EN fx-115ES PLUS fx-991ES PLUS C (2nd edition / NATURAL-V.P.A.M.) User’s Guide CASIO Worldwide Education Website https://edu.casio.com Manuals are available in multi languages at https://world.casio.
Table of Contents Before Using the Calculator.................................................... 4 About this Manual.................................................................................... 4 Initializing the Calculator.......................................................................... 4 Precautions.............................................................................................. 4 Safety Precautions..............................................................................
Independent Memory (M)..............................................................................34 Clearing the Contents of All Memories..........................................................35 Function Calculations............................................................ 36 Pi (π), Natural Logarithm Base e............................................................ 36 Trigonometric Functions........................................................................ 36 Hyperbolic Functions..........
Base-n Calculations (BASE-N).............................................................. 66 Specifying the Number Mode of a Particular Input Value..............................68 Converting a Calculation Result to another Type of Value............................68 Logical and Negation Operations..................................................................69 Equation Calculations (EQN)................................................................. 70 Changing the Current Equation Type Setting.....
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-115ES PLUS/fx-991ES PLUS C: Every 3 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 of nonuse. Press the key to turn the calculator back on. Adjusting Display Contrast 1. Press (SETUP) ( CONT 2. Use and to adjust display contrast. 3. After the setting is the way you want, press ). .
Example: (sin-1)* 1 * 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 operation ( ) before it. Note that this is not part of the actual key 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. This (STO).
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 multi-statement calculation. 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.
Calculation Modes and Calculator Setup Calculation Mode Before starting a calculation, you must first enter the correct mode as indicated in the table below.
Configuring the Calculator Setup Pressing (SETUP) displays the setup menu, which you can use to control how the calculations are executed and displayed. The setup menu has two screens, which you can jump between using and . Underlined ( ___ ) settings are initial defaults.
MthIO-LineO (Number Format: Norm 1) MthIO-LineO (Number Format: Norm 2) LineIO (Number Format: Norm 1) Note • The calculator switches to Linear Display automatically whenever you enter the STAT, BASE-N, MATRIX, or VECTOR Mode.
Number of Significant Digits Exponential Display Range (SETUP) (SETUP) (Norm 2) (Sci) - (Norm) (Norm 1) or 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: (LineIO) 100 ÷ 7 = 14.286 (Fix 3) 14.29 (Fix 2) Sci: The value you specify (from 0 to 9) controls the number of significant digits for displayed calculation results.
Specifying the Complex Number Format To specify this complex number format: Perform this key operation: Rectangular Coordinates (SETUP) (CMPLX) (a+bi) Polar Coordinates (SETUP) (CMPLX) (r∠θ) Specifying the Stat Format Specifies whether or not to display a FREQ (frequency) column in the STAT Mode Statistics Editor.
Do not use recurring decimal form (SETUP) (Rdec) (OFF) Specifying the Decimal Point Display Format Specifies whether to display a dot or a comma for the calculation result decimal point. A dot is always displayed during input. To specify this decimal point display format: Perform this key operation: Dot (.) (SETUP) (Disp) (Dot) Comma (,) (SETUP) (Disp) (Comma) Note • When dot is selected as the decimal point, the separator for multiple results is a comma (,).
Complex Number Format a+bi Stat Format OFF Table Format f(x),g(x) Recurring Decimal Format ON Decimal Point Dot 16
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 (INS). The and overwrite modes by performing the operations: 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. Example 1: π ÷ 6 = 1 π = 0.5235987756 (MthIO-MathO) 6 (π) 1 π 6 6 0.5235987756 Example 2: (√2 + 2) × √3 = √6 + 2√3 = 5.
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. • When ON is selected for Rdec on the setup menu, pressing will switch the calculation result to recurring decimal form. For details, see "Recurring Decimal Calculations".
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. • Results of calculations that mix fraction and decimal values are always decimal. • Fractions in calculation results are displayed after being reduced to their lowest terms.
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. 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.
123 123 (←) 0.123×103 (←) 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 quotient value only.
