high-powerera

1. Casio Fx-991es Plus Manual Standard Deviation
2. Casio 991es Calculator Manual

Difference between Casio fx-991es plus and fx-115es plus?

I bought a Casio fx-991es Plus back in high school, when I was taking Math 31. I bought this model because I read it was virtually identical to the Faculty of Engineering approved Casio fx-115es plus. Apparently the model number is different, but the calculator is identical?

Now that I'm taking STAT 151, looks like I need to get an approved non-programmable calculator for the exams, and get a gold sticker on it. Does anyone know if my Casio FX-991ES Plus calculator would still be approved? I'd honestly prefer not to spend another $24 for a new calculator.

E

fx-115ESfx-991ES

User's Guide

http://world.casio.com/edu/

RCA502160-001V01

CASIO Europe GmbH

Bornbarch 10, 22848 Norderstedt, Germany

About this Manual

•The MATH mark indicates an example that uses Math format, while theLINE mark indicates Linear format. For details about input/output formats, see “Specifying the Input/Output Format”.

•Keycap markings indicate what a key inputs or what function it performs.

Example: 1,2,+,-,!,A, etc.

•Pressing the 1orSkey followed by a second key performs the alternate function of the second key. The alternate function is indicated by the text printed above the key.

Alternate function

sin–1{D}

Keycap function s

•The following shows what the different colors of the alternate function key text mean.

•The following shows an example of how an alternate function operation is represented in this User’s Guide.

Example: 1s(sin–1)1=

Indicates the function that is accessed by the key operation (1s) before it. Note that this is not part of the actual key operation you perform.

•The following shows an example of how a key operation to select an on-screenmenu item is represented in this User’s Guide.

Example: 1(Setup)

Indicates the menu item that is selected by the number key operation (1) before it. Note that this is not part of the actual key operation you perform.

•The cursor key is marked with four arrows, indicating direction, as shown in the

•The displays and illustrations (such as key markings) shown in this User’s Guide and the separate Appendix 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.

kUsing the Separate Appendix

Whenever you see the symbol Appendix in this manual, it means you should refer to the separate Appendix.

Example numbers (like “<#021>”) in this User’s Guide refer to the corresponding example number in the Appendix.

Specify the angle unit in accordance with the marks in the Appendix:

Deg : Specify Degree for the angle unit.

Rad : Specify Radian for the angle unit.

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.

19(CLR)3(All)=(Yes)

•For information about calculation modes and setup settings, see “Calculation Modes and Calculator Setup”.

•For information about memory, see “Using Calculator Memory”.

Safety Precautions

Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference.

Caution

This symbol is used to indicate information that can result in personal injury or material damage if ignored.

Battery

•After removing the battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed.

•Keep batteries out of the reach of small children. If accidentally swallowed, consult with a physician immediately.

•Never charge the battery, try to take the battery apart, or allow the battery to become shorted. Never expose the battery to direct heat or dispose of it by incineration.

•Improperly using a battery can cause it to leak and damage nearby items, and can create the risk of fire and personal injury.

•Always make sure that the battery’s positive kand negativel ends are facing correctly when you load it into the calculator.

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

Disposing of the Calculator

•Never dispose of the calculator by burning it. Doing so can cause certain components to suddenly burst, creating the risk of fire and personal injury.

Handling Precautions

•Be sure to press the Okey before using the calculator for the first time.

•Even if the calculator is operating normally, replace the battery at least once every three years.

A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator.

•The battery that comes with this unit discharges slightly during shipment and storage. Because of this, it may require replacement sooner than the normal expected battery life.

•Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data.

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

Very low temperatures can cause slow display response, total failure of the display, and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might be exposed to very high temperatures. Heat can cause discoloration or deformation of the calculator’s case, and damage to internal circuitry.

•Avoid use and storage of the calculator in areas subjected to large amounts of humidity and dust.

Take care never to leave the calculator where it might be splashed by water or exposed to large amounts of humidity or dust. Such conditions can damage internal circuitry.

•Never drop the calculator or otherwise subject it to strong impact.

•Never twist or bend the calculator.

Avoid carrying the calculator in the pocket of your trousers or other tight-fittingclothing where it might be subjected to twisting or bending.

•Never try to take the calculator apart.

•Never press the keys of the calculator with a ballpoint pen or other pointed object.

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

If the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent. Wring out all excess liquid before wiping the calculator. Never use thinner, benzene or other volatile agents to clean the calculator. Doing so can remove printed markings and can damage the case.

Before Using the Calculator

kRemoving 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 below.

kTurning Power On and Off

•Press Oto turn on the calculator.

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

kAdjusting Display Contrast

1N(SETUP)c6(]CONT')

This displays the contrast adjustment screen. Use d ande to adjust display contrast. After the setting is the way you want, press

A.

•You can also adjust contrast using d ande while the mode menu (which appears when you pressN) is on the display.

Important!

•If adjusting display contrast does not improve display readability, it probably means that battery power is low. Replace the battery.

Important!

•For a very complex calculation or some other 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.

Calculation Modes and

Calculator Setup

kCalculation Modes

Specifying the Calculation Mode

(1)Press Nto display the mode menu.

(2)Press the number key that corresponds to the mode you want to select.

• To select the CMPLX Mode, for example, press 2.

kConfiguring the Calculator Setup

Pressing 1N(SETUP) displays the setup menu, which you can use to control how the calculations are executed and displayed. The setup menu has two screens, which you can jump between usingcandf.

c

f

•See “Adjusting Display Contrast” for information about how to use “]CONT'”.

Specifying the Input/Output Format

•Math format causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper.

•Linear format causes fractions and other expressions to be displayed in a single line.

Math

Calculation Result Display Examples

•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: 100 ÷ 7 = 14.286 (Fix3)

14.29(Fix2)

•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: 1 ÷ 7 = 1.4286 × 10–1(Sci5) 1.429 ×10–1(Sci4)

•Norm: Selecting one of the two available settings (Norm1, Norm2) determines the range in which results will be displayed in nonexponential format. Outside the specified range, results are displayed using exponential format.

Norm1: 10–2>x ,x >1010

Norm2: 10–9>x ,x >1010

Specifying the Fraction Display Format

Specifying the Complex Number Display Format

Specifying the Statistical Display Format

Use the following procedure to turn display of the frequency (FREQ) column of the STAT Mode STAT editor screen on or off.

Specifying the Decimal Point Display Format

•The setting you configure here is applied for calculation results only. The decimal point for input values is always a dot (.).

kInitializing the Calculation Mode and Other

Settings

Performing the following procedure initializes the calculation mode and other setup settings as shown below.

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

•To cancel initialization without doing anything, press A(Cancel) instead of=.

Inputting Expressions and

Values

kInputting a Calculation Expression Using

Standard Format

Your calculator lets you input calculation expressions just as they are written.Then simply press the =key to execute it.The calculator automatically judges the calculation priority sequence for addition, subtraction, multiplication, and division, functions, and parentheses.

Example: 2 (5 + 4) – 2 ×(–3)=

LINE

2(5+4)-

2*y3=

Inputting a Function with Parenthesis

When you input any of the functions shown below, it is automatically input with the open parenthesis (( ) character. Next, you need to input the argument and the closing parenthesis ()).

sin(, cos(, tan(, sin–1(,cos–1(,tan–1(,sinh(, cosh(, tanh(,sinh–1(,cosh–1(,tanh–1(,log(, ln(,e^(, 10^(,'(,3'(, Abs(, Pol(, Rec(,∫(,d/dx(,Σ(, P(, Q(, R(, arg(, Conjg(, Not(, Neg(, det(, Trn(, Rnd(

Example: sin 30 =

LINE

s30)=

Pressing sinputs “sin(”.

•Note that the input procedure is different if you want to use Math format. For more information, see “Inputting with Math Format”.

Omitting the Multiplication Sign

You can omit the multiplication sign (×) in any of the following cases.

•Before an open parentheses ((): 2× (5 + 4), etc.

•Before a function with parenthesis: 2 × sin(30), 2× '(3), etc.

•Before a prefix symbol (excluding the minus sign): 2 × h123, etc.

•Before a variable name, constant, or random number: 20 × A, 2× π, 2× i, etc.

Final Closed Parenthesis

You can omit one or more closed parentheses that come at the end of a calculation, immediately before the = key is pressed. For details, see “Omitting a Final Closed Parenthesis”.

Displaying a Long Expression

The display can show up to 14 characters at a time. Inputting the 15th character causes the expression to shift to the left. At this time, the ]indicator appears to the left of the expression, indicating that it runs off the left side of the screen.

