Casio Calculator fx 115ES User Manual

fx-115ES PLUS

fx-991ES PLUS C

User’s Guide

CASIO Worldwide Education Website

http://edu.casio.com

CASIO EDUCATIONAL FORUM

http://edu.casio.com/forum /

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Important Information

• The displays and illustrations (such as key markings) shown in this User’s

Guide are for illustrative purposes only, and may differ somewhat from the

actual items they represent.

• The contents of this manual are subject to change without notice.

• In no event shall CASIO Computer Co., Ltd. be liable to anyone for special,

collateral, incidental, or consequential damages in connection with or

arising out of the purchase or use of this product and items that come with

it. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of

any kind whatsoever by any other party arising out of the use of this product

and the items that come with it.

• Be sure to keep all user documentation handy for future reference.

Sample Operations

Sample operations in this manual are indicated by a

icon. Unless

specifically stated, all sample operations assume that the calculator is in its

initial default setup. Use the procedure under “Initializing the Calculator” to

return the calculator to its initial default setup.

For information about the B, b, v, and V marks that are shown

in the sample operations, see “Configuring the Calculator Setup”.

Initializing the Calculator

Perform the following procedure when you want to initialize the calculator and

return the calculation mode and setup to their initial default settings. Note that

this operation also clears all data currently in calculator memory.

!9(CLR)3(All)=(Yes)

Safety Precautions

Battery

• Keep batteries out of the reach of small children.

• Use only the type of battery specified for this calculator in this manual.

Handling Precautions

• Even if the calculator is operating normally, replace the battery at least

once every three years (LR44 (GPA76)).

A dead battery can leak, causing damage to and malfunction of the

calculator. Never leave a dead battery in the calculator. Do not try using

the calculator while the battery is completely dead.

• The battery that comes with the calculator discharges slightly during

shipment and storage. Because of this, it may require replacement

sooner than the normal expected battery life.

• Do not use an oxyride battery* or any other type of nickel-based

primary battery with this product. Incompatibility between such

batteries and product specifications can result in shorter battery life

and product malfunction.

• Avoid use and storage of the calculator in areas subjected to

temperature extremes, and large amounts of humidity and dust.

• Do not subject the calculator to excessive impact, pressure, or

bending.

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• Never try to take the calculator apart.

• Use a soft, dry cloth to clean the exterior of the calculator.

• Whenever discarding the calculator or batteries, be sure to do so in

accordance with the laws and regulations in your particular area.

* Company and product names used in this manual may be registered

trademarks or trademarks of their respective owners.

Removing the Hard Case

Before using the calculator, slide its hard

case downwards to remove it, and then affix

the hard case to the back of the calculator as

shown in the illustration nearby.

Turning Power On and Off

Press O to turn on the calculator.

Press 1A(OFF) to turn off the calculator.

Auto Power Off

Your calculator will turn off automatically if you do not perform any operation

for about 10 minutes. If this happens, press the O key to turn the calculator

back on.

Adjusting Display Contrast

Display the CONTRAST screen by performing the following key operation:

1N(SETUP)c8(]CONT'). Next, use d and e to adjust

contrast. After the setting is the way you want, press A.

Important: If adjusting display contrast does not improve display readability,

it probably means that battery power is low. Replace the battery.

Key Markings

Alternate function

Pressing the 1 or S key followed by a second

sin^–1D

key performs the alternate function of the second key.

The alternate function is indicated by the text printed

above the key.

The following shows what the different colors of the

alternate function key text mean.

Keycap function

If key marking text

is this color:

It means this:

Press 1 and then the key to access the

applicable function.

Yellow

Press S and then the key to input the

applicable variable, constant, or symbol.

Red

Purple (or enclosed

in purple brackets)

Enter the CMPLX Mode to access the function.

Green (or enclosed in

green brackets)

Enter the BASE-N Mode to access the function.

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Reading the Display

The display of the calculator shows expressions you input, calculation results,

and various indicators.

Input expression

Indicators

Math

Calculation result

• If a ' indicator appears on the right side of the calculation result, it means

the displayed calculation result continues to the right. Use e and d to

scroll the calculation result display.

• If a g indicator appears on the right side of the input expression, it means

the displayed calculation continues to the right. Use e and d to scroll the

input expression display. Note that if you want to scroll the input expression

while both the ' and g indicators are displayed, you will need to press A

first and then use e and d to scroll.

Display indicators

This

Means this:

indicator:

The keypad has been shifted by pressing the 1 key. The

keypad will unshift and this indicator will disappear when

you press a key.

The alpha input mode has been entered by pressing the

S key. The alpha input mode will be exited and this

indicator will disappear when you press a key.

There is a value stored in independent memory.

The calculator is standing by for input of a variable name to

assign a value to the variable. This indicator appears after

you press 1t(STO).

STO

The calculator is standing by for input of a variable name to

recall the variable’s value. This indicator appears after you

press t.

RCL

The calculator is in the STAT Mode.

The calculator is in the CMPLX Mode.

The calculator is in the MATRIX Mode.

The calculator is in the VECTOR Mode.

The default angle unit is degrees.

STAT

CMPLX

MAT

VCT

The default angle unit is radians.

The default angle unit is grads.

A fixed number of decimal places is in effect.

A fixed number of significant digits is in effect.

Natural Display is selected as the display format.

FIX

SCI

Math

Calculation history memory data is available and can be

replayed, or there is more data above/below the current

screen.

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The display currently shows an intermediate result of a

multi-statement calculation.

Disp

Important: For some type of calculation that takes a long time to execute,

the display may show only the above indicators (without any value) while it

performs the calculation internally.

Using Menus

Some of the calculator’s operations are performed using menus. Pressing

N or w, for example, will display a menu of applicable functions.

The following are the operations you should use to navigate between

menus.

• You can select a menu item by pressing the number key that corresponds

to the number to its left on the menu screen.

• The $ indicator in the upper right corner of a menu means there is another

menu below the current one. The ` indicator means another menu above.

Use c and f to switch between menus.

• To close a menu without selecting anything, press A.

Specifying the Calculation Mode

When you want to perform this type of

operation:

Perform this key

operation:

General calculations

N1(COMP)

N2(CMPLX)

N3(STAT)

Complex number calculations

Statistical and regression calculations

Calculations involving specific number

systems (binary, octal, decimal,

hexadecimal)

N4(BASE-N)

N5(EQN)

Equation solution

Matrix calculations

N6(MATRIX)

Generate a number table based on one or

two functions

N7(TABLE)

Vector calculations

Inequality solution

N8(VECTOR)

Nc1(INEQ)

Nc2(VERIF)

Nc3(DIST)

Verify a calculation

Distribution Calculations

Note: The initial default calculation mode is the COMP Mode.

Configuring the Calculator Setup

First perform the following key operation to display the setup menu:

1N(SETUP). Next, use c and f and the number keys to configure

the settings you want.

Underlined (___) settings are initial defaults.

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1MthIO 2LineIO Specifies the display format.

Math

Natural Display (MthIO) causes fractions,

irrational numbers, and other expressions to be

displayed as they are written on paper.

MthIO: Selects MathO or LineO. MathO displays input and calculation results

using the same format as they are written on paper. LineO displays input the

same way as MathO, but calculation results are displayed in linear format.

Linear Display (LineIO) causes fractions and

other expressions to be displayed in a single

line.

Note: • The calculator switches to Linear Display automatically whenever you

enter the STAT, BASE-N, MATRIX, or VECTOR Mode. • In this manual, the

B symbol next to a sample operation indicates Natural Display (MathO),

while the b symbol indicates Linear Display.

3Deg 4Rad 5Gra Specifies degrees, radians or grads as the angle

unit for value input and calculation result display.

Note: In this manual, the v symbol next to a sample operation indicates

degrees, while the V symbol indicates radians.

6Fix 7Sci 8Norm

Specifies the number of digits for display of a

calculation result.

Fix: The value you specify (from 0 to 9) controls the number of decimal

places for displayed calculation results. Calculation results are rounded off

to the specified digit before being displayed.

Example: b 100 ÷ 7 = 14.286 (Fix 3)

14.29 (Fix 2)

Sci: The value you specify (from 1 to 10) controls the number of significant

digits for displayed calculation results. Calculation results are rounded off to

the specified digit before being displayed.

Example: b 1 ÷ 7 = 1.4286 × 10^–1(Sci 5)

1.429 × 10^–1(Sci 4)

Norm: Selecting one of the two available settings (Norm 1, Norm 2)

determines the range in which results will be displayed in non-exponential

format. Outside the specified range, results are displayed using exponential

format.

Norm 1: 10^–2Ͼ |x|, |x| м 10¹⁰Norm 2: 10^–9Ͼ |x|, |x| м 10¹⁰

Example: b 1 ÷ 200 = 5 × 10^–3(Norm 1)

0.005 (Norm 2)

c1ab/c c2 d/c Specifies either mixed fraction (ab/c) or improper

fraction (d/c) for display of fractions in calculation results.

^{c3CMPLX 1a+b}i ; 2r∠ꢀ Specifies either rectangular coordinates

⁽a+bi) or polar coordinates (r∠ꢀ) for EQN Mode solutions.

c4STAT 1ON ; 2OFF Specifies whether or not to display a FREQ

(frequency) column in the STAT Mode Stat Editor.

c5TABLE 1f(x) ; 2f(x),g(x) ^{Specifies whether to use function}f(x)

^{only or the two functions}f(x) and g(x) in the TABLE Mode.

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c6Rdec 1ON ; 2OFF

Specifies whether or not to display

calculation results using recurring decimal form.

c7Disp 1Dot ; 2Comma Specifies whether to display a dot or

a comma for the calculation result decimal point. A dot is always displayed

during input.

Note: When dot is selected as the decimal point, the separator for multiple

results is a comma (,). When comma is selected, the separator is a

semicolon (;).

c8]CONT'

Adjusts display contrast. See “Adjusting Display

Contrast” for details.

Initializing Calculator Settings

Perform the following procedure to initialize the calculator, which returns the

calculation mode to COMP and returns all other settings, including setup

menu settings, to their initial defaults.

19(CLR)1(Setup)=(Yes)

Inputting Expressions and Values

Basic Input Rules

Calculations can be input in the same form as they are written. When you

press = the priority sequence of the input calculation will be evaluated

automatically and the result will appear on the display.

4 × sin30 × (30 + 10 × 3) = 120

Math

4*s30)*(30+10*3)=

*¹Input of the closing parenthesis is required for sin, sinh, and other functions

that include parentheses.

*²These multiplication symbols (×) can be omitted. A multiplication symbol

can be omitted when it occurs immediately before an opening parenthesis,

immediately before sin or other function that includes parentheses,

immediately before the Ran# (random number) function, or immediately

^{before a variable (A, B, C, D, E, F, M, X, Y), scientific constants, π or}e.

*³The closing parenthesis immediately before the = operation can be

omitted.

Input example omitting **²and )*³operations in the above

example.

Math

4s30)(30+10*3=

Note: • If the calculation becomes longer than the screen width during

input, the screen will scroll automatically to the right and the ] indicator will

appear on the display. When this happens, you can scroll back to the left by

using d and e to move the cursor. • When Linear Display is selected,

pressing f will cause the cursor to jump to the beginning of the calculation,

while c will jump to the end. • When Natural Display is selected, pressing

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e while the cursor is at the end of the input calculation will cause it to jump

to the beginning, while pressing d while the cursor is at the beginning will

cause it to jump to the end. • You can input up to 99 bytes for a calculation.

Each numeral, symbol, or function normally uses one byte. Some functions

require three to 13 bytes. • The cursor will change shape to k when there are

10 bytes or less of allowed input remaining. If this happens, end calculation

input and then press =.

Calculation Priority Sequence

The priority sequence of input calculations is evaluated in accordance with the

rules below. When the priority of two expressions is the same, the calculation

is performed from left to right.

1st

Parenthetical expressions

Functions that require an argument to the right and a closing

parenthesis “)” following the argument.

