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fx-50F PLUS User's Guide http://world.casio .com/edu/ RCA502903-001V01 E.
E-1 Getting Started Thank you f or purchasing this CASIO product. k Before using the calculator f or the fi rst time ... Tu rn o ver the calculator and slide it from the hard case as shown in the illustration. Next, slide the hard case onto the back of the calculator .
E-2 • The following shows the notation used in the man ual for menu items that appear on the display (which are e xecuted by pressing a number k ey). Example: b (Contrast) The notation in parentheses indicates the menu item accessed by the preceding number key .
E-3 Operating Precautions • Be sure to press the O key before using the calculator f or the fi rst time. • Even if the calculator is operating normally , replace the battery at least once every three years. A dead battery can leak, causing damage to and malfunction of the calculator.
E-4 Contents Getting Started ......................................................................................... 1 Before using the calculator f or the fi rst time... .................................................................... 1 Resetting the Calculator to Initial Defaults.
E-5 Coordinate Conv ersion (Rectangular ↔ P olar) ................................................................ 29 Other Functions ................................................................................................................ 31 Using 10 3 Engineering Notation (ENG) .
E-6 Before starting a calculation... k Tu r n i ng On the Calculator Press O . The calculator will enter the calculation mode (page 7) that it was in the last time you turned it off. A Adjusting Display Contrast If the fi gures on the display become hard to read, try adjusting display contrast.
E-7 Function Colors T o perform the function 7 AT e xt: Red Fr ame: Green Press a and then press the ke y (variable A). In the BASE Mode, press the ke y .
E-8 2. Perf orm one of the following operations to select the calculation mode y ou want. To select this calculation mode: Press this key: COMP (Computation) b (COMP) CMPLX (Complex Number) c (CMPLX) .
E-9 The follo wing explains ho w calculation results are display ed in accordance with the setting you specify . • F rom zero to nine decimal places are displa yed in accordance with the number of decimal places (Fix) you specify . Calculation results are rounded off to the specifi ed n umber of digits.
E-10 k Clearing the Calculation Mode and Setup Settings P erform the procedure described below to clear the current calculation mode and all setup settings and initialize the calculator to the f ollowing. Calculation Mode .............................
E-11 A Omitting the Multiplication Sign Y ou can omit the multiplication sign in the following cases. • Immediately before an open parenthesis: 2 × (5 + 4) • Immediately before a scientifi c fun.
E-12 k Editing a Calculation A Insert Mode and Overwrite Mode The calculator has two input modes. The inser t mode inser ts your input at the cursor location, shifting anything to the right of the cursor to make room. The o verwrite mode replaces the ke y operation at the cursor location with your input.
E-13 ddd D A Editing a Ke y Operation within an Expression With the inser t mode, use d and e to mov e the cursor to the right of the key operation you want to edit, press D to delete it, and then perform the correct ke y operation.
E-14 d 1 w • Instead of pressing e or d while an error message is display ed to fi nd the location of the error , you could also press A to clear the calculation. Basic Calculations Unless otherwise noted, the calculations in this section can be performed in any of the calculator’ s calculation mode, e xcept for the BASE Mode .
E-15 A Fraction Calculation Examples Example 1: 3 1 4 + 1 2 3 = 4 11 1 2 3 $ 1 $ 4+ 1 $ 2 $ 3 w Example 2: 4 – 3 1 2 = 1 2 4-3 $ 1 $ 2 w Example 3 : 2 3 + 1 2 = 7 6 (F raction Display F or mat: d/c).
E-16 k P ercent Calculations Inputting a value and with a percent (%) sign mak es the value a percent. The percent (%) sign uses the value immediately bef ore it as the argument, which is simply divided by 100 to get the percentage value . A P ercent Calculation Examples Example 1: 2 % = 0.
E-17 Example 8: What is the percentage change when a value is increased from 40 to 46? How about to 48? Inser t Mode (46-40)/40 ! ( (%) w eeee Y 8 w k Degree, Minute, Second (Sexa gesimal) Calculations Y ou can perform calculations using sexagesimal values, and y ou can conv ert between sexagesimal and decimal.
