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fx-991ZA PLUS II
User guide
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Casio fx-991ZA PLUS II User guide

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fx-991ZA PLUS II
(NATURAL-V.P.A.M.)
User’s Guide
EN
CASIO Worldwide Education Website
https://edu.casio.com
Manuals are available in multi languages at
https://world.casio.com/manual/calc/
Clearing the Contents of All Memories..........................................................29
Function Calculations............................................................30
Pi (π), Natural Logarithm Base e............................................................ 30
Trigonometric Functions........................................................................ 30
Hyperbolic Functions............................................................................. 30
Angle Unit Conversion........................................................................... 31
Exponential Functions............................................................................31
Logarithmic Functions............................................................................31
Power Functions and Power Root Functions.........................................32
Integration Calculations......................................................................... 33
Integration Calculation Precautions.............................................................. 34
Tips for Successful Integration Calculations................................................. 34
Differential Calculations......................................................................... 35
Differential Calculation Precautions.............................................................. 36
Σ Calculations........................................................................................ 36
Rectangular-Polar Coordinate Conversion............................................ 37
Factorial Function (!)..............................................................................38
Absolute Value Function (Abs)...............................................................38
Random Number (Ran#)........................................................................38
Random Integer (RanInt#)..................................................................... 38
Permutation (nPr) and Combination (nCr)............................................. 39
Rounding Function (Rnd).......................................................................39
Greatest Common Divisor (GCD) and Least Common Multiple (LCM).....
...............................................................................................................40
Using CALC........................................................................................... 40
Using SOLVE.........................................................................................41
Solution Screen Contents............................................................................. 43
Continue Screen........................................................................................... 43
Scientific Constants............................................................................... 44
Metric Conversion..................................................................................46
Using Calculation Modes.......................................................48
Complex Number Calculations (CMPLX)...............................................48
CMPLX Mode Calculation Examples............................................................ 49
Using a Command to Specify the Calculation Result Format....................... 49
Statistical Calculations (STAT)...............................................................49
Inputting Data................................................................................................50
Statistics Calculation Screen.........................................................................52
Using the Statistics Menu..............................................................................52
Calculating Estimated Values........................................................................57
Performing Normal Distribution Calculations................................................ 58
Base-n Calculations (BASE-N).............................................................. 58
Specifying the Number Mode of a Particular Input Value..............................60
Converting a Calculation Result to another Type of Value............................60
Logical and Negation Operations..................................................................61
2
To exit SOLVE:
Note
• During the time from when you press (SOLVE) until you exit SOLVE by pressing
Important!
• Depending on what you input for the initial value for X (solution variable), SOLVE may not be able to obtain solutions. If this happens, try changing the initial value so they are closer to the solution.
• SOLVE may not be able to determine the correct solution, even when one exists.
• SOLVE uses Newton's method, so even if there are multiple solutions, only one of them will be returned.
• Due to limitations in Newton's method, solutions tend to be difficult to obtain for equations like the following: y = sin(x), y = ex, y = √x.
, you should use Linear Display input procedures for input.
Solution Screen Contents
Solutions are always displayed in decimal form.
(1) Equation (The equation you input.) (2) Variable solved for (3) Solution (4) (Left Side) - (Right Side) result
"(Left Side) - (Right Side) result" shows the result when the right side of the equation is subtracted from the left side, after assigning the obtained value to the variable being solved for. The closer this result is to zero, the higher the accuracy of the solution.
Continue Screen
SOLVE performs convergence a preset number of times. If it cannot find a solution, it displays a confirmation screen that shows "Continue: [=]", asking if you want to continue.
43
Example: To generate a numerical table for the functions f(x) = x2 +
and g(x) = x2 -
1
for the range -1 ≦ x ≦ 1, incremented in steps of
2
0,5 (MthIO-MathO)
(TABLE)
(SETUP) (TABLE) (f(x),g(x))
(X) 1 2
・Pressing without inputting anything for g(x) will generate a numerical table based on f(x) only.
1 2
(X) 1 2
1 1 0 5
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.
Important!
• The function you input for numerical table generation is deleted whenever you display the setup menu in the TABLE Mode and switch between Natural Display and Linear Display.
70
Vector Answer Memory
Whenever the result of a calculation executed in the VECTOR Mode is a vector, the VctAns screen will appear with the result. The result also will be assigned to a variable named "VctAns". The VctAns variable can be used in calculations as described below.
• To insert the VctAns variable into a calculation, perform the following key operation: (VECTOR) (VctAns).
• Pressing any one of the following keys while the VctAns screen is displayed will switch automatically to the calculation screen:
, ,
, . The calculation screen will show the VctAns variable followed
by the operator or function for the key you pressed.
Assigning and Editing Vector Variable Data
Important!
• The following operations are not supported by the Vector Editor: , (M-), (STO). Pol, Rec, ÷R, and multi-statements also cannot be input with the
Vector Editor.
To assign new data to a vector variable:
1. Press
(VECTOR) (Dim), and then, on the menu that appears,
select the vector variable to which you want to assign data.
