E fx-115ES PLUS fx-991ES PLUS C User’s Guide CASIO Worldwide Education Website http://edu.casio.com CASIO EDUCATIONAL FORUM http://edu.casio.
Contents Important Information ............................................................. 2 Sample Operations .................................................................. 2 Initializing the Calculator ........................................................ 2 Safety Precautions .................................................................. 2 Handling Precautions.............................................................. 2 Removing the Hard Case ...............................................
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.
• 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.
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 e and d to scroll the calculation result display. • If a g indicator appears on the right side of the input expression, it means the displayed calculation continues to the right.
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. Pressing N or w, for example, will display a menu of applicable functions. The following are the operations you should use to navigate between menus.
1MthIO 2LineIO Specifies the display format. Natural Display (MthIO) causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper. Math MthIO: Selects MathO or LineO. MathO displays input and calculation results using the same format as they are written on paper. LineO displays input the same way as MathO, but calculation results are displayed in linear format. Linear Display (LineIO) causes fractions and other expressions to be displayed in a single line.
c6Rdec 1ON ; 2OFF Specifies whether or not to display calculation results using recurring decimal form. c7Disp 1Dot ; 2Comma 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 (;). c8]CONT' Contrast” for details. Adjusts display contrast.
e while the cursor is at the end of the input calculation will cause it to jump to the beginning, while pressing d 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 k when there are 10 bytes or less of allowed input remaining. If this happens, end calculation input and then press =.
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 dots × 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.
To insert a character or function into a calculation: Use d and e 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 A. 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.
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.
Math Return to initial display format (Norm 1): f 1 = 0.142857 = 0.1428571429 (Norm 1) 7 b 1'7= f Display as recurring decimal: Decimal value according to Norm 1 setting: f Return to initial display format (fraction): f 1 ÷ 7 = 0.1428571429 (Norm 1) = 0.
• The data size of value to be displayed as the recurring decimal must be no larger than 99 bytes. Each value and the decimal point require one byte, and each digit of the period requires one byte. The following, for example, would require of total of 8 bytes (4 bytes for the values, 1 byte for the decimal point, 3 bytes for the period): 0.
Toggling Calculation Results While Natural Display is selected, each press of f 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. π ÷ 6 = 1 π = 0.5235987756 6 15(π)/ 6 = B 1π 6 (' 2 + 2) × ' 3 =' 6 + 2' 3 = 5.913591358 f 0.5235987756 B (! 2 e+ 2 )*! 3 = ' 6 + 2' 3 f 5.
4−3 1 = 1 B 2 2 4 -1'(() 3 e 1 c 2 = b 4-3'1'2= 1 2 1{2 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 form: Perform the following key operation: 1f(<) To switch a calculation result between fraction and decimal form: Press f.
Multi-Statements You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press =. 3+3:3×3 3 + 3 S7(:) 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 = W 1.234×103 W 1234×100 Transform the value 123 to engineering notation, shifting the decimal point to the left.
Answer Memory (Ans) /Previous Answer Memory (PreAns) The last calculation result obtained is stored in Ans (answer) memory. The calculation result obtained prior to the last one is stored in PreAns (previous answer) memory. Displaying the result of a new calculation will move current Ans memory contents to PreAns memory and store the new calculation results in Ans memory. PreAns memory can be used only in the COMP Mode.
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.
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. Performing the operation 5 a '(÷R) 2 !t(STO))(X) (which assigns the result of 5÷R2 to X) will assign a value of 2 to X. • If a ÷R calculation is part of a multi-step calculation, only the quotient is passed on to the next operation.
Function Calculations For actual operations using each function, see the “Examples” section following the list below. π : π is displayed as 3.141592654, but π = 3.14159265358980 is used for internal calculations. e : e is displayed as 2.718281828, but e = 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. See 1 . sinh, cosh, tanh, sinh−1, cosh−1, tanh−1 : Hyperbolic functions.
can be specified within the range of –1 × 1010 a b 1 × 1010. See 10. 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. 9: Determines the product of f(x) over a given range. The calculation b ( f (x)) = f(a) × f(a+1) × f(a+2) × ... × f(b). The Natural Display x=a b input syntax is ( f (x)), while the Linear Display input syntax is (f(x), a, x=a formula is: b).