• When the quotient is not a positive integer, or if the remainder is not a positive integer or positive fractional value Example: 5 (÷R) 2 → Calculated as: -5 ÷ 2 Recurring Decimal Calculations Your calculator uses a recurring decimal when you input a value. Calculation results also can be displayed using recurring decimal form whenever applicable.
428571 Example 3: To calculate 1.021 + 2.312 ( 1 2 ) 021 ( ) 312 Calculation result displayed as recurring decimal value: Note • You can specify up to 14 decimal places for the recurring decimal period. If you input more than 14 decimal places, the value will be treated as a terminating decimal and not a recurring decimal. • Recurring decimal value input can be performed regardless of the Rdec setting on the setup menu.
Decimal value according to Norm 1 setting: Return to initial display format (fraction): Example 2: 1 ÷ 7 = 1 = 0.142857 = 0.1428571429 (Norm 1) (MthIO7 MathO) 7 1 Display as fraction: Display as recurring decimal: Return to initial display format (Norm 1): Example 3: 1 = 0.142857 = 0.
Example 4: 1 ÷ 7 = 0.1428571429 (Norm 1) = 1 1 = 0.142857 (LineIO) 7 7 Display as fraction: Display as recurring decimal: Return to initial display format (Norm 1): Conditions for Displaying a Calculation Result as a Recurring Decimal If a calculation result satisfies the following conditions, pressing will display it as a recurring decimal value. • The total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbol) must be no more than 10.
0 0 ( ( )3 ) 45 Example 2: 1.6 + 2.8 = 4.5 (MthIO-MathO) ( )6 ( )8 1 2 Example 3: To confirm the following: 0.123 = = 123 1234 , 0.1234 = , 0.12345 999 9999 12345 (MthIO-MathO) 99999 123 1234 12345 999 9999 99999 Prime Factorization In the COMP Mode, a positive integer no more than 10 digits long can be factored to prime factors.
1014 1014 (FACT) When you perform prime factorization on a value that includes a factor that is prime number with more than three digits, the part that cannot be factored will be enclosed in parentheses on the display. Example 2: To perform prime factorization on 4104676 (= 22 × 10132) 4104676 4104676 (FACT) Any one of the following operations will exit prime factorization result display. - Pressing (FACT) or . - Pressing any of the following keys: or .
(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.
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.
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.
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. e is displayed as 2.
(sinh) 1 1.175201194 (cosh-1) 1 0 Example 2: cosh-1 1 = 0 Angle Unit Conversion °, r, g : These functions specify the angle unit. ° specifies degrees, r radians, and g grads. Input a function from the menu that appears when you perform the following key operation: (DRG ).
2 (,) 16 (MthIO-MathO, MthIO-LineO) 4 2 16 4 Example 3: log2(43) = 6 (MthIO-MathO, MthIO-LineO) (x3) 2 6 Example 4: log2(4)3 = 8 (MthIO-MathO, MthIO-LineO) 2 (x3) 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 , , and are different Note that the input methods for , depending upon whether you are using Natural Display or Linear Display. Example 1: 1.
(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 22 , x-1. If you will be ignored. To input 2 , input 2 , (MthIO-MathO). • x2, x3, x-1 can be used in complex number calculations.
1 Example 2: ∫( 2 , 1, 5, 1 × 10-7) = 0.8 (LineIO) x 1 (X) (,) 1 1 (,) 5 (,) 0.8 7 π Example 3: ∫0 (sin x + cos x)2 dx = π (tol: Not specified) (MthIO-MathO) (Angle unit: Rad) (X) (X) 0 (π) π Integration Calculation Precautions • Integration calculation can be performed in the COMP Mode only. • The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot be used in f(x), a, b, or tol: ∫, d/dx, Σ, Π. • When using a trigonometric function in f(x), specify Rad as the angle unit.
(1) Positive Part (2) Negative Part 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. Differential Calculations Function for approximation of the derivative based on the central difference method.
( )3 (X) 5 (X) 2 2 (,) 1 (,) 7 12 Differential Calculation Precautions • Differential calculation can be performed in the COMP Mode only. • The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot be used in f(x), a, b, or tol: ∫, d/dx, Σ, Π. • 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 specifying tol, use value that is 1 × 10-14 or greater.