E-18 Example: T o convert 2.255 to sexagesimal 2.255 w $ $ Calculation History and Replay Calculation history maintains a record of each calculation you perform, including the expressions y ou input and calculation results. Y ou can use calculation histor y in the COMP , CMPLX, and BASE Modes.
E-19 k Using Replay While a calculation history record is on the display , press d or e to display the cursor and enter the editing mode. Pressing e displays the cursor at the beginning of the calculation expression, while d displays it at the end. After you make the changes y ou want, press w to ex ecute the calculation.
E-20 A Ans Update and Delete Timing When using Ans in a calculation, it is impor tant to keep in mind ho w and when its contents change. Note the following points .
E-21 A Inserting Ans into a Calculation Manually Y ou can inser t Ans into a calculation at the current cursor location by pressing the K key . Example 1: To use the result of 123 + 456 in another cal.
E-22 Note Pressing m or 1m (M–) while a calculation result is on the display will add it to or subtract it from independent memory . Important! The value that appears on the displa y when you press m or 1m (M–) at the end of a calculation in place of w is the result of the calculation (which is added to or subtracted from independent memory).
E-23 A Clearing the V alue Assigned to a V ariable (to 0) Example: To clear variable A 0 1t (ST O) - (A) A Calculation Example Using V ariables Example: To perform calculations that assign results to .
E-24 k Scientifi c Constants Y our calculator has 40 often-used scientifi c constants built in. Like π and e , each scientifi c constant has a unique display symbol. Scientifi c constants are supported in all modes, except f or the BASE Mode. A Inputting a Scientifi c Constant 1.
E-25 1 7 (CONST) ddd 4 ( ε 0 ) 1 7 (CONST) dd 1 ( ƫ 0 ) ) E A Ta b l e of Scientifi c Constants The numbers in the “No. ” column sho w the scientifi c constant menu page number on the left and the number ke y you need to press to select the constant when the proper menu page is display ed.
E-26 No. Scientifi c Constant Symbol V alue Unit 6-4 A vogadro constant N A 6.0221415×10 23 mol –1 7-1 Boltzmann constant k 1.3806505×10 –23 J K –1 7-2 Molar v olume of ideal gas V m 22.413996×10 –3 m 3 mol –1 7-3 Molar gas constant R 8.
E-27 k Tr igonometric and Inver se T rigonometric Functions sin(, cos(, tan(, sin –1 (, cos –1 (, tan –1 ( A Syntax and Input sin({ n }), cos({ n }), tan({ n }), sin –1 ({ n }), cos –1 ({ n }), tan –1 ({ n }) Example: sin 30 = 0.5, sin –1 0.
E-28 k Hyperbolic and In verse Hyperbolic Functions sinh(, cosh(, tanh(, sinh –1 (, cosh –1 (, tanh –1 ( A Syntax and Input sinh({ n }), cosh({ n }), tanh({ n }), sinh –1 ({ n }), cosh –1 ({ n }), tanh –1 ({ n }) Example: sinh 1 = 1.
E-29 k P ower Functions and P ower Root Functions x 2 , x 3 , x –1 , ^(, ' (, 3 ' (, x ' ( A Syntax and Input { n } x 2 ............................... { n } 2 (Square) { n } x 3 ............................... { n } 3 (Cube) { n } x –1 .
E-30 A Syntax and Input Rectangular-to-P olar Coordinate Conv ersion (P ol) P ol( x , y ) x : Rectangular coordinate x -value y : Rectangular coordinate y -value P olar-to-Rectangular Coordinate Conv .
E-31 k Other Functions x !, Abs(, Ran#, n P r , n C r , Rnd( The x !, n P r , and n C r functions can be used in the CMPLX Mode, but comple x number arguments are not suppor ted.
E-32 A P ermutation ( n P r )/Combination ( n C r ) Syntax: { n }P{ m }, { n }C{ m } Example: How many f our-person per mutations and combinations are possible f or a group of 10 people? 10 1 * ( n P .
E-33 (Rounded result) *14 E Using 10 3 Engineering Notation (ENG) Engineering notation (ENG) expresses quantities as a product of a positiv e number between 1 and 10 and a power of 10 that is alw ays a m ultiple of three. There are two types of engineering notation, ENG / and ENG , .
