1 – o2) + (α /2) 12/ 1 + 22/ 2
1-Prop Z Interval
Left, Right = x/n + Z(α /2) 1/n · (x/n · (1 – x/n))
Left, Right = (x1/n1 – x2/n2)
2-Prop Z Interval
+ Z(α /2) (x1/n1 · (1 – x1/n1))/n1 + (x2/n2 · (1 – x2/n2))/n2
1-Sample t Interval
Left, Right = o + tn−1(α /2) · sx/'
n
2-Sample t Interval
(pooled)
Left, Right = (o1 – o2) + tn1+n2−2 (α /2) sp2(1/n1 + 1/n2)
sp = ((n1 – 1)sx12 + (n2 – 1)sx22)/(n1 + n2 – 2)
Left, Right = (o1 – o2) + tdf (α /2) sx12/n1 + sx22/n2
2-Sample t Interval
(not pooled)
df = 1/(C 2/(n1 – 1) + (1 – C)2/(n2 – 1))
C = (sx12/n1)/(sx12/n1 + sx22/n2)
A: level of significance A = 1 − [C-Level ] C-Level : confidence level (0 C-Level 1)
Z(A/2): upper A/2 point of standard normal distribution
tdf (A/2): upper A/2 point of t distribution with df degrees of freedom
I Distribution (Continuous)
Distribution
Normal
Distribution
Probability Density
–
p(x) = 1 e
2
(x – )2
2
2
(
> 0)
–
Student-t
Distribution
C Distribution
p(x) =
1 1
2
df
2
2
df
x
ndf + ddf
2
p(x) =
ndf
ddf
2
2
F Distribution
df+1
x2
df + 1
1
+
2
df
p(x) =
df
df
2
df
2
Cumulative Distribution
2
2
–1
–
e
p=
x
2
(x 0)
ndf
ddf
ndf ndf
–1
2
x
2
– ndf + ddf
2
1 + ndf x
ddf
(x 0)
6-54
Upper
p(x)dx
Lower
Inverse Cumulative Distribution
Distribution
Normal
Distribution
p=
Upper
p=
p(x)dx
–
tail = Left
p(x)dx
Lower
tail = Right
p=
Upper
p(x)dx
Lower
tail = Central
Student-t
Distribution
p=
C Distribution
2
p(x)dx
Lower
F Distribution
I Distribution (Discrete)
Distribution
Probability
Binomial Distribution
p(x) = nC x p x(1–p)n – x
Poisson Distribution
p(x) =
Geometric Distribution
p(x) = p(1– p)x – 1
p(x) =
Hypergeometric
Distribution
Distribution
e– μ × μ x
x!
MC x
(x = 0, 1, ·······, n) n: number of trials
(x = 0, 1, 2, ···)
M: mean ( M 0)
(x = 1, 2, 3, ···)
× N – MC n – x
NC n
n: Number of elements extracted from population (0 x integer)
M: Number of elements contained in attribute A (0 M integer)
N: Number of population elements (n N, M N integer)
Cumulative Distribution
Inverse Cumulative Distribution
Binomial Distribution
X
p = p(x)
x=0
X
p H p(x)
x=0
Poisson Distribution
X
Geometric Distribution
p = p(x)
Hypergeometric
Distribution
p = p(x)
x=1
X
x=0
6-55
X
p H p(x)
x=1
X
p H p(x)
x=0
Chapter 7 Financial Calculation (TVM)
Important!
• The fx-7400Gɉ is not equipped with the TVM mode.
1. Before Performing Financial Calculations
From the Main Menu, enter the TVM mode and display the Financial screen like the one
shown below.
Financial 1 screen
Financial 2 screen
• {SMPL} … {simple interest}
• {CMPD} … {compound interest}
• {CASH} … {cash flow (investment appraisal)}
• {AMT} … {amortization}
• {CNVT} … {interest rate conversion}
• {COST} … {cost, selling price, margin}
• {DAYS} … {day/date calculations}
• {DEPR} … {depreciation calculations}
• {BOND} … {bond calculations}
I Setup Items
S Payment
• {BGN}/{END} … Specifies {beginning of the period}/{end of the period} payment
S Date Mode
• {365}/{360} … Specifies calculation according to a {365-day}/{360-day} year
S Periods/YR. (payment interval specification)
• {Annu}/{Semi} … {annual}/{semiannual}
Note the following points regarding Setup screen settings whenever using the TVM mode.
• The following graph Setup screen settings are all turned off for graphing in the TVM mode:
Axes, Grid, Dual Screen.
• Drawing a financial graph while the Label item is turned on, displays the label CASH for the
vertical axis (deposits, withdrawals), and TIME for the horizontal axis (frequency).
7-1
7
I Graphing in the TVM Mode
After performing a financial calculation, you can use (GRPH) to graph the results as shown
below.
• Pressing (TRCE) while a graph is on the display activates Trace, which can be used
to look up other financial values. In the case of simple interest, for example, pressing C
displays PV, SI, and SFV. Pressing B displays the same values in reverse sequence.
• Zoom, Scroll, and Sketch cannot be used in the TVM mode.
• Whether you should use a positive or a negative value for the present value (PV) or the
purchase price (PRC) depends on the type of calculation you are trying to perform.
• Note that graphs should be used only for reference purposes when viewing TVM mode
calculation results.
• Note that calculation results produced in this mode should be regarded as reference values
only.
