# Casio FX-100MS Manual

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### User reviews and opinions

badzil |
11:25am on Friday, October 22nd, 2010 |

I wanted a set of speakers for a small space and these were perfect. These work fine for any applications I use. I have not tried classical music. | |

JHepCat72 |
7:00am on Thursday, September 30th, 2010 |

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SuzyQ |
7:54am on Thursday, September 23rd, 2010 |

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5:30pm on Wednesday, July 28th, 2010 |

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Flávio Tonioli Mariotto |
8:54pm on Sunday, May 30th, 2010 |

I bought these for my laptop and they are actually not too bad considering the $30 price tag. I enjoy these speakers. They look great, and sound very good. I especially like the multiple inputs that allow for infinite flexibility in usage. TVs,... | |

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3:18pm on Thursday, April 22nd, 2010 |

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### Documents

fx-100MS fx-115MS (fx-912MS)

#### Users Guide 2

(Additional Functions)

#### kfx-912MS owners

Please be sure to read the important notice of this manual.

http://world.casio.com/edu_e/

#### Important!

Please keep your manual and all information handy for future reference.

CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.

#### Contents

Before getting started.. 2

#### kModes... 2

Mathematical Expression Calculations and Editing Functions.. 3

kReplay Copy... 3 kCALC Memory.. 4 kSOLVE Function.. 4

Scientific Function Calculations. 5

kInputting Engineering Symbols.. 5

Complex Number Calculations. 7

kAbsolute Value and Argument Calculation. 8 kRectangular Form Polar Form Display. 8 kConjugate of a Complex Number. 9

Base-n Calculations.. 9 Statistical Calculations.. 11

#### Normal Distribution.. 11

Differential Calculations.. 12 Integration Calculations.. 13 Power Supply... 14 Specifications.. 16

See the fx-95MS/fx-100MS/fx-115MS/fx-570MS/fx991MS Users Guide for details about the following items. Removing and Replacing the Calculators Cover/ Safety Precautions/ Handling Precautions/ Two-line Display/ Before getting started. (except for Modes)/ Basic Calculations/ Memory Calculations/ Scientific Function Calculations/ Equation Calculations/ Statistical Calculations/ Technical Information E-1

#### Before getting started.

k Modes

Before starting a calculation, you must first enter the correct mode as indicated in the table below. The following table shows the modes and required operations for the fx-100MS and fx-115MS.

fx-100MS and fx-115MS Modes

To perform this type of calculation: Basic arithmetic calculations Complex number calculations Standard deviation Regression calculations Base-n calculations Solution of equations Perform this key operation: To enter this mode: COMP CMPLX SD REG BASE EQN

#### F1 F2 FF1 FF2 FF3 FFF1

Pressing the F key more than three times displays additional setup screens. Setup screens are described where they are actually used to change the calculator setup. In this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section.

#### Example:

Complex Number Calculations

To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Complex Number Display Format: Fraction Display Format: Decimal Point Character: COMP Deg Norm 1, Eng OFF a+b i a b/c Dot

Mode indicators appear in the upper part of the display, except for the BASE indicators, which appear in the exponent part of the display. Engineering symbols are automatically turned off while the calculator is the BASE Mode. You cannot make changes to the angle unit or other display format (Disp) settings while the calculator is in the BASE Mode. The COMP, CMPLX, SD, and REG modes can be used in combination with the angle unit settings. Be sure to check the current calculation mode (SD, REG, COMP, CMPLX) and angle unit setting (Deg, Rad, Gra) before beginning a calculation.

Mathematical Expression Calculations and Editing Functions

Use the F key to enter the COMP Mode when you want to perform mathematical expression calculations or edit expressions. COMP.. F 1

#### k Replay Copy

Replay copy lets you recall multiple expressions from replay so they are connected as a multi-statement on the screen. Example: Replay memory contents: 1+1 2+2 3+3 4+4 5+5 6+6 Multi-statement: 4 + 4:5 + 5:6 + 6 Use [ and ] to display the expression 4 + 4. Press A [(COPY). E-3

You can also edit expressions on the display and perform other multi-statement operations. For more details about using multi-statements, see Multi-statements in the separate Users Guide. Only the expressions in replay memory starting from the currently displayed expression and continuing to the last expression are copied. Anything before the displayed expression is not copied.

#### k CALC Memory

CALC memory lets you temporarily store a mathematical expression that you need to perform a number of times using different values. Once you store an expression, you can recall it, input values for its variables, and calculate a result quickly and easily. You can store a single mathematical expression, with up to 79 steps. Note that CALC memory can be used in the COMP Mode and CMPLX Mode only. The variable input screen shows the values currently assigned to the variables. Example: Calculate the result for Y = X2 + 3X 12 when X = 7 (Result: 58 ), and when X = 8 (Result: 76 ).

#### (Input the function.)

p y p u p x K + 3 p x , 12 C (Input 7 for X? prompt.) 7= (Input 8 for X? prompt.) C8=

#### (Store the expression.)

Note that the expression you store is cleared whenever you start another operation, change to another mode, or turn off the calculator.