Intg: Determines the largest integer that does not exceed a value. See 21. 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 A. Integration and Differential Calculation Precautions • Integration and differential calculations can be performed in the COMP Mode (,1) only.
Examples bv s 30 )= sin 0.5 = 30° bv 1s(sin ) 0.5 )= 1 sin 30°= 0.5 −1 2 sinh 1 = 1.175201194 0.5 30 −1 wb(sinh) 1 )= 1.175201194 wf(cosh−1) 1 )= cosh–1 1 = 0 3 π /2 radians = 90°, 50 grads = 45° 0 v (15(π)/ 2 )1G(DRG')c(r)= 50 1G(DRG')d(g)= 90 45 4 To calculate e5 × 2 to three significant digits (Sci 3) 1N(SETUP)7(Sci)3 B b 1i(%) 5 e* 2 = 1i(%) 5 )* 2 = 2.97×102 2.
5 10 Σ (x + 1) = 20 x =1 B b 1&(8)S)(X)+ 1 e 1 e 5 = 1&(8)S)(X)+ 1 1)(,) 1 1)(,) 5 )= 20 20 5 11 (x + 1) = 720 x=1 B b a&(9)S)(X)+ 1 e 1 e 5 = a&(9)S)(X)+ 1 1)(,) 1 1)(,) 5 )= 720 720 12 To convert rectangular coordinates (' 2,' 2 ) to polar coordinates v B 1+(Pol)! 2 e1)(,)! 2 e)= r=2, =45 b 1+(Pol)! 2 )1)(,)! 2 ))= r= 2 = 45 To convert polar coordinates (' 2 , 45°) to rectangular coordinates v B 1-(Rec)! 2 e1)(,) 45 )= X=1, Y=1 13 (5 + 3) ! = 40320 14 |2 – 7| × 2 = 10 B b ( 5 + 3 )1E(x!)=
19 To determine the greatest common divisor of 28 and 35 S*(GCD) 28 1)(,) 35 )= To determine the least common multiple of 9 and 15 S/(LCM) 9 1)(,) 15 )= 7 45 20 To extract the integer part of −3.5 S+(Int)- 3.5 )= −3 21 To determine the largest integer that does not exceed −3.5 S-(Intg)- 3.5 )= −4 Complex Number Calculations (CMPLX) To perform complex number calculations, first press N2(CMPLX) to enter the CMPLX Mode.
Using a Command to Specify the Calculation Result Format Either of two special commands ('r∠ or 'a+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.
To store A + Bi and then determine ' 3 + i, 1 + ' 3 i using polar coordinates (r∠ ) v N2(CMPLX) S-(A)+Se(B)W(i) 12(CMPLX)3('r∠ ) CMPLX Math s! 3 )= 1 = s (or =) 1 =! 3 )= To exit CALC: A Note: During the time from when you press s until you exit CALC by pressing A, 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 (N1) only.
Math Input an initial value for X (Here, input 1): 1= To exit SOLVE: A Solution screen Note: During the time from when you press 1s(SOLVE) until you exit SOLVE by pressing A, 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.
Math Input an initial value for X (Here, input 1): 1= Math = 7 == Math = 13 == Statistical Calculations (STAT) To start a statistical calculation, perform the key operation N3(STAT) to enter the STAT Mode and then use the screen that appears to select the type of calculation you want to perform.
1 To select linear regression and input the following data: (170, 66), (173, 68), (179, 75) STAT N3(STAT)2(A+BX) STAT 170 = 173 = 179 =ce STAT 66 = 68 = 75 = Important: • All data currently input in the Stat Editor is deleted whenever you exit the STAT Mode, switch between the single-variable and a pairedvariable statistical calculation type, or change the Stat Format setting on the setup menu. • The following operations are not supported by the Stat Editor: m, 1m(M–), 1t(STO).