• Whenever performing an actual financial transaction, be sure to check any calculation results
obtained using this calculator with against the figures calculated by your financial institution.
2. Simple Interest
This calculator uses the following formulas to calculate simple interest.
S Formula
365-day Mode
360-day Mode
SI' = n × PV × i
365
SI' = n × PV × i
360
I%
100
I%
i=
100
i=
SI = –SI'
SFV = –(PV + SI' )
SI :
n :
PV :
I% :
SFV :
interest
number of interest periods
principal
annual interest
principal plus interest
Press (SMPL) from the Financial 1 screen to display the following input screen for simple
interest.
(SMPL)
n ........... number of interest periods (days)
I% ........ annual interest rate
PV ........ principal
7-2
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {SI} … {simple interest}
• {SFV} … {simple future value}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menus to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {GRPH} … {draws graph}
After drawing a graph, you can press (TRCE) to turn on trace and read calculation
results along the graph.
Each press of C while trace is turned on cycles the displayed value in the sequence: present
value (PV) m simple interest (SI) m simple future value (SFV). Pressing B cycles in the
reverse direction.
Press ) to return to the parameter input screen.
3. Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
S PV, PMT, FV, n
I%x0
PV = – ( PMT + FV)
PMT = –
log
PV + PMT
FV = –
I% 0
39 ï 307ðQ)9
)9 ï 307sQ39
α = (1+ i × S) ×
S=
{
n=
{
PV + FV
(1+ iS) × PMT – FV × i
(1+ iS) × PMT + PV × i
}
log (1+ i)
PV + FV
n
PV + FV
n=–
PMT
PMT = –
1–β
–n
, β = (1 + i)
i
0 .........Payment : End
(Setup Screen)
1 .........Payment : Begin
(Setup Screen)
i =
7-3
{
I%
............................... (P/Y = C/Y = 1)
100
C/Y
P/Y
I%
(1+
) –1 ..... (Other than
100 × [C/Y ]
those above)
SI %
i (effective interest rate)
i (effective interest rate) is calculated using Newton’s Method.
PV + A s 307 + B s FV = 0
To I % from i (effective interest rate)
i × 100 ................................. (P/Y = C/Y = 1)
I% =
{{
P/Y
}
(1+ i ) C/Y –1 × C/Y × 100... (Other than those above)
n ............ number of compound periods
I% ......... annual interest rate
PV ......... present value
307 ...... payment
FV ......... future value
P/Y ........ installment periods per year
C/Y ........ compounding periods per year
• A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a minus sign (–).
Press (CMPD) from the Financial 1 screen to display the following input screen for
compound interest.
(CMPD)
n ........... number of compound periods
I% ........ annual interest rate
PV ........ present value (loan amount in case of loan; principal in case of savings)
307 ..... payment for each installment (payment in case of loan; deposit in case of savings)
FV ........ future value (unpaid balance in case of loan; principal plus interest in case of
savings)
P/Y ....... installment periods per year
C/Y ....... compounding periods per year
Important!
Inputting Values
A period (n) is expressed as a positive value. Either the present value (PV) or future value
(FV) is positive, while the other (PV or FV) is negative.
Precision
This calculator performs interest calculations using Newton’s Method, which produces
approximate values whose precision can be affected by various calculation conditions.
Because of this, interest calculation results produced by this calculator should be used
keeping the above limitation in mind or the results should be verified.
7-4
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {n} … {number of compound periods}
• {I%} … {annual interest rate}
• {PV} … {present value} (Loan: loan amount; Savings: balance)
• {PMT} … {payment} (Loan: installment; Savings: deposit)
• {FV} … {future value} (Loan: unpaid balance; Savings: principal plus interest)
• {AMT} … {amortization screen}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menus to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {AMT} … {amortization screen}
• {GRPH} … {draws graph}
After drawing a graph, you can press (TRCE) to turn on trace and read calculation
results along the graph.
Press ) to return to the parameter input screen.
4. Cash Flow (Investment Appraisal)
This calculator uses the discounted cash flow (DCF) method to perform investment appraisal
by totalling cash flow for a fixed period. This calculator can perform the following four types of
investment appraisal.
• Net present value (NPV)
• Net future value (NFV)
• Internal rate of return (IRR)
• Payback period (PBP)
A cash flow diagram like the one shown below helps to visualize the movement of funds.
CF2 CF3 CF4
CF5
CF7
CF6
CF1
CF0
With this graph, the initial investment amount is represented by CF0. The cash flow one year
later is shown by CF1, two years later by CF2, and so on.
7-5
Investment appraisal can be used to clearly determine whether an investment is realizing
profits that were originally targeted.
S\
NPV
NPV = CF0 +
CF2
CF3
CFn
CF1
+
+
+…+
2
3
(1+ i) (1+ i)
(1+ i)
(1+ i)n
i=
I%
100
n: natural number up to 254
S\
NFV
NFV = NPV s (1 + i )n
S\
IRR
0 = CF0 +
CF2
CF3
CFn
CF1
+
+
+…+
2
3
(1 + i ) (1 + i ) (1 + i )
(1 + i )n
In this formula, NPV = 0, and the value of IRR is equivalent to i × 100. It should be noted,
however, that minute fractional values tend to accumulate during the subsequent calculations
performed automatically by the calculator, so NPV never actually reaches exactly zero. IRR
becomes more accurate the closer that NPV approaches to zero.