Note • The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot be used in f(x), a, or b: ∫, d/dx, Σ, Π. ∏ Calculations You can obtain the product of an input f(x) expression for a specific range. The calculation formula is: (f(x)) = f(a) × f(a + 1) × f(a + 2) × ⋯ × f(b). The Natural Display input syntax is (f(x)), while Linear Display input syntax is ∏(f(x), a, b). a and b are integers in the range of a < 1 × 1010, b < 1 × 1010, a ≦ b.
(1) Rectangular Coordinates (Rec) (2) Polar Coordinates (Pol) 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°.
Absolute Value Function (Abs) Note that the input method is different depending upon whether you are using Natural Display or Linear Display. Example: |2 - 7| × 2 = 10 (MthIO-MathO) (Abs) 2 7 2 10 (Abs) 2 7 2 10 (LineIO) Random Number (Ran#) Function that generates a pseudo random number in the range of 0.000 to 0.999. The result is displayed as a fraction when Natural Display is selected. Example: Generate three 3-digit random numbers.
(Results shown here are for illustrative purposes only. Actual results will differ.) Permutation (nPr) and Combination (nCr) Example: To determine the number of permutations and combinations possible when selecting four people from a group of 10. Permutations: 10 (nPr) 4 5040 Combinations: 10 (nCr) 4 210 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).
Example: To determine the greatest common divisor of 28 and 35 (GCD) 28 (,) 35 7 Least Common Multiple (LCM) LCM determines the least common multiple of two values. Example: To determine the least common multiple of 9 and 15 (LCM) 9 (,) 15 45 Integer Part of a Value (Int) and Largest Integer that does not Exceed a Value (Intg) Integer Part of a Value (Int) Extracts the integer part of a value. Example: To extract the integer part of -3.
• Equations 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 start a CALC operation after inputting an expression, press the key.
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 method 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.
0 1 2 (3) 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 pressing (SOLVE) until you exit SOLVE by , 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.
(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.
Scientific Constants Your calculator comes with 40 built-in scientific constants that can be used in any mode besides BASE-N. Each scientific constant is displayed as a unique symbol (such as π), which can be used inside of calculations. (CONST) To input a scientific constant into a calculation, press and then input the two-digit number that corresponds to the constant you want.
14: (λCp) proton Compton 13: (γp) proton gyromagnetic ratio wavelength 15: (λCn) neutron Compton 16: (R∞) Rydberg constant wavelength 18: (μp) proton magnetic moment 17: (u) atomic mass unit 19: (μe) electron magnetic 20: (μn) neutron magnetic moment 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 (237.
(CONV) and then input the two-digit number that corresponds to the command you want. Example 1: To convert 5 cm into inches (LineIO) 5 (CONV) (cm in) Example 2: To convert 100 g into ounces (LineIO) 100 (CONV) (g oz) Example 3: To convert -31°C into Fahrenheit (LineIO) 31 (CONV) (°C °F) The following shows the two-digit numbers for each of the metric conversion commands.
37: °F °C 38: °C °F 39: J cal 40: cal J Conversion formula data is based on the "NIST Special Publication 811 (2008)". Note • The J cal command performs conversion for values at a temperature of 15°C.
Using Calculation Modes Complex Number Calculations (CMPLX) To perform complex number calculations, first press enter the CMPLX Mode. (CMPLX) to 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.
CMPLX Mode Calculation Examples Example 1: (1 - i)-1 = 1 1 + i (MthIO-MathO) (Complex number format: a 2 2 +bi) 1 1 1 + i 2 2 (i) Example 2: (1 + i)2 + (1 - i)2 = 0 (MthIO-MathO) 1 (i) 1 (i) 0 Example 3: To obtain the conjugate complex number of 2 + 3i (Complex number format: a+bi) (CMPLX) (Conjg) 2 3 (i) 2-3i Example 4: To obtain the absolute value and argument of 1 + i (MthIOMathO) (Angle unit: Deg) Absolute Value (Abs): (Abs) 1 (i) √2 Argument (arg): (CMPLX) (arg) 1 (i) 45 Using a C
To select this type of statistical calculation: (Regression formula shown in parentheses) Press this key: Single-variable (X) (1-VAR) Paired-variable (X, Y), linear regression (y = A + Bx) (A+BX) Paired-variable (X, Y), quadratic regression (y = A + Bx + Cx2) (_+CX2) Paired-variable (X, Y), logarithmic regression (y = A + Blnx) (ln X) Paired-variable (X, Y), e exponential regression (y = A eBx) (e∧X) Paired-variable (X, Y), ab exponential (y = ABx) (A•B∧X) Paired-variable (X, Y), power regress
The Statistics Editor provides 40 rows for data input when there is an X column only or when there are X and Y columns, 20 rows when there are X and FREQ 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.