2. On the next menu that appears, select dimension (m).
3. Use the Vector Editor that appears to input the elements of the vector.
Example 2: To assign (2, -1, 2) to VctC
(VECTOR) (Dim) (VctC) (3)
2
1 2
To edit the elements of a vector variable:
1. Press (VECTOR) (Data), and then, on the menu that appears, select the vector variable you want to edit.
2. Use the Vector Editor that appears to edit the elements of the vector.
• Move the cursor to the cell that contains the element you want to change, input the new value, and then press
.
To copy vector variable (or VctAns) contents:
1. Use the Vector Editor to display the vector you want to copy.
• If you want to copy VctA, for example, perform the following key operation:
(VECTOR) (Data) (VctA).
• If you want to copy VctAns contents, perform the following to display the VctAns screen:
(VECTOR) (VctAns) .
72
4. After inputting values for all of the variables, press .
• This displays the calculation results.
• Pressing the input screen of the first variable.
Note
• To change the distribution calculation type after you enter the DIST Mode, press (STAT/DIST) (Type) and then select the distribution type you want.
• Distribution calculation accuracy is up to five significant digits.
or while a calculation result is displayed will return to
Variables that Accept Input
The following are distribution calculation variables that accept input values.
Normal PD ........................... x, σ, μ
Normal CD ........................... Lower, Upper, σ, μ
Inverse Normal .................... Area, σ, μ (Tail setting always left.)
Binomial PD, Binomial CD ... x (or List), N, p
Poisson PD, Poisson CD ..... x (or List), μ
x: data σ: standard deviation (σ < 0) μ: mean Lower: lower boundary Upper: upper boundary Tail: probability value tail specification Area: probability value (0 ≦ Area ≦ 1) List: sample data list N: number of trials p: success probability (0 ≦ p ≦ 1)
List Screen (Binomial PD, Binomial CD, Poisson PD, Poisson CD)
With Binomial PD, Binomial CD, Poisson PD, and Poisson CD, use the List Screen for sample data input. You can input up to 25 data samples for each variable. Calculation results are also displayed on the List Screen.
75
2
x = binomial probability of 10 ≒ 0,18594 x = binomial probability of 11 ≒ 0,12678
35
Result: 0,1760326634
• Pressing
Example 2: To calculate binomial probability for the sample data {10; 11;
12; 13; 14} when N = 15 and p = 0,6
or returns to the x input screen.
(DIST) (Binomial PD)
Display the List Screen: (List)
• To specify data using parameter format, press (Var).
10
11 12 13 14
15
0 6
Results:
77
• Your input exceeds the allowable input range (particularly when using functions).
• The calculation you are performing contains an illegal mathematical operation (such as division by zero).
Action:
• Check the input values, reduce the number of digits, and try again.
• When using independent memory or a variable as the argument of a function, make sure that the memory or variable value is within the allowable range for the function.
Stack ERROR
Cause:
• The calculation you are performing has caused the capacity of the numeric stack or the command stack to be exceeded.
• The calculation you are performing has caused the capacity of the matrix or vector stack to be exceeded.
Action:
• Simplify the calculation expression so it does not exceed the capacity of the stack.
• Try splitting the calculation into two or more parts.
Syntax ERROR
Cause:
• There is a problem with the format of the calculation you are performing.
Action:
• Make necessary corrections.
Argument ERROR
Cause:
• There is a problem with the argument of the calculation you are performing.
Action:
• Make necessary corrections.
Dimension ERROR (MATRIX and VECTOR Modes only)
Cause:
• The matrix or vector you are trying to use in a calculation was input without specifying its dimension.
84
• You are trying to perform a calculation with matrices or vectors whose dimensions do not allow that type of calculation.
Action:
• Specify the dimension of the matrix or vector and then perform the calculation again.
• Check the dimensions specified for the matrices or vectors to see if they are compatible with the calculation.
Variable ERROR (SOLVE feature only)
Cause:
• You did not specify a solution variable, and there is no X variable in the equation you input.
• The solution variable that you specified is not included in the equation you input.
Action:
• The equation you input must include an X variable when you do not specify the solution variable.
• Specify a variable that is included in the equation you input as the solution variable.
Can't Solve Error (SOLVE feature only)
Cause:
• The calculator could not obtain a solution.
Action:
• Check for errors in the equation that you input.
• Input a value for the solution variable that is close to the expected solution and try again.
Insufficient MEM Error
Cause:
• An attempt to generate a numerical table in the TABLE Mode whose conditions cause it to exceed the maximum number of allowable rows. The maximum number of rows is 30 when "f(x)" is selected for the setup menu table setting and 20 when "f(x),g(x)" is selected.
Action:
• Narrow the table calculation range by changing the Start, End, and Step values, and try again.
85
1. Press .
2. Press .
• This displays the information below.
- Calculator ID number (24-character string)
- 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.
92
0,707106781230 15
press after the argument to close the parentheses may cause
Example: (sin 30) + 15 (Angle Unit: Deg)
Natural Textbook Display Model:
Failure to press here as shown below will result in calculation of sin
45.
unwanted values or expressions to be included as part of the argument.
Older (S-V.P.A.M.) Model: 30 15 15,5
(LineIO) 30 15 15,5
94
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