S\
PBP
PBP =
{
0 .................................. (CF0 > 0)
NPVn
... (Other than those above)
n–
NPVn+1 – NPVn
n
NPVn =
k
=0
CFk
(1 + i)k
n: smallest positive integer that satisfies the conditions NPVn 0, NPVn+1 0, or 0
Press (CASH) from the Financial 1 screen to display the following input screen for Cash
Flow.
(CASH)
I% ........ interest rate
Csh ....... list for cash flow
If you have not yet input data into a list, press (LIST) and input data into a list.
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {NPV} … {net present value}
• {IRR} … {internal rate of return}
• {PBP} … {payback period}
• {NFV} … {net future value}
• {LIST} … {inputs data into a list}
• {LIST} … {specifies a list for data input}
7-6
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menus to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {GRPH} … {draws graph}
After drawing a graph, you can press (TRCE) to turn on trace and read calculation
results along the graph.
Press ) to return to the parameter input screen.
5. Amortization
This calculator can be used to calculate the principal and interest portion of a monthly
installment, the remaining principal, and amount of principal and interest repaid up to any
point.
S Formula
a
1 payment
c
b
1 ............ PM1 ................... PM2 .......... Last
Number of Payments
a: interest portion of installment PM1 (,17)
b: principal portion of installment PM1 (PRN)
c: balance of principal after installment PM2 (BAL)
e
1 payment
d
1............. PM1................ PM2 ............. Last
Number of Payments
d: total principal from installment PM1 to payment of installment PM2 (3PRN)
e: total interest from installment PM1 to payment of installment PM2 (3,17)
*a + b = one repayment (307)
7-7
a : ,17PM1 = I BALPM1–1 s i I s (307 sign)
b : PRNPM1 =307 + BALPM1–1 s i
c : BALPM2 = BALPM2–1 + PRNPM2
PM2
d : 3 PRN = PRNPM1 + PRNPM1+1 + … + PRNPM2
PM1
PM2
e : 3 ,17=,17PM1 +,17PM1+1 + … + ,17PM2
PM1
BAL0 = PV (,171 = 0 and PRN1 = 307 at beginning of installment term)
S Converting between the nominal interest rate and effective interest rate
The nominal interest rate (I% value input by user) is converted to an effective interest rate
(I%' ) for installment loans where the number of installments per year is different from the
number of compound interest calculation periods.
{
[C/Y ]
}
[P/Y ]
I%
I%' = (1+
) –1 × 100
100 × [C/Y ]
The following calculation is performed after conversion from the nominal interest rate to the
effective interest rate, and the result is used for all subsequent calculations.
i = I%'÷100
Press (AMT) from the Financial 1 screen to display the following input screen for
amortization.
(AMT)
PM1....... first installment of installments 1 through n
PM2....... second installment of installments 1 through n
n ........... installments
I% ........ interest rate
PV ........ principal
307 ..... payment for each installment
FV ........ balance following final installment
P/Y ....... installments per year
C/Y ....... compoundings per year
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {BAL} … {balance of principal after installment PM2}
• {INT} … {interest portion of installment PM1}
• {PRN} … {principal portion of installment PM1}
7-8
• {3INT} … {total interest paid from installment PM1 to installment PM2}
• {3PRN} … {total principal paid from installment PM1 to installment PM2}
• {CMPD} … {compound interest screen}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menus to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {CMPD} … {compound interest screen}
• {GRPH} … {draws graph}
After drawing a graph, you can press (TRCE) to turn on trace and read calculation
results along the graph.
The first press of (TRCE) displays ,17 and PRN when n = 1. Each press of C shows
,17 and PRN when n = 2, n = 3, and so on.
Press ) to return to the parameter input screen.
6. Interest Rate Conversion
The procedures in this section describe how to convert between the annual percentage rate
and effective interest rate.
S Formula
n
EFF = 1 +
APR/100
–1 s 100
n
EFF
APR = 1 +
100
1
n
APR : annual percentage rate (%)
EFF : effective interest rate (%)
n
: number of compoundings
–1 s n s100
Press (CNVT) from the Financial 1 screen to display the following input screen for interest
rate conversion.
(CNVT)
n ........... number of compoundings
I% ......... interest rate
7-9
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {EFF} … {converts annual percentage rate to effective interest rate}
• {APR} … {converts effective interest rate to annual percent rate}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menu to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
7. Cost, Selling Price, Margin
Cost, selling price, or margin can be calculated by inputting the other two values.
S Formula
&67 = SEL 1–
05*
100
&67
05*
1–
100
&67
s100
05*(%) = 1–
SEL
SEL =
&67 : cost
SEL : selling price
05* : margin
Press (COST) from the Financial 2 screen to display the following input screen.
(E)(COST)
Cst......... cost
Sel......... selling price
Mrg........ margin
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {COST} … {cost}
• {SEL} … {selling price}
• {MRG} … {margin}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
7-10
Use the following function menu to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
8. Day/Date Calculations
You can calculate the number of days between two dates, or you can determine what date
comes a specific number of days before or after another date.
Press (DAYS) from the Financial 2 screen to display the
following input screen for day/date calculation.
(E)(DAYS)
d1.......... date 1
d2.......... date 2
D .......... number of days
To input a date, first highlight d1 or d2. Pressing a number
key to input the month causes an input screen like the one
shown below to appear on the display.
Input the month, day, and year, pressing U after each.
