Casio fx-115ES PLUS, User Manual

Page 1: ...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 com forum ...

Page 2: ...der Calculations 18 Prime Factorization 19 Function Calculations 20 Complex Number Calculations CMPLX 25 Using CALC 26 Using SOLVE 27 Statistical Calculations STAT 29 Base n Calculations BASE N 33 Equation Calculations EQN 35 Matrix Calculations MATRIX 37 Creating a Number Table from Two Functions TABLE 39 Vector Calculations VECTOR 41 Inequality Calculations INEQ 43 Using VERIFY VERIF 45 Distribu...

Page 3: ...up 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 9 CLR 3 All Yes Safety Precautions Battery Keep batteries out of the reach of small children Use only the type of battery specified for this ...

Page 4: ...ay Contrast Display the CONTRAST screen by performing the following key operation 1N SETUP c8 CONT Next use d and e to adjust contrast After the setting is the way you want press A 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 1 or S key followed by a second key performs the alt...

Page 5: ... press a key The alpha input mode has been entered by pressing the S 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 indicator appears after you press 1t STO RCL The calculator is standing by for input o...

Page 6: ...r menu above Use c and f to switch between menus To close a menu without selecting anything press A Specifying the Calculation Mode When you want to perform this type of operation Perform this key operation General calculations N1 COMP Complex number calculations N2 CMPLX Statistical and regression calculations N3 STAT Calculations involving specific number systems binary octal decimal hexadecimal...

Page 7: ...lt 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 b 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 specif...

Page 8: ... the result will appear on the display 4 sin30 30 10 3 120 4 s30 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 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 immedia...

Page 9: ...the input value x2 x3 x 1 x r g t powers x roots 4th Fractions 5th Negative sign base n symbols d h b o Note When squaring a negative value such as 2 the value being squared must be enclosed in parentheses 2 w Since x2 has a higher priority than the negative sign inputting 2w would result in the squaring of 2 and then appending a negative sign to the result Always keep the priority sequence in min...

Page 10: ...ove the value or expression to the right of the cursor after 1Y 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 7 17 F 1 8 a 9 16 1...

Page 11: ...a Recurring Decimal When inputting a recurrent decimal press a k before inputting its period repetend and then input the period up to the ending value To input the recurring decimal 0 909090 0 90 perform the following operation 0 a k 90 Important If the value starts with an integer part like 12 3123123 do not include the integer part when inputting the period 12 312 Recurring decimal input is poss...

Page 12: ...such when ON is selected for the Rdec setting on the setup menu Pressing the f key will cycle between the available calculation result formats as shown below Fraction Recurring Decimal Decimal Value According to Display Norm Fix Sci Settings Or Decimal Value According to Display Norm Fix Sci Settings Recurring Decimal Fraction 7 1 0 142857 0 1428571429 Norm 1 B 1 7 Display as recurring decimal f D...

Page 13: ... 7 1 b 1 7 Display as fraction f Display as recurring decimal f Return to initial display format Norm 1 f Conditions for Displaying a Calculation Result as a Recurring Decimal If a calculation result satisfies the following conditions pressing f will display it as a recurring decimal value The total number of digits used in the mixed fraction including integer numerator denominator and separator s...

Page 14: ...mal point 3 bytes for the period 0 123 Note For information about switching the display format of a calculation result when OFF is selected for the Rdec setting on the setup menu see Toggling Calculation Results Recurring Decimal Examples 0 3 0 45 0 78 B 0 a k 3e 0 a k 45 f 1 6 2 8 4 5 B 1 a k 6e 2 a k 8 f To confirm the following 0 123 999 123 0 1234 9999 1234 0 12345 99999 12345 B 123 999 f 1234...

Page 15: ...lts pressing the f key will not convert the displayed value When ON is selected for Rdec on the setup menu pressing f will switch the calculation result to recurring decimal form For details see Recurring Decimal Calculations You cannot switch from decimal form to mixed fraction form if the total number of digits used in the mixed fraction including integer numerator denominator and separator symb...

Page 16: ...what percentage of 880 is 660 75 660 8801 75 Increase 2500 by 15 2875 2500 2500 151 2875 Discount 3500 by 25 2625 3500 3500 251 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 v...

Page 17: ...embers up to approximately 200 bytes of data for the newest calculation You can scroll through calculation history contents using f and c 1 1 2 1 1 2 2 2 4 2 2 4 3 3 6 3 3 6 Scrolls back f 4 Scrolls back again f 2 Note Calculation history data is all cleared whenever you press O when you change to a different calculation mode when you change the display format or whenever you perform any reset ope...

