Casio Fx 991es User Manual
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E
User’s Guide
CASIO Worldwide Education Website
http://edu.casio.com
CASIO EDUCATIONAL FORUM
http://edu.casio.com/forum/
Contents | |
Important Information ............................... | 2 |
Sample Operations................................. | 2 |
Initializing the Calculator ............................ | 2 |
Safety Precautions ................................. | 2 |
Handling Precautions............................... | 2 |
Removing the Hard Case ............................ | 3 |
Turning Power On and Off ........................... | 3 |
Adjusting Display Contrast .......................... | 3 |
Key Markings ...................................... | 3 |
Reading the Display ................................ | 4 |
Using Menus ...................................... | 5 |
Specifying the Calculation Mode ...................... | 5 |
Configuring the Calculator Setup ..................... | 5 |
Inputting Expressions and Values ..................... | 7 |
Toggling Calculation Results ......................... | 9 |
Basic Calculations ................................ | 10 |
Function Calculations .............................. | 13 |
Complex Number Calculations (CMPLX) .............. | 18 |
Using CALC...................................... | 19 |
Using SOLVE..................................... | 20 |
Statistical Calculations (STAT) ....................... | 22 |
26 | |
Equation Calculations (EQN) ........................ | 28 |
Matrix Calculations (MATRIX)........................ | 29 |
Creating a Number Table from a Function (TABLE) ...... | 32 |
Vector Calculations (VECTOR) ....................... | 33 |
Scientific Constants ............................... | 35 |
Metric Conversion ................................. | 37 |
Calculation Ranges, Number of Digits, | |
and Precision ..................................... | 38 |
Errors ........................................... | 40 |
Before Assuming Malfunction of the Calculator.. ....... | 41 |
Replacing the Battery.............................. | 42 |
Specifications .................................... | 42 |
Frequently Asked Questions........................ | 43 |
Important Information
•The displays and illustrations (such as key markings) shown in this User’s Guide are for illustrative purposes only, and may differ somewhat from the actual items they represent.
•The contents of this manual are subject to change without notice.
•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.
•Be sure to keep all user documentation handy for future reference.
Sample Operations
Sample operations in this manual are indicated by a icon. Unless specifically stated, all sample operations assume that the calculator is in its initial default setup. Use the procedure under “Initializing the Calculator” to return the calculator to its initial default setup.
For information about the , 1, B, and *marks that are shown in the sample operations, see “Configuring the Calculator Setup”.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculator and return the calculation mode and setup to their initial default settings. Note that this operation also clears all data currently in calculator memory.
(CLR) (All) (Yes)
Safety Precautions
Battery
•Keep batteries out of the reach of small children.
•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 at least once every three years (LR44 (GPA76)) or two years (R03
A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator. Do not try using the calculator while the battery is completely dead
•The battery that comes with the calculator discharges slightly during shipment and storage. Because of this, it may require replacement sooner than the normal expected battery life.
•Do not use an oxyride battery* or any other type of
•Avoid use and storage of the calculator in areas subjected to temperature extremes, and large amounts of humidity and dust.
•Do not subject the calculator to excessive impact, pressure, or
•Never try to take the calculator apart.
•Use a soft, dry cloth to clean the exterior of the calculator.
•Whenever discarding the calculator or batteries, be sure to do so in
accordance with the laws and regulations in your particular area.
*Company and product names used in this manual may be registered trademarks or trademarks of their respective owners.
Removing the Hard Case
Before using the calculator, slide its hard case downwards to remove it, and then affix the hard case to the back of the calculator as shown in the illustration nearby.
Turning Power On and Off
Press to turn on the calculator.
Press (OFF) to turn off the calculator.
Auto Power Off
Your calculator will turn off automatically if you do not perform any operation for about 10 minutes. If this happens, press the key to turn the calculator back on.
Adjusting Display Contrast
Display the CONTRAST screen by performing the following key operation:(SETUP)A (;CONT ). Next, use B and C to adjust contrast. After the setting is the way you want, press .
Important: If adjusting display contrast does not improve display readability, it probably means that battery power is low. Replace the battery.
Key Markings
Pressing the or key followed by a second key performs the alternate function of the second key. The alternate function is indicated by the text printed above the key.
The following shows what the different colors of the alternate function key text mean.
If key marking text | It means this: | |
is this color: | ||
Yellow | Press and then the key to access the | |
applicable function. | ||
Red | Press | and then the key to input the |
applicable variable, constant, or symbol. | ||
Purple (or enclosed | Enter the CMPLX Mode to access the function. | |
in purple brackets) |
Green (or enclosed in
Enter the
green brackets)
Reading the Display
The display of the calculator shows expressions you input, calculation results, and various indicators.
Input expression | Indicators |
Math | Math |
Calculation result
•If a indicator appears on the right side of the calculation result, it means the displayed calculation result continues to the right. Use C and B to scroll the calculation result display.
•If a E indicator appears on the right side of the input expression, it means the displayed calculation continues to the right. Use Cand Bto scroll the input expression display. Note that if you want to scroll the input expression while both the and Eindicators are displayed, you will need to press first and then use C and B to scroll.
Display indicators
This
Means this:
indicator:
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.
MThere is a value stored in independent memory.
The calculator is standing by for input of a variable name to | |
STO | assign a value to the variable. This indicator appears after |
you press =(STO). | |
The calculator is standing by for input of a variable name to | |
RCL | recall the variable’s value. This indicator appears after you |
press =. | |
STAT | The calculator is in the STAT Mode. |
CMPLX | The calculator is in the CMPLX Mode. |
MAT | The calculator is in the MATRIX Mode. |
VCT | The calculator is in the VECTOR Mode. |
The default angle unit is degrees. | |
The default angle unit is radians. | |
The default angle unit is grads. | |
FIX | A fixed number of decimal places is in effect. |
SCI | A fixed number of significant digits is in effect. |
Math | Natural Display is selected as the display format. |
Calculation history memory data is available and can be | |
> | replayed, or there is more data above/below the current |
screen. |
Disp
The display currently shows an intermediate result of a
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. Pressingor @, 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. Use A and D to switch between menus.
•To close a menu without selecting anything, press .
Specifying the Calculation Mode
When you want to perform this type of | Perform this key |
operation: | operation: |
General calculations | (COMP) |
Complex number calculations | (CMPLX) |
Statistical and regression calculations | (STAT) |
Calculations involving specific number | |
systems (binary, octal, decimal, | |
hexadecimal) | |
Equation solution | (EQN) |
Matrix calculations | (MATRIX) |
Generation of a number table based on an | (TABLE) |
expression | |
Vector calculations | (VECTOR) |
Note: The initial default calculation mode is the COMP Mode.
Configuring the Calculator Setup
First perform the following key operation to display the setup menu:(SETUP). Next, use A and D and the number keys to configure the settings you want.
Underlined ( ___ ) settings are initial defaults.
MthIO LineIO Specifies the display format.
Natural Display (MthIO) causes fractions, |
irrational numbers, and other expressions to be |
displayed as they are written on paper. |
Linear Display (LineIO) causes fractions and other expressions to be displayed in a single line.
Note: • The calculator switches to Linear Display automatically whenever you enter the STAT,
Deg Rad Gra Specifies degrees, radians or grads as the angle unit for value input and calculation result display.
Note: In this manual, the B symbol next to a sample operation indicates degrees, while the * symbol indicates radians.
Fix Sci Norm Specifies the number of digits for display of a calculation result.
Fix: The value you specify (from 0 to 9) controls the number of decimal places for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed.
Example: 1 100 ÷ 7 = 14.286 (Fix 3)
14.29(Fix 2)
Sci: The value you specify (from 1 to 10) controls the number of significant digits for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed.