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {PRD} … {number of days from d1 to d2 (d2 – d1)}
• {d1+D} … {d1 plus a number of days (d1 + D)}
• {d1–D} … {d1 minus a number of days (d1 – D)}
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menu to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• The Setup screen can be used to specify either a 365-day or 360-day year for financial
calculations. Day/date calculations are also performed in accordance with the current setting
for number of days in the year, but the following calculations cannot be performed when the
360-day year is set. Attempting to do so causes an error.
(Date) + (Number of Days)
(Date) – (Number of Days)
• The allowable calculation range is January 1, 1901 to December 31, 2099.
• 360-day Date Mode Calculations
The following describes how calculations are processed when 360 is specified for the Date
Mode item in the Setup screen.
• If d1 is day 31 of a month, d1 is treated as day 30 of that month is used.
• If d2 is day 31 of a month, d2 is treated as day 1 of the following month, unless d1 is day 30.
7-11
9. Depreciation
Depreciation lets you calculate the amount that a business expense can be offset by income
(depreciated) over a given year.
• This calculator supports the following four types of depreciation calculations.
straight-line (SL), fixed-percentage (FP), sum-of-the-years’-digits (SYD), or declining-balance
(DB).
• Any one of the above methods can be used to calculate depreciation for a specified period.
A table and graph of the depreciated amount and undepreciated amount in year j.
S Straight-Line Method (SL)
SLj
n
PV
FV
j
depreciation charge for the jth year
useful life
original cost (basis)
residual book value
year for calculation of depreciation
cost
Y−1 : number of months in the first year
of depreciation
(PV–FV ) {Y–1}
S
n
12
(PV–FV )
SLj =
n
(PV–FV ) 12–{Y–1}
S
SLn+1 =
n
12
SL1 =
({Y–1}x12)
:
:
:
:
:
S Fixed-Percentage Method (FP)
FPj : depreciation charge for the jth year
RDVj : remaining depreciable value at the
end of jth year
I% : depreciation ratio
I% {Y–1}
FP1 = PV s 100 s 12
I%
FPj = (RDVj–1 )9) s
100
FPn+1 = RDVn ({Y–1}x12)
RDV1 = PV – FV – FP1
RDVj = RDVj–1 – FPj
RDVn+1 = 0
({Y–1}x12)
S Sum-of-the-Years’-Digits Method (SYD)
{Y–1}
n (n 1)
n' = n –
2
12
(n' integer part +1)(n' integer part + 2*n' fraction part )
Z' =
2
n
{Y–1}
s
(PV – FV )
SYD1 =
Z
12
n'– M2
)(PV – FV – SYD1)
SYDj = (
( jx1)
Z'
n'– (n 1)2
12–{Y–1}
SYDn+1 = (
)(PV – FV – SYD1) s
({Y–1}x12)
Z'
12
Z=
RDV1 = PV – FV – SYD1
SYDj : depreciation charge for the jth year
RDVj : remaining depreciable value at the
end of jth year
RDVj = RDVj –1 – SYDj
7-12
S Declining-Balance Method (DB)
DB1 = PV s
DBj : depreciation charge for the jth year
RDVj : remaining depreciable value at the
end of jth year
I% : depreciation factor
I%
Y–1
s
100n
12
RDV1 = PV – FV – DB1
DBj = (RDVj–1 + FV ) s
I%
100n
RDVj = RDVj–1 – DBj
DBn +1 = RDVn
({Y–1}x12)
RDVn+1 = 0
({Y–1}x12)
Press (DEPR) from the Financial 2 screen to display the following input screen for
depreciation calculation.
(E)(DEPR)
n ............ useful life
I% ......... depreciation ratio in the case of the fixed percent (FP) method, depreciation factor in
the case of the declining balance (DB) method
PV ......... original cost (basis)
FV ......... residual book value
j ............. year for calculation of depreciation cost
Y−1........ number of months in the first year of depreciation
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {SL} … {Calculate depreciation for year j using the straight-line method}
• {FP} ... {FP} ....{Calculate depreciation for year j using the fixed-percentage method}
{I%} .....{Calculate depreciation ratio}
• {SYD} … {Calculate depreciation for year j using the sum-of-the-years’-digits method}
• {DB} … {Calculate depreciation for year j calculated using the declining-balance method}
Calculation Result Output Examples
{SYD}
{SYD} − {TABL}
7-13
{SYD} − {GRPH}
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menu to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {TABL} … {displays table}
• {GRPH} … {draws graph}
10. Bond Calculations
Bond calculation lets you calculate the purchase price or the annual yield of a bond.
Before starting bond calculations, use the Setup screen to configure “Date Mode” and
“Periods/YR.” settings (page 7-1).
S Formula
D
A
B
Redemption date (d2)
Issue date
Purchase date (d1)
Coupon Payment dates
PRC : price per $100 of face value
CPN : annual coupon rate (%)
YLD : yield to maturity (%)
A
: accrued days
0 : number of coupon payments per year (1=annual, 2=semi annual)
N
: number of coupon payments between settlement date and maturity date
RDB : redemption price or call price per $100 of face value
D : number of days in coupon period where settlement occurs
B
: number of days from settlement date until next coupon payment date = D − A
,17 : accrued interest
&67 : price including interest
S Price per $100 of face value (PRC)
• For one or fewer coupon period to redemption
RDV +
PRC = –
1+ (
B
D
×
CPN
M
YLD/100
M
7-14
+(
)
A
D
×
CPN
M
)
• For more than one coupon period to redemption
CPN
RDV
PRC = –
(1+
,17 –
A
D
s
YLD/100
0
CPN
0
0
N
)
(N–1+B/D )
– 3
k=1
(1+
YLD/100
0
A
+
)
D
(k–1+B/D )
s
CPN
0
&67 35&+ ,17
S Annual Yield (YLD)
YLD is calculated using Newton’s Method.