Page 18: ...esults in Ans memory PreAns memory can be used only in the COMP Mode PreAns memory contents are cleared whenever the calculator enters another mode from the COMP Mode To divide the result of 3 4 by 30 b 3 4 Continuing 30 123 456 579 B 123 456 789 579 210 Continuing 789 G For Tk 2 Tk 1 Tk Fibonacci sequence determine the sequence from T1 to T5 Note however that T1 1 and T2 1 B T1 1 1 Ans T1 1 T2 1 ...

Page 19: ... l M 0 To add the result of 10 5 to M Continuing 10 5l 50 To subtract the result of 10 5 from M Continuing 10 51l M 15 To recall the contents of M Continuing tl 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 A change the calculation mode or turn off the calculator PreAns me...

Page 20: ...r or if the remainder is not a positive integer or positive fractional value Example 5a R 2 Calculated as 5 2 Prime Factorization In the COMP Mode you can factor a positive integer up to 10 digits into prime factors up to three digits To perform prime factorization on 1014 1014 e FACT When you perform prime factorization on a value that includes a factor that is prime number with more than three d...

Page 21: ...l logarithm to base e See 6 x2 x3 x x 1 Powers power roots and reciprocals Note that the input methods for x and are different depending upon whether you are using Natural Display or Linear Display See 7 Note The following functions cannot be input in consecutive sequence x2 x3 x x 1 If you input 2ww for example the final w will be ignored To input 2 22 input 2w press the d key and then press w B ...

Page 22: ...you are using Natural Display or Linear Display See 14 Ran Generates a 3 digit pseudo random number that is less than 1 The result is displayed as a fraction when Natural Display is selected See 15 RanInt For input of the function of the form RanInt a b which generates a random integer within the range of a to b See 16 nPr nCr Permutation nPr and combination nCr functions See 17 Rnd Theargumentoft...

Page 23: ...ge Precautions for Differential Calculation Only If convergence to a solution cannot be found when tol input is omitted the tol value will be adjusted automatically to determine the solution Non consecutive points abrupt fluctuation extremely large or small points inflection points and the inclusion of points that cannot be differentiated or a differential point or differential calculation result ...

Page 24: ...log2 16 4 l21 16 4 B 2e16 4 To calculate ln 90 loge 90 to three significant digits Sci 3 1N SETUP 7 Sci 3 i90 4 50 100 1 2 103 1200 B 1 2 1063 1200 1 1 2 2 16 B 1 1 62 2 16 52 3 15625 5x 1w x3 15625 32 5 2 B 16 5e32 2 b 516 32 2 To calculate 2 3 3 2 4 242640687 to three decimal places Fix 3 1N SETUP 6 Fix 3 B 2e 3 3 2 1 4 243 b 2 3 4 243 1 e ln x 1 B 7iS X e1eS5 e 1 b 7iS X 1 11 S5 e 1 To obtain t...

Page 25: ... 459 48 117 Results shown here are for illustrative purposes only Actual results will differ To generate random integers in the range of 1 to 6 S RanInt 11 6 2 6 1 Results shown here are for illustrative purposes only Actual results will differ To determine the number of permutations and combinations possible when selecting four people from a group of 10 Permutations 101 nPr 4 5040 Combinations 10...

Page 26: ...2 6W i 2W i 3 i 2 45 2 2 i Bv Complex number format a bi 21 45 2 2 i 2 2 i 2 45 Bv Complex number format r 2e 2eW 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 The value of the calculation result is displayed in the range of 180 180 Display of the calculation result while Line...

Page 27: ...iables which you can then recall and execute in the COMP Mode N1 and the CMPLX Mode N2 The following describes the types of expressions you can save with CALC Expressions 2X 3Y 2AX 3BY C A Bi Multi statements X Y X X Y Equalities with a single variable on the left and an expression including variables on the right A B C Y X2 X 3 Use Ss to input the equals sign of the equality To store 3A B and the...

Page 28: ...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 p...

Page 29: ...end 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 form Equation The equation you input 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 var...

Page 30: ...X Y power regression y AxB 7 A X B Paired variable X Y inverse regression y A B x 8 1 X Pressing any of the above keys 1 to 8 displays the Stat Editor Note When you want to change the calculation type after entering the STAT Mode perform the key operation 11 STAT DIST 1 Type to display the calculation type selection screen Inputting Data Use the Stat Editor to input data Perform the following key ...

