Casio fx-991ES manual

E fx-1 15ES PLUS f x - 991ES PLUS C 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 ..............................................................[...]

E-2 Impor tant 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 f[...]

E-3 • 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 t[...]

E-4 Reading the Display The display of the calculator shows expressions you input, calculation results, and various indicators. Input expression Indicators 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 calc[...]

E-5 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 usin[...]

E-6 1 MthIO 2 LineIO Specifies the display format. Natural Display (MthIO) causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper. 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 Math[...]

E-7 c 6 Rdec 1 ON ; 2 OFF Specifies whether or not to display calculation results using recurring decimal form. c 7 Disp 1 Dot ; 2 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 i[...]

E-8 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 [...]

E-9 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. • Nesti[...]

E-10 T o 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. T o clear all of the calculation you are inputting: Press A . Recurring Decimal Calculations Your calcul[...]

E-11 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. Displaying a Calculation Result as a R[...]

E-12 Return to initial display format (Norm 1): f 7 1 = 0.142857 = 0.1428571429 (Norm 1) b 1 ' 7 = Display as recurring decimal: f Decimal value according to Norm 1 setting: f Return to initial display format (fraction): f 1 ÷ 7 = 0.1428571429 (Norm 1) = 0.142857 = 7 1 b 1 / 7 = Display as fraction: f Display as recurring decimal: f Return to[...]

E-13 • 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): 0.1[...]

E-14 T oggling 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 6 π = 0.5235987756 B 1 5 ( π ) / 6 = 1 6 π f 0.5235987756 ( ' 2 + 2) × '[...]

E-15 1 = 1 2 2 4 − 3 B 4 - 1 ' ( ( ) 3 e 1 c 2 = 1 2 b 4 - 3 ' 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. T o swit[...]

E-16 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 S 7 (:) 3 * 3 = 6 = 9 Using Engineering Notation A simple key operation transforms a displayed value to engineering notation. Transform the value 1234 to engineering not[...]

E-17 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 calcu[...]

E-18 V ariables (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 1t (STO) y (A) 8 To multiply the contents of variable A by 10 (Continuing) S y (A) * 10 = 80 To recall[...]

E-19 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 calculat[...]

E-20 Function Calculations For actual operations using each function, see the “Examples” section following the list below. π 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 , c[...]

E-21 can be specified within the range of –1 × 10 10  a  b  1 × 10 10 . 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 formula is:  ( f ( x )) x = a b = f ( a [...]

E-22 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 an[...]

E-23 Examples sin 30°= 0.5 bv s 30 )= 0.5 sin −1 0.5 = 30° bv 1 s (sin −1 ) 0.5 )= 30 sinh 1 = 1.175201194 w b (sinh) 1 )= 1.175201 194 cosh –1 1 = 0 w f (cosh −1 ) 1 )= 0 π /2 radians = 90°, 50 grads = 45° v ( 1 5 ( π ) / 2 ) 1G (DRG ' ) c ( r ) = 90 50 1G (DRG ' ) d ( g ) = 45 To calculate e 5 × 2 to three significant dig[...]

E-24 Σ x = 1 5 ( x + 1) = 20 B 1 & ( 8 ) S ) (X) + 1 e 1 e 5 = 20 b 1 & ( 8 ) S ) (X) + 1 1 ) (,) 1 1 ) (,) 5 )= 20  x =1 5 ( x + 1) = 720 B a & ( 9 ) S ) (X) + 1 e 1 e 5 = 720 b a & ( 9 ) S ) (X) + 1 1 ) (,) 1 1 ) (,) 5 )= 720 To convert rectangular coordinates ( ' 2 , ' 2 ) to polar coordinates v B 1 + (Pol) ! 2 e 1 [...]

E-25 To determine the greatest common divisor of 28 and 35 S * (GCD) 28 1 ) (,) 35 )= 7 To determine the least common multiple of 9 and 15 S / (LCM) 9 1 ) (,) 15 )= 45 To extract the integer part of −3.5 S + (Int) - 3.5 )= −3 To determine the largest integer that does not exceed −3.5 S - (Intg) - 3.5 )= −4 Complex Number Calculations (CMPLX[...]

E-26 Using a Command to Specify the Calculation Result Format Either of two special commands ( ' r ∠  or ' a + b i ) 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 = &a[...]

E-27 To store A + B i and then determine ' 3 + i , 1 + ' 3 i using polar coordinates ( r ∠  ) v N 2 (CMPLX) S - (A) + S e (B) W ( i ) 1 2 (CMPLX) 3 ( ' r ∠  ) 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 [...]

E-28 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 [...]

E-29 Input an initial value for X (Here, input 1): 1 = = 7 == = 13 == Statistical Calculations (ST A T) To start a statistical calculation, perform the key operation N 3 (STAT) to enter the STAT Mode and then use the screen that appears to select the type of calculation you want to perform. T o select this type of statistical calculation: (Regressi[...]

E-30 To select linear regression and input the following data: (170, 66), (173, 68), (179, 75) N 3 (STAT) 2 (A+BX) 170 = 173 = 179 = ce 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 paired- variable statistical calculation type, or chang[...]

E-31 • m , m 1 , m 2 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 V alue: minX*, minY, Maximum V alue: maxX*, maxY 1 1 (STAT/DIST) 6 (MinMax) 1 to 2 (When the single-variable statistical calculation is selected.) 1 1 (STAT[...]

E-32 A1 1 (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 + 2357.532ln x Calculating Estimated V alues Based on the regression formula obtained by paired-variable statistical calculation, the estimated value of[...]

E-33 A 3 1 1 (STAT/DIST) 5 (Distr) 4 ( ' t ) = 1 1 (STAT/DIST) 5 (Distr) 1 (P() G )= Results: Normalized variate ( ' t ): –0.762 P( t ): 0.223 Base- n Calculations (BASE-N) Press N 4 (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[...]