Press (BOND) from the Financial 2 screen to display the following input screen for Bond
calculation.
(E)(BOND)
d1.......... purchase date (month, date, year)
d2.......... redemption date (month, date, year)
RDV ...... redemption price per $100 of face value
CPN ...... coupon rate
PRC ...... price per $100 of face value
YLD ...... annual yield
After configuring the parameters, use one of the function menus noted below to perform the
corresponding calculation.
• {PRC} … {Calculate the bond’s price (PRC), accrued interest (INT), and cost of bond (CST)}
• {YLD} … {Calculate the yield to maturity}
Calculation Result Output Examples
{PRC}
{PRC} − {GRPH}
{PRC} − {MEMO}
An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function menu to maneuver between calculation result screens.
• {REPT} … {parameter input screen}
• {GRPH} … {draws graph}
• {MEMO} … {displays numbers of days used in calculations}
7-15
MEMO Screen
• The following describes the meaning of the MEMO screen display items.
PRD ... number of days from d1 to d2
N......... number of coupon payments between settlement date and maturity date
A ......... accrued days
B ......... number of days from settlement date until next coupon payment date (D−A)
D ........ number of days in coupon period where settlement occurs
• Each press of U while the MEMO screen is displayed cycles the Coupon Payment Day
(CPD) display sequentially from the redemption year up to the purchase year. This is true
only when the “Date Mode” setting on the “Setup” screen is “365”.
11. Financial Calculations Using Functions
Important!
• The following operations cannot be performed on the fx-7400Gɉ.
You can use special functions in the RUN • MAT mode or PRGM mode to perform calculations
that are the same as the TVM mode financial calculations.
Example
To calculate the total interest and principal paid for a 2-year (730-day)
$300 loan at a simple annual interest rate of 5%. Use a Date Mode
setting of 365.
1. From the Main Menu, enter the RUN • MAT mode.
2. Press the keys as follows.
*(E)(E)(E)(TVM)
(SMPL)(SI)FB? D \
B??U
(SFV)FB? D B??\
U
• Use the TVM mode Setup screen ( K(SET UP)) to change the Date Mode setting.
You also can use special commands (DateMode365, DateMode360) in the PRGM mode to
change the setting.
• For details about what you can do with the financial calculation functions and their syntax,
see “Performing Financial Calculations in a Program” (page 8-35).
7-16
Chapter 8 Programming
1. Basic Programming Steps
Commands and calculations are executed sequentially, just like manual calculation multistatements.
1. From the Main Menu, enter the PRGM mode. When you do, a program list appears on the
display.
Selected program area
(use D and A to move)
Files are listed in the alphabetic sequence of their names.
2. Register a file name.
3. Input the program.
4. Run the program.
• The values to the right of the program list indicate the number of bytes used by each
program.
• A file name can be up to eight characters long.
• The following are the characters you can use in a file name: A through Z, r, Q, spaces, [, ],
{, }, ’, ”, ~, 0 through 9, ., +, –, ×, ÷
• Registering a file name uses 32 bytes of memory.
To calculate the surface area (cm2) and volume (cm3) of three regular
octahedrons when the length of one side is 7, 10, and 15 cm,
respectively
Example
Store the calculation formula under the file name OCTA.
The following are the formulas used for calculating surface area S and volume
V of a regular octahedron for which the length of one side A is known.
A
'
2
S = 2'
3 A2, V = –––– A3
3
K PRGM
(NEW)H(O)((C)(T)T(A)U
)(PRGM)(?)??T(A)(E)(:)
A V()B ?T(A)V(E)(E)(<)
V()AB ?T(A),B
))
(EXE) or U
FU(Value of A)
U
S when A = 7
V when A = 7
8-1
8
UU
@?U
U
S when A = 10
V when A = 10
UU
@DU
U*
1
S when A = 15
V when A = 15
*1 Pressing U while the program’s final result is on the display exits the program.
• You can also run a program while in the RUN • MAT (or RUN) mode by inputting: Prog "" U.
• Pressing U while the final result of a program executed using this method is on the display
re-executes the program.
• An error occurs if the program specified by Prog "" cannot be found.
2. PRGM Mode Function Keys
• {NEW} ... {new program}
S When you are registering a file name
• {RUN}/{BASE} ... {general calculation}/{number base} program input
• {0} ... {password registration}
• {SYBL} ... {symbol menu}
S When you are inputting a program —— (RUN) … default
• {TOP}/{BTM} ... {top}/{bottom} of program
• {SRC} ... {search}
• {MENU} ... {mode menu}
• {STAT}/{MAT}*/{LIST}/{GRPH}/{DYNA}*/{TABL}/{RECR}*
... {statistic}/{matrix}/{list}/{graph}/{Dynamic Graph}/{Table}/{recursion} menu
• {Aja} ... {toggles between upper-case and lower-case input}
• {CHAR} ... {displays a screen for selecting various mathematical symbols, special symbols,
and accented characters}
* Not included on the fx-7400GII
• Pressing )(PRGM) displays the following program (PRGM) menu.