2nd

^{Functions that come after the input value (}x , x , x , x!, °’ ”, °, ^r, ^g,

–1

3rd

4th

^{%, '}t), powers (x^), roots (")

Fractions

^{Negative sign (–), base-}n symbols (d, h, b, o)

Note: When squaring a negative value (such as –2), the value

being squared must be enclosed in parentheses ((-2)w

^{=). Since}x has a higher priority than the negative sign,

5th

inputting -2w= would result in the squaring of 2 and then

appending a negative sign to the result. Always keep the priority

sequence in mind, and enclose negative values in parentheses

when required.

Metric conversion commands (cm'in, etc.),

STAT Mode estimated values (m, n, m¹, m²)

6th

7th

8th

9th

Multiplication where the multiplication sign is omitted

Permutation (nPr), combination (nCr), complex number polar

coordinate symbol (∠)

Dot product (·)

10th Multiplication (×), division (÷), remainder calculations (÷R)

11th Addition, subtraction (+, –)

12th Logical AND (and)

13th Logical OR, XOR, XNOR (or, xor, xnor)

Inputting with Natural Display

Selecting Natural Display makes it possible to input and display fractions

−1

^{and certain functions (log,}x , x , x^, ), #, ", x , 10^, e^, ∫ , d/dx, Σ, Π,

Abs) just as they are written in your textbook.

2 + 2

Math

1 + 2

'2+!2ee1+!2=

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Important: • Certain types of expressions can cause the height of a

calculation formula to be greater than one display line. The maximum

allowable height of a calculation formula is two display screens (31 dots × 2).

Further input will become impossible if the height of the calculation you are

inputting exceeds the allowable limit. • Nesting of functions and parentheses

is allowed. Further input will become impossible if you nest too many functions

and/or parentheses. If this happens, divide the calculation into multiple parts

and calculate each part separately.

Note: When you press = and obtain a calculation result using Natural

Display, part of the expression you input may be cut off. If you need to view

the entire input expression again, press A and then use d and e to

scroll the input expression.

Using Values and Expressions as Arguments

(Natural Display only)

A value or an expression that you have already input can be used as the

argument of a function. After you have input , for example, you can make

it the argument of ', resulting in

To input 1 +

and then change it to 1 +

Math

1+7'6

dddd1Y(INS)

As shown above, the value or expression to the right of the cursor after

1Y(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.)

This capability can be used with the following functions: ', &, 7,

17(F), 1&(8), a&(9), 16("), 1l($),

1i(%), !, 6, 1!(#), 1w(Abs).

Overwrite Input Mode (Linear Display only)

You can select either insert or overwrite as the input mode, but only while

Linear Display is selected. In the overwrite mode, text you input replaces the

text at the current cursor location. You can toggle between the insert and

overwrite modes by performing the operations: 1Y(INS). The cursor

^{appears as “}I” in the insert mode and as “ ” in the overwrite mode.

Note: Natural Display always uses the insert mode, so changing display

format from Linear Display to Natural Display will automatically switch to

the insert mode.

Correcting and Clearing an Expression

To delete a single character or function: Move the cursor so it is directly to

the right of the character or function you want to delete, and then press Y.

In the overwrite mode, move the cursor so it is directly under the character

or function you want to delete, and then press Y.

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To insert a character or function into a calculation: Use d and e to

move the cursor to the location where you want to insert the character or

function and then input it. Be sure always to use the insert mode if Linear

Display is selected.

To clear all of the calculation you are inputting: Press A.

Recurring Decimal Calculations

Your calculator uses a recurring decimal when you input a value. Calculation

results also can be displayed using recurring decimal form whenever

applicable.

Inputting a Recurring Decimal

When inputting a recurrent decimal, press a!(k) before inputting its

period (repetend) and then input the period up to the ending value. To input

the recurring decimal 0.909090.... (0.90), perform the following operation:

“0 .a!(k) 90”.

Important: • If the value starts with an integer part (like: 12.3123123...), do

not include the integer part when inputting the period (12.312). • Recurring

decimal input is possible only when Natural Display is selected.

To input 0.33333... (0.3)

Math

a!(k)

To input 1.428571428571... (1.428571)

Math

1.a!(k)

428571

To calculate 1.021 + 2.312

Math

1.a!(k)021e+

2.a!(k)312=

Calculation result displayed as recurring

decimal value:

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Note: • You can specify up to 14 decimal places for the recurring decimal

period. If you input more than 14 decimal places, the value will be treated as

a terminating decimal and not a recurring decimal. • Recurring decimal value

input can be performed regardless of the Rdec setting on the setup menu.

Displaying a Calculation Result as a Recurring

Decimal Value

Calculation results that can be displayed as recurring decimal values will be

displayed as such when ON is selected for the Rdec setting on the setup

menu. Pressing the f key will cycle between the available calculation result

formats as shown below.

Fraction

Recurring Decimal

Decimal Value According to Display (Norm, Fix, Sci) Settings

Recurring Decimal

Fraction

= 0.142857 = 0.1428571429 (Norm 1)

Math

1'7=

Display as recurring decimal:

Decimal value according to Norm 1 setting: f

Return to initial display format (fraction):

1 ÷ 7 =

= 0.142857 = 0.1428571429 (Norm 1)

Math

1/7!=

Display as fraction:

Display as recurring decimal:

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Math

Return to initial display format (Norm 1):

= 0.142857 = 0.1428571429 (Norm 1)

1'7=

Display as recurring decimal:

Decimal value according to Norm 1 setting: f

Return to initial display format (fraction):

1 ÷ 7 = 0.1428571429 (Norm 1) = 0.142857 =

1/7=

Display as fraction:

Display as recurring decimal:

Return to initial display format (Norm 1):

Conditions for Displaying a Calculation Result as a

Recurring Decimal

If a calculation result satisfies the following conditions, pressing f will

display it as a recurring decimal value.

• The total number of digits used in the mixed fraction (including integer,

numerator, denominator, and separator symbol) must be no more than

10.

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• The data size of value to be displayed as the recurring decimal must be no

larger than 99 bytes. Each value and the decimal point require one byte,

and each digit of the period requires one byte. The following, for example,

would require of total of 8 bytes (4 bytes for the values, 1 byte for the decimal

point, 3 bytes for the period): 0.123

Note: For information about switching the display format of a calculation

result when OFF is selected for the Rdec setting on the setup menu, see

“Toggling Calculation Results”.

Recurring Decimal Examples

0.3 + 0.45 = 0.78

Math

0.a!(k)3e+

0.a!(k)45=f

1.6 + 2.8 = 4.5

1.a!(k)6e+

2.a!(k)8=f

123

999

1234

9999

To confirm the following: 0.123 =

12345

, 0.1234 =

0.12345 =

99999

Math

123'999=

1234'9999=

12345'99999=

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Toggling Calculation Results

While Natural Display is selected, each press of f will toggle the currently

displayed calculation result between its fraction form and decimal form, its

' form and decimal form, or its π form and decimal form.

π ÷ 6 =

= 0.5235987756

15(π)/6=

0.5235987756

5.913591358

(

+ 2) ×

= 5.913591358

6 + 2 3

(!2e+2)*!3= '

6 + 2 3

While Linear Display is selected, each press of f will toggle the currently

displayed calculation result between its decimal form and fraction form.

1 ÷ 5 = 0.2 =

1/5=

0.2

1{5

1 –

= 0.2

1-4'5=

1{5

0.2

Important: • Depending on the type of calculation result that is on the display

when you press the f key, the conversion process may take some time

to perform. • With certain calculation results, pressing the f key will not

convert the displayed value. • When ON is selected for Rdec on the setup

menu, pressing f will switch the calculation result to recurring decimal form.

For details, see “Recurring Decimal Calculations”. • You cannot switch from

decimal form to mixed fraction form if the total number of digits used in the

mixed fraction (including integer, numerator, denominator, and separator

symbols) is greater than 10.

Note: With Natural Display (MathO), pressing 1= instead of = after

inputting a calculation will display the calculation result in decimal form.

Pressing f after that will switch the calculation result to recurring decimal

form, fraction form or π form. The ' form of the result will not appear in

this case.

Basic Calculations

Fraction Calculations

Note that the input method for fractions is different, depending upon whether

you are using Natural Display or Linear Display.

2' 3e+ 1' 2=

or ' 2c3e+'1c2 =

2' 3+ 1' 2=

7{6

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1{2

4-1'(()3e1c2=

4-3'1'2=

4 − 3

Note: • Mixing fractions and decimal values in a calculation while Linear

Display is selected will cause the result to be displayed as a decimal value.

• Fractions in calculation results are displayed after being reduced to their

lowest terms.

To switch a calculation result between improper fraction and mixed

fraction form: Perform the following key operation: 1f(

)

To switch a calculation result between fraction and decimal form:

Press f.

Percent Calculations

Inputting a value and pressing 1((%) causes the input value to become

a percent.

150 × 20% = 30

Calculate what percentage of 880 is 660. (75%)

660/8801((%)=

150*201((%)=

Increase 2500 by 15%. (2875)

2500+2500*151((%)=

2875

2625

Discount 3500 by 25%. (2625)

3500-3500*251((%)=

Degree, Minute, Second (Sexagesimal) Calculations

Performing an addition or subtraction operation between sexagesimal values,

or a multiplication or division operation between a sexagesimal value and a

decimal value will cause the result to be displayed as a sexagesimal value.

You also can convert between sexagesimal and decimal. The following

is the input format for a sexagesimal value: {degrees} $ {minutes} $

{seconds} $.

Note: You must always input something for the degrees and minutes, even

if they are zero.

2°20´30˝ + 39´30˝ = 3°00´00˝

2$20$30$+0$39$30$=

3°0´0˝

Convert 2°15´18˝ to its decimal equivalent.

2$15$18$= 2°15´18˝

(Converts sexagesimal to decimal.) $

2.255

(Converts decimal to sexagesimal.) $ 2°15´18˝

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Multi-Statements

You can use the colon character (:) to connect two or more expressions and

execute them in sequence from left to right when you press =.

3 + 3 : 3 × 3

3+3S7(:)3*3=

Using Engineering Notation

A simple key operation transforms a displayed value to engineering

notation.

Transform the value 1234 to engineering notation, shifting the

decimal point to the right.

1234=

1234

1.234×10³

1234×10⁰

Transform the value 123 to engineering notation, shifting the decimal

point to the left.

123=

123

1W(←)

1W(←) 0.000123×10⁶

0.123×10³

Calculation History

In the COMP, CMPLX, or BASE-N Mode, the calculator remembers up to

approximately 200 bytes of data for the newest calculation. You can scroll

through calculation history contents using f and c.

1 + 1 = 2

2 + 2 = 4

3 + 3 = 6

1+1=

2+2=

3+3=

(Scrolls back.) f

(Scrolls back again.) f

Note: Calculation history data is all cleared whenever you press O, when

you change to a different calculation mode, when you change the display

format, or whenever you perform any reset operation.

Replay

While a calculation result is on the display, you can press d or e to edit

the expression you used for the previous calculation.

4 × 3 + 2.5 = 14.5 b

4 × 3 − 7.1 = 4.9

4*3+2.5= 14.5

(Continuing) dYYYY-7.1=

4.9

Note: If you want to edit a calculation when the ' indicator is on the right

side of a calculation result display (see “Reading the Display”), press A

and then use d and e to scroll the calculation.

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Answer Memory (Ans)/Previous Answer Memory

(PreAns)

The last calculation result obtained is stored in Ans (answer) memory. The

calculation result obtained prior to the last one is stored in PreAns (previous

answer) memory. Displaying the result of a new calculation will move current

Ans memory contents to PreAns memory and store the new calculation

results in Ans memory. PreAns memory can be used only in the COMP

Mode. PreAns memory contents are cleared whenever the calculator enters

another mode from the COMP Mode.

