fx-3650P fx-3950P User's Guide Guía del usuario ES http://world.casio.
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.
ENGLISH E-1
Safety Precautions Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference. Caution This symbol is used to indicate information that can result in personal injury or material damage if ignored. Batteries • After removing the battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed. • Keep batteries out of the reach of small children.
• 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 these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. Handling Precautions • Be sure to press the 5 key before using the calculator for the first time.
• Never twist or bend the calculator. Avoid carrying the calculator in the pocket of your trousers or other tightfitting clothing where it might be subjected to twisting or bending. • Never try to take the calculator apart. • Never press the keys of the calculator with a ballpoint pen or other pointed object. • Use a soft, dry cloth to clean the exterior of the calculator.
Contents Safety Precautions ....................................................... 2 Handling Precautions .................................................. 3 Before getting started... ............................................... 7 k Key Markings ....................................................................................... 7 k Modes .................................................................................................. 8 k Input Capacity .............................................
k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, π, and Permutation/Combination ....... 23 k Angle Unit Conversion ....................................................................... 24 k Coordinate Conversion (Pol (x, y), Rec (r, θ )) .................................. 24 k Engineering Notation Calculations ..................................................... 25 Statistical Calculations .............................................. 25 Standard Deviation ...
Before getting started... kKey Markings Many of the calculator’s keys are used to perform more than one function. The functions marked on the keyboard are color coded to help you find the one you need quickly and easily. M– A M DT CL Function Color 1 2 M+ M– Orange 3 M Red 4 DT Blue Key Operation | A| Press A and then the key to perform the marked function. p| Press p and then the key to perform the marked function.
kModes Before starting a calculation, you must first enter the correct mode as indicated in the table below.
• You cannot make changes to the angle unit or other display format (Disp) settings while the calculator is in the BASE Mode. • The COMP, CMPLX, SD, and REG modes can be used in combination with the angle unit settings. • Be sure to check the current calculation mode (SD, REG, COMP, CMPLX) and angle unit setting (Deg, Rad, Gra) before beginning a calculation. kInput Capacity • The memory area used for calculation input can hold 79 “steps.
• Pressing the e or r key while a replay memory calculation is on the display changes to the editing screen. • Pressing the e or r key immediately after you finish a calculation displays the editing screen for that calculation. • Pressing t does not clear replay memory, so you can recall the last calculation even after you press t. • Replay memory capacity is 128 bytes for storage of both expressions and results. • Replay memory is cleared by any of the following actions.
u Norm 1 With Norm 1, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places. u Norm 2 With Norm 2, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places. • All of the examples in this manual show calculation results using the Norm 1 format.
kFraction Operations u Fraction Calculations • Values are displayed in decimal format automatically whenever the total number of digits of a fractional value (integer + numerator + denominator + separator marks) exceeds 10. • Example 1: 13 2 1 15 3 5 • Example 2: 3 2C3+1C5< 13 15.00 3C1C4+ 1C2C3< 4 11 12.00 1 2 11 1 4 4 3 12 • Example 3: 2 1 4 2 • Example 4: 1 1.6 2.1 2 2C4< 1 C 2 + 1.6 < • Results of calculations that mix fraction and decimal values are always decimal.
u Mixed Fraction ↔ Improper Fraction Conversion • Example: 1 2 5 ↔ 3 3 1C2C3< 1 2 3.00 AB 5 3.00 AB 1 2 3.00 • You can use the display setup (Disp) screen to specify the display format when a fraction calculation result is greater than one. • To change the fraction display format, press the q key a number of times until you reach the setup screen shown below. Disp 1 • Display the selection screen.
* As shown here, if you want to use the current Answer Memory value in a mark up or discount calculation, you need to assign the Answer Memory value into a variable and then use the variable in the mark up/ discount calculation. This is because the calculation performed when v is pressed stores a result to Answer Memory before the , key is pressed.