Page 31: ...ine and then perform the following key operation 11 STAT DIST 3 Edit 1 Ins To delete all Stat Editor contents In the Stat Editor perform the following key operation 11 STAT DIST 3 Edit 2 Del A Obtaining Statistical Values from Input Data To obtain statistical values press A while in the Stat Editor and then recall the statistical variable σx Σx2 etc you want Supported statistical variables and the...

Page 32: ...TAT DIST 5 Distr See Performing Normal Distribution Calculations for details To input the single variable data x 1 2 2 3 3 3 4 4 5 using the FREQ column to specify the number of repeats for each items xn freqn 1 1 2 2 3 3 4 2 5 1 and calculate the mean and population standard deviation 1N SETUP c4 STAT 1 ON N3 STAT 1 1 VAR 1 2 3 4 5 ce 1 2 3 2 A11 STAT DIST 4 Var 2 o A11 STAT DIST 4 Var 3 σx Resul...

Page 33: ...rtant 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 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...

Page 34: ...ry mode and calculate 112 12 N4 BASE N l BIN 11 1 Continuing from above switch to the hexadecimal mode and calculate 1F16 116 A6 HEX 1t F 1 Continuing from above switch to the octal mode and calculate 78 18 Ai OCT 7 1 Note Use the following keys to input the letters A through F for hexadecimal values A B w C s D c E t F In the BASE N Mode input of fractional decimal values and exponents is not sup...

Page 35: ...ons to convert the currently displayed calculation result to another type of value x DEC decimal 6 HEX hexadecimal l BIN binary i OCT octal To calculate 1510 3710 in the decimal mode and then convert the result to hexadecimal binary and octal Ax DEC 15 37 555 6 HEX 0000022B l BIN 0000001000101011 i OCT 00000001053 Logical and Negation Operations Your calculator provides you with logical operators ...

Page 36: ... bnY cn Simultaneous linear equations with three unknowns 2 anX bnY cnZ dn Quadratic equation 3 aX2 bX c 0 Cubic equation 4 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 3 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 th...

Page 37: ...the values of all Coefficient Editor coefficients to change to zero EQN Mode Calculation Examples x 2y 3 2x 3y 4 N5 EQN 1 anX bnY cn 1 2 3 2 3 4 X 1 c Y 2 x y z 2 x y z 0 x y z 4 N5 EQN 2 anX bnY cnZ dn 1 1 1 2 1 1 1 0 1 1 1 4 X 1 c Y 2 c Z 3 2x2 3x 6 0 B N5 EQN 3 aX2 bX c 0 2 3 6 X1 3 57 4 c X2 4 3 57 c X Value Minimum 3 4 c Y Value Minimum 57 8 The local minimum value is displayed when a 0 The l...

Page 38: ...isplay the Matrix Editor for input of the elements of the 2 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 1 4 MATRIX 2 Data 2 MatB 5 2 2 This will display the Matrix Editor for input of the elements of the 2 2 matrix you specified for MatB 5 Input the elements of MatB 2 1 1 2 6 Press A to advance to the calculation scre...

Page 39: ...Use the Matrix Editor that appears to input the elements of the matrix To assign 1 0 1 0 1 1 to MatC 14 MATRIX 1 Dim 3 MatC 4 2 3 1 0 1 0 1 1 To edit the elements of a matrix variable 1 Press 14 MATRIX 2 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...

Page 40: ...w to specify squaring and 1w x3 to specify cubing AMatAw AMatA1w x3 Determine the MatA row echelon form A 4 MATRIX c1 Ref MatA Determine the MatA reduced row echelon form A 4 MATRIX c2 Rref MatA Creating a Number Table from Two Functions TABLE TABLE generates a number table based on one or two functions You can use the function f x or the two functions f x and g x See Configuring the Calculator Se...

Page 41: ...umber 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 A while the number table screen is displayed will return to the function input screen...

Page 42: ...r VctA 3 Input the elements of VctA 1 2 4 Perform the following key operation 1 5 VECTOR 2 Data 2 VctB 2 2 This will display the Vector Editor for input of the 2 dimensional vector for VctB 5 Input the elements of VctB 3 4 6 Press A to advance to the calculation screen and perform the calculation VctA VctB 1 5 VECTOR 3 VctA 1 5 VECTOR 4 VctB This will display the VctAns screen with the calculation...