To divide the result of 3 × 4 by 30 b

3*4=

(Continuing) /30=

123 + 456 = 579

789 – 579 = 210

123+456=

(Continuing) 789-G=

For T^k+2= T^k+1+ T^k(Fibonacci sequence), determine the sequence

from T¹to T⁵. Note however, that T¹= 1 and T²= 1. B

= 1

(Ans = T¹= 1)

(Ans = T²= 1, PreAns = T¹= 1)

(Ans = T³= 2, PreAns = T²= 1)

= 1

= T²+ T¹= 1 + 1

G+SG(PreAns)=

= T³+ T²= 2 + 1

(Ans = T⁴= 3, PreAns = T³= 2)

= T⁴+ T³= 3 + 2

Result: The sequence is {1, 1, 2, 3, 5}.

E-17

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Variables (A, B, C, D, E, F, X, Y)

Your calculator has eight preset variables named A, B, C, D, E, F, X, and Y. You

can assign values to variables and also use the variables in calculations.

To assign the result of 3 + 5 to variable A

3+51t(STO)y(A)

To multiply the contents of variable A by 10

(Continuing) Sy(A)*10=

To recall the contents of variable A (Continuing) ty(A)

To clear the contents of variable A

01t(STO)y(A)

Independent Memory (M)

You can add calculation results to or subtract results from independent

memory. The “M” appears on the display when there is any value other than

zero stored in independent memory.

To clear the contents of M

01t(STO)l(M)

To add the result of 10 × 5 to M

(Continuing) 10*5l

To subtract the result of 10 + 5 from M

(Continuing) 10+51l(M–)

To recall the contents of M (Continuing) tl(M)

Note: Variable M is used for independent memory.

Clearing the Contents of All Memories

Ans memory, independent memory, and variable contents are retained even

if you press A, change the calculation mode, or turn off the calculator.

PreAns memory contents are retained even if you press A and turn off the

calculator without exiting the COMP Mode. Perform the following procedure

when you want to clear the contents of all memories.

!9(CLR)2(Memory)=(Yes)

Remainder Calculations

You can use the ÷R function in order to obtain the quotient and remainder

in a division calculation.

To calculate the quotient and remainder of 5 ÷ 2

Math

5a'(÷R)2=

Quotient Remainder

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Note: • Only the quotient value of a ÷R calculation is stored in Ans memory.

• Assigning the result of a remainder division calculation to a variable

will assign the quotient value only. Performing the operation 5a

'(÷R)2!t(STO))(X) (which assigns the result of 5÷R2 to X)

will assign a value of 2 to X. • If a ÷R calculation is part of a multi-step

calculation, only the quotient is passed on to the next operation. (Example:

10+17a'(÷R)6=→ 10 + 2) • Operation of the f and e keys is

disabled while a remainder division result is on the display.

Cases when Remainder Division becomes

Non-remainder Division

If either of the following conditions exists when you perform a remainder

division operation, the calculation will be treated as normal (non-remainder)

division.

• When either the dividend or the divisor is a very large value

Example: 20000000000 a'(÷R)17=

→ Calculated as: 20000000000 ÷ 17

• When the quotient is not a positive integer, or if the remainder is not a

positive integer or positive fractional value

Example: -5a'(÷R)2= → Calculated as: –5 ÷ 2

Prime Factorization

In the COMP Mode, you can factor a positive integer up to 10 digits into

prime factors up to three digits.

To perform prime factorization on 1014

1014=

!e(FACT)

When you perform prime factorization on a value that includes a factor that

is prime number with more than three digits, the part that cannot be factored

will be enclosed in parentheses on the display.

To perform prime factorization on 4104676 (= 2²× 1013²)

!e(FACT)

Any one of the following operations will exit prime factorization result

display.

• Pressing !e(FACT) or =.

• Pressing any of the following keys: . or e.

• Using the setup menu to change the angle unit setting (Deg, Rad, Gra) or

the display digits setting (Fix, Sci, Norm).

Note: • You will not be able to execute prime factorization while a decimal

value, fraction, or negative value calculation result is displayed. Trying to

do so will cause a math error (Math ERROR). • You will not be able to

execute prime factorization while the result of a calculation that uses Pol,

Rec, ÷R is displayed.

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Function Calculations

For actual operations using each function, see the “Examples” section

following the list below.

: π is displayed as 3.141592654, but π = 3.14159265358980 is used for

internal calculations.

e: e is displayed as 2.718281828, but e = 2.71828182845904 is used for

internal calculations.

sin, cos, tan, sin⁻¹, cos⁻¹, tan⁻¹: Trigonometric functions. Specify the

angle unit before performing calculations. See 1.

sinh, cosh, tanh, sinh⁻¹, cosh⁻¹, tanh⁻¹: Hyperbolic functions. Input a

function from the menu that appears when you press w. The angle unit

setting does not affect calculations. See

°, ^r, ^g: These functions specify the angle unit. ° specifies degrees, ^rradians,

and ^ggrads. Input a function from the menu that appears when you perform

the following key operation: 1G(DRG'). See 3.

$, %: Exponential functions. Note that the input method is different

depending upon whether you are using Natural Display or Linear Display.

See 4.

log: Logarithmic function. Use the l key to input log_ab as log (a, b). Base

^{10 is the default setting if you do not input anything for}a. The & key also

can be used for input, but only while Natural Display is selected. In this

case, you must input a value for the base. See

ln: Natural logarithm to base e. See

−1

x , x , x^, ), #, ", x : Powers, power roots, and reciprocals. Note

^{that the input methods for}x^, ), #, and " are different depending upon

whether you are using Natural Display or Linear Display. See

Note: • The following functions cannot be input in consecutive sequence:

−1

x , x , x^, x . If you input 2ww, for example, the final w will be ignored.

To input ², input 2w, press the d key, and then press w(B).

2²

−1

^•x , x , x can be used in complex number calculations.

: Function for performing numerical integration using the Gauss-Kronrod

method. Natural Display input syntax is

( ( )

, while Linear Display input

( )

_af x

∫

f x

syntax is

, a, b, tol). tol specifies tolerance, which becomes 1 ×

∫

10^–5when nothing is input for tol. Also see “Integration and Differential

Calculation Precautions” and “Tips for Successful Integration Calculations”

for more information. See

F: Function for approximation of the derivative based on the central

difference method. Natural Display input syntax is

_{x a}, while

( ( ))

f x ͦ

( ( )

f x

Linear Display input syntax is

, a, tol). tol specifies tolerance,

which becomes 1 × 10^–10when nothing is input for tol. Also see “Integration

and Differential Calculation Precautions” for more information. See

( ( ))

f x

8: Function that, for a specified range of

f(x), determines sum

x a

( ( ))

f x

(a) +

(a+1) +

(a+2) + ...+

(

). Natural Display input syntax is _{x a}

while Linear Display input syntax is Σ(f(x),

b).

and

are integers that

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can be specified within the range of –1 × 10¹⁰ꢀ

ꢁ

ꢀ 1 × 10¹⁰. See

Note: The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot

^{be used in}f(x), a, or b: ∫, d/dx, Σ, Π.

^{9: Determines the product of}f(x) over a given range. The calculation

( ( ))

formula is:

f x = f(a) × f(a+1) × f(a+2) × ... × f(b). The Natural Display

⌸

x a

( ( ))

input syntax is

f x ^{, while the Linear Display input syntax is ⌸(}f(x), a,

⌸

x a

b). a and b are ⁼integers in the range of a ꢀ 1 × 10¹⁰, b ꢀ 1 × 10¹⁰, a ꢁ b.

See

^{Note: The following cannot be used in}f(x): Pol, Rec, ÷R. The following cannot

^{be used in}f(x), a, or b: ∫, d/dx, Σ, ⌸.

Pol, Rec: Pol converts rectangular coordinates to polar coordinates, while

Rec converts polar coordinates to rectangular coordinates. See

Specify the angle unit before

performing calculations.

^Pol(x, y) = (r, ꢀ)

Rec(r, ꢀ) = (x, y)

^{The calculation result for}r and ꢀ

^{and for}x and y are each assigned

respectively to variables X and Y.

Calculation result θ is displayed

in the range of −180° ꢀ θ ꢁ

180°.

Rectangular

Coordinates (Rec)

Polar

Coordinates (Pol)

x!: Factorial function. See

Abs: Absolute value function. Note that the input method is different

depending upon whether you are using Natural Display or Linear Display.

See

Ran#: Generates a 3-digit pseudo random number that is less than 1.

The result is displayed as a fraction when Natural Display is selected.

See

^{RanInt#: For input of the function of the form RanInt#(}a, b), which generates

^{a random integer within the range of}a to b. See

nPr, nCr: Permutation (nPr) and combination (nCr) functions. See

Rnd:Theargumentofthisfunctionismadeadecimalvalueandthenrounded

in accordance with the current number of display digits setting (Norm, Fix, or

Sci). With Norm 1 or Norm 2, the argument is rounded off to 10 digits. With

Fix and Sci, the argument is rounded off to the specified digit. When Fix 3

is the display digits setting, for example, the result of 10 ÷ 3 is displayed

as 3.333, while the calculator maintains a value of 3.33333333333333 (15

digits) internally for calculation. In the case of Rnd(10÷3) = 3.333 (with Fix

3), both the displayed value and the calculator’s internal value become

3.333. Because of this a series of calculations will produce different results

depending on whether Rnd is used (Rnd(10÷3) × 3 = 9.999) or not used (10

÷ 3 × 3 = 10.000). See

GCD, LCM: GCD determines the greatest common divisor of two values,

while LCM determines the least common multiple. See

Int: Extracts the integer part of a value. See

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Intg: Determines the largest integer that does not exceed a value. See

Note: Using functions can slow down a calculation, which may delay display

of the result. Do not perform any subsequent operation while waiting for the

calculation result to appear. To interrupt an ongoing calculation before its

result appears, press A.

Integration and Differential Calculation Precautions

• Integration and differential calculations can be performed in the COMP

Mode (,1) only.

^{• The following cannot be used in}f(x): Pol, Rec, ÷R. The following cannot

^{be used in}f(x), a, b, or tol: ∫, d/dx, Σ, Π.

^{• When using a trigonometric function in}f(x), specify Rad as the angle

unit.

^{• A smaller}tol value increases precision, but it also increases calculation

^{time. When specifying}tol, use value that is 1 × 10^–14or greater.

Precautions for Integration Calculation Only

• Integration normally requires considerable time to perform.

^{• For}f(x) ꢀ 0 where a ꢁ x ꢁb (as in the case of ₀3x – 2 = –1), calculation

∫

will produce a negative result.

^{• Depending on the content of}f(x) and the region of integration, calculation

error that exceeds the tolerance may be generated, causing the calculator

to display an error message.

Precautions for Differential Calculation Only

^{• If convergence to a solution cannot be found when}tol input is omitted, the

tol value will be adjusted automatically to determine the solution.

• Non-consecutive points, abrupt fluctuation, extremely large or small points,

inflection points, and the inclusion of points that cannot be differentiated,

or a differential point or differential calculation result that approaches zero

can cause poor precision or error.

Tips for Successful Integration Calculations

When a periodic function or integration interval results in positive and

^negativef(x) function values

Perform separate integrations for each cycle, or for the positive part and the

negative part, and then combine the results.

^bf(x)dx = ^cf(x)dx + (– ^bf(x)dx)

∫

S Positive

Positive Part Negative Part

(S Positive) (S Negative)

S Negative

When integration values fluctuate widely due to minute shifts in the

integration interval

Divide the integration interval into multiple parts (in a way that breaks areas

of wide fluctuation into small parts), perform integration on each part, and

then combine the results.

f (x)

x₁

x₂

^bf(x)dx =

f(x)dx +

f(x)dx + .....