Input expression: 1111 + 2222 + 3333 + 444

Math

Displayed portion:

Cursor

•When the ]indicator is displayed, you can scroll left and view the hidden part by pressing thedkey.This will cause the'indicator to appear to the right of the expression. At this time, you can use theekey to scroll back.

Number of Input Characters (Bytes)

•You can input up to 99 bytes of data for a single expression.

Basically, each key operation uses up one byte. A function that requires two key operations to input (like 1s(sin–1))also uses only one byte. Note, however, that when you are inputting functions with Math format, each item you input uses up more than one byte. For more information, see “Inputting with Math Format”.

•Normally the input cursor appears as a straight vertical (I) or horizontal () flashing line on the display screen. When there are 10 or fewer bytes of input remaining in the current expression, the cursor changes shape toI to let you know. If theI cursor appears, terminate the expression at a convenient point and calculate the result.

kCorrecting an Expression

This section explains how to correct an expression as you are inputting it. The procedure you should use depends on whether you have insert or overwrite selected as the input mode.

About the Insert and Overwrite Input Modes

With the insert mode, the displayed characters shift to the left to make room when you input a new character.With the overwrite mode, any new character you input replaces the character at the current cursor position.The initial default input mode is insert.You can change to the overwrite mode when you need it.

• The cursor is a vertical flashing line (I) when the insert mode is selected. The cursor is a horizontal flashing line ( ) when the overwrite mode is selected.

•The initial default for Linear format input is the insert mode. You can switch to the overwrite mode by pressing 1Y(INS).

•With Math format, you can only use the insert mode. Pressing 1Y(INS) when the Math format is selected does not switch to the overwrite mode. See “Incorporating a Value into a Function” for more information.

•The calculator automatically changes to the insert mode whenever you change the input/output format from Linear to Math.

Changing the Character or Function You Just Input

Example: To correct the expression 369 × 13 so it becomes 369 × 12

LINE

369*13

Y

2

Deleting a Character or Function

Example: To correct the expression 369 × × 12 so it becomes 369 × 12

LINE Insert Mode:

369**12

dd

Y

Overwrite Mode:

369**12

ddd

Y

Correcting a Calculation

Example: To correct cos(60) so it becomes sin(60)

LINE Insert Mode:

c60)

dddY

s

Overwrite Mode:

c60)

dddd

s

Inserting Input into a Calculation

Always use the insert mode for this operation. Use d ore to move the cursor to the location where you want to insert new input, and then input what you want.

kDisplaying the Location of an Error

If an error message (like “Math ERROR” or “Syntax ERROR”) appears when you press =, pressdore. This will display the part of the calculation where the error occurred, with the cursor positioned at the error location. You can then make necessary corrections.

Example: When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2 =

Use the insert mode for the following operation.

LINE

14/0*2=

Press e ord.

This is causing the error.

d1

=

You can also exit the error screen by pressing A, which clears the calculation.

kInputting with Math Format

When inputting with Math format, you can input and display fractions and some functions using the same format as they appear in your textbook.

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.

Functions and Symbols Supported for Math Format Input

•The “Bytes” column shows the number of bytes of memory that are used up by input.

Math Format Input Examples

•The following operations are all performed while Math format is selected.

•Pay close attention to the location and size of the cursor on the display when you input using Math format.

Example 1: To input 23 + 1

Math

e+3

•When you press = and obtain a calculation result using Math format, part of the expression you input can be cut off as shown in the Example 3 screen shot. If you need to view the entire input expression again, pressAand then presse.

Incorporating a Value into a Function

When using Math format, you can incorporate part of an input expression (a value, an expression within parentheses, etc.) into a function.

Example: To incorporate the expression inside of the parentheses of 1 + (2 + 3) + 4 into the'function

Move the cursor to here.

Math

1Y(INS)

This changes the shape of the cursor as shown here.

Math

!

This incorporates the expression in the parentheses into the function '.

•If the cursor is located left of a particular value or fraction (instead of an open parentheses), that value or fraction will be incorporated into the function specified here.

•If the cursor is located left of function, the entire function is incorporated into the function specified here.

The following examples show the other functions that can be used in the above procedure, and the required key operations to use them.

Original Expression:

Original Expression:

You can also incorporate values into the following functions. 1l($),1i(%), !, 6,1!(#),1w(Abs)

Displaying Calculation Results in a Form that Includes '2, π, etc. (Irrational Number Form)

When “MthIO” is selected for the input/output format, you can specify whether calculation results should be displayed in a form that includes expressions like '2 andπ (irrational number form).

•Pressing =after inputting a calculation displays the result using irrational number form.

•Pressing 1= after inputting a calculation displays the result using decimal values.

Note

•When “LineIO” is selected for the input/output format, calculation results are always displayed using decimal values (no irrational number form) regardless of whether you press =or1=.

•π form (form that includesπ within irrational number display) display conditions are the same as those forS-Dconversion. For details, see “UsingS-DTransformation”.

Example 1: '2 +'8 = 3'2

1 !2e+!8=

Math

2 !2e+!81=

•The following are the calculations for which ' form (form that includes' within irrational number display) results can be displayed.

a.Arithmetic calculations of values with square root symbol ('),x2,x3,x–1

b.Trigonometric function calculations

c.Complex number Abs calculations

d.CMPLX Mode polar coordinate display (r θ )

The following are the input value ranges for which 'form is always used for display of trigonometric calculation results.

Calculation results may be displayed in decimal form for input values outside of the above ranges.

k 'Form Calculation Range

Note

When performing complex number calculations in the CMPLX Mode, the following conditions apply respectively to both the real part and the imaginary part.

Results that include square root symbols can have up to two terms (an integer term is also counted as a term).

' form calculation results use display formats like those shown

below.

± a'b , ±d ±a'b, ±a'b ±d'e c f

E-18

The following shows the range for each of the coefficients (a,b,c,d,e,f).

1 <a < 100, 1 <b < 1000, 1<c < 100 0<d < 100, 0<e < 1000, 1<f < 100

Example:

The underlined areas in the above examples indicate what caused decimal form to be used.

Reasons why the results of the examples are displayed in decimal form

-Value outside of the allowable range

-More than two terms in the calculation result

•Calculation results displayed in 'form are reduced to a common denominator.

•c′ is the least common multiple ofc andf.

•Since calculation results are reduced to a common denominator, they are displayed in ' form even if coefficients (a′,c′, andd′) are outside the corresponding ranges of coefficients (a,c, andd).

Example: '3+ '2= 10'3 + 11'2

•The result is displayed in decimal form even when any intermediate result has three or more terms.

Example: (1 + '2 +'3 )(1 –'2 –'3 )(=–4– 2'6 )

=–8.898979486

•If a term is encountered during the calculation cannot be displayed as a root (') form or a fraction, the calculation result is displayed in decimal form.

Example: log3 + '2 = 1.891334817

This section explains how to perform arithmetic, fraction, percent, and sexagesimal calculations.

All calculations in this section are performed in the COMP Mode (N1).

k Arithmetic Calculations

Use the +,-,*, and/keys to perform arithmetic calculations.

Example: 7 × 8 – 4 × 5 = 36

LINE

7*8-4*5=

•The calculator automatically judges the calculation priority sequence. For more information, see “Calculation Priority Sequence”.

Number of Decimal Places and Number of Significant Digits

You can specify a fixed number of decimal places and significant digits for the calculation result.

Example: 1 ÷ 6 =

LINE

Initial default setting (Norm1)

FIX

3 decimal places (Fix3)

SCI

3 significant digits (Sci3)

• For more information, see “Specifying the Number of Display Digits”.

Omitting a Final Closed Parenthesis

You can omit any closed parenthesis ( ) ) immediately preceding operation of the=key at the end of a calculation.

This is true only in the case of Linear format.

Example: (2 + 3) × (4 – 1) = 15

LINE

(2+3)* (4-1=

k Fraction Calculations

How you should input fractions depends on the input/output format that is currently selected.

•Under initial default settings, fractions are displayed as improper fractions.

•Fraction calculation results are always reduced before being displayed.

22

•If the total number of digits used for a mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10, the value is automatically displayed in decimal format.

•The result of a calculation that involves both fraction and decimal values is displayed in decimal format.

Switching between Improper Fraction and Mixed

between mixed fraction and improper fraction format.

Switching between Fraction and Decimal Format

f

•The format of the fraction depends on the currently selected fraction display format setting (improper fraction or mixed fraction).

•You cannot switch from decimal format to mixed fraction format if the total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10.

•For details about the fkey, see “UsingS-DTransformation”.

k Percent Calculations

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

<#009> If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight?

(160%) <#010> What is the percentage change when a value is increased

k Degree, Minute, Second (Sexagesimal)

Calculations

You can perform calculations using sexagesimal values, and convert values between sexagesimal and decimal.