• m, m1, m2 and n 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 11(STAT/DIST) 6(MinMax) 1 to 2 (When the single-variable statistical calculation is selected.) 11(STAT/DIST) 6(MinMax) 1 to 4 (When a paired-variable statistical calculation is selected.
A11(STAT/DIST)5(Reg)2(B)= Results: Linear Regression Correlation Coefficient: 0.923 Logarithmic Regression Correlation Coefficient: 0.998 Logarithmic Regression Formula: y = –3857.984 + 2357.532lnx Calculating Estimated Values Based on the regression formula obtained by paired-variable statistical calculation, the estimated value of y can be calculated for a given x-value.
STAT FIX STAT FIX A 3 11(STAT/DIST)5(Distr)4('t)= 11(STAT/DIST)5(Distr)1(P()G)= Results: Normalized variate ('t): –0.762 0.223 P(t): Base-n Calculations (BASE-N) Press N4(BASE-N) to enter the BASE-N Mode when you want to perform calculations using decimal, hexadecimal, binary, and/or octal values. 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.
Octal Positive: 00000000000 x 17777777777 Negative: 20000000000 x 37777777777 Decimal –2147483648 x 2147483647 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 determine the logical XOR of 10102 and 11002 (10102 xor 11002) A 1010 13(BASE)3(xor) 1100 = 0000000000000110 To determine the logical XNOR of 11112 and 1012 (11112 xnor 1012) A 1111 13(BASE)4(xnor) 101 = 1111111111110101 To determine the bitwise complement of 10102 (Not(10102)) A13(BASE)5(Not) 1010 )= 1111111111110101 To negate (take the two’s complement) of 1011012 (Neg(1011012)) A13(BASE)6(Neg) 101101 )= 1111111111010011 Note: In the case of a negative binary, octal or hexadecimal value, the calculator
• A message appears to let you know when there is no solution or when there are infinite solutions. Pressing A or = will return to the Coefficient Editor. Changing the Current Equation Type Setting Press N5(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.
x3 – 2x2 – x + 2 = 0 N5(EQN)4(aX3 + bX2 + cX + d = 0) 1 =- 2 =- 1 = 2 == c c (X1=) –1 (X2=) 2 (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.
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: 14(MATRIX)6(MatAns).
3 3 × MatA (Matrix scalar multiplication). A 3 *MatA= 4 Obtain the determinant of MatA (det(MatA)). A14(MATRIX)7(det) MatA)= 1 5 Obtain the transposition of MatC (Trn(MatC)). A14(MATRIX)8(Trn) MatC)= 6 Obtain the inverse matrix of MatA (MatA–1). Note: You cannot use 6 for this input. Use the E key to input “ –1”. AMatAE= 7 Obtain the absolute value of each element of MatB (Abs(MatB)). A1w(Abs) MatB)= 8 Determine the square and cube of MatA (MatA2, MatA3). Note: You cannot use 6 for this input.
• Be sure to input the X variable (S)(X)) when generating a number 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 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).
setting, while 20 rows are supported for the “f(x),g(x)” setting. • 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.
Assigning and Editing Vector Variable Data Important: The following operations are not supported by the Vector Editor: m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements also cannot be input with the Vector Editor. To assign new data to a vector variable: 1. Press 15(VECTOR)1(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.
4 VctA • VctB (Vector dot product) VCT AVctA15(VECTOR)7(Dot)VctB= 5 VctA × VctB (Vector cross product) VCT AVctA*VctB= 6 Obtain the absolute values of VctC. VCT A1w(Abs)VctC)= 7 Determine the angle formed by VctA and VctB to three decimal places (Fix 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 A will clear all of the coefficients to zero. Note: The following operations are not supported by the Coefficient Editor: m, 1m(M–), 1t(STO). Pol, Rec, ÷R, and multi-statements also cannot be input with the Coefficient Editor. 5. After all the values are the way you want, press =. • This will display the solutions.
2x3 − 3 x2 0 B Nc1(INEQ)2(aX3 + bX2 + cX + d) 3(aX3 + bX2 + cX + d 0) 2 =- 3 = Math Math = 3x3 + 3 x2 – x 0 B Nc1(INEQ)2(aX3 + bX2 + cX + d) 1(aX3 + bX2 + cX + d 0) 3 = 3 =- 1 = Math Math = Math eee 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.