#### k SOLVE Function

The SOLVE function lets you solve an expression using variable values you want, without the need to transform or simply the expression. Example: C is the time it would take for an object thrown straight up with initial velocity A to reach height B. E-4

Use the formula below to calculate initial velocity A for a height of B = 14 meters and a time of C = 2 seconds. Gravitational acceleration is D = 9.8 m/s2. (Result: A = 16.8 ) B AC 1 DC 2 2

#### (B?) (A?) (C?) (D?) (A?)

p2pup1-pk, R1\2T-ph-pkK AI 14 = ] 2= 9l8= [[ AI

The SOLVE function finds approximations based on Newtons method, which means that error can occur. Certain expressions or initial values may result in error without convergence of results. If an expression does not include an equals sign (=), the SOLVE function produces a solution for expression = 0.

Scientific Function Calculations

Use the F key to enter the COMP Mode when you want to perform basic arithmetic calculations. COMP.. F 1

k Inputting Engineering Symbols

#### COMP EQN CMPLX

Turning on engineering symbols makes it possible for you to use engineering symbols inside your calculations. E-5

To turn engineering symbols on and off, press the F key a number of times until you reach the setup screen shown below.

Press 1. On the engineering symbol setting screen that appears, press the number key ( 1 or 2) that corresponds to the setting you want to use.

1(Eng ON): Engineering symbols on (indicated by

#### Eng on the display)

2(Eng OFF): Engineering symbols off (no Eng

indicator) The following are the nine symbols that can be used when engineering symbols are turned on. To input this symbol: Perform this key operation: Ak k (kilo) M (Mega) AM G (Giga) Ag T (Tera) At m (milli) Am (micro) AN n (nano) An p (pico) Ap f (femto) Af Unit 1015

For displayed values, the calculator selects the engineering symbol that makes the numeric part of the value fall within the range of 1 to 1000. Engineering symbols cannot be used when inputting fractions. Example: = 0.9 m (milli)

#### F.. 1(Disp) 1

9 \ 10 =

When engineering symbols are turned on, even standard (non-engineering) calculation results are displayed using engineering symbols.

Use the F key to enter the CMPLX Mode when you want to perform calculations that include complex numbers. CMPLX... F 2 The current angle unit setting (Deg, Rad, Gra) affects CMPLX Mode calculations. You can store an expression in CALC memory while in the CMPLX Mode. Note that you can use variables A, B, C, and M only in the CMPLX Mode. Variables D, E, F, X, and Y are used by the calculator, which frequently changes their values. You should not use these variables in your expressions. The indicator RI in the upper right corner of a calculation result display indicates a complex number result. Press A r to toggle the display between the real part and imaginary part of the result. You can use the replay function in the CMPLX Mode. Since complex numbers are stored in replay memory in the CMPLX Mode, however, more memory than normal is used up. Example: (23 i)(45 i) 68 i

(Real part 6) (Imaginary part 8 i)

#### 2+3i+4+5i=

k Absolute Value and Argument Calculation

Supposing the imaginary number expressed by the rectangular form z = a + bi is represented as a point in the Gaussian plane, you can determine the absolute value (r) and argument ( ) of the complex number. The polar form is r. Example 1: To determine the absolute value (r) and argument () of 3+4i (Angle unit: Deg) (r = 5, = 53.13010235)

#### Imaginary axis

Real axis

#### (r 5 ) ( 53.13010235 )

AAR3+4iT= AaR3+4iT=

The complex number can also be input using the polar form r. Example 2: 1 i (Angle unit: Deg)

#### L 2 A Q 45 = Ar

k Rectangular Form Polar Form Display

You can use the operation described below to convert a rectangular form complex number to its polar form, and a polar form complex number to its rectangular form. Press A r to toggle the display between the absolute value (r) and argument ( ). Example: 1 i 1.(Angle unit: Deg)

1+iAY=Ar L 2 A Q 45 A Z = A r

You select rectangular form (a+bi) or polar form (r ) for display of complex number calculation results. F. 1(Disp) r

1(a+bi):Rectangular form 2(r): Polar form (indicated by r on the display)

k Conjugate of a Complex Number

For any complex number z where z = a+bi, its conjugate (z) is z = a bi. Example: To determine the conjugate of the complex number 1.23 + 2.34i (Result: 1.23 2.34 i )

A S R 1 l 23 + 2 l 34 i T = Ar

#### Base-n Calculations

Use the F key to enter the BASE Mode when you want to perform calculations using Base-n values. BASE... F F 3 In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values. You can specify the default number system to be applied to all input and displayed values, and the number system for individual values as you input them. You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent. If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. Negative binary, octal, and hexadecimal values are produced by taking the twos complement.

You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive or), xnor (exclusive nor), Not (bitwise complement), and Neg (negation). The following are the allowable ranges for each of the available number systems. 1000000000 x x 0111111111 Octal 4000000000 x x 3777777777 Decimal 2147483648 x 2147483647 Hexadecimal 80000000 x FFFFFFFF 0x 7FFFFFFF Binary Example 1: To perform the following calculation and produce a binary result: 1100012 Binary mode:

#### 10111 + 11010 =

Example 2: To perform the following calculation and produce an octal result: 76548

#### 1210 5168

Octal mode:

l l l 4 (o) 7654 \ l l l 1 (d) 12 =

Example 3: To perform the following calculation and produce a hexadecimal and a decimal result: 12016 or 11012 12dHexadecimal mode:

120 l 2 (or) l l l 3 (b) 1101 = Decimal mode: K

Example 4: To convert the value 2210 to its binary, octal, and hexadecimal equivalents. (101102 , 268 , 1616 ) Binary mode:

#### tb o h

0. 10110.