• {COM} ... {program command menu}
• {CTL} ... {program control command menu}
• {JUMP} ... {jump command menu}
• {?}/{<} ... {input}/{output} command
• {CLR}/{DISP} ... {clear}/{display} command menu
• {REL} ... {conditional jump relational operator menu}
8-2
• {I/O} ... {I/O control/transfer command menu}
• {:} ... {multi-statement command}
• {STR} ... {string command}
See “Command Reference” on page 8-7 for full details on each of these commands.
• Pressing K(SET UP) displays the mode command menu shown below.
• {ANGL}/{COOR}/{GRID}/{AXES}/{LABL}/{DISP}/{S/L}/{DRAW}/{DERV}/{BACK}/{FUNC}/
{SIML}/{S-WIN}/{LIST}/{LOCS}*/{T-VAR}/{3DSP}*/{RESID}/{CPLX}/{FRAC}/{Y • SPD}*/
{DATE}*/{PMT}*/{PRD}*/{INEQ}/{SIMP}/{Q1Q3}
* Not included on the fx-7400GII
See “Setup Screen Function Key Menus” on page 1-26 for details about each of these
commands.
S When you are inputting a program —— (BASE)*1
• {TOP}/{BTM}/{SRC}
• {MENU}
• {d~o} ... {decimal}/{hexadecimal}/{binary}/{octal} value input
• {LOG} ... {bitwise operator}
• {DISP} ... conversion of displayed value to {decimal}/{hexadecimal}/{binary}/{octal}
• {Aja}/{SYBL}
• Pressing )(PRGM) displays the following PRGM (PROGRAM) menu.
• {Prog} ... {program recall}
• {JUMP}/{?}/{<}
• {REL} ... {conditional jump relational operator menu}
• {:} ... {multi-statement command}
• Pressing K(SET UP) displays the mode command menu shown below.
• {Dec}/{Hex}/{Bin}/{Oct}
*1 Programs input after pressing (BASE) are indicated by B to the right of the file name.
• {EXE}/{EDIT} ... program {execute}/{edit}
• {NEW} ... {new program}
• {DEL}/{DEL • A} ... {specific program}/{all program} delete
• {SRC}/{REN} ... file name {search}/{change}
3. Editing Program Contents
I Debugging a Program
A problem in a program that keeps the program from running correctly is called a “bug”,
and the process of eliminating such problems is called “debugging”. Either of the following
symptoms indicates that your program contains bugs that require debugging.
8-3
• Error messages appearing when the program is run
• Results that are not within your expectations
S To eliminate bugs that cause error messages
An error message, like the one shown to the right, appears
whenever something illegal occurs during program execution.
When such a message appears, press ) to display the place in the program where the
error was caused. The cursor will be flashing at the location of the problem. Check the “Error
Message Table” (page A-1) for steps you should take to correct the situation.
• Note that pressing ) does not display the location of the error if the program is password
protected.
S To eliminate bugs that cause bad results
If your program produces results that are not what you normally expect, check the contents of
the program and make necessary changes.
(TOP) ... Moves the cursor to the top of the
program
(BTM)... Moves the cursor to the bottom of
the program
I Searching for Data Inside a Program
Example
To search for the letter “A” inside the program named OCTA
1. Recall the program.
2. Press (SRC) and input the data you want to find.
(SRC)
?T(A)
3. Press U to begin the search. The contents of the
program appear on the screen with the cursor located at
the first instance of the data you specified.*1
8-4
4. Each press of U or (SRC) causes the cursor to jump
to the next instance of the data you specified.*2
*1 The message “Not Found” appears when the search data you specify cannot be found in the
program.
*2 If there are no more instances of the data you specified, the search operation ends.
• You cannot specify the newline symbol (=) or display command (<) for the search data.
• Once the contents of the program are on the screen, you can use the cursor keys to move
the cursor to another location before searching for the next instance of the data. Only the
part of the program starting from the current cursor location is searched when you press U.
• Once the search finds an instance of your data, inputting characters or moving the cursor
causes the search operation to be cancelled.
• If you make a mistake while inputting characters to search for, press
and re-input from the beginning.
to clear your input
4. File Management
I Searching for a File
S To find a file using initial character search
Example
To use initial character search to recall the program named OCTA
1. While the program list is on the display, press (E)(SRC) and input the initial
characters of the file you want to find.
(E)(SRC)
H(O)((C)(T)
2. Press U to search.
• The name that starts with the characters you input
highlights.
• If there is no program whose file name starts with the characters you input, the message
“Not Found” appears on the display. If this happens, press ) to clear the error message.
I Editing a File Name
1. While the program list is on the display, use D and A to move the highlighting to the file
whose name you want to edit and then press (E)(REN).
2. Make any changes you want.
3. Press U to register the new name and return to the program list.
The program list is resorted according to the changes you made in the file name.
• If the modifications you make result in a file name that is identical to the name of a program
already stored in memory, the message “Already Exists” appears. When this happens, you
can perform either of the following two operations to correct the situation.
8-5
- Press ) to clear the error and return to the file name editing screen.
- Press
to clear the input file name and input a new one.
I Deleting a Program
S To delete a specific program
1. While the program list is on the display, use D and A to move the highlighting to the
name of the program you want to delete.
2. Press (DEL).
3. Press (YES) to delete the selected program or (NO) to abort the operation without
deleting anything.