Example: 1 1 ÷ 7 = 1.4286 σ | (Sci 5) |
1.429 σ | (Sci 4) |
Norm: Selecting one of the two available settings (Norm 1, Norm 2) determines the range in which results will be displayed in
Norm 1:
0.005 (Norm 2)
A ab/c A d/c Specifies either mixed fraction (ab/c) or improper fraction (d/c) for display of fractions in calculation results.
A CMPLX a+bi ; r θ Specifies either rectangular coordinates (a+bi) or polar coordinates (r θ) for EQN Mode solutions.
A STAT ON ; OFF Specifies whether or not to display a FREQ (frequency) column in the STAT Mode Stat Editor.
A Disp Dot ; Comma Specifies whether to display a dot or a comma for the calculation result decimal point. A dot is always displayed during input.
Note: When dot is selected as the decimal point, the separator for multiple results is a comma (,). When comma is selected, the separator is a semicolon (;).
A ;CONT Adjusts display contrast. See “Adjusting Display Contrast” 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.
(CLR) (Setup) (Yes)
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.
4 σσsin30σσ(30 + 10σσ3) = 120 | ||||||
4 Q30 30 10 | 3 | |||||
1 | ||||||
* | ||||||
*2 | *3 |
*1 Input of the closing parenthesis is required for sin, sinh, and other functions that include parentheses.
*2 These multiplication symbols (σ) can be omitted. A multiplication symbol can be omitted when it occurs immediately before an opening parenthesis, immediately before sin or other function that includes parentheses, immediately before the Ran# (random number) function, or immediately before a variable (A, B, C, D, E, F, M, X, Y), scientific constants,Π ore.
*3 The closing parenthesis immediately before the operation can be omitted.
Input example omitting | *2 and *3 operations in the above | ||
example. | |||
4 Q30 30 10 | 3 |
Note: • If the calculation becomes longer than the screen width during input, the screen will scroll automatically to the right and the ; indicator will appear on the display. When this happens, you can scroll back to the left by using B and C to move the cursor. • When Linear Display is selected, pressing Dwill cause the cursor to jump to the beginning of the calculation, while A will jump to the end. • When Natural Display is selected, pressing C while the cursor is at the end of the input calculation will cause it to jump to the beginning, while pressing B 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 Iwhen there are 10 bytes or less of allowed input remaining. If this happens, end calculation input and then press .
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.
1st | Parenthetical expressions |
2nd | Functions that require an argument to the right and a closing |
parenthesis “)” following the argument. | |
3rd | Functions that come after the input value (x2,x3, |
%, t), powers (x9), roots ( ) | |
4th | Fractions |
Negative sign | |
Note: When squaring a negative value (such as | |
being squared must be enclosed in parentheses ( 2 7 | |
5th | ). Since x2 has a higher priority than the negative sign, |
inputting 2 7 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. | |
6th | Metric conversion commands (cm in, etc.), |
STAT Mode estimated values (K, L, K1, K2) | |
7th | Multiplication where the multiplication sign is omitted |
8th | Permutation (nPr), combination (nCr), complex number polar |
coordinate symbol ( ) | |
9th | Dot product (·) |
10th | Multiplication, division (σ, ÷) |
11th | Addition, subtraction (+, |
12th | Logical AND (and) |
13th | Logical OR, XOR, XNOR (or, xor, xnor) |
Inputting with Natural Display
Selecting Natural Display makes it possible to input and display fractions and certain functions (log, x2,x3,x9, , , ,x−1, 109,e9,° ,d/dx,3, Abs) just as they are written in your textbook.
2 + '2 | |
1 + '2 | |
2 | 2 CC1 2 |
Important: • Certain types of expressions can cause the height of a calculation formula to be greater than one display line. The maximum allowable height of a calculation formula is two display screens (31 dotsσ 2). Further input will become impossible if the height of the calculation you are inputting exceeds the allowable limit. • Nesting of functions and parentheses is allowed. Further input will become impossible if you nest too many functions and/or parentheses. If this happens, divide the calculation into multiple parts and calculate each part separately.
Note: When you press and obtain a calculation result using Natural Display, part of the expression you input may be cut off. If you need to view the entire input expression again, press and then use B and C to scroll the input expression.
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
6 , for example, you can make
7 | 7 | ||
To input 1 + | and then change it to 1 +'6 | ||
6 | |||
1 7 6 | |||
BBBB&(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), log2(4), etc.)
This capability can be used with the following functions: , , ,( ), ( ), ( ), 5( ), 2( ), , ( ), @(Abs).
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 “I” in the insert mode and as “” in the overwrite mode.
Note: Natural Display always uses the insert mode, so changing display format from Linear Display to Natural Display will automatically switch to the insert mode.
Correcting and Clearing an Expression
To delete a single character or function: Move the cursor so it is directly to the right of the character or function you want to delete, and then press &. In the overwrite mode, move the cursor so it is directly under the character or function you want to delete, and then press &.
To insert a character or function into a calculation: Use B and C 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 .
Toggling Calculation Results
While Natural Display is selected, each press of 5 will toggle the currently displayed calculation result between its fraction form and decimal form, itsform and decimal form, or its Π form and decimal form.
Π ÷ 6 = | 1 | = 0.5235987756 |
6 |
(Π) 6 | 1 | f | 0.5235987756 | ||||
6 | |||||||
(' + 2) σ ' = | '6 + 2'3 | = 5.913591358 | |||||
2 | 3 | ||||||
2 C 2 | 3 '6 + 2'3 | 5.913591358 | |||||
f |
While Linear Display is selected, each press of 5 will toggle the currently displayed calculation result between its decimal form and fraction form.
1 | ÷ 5 = 0.2 = | 1 | ||||||||||
1 | ||||||||||||
5 | 0.2 | 1Y5 | ||||||||||
1 | 5 | f | ||||||||||
1 | – | 4 | = | 1 | = 0.2 | |||||||
1 | ||||||||||||
5 | 5 | 1Y5 | 0.2 | |||||||||
1 | 4 | 5 | f |
Important: • Depending on the type of calculation result that is on the display when you press the 5 key, the conversion process may take some time to perform. • With certain calculation results, pressing the 5 key will not convert the displayed value.
Note: With Natural Display, pressing instead of after inputting a calculation will display the calculation result in decimal form. Pressing 5 after that will switch to the fraction form orΠ form of the calculation result. The form of the result will not appear in this case.
Basic Calculations
Fraction Calculations
Note that the input method for fractions is different, depending upon whether you are using Natural Display or Linear Display.
2 | + | 1 | = | 7 | 2 3 C 1 2 7 | ||||||
3 | 2 | 6 | |||||||||
6 | |||||||||||
or 2 A3 C 1 A2 | 7 | ||||||||||
6 | |||||||||||
1 | 2 3 1 2 7Y6 | ||||||||||
1 | 1 | 1 | |||||||||
4 − 3 | 2 | = | 2 | 4 | ( | ) 3 C1 A2 | 2 | ||||
1 | 4 3 1 2 1Y2 |
Note: • Mixing fractions and decimal values in a calculation while Linear Display is selected will cause the result to be displayed as a decimal value.
• Fractions in calculation results are displayed after being reduced to their lowest terms.
To switch a calculation result between improper fraction and mixed fraction format: Perform the following key operation: 5( )
To switch a calculation result between fraction and decimal format:
Press 5.
Percent Calculations
Inputting a value and pressing (%) causes the input value to become a percent.
150 σσ20% = 30 | 150 20 (%) 30 |
Calculate what percentage of 880 is 660. (75%)
660 880 (%) 75
Increase 2500 by 15%. (2875)
2500 2500 15 (%) 2875
Discount 3500 by 25%. (2625)
3500 3500 25 (%) 2625
Degree, Minute, Second (Sexagesimal) Calculations
Performing an addition or subtraction operation between sexagesimal values, or a multiplication or division operation between a sexagesimal value and a decimal value will cause the result to be displayed as a sexagesimal value. You also can convert between sexagesimal and decimal. The following is the input format for a sexagesimal value: {degrees} {minutes} {seconds} .