To delete all Statistics Editor contents: In the Statistics Editor, perform the following key operation: (STAT/DIST) (Edit) (Del-A). Statistics Calculation Screen The Statistics Calculation Screen is for performing statistical calculations with the data you input with the Statistics Editor. Pressing the key while the Statistics Editor is displayed switches to the Statistics Calculation Screen.
(Var) Display the Var sub-menu of commands for calculating the mean, standard deviation, etc. Single-variable: (Distr) Display the Distr sub-menu of commands for normal distribution calculations • For more information, see "Performing Normal Distribution Calculations".
Distr Sub-menu ( (STAT/DIST) (Distr)) (P() (Q() (R() This menu can be used to calculate the probability of standard normal distribution. • For details see "Performing Normal Distribution Calculations".
(∑x4) Var Sub-menu ( Select this menu item: Sum of biquadrate of the X-data (STAT/DIST) (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/DIST) (Reg)) When you want to obtain this: (A) Regression coeffi
(minY) Minimum value of the Y-data (maxY) Maximum value of the Y-data Commands when Quadratic Regression Calculation (_+CX2) Is Selected Reg Sub-menu ( (STAT/DIST) (Reg)) 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 Note • x̂, x̂1, x̂2 and ŷ are
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. (SETUP) (STAT) (OFF) (SETUP) (Fix) (STAT) (A+BX) 20 110 200 290 3150 7310 8800 9310 (STAT/DIST) (Reg) (r) 0.
Performing Normal Distribution Calculations While single-variable statistical calculation is selected, you can perform normal distribution calculation using the functions shown below from the menu that appears when you perform the following key operation: (STAT/DIST) (Distr). P, Q, R: These functions take the argument t and determine a probability of standard normal distribution as illustrated below. t: This function is preceded by the argument X, and determines the X-x .
The initial default number mode when you enter the BASE-N Mode is decimal, which means input and calculation results use the decimal number format. Press one of the following keys to switch number modes: (DEC) for decimal, (HEX) for hexadecimal, (BIN) for binary, or (OCT) for octal.
Base-n Mode Input/Output Ranges Binary Positive: 0000000000000000 ≦ x ≦ 0111111111111111 Octal Positive: 00000000000 ≦ x ≦ 17777777777 Negative: 1000000000000000 ≦ x ≦ 1111111111111111 Decimal Hexadecimal Negative: 20000000000 ≦ x ≦ 37777777777 -2147483648 ≦ x ≦ 2147483647 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.
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. (BASE) to input these Use the menu that appears when you press logical operators and functions.
Example 4: To determine the logical XNOR of 11112 and 1012 (11112 xnor 1012) 1111 (BASE) (xnor) 101 1111111111110101 Example 5: To determine the bitwise complement of 10102 (Not(10102)) (BASE) (Not) 1010 1111111111110101 Example 6: To negate (take the two's complement) of 1011012 (Neg(1011012)) (BASE) (Neg) 101101 1111111111010011 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 t
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 = -3): 2 1 3 . • 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.
(EQN) (anX + bnY = cn) 2 3 1 2 3 4 (X=) -1 (Y=) 2 (X=) 1 (Y=) 2 (Z=) 3 Example 2: x - y + z = 2, x + y - z = 0, -x + y + z = 4 (EQN) (anX + bnY + cnZ = dn) 1 1 2 1 1 1 1 0 1 1 1 4 Example 3: 2x2 - 3x - 6 = 0 (MthIO-MathO) (aX2 + bX + c = 0) 3 6 (EQN) 2 (X1=) 3 + √57 4 (X2=) 3 - √57 4 (X-Value Minimum=)* 3 4 (Y-Value Minimum=)* - 57 8 * The local minimum value is displayed when a > 0. The local maximum value is displayed when a < 0.