• Press the number key ( 1, 2, or 3) that corresponds to the setup item you want to change. 1 (Fix): Number of decimal places 2 (Sci): Number of significant digits 3 (Norm): Exponential display format • Example 1: 200 7 14 (Specifies three decimal places.) 200 \ 7 - 14 < 400.00 F..... 1(Fix) 3 400.00000 200 \ 7 < 28.57100 - 14 < 400.00000 (Internal calculation continues using 12 digits.) FIX The following performs the same calculation using the specified number of decimal places.
kAnswer Memory • Whenever you press < after inputting values or an expression, the calculated result automatically updates Answer Memory contents by storing the result. • In addition to <, Answer Memory contents are also updated with result whenever you press A v, |, A {, or A j followed by a letter (A through D, or M, X, or Y). • You can recall Answer Memory contents by pressing g. • Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent.
kVariables • There are seven variables (A through D, M, X and Y), which can be used to store data, constants, results, and other values. • Use the following operation to delete data assigned to a particular variable: 0 A j 1. This operation deletes the data assigned to variable A. • Perform the following key operation when you want to clear the values assigned to all of the variables. A B 1(Mcl) < • Example: 193.2 23 8.4 193.2 A j 1 \ 23 < 193.2 28 6.
kAbsolute Value and Argument Calculation Supposing the imaginary number expressed by the rectangular form z = a + bi is represented as a point in the Gaussian plane, you can determine the absolute value (r) and argument ( ) of the complex number. The polar form is r⬔. • Example 1: To determine the absolute value (r) and argument ( ) of (r = 5, = 53.13010235 °) 3 + 4i (Angle unit: Deg) Imaginary axis Real axis AAR3+4iT< AaR3+4iT< (r 5 ) ( 53.
• You select rectangular form (a+bi) or polar form (r⬔ ) for display of complex number calculation results. F ..... 1(Disp) 1(a+bi):Rectangular form 2(r⬔): Polar form (indicated by “r⬔ ” on the display) kConjugate of a Complex Number For any complex number z where z = a+bi, its conjugate ( z ) is z = a – bi. • Example: To determine the conjugate of the complex number 1.23 + 2.34i (Result: 1.23 – 2.
• The following are the allowable ranges for each of the available number systems. Binary Octal Decimal Hexadecimal 1000000000 ⬉ x ⬉ 0⬉x⬉ 4000000000 ⬉ x ⬉ 0⬉x⬉ –2147483648 ⬉ x ⬉ 80000000 ⬉ x ⬉ 0⬉x⬉ 1111111111 0111111111 7777777777 3777777777 2147483647 FFFFFFFF 7FFFFFFF • Example 1: To perform the following calculation and produce a binary result: 101112 110102 1100012 tb 0. b 10111 + 11010 < 110001.
• Example 4: To perform the following calculation and produce an octal result: 76548 ÷ 1210 5168 to 0. o l l l 4 (o) 7654 \ l l l 1 (d) 12 < 516. o 0. H l l l 3 (b) 1101 < 12d. H K 301.
• Press the number key ( 1, 2, or 3 ) that corresponds to the angle unit you want to use. (90° = π 2 radians = 100 grads) • Example 1: sin 63°52 41 0.897859012 q ..... 1(Deg) S 63 I 52 I 41 I < π q ..... 2(Rad) WRAx\3T< • Example 2: cos ( • Example 3: cos 1 3 ) rad 0.5 2 π 0.25 π (rad) (rad) q ..... 2 (Rad) 2 4 AVRL2\2T
kSquare Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, π, and Permutation/Combination 2 3 5 5.287196909 • Example 1: • Example 2: 3 L2+L3-L5< 5 27 –1.290024053 A D 5 + A D D 27 < 3 1 • Example 3: 123 ( = 123 ( 7) ) 1.988647795 7 7 A H 123 < • Example 4: 123 302 1023 123 + 30 K < 12 N < • Example 5: 123 1728 • Example 6: 1 12 1 1 3 4 R3a,4aTa< • Example 7: 8! 40320 8Af< • Example 8: To generate a random number between 0.000 and 0.
kAngle Unit Conversion • Press A v to display the following menu. R G 1 2 D 3 • Pressing 1, 2, or 3 converts the displayed value to the corresponding angle unit. • Example: To convert 4.25 radians to degrees q ..... 1(Deg) 4.25 A v 2(R) < 4 . 25 r 243.5070629 kCoordinate Conversion (Pol (x, y), Rec (r, θ )) u Rectangular Coordinates u Polar Coordinates • Calculation results are automatically assigned to variables X and Y.
• Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r, ) (Angle unit: Rad) r 2 Af1P L3T< θ 1.047197551 0y • Press 0 x to display the value of r, or 0 y to display the value of . kEngineering Notation Calculations • Example 1: To convert 56,088 meters to kilometers → 56.088 10 3 (km) • Example 2: To convert 0.08125 grams to milligrams 56088 < J → 81.25 10–3 (mg) 0.