#### l l l 1(d) 22 =

Octal mode: Hexadecimal mode:

Example 5: To convert the value 51310 to its binary equivalent. Binary mode:

#### Ma t h ERROR

l l l 1(d) 513 =

You may not be able to convert a value from a number system whose calculation range is greater than the calculation range of the resulting number system. The message Math ERROR indicates that the result has too many digits (overflow).

#### Statistical Calculations

Normal Distribution

Use the F key to enter the SD Mode when you want to perform a calculation involving normal distribution. SD... F F 1 Press A D, which produces the screen shown below.

#### P ( Q ( R ( t

Input a value from 1 to 4 to select the probability distribution calculation you want to perform.

#### P(t) Q(t) R(t)

Example: To determine the normalized variate ( t) for x = 53 and normal probability distribution P(t) for the following data: 55, 54, 51, 55, 53, 53, 54, 52 (t = 0.284747398, P(t) = 0.38974 ) 55 S 54 S 51 S 55 S 53 S S 54 S 52 S 53 A D 4(t) = A D 1( P( ) D 0.28 F =

Differential Calculations

The procedure described below obtains the derivative of a function. Use the F key to enter the COMP Mode when you want to perform a calculation involving differentials. COMP.. F 1 Three inputs are required for the differential expression: the function of variable x, the point (a) at which the differential coefficient is calculated, and the change in x (x). A J expression P a P x T Example: To determine the derivative at point x = 2 for the function y = 3x2 5x + 2, when the increase or decrease in x is x = (Result: 7 )

#### AJ3pxK,5px+2P2P 2eD4T=

You can omit input of x, if you want. The calculator automatically substitutes an appropriate value for x if you do not input one. Discontinuous points and extreme changes in the value of x can cause inaccurate results and errors.

#### Integration Calculations

The procedure described below obtains the definite integral of a function. Use the F key to enter the COMP Mode when you want to perform integration calculations. COMP.. F 1 The following four inputs are required for integration calculations: a function with the variable x; a and b, which define the integration range of the definite integral; and n, which is the number of partitions (equivalent to N = 2n) for integration using Simpsons rule.

d expression P a P b P n F

Example: (Number of partitions n = 6)

15 (2x2 + 3x + 8) dx = 150.6666667

#### d2pxK+3px+ 8P1P5P6T=

You can specify an integer in the range of 1 to 9 as the number of partitions, or you can skip input of the number of partitions entirely, if you want. Internal integration calculations may take considerable time to complete. Display contents are cleared while an integration calculation is being performed internally.

#### Power Supply

The type of battery you should use depends on the model number of your calculator.

#### fx-115MS

The TWO WAY POWER system actually has two power supplies: a solar cell and a G13 Type (LR44) button battery. 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

Either of the following symptoms indicates battery power is low, and that the battery should be replaced. Display figures are dim and difficult to read in areas where there is little light available. Nothing appears on the display when you press the 5 key.

#### u To replace the battery

1 Remove the five screws that Screw hold the back cover in place and then remove the back cover. 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the five screws. 5 Press 5 to turn power on. Be sure not to skip this step.

#### fx-100MS

This calculator is powered by a single AA-size battery.

Dim figures on the display of the calculator indicate that battery power is low. Continued use of the calculator when the battery is low can result in improper operation. Replace the battery as soon as possible when display figures become dim.

#### To replace the battery

1 Press A i to turn power off. Screw 2 Remove the six screws that hold the back cover in place and then remove the back cover. 3 Remove the old battery. 4 Load a new battery into the unit with its positive k and negative l ends facing correctly. 5 Replace the back cover and secure it in place with the six screws. 6 Press 5 to turn power on.

#### Auto Power Off

Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on.

#### Specifications

Power Supply: fx-100MS: Single AA-size battery (R6P(SUM-3)) fx-115MS: Solar cell and a single G13 Type button battery (LR44) Battery Life: fx-100MS: Approximately 17,000 hours continuous display of flashing cursor. Approximately 2 years when left with power turned off. fx-115MS: Approximately 3 years (1 hour use per day). Dimensions: fx-100MS: 20.0 (H) 78 (W) 155 (D) mm 13/16 (H) 31/16 (W) 61/8 (D) fx-115MS: 12.7 (H) 78 (W) 154.5 (D) mm 1/2 (H) 31/16 (W) 61/16 (D) Weight: fx-100MS: 133 g (4.7 oz) including battery fx-115MS: 105 g (3.7 oz) including battery Power Consumption: 0.0002 W Operating Temperature: 0C to 40C (32F to 104F)

Important notice for fx-912MS owners

The names fx-912MS (Japan domestic model name) and fx-115MS (international model name) apply to the same model. Owners of the fx-912MS should refer to the description of fx-115MS. E-16

#### CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan

SA0206-D Printed in China CA 310074C-1

#### Contents

Removing and Replacing the Calculators Cover.. 1 Safety Precautions.. 2 Handling Precautions.. 3 Two-line Display.. 7 Before getting started.. 7

kModes... 7 kInput Capacity... 8 kMaking Corrections During Input.. 9 kReplay Function... 9 kError Locator... 9 kMulti-statements.. 10 kExponential Display Formats. 10 kDecimal Point and Separator Symbols. 11 k Initializing the Calculator.. 11