∫

f(x)dx

∫

x₁

x₂

x₃

x₄

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Examples

sin 30°= 0.5 bv

sin⁻¹0.5 = 30° bv 1s(sin⁻¹)0.5)=

s30)=

0.5

sinh 1 = 1.175201194

cosh^–11 = 0

wb(sinh)1)= 1.175201194

wf(cosh⁻¹)1)=

π/2 radians = 90°, 50 grads = 45°

(15(π)/2)1G(DRG')c(^r)=

501G(DRG')d(^g)=

To calculate e × 2 to three significant digits (Sci 3)

1N(SETUP)7(Sci)3

1i(%)5e*2=

1i(%)5)*2=

2.97×10²

log₁₀1000 = log 1000 = 3

log₂16 = 4

l1000)=

l21)(,)16)=

&2e16=

To calculate ln 90 (= log 90) to three significant digits (Sci 3)

1N(SETUP)7(Sci)3

i90)=

4.50×10⁰

1.2 × 10³= 1200 B

1.2*1063=

1200

15625

(1+1)²⁺²= 16

B (1+1)62+2=

(5²)³= 15625

(5x)1w(x )=

= 2

16(") 5e32=

516(")32)=

To calculate

places (Fix 3)

(= 3

= 4.242640687...) to three decimal

2 3

1N(SETUP)6(Fix)3 B

!2e*3=

4.243

!2)*3=

∫₁^e^ln(x) = 1

^{B 7iS)(X))e1eS5(}e)=

7iS)(X))1)(,)

^11)(,)S5(e))=

To obtain the derivative at point x = π/2 for the function y = sin(x)

17(F)sS)(X))

e'15(π)e2=

17(F)sS)(X))

1)(,)15(π)'2)=

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(x + 1) = 20

10 _x

1&(8)S)(X)+1e1e5=

1&(8)S)(X)+11)(,)1

1)(,)5)=

(x + 1) = 720

⌸

a&(9)S)(X)+1e1e5=

a&(9)S)(X)+11)(,)1

1)(,)5)=

720

To convert rectangular coordinates ( ) to polar coordinates

' '

1+(Pol)!2e1)(,)!2e)= r=2,ꢀ=45

1+(Pol)!2)1)(,)!2))=

r= 2

ꢀ= 45

To convert polar coordinates ( , 45°) to rectangular coordinates

1-(Rec)!2e1)(,)45)=

X=1, Y=1

40320

(5 + 3) ! = 40320

(5+3)1E(x!)=

|2 – 7| × 2 = 10

1w(Abs)2-7e*2=

1w(Abs)2-7)*2=

To obtain three random three-digit integers

10001.(Ran#)=

459

117

(Results shown here are for illustrative purposes only. Actual results will differ.)

To generate random integers in the range of 1 to 6

S.(RanInt)11)(,)6)=

(Results shown here are for illustrative purposes only. Actual results will differ.)

To determine the number of permutations and combinations

possible when selecting four people from a group of 10

Permutations:

101*(nPr)4=

5040

210

Combinations: 101/(nCr)4=

To perform the following calculations when Fix 3 is selected for the

number of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3

1N(SETUP)6(Fix)3 10/3*3=

10.000

9.999

10(Rnd)10/3)*3=

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To determine the greatest common divisor of 28 and 35

S*(GCD)281)(,)35)=

To determine the least common multiple of 9 and 15

S/(LCM)91)(,)15)=

To extract the integer part of −3.5

S+(Int)-3.5)=

−3

−4

To determine the largest integer that does not exceed −3.5

S-(Intg)-3.5)=

Complex Number Calculations (CMPLX)

To perform complex number calculations, first press N2(CMPLX) to

^{enter the CMPLX Mode. You can use either rectangular coordinates (}a+bi)

^{or polar coordinates (}r∠ꢀ) to input complex numbers. Complex number

calculation results are displayed in accordance with the complex number

format setting on the setup menu.

^{(2 + 6}i) ÷ (2i) = 3 – i (Complex number format: a + bi)

^(2+6W(i))/(2W(i))=

3–i

2 ∠ 45 =

i Bv (Complex number format: a + bi)

21-(∠)45=

'+'i

i = 2 ∠ 45 Bv (Complex number format: r∠ꢀ)

^!2e+!2eW(i)=

2∠45

Note: • If you are planning to perform input and display of the calculation

result in polar coordinate format, specify the angle unit before starting the

^{calculation. • The}ꢀ value of the calculation result is displayed in the range

^{of –180° ꢀ}ꢀ ꢁ 180°. • Display of the calculation result while Linear Display

^{is selected will show}a and bi (or r and ꢀ) on separate lines.

CMPLX Mode Calculation Examples

(1 – i)^–1=

B (Complex number format: a + bi)

^(1-W(i))E=

1 1

2 2

(1 + i)²+ (1 – i)²= 0 B

^(1+W(i))w+(1-W(i))w=

To obtain the conjugate complex number of 2 + 3i (Complex number

format: a + bi)

^{12(CMPLX)2(Conjg)2+3W(}i))=

2–3i

To obtain the absolute value and argument of 1 + i Bv

Absolute Value:

^1w(Abs)1+W(i)=

Argument:12(CMPLX)1(arg)1+W(i))=

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Using a Command to Specify the Calculation Result

Format

Either of two special commands ('r∠ꢀ or 'a+bi) can be input at the end

of a calculation to specify the display format of the calculation results. The

command overrides the calculator’s complex number format setting.

i = 2 ∠ 45, 2 ∠ 45 =

i Bv

^!2e+!2eW(i)12(CMPLX)3('r∠ꢀ)=

21-(∠)4512(CMPLX)4('a+bi)=

2∠45

'+'i

Using CALC

CALC lets you save calculation expressions that contain variables, which you

can then recall and execute in the COMP Mode (N1) and the CMPLX

Mode (N2). The following describes the types of expressions you can

save with CALC.

^{• Expressions: 2X + 3Y, 2AX + 3BY + C, A + B}i

• Multi-statements: X + Y : X (X + Y)

• Equalities with a single variable on the left and an expression including

variables on the right: A = B + C, Y = X²+ X + 3

(Use Ss(=) to input the equals sign of the equality.)

To store 3A + B and then substitute the following values to perform

the calculation: (A, B) = (5, 10), (7, 20)

Math

3S-(A)+Se(B)

Math

Prompts for input of a value for A

Current value of A

Math

5=10=

Math

s (or =)

7=20=

To exit CALC: A

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To store A + Bi and then determine

+ i, 1 +

i using polar

coordinates (r∠ꢀ)

CMPLX

Math

N2(CMPLX)

^{S-(A)+Se(B)W(}i)

^12(CMPLX)3('r∠ꢀ)

s!3)=1=

s (or =)1=!3)=

To exit CALC: A

Note: During the time from when you press s until you exit CALC by

pressing A, you should use Linear Display input procedures for input.

Using SOLVE

SOLVE uses Newton’s Law to approximate the solution of equations. Note

that SOLVE can be used in the COMP Mode (N1) only.

The following describes the types of equations whose solutions can be

obtained using SOLVE.

• Equations that include variable X: X²+ 2X – 2, Y = X + 5, X = sin(M), X

+ 3 = B + C

SOLVE solves for X. An expression like X²+ 2X – 2 is treated as X²+ 2X

– 2 = 0.

• Equations input using the following syntax: {equation}, {solution

variable}

SOLVE solves for Y, for example, when an equation is input as: Y = X + 5,

Important: • If an equation contains input functions that include an open

parenthesis (such as sin and log), do not omit the closing parenthesis.

^{• The following functions are not allowed inside of an equation: ∫,}d/dx, Σ,

Π, Pol, Rec, ÷R.

^{To solve}y = ax + b for x when y = 0, a = 1, and b = –2

Math

Sf(Y)Ss(=)S-(A)

S)(X)w+Se(B)

Math

1s(SOLVE)

Prompts for input of a value for Y

Current value of Y

Math

0=1=-2=

Current value of X

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Math

Input an initial value for X (Here, input 1): 1=

To exit SOLVE: A

Solution screen

Note: During the time from when you press 1s(SOLVE) until you exit

SOLVE by pressing A, you should use Linear Display input procedures

for input.

Important: • Depending on what you input for the initial value for X (solution

variable), SOLVE may not be able to obtain solutions. If this happens, try

changing the initial value so they are closer to the solution. • SOLVE may not

be able to determine the correct solution, even when one exists. • SOLVE

uses Newton’s Law, so even if there are multiple solutions, only one of them

will be returned. • Due to limitations in Newton’s Law, solutions tend to be

^{difficult to obtain for equations like the following:}y = sin(x), y = e^x, y =

^'x

Solution Screen Contents

Solutions are always displayed in decimal form.

Equation (The equation you input.)

Math

Variable solved for

Solution

(Left Side) – (Right Side) result

“(Left Side) – (Right Side) result” shows the result when the right side of the

equation is subtracted from the left side, after assigning the obtained value

to the variable being solved for. The closer this result is to zero, the higher

the accuracy of the solution.

Continue Screen

SOLVE performs convergence a preset number of times. If it cannot find a

solution, it displays a confirmation screen that shows “Continue: [=]”, asking

if you want to continue.

Press = to continue or A to cancel the SOLVE operation.

^{To solve}y = x – x + 1 for x when y = 3, 7, and 13

Math

Sf(Y)Ss(=)

S)(X)w-S)(X)+1

Math

1s(SOLVE)

Math

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Math

Input an initial value for X (Here, input 1): 1=

=7==

Math

=13==

Statistical Calculations (STAT)

To start a statistical calculation, perform the key operation N3(STAT)

to enter the STAT Mode and then use the screen that appears to select the

type of calculation you want to perform.

To select this type of statistical calculation:

Press this key:

(Regression formula shown in parentheses)

Single-variable (X)

1(1-VAR)

2(A+BX)

^{Paired-variable (X, Y), linear regression (}y = A + Bx)

Paired-variable (X, Y), quadratic regression

3(_+CX²)

4(ln X)

⁽y = A + Bx + Cx )

Paired-variable (X, Y), logarithmic regression

(y = A + Blnx)

^{Paired-variable (X, Y),}e exponential regression

⁵⁽e^X)

_Bx

⁽y = Ae )

^{Paired-variable (X, Y),}ab exponential regression

6(A•B^X)

7(A•X^B)

8(1/X)

⁽y = AB^x)

Paired-variable (X, Y), power regression ⁽y = Ax )

Paired-variable (X, Y), inverse regression

⁽y = A + B/x)

Pressing any of the above keys (1 to 8) displays the Stat Editor.

Note: When you want to change the calculation type after entering the STAT

Mode, perform the key operation 11(STAT/DIST)1(Type) to display

the calculation type selection screen.

Inputting Data

Use the Stat Editor to input data. Perform the following key operation to

display the Stat Editor: 11(STAT/DIST)2(Data).

The Stat Editor provides 40 rows for data input when there is an X column

only or when there are X and Y columns, 20 rows when there are X and FREQ

columns, or 26 rows when there are X, Y, and FREQ columns.

Note: Use the FREQ (frequency) column to input the quantity (frequency) of

identical data items. Display of the FREQ column can be turned on (displayed)

or off (not displayed) using the Stat Format setting on the setup menu.

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To select linear regression and input the following data:

(170, 66), (173, 68), (179, 75)

STAT

N3(STAT)2(A+BX)

STAT

170=173=179=ce

STAT

66=68=75=

Important: • All data currently input in the Stat Editor is deleted whenever

you exit the STAT Mode, switch between the single-variable and a paired-

variable statistical calculation type, or change the Stat Format setting on

the setup menu. • The following operations are not supported by the Stat

Editor: m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements

also cannot be input with the Stat Editor.

To change the data in a cell: In the Stat Editor, move the cursor to the cell

that contains the data you want to change, input the new data, and then

press =.

To delete a line: In the Stat Editor, move the cursor to the line that you want

to delete and then press Y.

To insert a line: In the Stat Editor, move the cursor to the location where

you want to insert the line and then perform the following key operation:

11(STAT/DIST)3(Edit)1(Ins).

To delete all Stat Editor contents: In the Stat Editor, perform the following

key operation: 11(STAT/DIST)3(Edit)2(Del-A).

Obtaining Statistical Values from Input Data

To obtain statistical values, press A while in the Stat Editor and then

recall the statistical variable (σx, Σx , etc.) you want. Supported statistical

variables and the keys you should press to recall them are shown below.

For single-variable statistical calculations, the variables marked with an

asterisk (*) are available.