• Example: To calculate σn 1, σn, o, n, Σx, and Σx2 for the following data : 55, 54, 51, 55, 53, 53, 54, 52 In the SD Mode: A B 1 (Scl) < (Stat clear) 55 S n= SD 1. Each time you press S to register your input, the number of data input up to that point is indicated on the display (n value). 54 S 51 S 55 S 53 S S 54 S 52 S Sample Standard Deviation (σn 1) = 1.407885953 Population Standard Deviation (σn) = 1.316956719 Arithmetic Mean (o) = 53.
• You can delete a data value displayed using [ and ] by pressing A U. Deleting a data value causes all values following it to be shifted up. • Data values you register are normally stored in calculator memory. The message “Data Full” appears and you will not be able to input any more data if there is no memory left for data storage. If this happens, press the < key to display the screen shown below. Ed i t OFF ESC 1 2 Press 2 to exit data input without registering the value you just input.
REG Regression Calculations Use the F key to enter the REG Mode when you want to perform statistical calculations using regression. REG .......................................................................................... F F 2 • Entering the REG Mode displays screens like the ones shown below. r L i n Log Ex p 1 2 Pw r 3 1 I nv Quad 2 3 e • Press the number key ( 1, 2, or 3) that corresponds to the type of regression you want to use.
To recall this type of value: Perform this key operation: AXr2 AXr3 AXrr1 AXrr2 yσn yσn-1 Regression coefficient A Regression coefficient B Regression calculation other than quadratic regression AXrr3 AXrrr1 AXrrr2 Correlation coefficient r m n • The following table shows the key operations you should use to recall results in the case of quadratic regression.
In the REG Mode: 1(Lin) A B 1 (Scl) < (Stat clear) 10 P1003 S n= REG 1. Each time you press S to register your input, the number of data input up to that point is indicated on the display (n value). 15 P 1005 S 20 P1010 S 25 P 1011 S 30 P 1014 S Regression Coefficient A = 997.4 Regression Coefficient B = 0.56 Correlation Coefficient r = 0.982607368 Atmospheric Pressure at 18°C = 1007.48 Temperature at 1000 hPa = 4.642857143 Coefficient of Determination = 0.
u Quadratic Regression • The regression formula for quadratic regression is: y = A + Bx + Cx2. • Example: xi yi 29 50 74 103 118 1.6 23.5 38.0 46.4 48.0 Perform quadratic regression to determine the regression formula terms for the data nearby. Next, use the regression formula to estimate the values for n (estimated value of y) for xi = 16 and m (estimated value of x) for yi = 20. In the REG Mode: r 3(Quad) A B 1 (Scl) < (Stat clear) 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S 103 P 46.4 S 118 P 48.
1 Linear Regression y = A + Bx u Regression coefficient A Σy – B.Σx A= n u Regression coefficient B B= n.Σxy – Σx .Σy n.Σx 2 – (Σx)2 u Correlation coefficient r r= n .Σxy – Σx .Σy {n .Σx – (Σx)2}{n .Σy 2 – (Σy)2} 2 2 Logarithmic Regression u Regression coefficient A Σy – B.Σlnx A= n y = A + B.ln x u Regression coefficient B B= n .Σ(lnx)y – Σlnx .Σy n .Σ(lnx)2 – (Σlnx)2 u Correlation coefficient r r= n .Σ(lnx)y – Σlnx .Σy . {n Σ(lnx)2 – (Σ lnx)2}{n .
5 Inverse Regression y = A + B ⴢ 1/x u Regression coefficient A u Regression coefficient B Σy – B.Σx –1 A= n B= Sxy Sxx u Correlation coefficient r r= Sxy Sxx .Syy 2 –1 2 Sxx = Σ(x –1)2 – (Σx ) , Syy = Σy 2– (Σy) n n –1 . Sxy = Σ(x –1)y – Σx Σy n 6 Quadratic Regression y = A + Bx + Cx2 u Regression coefficient A A= Σy Σx Σx2 –B –C n n n ( ) ( ) u Regression coefficient B B = (Sxy .Sx 2x 2 – Sx 2y .Sxx 2) ÷ {Sxx .Sx 2x 2 – (Sxx 2)2} u Regression coefficient C C = Sx 2y .Sxx – Sxy .
Differential Calculations COMP The procedure described below obtains the derivative of a function. Use the F key to enter the COMP Mode when you want to perform a calculation involving differentials. COMP ............................................................................................. F 1 • Three inputs are required for the differential expression: the function of variable x, the point (a) at which the differential coefficient is calculated, and the change in x (∆x).