E-34 Complex Number Calculations (CMPLX) To perform the example oper ations in this section, fi rst select CMPLX ( N 2 ) as the calculation mode. k Inputting Complex Number s A Inputting Imaginary Numbers ( i ) In the CMPLX Mode, the W ke y is used to input the imaginar y number i .
E-35 1E (Re ⇔ Im) Displays imaginary part. ( i symbol turns on during imaginar y par t display . ) A Default Complex Number Calculation Result Displa y Format Y ou can select either rectangular coordinate format or polar coordinate format for complex number calculation results.
E-36 A P olar Coordinate Format ( r ∠ Ƨ ) 1 , (SETUP) eee 2 ( r ∠ Ƨ ) Example 1: 2 × ( ' 3 + i ) = 2 ' 3 + 2 i = 4 ∠ 30 2*( 9 3)+ W ( i ) ) E 1E (Re ⇔ Im) ∠ symbol turns on dur ing display of Ƨ -value.
E-37 Absolute V alue: 1 ) (Abs) 2+2 W ( i ) ) E Argument: 1 ( (arg) 2+2 W ( i ) ) E k Overriding the Default Complex Number Displa y Format Y ou can use the procedures descr ibed below to ov erride the default comple x number display f or mat and specify a par ticular display f ormat for the calculation you are currently inputting.
E-38 Statistical Calculations (SD/REG) k Statistical Calculation Sample Data A Inputting Sample Data Yo u can input sample data either with statistical frequency turned on (FreqOn) or off (F reqOff). The calculator’ s initial default setting is F reqOn.
E-39 Example: To input the follo wing data Class V alue ( x ) Frequency (Freq) 24.5 4 25.5 6 26.5 2 24.5 1 , (;) 4 m (DT) m (DT) tells the calculator this is the end of the fi rst data item. 25.5 1 , (;) 6 m (DT) 26.5 1 , (;) 2 m (DT) Frequency Off (FreqOff) In this case, input each individual data item as shown belo w .
E-40 c c When the statistical frequency setting is F reqOn, data is display ed in the sequence: x 1 , F req1, x 2 , F req2, and so on. In the case of F reqOff, it is displa yed in the sequence: x 1 , x 2 , x 3 , and so on. Y ou can also use f to scroll in the rev erse direction.
E-41 A Deleting All Sample Data P erform the follo wing ke y operation to delete all sample data. 1 9 (CLR) 1 (Stat) E If you do not want to delete all sample data, press A in place of E in the abov e operation. A Statistical Calculations Using Input Sample Data To perform a statistical calculation, input the applicable command and then press E .
E-42 k Pe rforming P aired-variable Statistical Calculations To perform the example oper ations in this section, fi rst select REG ( N 5 ) as the calculation mode. A Regression Calculation T ypes The REG Mode lets you perf orm the seven types of reg ression listed below .
E-43 A Inputting Sample Data Frequency On (FreqOn) The follo wing shows the ke y operations required when inputting class values ( x 1 , y 1 ), ( x 2 , y 2 ), .
E-44 1 2 (S-V AR) 1 (V AR) e 1 E * This is one example of possible calculation results . A REG Mode Statistical Command Reference Sum and Number of Sample Command (S-SUM Menu) y y σ n y σ n – 1 12 3 y y σ n y σ n – 1 12 3 y 14 y 14 ƙ x 2 1 1 (S-SUM) 1 Obtains the sum of squares of the sample x -data.
E-45 y σ n 1 2 (S-V AR) 1 (V AR) e 2 Obtains the population standard deviation of the sample y -data. y σ n –1 1 2 (S-V AR) 1 (V AR) e 3 Obtains the sample standard deviation of the sample y -data.
E-46 Regression Coeffi cient and Estimated Value Commands f or Quadratic Regression (V AR Menu) For details about the f or mula that is ex ecuted by each of these commands , see “Regression Coeffi cient and Estimated V alue Calculation Formula T able” (page 47).
E-47 A Regression Coeffi cient and Estimated V alue Calculation Formula T able The follo wing table shows the calculation f or mulas used by the regression coeffi cient and estimated value commands f or each regression calculation type. Linear Regression Command Calculation Formula Regression F ormula Constant T er m a a = n Σ y i – b .