^{Sum: Σ}x *, Σx*, Σy , Σy, Σxy, Σx , Σx y, Σx

11(STAT/DIST) 3(Sum) 1 to 8

^{Number of Items:}n*, Mean: o*, p, Population Standard Deviation: σx*,

σy, Sample Standard Deviation: sx*, sy

11(STAT/DIST) 4(Var) 1 to 7

^{Regression Coefficients: A, B, Correlation Coefficient:}r, Estimated

Values: m, n

11(STAT/DIST) 5(Reg) 1 to 5

Regression Coefficients for Quadratic Regression: A, B, C, Estimated

Values: m¹, m², n

11(STAT/DIST) 5(Reg) 1 to 6

• See the table at the beginning of this section of the manual for the regression

formulas.

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• m, m¹, m²and n are not variables. They are commands of the type that take

an argument immediately before them. See “Calculating Estimated Values”

for more information.

Minimum Value: minX*, minY, Maximum Value: maxX*, maxY

11(STAT/DIST) 6(MinMax) 1 to 2

(When the single-variable statistical calculation is selected.)

11(STAT/DIST) 6(MinMax) 1 to 4

(When a paired-variable statistical calculation is selected.)

First Quartile: Q1, Median: med, Third Quartile: Q3

11(STAT/DIST) 6(MinMax) 3 to 5

(When the single-variable statistical calculation is selected.)

Note: While single-variable statistical calculation is selected, you can input

the functions and commands for performing normal distribution calculation

from the menu that appears when you perform the following key operation:

11(STAT/DIST) 5(Distr). See “Performing Normal Distribution

Calculations” for details.

^{To input the single-variable data}x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, using

the FREQ column to specify the number of repeats for each items

^({xn; freqn} = {1;1, 2;2, 3;3, 4;2, 5;1}), and calculate the mean and

population standard deviation.

1N(SETUP)c4(STAT)1(ON)

STAT

N3(STAT)1(1-VAR)

1=2=3=4=5=ce

1=2=3=2=

A11(STAT/DIST)4(Var)2(o)=

A11(STAT/DIST)4(Var)3(σx)=

Results: Mean: 3 Population Standard Deviation: 1.154700538

To calculate the linear regression and logarithmic regression

correlation coefficients for the following paired-variable data and

^{determine the regression formula for the strongest correlation: (}x, y)

= (20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3

(three decimal places) for results.

1N(SETUP)c4(STAT)2(OFF)

1N(SETUP)6(Fix)3

STAT

FIX

N3(STAT)2(A+BX)

20=110=200=290=ce

3150=7310=8800=9310=

A11(STAT/DIST)5(Reg)3(r)=

A11(STAT/DIST)1(Type)4(In X)

A11(STAT/DIST)5(Reg)3(r)=

A11(STAT/DIST)5(Reg)1(A)=

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A11(STAT/DIST)5(Reg)2(B)=

Results: Linear Regression Correlation Coefficient: 0.923

Logarithmic Regression Correlation Coefficient: 0.998

^{Logarithmic Regression Formula:}y = –3857.984 + 2357.532lnx

Calculating Estimated Values

Based on the regression formula obtained by paired-variable statistical

^{calculation, the estimated value of}y can be calculated for a given x-value.

^{The corresponding}x-value (two values, x¹and x², in the case of quadratic

^{regression) also can be calculated for a value of}y in the regression

formula.

To determine the estimate value for y when x = 160 in the

regression formula produced by logarithmic regression of the data

. Specify Fix 3 for the result. (Perform the following operation

after completing the operations in

A16011(STAT/DIST)5(Reg)5(n)=

Result: 8106.898

Important: Regression coefficient, correlation coefficient, and estimated

value calculations can take considerable time when there are a large number

of data items.

Performing Normal Distribution Calculations

While single-variable statistical calculation is selected, you can perform

normal distribution calculation using the functions shown below from

the menu that appears when you perform the following key operation:

11(STAT/DIST)5(Distr).

^{P, Q, R: These functions take the argument}t and determine a probability of

standard normal distribution as illustrated below.

P(t)

Q(t)

R(t)

0 t

^'t: This function is preceded by the argument X, and determines the

normalized variate

^{For the single variable data {}xn ; freqn} = {0;1, 1;2, 2;1, 3;2, 4;2, 5;2,

6;3, 7;4, 9;2, 10;1}, to determine the normalized variate ('t) when x

= 3, and P(t) at that point up to three decimal places (Fix 3).

1N(SETUP)c4(STAT)1(ON)

1N(SETUP)6(Fix)3N3(STAT)1(1-VAR)

STAT

FIX

0=1=2=3=4=5=6=7=9=

10=ce1=2=1=2=2=2=3=

4=2=1=

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STAT

FIX

A311(STAT/DIST)5(Distr)4('t)=

11(STAT/DIST)5(Distr)1(P()G)=

^{Results: Normalized variate ('}t): –0.762

^P(t):

0.223

Base-n Calculations (BASE-N)

Press N4(BASE-N) to enter the BASE-N Mode when you want to

perform calculations using decimal, hexadecimal, binary, and/or octal

values. The initial default number mode when you enter the BASE-N Mode

is decimal, which means input and calculation results use the decimal

number format. Press one of the following keys to switch number modes:

w(DEC) for decimal, 6(HEX) for hexadecimal, l(BIN) for binary, or

i(OCT) for octal.

To enter the BASE-N Mode, switch to the binary mode, and

calculate 11²+ 1²

N4(BASE-N)

l(BIN)

11+1=

Continuing from above, switch to the hexadecimal mode and

calculate 1F¹⁶+ 1¹⁶

A6(HEX)1t(F)+1=

Continuing from above, switch to the octal mode and calculate

+ 1⁸

Ai(OCT)7+1=

Note: •UsethefollowingkeystoinputthelettersAthroughFforhexadecimal

values: -(A), $(B), w(C), s(D), c(E), t(F). • In the BASE-N

Mode, input of fractional (decimal) values and exponents is not supported. If

a calculation result has a fractional part, it is cut off. • The input and output

ranges is 16 bits for binary values, and 32 bits for other types of values. The

following shows details about input and output ranges.

Input/Output Ranges

Base-n Mode

Positive: ^{0000000000000000 ꢁ}x ꢁ 0111111111111111

Binary

Negative: 1000000000000000 ꢁ x ꢁ 1111111111111111

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Positive: ^{00000000000 ꢁ}x ꢁ 17777777777

Negative: 20000000000 ꢁ x ꢁ 37777777777

^{–2147483648 ꢁ}x ꢁ 2147483647

Octal

Decimal

Hexadecimal

Positive: ^{00000000 ꢁ}x ꢁ 7FFFFFFF

Negative: 80000000 ꢁ x ꢁ FFFFFFFF

Specifying the Number Mode of a Particular Input

Value

You can input a special command immediately following a value to specify

the number mode of that value. The special commands are: d (decimal), h

(hexadecimal), b (binary), and o (octal).

To calculate 10¹⁰+ 10¹⁶+ 10²+ 10⁸and display the result as a decimal

value

Aw(DEC) 13(BASE)c1(d)10+

13(BASE)c2(h)10+

13(BASE)c3(b)10+

13(BASE)c4(o)10=

Converting a Calculation Result to another Type of

Value

You can use any one of the following key operations to convert the currently

displayed calculation result to another type of value: x(DEC) (decimal),

6(HEX) (hexadecimal), l(BIN) (binary), i(OCT)(octal).

To calculate 15¹⁰× 37¹⁰in the decimal mode, and then convert

the result to hexadecimal, binary, and octal

Ax(DEC)15*37=

6(HEX)

555

0000022B

l(BIN) 0000001000101011

00000001053

i(OCT)

Logical and Negation Operations

Your calculator provides you with logical operators (and, or, xor, xnor) and

functions (Not, Neg) for logical and negation operations on binary values.

Use the menu that appears when you press 13(BASE) to input these

logical operators and functions.

All of the following examples are performed in the binary mode (l(BIN)).

To determine the logical AND of 1010²and 1100²(1010²and 1100²

)

A101013(BASE)1(and)1100= 0000000000001000

To determine the logical OR of 1011²and 11010²(1011²or 11010²

)

A101113(BASE)2(or)11010= 0000000000011011

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To determine the logical XOR of 1010²and 1100²(1010²xor 1100²

)

A101013(BASE)3(xor)1100= 0000000000000110

To determine the logical XNOR of 1111²and 101²(1111²xnor 101²

)

A111113(BASE)4(xnor)101= 1111111111110101

To determine the bitwise complement of 1010²(Not(1010²))

A13(BASE)5(Not)1010)= 1111111111110101

To negate (take the two’s complement) of 101101²(Neg(101101²))

A13(BASE)6(Neg)101101)= 1111111111010011

Note: In the case of a negative binary, octal or hexadecimal value, the

calculator converts the value to binary, takes the two’s complement, and

then converts back to the original number base. For decimal (base-10)

values, the calculator merely adds a minus sign.

Equation Calculations (EQN)

You can use the following procedure in the EQN Mode to solve simultaneous

linear equations with two or three unknowns, quadratic equations, and cubic

equations.

1. Press N5(EQN) to enter the EQN Mode.

2. On the menu that appears, select an equation type.

To select this calculation type:

Press this key:

Simultaneous linear equations with two

unknowns

1(aⁿX + bⁿY = cⁿ

)

Simultaneous linear equations with

three unknowns

2(aⁿX + bⁿY + cⁿZ = dⁿ

)

3(aX²+ bX + c = 0)

4(aX³+ bX²+ cX + d = 0)

Quadratic equation

Cubic equation

3. Use the Coefficient Editor that appears to input coefficient values.

^{• To solve 2}x + x – 3 = 0, for example, press 3 in step 2, and then input

^{the following for the coefficients (}a = 2, b = 1, c = –3): 2=1=-

3=.

• To change a coefficient value you already have input, move the cursor

to the appropriate cell, input the new value, and then press =.

• Pressing A will clear all of the coefficients to zero.

Important: The following operations are not supported by the Coefficient

Editor: m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements

also cannot be input with the Coefficient Editor.

4. After all the values are the way you want, press =.

• This will display a solution. Each press of = will display another

solution. Pressing = while the final solution is displayed will return to

the Coefficient Editor.

• You can scroll between the solutions using the c and f keys.

• To return to the Coefficient Editor while any solution is displayed, press

Note: • Even if Natural Display is selected, the solutions of simultaneous

linear equations are not displayed using any form that includes '.

• Values cannot be converted to engineering notation on the solution screen.

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• A message appears to let you know when there is no solution or when

there are infinite solutions. Pressing A or = will return to the Coefficient

Editor.

Changing the Current Equation Type Setting

Press N5(EQN) and then select an equation type from the menu that

appears. Changing the equation type causes the values of all Coefficient

Editor coefficients to change to zero.

EQN Mode Calculation Examples

x + 2y = 3, 2x + 3y = 4

Math

N5(EQN)1(aⁿX + bⁿY = cⁿ

)

1=2=3=

2=3=4=

(X=) –1

(Y=) 2

x – y + z = 2, x + y – z = 0, –x + y + z = 4

N5(EQN)2(aⁿX + bⁿY + cⁿZ = dⁿ

)

Math

1=-1=1=2=

1=1=-1=0=

-1=1=1= 4 =

(X=) 1

(Y=) 2

(Z=) 3

2x – 3x – 6 = 0

N5(EQN)3(aX²+ bX + c = 0)

2=-3=-6==

3 + 57

(X =)

3 – 57

(X =)

(X-Value Minimum=)*

(Y-Value Minimum=)*

–

* The local minimum value is displayed when aϾ0. The local maximum value

^{is displayed when}aꢀ0.

x –

x + 2 = 0

2 2

N5(EQN)3(aX²+ bX + c = 0)

1=-2!2)=2==

(X=)

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x – 2x – x + 2 = 0

N5(EQN)4(aX³+ bX²+ cX + d = 0)

1=-2=-1=2==

(X =) –1

(X =) 2

(X =) 1

Matrix Calculations (MATRIX)

Use the MATRIX Mode to perform calculations involving matrices of up to 3

rows by 3 columns. To perform a matrix calculation, you first assign data to

special matrix variables (MatA, MatB, MatC), and then use the variables in

the calculation as shown in the example below.