Note! • You can specify an integer in the range of 1 to 9 as the number of partitions, or you can skip input of the number of partitions entirely, if you want. • Internal integration calculations may take considerable time to complete. • Display contents are cleared while an integration calculation is being performed internally. • The conditions described below can cause reduced calculation precision or slower calculation speed.
PRGM Storing a Program Use the following procedure to specify the Edit Prog Mode and store a program in memory. Edit Prog ............................................................................. F F F 1 • Example: To create a program that uses Heron’s formula to calculate the area of a triangle based on the lengths of its three sides Note that: s = (A + B + C) /2. Formula: S = s (s – A)(s – B)(s – C) 1. Enter the Edit Prog Mode, which displays the screen shown below.
• To input a question mark (?), right arrow (→), colon (:), or output command (^), press A ?, and then use number keys 1 through 4 to select the mark or command you want. See “Useful Program Commands” on page 40 for more information. 4. Press t F F F 2 to exit program input. u Program Storage Notes • Use the syntax below to prompt for input of a value by the person running the program, which will be assigned to the variable whose name is indicated by the program.
capacity, you will need to free up more memory capacity by deleting programs or statistical data you no longer need. • See page 44 for information about how bytes are counted and how memory is shared by statistical data. kEditing a Program • While a program’s contents are on the display in the Edit Prog Mode, you can use e and r to move the cursor to the location you want to edit. • Press [ to delete the function at the current cursor location.
3. Press < to resume program execution. The program number disappears after program execution is complete. Ans 600. (Area) u Program Execution Notes • Pressing < after program execution finishes causes the same program to be executed again. • You can also run a program from the Run Prog screen by using number keys 1 through 4 to specify a program number (P1 through P4).
PCL Deleting a Program Use the following procedure to specify the Clear Prog Mode and delete a program from memory. Clear Prog .......................................................................... F F F 3 • You can also enter the Clear Prog Mode by pressing [ while the Edit Prog screen is on the display. • You can select programs individually by specifying a program number from P1 through P4. 1. Enter the Clear Prog Mode, which displays the screen shown below. PRGM C l ea r P r og P–1234 247 2.
u Basic Commands ? → : ^ 1 2 3 4 1 (?) .......... Operator input command 2 (→) ........ Assign to variable command 3 (:) ........... Multi-statement separator code 4 (^) ........ Output command u Conditional Jump Commands S = G > > 1 2 3 4 5 1 (S) ........ Jump code (when condition is met) 2 (=) .......... Relational operator 3 (G) ......... Relational operator 4 (>) .......... Relational operator 5 (>) .......... Relational operator u Unconditional Jump Commands Go t o L b l 1 2 1 (Goto) ....
• Example: Use Heron’s formula to perform a series of calculations to determine the area of triangles for which the length of side A is fixed, and the lengths of sides B and C are variable. Program ?→A: Lbl 1: ?→B: ?→C: (A + B + C) ÷ 2→D^D × (D – A) × (D – B) × (D – C): Ans^Goto 1 kConditional Jump Using a Relational Operator You can use relational operators so program execution compares two values and then decides which processing should be performed based on the relationship between the two values.
u Inputting Statistical Data If you select the SD Mode or REG Mode before specifying a program number (P1 through P4), you can input statistical data as part of your program. • Input statistical data using the S key, just as you normally do (page 25). • In addition to values, you can also input calculation expressions as data. • Example 1: To determine o of the following data (o = 30.
Statistical Data Memory and Program Memory The following shows how the calculator uses memory for storage of statistical data and programs. (a) Statistical data only (256 bytes) Statistical Data (b) Shared between statistical data and programs (360 bytes) Programs ← (c) Shared between program management and statistical data (24 bytes) kStatistical Data • Each x-data or y-data (for regression calculations) item and each frequency value (other than 1) that you input uses up eight bytes of memory.
• Trying to input a data item that takes up more bytes than are currently available in memory area (b) causes the message “Data Full” to appear on the display. If this happens, you can press < 1 to select “EditOFF.” Though this will allow you to input more statistical data items (and free up memory area (b) for program storage), it also deletes the data items that are currently stored in memory areas (a) and (b). Also, the data items you input after pressing < 1 will not be saved.
Technical Information kWhen you have a problem...... If calculation results are not what you expect or if an error occurs, perform the following steps. 1. Press A B 2(Mode) < to initialize all modes and settings. 2. Check the formula you are working with to confirm it is correct. 3. Enter the correct mode and try performing the calculation again. If the above steps do not correct the problem, press the 5 key.