Inputting Sexagesimal Values

The following is the syntax for inputting a sexagesimal value. {Degrees}e{Minutes}e{Seconds}e

Appendix <#011> Input 2°0´30˝.

•Note that you must always input something for the degrees and minutes, even if they are zero.

Sexagesimal Calculations

•Performing the following types of sexagesimal calculations produces a sexagesimal result.

-Addition or subtraction of two sexagesimal values

-Multiplication or division of a sexagesimal value and a decimal value

Appendix <#012> 2°20´30˝ + 39´30˝ = 3°00´00˝

Converting Values between Sexagesimal and Decimal

Pressing ewhile a calculation result is displayed toggles the value between sexagesimal and decimal.

Appendix <#013> Convert 2.255 to its sexagesimal equivalent.

Using Multi-statementsin

Calculations

You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press =.

Example: To create amulti-statementthat performs the following two calculations: 3 + 3 and 3 × 3

LINE

3+3S7(:)3*3

Disp

=

“Disp” indicates this is an intermediate result of a multi-statement.

=

Using Calculation History

Memory and Replay

Calculation history memory maintains a record of each calculation expression you input and execute, and its result.

Modes that support calculation history memory: COMP (N1), CMPLX (N2),BASE-N(N4)

Recalling Calculation History Memory Contents

Press ftoback-stepthrough calculation history memory contents. Calculation history memory shows both calculation expressions and results.

Example:

LINE

1+1=

2+2=

3+3=

f

f

•Note that calculation history memory contents are cleared whenever you turn off the calculator, press the Okey, change to the calculation mode or the input/output format, or perform any reset operation.

•Calculation history memory is limited. When the calculation you are performing causes calculation history memory to become full, the oldest calculation is deleted automatically to make room for the new calculation.

Replay Function

While a calculation result is on the display, you can press Aand thend ore to edit the expression you used for the previous calculation. If you are using Linear format, you can display the expression by pressingd ore, without pressingAfirst.

Appendix <#014>

Using Calculator Memory

This section uses the COMP Mode (N1) to demonstrate how you can use memory.

k Answer Memory (Ans)

Answer Memory Overview

•Answer Memory contents are updated whenever you execute a calculation using any one of the following keys: =,1=,m,1m(M–),t,1t(STO). Answer Memory can hold up to 15 digits.

•Answer Memory contents are not change if an error occurs during the current calculation.

•Answer Memory contents are maintained even if you press the Akey, change the calculation mode, or turn off the calculator.

•If a CMPLX Mode calculation produces a complex number result, both the real part and imaginary part are stored in Answer Memory. In this case, however, the imaginary part will be cleared from Answer Memory if you change to another calculation mode.

Using Answer Memory to Perform a Series of Calculations

Example: To divide the result of 3 × 4 by 30

LINE

3*4=

(Continuing)/30=

Pressing /automatically inputs “Ans” command.

•With the above procedure, you need to perform the second calculation immediately after the first one. If you need to recall Answer Memory contents after pressing A, press theGkey.

Inputting Answer Memory Contents into an Expression

Example: To perform the calculations shown below:

LINE

123+456=

789-G=

k Independent Memory (M)

You can add calculation results to or subtract results from independent memory. The “M” appears on the display when independent memory contains a value.

Independent Memory Overview

•The following is a summary of the different operations you can perform using independent memory.

•You can also insert the M variable into a calculation, which tells the calculator to use the current independent memory contents at that location. The following is the key operation for inserting the M variable.

Sm(M)

•The “M” indicator appears in the upper left of the display when there is any value other than zero stored in independent memory.

•Independent memory contents are maintained even if you press the Akey, change the calculation mode, or turn off the calculator.

Calculation Examples Using Independent Memory

•If the “M” indicator is on the display, perform the procedure under “Clearing Independent Memory” before performing this example.

Clearing Independent Memory

Press01t(STO)m. This clears independent memory and causes the “M” indicator to disappear from the display.

k Variables (A, B, C, D, X, Y)

Variable Overview

•You can assign a specific value or a calculation result to a variable. Example: To assign the result of 3 + 5 to variable A.

3+51t(STO)y(A)

•Use the following procedure when you want to check the contents of a variable.

Example: To recall the contents of variable A ty(A)

•The following shows how you can include variables inside of an expression.

Example: To multiply the contents of variable A by the contents of variable B

Sy(A)*Se(B)=

•Variable contents are maintained even if you press the Akey, change the calculation mode, or turn off the calculator.

Appendix <#015>

Clearing the Contents of a Specific Variable

Press 01t(STO) and then press the key for the name of the variable whose contents you want to clear. To clear the contents of variable A, for example, press01t(STO)y(A).

k Clearing the Contents of All Memories

Use the following procedure to clear the contents of Answer Memory, independent memory, and all of the variables.

Press 19(CLR)2(Memory)=(Yes).

•To cancel the clear operation without doing anything, press A(Cancel) instead of=.

Using CALC

The CALC feature lets you input a calculation expression that contains variables, and then assign values to the variables and perform the calculation.

You can use CALC in the COMP Mode (N1) and in the CMPLX Mode (N2).

k Expressions Supported by CALC

The following describes the types of expressions that can be used with CALC.

u Expressions that contain variables

Example: 2X + 3Y, 5B + 3i, 2AX + 3BY + C

u Multi-statements

Example: X + Y : X (X + Y)

u Expressions with a single variable on the left

Example: {variable} = {expression}

The expression on the right of the equals sign (input using Ss(=)) can contain variables.

Example: Y = 2X, A = X2 + X + 3

k Example Calculation Using CALC

To start a CALC operation after inputting an expression, press the skey.

Example:

LINE

3*Sy(A)

s

Prompts for input of a value for A.

Current value of A

5=

s

(or=)

10=

•To exit CALC, press A.

•If the expression you are using contains more than one variable, an input prompt appears for each one.

Appendix

<#016> Calculate an +1 = an + 2n (a1 = 1) as the value of an changes from a2 to a5. (Results: a2 = 3, a3 = 7, a4 = 13, a5 = 21)

SOLVE uses Newton’s Method of approximation to solve an equation.

You can use SOLVE in the COMP Mode (N1) only.

k Rules Governing Equations when Using

SOLVE

•You can use the following types of syntax for the solution variable. Example: Y = X + 5, Y (Solves for Y.);

XB = C + D, B (Solves for B.)

The following shows the syntax for the log function.

•Unless you specify otherwise, an equation is solved for X. Example: Y = X + 5, X = sin(M), X + 3 = B + C,

XY + C (Treated as XY + C = 0.)

•SOLVE cannot be used to solve an equation that contains an integral, derivative, Σ( function, Pol( function, Rec( function, or

•An error (Variable ERROR) occurs when the solution variable is not included in the expression being solved.

k Example SOLVE Operation

Example: To solvey =ax2 +b forx wheny = 0,a = 1, andb =–2.

MATH

Math

Sf(Y)Ss(=)Sy(A)

S)(X)w+Se(B)

1)(,)S)(X)

Math

1s(SOLVE)

Prompts for input of a value for Y.

Current value of Y

Math

0=

Math

1=

Math

y2=

Current value of X

Math

=

Solution Screen

• To interrupt an ongoing SOLVE operation, press A.

Precautions when Using SOLVE

•SOLVE may not be able to obtain a solution because of the initial value (assumed value) of the solution variable. If this happens, try changing the initial value of the solution variable.

•SOLVE may not be able to determine the correct solution, even when one exists.

•SOLVE uses Newton’s Method, so even if there are multiple solutions, only one of them will be returned.

•Newton’s Method can have problems obtaining solutions for the following types of functions.

-A periodic function (y = sin(x), etc.)

-A function whose graph includes a steep slope (y =ex,y =1/x, etc.)

-A discontinuous function (y ='x, etc.)

Solution Screen Contents

Input equation

•The “(left side) – (right side) form result” shows the result when the obtained solution is assigned to the solution variable. The closer this value is to zero, the higher is the precision of the obtained 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 orAto cancel the SOLVE operation.

Appendix

<#017> Solve y =x2 –x + 1 forx wheny = 3, 7, 13, and 21. (Solutions:x = 2, 3, 4, 5 wheny = 3, 7, 13, 21 respectively)

*1 Assigns 3 to Y.

*2 Assigns an initial value of 1 to X.

Function Calculations

This section explains how to use the calculator’s built-infunctions.

The functions available to you depends on the calculation mode you are in.The explanations in this section are mainly about the functions that are available in all calculation modes. All of the examples in this section show operation in the COMP Mode (N1).