2 –1

–1 2

2 1

1 1

To assign

to MatA and

to MatB, and then perform

2 1

1 1

2 –1

–1 2

the following calculations:

(MatA×MatB),

2 1

1 1

2 –1

–1 2

(MatA+MatB)

1. Press N6(MATRIX) to enter the MATRIX Mode.

2. Press 1(MatA)5(2×2).

MAT

• This will display the Matrix Editor for input

of the elements of the 2 × 2 matrix you

specified for MatA.

“A” stands for “MatA”.

3. Input the elements of MatA: 2=1=1=1=.

4. Perform the following key operation: 1 4 (MATRIX)2 (Data)

2(MatB)5(2×2).

• This will display the Matrix Editor for input of the elements of the 2 × 2

matrix you specified for MatB.

5. Input the elements of MatB: 2=-1=-1=2=.

6. Press A to advance to the calculation screen, and perform the first

calculation (MatA×MatB): 14(MATRIX)3(MatA)*14(MATRIX)

4(MatB)=.

• This will display the MatAns screen with the calculation results.

MAT

“Ans” stands for

“MatAns”.

→

Note: “MatAns” stands for “Matrix Answer Memory”. See “Matrix Answer

Memory” for more information.

7. Perform the next calculation (MatA+MatB): A 1 4 (MATRIX)

3(MatA)+14(MATRIX)4(MatB)=.

MAT

→

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Matrix Answer Memory

Whenever the result of a calculation executed in the MATRIX Mode is a

matrix, the MatAns screen will appear with the result. The result also will be

assigned to a variable named “MatAns”.

The MatAns variable can be used in calculations as described below.

• To insert the MatAns variable into a calculation, perform the following

key operation: 14(MATRIX)6(MatAns).

• Pressing any one of the following keys while the MatAns screen is

displayed will switch automatically to the calculation screen: +, -, *,

^{/, E, w, 1w(}x ). The calculation screen will show the MatAns

variable followed by the operator or function for the key you pressed.

Assigning and Editing Matrix Variable Data

Important: The following operations are not supported by the Matrix Editor:

m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements also

cannot be input with the Matrix Editor.

To assign new data to a matrix variable:

1. Press 14(MATRIX)1(Dim), and then, on the menu that appears,

select the matrix variable to which you want to assign data.

^{2. On the next menu that appears, select dimension (}m×n).

3. Use the Matrix Editor that appears to input the elements of the matrix.

1 0 –1

0 –1 1

To assign

to MatC

MAT

14(MATRIX)

1(Dim)3(MatC)4(2×3)

1=0=-1=0=-1=1=

To edit the elements of a matrix variable:

1. Press 14(MATRIX)2(Data), and then, on the menu that appears,

select the matrix variable you want to edit.

2. Use the Matrix Editor that appears to edit the elements of the matrix.

• Move the cursor to the cell that contains the element you want to change,

input the new value, and then press =.

To copy matrix variable (or MatAns) contents:

1. Use the Matrix Editor to display the matrix you want to copy.

• If you want to copy MatA, for example, perform the following key

operation: 14(MATRIX)2(Data)1(MatA).

• If you want to copy MatAns contents, perform the following to display the

MatAns screen: A14(MATRIX)6(MatAns)=.

2. Press 1t(STO), and then perform one of the following key operations

to specify the copy destination: -(MatA), $(MatB), or w(MatC).

• This will display the Matrix Editor with the contents of the copy

destination.

Matrix Calculation Examples

2 1

1 1

2 –1

–1 2

The following examples use MatA =

1 0 –1

and MatB =

from

and MatC =

from

. You can input a matrix variable into a key

0 –1 1

operation by pressing 14(MATRIX) and then pressing one of the

following number keys: 3(MatA), 4(MatB), 5(MatC).

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3 × MatA (Matrix scalar multiplication).

A3*MatA=

Obtain the determinant of MatA (det(MatA)).

A14(MATRIX)7(det) MatA)=

Obtain the transposition of MatC (Trn(MatC)).

A14(MATRIX)8(Trn) MatC)=

Obtain the inverse matrix of MatA (MatA^–1).

Note: You cannot use 6 for this input. Use the E key to input “^–1”.

AMatAE=

Obtain the absolute value of each element of MatB (Abs(MatB)).

A1w(Abs) MatB)=

Determine the square and cube of MatA (MatA², MatA³).

Note: You cannot use 6 for this input. Use w to specify squaring, and

^1w(x ) to specify cubing.

AMatAw=

^AMatA1w(x )=

Determine the MatA=

row echelon form.

A!4(MATRIX)c1(Ref)MatA)=

Determine the MatA=

reduced row echelon form.

A!4(MATRIX)c2(Rref)MatA)=

Creating a Number Table from Two

Functions (TABLE)

TABLE generates a number table based on one or two functions. You can

^{use the function}f(x) or the two functions f(x) and g(x). See “Configuring the

Calculator Setup” for more information.

Perform the following steps to generate a number table.

1. Press N7(TABLE) to enter the TABLE Mode.

^{2. Use the X variable to input two functions, one in the format}f(x) and the

^{other in the format}g(x).

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• Be sure to input the X variable (S)(X)) when generating a number

table. Any variable other than X is handled as a constant.

^{• If you are using a single function, input a function in the format}f(x)

only.

^{• The following cannot be used in the function: Pol, Rec, ∫,}d/dx, Σ, Π.

3. In response to the prompts that appear, input the values you want to use,

pressing = after each one.

For this prompt: Input this:

Start?

End?

Input the lower limit of X (Default = 1).

Input the upper limit of X (Default = 5).

Note: Make sure that the End value is always

greater than the Start value.

Step?

Input the increment step (Default = 1).

Note: The Step specifies by how much the Start

value should be sequentially incremented as the

number table is generated. If you specify Start = 1

and Step = 1, X sequentially will be assigned the

values 1, 2, 3, 4, and so on to generate the number

table until the End value is reached.

• Inputting the Step value and pressing = generates and displays the

number table in accordance with the parameters you specified.

• Pressing A while the number table screen is displayed will return to

the function input screen in step 2.

( ) =

f x

To generate a number table for the functions

and

g(x) = x −

for the range –1 ꢁ x ꢁ 1, incremented in steps of 0.5

Math

N7(TABLE)

Math

1N(SETUP)c5(TABLE)2(f(x),g(x))

S)(X)x+1'2

Math

^{• Pressing = without inputting anything for}g(x) will generate a number

^{table based on}f(x) only.

Math

S)(X)x-1'2

Math

=-1=1=0.5=

Note: • The maximum number of rows in the generated number table depends

on the setup menu table setting. Up to 30 rows are supported for the “f(x)”

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setting, while 20 rows are supported for the “f(x),g(x)” setting. • You can

use the number table screen for viewing values only. Table contents cannot

be edited. • The number table generation operation causes the contents of

variable X to be changed.

Important: The function you input for number table generation is deleted

whenever you display the setup menu in the TABLE Mode and switch between

Natural Display and Linear Display.

Vector Calculations (VECTOR)

Use the VECTOR Mode to perform 2-dimensional and 3-dimensional vector

calculations. To perform a vector calculation, you first assign data to special

vector variables (VctA, VctB, VctC), and then use the variables in the

calculation as shown in the example below.

To assign (1, 2) to VctA and (3, 4) to VctB, and then perform the

following calculation: (1, 2) + (3, 4)

1. Press N8(VECTOR) to enter the VECTOR Mode.

2. Press 1(VctA)2(2).

VCT

• This will display the Vector Editor for input

of the 2-dimensional vector for VctA.

“A” stands for “VctA”.

3. Input the elements of VctA: 1=2=.

4. Perform the following key operation: 1 5 (VECTOR)2 (Data)

2(VctB)2(2).

• This will display the Vector Editor for input of the 2-dimensional vector

for VctB.

5. Input the elements of VctB: 3=4=.

6. Press A to advance to the calculation screen, and perform the calculation

(VctA + VctB): 1 5 (VECTOR)3 (VctA)+ 1 5 (VECTOR)

4(VctB)=.

• This will display the VctAns screen with the calculation results.

VCT

“Ans” stands for

“VctAns”.

→

Note: “VctAns” stands for “Vector Answer Memory”. See “Vector Answer

Memory” for more information.

Vector Answer Memory

Whenever the result of a calculation executed in the VECTOR Mode is a

vector, the VctAns screen will appear with the result. The result also will be

assigned to a variable named “VctAns”.

The VctAns variable can be used in calculations as described below.

• To insert the VctAns variable into a calculation, perform the following key

operation: 15(VECTOR)6(VctAns).

• Pressing any one of the following keys while the VctAns screen is displayed

will switch automatically to the calculation screen: +, -, *, /. The

calculation screen will show the VctAns variable followed by the operator

for the key you pressed.

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Assigning and Editing Vector Variable Data

Important: The following operations are not supported by the Vector Editor:

m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements also

cannot be input with the Vector Editor.

To assign new data to a vector variable:

1. Press 15(VECTOR)1(Dim), and then, on the menu that appears,

select the vector variable to which you want to assign data.

^{2. On the next menu that appears, select dimension (}m).

3. Use the Vector Editor that appears to input the elements of the vector.

To assign (2, –1, 2) to VctC

VCT

15(VECTOR)1(Dim)3(VctC)1(3)

2=-1=2=

To edit the elements of a vector variable:

1. Press 15(VECTOR)2(Data), and then, on the menu that appears,

select the vector variable you want to edit.

2. Use the Vector Editor that appears to edit the elements of the vector.

• Move the cursor to the cell that contains the element you want to change,

input the new value, and then press =.

To copy vector variable (or VctAns) contents:

1. Use the Vector Editor to display the vector you want to copy.

• If you want to copy VctA, for example, perform the following key operation:

15(VECTOR)2(Data)1(VctA).

• If you want to copy VctAns contents, perform the following to display the

VctAns screen: A15(VECTOR)6(VctAns)=.

2. Press 1t(STO), and then perform one of the following key operations

to specify the copy destination: -(VctA), $(VctB), or w(VctC).

• This will display the Vector Editor with the contents of the copy

destination.

Vector Calculation Examples

The following examples use VctA = (1, 2) and VctB = (3, 4) from

, and VctC =

(2, –1, 2) from

. You can input a vector variable into a key operation by

pressing 15(VECTOR) and then pressing one of the following number

keys: 3(VctA), 4(VctB), 5(VctC).

3 × VctA (Vector scalar multiplication), 3 × VctA – VctB (Calculation

example using VctAns)

VCT

A3*VctA=

VCT

-VctB=

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VctA • VctB (Vector dot product)

VCT

AVctA15(VECTOR)7(Dot)VctB=

VctA × VctB (Vector cross product)

AVctA*VctB=

Obtain the absolute values of VctC.

A1w(Abs)VctC)=

Determine the angle formed by VctA and VctB to three decimal

places (Fix 3). v

•

(A B)

^(cosꢀ =

, which becomes ꢀ = cos^–1

)

A B

Խ ԽԽ Խ

1N(SETUP)6(Fix)3

A(VctA15(VECTOR)7(Dot)VctB)/

VCT

FIX

(1w(Abs)VctA)1w(Abs)

VctB))=

1c(cos^–1)G)=

Inequality Calculations (INEQ)

You can use the following procedure to solve a quadratic inequality or cubic

inequality.

1. Press Nc1(INEQ) to enter the INEQ Mode.

2. On the menu that appears, select an inequality type.

To select this inequality type:

Press this key:

1(aX²+ bX + c )

2(aX³+ bX²+ cX + d )

Quadratic inequality

Cubic inequality

3. On the menu that appears, use keys 1 through 4 to select the inequality

symbol type and orientation.

4. Use the Coefficient Editor that appears to input coefficient values.

^{• To solve}x + 2x – 3 < 0, for example, input the coefficients a = 1, b = 2,

c = –3 by pressing 1=2=-3=.

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• To change a coefficient value you already have input, move the cursor

to the appropriate cell, input the new value, and then press =.

• Pressing A will clear all of the coefficients to zero.

Note: The following operations are not supported by the Coefficient Editor:

m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements also

cannot be input with the Coefficient Editor.