Page 43: ...or 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 15 VECTOR 2 Data 1 VctA If you want to copy VctAns contents perform the following to display the VctAns screen A15 VECTOR 6 Vc...

Page 44: ...wing procedure to solve a quadratic inequality or cubic inequality 1 Press Nc1 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 1 aX2 bX c Cubic inequality 2 aX3 bX2 cX d 3 On the menu that appears use keys 1 through 4 to select the inequality symbol type and orientation 4 Use the Coefficient Editor ...

Page 45: ...utions To return to the Coefficient Editor while the solutions are displayed press A Note Values cannot be converted to engineering notation on the solution screen Changing the Inequality Type Press Nc1 INEQ and then select an inequality type from the menu that appears Changing the inequality type causes the values of all Coefficient Editor coefficients to change to zero INEQ Mode Calculation Exam...

Page 46: ...l numbers x2 0 B Nc1 INEQ 1 aX2 bX c 3 aX2 bX c 0 1 0 0 No Solution appears on the solution screen when no solution exists for an inequality such as X2 0 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 To verify whether 4 9 12 is tru...

Page 47: ...ator performs a mathematical operation on the input expression and then displays TRUE or FALSE based on the result Because of this calculation error can occur or a mathematically correct result may not be able to be displayed when the input calculation expression includes calculation that approaches the singular point or inflection point of a function or when the input expression contains multiple...

Page 48: ...rmal cumulative distribution 3 Inverse Normal Binomial probability 4 Binomial PD Binomial cumulative distribution c1 Binomial CD Poisson probability c2 Poisson PD Poisson cumulative distribution c3 Poisson CD 3 Input values for the variables With Binomial PD Binomial CD Poisson PD and Poisson CD you can input sample data and then perform calculations 4 After inputting values for all of the variabl...

Page 49: ... List Screen for sample data input You can input up to 25 data samples for each variable Calculation results are also displayed on the List Screen Distribution calculation type Value at current cursor position X Sample data Ans Calculation results To edit sample data Move the cursor to the cell that contains the sample data you want to edit input the new sample data and then press To delete sample...

Page 50: ... x binomial probability of 11 ⱌ 0 12678 x binomial probability of 12 ⱌ 0 063388 x binomial probability of 13 ⱌ 0 021942 x binomial probability of 14 ⱌ 4 7018 10 3 Pressing returns to the N input screen Pressing A returns to the List Screen input data samples are stored Note The following cannot be used in the distribution calculations Pol Rec R d dx When data is specified using parameter format ca...

Page 51: ...vacuum and display its value A17 CONST 28 C0 To calculate C0 1 ε0μ0 B A 1c 17 CONST 32 ε0 17 CONST 33 0 The following shows the two digit numbers for each of the scientific constants 01 mp proton mass 02 mn neutron mass 03 me electron mass 04 m muon mass 05 a0 Bohr radius 06 h Planck constant 07 N nuclear magneton 08 B Bohr magneton 09 h Planck constant rationalized 10 α fine structure constant 11...

Page 52: ...sius temperature 39 G Newtonian constant of gravitation 40 atm standard atmosphere The values are based on CODATA 2010 recommended values Metric Conversion The calculator s built in metric conversion commands make it simple to convert values from one unit to another You can use the metric conversion commands in any calculation mode except for BASE N and TABLE To input a metric conversion command i...

Page 53: ...ture 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 1 10 99 to 9 999999999 1099 or 0 Number of Digits for Internal Calculation 15 digits Precision In general 1 at the 10th digit for a single ...

Page 54: ...0 r n n r are integers 1 n r 1 10100 or 1 n n r 1 10100 Pol x y x y 9 999999999 1099 x2 y2 9 999999999 1099 Rec r 0 r 9 999999999 1099 Same as sinx a b c 1 10100 0 b c The display seconds value is subject to an error of 앧1 at the second decimal place x 1 10100 Decimal Sexagesimal Conversions 0 0 0 x 9999999 59 59 xy x 0 1 10100 ylogx 100 x 0 y 0 x 0 y n m 2n 1 m n are integers However 1 10100 ylog...

Page 55: ...error message display Pressing d or e to display the location of the error or pressing A to clear the message and calculation Displaying the Location of an Error While an error message is displayed press d or e 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 a...

Page 56: ...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...

Page 57: ...ializes 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 19 CLR 1 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 ...

Page 58: ...rmed Use this memory to carry the result of one calculation on to the next PreAns Memory Stores the result of calculation before the last one PreAns memory can be used only in the COMP Mode 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 k What is the...

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