•Certain function calculations may take some time to display calculation results. Before performing an operation, be sure to wait until execution of the current operation is complete.You can interrupt an ongoing operation by pressing A.

k Pi (π) and Natural Logarithm Basee

You can input pi (π) or natural logarithm basee into a calculation. The following shows the required key operations and the values this calculator uses for pi (π) ande.

π = 3.14159265358980 (15(π))

e= 2.71828182845904 (S5(e))

•You can use π ande in any calculation mode except forBASE-N.

kTrigonometric and Inverse Trigonometric

Functions

•Trigonometric and inverse trigonometric functions can be used in the COMP, STAT, EQN, MATRIX, TABLE, and VECTOR calculation modes. They can also be used in the CMPLX Mode, as long as complex numbers are not used for their arguments.

•The angle unit required by trigonometric and inverse trigonometric functions is one specified as the calculator’s default angle unit. Before performing a calculation, be sure to specify the default angle unit you want to use. See “Specifying the Default Angle Unit” for more information.

Appendix <#018> sin 30 = 0.5,sin–10.5= 30

k Hyperbolic and Inverse Hyperbolic

Functions

Hyperbolic and inverse hyperbolic functions can be used in the same modes as the trigonometric functions. Pressing the wkey displays a menu of functions. Press the number key that corresponds to the function you want to input.

Appendix <#019> sinh 1 = 1.175201194,cosh–11 = 0

kConverting an Input Value to the

Calculator’s Default Angle Unit

After inputting a value, press 1G(DRG') to display the angle unit specification menu shown below. Press the number key that corresponds to the angle unit of the input value. The calculator will automatically convert it to the calculator’s default angle unit.

Example: To convert the following values to degrees:

π radians = 90°, 50 grads = 45° 2

The following procedure assumes that the calculator’s default angle unit is degrees.

LINE

(15(π)/2)

1G(DRG')2(r)=

501G(DRG')

3(g)=

Appendix

<#020> cos (π radians) =–1,cos (100 grads) = 0 <#021>cos–1(–1)= 180

cos–1(–1)=π

kExponential Functions and Logarithmic

Functions

•Exponential and logarithmic functions can be used in the same modes as the trigonometric functions.

•For the logarithmic function “log(”, you can specify base m using the syntax “log (m,n)”.

If you input only a single value, a base of 10 is used for the calculation.

•“ln(” is a natural logarithm function with base e.

•You can also use the &key when inputting an expression with the form of “logmn” while using Math format. For details, see

Appendix <#022>. Note that you must input the base (basem)

when using the &key for input.

Appendix <#023> to <#025>

*1 A base of 10 (common logarithm) is used if no base is specified.

kPower Functions and Power Root

Functions

•Power functions and power root functions can be used in the COMP, STAT, EQN, MATRIX, TABLE, and VECTOR calculation modes.

•The X2, X3,X–1functions can be used in complex number calculations in the CMPLX Mode, and complex number arguments are supported.

•The X^,'(,3'(,^'( functions can be used in the CMPLX Mode, as long as complex numbers are not used as their arguments.

Appendix <#026> to <#030>

kIntegration Calculations

This calculator performs integration using the Gauss-Kronrodmethod of numerical integration.

∫(f(x),a,b,tol)

f(x): Function of X (Allnon-Xvariables are treated as constants.)

Integration interval lower limit Integration interval upper limit

Tolerance range (input/output format: Linear)

•You can omit specification of the tolerance range. A default value of 1 × 10–5is used when you do.

•∫(,d/dx(, Pol(, Rec(, andΣ( cannot be used withinf(x),a,b, ortol.

•Integration calculations can be performed in the COMP Mode only.

•The integration result will be negative when f(x) < 0 within an

integration interval that conforms with a <x <b. Example:∫(0.5X2 – 2,–2,2) =–5.333333333

•A “Time Out” error occurs when an integration calculation ends without the ending condition being fulfilled.

•When performing an integration calculation involving trigonometric functions, specify Rad as the calculator’s default angle unit.

•Integration calculations can take considerable time to complete.

•A smaller tol value provides better precision, but it also causes the calculation to take more time. Specify atol value that is 1 ×10–14or greater.

•You cannot input a tol value when using Math format.

•There may be large error in obtained integration values and errors may occur due to the type of function being integrated, the presence of positive and negative values in the integration interval, or the interval.

•Pressing Awill interrupt an ongoing integration calculation.

Tips on Improving Integration Value Accuracy

•When a periodic function or integration interval results in positive and negative f(x) function values

Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results.

S Positive

S Negative

b c b

∫a f(x)dx =∫a f(x)dx+ (–∫cf(x)dx)

•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.

kDifferential Calculations

Your calculator performs differential calculations by approximating the derivative based on centered difference approximation.

d/dx(f(x),a,tol)

f(x): Function of X (Allnon-Xvariables are treated as constants.)

a: Input a value to specify the point for which the derivative should be obtained (differential point)

tol: Tolerance range (input/output format: Linear)

•You can omit specification of the tolerance range. A default value of 1 × 10–10is used when you do.

•∫(,d/dx(, Pol(, Rec(, andΣ( cannot be used withinf(x),a, ortol.

•Differential calculations can be performed in the COMP Mode only.

•When performing a differential calculation involving trigonometric functions, specify Rad as the calculator’s default angle unit.

•A “Time Out” error occurs when a differential calculation ends without the ending condition being fulfilled.

•A smaller tol value provides better precision, but it also causes the calculation to take more time. Specify atol value that is 1 ×10–14or greater.

•You cannot input a tol value when using Math format.

•Inaccurate results and errors can be caused by the following :

-discontinuous points in x values

-extreme changes in x values

-inclusion of the local maximum point and local minimum point in x values

-inclusion of the inflection point in x values

-inclusion of undifferentiable points in x values

-differential calculation results approaching zero

•Pressing Awill interrupt an ongoing differential calculation.

Appendix

<#033> Determine f ’(π ) whenf(x) = sin(x)

2

(tol specification omitted.) <#034>dxd (3x2 – 5x + 2, 2,1×10–12)= 7

kΣ Calculations

With Σ(, you can obtain the sum of an inputf(x) expression for a specific range.Σ calculations are performed using the following formula.

Σ(f(x),a,b) =f(a) +f(a + 1) + .. +f(b)

f(x): Function of X (Allnon-Xvariables are treated as constants.)

a: Calculation range start pointb: Calculation range end point

•a andb are integers in the range of–1× 1010 <a < b < 1 × 1010.

•The calculation step is fixed at 1.

•∫(,d/dx(, Pol(, Rec(, andΣ( cannot be used withinf(x),a, orb.

•Pressing Awill interrupt an ongoingΣ calculation.

Appendix <#035>Σ (X + 1, 1, 5) = 20

kRectangular-PolarCoordinate Conversion

•Coordinate conversion can be performed in the COMP, STAT, MATRIX, and VECTOR calculation modes.

Converting to Polar Coordinates (Pol)

Pol(X, Y) X: Specifies the rectangular coordinate X value

Y:Specifies the rectangular coordinate Y value

•Calculation result θ is displayed in the range of–180°<θ <180°.

•Calculation result θ is displayed using the calculator’s default angle unit.

•Calculation result r is assigned to variable X, whileθ is assigned to Y.

Converting to Rectangular Coordinates (Rec)

Rec(r,θ)r : Specifiesr value of polar coordinate

θ: Specifies θ value of polar coordinate

•Input value θ is treated as an angle value, in accordance with the calculator’s default angle unit setting.

•Calculation result x is assigned to variable X, whiley is assigned to Y.

•If you perform coordinate conversion inside of an expression instead of a stand-aloneoperation, the calculation is performed using only the first value (either ther-valueor theX-value)produced by the conversion.

Example: Pol ('2,'2) + 5 = 2 + 5 = 7

Appendix <#036> to <#037>

kOther Functions

This section explains how to use the functions shown below.

!, Abs(, Ran#, nPr,nCr, Rnd(

•These functions can be used in the same modes as the trigonometric functions. In addition, the Abs( and Rnd( functions can be used in complex number calculations in the CMPLX Mode.

Factorial (!)

This function obtains the factorials of a value that is zero or a positive integer.

Appendix <#038> (5 + 3)! = 40320

Absolute Value Calculation (Abs)

When you are performing a real number calculation, this function simply obtains the absolute value.

Appendix <#039> Abs (2 – 7) = 5

Random Number (Ran#)

This function generates a 3-digitpseudo random number that is less than 1.

Appendix

<#040> Generate three 3-digitrandom numbers.

The random 3 digit decimal values are converted to 3-digitinteger values by multiplying by 1000.

Note that the values shown here are examples only. Values actually generated by your calculator will be different.