Note: You must always input something for the degrees and minutes, even if they are zero.
2°20´30˝ + 39´30˝ = 3°00´00˝ 2 20 30 0 39 30 3°0´0˝
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˝ |
You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press .
3 + 3 : 3 σ 3 | 3 3 (:) 3 3 | 6 |
9 |
Using Engineering Notation
A simple key operation transforms a displayed value to engineering notation.
Transform the value 1234 to engineering notation, shifting the decimal point to the right.
1234 | 1234 |
$ 1.234×103 $ 1234×100
Transform the value 123 to engineering notation, shifting the decimal point to the left.
123 | 123 |
$(κ)0.123×103$(κ)0.000123×106
Calculation History
In the COMP, CMPLX, or
1 + 1 = 2 | 1 1 | 2 | |
2 + 2 = 4 | 2 2 | 4 | |
3 + 3 = 6 | 3 3 | 6 | |
(Scrolls back.) | D | 4 | |
(Scrolls back again.) | D | 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 any reset operation.
Replay
While a calculation result is on the display, you can press B or C to edit the expression you used for the previous calculation.
4 | × 3 | + 2.5 | = 14.5 | 1 | 4 3 2.5 | 14.5 |
4 | × 3 | − 7.1 | = 4.9 | (Continuing) B&&&& 7.1 | 4.9 |
Note: If you want to edit a calculation when the indicator is on the right side of a calculation result display (see “Reading the Display”), press and then use B and C to scroll the calculation.
Answer Memory (Ans)
The last calculation result obtained is stored in Ans (answer) memory. Ans memory contents are updated whenever a new calculation result is displayed.
To divide the result of 3 σ 4 by 30 | 1 | ||
3 4 | |||
(Continuing) | 30 | ||
123 | + 456 = 579 123 456 | ||
789 | – 579 = 210 | ||
(Continuing) 789 |
Variables (A, B, C, D, E, F, X, Y)
Your calculator has eight preset variables named A, B, C, D, E, F, X, and Y. You can assign values to variables and also use the variables in calculations.
To assign the result of 3 + 5 to variable A | |||
3 5 =(STO)E(A) | 8 | ||
To multiply the contents of variable A by 10 | |||
(Continuing) | E(A) | 10 | 80 |
To recall the contents of variable A (Continuing) | =E(A) | 8 | |
To clear the contents of variable A | 0 =(STO)E(A) | 0 |
Independent Memory (M)
You can add calculation results to or subtract results from independent memory. The “M” appears on the display when there is any value other than zero stored in independent memory.
To clear the contents of M | 0 =(STO)J(M) | 0 | |
To add the result of 10 σ 5 to M | (Continuing) | 10 5 J | 50 |
To subtract the result of 10 + 5 from M | 15 | ||
(Continuing) 10 5 | |||
To recall the contents of M | (Continuing) | =J(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 even if you press , change the calculation mode, or turn off the calculator. Perform the following procedure when you want to clear the contents of all memories.
(CLR) (Memory) (Yes)
Function Calculations
For actual operations using each function, see the “Examples” section following the list below.
: Π is displayed as 3.141592654, butΠ = 3.14159265358980 is used for internal calculations.
e: e is displayed as 2.718281828, bute = 2.71828182845904 is used for internal calculations.
sin, cos, tan, sin−1, cos−1, tan−1 : Trigonometric functions. Specify the angle unit before performing calculations. See1.
sinh, cosh, tanh, sinh−1, cosh−1, tanh−1 :Hyperbolic functions. Input a function from the menu that appears when you press @. The angle unit setting does not affect calculations. See 2.
°, r, g : These functions specify the angle unit. ° specifies degrees,r radians, andg grads. Input a function from the menu that appears when you perform the following key operation: (DRG ). See3.
, : Exponential functions. Note that the input method is different depending upon whether you are using Natural Display or Linear Display. See4.
log: Logarithmic function. Use the 5 key to input logab as log (a,b). Base 10 is the default setting if you do not input anything fora. The key also can be used for input, but only while Natural Display is selected. In this case, you must input a value for the base. See5.
ln: Natural logarithm to basee. See6.
x2, x3, x9, , , ,x−1 : Powers, power roots, and reciprocals. Note that the input methods forx9, , , and are different depending upon whether you are using Natural Display or Linear Display. See7.
Note: The following functions cannot be input in consecutive sequence:x2,x3,x9,x−1. If you input 277, for example, the final 7will be ignored. To input222 , input 27, press the B key, and then press 7.
: Function for performing numerical integration using the
: Function for approximation of the derivative based on the central
difference method. Natural Display input syntax is | d | ( f(x))x= a, while | ||
dx | ||||
Linear Display input syntax is | d | ( f(x),a,tol).tol specifies tolerance, | ||
dx |
which becomes 1
b
: Function that, for a specified range of f(x), determines sum ( f(x)) x=a
b
= f(a) +f(a+1) +f(a+2) + ..+f(b). Natural Display input syntax is (f(x)),x=a
while Linear Display input syntax is 3(f(x),a,b).a andb are integers that can be specified within the range of
10.
Note: The following cannot be used inf(x),a, orb: Pol, Rec,°,d/dx,3.
Pol, Rec : Pol converts rectangular coordinates to polar coordinates, while Rec converts polar coordinates to rectangular coordinates. See11 .
Rec(r,θ) = (x,y)
Polar
Coordinates (Pol)
Specify the angle unit before performing calculations.
The calculation result for r andθ and forx andy are each assigned respectively to variables X and Y. Calculation resultΘ is displayed in the range of −180°Θ 180°.
x! : Factorial function. See12 .
Abs : Absolute value function. Note that the input method is different depending upon whether you are using Natural Display or Linear Display. See13 .
Ran# : Generates a
RanInt# : For input of the function of the form RanInt#(a,b), which generates a random integer within the range ofa tob. See15 .
nPr, nCr: Permutation (nPr) and combination (nCr) functions. See16 .
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. In the case of Rnd(10÷3) = 3.333 (with Fix 3), both the displayed value and the calculator’s internal value become 3.333. Because of this a series of calculations will produce different results depending on whether Rnd is used (Rnd(10÷3)σ 3 = 9.999) or not used (10 ÷ 3σσ3 = 10.000). See17 .
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 .
Integration and Differential Calculation Precautions
•Integration and differential calculations can be performed in the COMP Mode ( ) only.
•The following cannot be used in f(x),a,b, ortol: Pol, Rec,°,d/dx,3.
•When using a trigonometric function in f(x), specify Rad as the angle unit.
•A smaller tol value increases precision, but it also increases calculation time. When specifyingtol, use value that is 1σ
Precautions for Integration Calculation Only
• Integration normally requires considerable time to perform.
1
• For f(x) 0 wherea x b (as in the case of0 3x2 – 2 =
• Depending on the content of f(x) and the region of integration, calculation error that exceeds the tolerance may be generated, causing the calculator to display an error message.
Precautions for Differential Calculation Only
•If convergence to a solution cannont be found when tol input is omitted, thetol value will be adjusted automatically to determine the solution.
