EN fx-82ZA PLUS II (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.................................................... 4 About this Manual.................................................................................... 4 Initializing the Calculator.......................................................................... 4 Precautions.............................................................................................. 4 Safety Precautions..............................................................................
Clearing the Contents of All Memories..........................................................28 Function Calculations............................................................ 29 Pi (π), Natural Logarithm Base e............................................................ 29 Trigonometric Functions........................................................................ 29 Hyperbolic Functions............................................................................. 29 Angle Unit Conversion...........
Specifications.........................................................................................59 Verifying the Authenticity of Your Calculator.......................................... 59 Frequently Asked Questions.................................................61 Frequently Asked Questions..................................................................
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-82ZA PLUS II: Every two years • A dead battery can leak, causing damage to and malfunction of 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 or approximately 60 minutes of non-use. 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 ). .
* Indicates the function that is accessed by the key operation ( ) before it. Note that this is not part of the actual key operation you perform. • The following shows an example of how a key operation to select an onscreen menu item is represented in this manual. Example: (COMP)* * Indicates the menu item that is selected by the number key ) before it. Note that this is not part of the actual key operation ( operation you perform.
Display indicators This indicator: Means this: The keypad has been shifted by pressing the key. The keypad will unshift and this indicator will disappear when you press a key. The alpha input mode has been entered by pressing the 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.
Important! • For some type of calculation that takes a long time to execute, the display may show only the above indicators (without any value) while it performs the calculation internally. Using Menus Some of the calculator's operations are performed using menus. Pressing or , for example, will display a menu of applicable functions. The following are the operations you should use to navigate between menus.
Calculation Modes and Calculator Setup Calculation Mode Before starting a calculation, you must first enter the correct mode as indicated in the table below.
Specifying the Display Format To specify this display format: Perform this key operation: Natural Display (MthIO-MathO) (SETUP) (MthIO) (MathO) Natural Display (MthIO-LineO) (SETUP) (MthIO) (LineO) Linear Display (LineIO) (SETUP) (LineIO) 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.
LineIO (Number Format: Norm 1) Note • The calculator switches to Linear Display automatically whenever you enter the STAT or BASE-N 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.
Sci: The value you specify (from 0 to 9) controls the number of significant digits for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed. Example: (LineIO) 1 ÷ 7 = 1,4286 × 10-1 (Sci 5) 1,429 × 10-1 (Sci 4) 1,428571429 × 10-1 (Sci 0) Norm: Selecting one of the two available settings (Norm 1, Norm 2) determines the range in which results will be displayed in exponential format.
f(x) and g(x) (SETUP) (TABLE) (f(x),g(x)) Specifying the Auto Power Off Setting You can specify a trigger time of 10 minutes or 60 minutes for Auto Power Off. To specify this: Perform this key operation: 10 Minutes (SETUP) (APO) (10Min.) 60 Minutes (SETUP) (APO) (60Min.) Adjusting Display Contrast (SETUP) ( CONT See "Getting Started" for details.
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.
• When Natural Display is selected, pressing while the cursor is at the end of the input calculation will cause it to jump to the beginning, while pressing while the cursor is at the beginning will cause it to jump to the end. • You can input up to 99 bytes for a calculation. Each numeral, symbol, or function normally uses one byte. Some functions require three to 13 bytes. • The cursor will change shape to when there are 10 bytes or less of allowed input remaining.
± a√b, ± d ± a√b, ± a'√b ± d'√e c' * The ranges of the coefficients (a, b, c, d, e, f) are as shown below. 1 ≦ a < 100, 1 < b < 1000, 1 ≦ c < 100 0 ≦ d < 100, 0 ≦ e < 1000, 1 ≦ f < 100 (a, b, c, d, e, f are integers) Example: 10√2 + 15 × 3√3 = 45√3 + 10√2 √ form 99√999 = 3129,089165 (= 297√111) decimal form Using Values and Expressions as Arguments (Natural Display only) A value or an expression that you have already input can be used as the 7 argument of a function.
Overwrite Input Mode (Linear Display only) You can select either insert or overwrite as the input mode, but only while Linear Display is selected. In the overwrite mode, text you input replaces the text at the current cursor location. You can toggle between the insert and overwrite modes by performing the operations: (INS). The cursor appears as " " in the insert mode and as " " in the overwrite mode.