Permutation (nPr) and Combination (nCr)

These functions make it possible to perform permutation and

combination calculations.

n andr must be integers in the range of 0<r <n < 1 × 1010.

Appendix

<#041> How many four-personpermutations and combinations are possible for a group of 10 people?

Rounding Function (Rnd)

This function rounds the value or the result of the expression in the function’s argument to the number of significant digits specified by the number of display digits setting.

Display Digits Setting: Norm1 or Norm2

The mantissa is rounded to 10 digits.

Display Digits Setting: Fix or Sci

The value is rounded to the specified number of digits.

Example: 200 ÷ 7 × 14 = 400

LINE

200/7*14=

(Specifies three decimal places.)

FIX

1N6(Fix)3

(Calculation is performed internally using 15 digits.)

FIX

200/7=

FIX

*14=

The following performs the same calculation with rounding.

FIX

200/7=

(Round the value to the specified number of digits.)

FIX

10(Rnd)=

(Check rounded result.)

FIX

*14=

kPractical Examples

<#043> Confirm that the two sides of the following equation are

equal:

1

n!

Transforming Displayed

Values

You can use the procedures in this section to transform a displayed value to engineering notation, or to transform between standard form and decimal form.

kUsing Engineering Notation

A simple key operation transforms a displayed value to engineering notation.

Appendix

<#044> Transform the value 1,234 to engineering notation, shifting the decimal point to the right.

<#045> Transform the value 123 to engineering notation, shifting the decimal point to the left.

kUsingS-DTransformation

You can use S-Dtransformation to transform a value between its decimal (D) form and its standard (S) form (fraction,π).

Formats Supported for S-DTransformation

S-Dtransformation can be used to transform a displayed decimal calculation result to one of the forms described below. PerformingS-Dtransformation again converts back to the original decimal value.

Note

•When you transform from decimal form to standard form, the calculator automatically decides the standard form to use. You cannot specify the standard form.

Fraction: The current fraction display format setting determines whether the result is an improper fraction or mixed fraction.

π: The following are theπ forms that are supported. This is true only in the case of Math format.

nπ (n is an integer.)

•Transformation to a fractional π form is limited to inverse trigonometric function results and values that are normally expressed in radians.

•After obtaining a calculation result in 'form, you can convert it to decimal form by pressing thef key. When the original calculation result is in decimal form, it cannot be converted to' form.

Examples of S-DTransformation

Note that S-Dtransformation can take some time to perform.

Example: Fraction→ Decimal

'5c6=

• Each press of the fkey toggles between the two forms.

f

f

Appendix

<#046> π Fraction→ Decimal

<#047> '→ Decimal

Complex Number Calculations

(CMPLX)

Your calculator can perform the following complex number calculations.

•Addition, subtraction, multiplication, division

•Argument and absolute value calculations

•Reciprocal, square and cube calculations

•Conjugate complex number calculations

All calculations in this section are performed in the CMPLX Mode (N2).

kInputting Complex Numbers

•In the CMPLX Mode, the Wkey changes function to become an imaginary numberi input key. In this section, theWkey is referred to as the ikey. Use the ikey when inputting a complex number of the formata +bi. The key operation below shows how to input 2 + 3i, for example.

CMPLX Math

2+3i

•You can also input complex numbers using polar coordinate format (r θ ). The key operation below shows how to input 5 30, for

example.

CMPLX Math

51y( )30

•The angle unit for argument θ input and result display is the calculator’s default angle unit.

kCalculation Result Display Format

Your calculator can display complex number calculation results in rectangular coordinate or polar coordinate format. You can select the coordinate format by configuring the calculator’s setup. For more information, see “Specifying the Complex Number Display Format”.

Examples of Calculation Results Using Rectangular Coordinate Format (a +bi)

Example 1: 2 ('3 +i) = 2'3 + 2i = 3.464101615 + 2i

2*(!3e+i)=

•With Linear format, the real part and imaginary part are shown in two different lines.

•With Linear format, the absolute value and argument are shown in two different lines.

1+i=

• Argument θ is output in the range of–180°<θ <180°.

Specifying the Calculation Result Display Format

You can override complex number display settings and specify the format that should be used to display calculation results.

•To specify rectangular coordinate format for the calculation result, perform the following key operation at the end of the calculation. 12(CMPLX)4('a+bi)

•To specify polar coordinate format for the calculation result, perform

the following key operation at the end of the calculation. 12(CMPLX)3('r θ )

Appendix <#049> 1 +i (='2 45) = 1.414213562 45

kConjugate Complex Number (Conjg)

You can use the following operation to obtain a conjugate complex number.

12(CMPLX)2(Conjg)

Appendix

<#050> Determine the conjugate of the complex number 2 + 3i.

kAbsolute Value and Argument (Abs, arg)

You can use the following procedure to obtain the absolute value ( Z ) and argument (arg) on the Gaussian plane for a complex number of the format Z = a +bi.

1w(Abs);12(CMPLX)1(arg)

Appendix

<#051> Obtain the absolute value and argument of 2 + 2i.

*1 Absolute Value *2 Argument

Statistical Calculation (STAT)

All calculations in this section are performed in the STAT Mode (N3).

Selecting a Statistical Calculation Type

In the STAT Mode, display the statistical calculation type selection screen.

kStatistical Calculation Types

kInputting Sample Data

Displaying the STAT Editor Screen

The STAT editor screen appears after you enter the STAT Mode from another mode. Use the STAT menu to select a statistical calculation type.To display the STAT editor screen from another STAT Mode screen, press 11(STAT)2(Data).

STAT Editor Screen

There are two STAT editor screen formats, depending on the type of statistical calculation you selected.

Single-variableStatisticsPaired-variableStatistics

•The first line of the STAT editor screen shows the value for the first sample or the values for their first pair of samples.

FREQ (Frequency) Column

If you turn on the Statistical Display item on the calculator’s setup screen, a column labeled “FREQ” will also be included on the STAT editor screen.

You can use the FREQ column to specify the frequency (the number of times the same sample appears in the group of data) of each sample value.

Rules for Inputting Sample Data on the STAT Editor Screen

•Data you input is inserted into the cell where the cursor is located. Use the cursor keys to move the cursor between cells.

STAT

Cursor

•The values and expressions you can input on the STAT editor screen are the same as those you can input in the COMP Mode with Linear format.

•Pressing Awhile inputting data clears your current input.

•After inputting a value, press =. This registers the value and displays up to six of its digits in the currently selected cell.

Example: To input the value 123.45 in cell X1

(Move the cursor to cell X1.)

STAT

123.45

The value you input appears in the formula area.

STAT

=

Registering a value causes the cursor to move down one cell.

STAT Editor Screen Input Precautions

•The number of lines in STAT editor screen (the number of sample data values you can input) depends on the type of statistical data you selected, and on the Statistical Display setting of the calculator’s setup screen.

•The following types of input are not allowed on the STAT editor screen.

•m,1m(M–)operations

•Assignment to variables (STO)

Precautions Concerning Sample Data Storage

Sample data you input is deleted automatically whenever you change to another mode from the STAT Mode or change the Statistical Display setting (which causes the FREQ column to be shown or hidden) on the calculator’s setup screen.

Editing Sample Data

Replacing the Data in a Cell

(1)On the STAT editor screen, move the cursor to the cell you want to edit.

(2)Input the new data value or expression, and then press =.

Important!

•Note that you must totally replace the existing data of the cell with new input. You cannot edit parts of the existing data.

Deleting a Line

(1)On the STAT editor screen, move the cursor to the line you want to delete.

(2)Press Y.

Inserting a Line

(1)On the STAT editor screen, move the cursor to the line that will be under the line you will insert.

(2)Press 11(STAT)3(Edit).

(3)Press 1(Ins).

Important!

•Note that the insert operation will not work if the maximum number of lines allowed for the STAT editor screen are already used.

Deleting All STAT Editor Contents

(1)Press 11(STAT)3(Edit).

(2)Press 2(Del-A).

• This clears all of the sample data on the STAT editor screen.

Note

•Note that you can perform the procedures under “Inserting a Line” and “Deleting All STAT Editor Contents” only when the STAT editor screen is on the display.

kSTAT Calculation Screen

The STAT calculation screen is for performing statistical calculations with the data you input with the STAT editor screen. Pressing the Akey while the STAT editor screen is displayed switches to the STAT calculation screen.

The STAT calculation screen also uses Linear format, regardless of the current input/output format setting on the calculator’s setup screen.

kUsing the STAT Menu

While the STAT editor screen or STAT calculation screen is on the display, press 11(STAT) to display the STAT menu.

The content to the STAT menu depends on whether the currently selected statistical operation type uses a single variable or paired variables.