(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. Example 1: To assign to MatA and perform the following calculations: + 1. Press × to MatB, and then (MatA×MatB), (MatA+MatB) (MATRIX) to enter the MATRIX Mode. 2. Press (MatA) (2×2).
(2) "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) . 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.
Example 2: To assign 1 to MatC (MATRIX) (Dim) (MatC) (2×3) 1 0 1 1 0 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.
(MATRIX) (MATRIX) (MatC) (Trn) Example 6: Obtain the inverse matrix of MatA (MatA-1). Note: You cannot use for this input. Use the key to input "-1". (MATRIX) (MatA) Example 7: Obtain the absolute value of each element of MatB (Abs(MatB)). (Abs) (MATRIX) (MatB) Example 8: Determine the square and cube of MatA (MatA2, MatA3). Note: You cannot use for this input. Use to specify squaring, and 3 (x ) to specify cubing.
2. Use the X variable to input two functions, one in the format f(x) and the other in the format g(x). • Be sure to input the X variable ( (X)) when generating a numerical table. Any variable other than X is handled as a constant. • If you are using a single function, input a function in the format f(x) only. • The following cannot be used in the function: Pol, Rec, ∫, d/dx, Σ, Π. 3. In response to the prompts that appear, input the values you want to after each one.
Example: To generate a numerical table for the functions f(x) = x2 + 1 2 1 for the range -1 ≦ x ≦ 1, incremented in steps of 2 0.5 (MthIO-MathO) and g(x) = x2 - (TABLE) (SETUP) (TABLE) (X) (f(x),g(x)) 1 2 ・Pressing without inputting anything for g(x) will generate a numerical table based on f(x) only. (X) 1 1 1 0 2 5 Note • You can use the numerical table screen for viewing values only. Table contents cannot be edited.
Vector Calculations (VECTOR) Use the VECTOR Mode to perform 2-dimensional and 3-dimensional vector calculations. To perform a vector calculation, you first assign data to special vector variables (VctA, VctB, VctC), and then use the variables in the calculation as shown in the example below. Example 1: To assign (1, 2) to VctA and (3, 4) to VctB, and then perform the following calculations: (1, 2) + (3, 4) (VECTOR) to enter the VECTOR Mode. 1. Press 2. Press (VctA) (2).
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 (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 Example 1, and VctC = (2, -1, 2) from Example 2.
(SETUP) (Fix) (VECTOR) (VctA) (VECTOR) (Dot) (VECTOR) (VctB) (Abs) (VECTOR) (VctA) (Abs) (VECTOR) (VctB) (cos-1) Inequality Calculations (INEQ) You can use the following procedure to solve a quadratic inequality or cubic inequality. 1. Press (INEQ) to enter the INEQ Mode. 2. On the menu that appears, select an inequality type. To select this inequality type: Press this key: Quadratic inequality (aX2 + bX + c) Cubic inequality (aX3 + bX2 + cX + d) 3.
5. After all the values are the way you want, press . • This will display the solutions. • To return to the Coefficient Editor while the solutions are displayed, press . Note • Values cannot be converted to engineering notation on the solution screen. Changing the Inequality Type (INEQ) and then select an inequality type from the menu Press that appears. Changing the inequality type causes the values of all Coefficient Editor coefficients to change to zero.
Note: Solutions are displayed as shown here when Linear Display is selected. Example 3: 2x3 - 3x2 ≧ 0 (MthIO-MathO) (INEQ) (aX3 + bX2 + cX + d) (aX3 + bX2 + cX + d ≧ 0) 2 3 Example 4: 3x3 + 3x2 - x > 0 (MthIO-MathO) (INEQ) (aX3 + bX2 + cX + d) (aX3 + bX2 + cX + d > 0) 3 1 3 Note: Solutions are displayed as shown here when Linear Display is selected. Special Solution Display • "All Real Numbers" appears on the solution screen when the solution of an inequality is all numbers.