2. Input 4' 9 = 12. 4 ! 9 e1 6 (VERIFY) 1 (=)12 • You can select the equality symbol or inequality symbol from the menu that appears when you press 16(VERIFY). 3. To verify, press =. Math You can input the following expressions for verification in the VERIFY Mode. • Equalities or inequalities that include one relational operator 4 = 16, 4 3, π 3, 1 + 2 5, (3 × 6) (2 + 6) × 2, etc.
VERIFY Mode Calculation Examples To verify log2 log3 log4 l 2 )16 (VERIFY) 4 ( ) l 3 )16 (VERIFY) 4 ( ) l 4 )= To verify 0 2 ( 89 ) – 89 B 0 16 (VERIFY) 4 ( ) 8 ' 9 ew- 8 ' 9 = To verify 52 = 25 = 625 B 5 w16 (VERIFY) 1 (=) 25 16 (VERIFY) 1 (=) ! 625 = Distribution Calculations (DIST) You can use the procedures below to perform seven different types of distribution calculations. 1. Press Nc3(DIST) to enter the DIST Mode. 2. On the menu that appears, select a distribution calculation type.
Variables that Accept Input The following are distribution calculation variables that accept input values. Normal PD ........................... x, σ, Normal CD ........................... Lower, Upper, σ, Inverse Normal .................... Area, σ, (Tail setting always left.) Binomial PD, Binomial CD ... x (or List), N, p Poisson PD, Poisson CD .....
35 = Result: 0.1760326634 • Pressing = or A returns to the x input screen. To calculate binomial probability for the sample data {10, 11, 12, 13, 14} when N=15 and p=0.6 Nc3(DIST)4(Binomial PD) Display the List Screen: 1(List) • To specify data using parameter format, press 2(Var). 10 = 11 = 12 = 13 = 14 = = 15 = 0.6 = ecccc Results: x = binomial probability of 10 ⱌ 0.18594 x = binomial probability of 11 ⱌ 0.12678 x = binomial probability of 12 ⱌ 0.063388 x = binomial probability of 13 ⱌ 0.
Ans column of the List Screen when the value input for the corresponding sample data is outside the allowable range. 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. To input a scientific constant into a calculation, press 17(CONST) and then input the two-digit number that corresponds to the constant you want.
23: (e) elementary charge 24: (NA) Avogadro constant 25: (k) Boltzmann constant 26: (Vm) molar volume of ideal gas (273.
The following shows the two-digit numbers for each of the metric conversion commands.
sin–1x cos–1x 0 |x| 1 tan–1x sinhx coshx sinh–1x 0 |x| 9.999999999 × 1099 cosh–1x 1 x 4.999999999 × 1099 tanhx 0 |x| 9.999999999 × 1099 tanh–1x 0 |x| 9.999999999 × 10–1 logx/lnx 0 x 9.999999999 × 1099 0 |x| 230.2585092 0 |x| 4.999999999 × 1099 10x –9.999999999 × 1099 x 99.99999999 ex x ' x2 x –1 3 ' x x! –9.999999999 × 1099 x 230.
• Precision is basically the same as that described under “Calculation Range and Precision”, above. y , 3', x!, nPr, nCr type functions require consecutive internal • xy, x' calculation, which can cause accumulation of errors that occur with each calculation. • Error is cumulative and tends to be large in the vicinity of a function’s singular point and inflection point. • The range for calculation results that can be displayed in π form when using Natural Display is |x| 106.
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.
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.
Specifications Power Requirements: Built-in solar cell; button battery LR44 (GPA76) × 1 Approximate Battery Life: 3 years (based on one hour of operation per day) Operating Temperature: 0°C to 40°C (32°F to 104°F) Dimensions: 11.1 (H) × 80 (W) × 162 (D) mm 3 /8⬙ (H) × 31/8⬙ (W) × 63/8⬙ (D) Approximate Weight: 95 g (3.
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