EN fx-82AU PLUS II (2nd edition / NATURAL-V.P.A.M.) User’s Guide CASIO Worldwide Education Website https://edu.casio.com Manuals are available in multi languages at https://world.casio.
Table of Contents Before Using the Calculator.................................................... 3 About this Manual.................................................................................... 3 Initializing the Calculator.......................................................................... 3 Precautions.............................................................................................. 3 Safety Precautions..............................................................................
Function Calculations............................................................ 27 Pi (π), Natural Logarithm Base e............................................................ 27 Trigonometric Functions........................................................................ 27 Hyperbolic Functions............................................................................. 27 Angle Unit Conversion........................................................................... 28 Exponential Functions..........
Before Using the Calculator About this Manual • 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.
• Use only the type of battery specified for this calculator in this manual. Handling Precautions • Even if the calculator is operating normally, replace the battery according to the schedule shown below. Continued use after the specified number of years may result in abnormal operation. Replace the battery immediately after display figures become dim. fx-82AU PLUS II: Every 2 years • A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator.
Turning Power On and Off • Press • Press to turn on the calculator. (OFF) to turn off the calculator. Note • The calculator also will turn off automatically after approximately 10 minutes of nonuse. Press the key to turn the calculator back on. Adjusting Display Contrast 1. Press (SETUP) ( CONT 2. Use and to adjust display contrast. 3. After the setting is the way you want, press ). .
• The following shows an example of how a key operation to select an onscreen menu item is represented in this manual. (COMP)* Example: * Indicates the menu item that is selected by the number key operation ( ) 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 illustration nearby. In this manual, cursor key operation is indicated as , , , and .
The alpha input mode has been entered by pressing the key. The alpha input mode will be exited and this indicator will disappear when you press a key. M There is a value stored in independent memory. STO The calculator is standing by for input of a variable name to assign a value to the variable. This indicator appears after you press (STO). RCL The calculator is standing by for input of a variable name to recall the variable's value. This indicator appears after you press .
Using Menus Some of the calculator's operations are performed using menus. Pressing or , for example, will display a menu of applicable functions. The following are the operations you should use to navigate between menus. • You can select a menu item by pressing the number key that corresponds to the number to its left on the menu screen. • The indicator in the upper right corner of a menu means there is another menu below the current one. The indicator means another menu above.
Calculation Modes and Calculator Setup Calculation Mode Before starting a calculation, you must first enter the correct mode as indicated in the table below. When you want to perform this type of operation: Perform this key operation: General calculations (COMP) Statistical and regression calculations (STAT) Verify a calculation (VERIF) Note • The initial default calculation mode is the COMP Mode.
Natural Display (MthIO-LineO) (SETUP) (MthIO) Linear Display (LineIO) (SETUP) (LineIO) (LineO) Natural Display (MthIO-MathO, MthIO-LineO) causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper. MthIO-MathO displays input and calculation results using the same format as they are written on paper. MthIO-LineO displays input the same way as MthIO-MathO, but calculation results are displayed in linear format.
Note • The calculator switches to Linear Display automatically whenever you enter the STAT Mode. Specifying the Default Angle Unit To specify this as the default angle unit: Perform this key operation: Degrees (SETUP) (Deg) Radians (SETUP) (Rad) Grads (SETUP) (Gra) 90°= π/2 radians = 100 grads Specifying the Number Format Specifies the number of digits for display of a calculation result.
format. Outside the specified range, results are displayed using nonexponential format. Norm 1: 10-2 > |x|, |x| ≧ 1010 Norm 2: 10-9 > |x|, |x| ≧ 1010 Example: (LineIO) 1 ÷ 200 = 5 × 10-3 (Norm 1) 0.005 (Norm 2) Specifying the Fraction Display Format To specify this fraction display format: Perform this key operation: Mixed (SETUP) (ab/c) Improper (SETUP) (d/c) Specifying the Stat Format Specifies whether or not to display a FREQ (frequency) column in the STAT Mode Statistics Editor.