•
Tips for Successful Integration Calculations
When a periodic function or integration interval results in positive and negative f(x) function values
Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results.
b | c | b | ||||||
a | f(x)dx = | f(x)dx + (–f(x)dx) | ||||||
a | c | |||||||
S Positive | ||||||||
Positive Part | Negative Part | |||||||
S Negative | ||||||||
(S Positive) | (S Negative) |
When integration values fluctuate widely due to minute shifts in the integration interval
Divide the integration interval into multiple parts (in a way that breaks areas of wide fluctuation into small parts), perform integration on each part, and then combine the results.
f (x) | b | x1 | |
f(x)dx = | f(x)dx+ | ||
a | b | a | |
+ | |||
f(x)dx | |||
x | x4 | ||
a x1x2x3x4 | |||
0 | b |
Examples
1 | sin 30°= 0.5 | 1B | Q30 | 0.5 | |||
sin−10.5 = 30° | 1B Q(sin−1) 0.5 | 30 | |||||
2 | sinh 1 = 1.175201194 | @@(sinh) 1 | 1.175201194 | ||||
@D(cosh−1) 1 | 0 | ||||||
3 | ΠΠ/2 radians = 90°, 50 grads = 45° | B | |||||
(Π) 2 (DRG )A(r) | 90 | ||||||
50 (DRG )B(g) | 45 | ||||||
4 | To calculate e5 σ 2 to three significant digits (Sci 3) | ||||||
(SETUP) (Sci) | |||||||
2( ) 5 C 2 | 2.97×102 | ||||||
1 | 2( ) 5 2 | 2.97×102 | |||||
5 | log101000 = log 1000 = 3 | 51000 | 3 | ||||
log216 = 4 | 52 (,) 16 | 4 | |||||
2 C16 | 4 | ||||||
6 | To calculate ln 90 (= loge 90) to three significant digits (Sci 3) | ||||||
(SETUP) (Sci) | 290 | 4.50×100 | |||||
7 | 1.2 σσ103 = 1200 | 1.2 10 3 | 1200 | ||||
(1+1)2+2 = 16 1 1 2 2 | 16 | ||||||
(52)3 = 15625 | 5 V 7(x3) | 15625 | |||||
5 32 = 2 | ( ) 5 C32 | 2 | |||||
1 5 ( ) 32 | 2 | ||||||
To calculate | '2 | × 3 | 2 | ||||||
(= 3' = 4.242640687..) to three decimal | |||||||||
places (Fix 3) | |||||||||
(SETUP) (Fix) | 2 C 3 | 3'2 | |||||||
4.243 | |||||||||
1 | 2 3 | 4.243 | |||||||
8 | 1eln(x) = 1 | ||||||||
2 | (X) C1 C (e) | 1 | |||||||
1 | 2 | (X) (,) | |||||||
1 (,) (e) | 1 | ||||||||
9 | To obtain the derivative at point x =Π/2 for the functiony = sin(x) | ||||||||
* | |||||||||
( )? (X) | |||||||||
C (Π)C2 | 0 | ||||||||
1 | ( )? (X) | ||||||||
(,) (Π) 2 | 0 | ||||||||
5 | |||||||||
10 (x + 1) = 20 | |||||||||
x = 1 | 20 | ||||||||
( ) (X) 1 C1 C5 | |||||||||
1 ( ) | (X) 1 (,) 1 | ||||||||
(,) 5 | 20 |
11 To convert rectangular coordinates ('2 , '2 ) to polar coordinates
B
(Pol) 2 C (,) 2 C r=2,θ=45
1 (Pol) 2 (,) 2 r= 2
θ= 45
To convert polar coordinates ('2 , 45°) to rectangular coordinates
B
(Rec) 2 C (,) 45 X=1, Y=1
12 | (5 + 3) ! = 40320 | 5 3 (x!) | 40320 |
13 | 2 – 7 σ 2 = 10 | 10 | |
@(Abs) 2 7 C 2 | |||
1 | @(Abs) 2 7 2 | 10 | |
14 To obtain three random | |||
1000 (Ran#) | 459 | ||
48 | |||
117 |
(Results shown here are for illustrative purposes only. Actual results will differ.)
15 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.)
16 To determine the number of permutations and combinations possible when selecting four people from a group of 10
Permutations: 10 (nPr) 4 | 5040 | |||
Combinations: 10 (nCr) 4 | 210 | |||
17 To perform the following calculations when Fix 3 is selected for the | ||||
number of display digits: 10 ÷ 3 σ 3 and Rnd(10 ÷ 3)σ 3 | 1 | |||
(SETUP) (Fix) | 10 3 3 | 10.000 | ||
(Rnd) 10 3 3 | 9.999 |
Complex Number Calculations
(CMPLX)
To perform complex number calculations, first press (CMPLX) to enter the CMPLX Mode. You can use either rectangular coordinates (a+bi) or polar coordinates (r θ) to input complex numbers. Complex number calculation results are displayed in accordance with the complex number format setting on the setup menu.
(2 + 6i) ÷ (2i) = 3 –i (Complex number format:a +bi)
2 6 $(i) 2 $(i)
2 45 = '2 + '2 i B (Complex number format:a +bi)
'2 +'2i
'2 + '2 i = 2 45 B (Complex number format:r θ)
2 C 2 C$(i)2 45
Note: • If you are planning to perform input and display of the calculation result in polar coordinate format, specify the angle unit before starting the calculation. • Theθ value of the calculation result is displayed in the range of
CMPLX Mode Calculation Examples
(1 – | 1 | + | 1 | i (Complex number format:a +bi) | ||||
2 | 2 | 1 $(i) | 1 | + | 1 | i | ||
2 | ||||||||
2 | ||||||||
(1 + i)2 + (1 –i)2 = 0 | ||||||||
1 $(i) 7 1 $(i) 7 | 0 |
To obtain the conjugate complex number of 2 + 3i (Complex number format:a +bi)
(CMPLX) (Conjg) 2 3 $(i)
To obtain the absolute value and argument of 1 + i B | |
Absolute Value: @(Abs) 1 $(i) | '2 |
Argument: (CMPLX) (arg)1 $(i) | 45 |
Using a Command to Specify the Calculation Result Format
Either of two special commands ( r θ ora+bi) can be input at the end of a calculation to specify the display format of the calculation results. The command overrides the calculator’s complex number format setting.
'2 + '2 i = 2 45, 2 45 = '2 + '2i B | |
2 C 2 C$(i) (CMPLX) (r θ) | 2 45 |
2 ( ) 45 (CMPLX) ( a+bi) | '2 +'2i |
Using CALC
CALC lets you save calculation expressions that contain variables, which you can then recall and execute in the COMP Mode ( ) and the CMPLX Mode ( ). The following describes the types of expressions you can save with CALC.
•Expressions: 2X + 3Y, 2AX + 3BY + C, A + Bi
•
•Equalities with a single variable on the left and an expression including variables on the right: A = B + C, Y = X2 + X + 3
(Use <(=) to input the equals sign of the equality.)
To store 3A + B and then substitute the following values to perform the calculation: (A, B) = (5, 10), (7, 20)
3 (A) 4(B)
Math
<
Prompts for input of a value for A | Current value of A |
5 10
< (or )
7 20
To exit CALC:
To store A + Bi and then determine '3 +i, 1 + '3i using polar coordinates (r θ) B
(CMPLX) | CMPLX Math |
(A) 4(B)$(i)
(CMPLX) ( r θ)
<3 1
<(or ) 1 3
To exit CALC:
Note: During the time from when you press < until you exit CALC by pressing , you should use Linear Display input procedures for input.
Using SOLVE
SOLVE uses Newton’s Law to approximate the solution of equations. Note that SOLVE can be used in the COMP Mode ( ) only.
The following describes the types of equations whose solutions can be obtained using SOLVE.
•Equations that include variable X: X2 + 2X – 2, Y = X + 5, X = sin(M), X + 3 = B + C
SOLVE solves for X. An expression like X2 + 2X – 2 is treated as X2 + 2X
– 2 = 0.
•Equations input using the following syntax: {equation}, {solution variable}
SOLVE solves for Y, for example, when an equation is input as: Y = X + 5, Y
Important: • If an equation contains input functions that include an open parenthesis (such as sin and log), do not omit the closing parenthesis.
• The following functions are not allowed inside of an equation: °,d/dx,3, Pol, Rec.
To solve y =ax2 +b forx wheny = 0,a = 1, andb =
5(Y) <(=) (A)(X)7 4(B)
Math
<(SOLVE)
Prompts for input of a value for Y | Current value of Y |
Math
0 1 2
Current value of X
Input an initial value for X (Here, input 1): 1
Solution screen
To exit SOLVE:
Note: During the time from when you press <(SOLVE) until you exit SOLVE by pressing , you should use Linear Display input procedures for input.