#### Basic Calculations.. 11

k Arithmetic Calculations.. kFraction Operations.. kPercentage Calculations.. kDegrees, Minutes, Seconds Calculations. kFIX, SCI, RND... kAnswer Memory... kConsecutive Calculations. kIndependent Memory.. k Variables.. 17

#### Memory Calculations.. 16

Scientific Function Calculations.. 18

kTrigonometric/Inverse Trigonometric Functions. 18 kHyperbolic/Inverse Hyperbolic Functions. 19

kCommon and Natural Logarithms/ Antilogarithms.. 19 kSquare Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, , and Permutation/Combination. 20 kAngle Unit Conversion... 21 kCoordinate Conversion (Pol (x, y), Rec (r, )).. 21 kEngineering Notation Calculations.. 22

Equation Calculations. 22

kQuadratic and Cubic Equations.. 22 kSimultaneous Equations.. 24

Statistical Calculations.. 26

Standard Deviation.. 26 Regression Calculations.. 28

Technical Information.. 32

kWhen you have a problem.. kError Messages... kOrder of Operations.. kStacks... kInput Ranges.. 36

Power Supply (fx-95MS only).. 38 Specifications (fx-95MS only). 39

#### Two-line Display

The two-line display makes it possible to view both the calculation formula and its result at the same time.

The upper line shows the calculation formula. The lower line shows the result. A separator symbol is displayed every three digits when the integer part of the mantissa has more than three digits.

#### Before getting started.

k Modes

Before starting a calculation, you must first enter the correct mode as indicated in the table below. The following table shows the modes and required operations for the fx-95MS only. Users of other models should refer to the Users Guide 2 (Additional Functions) for information about modes and their selection.

#### fx-95MS Modes

To perform this type of calculation: Basic arithmetic calculations Standard deviation Regression calculations Solution of equations 7 Perform this To enter key operation: this mode:

#### F1 F2 F3 FF1

COMP SD REG EQN

Pressing the F key more than twice displays additional setup screens. Setup screens are described in the sections of this manual where they are actually used to change the calculator setup. In this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section.

#### Example:

Equation Calculations

To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Fraction Display Format: Decimal Point Character: COMP Deg Norm 1 a b/c Dot

Mode indicators appear in the upper part of the display. Be sure to check the current calculation mode (SD, REG, COMP) and angle unit setting (Deg, Rad, Gra) before beginning a calculation.

#### k Input Capacity

The memory area used for calculation input can hold 79 steps. One step is taken up each time you press a number key or arithmetic operator key ( +, ,, -, \ ). A A or p key operation does not take up a step, so inputting A D, for example, takes up only one step. You can input up to 79 steps for a single calculation. Whenever you input the 73rd step of any calculation, the cursor changes from _ to k to let you know memory is running low. If you need to input more than 79 steps, you should divide your calculation into two or more parts. Pressing the g key recalls the last result obtained, which you can use in a subsequent calculation. See Answer Memory for more information about using the g key.

k Making Corrections During Input

Use e and r to move the cursor to the location you want. Press [ to delete the number or function at the current cursor position. Press A K to change to an insert cursor t. Inputting something while the insert cursor is on the display inserts the input at the insert cursor position. Pressing A K, or = returns to the normal cursor from the insert cursor.

#### k Replay Function

Every time you perform a calculation, the replay function stores the calculation formula and its result in replay memory. Pressing the [ key displays the formula and result of the calculation you last performed. Pressing [ again back steps sequentially (new-to-old) through past calculations. Pressing the e or r key while a replay memory calculation is on the display changes to the editing screen. Pressing the e or r key immediately after you finish a calculation displays the editing screen for that calculation. Pressing t does not clear replay memory, so you can recall the last calculation even after you press t. Replay memory capacity is 128 bytes for storage of both expressions and results. Replay memory is cleared by any of the following actions. When you press the 5 key When you initialize modes and settings by pressing A B 2 (or 3) =. When you change from one calculation mode to another When you turn off the calculator.

#### k Error Locator

Pressing r or e after an error occurs displays the calculation with the cursor positioned at the location where the error occurred. 9

#### k Multi-statements

A multi-statement is an expression that is made up of two or more smaller expressions, which are joined using a colon ( : ). Example: To add 2 + 3 and then multiply the result by 4 2+3p\g-4=

k Exponential Display Formats

This calculator can display up to 10 digits. Larger values are automatically displayed using exponential notation. In the case of decimal values, you can select between two formats that determine at what point exponential notation is used. To change the exponential display format, press the F key a number of times until you reach the exponential display format setup screen shown below.

#### F i x Sc i No r m

Press 3. On the format selection screen that appears, press 1 to select Norm 1 or 2 for Norm 2.

#### u Norm 1

With Norm 1, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places.

#### u Norm 2

With Norm 2, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places. All of the examples in this manual show calculation results using the Norm 1 format.

k Decimal Point and Separator Symbols

You can use the display setup (Disp) screen to specify the symbols you want for the decimal point and 3-digit separator. To change the decimal point and separator symbol setting, press the F key a number of times until you reach the setup screen shown below.

Display the selection screen. fx-95MS: 1r Other Models: 1 r r Press the number key ( 1 or 2) that corresponds to the setting you want to use.

1(Dot): Period decimal point, comma separator 2(Comma): Comma decimal point, period separator

k Initializing the Calculator

Perform the following key operation when you want to initialize the calculation mode and setup, and clear replay memory and variables.