5. After all the values are the way you want, press =.

• This will display the solutions.

• To return to the Coefficient Editor while the solutions are displayed, press

Note: Values cannot be converted to engineering notation on the solution

screen.

Changing the Inequality Type

Press Nc1(INEQ) and then select an inequality type from the menu

that appears. Changing the inequality type causes the values of all Coefficient

Editor coefficients to change to zero.

INEQ Mode Calculation Examples

x + 2x – 3 < 0

Nc1(INEQ)1(aX²+ bX + c)

2(aX²+ bX + c < 0)

1=2=-3=

Math

x + 2x – 3 м 0

Math

Nc1(INEQ)1(aX²+ bX + c)

3(aX²+ bX + c м 0)

1=2=-3=

Note: Solutions are displayed as shown

here when Linear Display is selected.

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2x − 3x м 0

Math

Nc1(INEQ)2(aX³+ bX²+ cX + d)

3(aX³+ bX²+ cX + d м 0)

2=-3=

3x + 3x – x Ͼ 0

Math

Nc1(INEQ)2(aX³+ bX²+ cX + d)

1(aX³+ bX²+ cX + d Ͼ 0)

3=3=-1=

eee

Note: Solutions are displayed as shown

here when Linear Display is selected.

Special Solution Display

• “All Real Numbers” appears on the solution screen when the solution of an

inequality is all numbers.

x м 0

Math

Nc1(INEQ)1(aX²+ bX + c)

3(aX²+ bX + c м 0)

1=0=0==

• “No-Solution” appears on the solution screen when no solution exists for

an inequality (such as X²< 0).

Using VERIFY (VERIF)

VERIFY is a function you can use to verify whether an input equality or

inequality is true (indicated by TRUE) or false (indicated by FALSE). The

following shows the general procedure for using VERIFY.

To verify whether 4

= 12 is true

1. Press Nc2(VERIF) to enter the VERIFY Mode.

Math

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2. Input 4

= 12.

4!9e16(VERIFY)1(=)12

• You can select the equality symbol or

inequality symbol from the menu that

appears when you press 16(VERIFY).

Math

3. To verify, press =.

You can input the following expressions for verification in the VERIFY

Mode.

• Equalities or inequalities that include one relational operator 4 =

4 ꢂ 3, π Ͼ 3, 1 + 2 ꢁ 5, (3 × 6) ꢀ (2 + 6) × 2, etc.

• Equalities or inequalities that include multiple relational operators 1 ꢁ 1 ꢀ

1 + 1, 3 ꢀ π ꢀ 4, 2²= 2 + 2 = 4, 2 + 2 = 4 ꢀ 6, 2 + 3 = 5 ꢂ 2 + 5 = 8, etc.

Note: • The verification result will cause 1 to be assigned to Ans memory

when TRUE and 0 when FALSE. • The input expression can be a total of

99 bytes, including the left side, right side, and relational operators. • Any

variable (A, B, C, D, E, F, X, Y, M) input into an expression is treated as a

value, using the value currently assigned to the variable. • ÷R, Pol and Rec

functions cannot be used in an expression.

In the VERIFY Mode, the calculator performs a mathematical operation

on the input expression and then displays TRUE or FALSE based on the

result. Because of this, calculation error can occur or a mathematically

correct result may not be able to be displayed when the input calculation

expression includes calculation that approaches the singular point or

inflection point of a function, or when the input expression contains multiple

calculation operations.

Expression Input Precautions

The following types of expressions cause a Syntax ERROR and cannot

be verified.

• An expression with nothing on the left side or right side (Example: = 5')

• An expression in which a relational operator is inside of a fraction or function

1 = 1

(Example:

, cos (8 ꢁ 9))

• An expression in which a relational operator is enclosed in parentheses

(Example: 8 ꢀ (9 ꢀ 10))

• An expression in which multiple relational operators that are not oriented

in the same direction (Example: 5 ꢁ 6 м 4)

• An expression that contains two of the following operators in any combination

(Example: 4 ꢀ 6 ꢂ 8)

• An expression that contains consecutive relational operators

(Example: 5 м Ͼ 9)

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VERIFY Mode Calculation Examples

To verify log2 ꢀ log3 ꢀ log4

l2)16(VERIFY)4(ꢀ)

l3)16(VERIFY)4(ꢀ)

l4)=

To verify 0 ꢀ

–

( )

016(VERIFY)4(ꢀ)

8'9ew-8'9=

To verify 5²= 25 =

625

5w16(VERIFY)1(=)

2516(VERIFY)1(=)!625=

Distribution Calculations (DIST)

You can use the procedures below to perform seven different types of

distribution calculations.

1. Press Nc3(DIST) to enter the DIST Mode.

2. On the menu that appears, select a distribution calculation type.

To select this type of calculation:

Normal probability density

Press this key:

1(Normal PD)

Normal cumulative distribution

Inverse normal cumulative distribution

Binomial probability

2(Normal CD)

3(Inverse Normal)

4(Binomial PD)

c1(Binomial CD)

c2(Poisson PD)

c3(Poisson CD)

Binomial cumulative distribution

Poisson probability

Poisson cumulative distribution

3. Input values for the variables.

• With Binomial PD, Binomial CD, Poisson PD, and Poisson CD, you can

input sample data and then perform calculations.

4. After inputting values for all of the variables, press =.

• This displays the calculation results.

• Pressing = or A while a calculation result is displayed will return to

the input screen of the first variable

Note: • To change the distribution calculation type after you enter the DIST

Mode, press !1(STAT/DIST)1(Type) and then select the distribution

type you want. • Distribution calculation accuracy is up to five significant

digits.

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Variables that Accept Input

The following are distribution calculation variables that accept input values.

^{Normal PD...........................}x, σ, ꢁ

Normal CD........................... Lower, Upper, σ, ꢁ

Inverse Normal .................... Area, σ, ꢁ (Tail setting always left.)

^{Binomial PD, Binomial CD...}x (or List), N, p

^{Poisson PD, Poisson CD.....}x (or List), ꢁ

x: data, σ: standard deviation (σ Ͼ 0), ꢁ: mean, Lower: lower boundary, Upper:

upper boundary, Tail: probability value tail specification, Area: probability

value (0 ꢁ Area ꢁ 1), List: sample data list, N: number of trials, p: success

probability (0 ꢁ p ꢁ 1)

List Screen (Binomial PD, Binomial CD, Poisson PD,

Poisson CD)

With Binomial PD, Binomial CD, Poisson PD, and Poisson CD, use the List

Screen for sample data input. You can input up to 25 data samples for each

variable. Calculation results are also displayed on the List Screen.

Distribution calculation type

Value at current cursor position

X: Sample data Ans: Calculation results

To edit sample data: Move the cursor to the cell that contains the sample

data you want to edit, input the new sample data, and then press =.

To delete sample data: Move the cursor to the sample data you want to

delete and then press D.

To insert sample data: Move the cursor to the position where you want to

insert the sample data, press !1(STAT/DIST)2(Edit)1(Ins), and

then input the sample data.

To delete all sample data: Press !1(STAT/DIST)2(Edit)2(Del-A).

DIST Mode Calculation Examples

To calculate the normal probability density when x=36, σ=2, ꢁ=35

Nc3(DIST)

1(Normal PD)

36=

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35=

Result: 0.1760326634

^{• Pressing = or A returns to the}x input screen.

To calculate binomial probability for the sample data {10, 11, 12, 13,

14} when N=15 and p=0.6

Nc3(DIST)4(Binomial PD)

Display the List Screen:

1(List)

• To specify data using parameter format, press 2(Var).

10=11=12=13=14=

15=

0.6=

ecccc

^Results:x = binomial probability of 10 Լ 0.18594

x = binomial probability of 11 Լ 0.12678

x = binomial probability of 12 Լ 0.063388

x = binomial probability of 13 Լ 0.021942

x = binomial probability of 14 Լ 4.7018 × 10⁻³

• Pressing = returns to the N input screen. Pressing A returns to the List

Screen (input data samples are stored).

Note • The following cannot be used in the distribution calculations:

^{Pol, Rec, ÷R, ∫,}d/dx. • When data is specified using parameter format,

calculation results are stored in Ans memory. • An error message appears

if the input value is outside the allowable range. “ERROR” will appear in the

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Ans column of the List Screen when the value input for the corresponding

sample data is outside the allowable range.

Scientific Constants

Your calculator comes with 40 built-in scientific constants that can be used in

any mode besides BASE-N. Each scientific constant is displayed as a unique

symbol (such as π), which can be used inside of calculations.

To input a scientific constant into a calculation, press 17(CONST) and

then input the two-digit number that corresponds to the constant you want.

To input the scientific constant C⁰(speed of light in a vacuum), and

display its value

A17(CONST)

Math

28(C⁰)=

To calculate C⁰

₀μ₀

Math

A'1c!17(CONST)32(ε⁰

)

^17(CONST)33(ꢁ⁰)=

The following shows the two-digit numbers for each of the scientific

constants.

01: (mp) proton mass

03: (me) electron mass

05: (a⁰) Bohr radius

02: (mn) neutron mass

^{04: (m}ꢁ) muon mass

06: (h) Planck constant

08: (ꢁB) Bohr magneton

^{07: (}ꢁN) nuclear magneton

09: (h) Planck constant,

10: (α) fine-structure constant

rationalized

11: (re) classical electron radius

12: (λc) Compton wavelength

14: (λcp) proton Compton

13: (γp) proton gyromagnetic ratio

wavelength

15: (λcn) neutron Compton

16: (R∞) Rydberg constant

wavelength

^{18: (}ꢁp) proton magnetic

17: (u) atomic mass constant

moment

20: (ꢁn) neutron magnetic

^{19: (}ꢁe) electron magnetic moment

^{21: (}ꢁꢁ) muon magnetic moment

moment

22: (F) Faraday constant

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23: (e) elementary charge

25: (k) Boltzmann constant

27: (R) molar gas constant

29: (C¹) first radiation constant

24: (NA) Avogadro constant

26: (Vm) molar volume of ideal

gas (273.15K, 100kPa)

28: (C⁰) speed of light in vacuum

30: (C²) second radiation

constant

31: (σ) Stefan-Boltzmann constant 32: (ε⁰) electric constant

34: (φ⁰) magnetic flux quantum

^{33: (}ꢁ⁰) magnetic constant

35: (g) standard acceleration of

36: (G⁰) conductance quantum

gravity

37: (Z⁰) characteristic impedance of

38: (t) Celsius temperature

vacuum

39: (G) Newtonian constant of

40: (atm) standard atmosphere

gravitation

The values are based on CODATA (2010) recommended values.

Metric Conversion

The calculator’s built-in metric conversion commands make it simple to

convert values from one unit to another. You can use the metric conversion

commands in any calculation mode except for BASE-N and TABLE.

To input a metric conversion command into a calculation, press

18(CONV) and then input the two-digit number that corresponds to

the command you want.

To convert 5 cm into inches

A518(CONV)

02(cm'in)=

To convert 100 g into ounces

A10018(CONV)22(g'oz)=

To convert –31°C into Fahrenheit

A-3118(CONV)38(°C'°F)=

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The following shows the two-digit numbers for each of the metric conversion

commands.

01: in'cm

05: yd'm

02: cm'in

06: m'yd

03: ft'm

04: m'ft

07: mile'km

11: acre'm²

08: km'mile

12: m²'acre

09: n mile'm

10: m'n mile

13: gal (US)'R 14: R'gal (US) 15: gal (UK)'R 16: R'gal (UK)

17: pc'km

21: oz'g

18: km'pc

22: g'oz

19: km/h'm/s

23: lb'kg

20: m/s'km/h

24: kg'lb

25: atm'Pa

29: hp'kW

33: kgf • m'J

37: °F'°C

26: Pa'atm

30: kW'hp

34: J'kgf • m

38: °C'°F

27: mmHg'Pa 28: Pa'mmHg

31: kgf/cm²'Pa 32: Pa'kgf/cm²

35: lbf/in²'kPa 36: kPa'lbf/in²

39: J'cal

40: cal'J

Conversion formula data is based on the “NIST Special Publication 811

(1995)”.

