# Casio FX-82MS

# Manual

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### User reviews and opinions

Haraldsvang |
10:42pm on Wednesday, August 18th, 2010 |

casio calculator I have had this calculator since 1979 and it is still going strong, never waivered but a bit battered now. |

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### Documents

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-fitting clothing 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 moisture 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.

#### 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.. 8 kReplay Function... 9 kError Locator... 9 kMulti-statements.. 9 kExponential Display Formats. 10 kDecimal Point and Separator Symbols. 10 kInitializing the Calculator.. 11

#### Basic Calculations.. 11

kArithmetic Calculations... 11 kFraction Operations... 11 kPercentage Calculations.. 13 kDegrees, Minutes, Seconds Calculations. 14 kFIX, SCI, RND... 15

#### Memory Calculations.. 16

kAnswer Memory... kConsecutive Calculations. kIndependent Memory.. kVariables.. 16 17

Scientific Function Calculations.. 17

kTrigonometric/Inverse Trigonometric Functions. 18 kHyperbolic/Inverse Hyperbolic Functions. 18 E-5

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

Statistical Calculations.. 21

Standard Deviation.. 21 Regression Calculations.. 24

Technical Information.. 28

kWhen you have a problem.. kError Messages... kOrder of Operations.. kStacks... kInput Ranges.. 32

Power Supply.. 34 Specifications.. 37

#### 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. To perform this type of calculation: Basic arithmetic calculations Standard deviation Regression calculations Perform this To enter key operation: this mode:

#### F1 F2 F3

COMP SD REG

Pressing the F key more than once 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:

#### Statistical Calculations

SD REG

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.

#### 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.

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. For details, see Order of Operations. 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

11 Example 2: 3C1C4+ 1C2C3= Example 3: 1 Example 4: 1.6 2.1 2

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

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. Example 1: 2.3 (Decimal Fraction) 4 2.75 = 2.75

#### 4.4.00

1 Example 2: 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. 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 , E-13

Example 5: To discount the sum of 168, 98, and 734 by 20% (800) 168 + 98 + 734 = g A j 1 * 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 (160%) increase in weight? 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=

#### p 1 - 20 A v , *

k Degrees, Minutes, Seconds Calculations

You can perform sexagesimal calculations using degrees (hours), minutes, and seconds, and convert between sexagesimal and decimal values. Example 1: To convert the decimal value 2.258 to a sexagesimal value and then back to a decimal value 2.258 =

#### 2.258 21528.8 2.258

Example 2: To perform the following calculation: 123456 3.I 34 I 56 I - 3.45 = E-14

#### 432431.2

k FIX, SCI, RND

To change the settings for the number of decimal places, the number of significant digits, or the exponential display format, press the F key a number of times until you reach the setup screen shown below.

Press the number key ( 1, 2, or 3) that corresponds to the setup item you want to change.

1 (Fix): Number of decimal places 2 (Sci): Number of significant digits 3 (Norm): Exponential display format

#### Example 1: \ 7 - 14 =

(Specifies three decimal places.)

#### 400.00

F.. 1(Fix) 3

#### 200 \ 7 =

400.00000 28.57100 400.00000

(Internal calculation continues using 12 digits.)

#### - 14 =

The following performs the same calculation using the specified number of decimal places. 200 \ 7 =

#### (Internal rounding)

28.57100 28.57100 399.99400

#### AQ - 14 =

Press F.. 3(Norm) 1 to clear the Fix specification. Example 2: 1 3, displaying result with two significant digits (Sci 2)

#### F.. 2(Sci) \ 3 =

Press F.. 3(Norm) 1 to clear the Sci specification. E-15

#### Memory Calculations

Use the F key to enter the COMP Mode when you want to perform a calculation using memory. COMP... F 1

#### k Answer Memory

Whenever you press = after inputting values or an expression, the calculated result automatically updates Answer Memory contents by storing the result. In addition to =, Answer Memory contents are also updated with result whenever you press A v, |, A {, or A j followed by a letter (A through F, or M, X, or Y). You can recall Answer Memory contents by pressing g. Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent. Answer Memory contents are not updated if the operation performed by any of the above key operations results in an error.

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+). E-16

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 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 scientific function 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)

Example 1: sin 6352o41 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.. 2 (Rad) q

#### 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: sinh

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

30 4.094622224

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: 23 0.125 Example 6: (2)4 16

#### RD2TW4=

Negative values inside of calculations must be enclosed within parentheses. For details, see Order of Operations.