#### A B 3(All) =

Basic Calculations

k Arithmetic Calculations

Use the F key to enter the COMP Mode when you want to perform basic calculations. COMP... F 1 Negative values inside of calculations must be enclosed within parentheses. sin 1.23 S R D 1.23 T 11

It is not necessary to enclose a negative exponent within parentheses. sin 2.S 2.34 e D 5 Example 1: 3(5109) 1.5108 3-5eD9= Example 2: 5(97) 80 5-R9+7T= You can skip all T operations before =.

#### k Fraction Operations

uFraction Calculations

Values are displayed in decimal format automatically whenever the total number of digits of a fractional value (integer + numerator + denominator + separator marks) exceeds 10. Example 1:

#### 2C3+1C5=

13 15.00

#### Example 2: 3

3C1C4+ 1C2C3=

#### 2C4= 1 C 2 + 1.6 =

Example 3: Example 4:

#### 1 1.6 2.1 2

Results of calculations that mix fraction and decimal values are always decimal.

uDecimal Fraction Conversion

Use the operation shown below to convert calculation results between decimal values and fraction values. Note that conversion can take as long as two seconds to perform. 12

#### Example 1: 2.75 2

3 (Decimal Fraction) 4 2.75 = 2.75

#### Example 2: 11 4

4.4.00

1 0.5 (Fraction Decimal) 2 1C2=

#### 1 2.00 0.2.00

uMixed Fraction Improper Fraction Conversion

#### Example: 3 1C2C3=

3.3.2 3.00

You can use the display setup (Disp) screen to specify the display format when a fraction calculation result is greater than one. To change the fraction display format, press the q key a number of times until you reach the setup screen shown below.

Display the selection screen. fx-95MS: 1 Other Models: 1 r Press the number key ( 1 or 2) that corresponds to the setting you want to use.

1(a b/c): Mixed fraction 2(d/c): Improper fraction

An error occurs if you try to input a mixed fraction while the d/c display format is selected.

k Percentage Calculations

Example 1 : To calculate 12% of 1500 (180) 1500 - 12 A v Example 2: To calculate what percentage of 880 is 660 (75%) 660 \ 880 A v Example 3 : To add 15% onto 2500 (2875) 2500 - 15 A v + Example 4 : To discount 3500 by 25% (2625) 3500 - 25 A v , Example 5: To discount the sum of 168, 98, and 734 by 20% (800) 168 + 98 + 734 = g A j 1 p 1 - 20 A v , * As shown here, if you want to use the current Answer Memory value in a mark up or discount calculation, you need to assign the Answer Memory value into a variable and then use the variable in the mark up/discount calculation. This is because the calculation performed when v is pressed stores a result to Answer Memory before the , key is pressed. Example 6: If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? (160%) 300 + 500 A v Example 7: What is the percentage change when a value is increased from 40 to 46? How about to 48? (15%, 20%) 46 , 40 A v eeeeee8= 14

k Consecutive Calculations

You can use the calculation result that is currently on the display (and also stored in Answer Memory) as the first value of your next calculation. Note that pressing an operator key while a result is displayed causes the displayed value to change to Ans, indicating it is the value that is currently stored in Answer Memory. The result of a calculation can also be used with a subsequent Type A function (x2, x3, x1, x!, DRG'), +, , ^(xy), x , , , nPr and nCr.

#### k Independent Memory

Values can be input directly into memory, added to memory, or subtracted from memory. Independent memory is convenient for calculating cumulative totals. Independent memory uses the same memory area as variable M. To clear independent memory (M), input 0 A j 3 (M+). Example: ) 90 (Total) 23 + 9 A j 3 (M+) 53 , 6 | 45 - 2 A {

#### k Variables

There are nine variables (A through F, M, X and Y), which can be used to store data, constants, results, and other values. Use the following operation to delete data assigned to a 17

particular variable: 0 A j 1. This operation deletes the data assigned to variable A. Perform the following key operation when you want to clear the values assigned to all of the variables.

#### A B 1(Mcl) =

Example: 193.8.4 193.6.9 193.2 A j 1 \ 23 =

#### p 1 \ 28 =

Scientific Function Calculations

Use the F key to enter the COMP Mode when you want to perform basic arithmetic calculations. COMP... F 1 Certain types of calculations may take a long time to complete. Wait for the result to appear on the display before starting the next calculation. = 3.14159265359

k Trigonometric/Inverse Trigonometric Functions

To change the default angle unit (degrees, radians, grads), press the F key a number of times until you reach the angle unit setup screen shown below.