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 Law, so even if there are multiple solutions, only one of them will be returned. • Due to limitations in Newton’s Law, solutions tend to be difficult to obtain for equations like the following:y = sin(x),y =ex,y ='x .
Solution Screen Contents
Solutions are always displayed in decimal format.
Equation (The equation you input.)
Math
Variable solved for | Solution |
(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.
Press to continue or to cancel the SOLVE operation.
To solve y =x2 –x + 1 forx wheny = 3, 7, and 13
5(Y) <(=)
(X)7 (X) 1
<(SOLVE)
3
Input an initial value for X (Here, input 1): 1
7
13
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.
To select this type of statistical calculation: | Press this key: |
(Regression formula shown in parentheses) | |
(A+BX) | |
( _+CX2) | |
2 | |
( y = A + Bx + Cx ) | |
(ln X) | |
( y = A + Blnx) | |
(e^X) | |
( y = AeBx) | |
(A•B^X) | |
( y = ABx) | |
(A•X^B) | |
(1/X) | |
( y = A + B/x) |
Pressing any of the above keys ( to ) displays the Stat Editor.
Note: When you want to change the calculation type after entering the STAT Mode, perform the key operation (STAT) (Type) to display the calculation type selection screen.
Inputting Data
Use the Stat Editor to input data. Perform the following key operation to display the Stat Editor: (STAT) (Data).
The Stat Editor provides 80 rows for data input when there is an X column only, 40 rows when there are X and FREQ columns or X and Y columns, or 26 rows when there are X, Y, and FREQ columns.
Note: Use the FREQ (frequency) column to input the quantity (frequency) of identical data items. Display of the FREQ column can be turned on (displayed) or off (not displayed) using the Stat Format setting on the setup menu.
1 To select linear regression and input the following data: (170, 66), (173, 68), (179, 75)
STAT
(STAT) (A+BX)
STAT
170 173 179 AC
STAT
66 68 75
Important: • All data currently input in the Stat Editor is deleted whenever you exit the STAT Mode, switch between the
To change the data in a cell: In the Stat 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 Stat Editor, move the cursor to the line that you want to delete and then press &.
To insert a line: In the Stat Editor, move the cursor to the location where you want to insert the line and then perform the following key operation:(STAT) (Edit) (Ins).
To delete all Stat Editor contents: In the Stat Editor, perform the following key operation: (STAT) (Edit)
Obtaining Statistical Values from Input Data
To obtain statistical values, press while in the Stat Editor and then recall the statistical variable (xΣn,3x2, etc.) you want. Supported statistical variables and the keys you should press to recall them are shown below. For
Sum: 3x2*,3x*,3y2,3y,3xy,3x3,3x2y,3x4
(STAT) (Sum) to
Number of Items: n*, Mean:M*, N, Population Standard Deviation:xΣn*, yΣn, Sample Standard Deviation:
(STAT) (Var) to
Regression Coefficients: A, B, Correlation Coefficient:r, Estimated Values:K, L
(STAT) (Reg) to
Regression Coefficients for Quadratic Regression: A, B, C, Estimated Values:K1, K2, L
(STAT) (Reg) to
•See the table at the beginning of this section of the manual for the regression formulas.
•K,K1,K2 andL are not variables. They are commands of the type that take an argument immediately before them. See “Calculating Estimated Values” for more information.
Minimum Value: minX*, minY, Maximum Value:maxX*, maxY
(STAT) (MinMax) to
Note: While
2 To input the
(SETUP)A (STAT) (ON)
(STAT) | STAT |
1 2 3 4 5 AC | |
1 2 3 2 |
(STAT) (Var) (M)
(STAT) (Var) (xΣn)
Results: Mean: 3 Population Standard Deviation: 1.154700538
3 To calculate the linear regression and logarithmic regression correlation coefficients for the following
(SETUP)A (STAT) (OFF)
(SETUP) (Fix)
(STAT) (A+BX) | STAT | FIX |
20 110 200 290 AC | ||
3150 7310 8800 9310 |
(STAT) (Reg) (r)
(STAT) (Type) (In X)
(STAT) (Reg) (r)
(STAT) (Reg) (A)
(STAT) (Reg) (B)
Results: Linear Regression Correlation Coefficient: 0.923 Logarithmic Regression Correlation Coefficient: 0.998
Logarithmic Regression Formula: y =
Calculating Estimated Values
Based on the regression formula obtained by
4 To determine the estimate value fory whenx = 160 in the regression formula produced by logarithmic regression of the data in3. Specify Fix 3 for the result. (Perform the following operation after completing the operations in3.)
160 (STAT) (Reg) (L)
Result: 8106.898
Important: Regression coefficient, correlation coefficient, and estimated value calculations can take considerable time when there are a large number of data items.
Performing Normal Distribution Calculations
While
P, Q, R: These functions take the argumentt and determine a probability of standard normal distribution as illustrated below.
P (t) | Q (t) | R (t) |
0 t | 0 t | 0 t |
t: This function is preceded by the argument X, and determines the
normalized variate .
5 For the single variable data {xn ; freqn} = {0;1, 1;2, 2;1, 3;2, 4;2, 5;2, 6;3, 7;4, 9;2, 10;1}, to determine the normalized variate (t) whenx = 3, and P(t) at that point up to three decimal places (Fix 3).
(SETUP)A (STAT) (ON)
(SETUP) (Fix) (STAT)
0 1 2 3 4 5 6 7 9 | STAT | FIX |
10 AC1 2 1 2 2 2 3 | ||
4 2 1 | ||
STAT | FIX | |
3 (STAT) (Distr) ( t) |
STAT | FIX |
(STAT) (Distr) (P()
Results: Normalized variate (t): | |
P(t): | 0.223 |
Press
To enter the
5(BIN)
11 1
Continuing from above, switch to the hexadecimal mode and calculate 1F16 + 116
(HEX) 1 @(F) 1
Continuing from above, switch to the octal mode and calculate 78 + 18
2(OCT) 7 1
Note: • Use the following keys to input the letters A through F for hexadecimal values: (A), (B), @(C), Q(D), A(E), R(F). • In the
Input/Output Ranges |
Binary
Positive: 0000000000000000 x 0111111111111111 Negative: 1000000000000000x 1111111111111111
Octal
Positive: 00000000000 x 17777777777
Negative: 20000000000 x 37777777777
Decimal |
Hexadecimal
Positive: 00000000 x 7FFFFFFF
Negative: 80000000 x FFFFFFFF
Specifying the Number Mode of a Particular Input Value
You can input a special command immediately following a value to specify the number mode of that value. The special commands are: d (decimal), h (hexadecimal), b (binary), and o (octal).
To calculate 1010 + 1016 + 102 + 108 and display the result as a decimal value
7(DEC) (BASE)A (d) 10 | |
(BASE)A (h) 10 | |
(BASE)A (b) 10 | |
(BASE)A (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 currently displayed calculation result to another type of value: V(DEC) (decimal),(HEX) (hexadecimal), 5(BIN) (binary), 2(OCT)(octal).
To calculate 1510 σ 3710 in the decimal mode, and then convert the result to hexadecimal, binary, and octal
V(DEC) 15 37 | 555 |
(HEX) | 0000022B |
5(BIN) 0000001000101011
2(OCT) 00000001053
Logical and Negation Operations
Your calculator provides you with logical operators (and, or, xor, xnor) and functions (Not, Neg) for logical and negation operations on binary values. Use the menu that appears when you press (BASE) to input these logical operators and functions.
All of the following examples are performed in the binary mode (5(BIN)).