STAT Menu Items

Common Items

Single-variableMenu Item

Select this

menu item: When you want to do this:

Display the Distr sub-menuof commands for7Distr normal distribution calculations

• For more information, see “Distr Sub-menu”.

Paired-variableMenu Item

Select this

menu item: When you want to do this:

Display the Reg sub-menuof commands for regression calculations

7Reg

• For details see “Commands when Linear Regression Calculation (A+BX) Is Selected” and “Commands when Quadratic Regression Calculation (_+CX2) Is Selected”.

Single-variable(1-VAR)Statistical Calculation Commands

The following are the commands that appear on the sub-menusthat appear when you select4(Sum),5(Var),6(MinMax), or7(Distr) on the STAT menu while asingle-variablestatistical calculation type is selected.

See Appendix <#052> for information about the calculation formula used for each command.

Sum Sub-menu(11(STAT)4(Sum))

Distr Sub-menu(11(STAT)7(Distr))

1P(2Q(3R(4't

This menu can be used to calculate the probability of standard normal distribution. Normalized variate t is calculated with the expression shown below, using the mean value (o) and population standard deviation value (xσn) obtained from the data input on the STAT editor screen.

Standard Normal Distribution

Appendix Single-variableStatistical Calculation

<#053> Select single-variable(1-VAR)and input the following data:

• Examples <#056> through <#059> all use the same data as Example <#055>.

<#056> Calculate sum of squares of the sample data and sum of the sample data.

<#057> Calculate number of samples, mean, and population standard deviation.

<#058> Calculate minimum value and maximum value.

<#059> Performing standard normal distribution approximation on the input sample data (from Example <#055>) produces the probabilities shown below.

Distribution probability that is a value less than the normalized variate when the sample value is 3 (P value for normalized variate when X = 3)

Distribution probability that is a value greater than the normalized variate when the sample value is 7 (R value for normalized variate when X = 7)

Commands when Linear Regression Calculation (A+BX) Is Selected

With linear regression, regression is performed in accordance with the following model equation.

y = A+ BX

The following are the commands that appear on the sub-menusthat appear when you select4(Sum),5(Var),6(MinMax), or7(Reg) on the STAT menu while linear regression is selected as the statistical calculation type.

See Appendix <#060> for information about the calculation formula used for each command.

Sum Sub-menu(11(STAT)4(Sum))

Reg Sub-menu(11(STAT)7(Reg))

Appendix Linear Regression Calculation: <#061> to <#064>

•Examples <#062> through <#064> all use the data input in Example

<#061>.

*1 Estimated Value (y =–3→ m = ?)

*2 Estimated Value (x = 2→ n = ?)

Commands when Quadratic Regression Calculation (_+CX2) Is Selected

With quadratic regression, regression is performed in accordance with the following model equation.

y = A+ BX+ CX2

See Appendix <#065> for information about the calculation formula used for each command.

Reg Sub-menu(11(STAT)7(Reg))

•Sum sub-menu(sums), Varsub-menu(number of samples, mean, standard deviation), and MinMaxsub-menu(maximum value, minimum value) operations are the same those for linear regression calculations.

Appendix Quadratic Regression Calculation: <#066> to <#068>

•Examples <#066> through <#068> all use the data input in Example <#061>.

Comments for Other Types of Regression

For details about the calculation formula of the command included in each regression type, refer to the indicated calculation formulas

( Appendix <#069> to <#073>).

Appendix Comparison of Regression Curves

• The following example uses the data input in Example <#061>. <#074> Compare the correlation coefficient for logarithmic, e

exponential, ab exponential, power, and inverse regression. (FREQ: OFF)

Appendix Other Types of Regression Calculation: <#075> to

<#079>

Command Usage Tips

•The commands included in the Reg sub-menucan take a long time to execute in logarithmic,e exponential,ab exponential, or power regression calculation when there are a large number of data samples.

The BASE-NMode lets you perform arithmetic calculations, negative value calculations, and logical operations with binary, octal, decimal, and hexadecimal values.

All calculations in this section are performed in the BASE-NMode (N4).

kNumber Base Setting and Value Input

Use the keys listed below to specify the number base.

The key markings used in this section are the ones that are above each key, on the right.

•The current number base setting is indicated in the second line of the display.

•The initial default number base setting when you enter the BASE- N Mode is always decimal (DEC).

Inputting Values

In the BASE-NMode, you can input values using the currently selected number base.

•A Syntax ERROR occurs if you input values that are not allowed for the currently selected number base (such as inputting 2 while binary is selected).

•You cannot input fractional values or exponential values in the BASE-NMode. If a calculation produces a fractional value, the decimal part is cut off.

Inputting Hexadecimal Values

Use the keys shown below to input the alphabetic letters (A, B, C, D, E, F) required for hexadecimal values.

y e w s c t

Value Ranges

•The allowable calculation range is narrower from binary (16 bits) than it is for the other number systems (32 bits).

•A Math ERROR occurs when a calculation result is outside the applicable range for the number system being used.

Specifying the Base during Input

The BASE-NMode lets you override the current default number base setting and input a particular value using a different base. When inputting the value, press13(BASE)c to display page two of the BASE menu, and then press the number key that corresponds to the base you want to specify.

Press this key: To specify this number base:

The key operation below shows how to input a value of 3 using the decimal number base, for example.

Ab13(BASE)c1(d)3

The value you input here is decimal number base.

Appendix

<#080> Calculate 12 + 12 in binary. <#081> Calculate 78 + 18 in octal.

<#082> Calculate 1F16 + 116 in hexadecimal.

<#083> Convert the decimal value 3010 to binary, octal, and hexadecimal.

<#084> Transform the result of 510 + 516 to binary.

kNegative Number Calculations and Logical

Operations

To input a negative number calculation or logical operation command, press 13(BASE) to display page one of the BASE menu, and then press the number key that corresponds to the command you want to specify.

Press this key: When you want to input this:

Logical operator “and” (logical product), which

1(and)

returns the result of a bitwise AND

2(or)

Logical operator “or” (logical sum), which returns the result of a bitwise OR

Logical operator “xor” (exclusive logical sum),

3(xor)

which returns the result of a bitwise XOR

Logical operator “xnor” (exclusive negative 4(xnor) logical sum), which returns the result of a bitwise

XNOR

Press this key: When you want to input this:

5(Not)

“Not(” function, which returns the result of a bitwise complement

“Neg(” function, which returns the result of a

6(Neg)

two’s complement

•Negative binary, octal, and hexadecimal values are produced by taking the binary two’s complement and then returning the result to the original number base. With the decimal number base, negative values are displayed with a minus sign.

Appendix

Examples <#085> through <#090> show examples of calculations with negative binary values and examples of logical operations. Before starting each calculation, be sure to press Abfirst.

All calculations in this section are performed in the EQN Mode (N5).

kEquation Types

An equation type menu appears when you press N5(EQN) and enter the EQN Mode.

Changing the Current Equation Type Setting

Press N5(EQN) tore-enterthe EQN Mode.This clears all current EQN Mode input and displays the equation type menu described above.

kInputting Coefficients

Use the coefficient editor screen to input the coefficients of an equation. The coefficient editor screen shows input cells for each of the coefficients required by the currently selected equation type.

Rules for Inputting and Editing Coefficients

•Data you input is inserted into the cell where the cursor is located. When you register input into a cell, the cursor moves to the next cell to the right.

•When simultaneous linear equations with three unknowns or cubic equation is selected as the equation type, the d column will not be visible on the display when the coefficient editor screen is first displayed. Thed column will become visible when you move the cursor to it, which causes the screen to shift.

•The values and expressions you can input on the coefficient editor screen are the same as those you can input in the COMP Mode with Linear format.

•Pressing Awhile inputting data clears your current input.

•After inputting data, press =.This registers the value and displays up to six of its digits in the currently selected cell.

•To change the contents of a cell, use the cursor keys to move the cursor to the cell and then input the new data.

Initializing All Coefficients to Zero

You can clear all coefficients to zero by pressing the Akey while inputting values on the coefficient editor screen.

Coefficient Editor Screen Input Precautions

Coefficient editor screen precautions are basically the same as those for the STAT editor screen. The only difference is that the first STAT editor screen precaution does not apply in the case of the coefficient editor screen.For details, see “STAT Editor Screen Input Precautions”.

kSolution Display

After inputting and registering values on the coefficient editor screen, press =to display the solution(s) for the equation.

•Each press of =displays the next solution, if there is one. Pressing= while the final solution is displayed returns to the coefficient editor screen.

•In the case of simultaneous linear equations, you can use f andc to switch the display between the solutions for X and Y (and Z).