Adjusting Display Contrast (SETUP) ( CONT See "Getting Started" for details. ) Initializing Calculator Settings Perform the following procedure to initialize the calculator, which returns the calculation mode to COMP and returns all other settings, including setup menu settings, to their initial defaults.
Inputting Expressions and Values Basic Input Rules Calculations can be input in the same form as they are written. When you press the priority sequence of the input calculation will be evaluated automatically and the result will appear on the display. Example 1: 4 × sin30 × (30 + 10 × 3) = 120 *1 Input of the closing parenthesis is required for sin, sinh, and other functions that include parentheses. *2 These multiplication symbols (×) can be omitted.
Examples: 6 ÷ 2 (1 + 2) → 6 ÷ (2 (1 + 2)) 6 ÷ A (1 + 2) → 6 ÷ (A (1 + 2)) 1 ÷ (2 + 3) sin(30) → 1 ÷ ((2 + 3) sin(30)) - When a multiplication sign is omitted immediately before a variable, a constant, etc. Examples: 6 ÷ 2π → 6 ÷ (2π) 2 ÷ 2√2 → 2 ÷ (2√2) 4π ÷ 2π → 4π ÷ (2π) - When inputting a function that uses commas (such as Pol, Rec, and RanInt#), be sure to input the closed parentheses required by the expression.
• The cursor will change shape to when there are 10 bytes or less of allowed input remaining. If this happens, end calculation input and then press . Inputting with Natural Display Selecting Natural Display makes it possible to input and display fractions and certain functions ( , , , , , , , , , Abs) just as they are written in your textbook.
1 7 6 (INS) As shown above, the value or expression to the right of the cursor after (INS) are pressed becomes the argument of the function that is specified next. The range encompassed as the argument is everything up to the first open parenthesis to the right, if there is one, or everything up to the first function to the right (sin(30), log(4), etc.) This capability can be used with the following functions: , ( ), ( ), ( ), ( ), , , ( ), .
To insert a character or function into a calculation: Use and to move the cursor to the location where you want to insert the character or function and then input it. Be sure always to use the insert mode if Linear Display is selected. To clear all of the calculation you are inputting: Press .
Basic Calculations key to enter the COMP Mode when you want to perform Use the basic calculations. (COMP) Toggling Calculation Results Each press of will toggle the currently displayed calculation result between its decimal form and fraction form. Example 1: 1 ÷ 5 = 0.2 = 1 (MthIO-LineO) 5 1 Example 2: 1 ÷ 5 = 0.2 = 5 1 (LineIO) 5 1 Example 3: 1 - 1 5 0.2 5 0.2 1 5 5 1 5 0.2 4 1 = = 0.
Note • With Natural Display (MathO), pressing instead of after inputting a calculation will display the calculation result in decimal form. Fraction Calculations Note that the input method for fractions is different, depending upon whether you are using Natural Display or Linear Display.
Percent Calculations Inputting a value and pressing become a percent. (%) causes the input value to Example 1: 150 × 20% = 30 150 20 (%) 30 Example 2: Calculate what percentage of 880 is 660 (75%) 660 880 (%) 75 Example 3: Increase 2500 by 15% (2875) 2500 2500 15 (%) 2875 Example 4: Decrease 3500 by 25% (2625) 3500 3500 25 (%) 2625 Degree, Minute, Second (Sexagesimal) Calculations You can perform calculations using sexagesimal values, and convert values between sexagesimal and decimal.
2 15 18 2°15’18” (Converts sexagesimal to decimal.) 2.255 (Converts decimal to sexagesimal.) 2°15’18” Multi-Statements You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press . Example: 3 + 3 : 3 × 3 3 3 (:) 3 3 6 9 Using Engineering Notation A simple key operation transforms a displayed value to engineering notation. Example 1: Transform the value 1234 to engineering notation, shifting the decimal point to the right.