To determine the logical AND of 10102 and 11002 (10102 and 11002)1010 (BASE) (and) 11000000000000001000
To determine the logical OR of 10112 and 110102 (10112 or 110102)1011 (BASE) (or) 110100000000000011011
To determine the logical XOR of 10102 and 11002 (10102 xor 11002)1010 (BASE) (xor) 11000000000000000110
To determine the logical XNOR of 11112 and 1012 (11112 xnor 1012)1111 (BASE) (xnor) 1011111111111110101
To determine the bitwise complement of 10102 (Not(10102))
(BASE) (Not) 1010 1111111111110101
To negate (take the two’s complement) of 1011012 (Neg(1011012))(BASE) (Neg) 1011011111111111010011
Note: In the case of a negative binary, octal or hexadecimal value, the calculator converts the value to binary, takes the two’s complement, and then converts back to the original number base. For decimal
Equation Calculations (EQN)
You can use the following procedure in the EQN Mode to solve simultaneous linear equations with two or three unknowns, quadratic equations, and cubic equations.
1.Press (EQN) to enter the EQN Mode.
2.On the menu that appears, select an equation type.
To select this calculation type: | Press this key: | |
Simultaneous linear equations with two | (anX + bnY = cn) | |
unknowns | ||
Simultaneous linear equations with | (anX + bnY + cnZ = dn) | |
three unknowns | ||
Quadratic equation | (aX2 | + bX + c = 0) |
Cubic equation | (aX3 | + bX2 + cX + d = 0) |
3.Use the Coefficient Editor that appears to input coefficient values.
•To solve 2x2 +x – 3 = 0, for example, press in step 2, and then input the following for the coefficients (a = 2,b = 1,c =
•To change a coefficient value you already have input, move the cursor to the appropriate cell, input the new value, and then press .
•Pressing will clear all of the coefficients to zero.
Important: The following operations are not supported by the Coefficient Editor: 6,
4.After all the values are the way you want, press .
•This will display a solution. Each press of will display another solution. Pressing while the final solution is displayed will return to the Coefficient Editor.
•You can scroll between the solutions using the A and D keys.
•To return to the Coefficient Editor while any solution is displayed, press
.
Note: • Even if Natural Display is selected, the solutions of simultaneous linear equations are not displayed using any form that includes . • Values cannot be converted to engineering notation on the solution screen.
Changing the Current Equation Type Setting
Press (EQN) and then select an equation type from the menu that appears. Changing the equation type causes the values of all Coefficient Editor coefficients to change to zero.
EQN Mode Calculation Examples
x + 2y = 3, 2x + 3y = 4 | ||||||||
(EQN) (anX + bnY = cn) | ||||||||
Math | ||||||||
1 2 3 | ||||||||
2 3 4 | ||||||||
(X=) | ||||||||
A | (Y=) | 2 | ||||||
x –y +z = 2,x +y –z = 0, | ||||||||
(EQN) (anX + bnY + cnZ = dn) | ||||||||
1 1 1 2 | ||||||||
Math | ||||||||
1 1 1 0 | ||||||||
1 1 1 4 | ||||||||
(X=) | 1 | |||||||
A | (Y=) | 2 | ||||||
A | (Z=) | 3 | ||||||
x2 + x+ | 3 | = 0 | ||||||
4 | ||||||||
(EQN) (aX2 + bX + c = 0) | 1 | '2 | ||||||
1 1 3 4 (X1=) – | + | i | ||||||
2 | 2 | |||||||
A | (X2=) – | 1 | – | '2 | i | |||
2 | 2 | |||||||
x2 – 2'2x + 2 = 0 | ||||||||
(EQN) (aX2 + bX + c = 0) | ||||||||
1 2 2 2 | (X=) '2 | |||||||
x3 – 2x2 –x + 2 = 0 | ||||||||
(EQN) (aX3 + bX2 + cX + d = 0) | ||||||||
1 2 1 2 | (X1=) | |||||||
A | (X2=) | 2 | ||||||
A | (X3=) | 1 |
Matrix Calculations (MATRIX)
Use the MATRIX Mode to perform calculations involving matrices of up to 3 rows by 3 columns. To perform a matrix calculation, you first assign data to special matrix variables (MatA, MatB, MatC), and then use the variables in the calculation as shown in the example below.
1 To assign2 | 1 | to MatA and | 2 | |||||
1 | 1 | 2 | ||||||
the following calculations: 2 | 1 | × | 2 | |||||
1 | 1 | 2 | ||||||
2 | 1 + | 2 | (MatA+MatB) | |||||
1 | 1 | 2 |
1.Press (MATRIX) to enter the MATRIX Mode.
2.Press (MatA) (2σ2).
• This will display the Matrix Editor for input | MAT |
of the elements of the 2 σ 2 matrix you | |
specified for MatA. | |
“A” stands for “MatA”. |
3.Input the elements of MatA: 2 1 1 1 .
4.Perform the following key operation: (MATRIX) (Data)(MatB) (2σ2).
•This will display the Matrix Editor for input of the elements of the 2 σ 2 matrix you specified for MatB.
5.Input the elements of MatB: 2 1 1 2 .
6.Press to advance to the calculation screen, and perform the first
calculation (MatAσMatB): (MATRIX) (MatA) | (MATRIX) | ||||
(MatB) . | |||||
• This will display the MatAns screen with the calculation results. Arrow keys to move, ZXC to do stuff. Ported from GameMaker 8.1 to HTML5 with GameMaker: Studio. Original game by Derek Yu, ported by Darius Kazemi (me). Special thanks to the team at YoYo Games for helping with bugfixes and polish when I was too busy to do so! See this article for some technical details on the port. For some technical details. Oct 13, 2015 You may not post new threads; You may not post replies; You may not post attachments; You may not edit your posts. Minder with cheats: Unlimited health. Hello there, This is another little game that I made. Like so many others, after playing Spelunky I got interested in random level generation and this game is sort of the result of that interest. The level generation here is nothing like the way it’s done in Spelunky though, but I still think it’s quite fun to play. Spelunky hacked online. | |||||
MAT | MAT | “Ans” stands for | |||
“MatAns”. |
Note: “MatAns” stands for “Matrix Answer Memory”. See “Matrix Answer Memory” for more information.
7.Perform the next calculation (MatA+MatB): (MATRIX)(MatA) (MATRIX) (MatB) .
MAT | MAT |
Matrix Answer Memory
Whenever the result of a calculation executed in the MATRIX Mode is a matrix, the MatAns screen will appear with the result. The result also will be assigned to a variable named “MatAns”.
The MatAns variable can be used in calculations as described below.
•To insert the MatAns variable into a calculation, perform the following key operation: (MATRIX) (MatAns).
•Pressing any one of the following keys while the MatAns screen is
displayed will switch automatically to the calculation screen: , , , , 7, 7(x3). The calculation screen will show the MatAns variable followed by the operator or function for the key you pressed.
Assigning and Editing Matrix Variable Data
Important: The following operations are not supported by the Matrix Editor: 6,
To assign new data to a matrix variable:
1.Press (MATRIX) (Dim), and then, on the menu that appears, select the matrix variable to which you want to assign data.
2.On the next menu that appears, select dimension (mσn).
3. Use the Matrix Editor that appears to input the elements of the matrix.
2 | To assign 1 | 0 | |
0 | 1 | ||
(MATRIX) | |||
(Dim) (MatC) (2σ3) | |||
1 0 1 0 1 1 |
To edit the elements of a matrix variable:
1.Press (MATRIX) (Data), and then, on the menu that appears, select the matrix variable you want to edit.
2.Use the Matrix Editor that appears to edit the elements of the matrix.
•Move the cursor to the cell that contains the element you want to change, input the new value, and then press .
To copy matrix variable (or MatAns) contents:
1.Use the Matrix Editor to display the matrix you want to copy.
•If you want to copy MatA, for example, perform the following key operation: (MATRIX) (Data) (MatA).
•If you want to copy MatAns contents, perform the following to display the MatAns screen: (MATRIX) (MatAns) .