Basic Calculations key to enter the COMP Mode when you want to perform Use the basic calculations. (COMP) Toggling Calculation Results While Natural Display is selected, each press of will toggle the currently displayed calculation result between its fraction form and decimal form, its √ form and decimal form, or its π form and decimal form.
Important! • Depending on the type of calculation result that is on the display when you press the key, the conversion process may take some time to perform. • With certain calculation results, pressing the key will not convert the displayed value. • You cannot switch from decimal form to mixed fraction form if the total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10.
• Fractions in calculation results are displayed after being reduced to their lowest terms. To switch a calculation result between improper fraction and mixed fraction form: d Perform the following key operation: (ab c c) To switch a calculation result between fraction and decimal form: . Press Percent Calculations (%) causes the input value to Inputting a value and pressing become a percent.
Note • You must always input something for the degrees and minutes, even if they are zero. Example 1: 2°20’30” + 39’30” = 3°00’00” 2 20 30 0 39 30 3°0’0” Example 2: Convert 2°15’18” to its decimal equivalent. 2 15 18 2°15’18” (Converts sexagesimal to decimal.) 2,255 (Converts decimal to sexagesimal.) 2°15’18” 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 .
0,000123×106 (←) Remainder Calculations You can use the ÷R function to obtain the quotient and remainder in a division calculation. Example: To calculate the quotient and remainder of 5 ÷ 2 (quotient = 2, remainder = 1) (MthIO-MathO) 5 (÷R) 2 5 (÷R) 2 (LineIO) Note • Only the quotient value of a ÷R calculation is stored in Ans memory. • Assigning the result of a remainder division calculation to a variable will assign the (÷R) 2 quotient value only.
Prime Factorization In the COMP Mode, a positive integer no more than 10 digits long can be factored to prime factors. 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: 1+1=2 1 1 2 2+2=4 2 2 4 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.
3 (Continuing) 4 12 30 Inputting Ans Memory Contents into an Expression Example: To perform the calculations shown below: 123 456 579 (Continuing) 789 Using PreAns Memory Example: For Tk+2 = Tk+1 + Tk (Fibonacci sequence), determine the sequence from T1 to T5. Note however, that T1 = 1 and T2 = 1.
T5 = T4 + T3 = 3 + 2 Result: The sequence is {1, 1, 2, 3, 5}. 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 recall the contents of M (Continuing) (M) 35 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. and turn PreAns memory contents are retained even if you press off the calculator without exiting the COMP Mode. 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.
(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 ).
2 (;) 16 (MthIO-MathO, MthIO-LineO) 2 4 16 4 Example 3: log2(43) = 6 (MthIO-MathO, MthIO-LineO) 2 6 Example 4: log2(4)3 = 8 (MthIO-MathO, MthIO-LineO) 2 4 8 Example 5: To calculate ln 90 (= loge 90) to three significant digits (Sci 3) (SETUP) (Sci) 90 4,50×100 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.
(MthIO-MathO) 2 3√2 4,243 (LineIO) 2 3 4,243 Example 6: 3√5 + 3√-27 = -1,290024053 (LineIO) ( ( Example 7: 1 1 1 3 4 )5 27 ) -1,290024053 = 12 (LineIO) 3 4 12 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 22 will be ignored. To input 2 , input 2 (MthIO-MathO).
Specify the angle unit before performing calculations. The calculation result for r and θ and for x and y are each assigned respectively to variables X and Y. Calculation result θ is displayed in the range of -180° < θ ≦ 180°.
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. Example: Generate three 3-digit random numbers. The random 3-digit decimal values are converted to 3-digit integer values by multiplying by 1000. 1000 (Ran#) 634 92 175 (Results shown here are for illustrative purposes only. Actual results will differ.
Rounding Function (Rnd) The argument of this function is made a decimal value and then rounded in accordance with the current number of display digits setting (Norm, Fix, or Sci). With Norm 1 or Norm 2, the argument is rounded off to 10 digits. With Fix and Sci, the argument is rounded off to the specified digit. When Fix 3 is the display digits setting, for example, the result of 10 ÷ 3 is displayed as 3,333, while the calculator maintains a value of 3,33333333333333 (15 digits) internally for calculation.
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 display the Statistics Editor: The number of data rows that can be input depends on the number of columns: 80 rows for one column, 40 rows for two columns, 26 rows for three columns.
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.