•When there are multiple solutions for a quadratic or cubic equation, you can use the fandckeys to scroll the display between X1, X2, and X3. The actual number of solutions depends on the equation.

•Pressing Awhile a solution is displayed will return to the coefficient editor screen.

•The display format of solutions is in accordance with the input/ output format and complex number display format settings of the calculator’s setup screen.

•Note that you cannot transform values to engineering notation while an equation solution is displayed.

Appendix Equation Calculation: <#091> to <#095>

You can save matrices under the names “MatA”, “MatB”, and “MatC” in matrix memory. Matrix calculation results are stored in a special Matrix Answer Memory named “MatAns”.

All calculations in this section are performed in the MATRIX Mode (N6).

kCreating and Managing a Matrix

Creating a Matrix and Storing It in Matrix Memory

(1)In the MATRIX Mode, press 14(MATRIX)1(Dim).

•This displays the matrix selection screen.

•Note that the matrix selection screen also appears whenever you enter the MATRIX Mode.

(2)Press a number key (1,2, or3) to specify the name of the matrix you want to select.

•This displays a screen for configuring dimension settings.

c

f

(3)Press a number key (1 through6) to specify the matrix dimension you want to use.

• Pressing a number key to specify the matrix dimension causes

the matrix editor screen to appear.

MAT

“A” stands for “MatA”.

(4)Use the matrix editor screen to input each of the elements into the matrix.

•Input is subject to the same rules as those that govern the coefficient editor screen in the EQN Mode. For more information, see “Rules for Inputting and Editing Coefficients”.

•If you want to create another matrix, repeat this procedure from step (1).

Copying the Contents of One Matrix to Another Matrix

(1)Use the matrix editor screen to display the matrix you want to copy, or display the Matrix Answer Memory screen.

•If you want to copy Matrix A, for example, press 14(MATRIX)2(Data)1(MatA).

(2)Press 1t(STO).

•This causes the “STO” indicator to appear on the display.

(3)Specify the destination of the copy operation.

•Pressing e(MatB) copies the matrix to Matrix B, and displays the matrix editor screen for Matrix B.

kPerforming Matrix Calculations

Pressing Awhile the matrix selection screen or matrix editor screen is on the display switches to the matrix calculation screen.

Matrix Answer Memory Screen

The Matrix Answer Memory (MatAns) screen shows the results of matrix calculations.

MAT

Stands for “MatAns”.

•You cannot edit the contents of a cell.

•To switch to the matrix calculation screen, press A.

•While the MatAns screen is on the display, you can press an arithmetic operator key (like +or-)and use the screen contents in a subsequent calculation, just as with Answer Memory contents. For more information, see “Using Answer Memory to Perform a Series of Calculations”.

kMatrix Menu Items

The following are the menu items on the matrix menu that appears when you press 14(MATRIX).

• The following examples use the matrices input in Examples <#096> and <#097> (MatA, MatB, MatC).

<#098> MatA + MatB (Adding Two Matrices)

<#099> MatA × MatB, MatB × MatA – MatA × MatB (Multiplying Two Matrices)

<#100> 3 × MatA (Matrix Scalar Multiplication)

<#101> Obtain the determinant of Matrix A (det(MatA)). <#102> Obtain the transposition of Matrix C (Trn(MatC)). <#103> Obtain the inverse matrix of Matrix A (MatA–1).

•Use the Ekey to input “–1”.Note that you cannot use 6for this input.

<#104> Obtain the absolute value (Abs(MatB)) of each element of Matrix B.

• Use 1w(Abs).

<#105> Determine the square (MatA2) or cube (MatA3) of Matrix A.

•Use wto specify squaring, and 1w(x3) to specify cubing. Note that you cannot use 6for this input.

Generating a Number Table from a Function (TABLE)

All calculations in this section are performed in the TABLE Mode (N7).

kConfiguring a Number Table Generation

Function

The procedure below configures the number table generation function with the following settings.

Function: f(x) =x2 +1 2

Start Value: 1, End Value: 5, Step Value: 1

LINE

(1)Press N7(TABLE).

(2)Input the function.

(3)After making sure the function is the way you want, press =.

• This displays the start value input screen.

Indicates the initial default start value of 1.

•If the initial value is not 1, press 1to specify the initial start value for this example.

(4)After specifying the start value, press =.

• This displays the end value input screen.

Indicates the initial default end value of 5.

•Specify the end value.

(5)After specifying the end value, press =.

•This displays the step value input screen.

Indicates the initial default step value of 1.

•Specify the step value.

•For details about specifying the start, end, and step values, see “Start, End, and Step Value Rules”.

(6)After specifying the step value, press =.

•Pressing the Akey returns to the function editor screen.

kSupported Function Types

•Except for the X variable, other variables (A, B, C, D, Y) and independent memory (M) are all treated as values (the current variable assigned to the variable or stored in independent memory).

•Only variable X can be used as the variable of a function.

•The derivative (d/dx), integration (∫), coordinate conversion (Pol, Rec), and sum (Σ) functions cannot be used for a number table

generation function.

•Note that the number table generation operation causes the contents of variable X to be changed.

kStart, End, and Step Value Rules

•Linear format is always used for value input.

•You can specify either values or calculation expressions (which must produce a numeric result) for Start, End, and Step.

•Specifying an End value that is less than the Start value causes an error, so the number table is not generated.

•The specified Start, End, and Step values should produce a maximum of 30 x-valuesfor the number table being generated. Executing a number generation table using a Start, End, and Step

value combination that produces more than 30 x-valuescauses

Note

•Certain functions and Start, End, Step value combinations can cause number table generation to take a long time.

kNumber Table Screen

The number table screen shows x-valuescalculated using the specified Start, End, and Step values, as well as the values obtained when eachx-valueis substituted in the functionf(x).

•Note that you can use the number table screen for viewing values only. Table contents cannot be edited.

•Pressing the Akey returns to the function editor screen.

kTABLE Mode Precautions

Note that changing the input/output format settings (Math format or Linear format) on the calculator’s setup screen while in the TABLE Mode clears the number table generation function.

Vector Calculations (VECTOR)

You can save vectors under the names “VctA”, “VctB”, and “VctC” in vector memory. Vector calculation results are stored in a special Vector Answer Memory named “VctAns”.

All calculations in this section are performed in the VECTOR Mode (N8).

kCreating and Managing a Vector

Creating a Vector and Saving It in Vector Memory

(1)In the VECTOR Mode, press 15(VECTOR)1(Dim).

•This displays a vector selection screen.

•Note that the vector selection screen also appears whenever you enter the VECTOR Mode.

(2)Press a number key (1,2, or3) to specify the name of the vector you want to select.

•This displays a screen for configuring dimension settings.

(3)Press a number key (1or2) to specify the vector dimension you want to use.

•You can select either 3-dimension(1) or2-dimension(2).

•Pressing a number key to specify the dimension displays the vector editor screen.

VCT

“A” stands for “VctA”.

(4)Use the vector editor screen to input each element.

•Input is subject to the same rules as those that govern the coefficient editor screen in the EQN Mode. For more information, see “Rules for Inputting and Editing Coefficients”.

•If you want to create another vector, repeat this procedure from step (1).

Copying the Contents of One Vector to Another Vector

You can copy the contents of Vector Answer Memory (VctAns) or of a vector in vector memory to another vector in vector memory. The vector copy operation is basically the same as the matrix copy operation. See “Copying the Contents of One Matrix to Another Matrix” for more information.

kPerforming Vector Calculations

To perform a vector calculation, display the vector calculation screen by pressing the Akey.

Vector Answer Memory Screen

The Vector Answer Memory screen shows the result of the last vector calculation.

VCT

Stands for “VctAns”.

•You cannot edit the contents of a cell.

•To switch to the vector calculation screen, press A.

kVector Menu Items

The following are the menu items on the vector menu that appears when you press 15(VECTOR).

Appendix

<#106> Store VctA = (1, 2) and VctC = (2, –1,2).

<#107> Copy VctA = (1, 2) to VctB and then edit Vector B to VctB = (3, 4).

•The following examples use the vectors input in Examples <#106> and <#107> (VctA, VctB, VctC).

<#108> VctA + VctB (Vector Addition) <#109> 3 × VctA (Vector Scalar Multiplication)

VctB – 3 × VctA (Calculation example using VctAns) <#110> VctA• VctB (Vector Dot Product)

<#111> VctA × VctB (Vector Cross Product) <#112> Obtain the absolute values of VctC.

<#113> Determine the size of the angle (angle unit: Deg) formed by vectors A = (–1,0, 1) and B = (1, 2, 0), and one of the size 1 vectors perpendicular to both A and B.