2.Press =(STO), and then perform one of the following key operations to specify the copy destination: (MatA), (MatB), or @(MatC).
•This will display the Matrix Editor with the contents of the copy destination.
Matrix Calculation Examples
The following examples use MatA = | 2 | 1 | and MatB = | 2 | from | 1 | , | ||||||
1 | 1 | 2 | |||||||||||
1 | 0 | ||||||||||||
and MatC = | from | 2 | . You can input a matrix variable into a key | ||||||||||
0 |
operation by pressing (MATRIX) and then pressing one of the following number keys: (MatA), (MatB), (MatC).
3 | 3 × MatA (Matrix scalar multiplication). |
3 MatA | |
4 | Obtain the determinant of MatA (det(MatA)). |
(MATRIX) (det) MatA | 1 |
5 | Obtain the transposition of MatC (Trn(MatC)). |
(MATRIX) (Trn) MatC | |
6 | Obtain the inverse matrix of MatA |
Note: You cannot use for this input. Use the key to input “
MatA
7 Obtain the absolute value of each element of MatB (Abs(MatB)).
@(Abs) MatB
8 Determine the square and cube of MatA (MatA2, MatA3).
Note: You cannot use for this input. Use 7 to specify squaring, and7(x3) to specify cubing.
MatA7
MatA 7(x3)
Creating a Number Table from a
Function (TABLE)
TABLE generates a number table for x andf(x) using an inputf(x) function. Perform the following steps to generate a number table.
1.Press (TABLE) to enter the TABLE Mode.
2.Input a function in the format f(x), using the X variable.
• Be sure to input the X variable ( (X)) when generating a number table. Any variable other than X is handled as a constant.
•The following cannot be used in the function: Pol, Rec, °,d/dx,3.
3.In response to the prompts that appear, input the values you want to use, pressing after each one.
For this prompt: Input this:
Start? | Input the lower limit of X (Default = 1). |
End? | Input the upper limit of X (Default = 5). |
Note: Make sure that the End value is always | |
greater than the Start value. | |
Step? | Input the increment step (Default = 1). |
Note: The Step specifies by how much the Start | |
value should be sequentially incremented as the | |
number 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 number | |
table until the End value is reached. |
•Inputting the Step value and pressing generates and displays the number table in accordance with the parameters you specified.
•Pressing while the number table screen is displayed will return to the function input screen in step 2.
To generate a number table for the function f(x) =x2 + | 1 | for the | |
2 | |||
range | |||
(TABLE) | Math |
Math
(X)V 1 2
Math
1 1 0.5
Note: • You can use the number table screen for viewing values only. Table contents cannot be edited. • The number table generation operation causes the contents of variable X to be changed.
Important: The function you input for number table generation is deleted whenever you display the setup menu in the TABLE Mode and switch between Natural Display and Linear Display.
Vector Calculations (VECTOR)
Use the VECTOR Mode to perform
1 To assign (1, 2) to VctA and (3, 4) to VctB, and then perform the following calculation: (1, 2) + (3, 4)
1.Press (VECTOR) to enter the VECTOR Mode.
2.Press (VctA) (2).
• This will display the Vector Editor for input | VCT |
of the | |
“A” stands for “VctA”. |
3.Input the elements of VctA: 1 2 .
4.Perform the following key operation: (VECTOR) (Data)(VctB) (2).
•This will display the Vector Editor for input of the
5.Input the elements of VctB: 3 4 .
6.Press to advance to the calculation screen, and perform the calculation (VctA + VctB): (VECTOR) (VctA) (VECTOR)(VctB) .
•This will display the VctAns screen with the calculation results.
VCT | VCT | “Ans” stands for |
“VctAns”. |
Note: “VctAns” stands for “Vector Answer Memory”. See “Vector Answer Memory” for more information.
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 for the key you pressed.
Assigning and Editing Vector Variable Data
Important: The following operations are not supported by the Vector Editor: 6,
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.
2 To assign (2,
(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) .
2.Press =(STO), and then perform one of the following key operations to specify the copy destination: (VctA), (VctB), or @(VctC).
•This will display the Vector Editor with the contents of the copy destination.
Vector Calculation Examples
The following examples use VctA = (1, 2) and VctB = (3, 4) from 1, and VctC = (2,
pressing (VECTOR) and then pressing one of the following number keys: (VctA), (VctB), (VctC).
3 3 × VctA (Vector scalar multiplication), 3 × VctA – VctB (Calculation
example using VctAns) | ||
3 | VctA | |
VctB | ||
4 | VctA • VctB (Vector dot product) | |
VctA (VECTOR) (Dot)VctB | ||
5 | VctA σσVctB (Vector cross product) | |
VctA | VctB | |
6 | Obtain the absolute values of VctC. | |
@(Abs)VctC |
7 Determine the angle formed by VctA and VctB to three decimal places (Fix 3). B
(cos θ = | (A• B) | , which becomes θ = | (A• B) | ) |
A B | A B |
(SETUP) (Fix)
VctA (VECTOR) (Dot)VctB
VCTFIX
@(Abs)VctA @(Abs)
VctB
VCTFIX
Scientific Constants
Your calculator comes with 40
To input a scientific constant into a calculation, press (CONST) and then input the
To input the scientific constant C0 (speed of light in a vacuum), and display its value
(CONST)
(C0)
To calculate C0 = | 1 |
0 0 |
1 A (CONST) (Ε0)(CONST) (μ0)
The following shows the
01: (mp) proton mass | 02: (mn) neutron mass |
03: (me) electron mass | 04: (mμ) muon mass |
05: (a0) Bohr radius | 06: (h) Planck constant |
07: (μN) nuclear magneton | 08: (μB) Bohr magneton |
09: (+) Planck constant, | 10: (Α) |
rationalized | |
11: (re) classical electron radius | 12: (Λc) Compton wavelength |
13: (Γp) proton gyromagnetic ratio | 14: (Λcp) proton Compton |
wavelength | |
15: (Λcn) neutron Compton | 16: (Rδ) Rydberg constant |
wavelength | |
17: (u) atomic mass constant | 18: (μp) proton magnetic |
moment | |
19: (μe) electron magnetic moment | 20: (μn) neutron magnetic |
moment | |
21: (μμ) muon magnetic moment | 22: (F) Faraday constant |
23: (e) elementary charge | 24: (NA) Avogadro constant |
25: (k) Boltzmann constant | 26: (Vm) molar volume of ideal |
gas | |
27: (R) molar gas constant | 28: (C0) speed of light in vacuum |
29: (C1) first radiation constant | 30: (C2) second radiation |
constant | |
31: (Σ) | 32: (Ε0) electric constant |
33: (μ0) magnetic constant | 34: (Φ0) magnetic flux quantum |
35: (g) standard acceleration of
36: (G0) conductance quantum
gravity
37: (Z0) characteristic impedance of
38: (t) Celsius temperature
vacuum
39: (G) Newtonian constant of
40: (atm) standard atmosphere
gravitation
The values are based on CODATA recommended values (March 2007).
Metric Conversion
The calculator’s
To input a metric conversion command into a calculation, press(CONV) and then input the
To convert 5 cm into inches 1
5 (CONV)
(cm in)
To convert 100 g into ounces 1
100 (CONV) (g oz)
To convert
31 (CONV) (°C °F)
The following shows the
01: in cm | 02: cm in | 03: ft m | 04: m ft |
05: yd m | 06: m yd | 07: mile km | 08: km mile |
09: n mile m | 10: m n mile | 11: acre m2 | 12: m2 acre |
13: gal (US) | 14: gal (US) | 15: gal (UK) | 16: gal (UK) |
17: pc km | 18: km pc | 19: km/h m/s | 20: m/s km/h |
21: oz g | 22: g oz | 23: lb kg | 24: kg lb |
25: atm Pa | 26: Pa atm | 27: mmHg Pa | 28: Pa mmHg |
29: hp kW | 30: kW hp | 31: kgf/cm2 Pa | 32: Pa kgf/cm2 |
33: kgf • m J | 34: J kgf • m | 35: lbf/in2 kPa | 36: kPa lbf/in2 |
37: °F °C | 38: °C °F | 39: J cal | 40: cal J |
Conversion formula data is based on the “NIST Special Publication 811 (1995)”.