Creating a Numerical Table from Two Functions (TABLE) TABLE generates a numerical table based on one or two functions. You can use the function f(x) or the two functions f(x) and g(x). See "Configuring the Calculator Setup" for more information. Perform the following steps to generate a numerical table. 1. Press (TABLE) to enter the TABLE Mode. 2. Use the X variable to input two functions, one in the format f(x) and the other in the format g(x).
Input the increment step (Default = 1). Note: The Step specifies by how much the Start value should be sequentially incremented as the numerical table is generated. If you specify Start = 1 and Step = 1, X sequentially will be assigned the values 1, 2, 3, 4, and so on to generate the numerical table until the End value is reached. Step? • Inputting the Step value and pressing generates and displays the numerical table in accordance with the parameters you specified.
Note • You can use the numerical table screen for viewing values only. Table contents cannot be edited. • The numerical table generation operation causes the contents of variable X to be changed. • The maximum number of rows in the generated numerical table depends on the setup menu table setting. Up to 30 rows are supported for the "f(x)" setting, while 20 rows are supported for the "f(x),g(x)" setting.
Example 2: Continuing from above, switch to the hexadecimal mode and calculate 1F16 + 116 (HEX) 1 (F) 1 Example 3: Continuing from above, switch to the octal mode and calculate 78 + 18 (OCT) 7 1 Note • Use the following keys to input the letters A through F for hexadecimal values: (A), (B), (C), (D), (E), (F). • In the BASE-N Mode, input of fractional (decimal) values and exponents is not supported. If a calculation result has a fractional part, it is cut off.
(DEC) (BASE) (BASE) (BASE) (BASE) (d) 10 (h) 10 (b) 10 (o) 10 36 Converting a Calculation Result to another Type of Value You can use any one of the following key operations to convert the (DEC) currently displayed calculation result to another type of value: (decimal), (HEX) (hexadecimal), (BIN) (binary), (OCT) (octal).
(xnor) Logical operator "xnor" (exclusive negative logical sum), which returns the result of a bitwise XNOR (Not) "Not(" function, which returns the result of a bitwise complement (Neg) "Neg(" function, which returns the result of a two's complement All of the following examples are performed in the binary mode ( (BIN)).
Ratio Calculations The RATIO Mode lets you determine the value of X in the ratio expression a : b = X : d (or a : b = c : X) when the values of a, b, c and d are known. The following shows the general procedure for using RATIO. 1. Press (RATIO) to enter the RATIO Mode. 2. On the menu that appears, select (a:b=X:d) or (a:b=c:X). 3. On the Coefficient Editor screen that appears, input up to 10 digits for each of the required values (a, b, c, d).
Changing the Ratio Expression Type Re-enter the RATIO Mode and select the ratio expression type you want from the menu that appears. Changing the ratio expression type causes the values of all Coefficient Editor coefficients to change to zero.
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.
Action: • Input only integers for the argument. Before Assuming Malfunction of the Calculator... Perform the following steps whenever an error occurs during a calculation or when calculation results are not what you expected. If one step does not correct the problem, move on to the next step. Note that you should make separate copies of important data before performing these steps. 1. Check the calculation expression to make sure that it does not contain any errors. 2.
3. Remove the battery, and then load a new battery with its plus (+) and minus (-) ends facing correctly. 4. Replace the cover. 5. Initialize the calculator: (CLR) (All) (Yes). • 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.
7 Multiplication where the multiplication sign is omitted 8 Permutation (nPr), combination (nCr) 9 Multiplication (×), division (÷), remainder calculations (÷R) 10 Addition (+), subtraction (-) 11 and (logical operator) 12 or, xor, xnor (logical operators) Note • When squaring a negative value (such as -2), the value being squared must be the negative sign, inputting ).
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.
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. • The range for calculation results that can be displayed in π form when using Natural Display is |x| < 106.
- QR Code for accessing the Worldwide Education Service (https://wes.casio.com/calc/) 3. Access the above site. 4. Follow the instructions on the display to verify the authenticity of your calculator. Press 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.
press after the argument to close the parentheses may cause unwanted values or expressions to be included as part of the argument. Example: (sin 30) + 15 (Angle Unit: Deg) Older (S-V.P.A.M.) Model: 30 15 15,5 15 15,5 Natural Textbook Display Model: (LineIO) Failure to press 45.
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