#### Deg Rad G r a

Press the number key ( 1, 2, or 3 ) that corresponds to the angle unit you want to use. (90 =

#### radians = 100 grads) 18

Example 1: sin 63 52o41 0.897859012

q.. 1(Deg) S 63 I 52 I 41 I =

#### Example 2: cos

rad 0.5 3

#### q.. 2(Rad) WRAx\3T=

Example 3 : cos1

#### 2 (rad) 0.25 (rad) 2 4

q.. 2 (Rad) AVRL2\2T=g\Ax=

Example 4: tan1 0.741 36.53844577

#### q.. 1(Deg) A g 0.741 =

k Hyperbolic/Inverse Hyperbolic Functions

Example 1: sinh 3.6 18.28545536 Example 2: sinh4.094622224

#### M S 3.6 = M A j 30 =

k Common and Natural Logarithms/ Antilogarithms

Example 1: log 1.23 0.089905111

R 1.23 = T 90 = TpP= A U 10 = A Q 1.5 =

Example 2: In 90 (= loge 90) = 4.49980967 ln e 1 Example 3: e10 22026.46579 Example 4: 10 31.6227766

#### Example 5: 19

k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, , and Permutation/Combination

#### Example 1:

5 5.287196909

#### L2+L3-L5=

Example 2: 1.290024053

#### A D 5 + A D R D 27 T =

Example 3:

123 ( = ) 1.A H 123 = 123 + 30 K = 12 N * =

Example 4: 1023 Example 5: 123 1728

* A N in the case of fx-570MS/fx-991MS. 1 Example 6: 4 R3a,4aTa= Example 7: 8! 40320 8Af=

Example 8: To generate a random number between 0.000 and 0.999

#### Example 9: 3 9.424777961

0.66400

(The above value is a sample only. Results differ each time.)

Example 10: To determine how many different 4-digit values can be produced using the numbers 1 through 7 Numbers cannot be duplicated within the same 4-digit value (1234 is allowed, but 1123 is not). (840) 7Am4= Example 11: To determine how many different 4-member groups can be organized in a group of 10 individuals (210) 10 n* 4 = 20

* A n in the case of fx-100MS/fx-115MS/fx-570MS/ fx-991MS.

#### k Angle Unit Conversion

Press A v to display the following menu.

Pressing 1, 2, or 3 converts the displayed value to the corresponding angle unit. Example: To convert 4.25 radians to degrees

#### q.. 1(Deg)

4.25 A v 2(R) =

#### 4. 25 r

243.5070629

k Coordinate Conversion (Pol (x, y), Rec (r, ))

Calculation results are automatically assigned to variables E and F. Example 1: To convert polar coordinates (r2, 60) to rectangular coordinates (x, y) (Deg) x1 y 1.732050808

#### A F 2 P 60 T = 0o

Press 0 n to display the value of x, or 0 o to display the value of y. Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r,) (Rad) r2 f* 1 P L 3 T = * A f in the case of fx-100MS/fx-115MS/fx-570MS/ fx-991MS.

#### 1.047197551

Press 0 n to display the value of r, or 0 o to display the value of. 21

k Engineering Notation Calculations

Example 1: To convert 56,088 meters to kilometers 56.3 (km) 81.3 (mg) 56088 = J

Example 2: To convert 0.08125 grams to milligrams 0.08125 = J

The EQN Mode lets you solve equations up to three degrees and simultaneous linear equations with up to three unknowns. Use the F key to enter the EQN Mode when you want to solve an equation. EQN. F F 1 (fx-95MS) F F F 1 (Other Models)

k Quadratic and Cubic Equations

Quadratic Equation: ax2 + bx + c = 0 Cubic Equation: ax3 + bx2 + cx + d = 0 Entering the EQN Mode and pressing r displays the initial quadratic/cubic equation screen.

#### Deg r ee?

Use this screen to specify 2 (quadratic) or 3 (cubic) as the degree of the equation, and input values for each of the coefficients.

Coefficient name Arrow indicates direction you should scroll to view other elements.

#### Element value

Any time until you input a value for the final coefficient (c for a quadratic equation, d for a cubic equation), you can use the [ and ] keys to move between coefficients on the screen and make changes, if you want. Note that you cannot input complex numbers for coefficients. Calculation starts and one of the solutions appears as soon as you input a value for the final coefficient.

Variable name Arrow indicates direction you should scroll to view other solutions.

#### Solution

Press the ] key to view other solutions. Use [ and ] to scroll between all of the solutions for the equation. Pressing the t key at this point returns to the coefficient input screen. Certain coefficients can cause calculation to take more time. Example 1: To solve the equation x3 2x2 x + 2 = 0 ( x = 2, 1, 1) (Degree?) 3 (a?) (b?) (c?) (d?) (x1 = 2) (x2 = 1) (x3 = 1) If a result is a complex number, the real part of the first solution appears first. This is indicated by the RI symbol on the display. Press A r to toggle the display between the real part and imaginary part of a solution. 23 1= D2= D1= 2= ] ]

#### 0.75 i

Example 2: To solve the equation 8x2 4x + 5 = 0 ( x = 0.25 0.75 i) (Degree?) (a?) (b?) (c?) (x1 = 0.25 + 0.75i) (x2 = 0.25 0.75i) 2 8= D4= 5= ]

#### k Simultaneous Equations

Simultaneous Linear Equations with Two Unknowns: a1x + b1y = c1 a2x + b2y = c2 Simultaneous Linear Equations with Three Unknowns: a1x + b1y + c1z = d1 a2x + b2y + c2z = d2 a3x + b3y + c3z = d3 Entering the EQN Mode displays the initial simultaneous equation screen.

#### Coefficient name

Unk now ns?

Use this screen to specify 2 or 3 as the number of unknowns, and input values for each of the coefficients.

Arrow indicates direction you should scroll to view other elements.

Any time until you input a value for the final coefficient (c2 for two unknowns, d3 for three unknowns), you can use the [ and ] keys to move between coefficients on the screen and make changes, if you want. Note that you cannot input complex numbers for coefficients. Calculation starts and one of the solutions appears as soon as you input a value for the final coefficient.