Example 1: To perform prime factorization on 1014 1014 1014 (FACT) When you perform prime factorization on a value that includes a factor that is prime number with more than three digits, the part that cannot be factored will be enclosed in parentheses on the display. Example 2: To perform prime factorization on 4104676 (= 22 × 10132) 4104676 4104676 (FACT) Any one of the following operations will exit prime factorization result display. - Pressing (FACT) or . or .
3+3=6 3 3 6 (Scrolls back.) 4 (Scrolls back again.) 2 Note • Calculation history data is all cleared whenever you press , when you change to a different calculation mode, when you change the display format, or whenever you perform the following operations: (CLR) (All) (CLR) (Setup) (Yes), (Yes). Replay While a calculation result is on the display, you can press edit the expression you used for the previous calculation.
(MthIO-LineO) 123 456 579 (Continuing) 789 Variables (A, B, C, D, E, F, M, X, Y) Your calculator has nine preset variables named A, B, C, D, E, F, M, X, and Y. You can assign values to variables and use the variables in calculations.
To subtract the result of 10 + 5 from M (Continuing) 10 5 (M-) 15 (Continuing) (M) 35 To recall the contents of M Note • Variable M is used for independent memory. Clearing the Contents of All Memories Ans memory, independent memory, and variable contents are retained , change the calculation mode, or turn off the even if you press calculator. Perform the following procedure when you want to clear the contents of all memories.
Function Calculations key to enter the COMP Mode when you want to perform Use the function calculations. (COMP) Note: Using functions can slow down a calculation, which may delay display of the result. Do not perform any subsequent operation while waiting for the calculation result to appear. To interrupt an ongoing calculation before its result appears, press . Pi (π), Natural Logarithm Base e π is displayed as 3.141592654, but π = 3.14159265358980 is used for internal calculations. e is displayed as 2.
(sinh) 1 1.175201194 (cosh-1) 1 0 Example 2: cosh-1 1 = 0 Angle Unit Conversion °, r, g : These functions specify the angle unit. ° specifies degrees, r radians, and g grads. Input a function from the menu that appears when you perform the following key operation: (DRG ).
Power Functions and Power Root Functions Note that the input methods for , , , and are different depending upon whether you are using Natural Display or Linear Display. Example 1: 1.2 × 103 = 1200 (MthIO-LineO) 1 2 10 3 1200 2 16 Example 2: (1 + 1)2+2 = 16 (MthIO-LineO) 1 1 2 Example 3: (52)3 = 15625 5 15625 Example 4: 5√32 = 2 (MthIO-LineO) ( (LineIO) 5 )5 ( 32 2 ) 32 2 Example 5: To calculate √2 × 3 (= 4.242640687...
Note • The following functions cannot be input in consecutive sequence: x2, x3, input 2 , for example, the final press the key, and then press , x-1. If you 2 will be ignored. To input 22 , input 2 , (MthIO-LineO). Rectangular-Polar Coordinate Conversion Pol converts rectangular coordinates to polar coordinates, while Rec converts polar coordinates to rectangular coordinates. (1) Rectangular Coordinates (Rec) (2) Polar Coordinates (Pol) Specify the angle unit before performing calculations.
(MthIO-LineO) (Rec) 2 (,) 45 X = 1, Y = 1 Factorial Function (!) Example: (5 + 3)! = 40320 5 3 40320 Absolute Value Function (Abs) Note that the input method is different depending upon whether you are using Natural Display or Linear Display. Example: |2 - 7| × 2 = 10 (MthIO-LineO) 2 7 2 10 2 7 2 10 (LineIO) Random Number (Ran#) Function that generates a pseudo random number in the range of 0.000 to 0.999. The result is displayed as a fraction when Natural Display is selected.
Random Integer (RanInt#) For input of the function of the form RanInt#(a, b), which generates a random integer within the range of a to b. Example: To generate random integers in the range of 1 to 6 (RanInt) 1 (,) 6 2 6 1 (Results shown here are for illustrative purposes only. Actual results will differ.) Permutation (nPr) and Combination (nCr) Example: To determine the number of permutations and combinations possible when selecting four people from a group of 10.