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

#### 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 =

#### Example 4: 1023

123 + 30 K = 12 N =

Example 5: 1 Example 6: 4 Example 7: 8! 40320

#### R3a,4aTa=

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 (840) value (1234 is allowed, but 1123 is not). 7Am4= Example 11: To determine how many different 4-member groups can be organized in a group of 10 individuals (210) 10 n 4 =

#### 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 r 4.25 A v 2(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. E-20

Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r,) (Rad) r2

#### 1.047197551

f1P L3T= 0o

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

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

#### 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 In the SD Mode and REG Mode, the | key operates as the S key. 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 (x2 ) = 22805

AX3= AX2= AX1= AU3= AU2= AU1=

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 110 ten times, for example, press 110 A G 10 S. You can perform the above key operations in any order, and not necessarily that shown above. While inputting data or after inputting data is complete, you can use the [ and ] keys to scroll through data you have input. If you input multiple entries of the same data using A G to specify the data frequency (number of data items) as described above, scrolling through data shows both the data item and a separate screen for the data frequency (Freq). E-22

You can then edit the displayed data, if you want. Input the new value and then press the = key to replace the old value with the new one. This also means that if you want to perform some other operation (calculation, recall of statistical calculation results, etc.), you should always press the t key first to exit data display. Pressing the S key instead of = after changing a value on the display registers the value you input as a new data item, and leaves the old value as it is. You can delete a data value displayed using [ and ] by pressing A U. Deleting a data value causes all values following it to be shifted up. Data values you register are normally stored in calculator memory. The message Data Full appears and you will not be able to input any more data if there is no memory left for data storage. If this happens, press the = key to display the screen shown below.

#### Ed i t OFF ESC

Press 2 to exit data input without registering the value you just input. Press 1 if you want to register the value you just input, without saving it in memory. If you do this, however, you will not be able to display or edit any of the data you have input. To delete data you have just input, press A U. After inputting statistical data in the SD Mode or REG Mode, you will be unable to display or edit individual data items any longer after perform either the following operations. Changing to another mode Changing the regression type (Lin, Log, Exp, Pwr, Inv, Quad)

#### Regression Calculations

Use the F key to enter the REG Mode when you want to perform statistical calculations using regression. REG... F 3 In the SD Mode and REG Mode, the | key operates as the S key. Entering the REG Mode displays screens like the ones shown below.

#### L i n Log Ex p

I nv Quad

Press the number key ( 1, 2, or 3) that corresponds to the type of regression you want to use. 1 (Lin) : Linear regression 2 (Log) : Logarithmic regression 3 (Exp) : Exponential regression r 1 (Pwr) : Power regression r 2 (Inv) : Inverse regression r 3 (Quad) : Quadratic regression Always start data input with A B 1 (Scl) = to clear statistical memory. Input data using the key sequence shown below. <x-data> P <y-data> S The values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below.

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.

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

#### 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. E-25

Example: Atmospheric Pressure vs. Temperature Temperature Atmospheric Perform linear regression to dePressure termine the regression formula 10C 1003 hPa terms and correlation coefficient 15C 1005 hPa for the data nearby. Next, use 20C 1010 hPa the regression formula to esti25C 1011 hPa mate atmospheric pressure at 30C 1014 hPa 5C 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 Atmospheric Pressure at 5C = 994.6

#### AXrr1= AXrr2= AXrr3=

ED5FAXrrr2=

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 + BIn x) y A B 1/x

#### u Quadratic Regression

The regression formula for quadratic regression is: y = A + Bx + Cx2. Example:

#### 1.6 23.5 38.0 46.4 48.0

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.

#### In the REG Mode:

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 AXrr1= Regression Coefficient B = 1.495939413 AXrr2=

Regression Coefficient C = 6.71629667 i10 3

#### AXrr3=

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 =

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. Do not use variables A through F, X, or Y to store data when performing statistical calculations. These variables are used for statistical calculation temporary memory, so any data you may have assigned to them may be replaced by other values during statistical calculations. Entering the REG Mode and selecting a regression type (Lin, Log, Exp, Pwr, Inv, Quad) clear variables A through F, X, and Y. Changing from one regression type to another inside the REG Mode also clears these variables.

#### 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 Stacks

This calculator uses memory areas, called stacks, to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (Stack ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded. Example:

#### 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 tan1x sinhx coshx 0 x x 9.x 230.2585092

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.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)!} 110100 E-32

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

Functions

Input Range 0 n 11010, 0 r n (n, r are integers) 1 [n!/{r!(nr)!}] 110100

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

#### SD (REG)

xn, yn, o, p : n G 0 xn1, yn1, A, B, r : n G 0, 1

* 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 3 x , nPr, nCr, etc.) in the case of ^(x y), y , x!, In the vicinity of a functions singular point and point of inflection, errors are cumulative and may become large. E-33

#### Power Supply

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

#### fx-85MS/fx-300MS

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 six screws that 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 six screws. 5 Press 5 to turn power on. Be sure not to skip this step.

#### Screw Screw

fx-83MS/fx-270MS/fx-350MS

This calculator is powered by single G13 Type (LR44) button 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 off power. 2 Remove the screw that holds the battery cover in place and then remove the battery cover. 3 Remove the old battery. 4 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). 5 Replace the battery cover and secure it in place with the screw. 6 Press 5 to turn power on.