Using VERIFY (VERIF) VERIFY is a function you can use to verify whether an input equality or inequality is true (indicated by TRUE) or false (indicated by FALSE). The following shows the general procedure for using VERIFY. Example: To verify whether 4√9 = 12 is true (MthIO-MathO) 1. Press (VERIF) to enter the VERIFY Mode. 2. Input 4√9 = 12. 4 9 (VERIF) (=) 12 • You can select the equality symbol or inequality symbol from the menu that appears when you press (VERIFY). 3. To verify, press .
• Any variable (A, B, C, D, E, F, X, Y, M) input into an expression is treated as a value, using the value currently assigned to the variable. • ÷R, Pol and Rec functions cannot be used in an expression. • In the VERIFY Mode, the calculator performs a mathematical operation on the input expression and then displays TRUE or FALSE based on the result.
5 25 (VERIFY) (VERIFY) (=) (=) 625 Distribution Calculations (DIST) You can use the procedures below to perform seven different types of distribution calculations. 1. Press (DIST) to enter the DIST Mode. 2. On the menu that appears, select a distribution calculation type.
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. 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.
To edit sample data: Move the cursor to the cell that contains the data you want to edit, input the new data, and then press . To delete data: Move the cursor to the sample data you want to delete and then press . To insert sample data: Move the cursor to the position where you want to insert the sample data, (STAT/DIST) (Edit) (Ins), and then input the sample press data. To delete all sample data: Press (STAT/DIST) (Edit) (Del-A).
(DIST) (Binomial PD) Display the List Screen: (List) • To specify data using parameter format, press 10 11 12 13 (Var). 14 15 0 6 Results: x = binomial probability of 10 ≒ 0.18594 x = binomial probability of 11 ≒ 0.12678 x = binomial probability of 12 ≒ 0.063388 x = binomial probability of 13 ≒ 0.021942 x = binomial probability of 14 ≒ 4.7018 × 10-3 • Pressing returns to the N input screen. Pressing List Screen (input data samples are stored).
• An error message appears if the input value is outside the allowable range. "ERROR" will appear in the Ans column of the List Screen when the value input for the corresponding sample data is outside the allowable range.
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.
• 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.
Time Out Error Cause: • The current differential or integration calculation ends without the ending condition being fulfilled. Action: • Try increasing the tol 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.
1. Press (OFF) to turn off the calculator. 2. On the back of the calculator, remove the screws and the cover. 3. Remove the battery, and then load a new battery with its plus (+) and minus (-) ends facing correctly. 4. Replace the cover. (CLR) (All) (Yes). 5. Initialize the calculator: • Do not skip the above step! Calculation Priority Sequence The priority sequence of input calculations is evaluated in accordance with the rules below.
5 Negative sign ((-)), base-n symbols (d, h, b, o) 6 Metric conversion commands (cm in, etc.
Precision In general, ±1 at the 10th digit for a single calculation. Precision for exponential display is ±1 at the least significant digit. Errors are cumulative in the case of consecutive calculations. 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 ex 0 ≦ |x| < 9 × 109 0 ≦ |x| < 157079632.7 0 ≦ |x| < 1 × 1010 Same as sinx, except when |x| = (2n-1) × 90.
√x 0 ≦ x < 1 × 10100 x2 |x| < 1 × 1050 x-1 |x| < 1 × 10100; x ≠ 0 √x 3 |x| < 1 × 10100 x! 0 ≦ x ≦ 69 (x is an integer) nPr nCr Pol(x, y) Rec(r, θ) °’ ” ← °’ ” xy x √y b a /c 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.
RanInt#(a, b) a < b; |a|, |b| < 1 × 1010; b - a < 1 × 1010 GCD(a, b) |a|, |b| < 1 × 1010 (a, b are integers) LCM(a, b) 0 ≦ a, b < 1 × 1010 (a, b are integers) • Precision is basically the same as that described under "Calculation Range and Precision", above. 3 x • xy, √y, √ , x!, nPr, nCr type functions require consecutive internal calculation, which can cause accumulation of errors that occur with each calculation.
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. 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? (SETUP) (LineIO). See → Perform the following key operation: "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. 30 here as shown below will result in calculation of sin 30 103 15 0.
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