Example: To perform the following calculations when Fix 3 is selected for the number of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3 (LineIO) (SETUP) (Fix) 10 3 3 (Rnd) 10 3 3 10.000 9.999 Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Greatest Common Divisor (GCD) GCD determines the greatest common divisor of two values. Example: To determine the greatest common divisor of 28 and 35 (GCD) 28 (,) 35 7 Least Common Multiple (LCM) LCM determines the least common multiple of two values.
Using Calculation Modes Statistical Calculations (STAT) To start a statistical calculation, perform the key operation (STAT) to enter the STAT Mode and then use the screen that appears to select the type of calculation you want to perform.
Note • When you want to change the calculation type after entering the STAT Mode, perform (STAT) the key operation (Type) to display the calculation type selection screen. Inputting Data Use the Statistics Editor to input data. Perform the following key operation (STAT) (Data).
To change the data in a cell: In the Statistics Editor, move the cursor to the cell that contains the data . you want to change, input the new data, and then press To delete a line: In the Statistics Editor, move the cursor to the line that you want to delete and then press . To insert a line: In the Statistics Editor, move the cursor to the location where you want to insert the line and then perform the following key operation: (STAT) (Edit) (Ins).
Statistics Menu Items Common Items Select this menu item: When you want to obtain this: (Type) Display the calculation type selection screen (Data) Display the Statistics Editor (Sum) Display the Sum sub-menu of commands for calculating sums (Var) Display the Var sub-menu of commands for calculating the mean, standard deviation, etc.
Var Sub-menu ( Select this menu item: (STAT) (Var)) When you want to obtain this: (n) Number of samples (x) Mean of the sample data (σx) Population standard deviation (sx) Sample standard deviation MinMax Sub-menu ( Select this menu item: (STAT) (MinMax)) When you want to obtain this: (minX) Minimum value (maxX) Maximum value (Q1) First quartile (med) Median (Q3) Third quartile Commands when Linear Regression Calculation (A+BX) Is Selected (STAT) (Sum)) Sum Sub-menu ( Select this m
(∑x2y) Sum of (X-data squares × Y-data) (∑x4) Sum of biquadrate of the X-data Var Sub-menu ( Select this menu item: (STAT) (Var)) When you want to obtain this: (n) Number of samples (x) Mean of the X-data (σx) Population standard deviation of the X-data (sx) Sample standard deviation of the X-data (y) Mean of the Y-data (σy) Population standard deviation of the Y-data (sy) Sample standard deviation of the Y-data Reg Sub-menu ( Select this menu item: (STAT) (Reg)) When you want to ob
(maxX) Maximum value of the X-data (minY) Minimum value of the Y-data (maxY) Maximum value of the Y-data Commands when Quadratic Regression Calculation (_+CX2) Is Selected (STAT) (Reg)) Reg Sub-menu ( Select this menu item: When you want to obtain this: (A) Regression coefficient constant term A (B) Linear coefficient B of the regression coefficients (C) Quadratic coefficient C of the regression coefficients (x̂1) Estimated value of x1 (x̂2) Estimated value of x2 (ŷ) Estimated value of y
(STAT) (Var) (σx) 1.154700538 Results: Mean: 3, Population Standard Deviation: 1.154700538 Example 3: To calculate the linear regression and logarithmic regression correlation coefficients for the following paired-variable data and determine the regression formula for the strongest correlation: (x, y) = (20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3 (three decimal places) for results.
Using VERIFY (VERIF) VERIFY is a function you can use to verify whether an input equality or inequality is true (indicated by TRUE) or false (indicated by FALSE). The following shows the general procedure for using VERIFY. Example: To verify whether 4√9 = 12 is true (MthIO-LineO) 1. Press (VERIF) to enter the VERIFY Mode. 2. Input 4√9 = 12. 4 9 (VERIFY) (=) 12 • You can select the equality symbol or inequality symbol from the menu that appears when you press (VERIFY). 3. To verify, press .