#### fx-82MS

This calculator is powered by a single AA-size 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-82MS: Single AA-size battery (R6P (SUM-3)) fx-83MS/fx-270MS/fx-350MS: Single G13 Type button battery (LR44) fx-85MS/fx-300MS: Solar cell and a single G13 Type button battery (LR44) Battery Life: fx-82MS: Approximately 17,000 hours continuous display of flashing cursor. Approximately 2 years when left with power turned off. fx-83MS/fx-270MS/fx-350MS: Approximately 9,000 hours continuous display of flashing cursor. Approximately 3 years when left with power turned off. fx-85MS/fx-300MS: Approximately 3 years (1 hour use per day). Dimensions: fx-82MS: 18.6 (H) 85 (W) 156 (D) mm 3/4 (H) 3 3/8 (W) 6 1/8 (D) fx-83MS/fx-85MS/fx-270MS/fx-300MS/fx-350MS: 12.2 (H) 85 (W) 155 (D) mm 1/2 (H) 3 3/8 (W) 6 1/8 (D) Weight: fx-82MS: 125 g (4.4 oz) including battery fx-83MS/fx-85MS/fx-270MS/fx-300MS/fx-350MS: 100 g (3.5 oz) including battery Power Consumption: 0.0002 W Operating Temperature: 0C to 40C (32F to 104F)

#### CASIO COMPUTER CO., LTD.

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

SA0311-C Printed in China CA 310120-001V03

#### Using Casio fx82MS

Statistical calculations

#### Learning Skills

Introduction:

This sheet will teach you how to use the Casio fx82MS calculator to perform statistical operations. See also our handout for mathematical functions. Any further queries please contact Student Central.

This sheet will teach you to:

Put your calculator into statistical mode Enter observations Display the descriptive statistics Enter group data Perform linear regression

#### 1. Statistical Mode

To put your calculator into statistics mode press MODE 2

A small SD will appear on the display

To clear the statistical memory press, this should be done before entering any new data. SHIFT CLR 1 =

2. Entering single variable observations

To enter observations press M+ after entering the observation

#### Number of scores

The number of scores (n) is 4 this is displayed while entering

Example 2.1 Enter 10, 12, 13, 16 Calculator steps: 10 M+ 12 M+ 13 M+

#### Page 1 of 5

Learning Skills @ CSU

3. Display the Descriptive Statistics

Calculator symbol mean Sample standard deviation Population standard deviation Sample variance Scores added up

#### Common symbol

Calculator steps

#### answer

SHIFT SHIFT

#### 12.75 2.5

3 = 2 =

#### 6.25 51

Scores squared then added up

By using the shift key you are accessing the S-VAR key for the mean and standard deviations and the SSUM key for the sums of the scores.

4. Entering observations from a frequency table

To enter observations from a frequency table type in; Observation Example 4.1: Enter the following table into your calculator score Calculator steps: SHIFT CLR 1 , , , , = M+ M+ M+ M+ frequency SHIFT , frequency M+

1. Remember when entering new data you must clear the memory first 2. The comma (,) key is next to the M+ key 3. The total number of observations is 33 colon

#### SHIFT SHIFT SHIFT SHIFT

By using the shift key you are accessing the semi which is used to separate the score from its frequency. Page 2 of 5

Once the observations are entered the mean and standard deviation are found as above. If the scores are a sample If the scores are a population

#### x 12.394 s 2.263

12.394

#### 5. Entering Grouped data

To enter grouped data you first have to find the midpoint of each group. This is done by adding together the lowest and highest value from each group and then dividing it by two. We then use these as our observations. Example 5.1: group > 0 up to and including 10 >10 up to and including 20 >20 up to and including 30 >30 up to and including 40 To find the midpoint of each group: (0+10)/2=5 (10+20)/2=15 (20+30)/2=25 (30+40)/2=35 Calculator steps: SHIFT CLR 1 = (n = 109) If the scores are a sample Approximate: Approximate: Approximate: If the scores are a population Approximate: Approximate: Approximate:

#### frequency 21 30

AC M+ M+ M+ M+ The mean and standard deviation are only approximate because we are using each class centre to approximate the individual observations

#### , , , ,

20.138

#### 11.220

s 11.272

#### s 2 127.064

125.898

#### Page 3 of 5

6. Linear Regression Mode

To put your calculator into statistics mode press MODE 3 1

A small REG will appear on the display

Again it is necessary to clear previous data before entering any new information. SHIFT CLR 1 =

7. Entering x and y data sets

To enter x and y observations press x value , y value M+

Example 7.1 x score (independent variable) 10 y score (dependent variable) 27

Calculator steps: SHIFT 10 , , , , , CLR M+ M+ M+ M+ M+ =

#### Page 4 of 5

8. Regression output

SHIFT 2 and the right replay arrow twice 1 = this will give A the y-intercept of the regression line

#### A = 16.189

SHIFT 2 and the right replay arrow twice 2 = this will give B the slope of the regression line

#### B = 0.946

SHIFT 2 and the right replay arrow twice this will give r the correlation coefficient

#### = r = 0.417

The means and sums are found by using the S-VAR and S-SUM keys and the right replay arrow key. When you have finished your regression question it is important to get out of that mode before doing any other calculations.

#### 9. For more information

Visit our Learning Skills website at http://www.csu.edu.au/division/studserv/learning/index.html

#### Copyright

Learning Skills, Charles Sturt University, December 2008

#### Page 5 of 5

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