S To delete all programs
1. While the program list is on the display, press (DEL • A).
2. Press (YES) to delete all the programs in the list or (NO) to abort the operation
without deleting anything.
• You also can delete all programs by entering the MEMORY mode from the Main Menu. See
“Chapter 11 Memory Manager” for details.
I Registering a password
When inputting a program, you can protect it with a password that limits access to the program
contents to those who know the password.
• You do not need to input the password to run a program.
• The password input procedure is identical to that used for file name input.
1. While the program list is on the display, press (NEW) and input the file name of the new
program file.
2. Press (0) and then input the password.
3. Press U to register the file name and password. Now you can input the contents of the
program file.
4. After inputting the program, press )(QUIT) to
exit the program file and return to the program list.
Files that are password protected are indicated by an
asterisk to the right of the file name.
I Recalling a Password Protected Program
1. In the program list, use D and A to move the highlighting to the name of the program you
want to recall.
2. Press (EDIT).
3. Input the password and press U to recall the program.
• Inputting the wrong password when recalling a password protected program causes the
message “Mismatch” to appear.
8-6
5. Command Reference
I Command Index
Break....................................................8-10
RclCapt ................................................8-21
CloseComport38k ................................8-17
Receive( ...............................................8-17
ClrGraph ............................................. 8-14
Receive38k ..........................................8-18
ClrList ..................................................8-14
Return ..................................................8-11
ClrMat ..................................................8-14
Send( ...................................................8-17
ClrText .................................................8-14
Send38k ...............................................8-18
DispF-Tbl, DispR-Tbl ...........................8-14
Stop .................................................... 8-11
Do~LpWhile .........................................8-10
StrCmp(................................................8-19
DrawDyna ........................................... 8-14
StrInv( ..................................................8-19
DrawFTG-Con, DrawFTG-Plt ..............8-15
StrJoin(.................................................8-19
DrawGraph ..........................................8-15
StrLeft( .................................................8-19
DrawR-Con, DrawR-Plt .......................8-15
StrLen( .................................................8-19
DrawR3-Con, DrawR3-Plt ...................8-15
StrLwr( .................................................8-19
DrawStat ..............................................8-15
StrMid( .................................................8-20
DrawWeb ............................................ 8-15
StrRight( ...............................................8-20
Dsz ......................................................8-12
StrRotate(.............................................8-20
Exp(......................................................8-19
StrShift( ................................................8-20
ExpStr( .............................................8-19
StrSrc( ..................................................8-20
For~To~(Step~)Next ..............................8-9
StrUpr( .................................................8-20
Getkey .................................................8-16
While~WhileEnd ..................................8-10
Goto~Lbl ............................................. 8-12
? (Input Command) ................................8-8
If~Then~(Else~)IfEnd ............................8-9
< (Output Command) ...........................8-8
Isz ........................................................8-12
: (Multi-statement Command) ................8-8
Locate ..................................................8-17
= (Carriage Return) .............................8-8
Menu ....................................................8-13
’ (Comment Text Delimiter) ....................8-8
OpenComport38k ................................8-17
2 (Jump Code) ...................................8-13
Prog .....................................................8-11
=, x, >, <, r, b (Relational Operators) ..8-18
PlotPhase.............................................8-16
+ ...........................................................8-20
The following are conventions that are used in this section when describing the various
commands.
Boldface Text ............. Actual commands and other items that always must be input are
shown in boldface.
{Curly Brackets} ........... Curly brackets are used to enclose a number of items, one of which
must be selected when using a command. Do not input the curly
brackets when inputting a command.
[Square Brackets] ........ Square brackets are used to enclose items that are optional. Do not
input the square brackets when inputting a command.
Numeric Expressions ... Numeric expressions (such as 10, 10 + 20, A) indicate constants,
calculations, numeric constants, etc.
Alpha Characters ......... Alpha characters indicate literal strings (such as AB).
8-7
I Basic Operation Commands
? (Input Command)
Function: Prompts for input of values for assignment to variables during program execution.
Syntax: ? m , "" ? m
Example: ? m A=
Description:
• This command momentarily interrupts program execution and prompts for input of a value
or expression for assignment to a variable. If you do not specify a prompt, execution of this
command causes “?” to appear indicating the calculator is standing by for input. If a prompt
is specified, “?” appears to prompt input. Up to 255 bytes of text can be used for a
prompt.
• Input in response to the input command must be a value or an expression, and the
expression cannot be a multi-statement.
• You can specify a list name, matrix name, string name, function memory (fn), graph (Yn), etc.
as a variable name.
< (Output Command)
Function: Displays an intermediate result during program execution.
Description:
• This command momentarily interrupts program execution and displays alpha character text
or the result of the calculation immediately before the command.
• The output command should be used at locations where you would normally press the U
key during a manual calculation.
: (Multi-statement Command)
Function: Connects two statements for sequential execution without stopping.
Description:
• Unlike the output command (<), statements connected with the multi-statement command
are executed non-stop.
• The multi-statement command can be used to link two calculation expressions or two
commands.
• You can also use a carriage return indicated by = in place of the multi-statement command.
= (Carriage Return)
Function: Connects two statements for sequential execution without stopping.
Description:
• Operation of the carriage return is identical to that of the multi-statement command.
• You can create a blank line in a program by inputting a carriage return only. Using a carriage
return in place of the multi-statement command makes the displayed program easier to read.