Note: The J'cal command performs conversion for values at a temperature

of 15°C.

Calculation Ranges, Number of Digits,

and Precision

The calculation range, number of digits used for internal calculation, and

calculation precision depend on the type of calculation you are performing.

Calculation Range and Precision

Calculation Range

1 × 10^–99to 9.999999999 × 10⁹⁹or 0

Number of Digits for Internal

Calculation

15 digits

In general, 1 at the 10th digit for a single

calculation. Precision for exponential

display is 1 at the least significant digit.

Errors are cumulative in the case of

consecutive calculations.

Precision

Function Calculation Input Ranges and Precision

Functions

Input Range

0 ꢁ |x| ꢀ 9 × 10⁹

DEG

RAD

GRA

DEG

RAD

GRA

DEG

RAD

GRA

^sinx

0 ꢁ |x| ꢀ 157079632.7

0 ꢁ |x| ꢀ 1 × 10¹⁰

0 ꢁ |x| ꢀ 9 × 10⁹

cosx

tanx

0 ꢁ |x| ꢀ 157079632.7

0 ꢁ |x| ꢀ 1 × 10¹⁰

^{Same as sin}x, except when |x| = (2n–1) × 90.

^{Same as sin}x, except when |x| = (2n–1) × π/2.

^{Same as sin}x, except when |x| = (2n–1) × 100.

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sin^–1x

0 ꢁ |x| ꢁ 1

0 ꢁ |x| ꢁ 9.999999999 × 10⁹⁹

^cos^–1x

tan^–1x

sinhx

0 ꢁ |x| ꢁ 230.2585092

^coshx

sinh^–1x

0 ꢁ |x| ꢁ 4.999999999 × 10⁹⁹

1 ꢁ x ꢁ 4.999999999 × 10⁹⁹

0 ꢁ |x| ꢁ 9.999999999 × 10⁹⁹

0 ꢁ |x| ꢁ 9.999999999 × 10^–1

0 ꢀ x ꢁ 9.999999999 × 10⁹⁹

–9.999999999 × 10⁹⁹ꢁ x ꢁ 99.99999999

–9.999999999 × 10⁹⁹ꢁ x ꢁ 230.2585092

0 ꢁ x ꢀ 1 × 10¹⁰⁰

cosh^–1x

tanhx

tanh^–1x

logx/lnx

10^x

e^x

^'x

|x| ꢀ 1 × 10⁵⁰

–1

|x| ꢀ 1 × 10¹⁰⁰; x G 0

|x| ꢀ 1 × 10¹⁰⁰

^{0 ꢁ}x ꢁ 69 (x is an integer)

^{0 ꢁ}n ꢀ 1 × 10¹⁰, 0 ꢁ r ꢁ n (n, r are integers)

1 ꢁ {n!/(n–r)!} ꢀ 1 × 10¹⁰⁰

nPr

^{0 ꢁ}n ꢀ 1 × 10¹⁰, 0 ꢁ r ꢁ n (n, r are integers)

1 ꢁ n!/r! ꢀ 1 × 10¹⁰⁰or 1 ꢁ n!/(n–r)! ꢀ 1 × 10¹⁰⁰

nCr

|x|, |y| ꢁ 9.999999999 × 10⁹⁹

Pol(x, y)

Rec(r, ꢀ)

x y

ꢁ 9.999999999 × 10⁹⁹

^{0 ꢁ}r ꢁ 9.999999999 × 10⁹⁹

ꢀ: Same as sinx

|a|, b, c ꢀ 1 × 10¹⁰⁰; 0 ꢁ b, c

The display seconds value is subject to an error of ȗ1 at

the second decimal place.

°’ ”

|x| ꢀ 1 × 10¹⁰⁰

Decimal ↔ Sexagesimal Conversions

0°0´0˝ ꢁ |x| ꢁ 9999999°59´59˝

x Ͼ 0: –1 × 10¹⁰⁰ꢀ ylogx ꢀ 100

x = 0: y Ͼ 0

x^y

x ꢀ 0: y = n,

(m, n are integers)

2 +1

However: –1 × 10¹⁰⁰ꢀ ylog |x| ꢀ 100

y ^{Ͼ 0:}x G 0, –1 × 10¹⁰⁰ꢀ 1/x logy ꢀ 100

y = 0: x Ͼ 0

2 +1

y ꢀ 0: x = 2n+1,

(m G 0; m, n are integers)

However: –1 × 10¹⁰⁰ꢀ 1/x log |y| ꢀ 100

Total of integer, numerator, and denominator must be 10

digits or less (including division marks).

a^b/

| | | |

a ꢀ b; a , b ꢀ 1 × 10 ; b – a ꢀ 1 × 10

^RanInt#(a, b)

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• Precision is basically the same as that described under “Calculation Range

a_ynd_xPrecision”, above.

^•x , y^,', x!, nPr, nCr type functions require consecutive internal

calculation, which can cause accumulation of errors that occur with each

calculation.

• Error is cumulative and tends to be large in the vicinity of a function’s singular

point and inflection point.

• The range for calculation results that can be displayed in π form when using

Natural Display is |x| ꢀ 10⁶. Note, however, that internal calculation error

can make it impossible to display some calculation results in π form. It also

can cause calculation results that should be in decimal form to appear in

π form.

Errors

The calculator will display an error message whenever an error occurs for

any reason during a calculation. There are two ways to exit an error message

display: Pressing d or e to display the location of the error, or pressing

A to clear the message and calculation.

Displaying the Location of an Error

While an error message is displayed, press d or e to return to the

calculation screen. The cursor will be positioned at the location where

the error occurred, ready for input. Make the necessary corrections to the

calculation and execute it again.

When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2 =

Math

14/0*2=

Math

e (or d)

Math

d1=

Clearing the Error Message

While an error message is displayed, press A to return to the calculation

screen. Note that this also clears the calculation that contained the error.

Error Messages

Math ERROR

Cause: • The intermediate or final result of the calculation you are performing

exceeds the allowable calculation range. • Your input exceeds the allowable

input range (particularly when using functions). • The calculation you are

performing contains an illegal mathematical operation (such as division

by zero).

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Action: • Check the input values, reduce the number of digits, and try again.

• When using independent memory or a variable as the argument of a function,

make sure that the memory or variable value is within the allowable range

for the function.

Stack ERROR

Cause: • The calculation you are performing has caused the capacity of

the numeric stack or the command stack to be exceeded. • The calculation

you are performing has caused the capacity of the matrix or vector stack

to be exceeded.

Action: • Simplify the calculation expression so it does not exceed the

capacity of the stack. • Try splitting the calculation into two or more parts.

Syntax ERROR

Cause: There is a problem with the format of the calculation you are

performing.

Action: Make necessary corrections.

Argument ERROR

Cause: There is a problem with the argument of the calculation you are

performing.

Action: Make necessary corrections.

Dimension ERROR (MATRIX and VECTOR Modes only)

Cause: • The matrix or vector you are trying to use in a calculation was input

without specifying its dimension. • You are trying to perform a calculation with

matrices or vectors whose dimensions do not allow that type of calculation.

Action: • Specify the dimension of the matrix or vector and then perform

the calculation again. • Check the dimensions specified for the matrices or

vectors to see if they are compatible with the calculation.

Variable ERROR (SOLVE feature only)

Cause: • You did not specify a solution variable, and there is no X variable

in the equation you input. • The solution variable that you specified is not

included in the equation you input.

Action: • The equation you input must include an X variable when you do

not specify the solution variable. • Specify a variable that is included in the

equation you input as the solution variable.

Can’t Solve Error (SOLVE feature only)

Cause: The calculator could not obtain a solution.

Action: • Check for errors in the equation that you input. • Input a value

for the solution variable that is close to the expected solution and try again.

Insufficient MEM Error

Cause: An attempt to generate a number table in the TABLE Mode whose

conditions cause it to exceed the maximum number of allowable rows. The

maximum number of rows is 30 when “f(x)” is selected for the setup menu

table setting and 20 when “f(x),g(x)” is selected.

Action: Narrow the table calculation range by changing the Start, End, and

Step values, and try again.

Time Out Error

Cause: The current differential or integration calculation ends without the

ending condition being fulfilled. The current distribution calculation ends

without the ending condition being fulfilled.

tol value.

Action: Differential or integration calculation: Try increasing the

Note that this also decreases solution precision.

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Before Assuming Malfunction of the

Calculator...

Perform the following steps whenever an error occurs during a calculation

or when calculation results are not what you expected. If one step does not

correct the problem, move on to the next step.

Note that you should make separate copies of important data before

performing these steps.

1. Check the calculation expression to make sure that it does not contain any

errors.

2. Make sure that you are using the correct mode for the type of calculation

you are trying to perform.

3. If the above steps do not correct your problem, press the O key. This will

cause the calculator to perform a routine that checks whether calculation

functions are operating correctly. If the calculator discovers any abnormality,

it automatically initializes the calculation mode and clears memory contents.

For details about initialized settings, see “Configuring the Calculator

Setup”.

4. Initialize all modes and settings by performing the following operation:

19(CLR)1(Setup)=(Yes).

Replacing the Battery

A low battery is indicated by a dim display, even if contrast is adjusted, or by

failure of figures to appear on the display immediately after you turn on the

calculator. If this happens, replace the battery with a new one.

Important: Removing the battery will cause all of the calculator’s memory

contents to be deleted.

1. Press 1A(OFF) to turn off the calculator.

• To ensure that you do not accidentally turn on power while replacing the

battery, slide the hard case onto the front of the calculator.

Screw

2. Remove the cover as shown in the illustration and

replace the battery, taking care that its plus (+) and

minus (–) ends are facing correctly.

3. Replace the cover.

4. Initialize the calculator:

O19(CLR)3(All)=(Yes)

• Do not skip the above step!

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Specifications

Power Requirements:

Built-in solar cell; button battery LR44 (GPA76) × 1

Approximate Battery Life:

3 years (based on one hour of operation per day)

Operating Temperature: 0°C to 40°C (32°F to 104°F)

Dimensions: 11.1 (H) × 80 (W) × 162 (D) mm

⁸Љ (H) × 3¹/⁸Љ (W) × 6³/⁸Љ (D)

Approximate Weight: 95 g (3.4 oz) including the battery

Frequently Asked Questions

k How can I perform input and display results the same way I did on a

model that does not have Natural Textbook Display?

Perform the following key operation: 1N(SETUP)2(LineIO). See

“Configuring the Calculator Setup” on page E-5 for more information.

k How can I change a fraction form result to decimal form?

How can I change a fraction form result produced by a division

operation to decimal form?

See “Toggling Calculation Results” on page E-14 for the procedure.

k What is the difference between Ans memory, PreAns memory,

independent memory, and variable memory?

Each of these types of memory acts like “containers” for temporary storage

of a single value.

Ans Memory: Stores the result of the last calculation performed. Use this

memory to carry the result of one calculation on to the next.

PreAns Memory: Stores the result of calculation before the last one.

PreAns memory can be used only in the COMP Mode.

Independent Memory: Use this memory to totalize the results of multiple

calculations.

Variables: This memory is helpful when you need to uses the same value

multiple times in one or more calculations.

k What is the key operation to take me from the STAT Mode or TABLE

Mode to a mode where I can perform arithmetic calculations?

Press N1(COMP).

k How can I return the calculator to its initial default settings?

Perform the following operation: 19(CLR)1(Setup)=(Yes)

k When I execute a function calculation, why do I get a calculation result

that is completely different from older CASIO calculator models?

With a Natural Textbook Display model, the argument of a function that

uses parentheses must be followed by a closing parenthesis. Failing to

press )after the argument to close the parentheses may cause unwanted

values or expressions to be included as part of the argument.

Example: (sin 30) + 15 v

Older (S-VPAM) Model:

s30+15= 15.5

Natural Textbook Display Model: b s30)+15= 15.5

Failure to press ) here as shown below will result in calculation of sin 45.

s30+15= 0.7071067812

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CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome

Shibuya-ku, Tokyo 151-8543, Japan

SA1111-A

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