• Pol and Rec functions cannot be used in an expression. • In the VERIFY Mode, the calculator performs a mathematical operation on the input expression and then displays TRUE or FALSE based on the result.
5 25 (VERIFY) (VERIFY) (=) (=) 625 44
Technical Information Errors The calculator will display an error message whenever an error occurs for any reason during a calculation. There are two ways to exit an error message display: Pressing or to display the location of the error, or pressing to clear the message and calculation. Displaying the Location of an Error While an error message is displayed, press or to return to the calculation screen. The cursor will be positioned at the location where the error occurred, ready for input.
• 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.
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 key. This will cause the calculator to perform a routine that checks whether calculation functions are operating correctly.
3. Remove the battery, and then load a new battery with its plus (+) and minus (-) ends facing correctly. 4. Replace the cover. (CLR) (All) (Yes). 5. Initialize the calculator: • Do not skip the above step! Calculation Priority Sequence The priority sequence of input calculations is evaluated in accordance with the rules below. When the priority of two expressions is the same, the calculation is performed from left to right.
8 Permutation (nPr), combination (nCr) 9 Multiplication (×), division (÷) 10 Addition (+), subtraction (-) Note • When squaring a negative value (such as -2), the value being squared must be enclosed in parentheses ( the negative sign, inputting ). Since x2 has a higher priority than 2 2 would result in the squaring of 2 and then appending a negative sign to the result. • Always keep the priority sequence in mind, and enclose negative values in parentheses when required.
Function Calculation Input Ranges and Precision Functions Input Range Deg sinx cosx Rad Gra Deg tanx Rad Gra sin-1x, cos-1x tan-1x sinhx, coshx sinh-1x cosh-1x tanhx tanh-1x logx, lnx 10x 0 ≦ |x| < 9 × 109 0 ≦ |x| < 157079632.7 0 ≦ |x| < 1 × 1010 Same as sinx, except when |x| = (2n-1) × 90. Same as sinx, except when |x| = (2n-1) × π/2. Same as sinx, except when |x| = (2n-1) × 100. 0 ≦ |x| ≦ 1 0 ≦ |x| ≦ 9.999999999 × 1099 0 ≦ |x| ≦ 230.2585092 0 ≦ |x| ≦ 4.999999999 × 1099 1 ≦ x ≦ 4.
x! nPr nCr Pol(x, y) Rec(r, θ) °’ ” ← °’ ” xy 0 ≦ x ≦ 69 (x is an integer) 0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r are integers) 1 ≦ {n!/(n-r)!} < 1 × 10100 0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r are integers) 1 ≦ n!/r! < 1 × 10100 or 1 ≦ n!/(n-r)! < 1 × 10100 |x|, |y| ≦ 9.999999999 × 1099 √x2 + y2 ≦ 9.999999999 × 1099 0 ≦ r ≦ 9.999999999 × 1099 θ: Same as sinx a°b’c”: |a|, b, c < 1 × 10100; 0 ≦ b, c The display seconds value is subject to an error of ±1 at the second decimal place.
• Precision is basically the same as that described under "Calculation Range and Precision", above. x 3 • xy, √y, √ , x!, nPr, nCr type functions require consecutive internal calculation, which can cause accumulation of errors that occur with each calculation. • Error is cumulative and tends to be large in the vicinity of a function's singular point and inflection point.
4. Follow the instructions on the display to verify the authenticity of your calculator. to return to the mode menu.
Frequently Asked Questions Frequently Asked Questions ■ How can I perform input and display results the same way I did on a model that does not have Natural Textbook Format? → Perform the following key operation: (SETUP) (LineIO). See "Configuring the Calculator Setup" for more information. ■ How can I change a fraction form result to decimal form? How can I change a fraction form result produced by a division operation to decimal form? → See "Toggling Calculation Results" for the procedure.
Older (S-V.P.A.M.) Model: 30 15 15.5 15 15.5 Natural Textbook Display Model: (LineIO) Failure to press 45. 30 here as shown below will result in calculation of sin 30 55 15 0.
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