’ (Comment Text Delimiter)
Function: Indicates comment text inserted inside a program.
Description: Anything following the apostrophe is treated as non-executable comment text.
8-8
I Program Commands (COM)
If~Then~(Else~)IfEnd
Function: The Then-statement is executed only when the If-condition is true (non-zero). The
Else-statement is executed when the If-condition is false (0). The IfEnd-statement is always
executed following either the Then-statement or Else-statement.
Syntax:
If
numeric expression
_
:
^
_
:
^
Then
Else
_
:
^
_
:
^
_
:
^
IfEnd
Parameters: condition, numeric expression
Description:
(1) If ~ Then ~ IfEnd
• When the condition is true, execution proceeds with the Then-statement and then
continues with the statement following IfEnd.
• When the condition is false, execution jumps to the statement following IfEnd.
(2) If ~ Then ~ Else ~ IfEnd
• When the condition is true, execution proceeds with the Then-statement and then jumps
to the statement following IfEnd.
• When the condition is false, execution jumps to the Else-statement and then continues
with the statement following IfEnd.
For~To~(Step~)Next
Function: This command repeats everything between the For-statement and the Nextstatement. The starting value is assigned to the control variable with the first execution, and
the value of the control variable is changed according to the step value with each execution.
Execution continues until the value of the control variable exceeds the ending value.
Syntax: For m To
Step
_
:
^
Next
Parameters:
• control variable name: A to Z
• starting value: value or expression that produces a value (i.e. sin x, A, etc.)
• ending value: value or expression that produces a value (i.e. sin x, A, etc.)
• step value: numeric value (default: 1)
Description:
• The default step value is 1.
• Making the starting value less than the ending value and specifying a positive step value
causes the control variable to be incremented with each execution. Making the starting
value greater than the ending value and specifying a negative step value causes the control
variable to be decremented with each execution.
8-9
Do~LpWhile
Function: This command repeats specific commands as long as its condition is true (nonzero).
Syntax:
Do
_
:
^
_
:
^
LpWhile
numeric expression
Parameters: expression
Description:
• This command repeats the commands contained in the loop as long as its condition is true
(non-zero). When the condition becomes false (0), execution proceeds from the statement
following the LpWhile-statement.
• Since the condition comes after the LpWhile-statement, the condition is tested (checked)
after all of the commands inside the loop are executed.
While~WhileEnd
Function: This command repeats specific commands as long as its condition is true (nonzero).
Syntax:
While
numeric expression
_
:
^
_
:
^
WhileEnd
Parameters: expression
Description:
• This command repeats the commands contained in the loop as long as its condition is true
(non-zero). When the condition becomes false (0), execution proceeds from the statement
following the WhileEnd-statement.
• Since the condition comes after the While-statement, the condition is tested (checked) before
the commands inside the loop are executed.
I Program Control Commands (CTL)
Break
Function: This command breaks execution of a loop and continues from the next command
following the loop.
Syntax: Break=
Description:
• This command breaks execution of a loop and continues from the next command following
the loop.
• This command can be used to break execution of a For-statement, Do-statement, and Whilestatement.
8-10
Prog
Function: This command specifies execution of another program as a subroutine. In the
RUN • MAT (or RUN) mode, this command executes a new program.
Syntax: Prog "file name"=
Example: Prog "ABC"=
Description:
• Even when this command is located inside of a loop, its execution immediately breaks the
loop and launches the subroutine.
• This command can be used as many times as necessary inside of a main routine to call up
independent subroutines to perform specific tasks.
• A subroutine can be used in multiple locations in the same main routine, or it can be called
up by any number of main routines.
Main Routine
A
Subroutines
D
Prog "D"
Prog "C"
C
E
Prog "E"
Prog "I"
Level 1 Level 2
I
J
Prog "J"
Level 3
Level 4
• Calling up a subroutine causes it to be executed from the beginning. After execution of the
subroutine is complete, execution returns to the main routine, continuing from the statement
following the Prog command.
• A Goto~Lbl command inside of a subroutine is valid inside of that subroutine only. It cannot
be used to jump to a label outside of the subroutine.
• If a subroutine with the file name specified by the Prog command does not exist, an error
occurs.
• In the RUN • MAT (or RUN) mode, inputting the Prog command and pressing U launches
the program specified by the command.
Return
Function: This command returns from a subroutine.
Syntax: Return=
Description: Execution of the Return command inside a main routine causes execution of
the program to stop. Execution of the Return command within a subroutine terminates the
subroutine and returns to the program from which the subroutine was jumped to.
Stop
Function: This command terminates execution of a program.
Syntax: Stop=
Description:
• This command terminates program execution.
• Execution of this command inside of a loop terminates program execution without an error
being generated.
8-11
I Jump Commands (JUMP)
Dsz
Function: This command is a count jump that decrements the value of a control variable by 1,
and then jumps if the current value of the variable is zero.
Syntax:
Variable Value x 0
_
Dsz : :
^
Variable Value = 0
Parameters: variable name: A to Z, r, Q
[Example] Dsz B : Decrements the value assigned to variable B by 1.
Description: This command decrements the value of a control variable by 1, and then tests
(checks) it. If the current value is non-zero, execution continues with the next statement. If the
current value is zero, execution jumps to the statement following the multi-statement command
(:), display command (<), or carriage return (=).
Goto~Lbl
Function: This command performs an unconditional jump to a specified location.
Syntax: Goto
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