Press the ] key to view other solutions. Use [ and ] to scroll between all of the solutions for the equation. Pressing the t key at this point returns to the coefficient input screen. Example: To solve the following simultaneous equations 2x + 3y z = 15 3x 2y + 2z = 4 5x + 3y 4z = 9 ( x = 2, y = 5, z = 4) (Unknowns?) (a1?). (d1?) (a2?). (d2?) (a3?). (d3?) (x = 2) (y = 5) (z = 4) = 3 = D1 = 15 = 3=D2=2=4= 5=3=D4=9=

#### Statistical Calculations

Standard Deviation

#### SD REG SD

Use the F key to enter the SD Mode when you want to perform statistical calculations using standard deviation. SD. F 2 (fx-95MS) F F 1 (Other Models) Always start data input with A B 1 (Scl) = to clear statistical memory. Input data using the key sequence shown below. <x-data> S Input data is used to calculate values for n, x, x2, o, n and n-1, which you can recall using the key operations noted nearby.

To recall this type of value: Perform this key operation:

#### x2 x n o n n-1

AU1 AU2 AU3 AX1 AX2 AX3

Example: To calculate n1, n, o, n, x, and x2 for the following data : 55, 54, 51, 55, 53, 53, 54, 52 In the SD Mode: A B 1 (Scl) = (Stat clear) 55 S

Each time you press S to register your input, the number of data input up to that point is indicated on the display (n value).

54 S 51 S 55 S 53 S S 54 S 52 S

Sample Standard Deviation (n1) = 1.407885953

Population Standard Deviation (n) = 1.316956719 Arithmetic Mean (o) = 53.375 Number of Data (n) = 8 Sum of Values (x) = 427 Sum of Squares of Values (x 2 ) = 22805

#### AX2= AX1= AU3= AU2= AU1=

Data Input Precautions S S inputs the same data twice.

x2 x n y2 y xy o xn xn-1 p yn yn-1

Regression coefficient A Regression coefficient B Regression calculation other than quadratic regression Correlation coefficient r

AU1 AU2 AU3 AUr1 AUr2 AUr3 AX1 AX2 AX3 AXr1 AXr2 AXr3 AXrr1 AXrr2

#### AXrr3 AXrrr1 AXrrr2

The following table shows the key operations you should use to recall results in the case of quadratic regression.

#### x3 x2y x4

Regression coefficient C

#### m1 m2 n

AUrr1 AUrr2 AUrr3 AXrr3 AXrrr1 AXrrr2 AXrrr3

The values in the above tables can be used inside of expressions the same way you use variables.

#### u Linear Regression

The regression formula for linear regression is: y = A + Bx. Example: Atmospheric Pressure vs. Temperature

Temperature Atmospheric Pressure

#### 10C 15C 20C 25C 30C

1003 hPa 1005 hPa 1010 hPa 1011 hPa 1014 hPa

Perform linear regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate atmospheric pressure at 18C and temperature at 1000 hPa. Finally, calculate the coefficient of determination (r 2 ) and sample covariance.

#### In the REG Mode:

1(Lin) A B 1 (Scl) = (Stat clear)

#### 10 P1003 S

15 P 1005 S 20 P1010 S 25 P 1011 S 30 P 1014 S

Regression Coefficient A = 997.4 Regression Coefficient B = 0.56 Correlation Coefficient r = 0.982607368

#### AXrr1= AXrr2= AXrr3=

Atmospheric Pressure at 18C = 1007.48

#### 18 A X r r r 2 = 30

Temperature at 1000 hPa = 4.642857143

#### 1000 A X r r r 1 =

Coefficient of Determination = 0.965517241

#### Sample Covariance = 35

AXrr3K= EAUr3, AU3-AX1AXr1F\ EAU3,1F=

u Logarithmic, Exponential, Power, and Inverse Regression

Use the same key operations as linear regression to recall results for these types of regression. The following shows the regression formulas for each type of regression. Logarithmic Regression Exponential Regression Power Regression Inverse Regression y A B In x y A eBx (In y In A + Bx) y A xB (In y In A + B In x) y A B 1/x

#### u Quadratic Regression

The regression formula for quadratic regression is: y = A + Bx + Cx2. Example: Perform quadratic regression to determine the regression formula terms for the data nearby. Next, use the regression formula to estimate the values for n (estimated value of y) for xi = 16 and m (estimated value of x) for yi = 20.

#### 1.6 23.5 38.0 46.4 48.0

r 3(Quad) A B 1 (Scl) = (Stat clear) 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S 103 P 46.4 S 118 P 48.0 S

Regression Coefficient A = 35.59856934 Regression Coefficient B = 1.495939413

Regression Coefficient C = 6.71629667 i10 3

n when xi is 16 = 13.38291067 m1 when yi is 20 = 47.14556728 m2 when yi is 20 = 175.5872105

16 A X r r r 3 = 20 A X r r r 1 = 20 A X r r r 2 =

#### Data Input Precautions

S S inputs the same data twice. You can also input multiple entries of the same data using A G. To input the data 20 and 30 five times, for example, press 20 P 30 A G 5 S. The above results can be obtained in any order, and not necessarily that shown above. Precautions when editing data input for standard deviation also apply for regression calculations.

#### Technical Information

k When you have a problem.