E-48 Logarithmic Regression Command Calculation Formula Regression F ormula Constant T er m a a = n Σ y i – b . Σ ln x i Regression Coeffi cient b b = n . Σ ( ln x i ) 2 – ( Σ ln x i ) 2 n . Σ ( ln x i ) y i – Σ ln x i . Σ y i Correlation Coeffi cient r r = { n .
E-49 Command Calculation Formula Estimated V alue m m = ln b ln y – ln a Estimated V alue n n = ab x Po wer Regression Command Calculation Formula Regression F ormula Constant T er m a a = exp () n Σ ln y i – b . Σ ln x i Regression Coeffi cient b b = n .
E-50 Command Calculation Formula Estimated V alue m m = y – a b Estimated V alue n n = a+ x b k Statistical Calculation Examples This section provides some actual e xamples of statistical calculation examples as the y are performed on your calculator .
E-51 Example 2: The nearby data sho ws how the weight of a newborn at various numbers of da ys after bir th. 1 Obtain the regression f ormula and correlation coeffi cient produced by linear regression of the data. 2 Obtain the regression f ormula and correlation coeffi cient produced by logarithmic regression of the data.
E-52 Regression Coeffi cient b: 1 2 (S-V AR) 1 (V AR) ee 2 (b) E Correlation Coeffi cient: 1 2 (S-V AR) 1 (V AR) ee 3 (r ) E 3 We i ght Prediction The absolute value of the correlation coeffi cient for logarithmic regression is closer to 1, so perform the weight prediction calculation using logarithmic regression.
E-53 A Example Base- n Calculations Example 1: To select binary as the number base and calculate 1 2 + 1 2 A l (BIN) 1+1 E Example 2: To select octal as the number base and calculate 7 8 + 1 8 A i (OCT) 7+1 E • Inputting an invalid v alue causes a Syntax ERROR.
E-54 k Con ver ting a Displayed Result to another Number Base Pressing x (DEC), M (HEX), l (BIN), or i (OCT) while a calculation result is display ed will conv er t the result to the corresponding number base.
E-55 A Example Calculation Using Base- n Specifi cation Example: To perform the calculation 5 10 + 5 16 , and display the result in binary A l (BIN) X (LOGIC) d 1 (d) 5+ X (LOGIC) d 2 (h) 5 E k P erf.
E-56 A Complement/In version (Not) Returns the complement (bitwise inversion) of a v alue. Example: Not(1010 2 ) = 1111110101 2 X (LOGIC) e 2 (Not) 1010) E A Negation (Neg) Returns the twos complement of a value.
E-57 E (Prompt for input f or variable a ) Input 8 for v ariable a : 8 E Input 5 for v ariable b : 5 E Input 5 for v ariable c : 5 E • As shown above , the calculation result appears after you assign v alues to all of the required variables .
E-58 A Displaying a Built-in Form ula While inputting values f or the variables of a f or mula, you can displa y the formula by pressing 1 G (LOOK). (V alue Input Screen) 1 G (LOOK) • If the formula is too long to fi t on the displa y use the e ke y to scroll to the right to view the missing par t.
E-59 No . 05 Normal Probability Function Q( x ) Uses Hastings’ estimate formula to determine the probability of a standard nor mal distribution Q( x ) illustrated below when the standardiz ed variate ( x ) is known. Important! Since this is an estimate formula, proper precision ma y not be obtainable.
E-60 No . 10 V oltage Gain Determines the voltage gain ( G ) of an amplifi er circuit when input voltage ( E ) and output voltage ( E´ ) are known. G[ d B] = 20 log 10 ( E ' / E > 0) E ' E () [ d B] G[ d B] = 20 log 10 ( E ' / E > 0) E ' E () [ d B] Units: E and E Ϣ : V , G : d B No .
E-61 No . 15 Cycle of Simple P endulum Determines the cycle ( T ) of a simple pendulum with a string of length . T = 2 π g ( g : gra vitational acceleration, > 0 ) T = 2 π g ( g : gra vitational acceleration, > 0 ) Units: : m , T : seconds No .
E-62 No . 21 Bernoulli’ s Theorem Determines the fi x ed value ( C ) of an inviscid fl uid (steady fl ow , incompressible fl uid) when the fl ow velocity ( v ), location (height) ( z ), specifi c weight ( ρ ), and pressure ( P ) are known.