E-34 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 V alue You can input a special command immediately following a value to[...]

E-35 To determine the logical XOR of 1010 2 and 1100 2 (1010 2 xor 1100 2 ) A 1010 1 3 (BASE) 3 (xor) 1100 = 0000000000000110 To determine the logical XNOR of 1111 2 and 101 2 (1111 2 xnor 101 2 ) A 1111 1 3 (BASE) 4 (xnor) 101 = 1111111111110101 To determine the bitwise complement of 1010 2 (Not(1010 2 )) A1 3 (BASE) 5 (Not) 1010 )= 11111111111101[...]

E-36 • 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 T ype Setting Press N 5 (EQN) and then select an equation type from the menu that appears. Changing the equation type causes the values of all Coefficient Edi[...]

E-37 x 3 – 2 x 2 – x + 2 = 0 N 5 (EQN) 4 (aX 3 + bX 2 + cX + d = 0) 1 = - 2 = - 1 = 2 == (X 1 =) –1 c (X 2 =) 2 c (X 3 =) 1 Matrix Calculations (MA TRIX) 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, M[...]

E-38 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 th[...]

E-39 3 × MatA (Matrix scalar multiplication). A 3 * MatA = Obtain the determinant of MatA (det(MatA)). A1 4 (MATRIX) 7 (det) MatA )= 1 Obtain the transposition of MatC (Trn(MatC)). A1 4 (MATRIX) 8 (Trn) MatC )= Obtain the inverse matrix of MatA (MatA –1 ). Note: You cannot use 6 for this input. Use the E key to input “ –1 ”. A MatA E = Obt[...]

E-40 • 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, inp[...]

E-41 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 [...]

E-42 Assigning and Editing V ector V ariable 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. T o assign new data to a vector variable: 1. Press 1 5 (VECTOR) 1 (Dim), and then, on the menu that appears, select th[...]

E-43 VctA • VctB (Vector dot product) A VctA 1 5 (VECTOR) 7 (Dot) VctB = VctA × VctB (Vector cross product) A VctA * VctB = Obtain the absolute values of VctC. A1w (Abs) VctC )= Determine the angle formed by VctA and VctB to three decimal places (Fix 3). v (cos  = (A • B)  A  B  , which becomes  = cos –1 (A • B)  A [...]

E-44 • 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 canno[...]

E-45 2 x 3 − 3 x 2  0 B N c 1 (INEQ) 2 (aX 3 + bX 2 + cX + d) 3 (aX 3 + bX 2 + cX + d  0) 2 = - 3 = = 3 x 3 + 3 x 2 – x  0 B N c 1 (INEQ) 2 (aX 3 + bX 2 + cX + d) 1 (aX 3 + bX 2 + cX + d  0) 3 = 3 = - 1 = = eee Note: Solutions are displayed as shown here when Linear Display is selected. Special Solution Display • “All Real Numbe[...]

E-46 2. Input 4 ' 9 = 12. 4 ! 9 e 1 6 (VERIFY) 1 (=)12 • You can select the equality symbol or inequality symbol from the menu that appears when you press 1 6 (VERIFY). 3. To verify, press = . You can input the following expressions for verification in the VERIFY Mode. • Equalities or inequalities that include one relational operator 4 = 1[...]

E-47 VERIFY Mode Calculation Examples To verify log2  log3  log4 l 2 ) 1 6 (VERIFY) 4 (  ) l 3 ) 1 6 (VERIFY) 4 (  ) l 4 )= To verify 0  – ( ) 9 8 9 8 2 B 0 1 6 (VERIFY) 4 (  ) 8 ' 9 e w - 8 ' 9 = To verify 5 2 = 25 = 625 B 5 w 1 6 (VERIFY) 1 (=) 25 1 6 (VERIFY) 1 (=) ! 625 = Distribution Calculations (DIST) You can us[...]

E-48 V ariables 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[...]

E-49 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 N c 3 (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[...]

E-50 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 ca[...]

E-51 23: (e) elementary charge 24: (NA) Avogadro constant 25: (k) Boltzmann constant 26: (Vm) molar volume of ideal gas (273.15K, 100kPa) 27: (R) molar gas constant 28: (C 0 ) speed of light in vacuum 29: (C 1 ) first radiation constant 30: (C 2 ) second radiation constant 31: ( σ ) Stefan-Boltzmann constant 32: ( ε 0 ) electric constant 33: ( ?[...]

E-52 The following shows the two-digit numbers for each of the metric conversion commands. 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 ' m 2 12: m 2 ' acre 13: gal (US) ' R 14: R ' gal (US)[...]

E-53 sin –1 x 0  | x |  1 cos –1 x tan –1 x 0  | x |  9.999999999 × 10 99 sinh x 0  | x |  230.2585092 cosh x sinh –1 x 0  | x |  4.999999999 × 10 99 cosh –1 x 1  x  4.999999999 × 10 99 tanh x 0  | x |  9.999999999 × 10 99 tanh –1 x 0  | x |  9.999999999 × 10 –1 log x /ln x 0  x  9.[...]

E-54 • Precision is basically the same as that described under “Calculation Range and Precision”, above. • x y , x ' y , 3 ' , x !, n P r , n C r 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 vic[...]

E-55 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 numer[...]

E-56 Befor e 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. Che[...]

E-57 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 T emperature: 0°C to 40°C (32°F to 104°F) Dimensions: 11.1 (H) × 80 (W) × 162 (D) mm 3 / 8 ⬙ (H) × 3 1 / 8 ⬙ (W) × 6 3 / 8 ⬙ (D) Approximate Weight: 95 g (3.[...]

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