(A × B) *2 Size 1 vector perpendicular to both A and B = A × B

Scientific Constants

Your calculator comes with 40 built-inconstants that are commonly used in scientific calculations. You can use the scientific constants in any calculation mode except forBASE-N.

•To recall a scientific constant, press 17(CONST).This displays the scientific constant menu. Input thetwo-digitnumber that corresponds to the constant you want to recall. When you recall a constant, its unique symbol appears on the display.

•The following are all of the built-inscientific constants.

01:proton mass; 02: neutron mass; 03: electron mass; 04: muon mass; 05: Bohr radius; 06: Planck constant; 07: nuclear magneton;

08:Bohr magneton; 09: Planck constant, rationalized; 10: finestructure constant; 11: classical electron radius; 12: Compton wavelength; 13: proton gyromagnetic ratio; 14: proton Compton wavelength; 15: neutron Compton wavelength; 16: Rydberg constant; 17: atomic mass unit; 18: proton magnetic moment; 19: electron magnetic moment; 20: neutron magnetic moment; 21: muon magnetic moment; 22: Faraday constant; 23: elementary charge; 24: Avogadro constant; 25: Boltzmann constant; 26: molar volume of ideal gas; 27: molar gas constant; 28: speed of light in vacuum; 29: first radiation constant; 30: second radiation constant;

31:Stefan-Boltzmannconstant; 32: electric constant; 33: magnetic constant; 34: magnetic flux quantum; 35: standard acceleration of gravity; 36: conductance quantum; 37: characteristic impedance of vacuum; 38: Celsius temperature; 39: Newtonian constant of gravitation; 40: standard atmosphere

•The values are based on ISO Standards (1992) and CODATA Recommended Values (1998). For details, see Appendix <#114>.

Appendix <#115> and <#116>

Perform all of these examples in the COMP Mode (N1).

Metric Conversion

The calculator’s built-inmetric 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 forBASE-Nand TABLE.

To recall a metric conversion command, press 18(CONV).This displays the metric conversion command menu. Input thetwo-digitnumber that corresponds to the metric conversion you want to recall.

See Appendix <#117> for a list of all of the metric conversion

commands and conversion formulas.

•Conversion formula data is based on the “NIST Special Publication 811 (1995)”.

* “cal” uses the NIST value at 15°C.

Appendix <#118> to <#120>

Perform all of these examples in the COMP Mode (N1).

Technical Information

k Calculation Priority Sequence

The calculator performs calculations according to a calculation priority sequence.

•Basically, calculations are performed from left to right.

•Expressions within parentheses have the highest priority.

•The following shows the priority sequence for each individual command.

1.Function with parentheses: Pol(, Rec(

∫(,d/dx(, Σ( P(, Q(, R(

sin(, cos(, tan(, sin–1(,cos–1(,tan–1(,sinh(, cosh(, tanh(,sinh–1(,cosh–1(,tanh–1(

log(, ln(, e^(, 10^(,'(,3'( arg(, Abs(, Conjg(

Not(, Neg( det(, Trn( Rnd(

2.Functions preceded by values, powers, power roots: x2,x3,x–1,x!, ° ’ ”, °,r,g, ^(,x'(

Normalized variate: 't Percent: %

3.Fractions: ab/c

4.Prefix symbol: (–)(negative sign)

d, h, b, o (base n symbol)

5.Metric conversion commands: cm'in, etc. Statistical estimated value calculation:m,n,m1,m2

6.Permutations, combinations: nPr,nCr Complex polar form symbol:

7.Dot product: • (Dot)

8.Multiplication and division: ×,÷

Multiplication where sign is omitted: Multiplication sign omitted immediately before π, e, variables, scientific constants (2π, 5A, πA, 3mp, 2i, etc.), functions with parentheses (2'(3), Asin(30), etc.)

9.Addition and subtraction: +, –

10.Logical AND: and

11.Logical OR, XOR, XNOR: or, xor, xnor

If a calculation contains a negative value, you may need to enclose the negative value in parentheses. If you want to square the value –2,for example, you need to input:(–2)2.This is becausex2 is a function preceded by a value (Priority 2, above), whose priority is greater than the negative sign, which is a prefix symbol (Priority 4).

Multiplication and division, and multiplication where the sign is omitted are the same priority (Priority 8), so these operations are performed from left to right when both types are mixed in the same calculation. Enclosing an operation within parentheses causes it to be performed first, so the use of parentheses can result in different calculation results.

kStack Limitations

This calculator uses memory areas called stacks to temporarily store lower calculation priority sequence values, commands, and functions.Thenumeric stack has 10 levels and thecommand stack has 24 levels, as shown in the illustration below.

A Stack ERROR occurs when the calculation you are performing causes the capacity of either stack to be exceeded.

Stack Issues to Keep in Mind for Each Mode

•In the CMPLX Mode, each input value uses two levels of the numeric stack, regardless of whether the input value is a real number or a complex number. This means that the numeric stack effectively has only five levels in the CMPLX Mode.

•The MATRIX Mode uses its own matrix stack, which is used in combination with thegeneral-purposenumeric stack.The matrix stack has three levels. Performing a calculation that involves a matrix causes one level of the matrix stack to be used for storage of the result. Squaring, cubing, or inverting a matrix also uses one level of the matrix stack.

•The VECTOR Mode uses its own vector stack, which is used in combination with thegeneral-purposenumeric stack. The vector stack has five levels.Vector stack usage follows the same rules as the matrix stack, described above.

kCalculation Ranges, Number of Digits, and Precision

The calculation range, number of digits used for internal calculation, and calculation precision depends on the type of calculation you are performing.

Calculation Range and Precision

•Precision is basically the same as that described under “Calculation Range and Precision”, above.

•^(xy),x'y,3',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.

kError Messages

The calculator will display an error message when a result exceeds the calculation range, when you attempt an illegal input, or whenever any other similar problem occurs.

When an error message appears..

The following are general operations you can use when any error message appears.

•Pressing d ore displays to the calculation expression editing screen you were using before the error message appeared, with the cursor located at the position of the error. For more information, see “Displaying the Location of an Error”.

•Pressing Aclears the calculation expression you input before the error message appeared. You can thenre-inputandre-executethe calculation, if you want. Note that in this case, the original calculation will not be retained in calculation history memory.

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).

•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 stack to be exceeded.

Casio Fx-991es Plus Manual Standard Deviation

•The calculation you are performing has caused the capacity of the 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

•There is not enough memory to perform your calculation.

•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.

•Action

•Try increasing the tol value. Note that this also decreases solution precision.

kBefore 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 Okey. 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 “Initializing the Calculation Mode and Other Settings” under “Calculation Modes and Calculator Setup”.

(4)Initialize all modes and settings by performing the following operation: 19(CLR)1(Setup)=(Yes).

Reference

kPower Requirements and Battery Replacement

Your calculator uses a TWO WAY POWER system that combines a solar cell with G13 type button battery (LR44).

Normally, calculators equipped with a solar cell alone can operate only when relatively bright light is present. The TWO WAY POWER system, however, lets you continue to use the calculator as long as there is enough light to read the display.

Replacing the Battery

Dim display figures when available lighting is dim or failure of anything to appear on the display immediately when you turn on the calculator indicates that button battery power is low. Note that you will not be able to use the calculator if its button battery is dead. When any of these symptoms occur, replace the button battery.

Even if the calculator is operating normally, replace the battery at least once every three years.

Important!

•Removing the button battery from the calculator causes independent memory contents and values assigned to variables to be cleared.

2On the back of the calculator, remove the screw and the battery cover.

3 Remove the old battery.

4Wipe a new battery with a dry cloth, and then load it into the calculator with its positive k side facing upwards (so you can see it).

5 Replace the battery cover and secure it in place with its screw.

6Perform the following key operation: O19(CLR)3(All)=(Yes).

• Make sure you perform the above key operation. Do not skip it.

Auto Power Off

Your calculator will turn off automatically if you do not perform any operation for about six minutes. If this happens, press the Okey to turn the calculator back on.

Specifications

Power Requirements:

Solar Cell: Built into the front of the calculator

Button Battery: G13 Type (LR44) × 1

Battery Life: Approximately 3 years (Based on one hour of operation per day.)

Casio 991es Calculator Manual

Operating Temperature: 0°C to 40°C

Dimensions: 12.2 (H) × 80 (W) × 161 (D) mm1/2 (H) 31/8 (W) 65/16 (D)

Approximate Weight: 105g (3.7 oz) including the battery

Bundled Items: Hard Case

CASIO COMPUTER CO., LTD.

6-2,Hon-machi1-chome

Shibuya-ku,Tokyo151-8543,Japan