If calculation results are not what you expect or if an error occurs, perform the following steps. 1. Press A B 2(Mode) = to initialize all modes and settings. 2. Check the formula you are working with to confirm it is correct. 3. Enter the correct mode and try performing the calculation again. If the above steps do not correct the problem, press the 5 key. The calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. Make sure you always keep written copies of all important data.

#### k Error Messages

The calculator is locked up while an error message is on 32

the display. Press t to clear the error, or press e or r to display the calculation and correct the problem. See Error Locator for details.

#### Math ERROR

Causes Calculation result is outside the allowable calculation range. An attempt to perform a function calculation using a value that exceeds the allowable input range. An attempt to perform an illogical operation (division by zero, etc.) Action Check your input values and make sure they are all within the allowable ranges. Pay special attention to values in any memory areas you are using.

#### Stack ERROR

Cause The capacity of the numeric stack or operator stack is exceeded. Action Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels. Divide your calculation into two or more separate parts.

#### Syntax ERROR

Cause An attempt to perform an illegal mathematical operation. Action Press e or r to display the calculation with the cursor located at the location of the error and make required corrections.

#### Arg ERROR

Cause Improper use of an argument 33

Action Press e or r to display the location of the cause of the error and make required corrections.

#### Numeric Stack 5 4

Command Stack

Calculations are performed in sequence according to Order of Operations. Commands and values are deleted from the stack as the calculation is performed.

#### k Input Ranges

Internal digits: 12 Accuracy*: As a rule, accuracy is 1 at the 10th digit. Functions sinx Input Range DEG 0 x 4.4999999991010 RAD 0 x 785398163.3 GRA 0 x 4.9999999991010 cosx DEG 0 x 4.5000000081010 RAD 0 x 785398164.9 GRA 0 x 5.0000000091010 tanx DEG Same as sinx, except when x= (2n-1)90. RAD Same as sinx, except when x= (2n-1)/2. GRA Same as sinx, except when x= (2n-1)100. sin1x cos1x tan x

#### 0 x x 9.x 230.2585092

sinhx coshx

sinh1x 0 x 4.9999999991099 cosh1x 1 x 4.9999999991099 tanhx

#### 0 x 9.9999999991099

tanh x 0 x 9.999999999101 logx/lnx 0 x 9.9999999991099 10x 9.9999999991099 x 99.99999999 9.9999999991099 x 230.2585092

#### Functions

Input Range 0 x x x ; x G 0 x 0 x 69 (x is an integer) 0 n 11010, 0 r n (n, r are integers) 1 {n!/(nr)!} n 11010, 0 r n (n, r are integers) 1 [n!/{r!(nr)!}] 110100

#### x x2 1/x 3 x x!

49 Pol(x, y) x, y 9.99999999910 (x2+y2) 9.Rec(r, ) 0 r 9.99999999910 : Same as sinx a, b, c 110100 0 b, c x110100 Decimal Sexagesimal Conversions 000 x 99999959 x0: 110100ylogx100 ^(xy) x0: yx0: yn, 2n+1 (n is an integer) However: 110100 ylogx100

#### y0: x G 0

1101001/x logy100 y0: xy0: x2n1, n (n G 0; n is an integer) However: 110100 1/x logy100 Total of integer, numerator, and denominator must be 10 digits or less (including division marks). x 11050 y 11050 n 110100 xn, yn, o, p : n G 0 xn1, yn1, A, B, r : n G 0, 1 37

#### SD (REG)

* For a single calculation, calculation error is 1 at the 10th digit. (In the case of exponential display, calculation error is 1 at the last significant digit.) Errors are cumulative in the case of consecutive calculations, which can also cause them to become large. (This is also true of internal consecutive calculations that are performed x 3 in the case of ^(x y), y , x!, , nPr, nCr, etc.) In the vicinity of a functions singular point and point of inflection, errors are cumulative and may become large.

#### Power Supply

(fx-95MS only)

Users of other models should refer to the Users Guide 2 (Additional Functions). This calculator is powered by a single AA-size battery.

#### Replacing the Battery

Dim figures on the display of the calculator indicate that battery power is low. Continued use of the calculator when the battery is low can result in improper operation. Replace the battery as soon as possible when display figures become dim.

To replace the battery 1 Press A i to turn power off. Screw

2 Remove the six screws that hold the back cover in place and then remove the back cover. 3 Remove the old battery. 4 Load a new battery into the unit with its positive k and negative l ends facing correctly. 5 Replace the back cover and secure it in place with the six screws. 6 Press 5 to turn power on. 38

#### u Auto Power Off

Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on.

#### Specifications

Users of other models should refer to the Users Guide 2 (Additional Functions). Power Supply: Single AA-size battery (R6P (SUM-3)) Battery Life: Approximately 17,000 hours continuous display of flashing cursor. Approximately 2 years when left with power turned off. 19.5 (H) i 78 (W) i 155 (D) mm 3/4 (H) 31/16 (W) 61/8 (D) 130 g (4.6 oz) including battery

#### Dimensions: Weight:

Power Consumption: 0.0002 W Operating Temperature: 0C to 40C (32F to 104F)

Important notice for fx-912MS owners

The names fx-912MS (Japan domestic model name) and fx-115MS (international model name) apply to the same model. Owners of the fx-912MS should refer to the description of fx-115MS. 39

#### CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan

SA0206-E Printed China SA0206-D Printed in in China CACA 310067-1 310063-1

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