E-63 k Creating a Program A Creating a New Pr ogram Example: To create a program that con verts inches to centimeters (1 inch = 2.54 cm) ? → A : A × 2.54 1. Press , g (PRGM) to enter the PRGM Mode. 2. Press b (EDIT). Program areas that already contain program data (P1 through P4) Remaining program memory capacity 3.
E-64 6. After inputting the program, press A or ! 5 (EXIT). • T o run the program you just created, press w here to display the R UN Program screen. For more information, see “Running a Prog ram” below . • T o return to the nor mal calculation screen, press , b to enter the COMP Mode.
E-65 2. Press d (DEL). Program areas that already contain program data (P1 through P4) Remaining program memory capacity 3. Use number keys b through e to select the program area whose progr am you want to delete.
E-66 → (V ariable Assignment) Syntax {expression ; ?} → {v ariable} Function Assigns the value obtained b y the element on the left to the variable on the right. Example A+5 → A : (Separator Code) Syntax {statement} : {statement} : ... : {statement} Function Separates statements.
E-67 Example Lbl 1 : ? → A : A > 0 S ' (A) ^ Goto 1 =, ≠ , > , > , < , < (Relational Operators) Syntax {expression} {relational oper ator} {expression} Function These commands ev aluate the expressions on either side , and return a value of true (1) or false (0).
E-68 For~T o~Next Syntax For {e xpression (star ting value)} → {variable (control v ariable)} T o {expression (ending value)} : {statement} : ... {statement} : Next : .... Function Execution of the statements from F or to Next repeats as the control variable is incremented by 1 with each e xecution, starting from the star ting value.
E-69 Important! With some setup commands, the settings you confi gure remain in effect e ven after you fi nish running the program. Angle Unit Commands Deg, Rad, Gra (COMP , CMPLX, SD , REG) Syntax .
E-70 A Clear Commands ClrMemory (COMP , CMPLX, BASE) Syntax .. : ClrMemory : .. Operation ! j (CLR) b (Mem) Function This command clears all variables (A, B , C, D , X, Y , M) to zero. Note To clear a specifi c variable, use 0 → {variable}. ClrStat (SD , REG) Syntax .
E-71 Important! To input a semicolon (;) in the abov e syntax, press ! , (;). T o input a comma (,), press , . Operation l (Inputs DT .) Function Use this command to input one set of sample data. The DT command functions the same wa y as the l ke y ( DT k ey) in the SD Mode and REG Mode.
E-72 Sequence Operation Type Description 7M u l t i plication, Division Omitted Multiplication Sign ×, ÷ Multiplication sign can be omitted immediately before π , e , variables, scientifi c constants (2 π , 5A, π A, 3mp, 2 i , etc.), and parenthetical functions (2 ' (3), Asin(30), etc.
E-73 Note When inputting a value in the CMPLX Mode, each v alue takes up two stack lev els: one for the real part and one for the imaginary par t. This means that the numeric stack has only fi ve le vels in the CMPLX Mode.
E-74 Functions Input Range e x –9.999999999×10 99 < x < 230.2585092 ' x 0 < x < 1×10 100 x 2 | x | < 1×10 50 1/ x | x | < 1×10 100 ; x G 0 3 ' x | x | < 1×10 100 .
E-75 A Recovering fr om an Error Message Y ou can recover from an error message b y performing the ke y operations described below , regardless of the error type.
E-76 Data Full Cause Y ou are attempting to store sample data in the SD Mode or REG Mode when the allowab le number of data samples are already stored in memory . Action K eep the n umber of data samples within the allowab le limit. For more information, see “Maxim um Number of Input Data Items” on page 38.
E-77 1. Press !A (OFF) to turn off the calculator. To ensure that you do not accidentally turn on the calculator while replacing the battery , slide the hard case into the front of the calculator . 2. On the back of the calculator , remov e the screw and the battery cover .
CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany This mark applies in EU countries only ..
CASIO COMPUTER CO., L TD. 6-2, Hon-machi 1-chome Shibuya-ku, T okyo 151-8543, Japan SA0603-A Printed in China.
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