• Divide your calculation into two or more separate parts. Syntax ERROR • Cause • A calculation formula or program formula contains an error. • There is a colon (:) or output command (^) at the end of the program. • Action • Press e or r to display the calculation with the cursor located at the location of the error and make required corrections. • Delete the colon (:) or output command (^) at the end of the program.
Angle unit conversions (DRG') 3 Powers and roots: ^ (xy), x 4 ab/c 5 Abbreviated multiplication format in front of π, e (natural logarithm base), memory name, or variable name: 2π, 3e, 5A, πA, etc. 6 Type B functions: With these functions, the function key is pressed and then the value is entered.
kStacks This calculator uses memory areas, called “stacks,” to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (Stack ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded.
k Input Ranges Internal digits: 12 Accuracy*: As a rule, accuracy is ±1 at the 10th digit. Functions Input Range DEG sinx cosx tanx sin–1x cos–1x tan–1x sinhx coshx 0 x 4.499999999 1010 RAD 0 x 785398163.3 GRA 0 x 4.999999999 1010 DEG 0 x 4.500000008 1010 RAD 0 x 785398164.9 GRA 0 x 5.000000009 1010 DEG Same as sinx, except when x = (2n-1) 90. RAD Same as sinx, except when x = (2n-1) π/2. GRA Same as sinx, except when x = (2n-1) 100.
Functions x! n Pr nCr Input Range 0 x 69 (x is an integer) 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!(n–r)!}] 1 10100 Pol (x, y) x , y 9.999999999 1049 (x2+y2) 9.999999999 1099 Rec(r, ) 0 r 9.
* For a single calculation, calculation error is ±1 at the 10th digit. (In the case of exponential display, calculation error is ±1 at the last significant digit.) Errors are cumulative in the case of consecutive calculations, which can also cause them to become large. (This is also true of internal consecutive calculations that are performed in the case of ^(xy), x y , x!, 3 , nPr, nCr, etc.) In the vicinity of a function’s singular point and point of inflection, errors are cumulative and may become large.
• To replace the battery 1 Remove the six screws that hold the back cover in place and then remove the back cover. Screw Screw 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the six screws. 5 Press 5 to turn power on. Be sure not to skip this step. fx-3950P This calculator is powered by single G13 Type (LR44) button battery.
Auto Power Off Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on. Specifications Power Supply: fx-3950P: Single G13 Type button battery (LR44) fx-3650P: Solar cell and a single G13 Type button battery (LR44) Battery Life: fx-3950P: Approximately 9,000 hours continuous display of flashing cursor. Approximately 3 years when left with power turned off. fx-3650P: Approximately 3 years (1 hour use per day).
Practical Examples/Ejemplos prácticos kProgram Library kBiblioteca de programas Problem: Quadratic Equation Create a program that solves the quadratic equation ax2 + bx + c = 0 for x, when values are provided for a, b, and c. Problema: Ecuación cuadrática Crear un programa que resuelva la ecuación cuadrática ax2 + bx + c = 0 para x, cuando se proporcionan valores para a, b y c. x = (–b ± b2 – 4ac)/2a (b2 – 4ac > 0) Program Press F F F 1 to display the Edit Prog screen.
Program Execution / Ejecución de programa Display / Presentación Operation / Operación > 1 (Example: Program P1) (Ejemplo: Programa P1) 2< A? B? D7< C? 6< X = 1.5 (Value appears in line 2 of display.) (El valor aparece en la línea 2 de la presentación.) X=2 (Value appears in line 2 of display.) (El valor aparece en la línea 2 de la presentación.
Problem: Solution of a Triangle when Two Sides and Their Angle are Known Problema: Solución de un triángulo cuando se conocen dos lados y su ángulo. Create a program that calculates the remaining side and two angles of a triangle when the length of two sides (a, b) and the angle they form (γ ) are known. Crear un programa que calcule el lado restante y dos ángulos de un triángulo, cuando se conocen la longitud de los dos lados (a y b) y el ángulo que forman (γ ).
Program Execution / Ejecución de programa Display / Presentación Operation / Operación > 2 (Example: Program P2) A? B? D? 597.8321153 (Area)/(Area) 40.30827888 (Length of side c) (Longitud de lado c) 46.34318362 (Angle α)/(Angulo α) 46°20°35.46 67.96709416 (Angle β )/(Angulo β ) 67°58°1.54 (Ejemplo: Programa P2) 32 < 41 < 65 I 41 I 23 I < < < AO < AO Note • The conditional jump in the latter part of the program performs a process that determines whether angle α is an acute angle or an obtuse angle.
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