Note: The J cal command performs conversion for values at a temperature of 15°C.
Calculation Ranges, Number of Digits,
and Precision
The calculation range, number of digits used for internal calculation, and calculation precision depend on the type of calculation you are performing.
Calculation Range and Precision
Calculation Range | π1σ |
Number of Digits for Internal | 15 digits |
Calculation | |
Precision | In general, π1 at the 10th digit for a single |
calculation. Precision for exponential | |
display is π1 at the least significant digit. | |
Errors are cumulative in the case of | |
consecutive calculations. |
Function Calculation Input Ranges and Precision
Functions | Input Range | |||
DEG | 0 | x 9σσ109 | ||
sinx | RAD | 0 | x 157079632.7 | |
GRA | 0 | x 1σσ1010 | ||
DEG | 0 | x 9σσ109 | ||
cosx | RAD | 0 | x 157079632.7 | |
GRA | 0 | x 1σσ1010 | ||
DEG | Same as sinx, except whenx = | |||
tanx | RAD | Same as sinx, except whenx = | ||
GRA | Same as sinx, except whenx = | |||
0 | x 1 | |||
0 | x 9.999999999σσ1099 | |||
sinhx | 0 | x 230.2585092 | ||
coshx | ||||
0 | x 4.999999999σσ1099 | |||
1 | x 4.999999999σσ1099 | |||
tanhx | 0 | x 9.999999999σσ1099 |
0 | x 9.999999999 | |||||||||||
logx/lnx | 0 | x 9.999999999σσ1099 | ||||||||||
10x | ||||||||||||
ex | ||||||||||||
'x | 0 | x 1σσ10100 | ||||||||||
x2 | x 1σσ1050 | |||||||||||
x 1σσ10100 ;x & 0 | ||||||||||||
3 x | x 1σσ10100 | |||||||||||
x! | 0 | x 69 (x is an integer) | ||||||||||
nPr | 0 | n 1σσ1010, 0r n (n,r are integers) | ||||||||||
1 | ||||||||||||
nCr | 0 | n 1σσ1010, 0r n (n,r are integers) | ||||||||||
1 | n!/r! 1σσ10100 or 1 | |||||||||||
Pol(x,y) | x ,y 9.999999999σσ1099 | |||||||||||
x2 +y2 9.999999999σσ1099 | ||||||||||||
Rec(r,θ) | 0 | r 9.999999999σσ1099 | ||||||||||
θ: Same as sinx | ||||||||||||
a ,b,c 1σσ10100 | ||||||||||||
°’ ” | 0 | b, c | ||||||||||
The display seconds value is subject to an error of 21 at | ||||||||||||
the second decimal place. | ||||||||||||
x 1σσ10100 | ||||||||||||
Decimal ϕ Sexagesimal Conversions | ||||||||||||
0°0 0˝ x 9999999°59 59˝ | ||||||||||||
x 0: | ||||||||||||
xy | x = 0:y 0 | m | ||||||||||
x | 0: y =n,2n+1 (m,n are integers) | |||||||||||
However: | ||||||||||||
y 0:x & 0, | ||||||||||||
x | y = 0:x 0 | 2n+1 | ||||||||||
y | y | 0: x = 2n+1, | (m | & | 0; m,n are integers) | |||||||
m | ||||||||||||
However: | ||||||||||||
ab/c | Total of integer, numerator, and denominator must be 10 | |||||||||||
digits or less (including division marks). | ||||||||||||
RanInt#(a,b) | a b;a ,b 1σσ1010;b –a 1σσ1010 |
•Precision is basically the same as that described under “Calculation Range and Precision”, above.
•xy, 'x y,3 ,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.
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 B or C to display the location of the error, or pressingto clear the message and calculation.
Displaying the Location of an Error
While an error message is displayed, press B or C to return to the calculation screen. The cursor will be positioned at the location where the error occurred, ready for input. Make the necessary corrections to the calculation and execute it again.
When you input 14 ÷ 0 σ 2 = by mistake instead of 14 ÷ 10σ 2 =
Math
14 0 2
C (or B)
B1
Clearing the Error Message
While an error message is displayed, press to return to the calculation screen. Note that this also clears the calculation that contained the error.
Error Messages
Math ERROR
Cause: • The intermediate or final result of the calculation you are performing exceeds the allowable calculation range. • 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. • 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: The configuration of TABLE Mode parameters caused more than 30
Action: Narrow the table calculation range by changing the Start, End, and Step values, and try again.
Time Out Error
Cause: The current differential or integration calculation ends without the ending condition being fulfilled.
Action: Try increasing thetol value. Note that this also decreases solution precision.
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.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. If the calculator discovers any abnormality, it automatically initializes the calculation mode and clears memory contents.
For details about initialized settings, see “Configuring the Calculator Setup”.
4.Initialize all modes and settings by performing the following operation:(CLR) (Setup) (Yes).
Replacing the Battery
A low battery is indicated by a dim display, even if contrast is adjusted, or by failure of figures to appear on the display immediately after you turn on the calculator. If this happens, replace the battery with a new one.
Important: Removing the battery will cause all of the calculator’s memory contents to be deleted.
1.Press (OFF) to turn off the calculator.
•To ensure that you do not accidentally turn on power while replacing the battery, slide the hard case onto the front of the calculator
2.Remove the cover as shown in the illustration and replace the battery, taking care that its plus (+) and minus
Screw
Screw | Screw |
3.Replace the cover.
4.Initialize the calculator: (CLR) (All) (Yes)
•Do not skip the above step!
Specifications
Power Requirements:
Approximate Battery Life:
Power Consumption: 0.0002 W
Operating Temperature: 0°C to 40°C (32°F to 104°F)
Dimensions:
Approximate Weight:
Frequently Asked Questions
IHow can I perform input and display results the same way I did on a model that does not have Natural Textbook Display?
Casio Fx 991es User Manual Free
Perform the following key operation: (SETUP) (LineIO). See “Configuring the Calculator Setup” on page
IHow can I change a fraction format result to decimal format?
How can I change a fraction format result produced by a division operation to decimal format?
See “Toggling Calculation Results” on page
IWhat is the difference between Ans memory, independent memory, and variable memory?
Each of these types of memory acts like “containers” for temporary storage of a single value.
Ans Memory: Stores the result of the last calculation performed. Use this memory to carry the result of one calculation on to the next.Independent Memory: Use this memory to totalize the results of multiple calculations.
Variables: This memory is helpful when you need to uses the same value multiple times in one or more calculations.
IWhat is the key operation to take me from the STAT Mode or TABLE
Mode to a mode where I can perform arithmetic calculations?
Press (COMP).
IHow can I return the calculator to its initial default settings?
Perform the following operation: (CLR) (Setup) (Yes)
IWhen I execute a function calculation, why do I get a calculation result that is completely different from older CASIO calculator models?
With a Natural Textbook Display model, the argument of a function that uses parentheses must be followed by a closing parenthesis. Failing to press after the argument to close the parentheses may cause unwanted values or expressions to be included as part of the argument.
Casio Fx 991ms User Manual
Example: (sin 30) + 15 B | Q30 15 15.5 |
Older |
Natural Textbook Display Model: 1 Q30 15 15.5
Failure to press here as shown below will result in calculation of sin 45.
Casio Fx-991es Plus
Q30 15 0.7071067812
Manufacturer:
CASIO COMPUTER CO., LTD.
Responsible within the European Union: CASIO EUROPE GmbH
Bornbarch 10
Casio Fx 991es Emulator
22848 Norderstedt, Germany
CASIO COMPUTER CO., LTD.