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Casio fx-115ES User Manual

Casio fx-115es fx-991es calculator user's guide
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User's Guide


Table of Contents

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  • Page 1 User's Guide RCA502160-001V01...
  • Page 2 CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany...
  • Page 3: About This Manual

    About this Manual • The MATH mark indicates an example that uses Math format, while the LINE mark indicates Linear format. For details about input/output formats, see “Specifying the Input/Output Format”. • Keycap markings indicate what a key inputs or what function it performs.
  • Page 4: Initializing The Calculator

    • 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.
  • Page 5: Safety Precautions

    This symbol is used to indicate information that can result in personal injury or material damage if ignored. Battery • 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.
  • Page 6: Handling Precautions

    • 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.
  • Page 7: Before Using The Calculator

    Removing the Hard Case Before using the calculator, slide its hard case downwards to remove it, and then affix the hard case to the back of the calculator as shown in the illustration below. k Turning Power On and Off •...
  • Page 8: About The Display

    There is a value stored in independent memory. 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).
  • Page 9: Modes And Setup

    (2) Press the number key that corresponds to the mode you want to select. • To select the CMPLX Mode, for example, press 2. k Configuring the Calculator Setup Pressing 1N(SETUP) displays the setup menu, which you can use to control how the calculations are executed and displayed. The setup menu has two screens, which you can jump between using c and f.
  • Page 10 • See “Adjusting Display Contrast” for information about how to use “]CONT'”. Specifying the Input/Output Format For this input/output format: Math Linear • Math format causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper. •...
  • Page 11 • Norm: Selecting one of the two available settings (Norm1, Norm2) determines the range in which results will be displayed in non- exponential format. Outside the specified range, results are displayed using exponential format. –2 >  Norm1: 10 –9 >...
  • Page 12: Inputting Expressions And Values

    Standard Format Your calculator lets you input calculation expressions just as they are written. Then simply press the = key to execute it. The calculator automatically judges the calculation priority sequence for addition, subtraction, multiplication, and division, functions, and parentheses.
  • Page 13: Omitting The Multiplication Sign

    Example: sin 30 = LINE • Note that the input procedure is different if you want to use Math format. For more information, see “Inputting with Math Format”. Omitting the Multiplication Sign You can omit the multiplication sign (×) in any of the following cases. •...
  • Page 14 See “Incorporating a Value into a Function” for more information. • The calculator automatically changes to the insert mode whenever you change the input/output format from Linear to Math. Changing the Character or Function You Just Input Example: To correct the expression 369 ×...
  • Page 15 Deleting a Character or Function Example: To correct the expression 369 × × 12 so it becomes 369 × 12 LINE Insert Mode: 369**12 Overwrite Mode: 369**12 Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) LINE Insert Mode: Overwrite Mode: Inserting Input into a Calculation Always use the insert mode for this operation.
  • Page 16 k Displaying the Location of an Error If an error message (like “Math ERROR” or “Syntax ERROR”) appears when you press =, press d or e. This will display the part of the calculation where the error occurred, with the cursor positioned at the error location.
  • Page 17 Functions and Symbols Supported for Math Format Input • The “Bytes” column shows the number of bytes of memory that are used up by input. Function/Symbol Improper Fraction Mixed Fraction log(a,b) (Logarithm) (Power of 10) (Power of Square Root Cube Root Square, Cube Reciprocal Power...
  • Page 18 Example 3: To input (1 + MATH (1+'2c5e) • When you press = and obtain a calculation result using Math format, part of the expression you input can be cut off as shown in the Example 3 screen shot. If you need to view the entire input expression again, press A and then press e.
  • Page 19 Original Expression: Function Integral Derivative Σ Calculation You can also incorporate values into the following functions. 1l($), 1i(%), !, 6, 1!(#), 1w(Abs) Displaying Calculation Results in a Form that Includes ' etc. (Irrational Number Form) When “MthIO” is selected for the input/output format, you can specify whether calculation results should be displayed in a form that includes expressions like ' 2 and •...
  • Page 20 Example 2: sin (60) = MATH –1 Example 3: sin (0.5) = MATH 1s(sin • The following are the calculations for which ' form (form that includes ' within irrational number display) results can be displayed. a. Arithmetic calculations of values with square root symbol ('), –1 b.
  • Page 21 The following shows the range for each of the coefficients ( 1 < < 100, 1 < 0 < < 100, 0 < Example: 2' 3 × 4 = 8' 3 35' 2 × 3 = 148.492424 (= 105' 2) 150' 2 = 8.485281374 2 ×...
  • Page 22: Basic Calculations

    Use the +, -, *, and / keys to perform arithmetic calculations. Example: 7 × 8 – 4 × 5 = 36 LINE 7*8-4*5= • The calculator automatically judges the calculation priority sequence. For more information, see “Calculation Priority Sequence”. Number of Decimal Places and Number of...
  • Page 23: Fraction Calculations

    Omitting a Final Closed Parenthesis You can omit any closed parenthesis ( ) ) immediately preceding operation of the = key at the end of a calculation. This is true only in the case of Linear format. Example: (2 + 3) × (4 – 1) = 15 LINE (2+3)* k Fraction Calculations...
  • Page 24: Percent Calculations

    Switching between Fraction and Decimal Format • The format of the fraction depends on the currently selected fraction display format setting (improper fraction or mixed fraction). • You cannot switch from decimal format to mixed fraction format if the total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10.
  • Page 25: Using Multi-Statements In Calculations

    Sexagesimal Calculations • Performing the following types of sexagesimal calculations produces a sexagesimal result. - Addition or subtraction of two sexagesimal values - Multiplication or division of a sexagesimal value and a decimal value Appendix <#012> 2°20´30˝ + 39´30˝ = 3°00´00˝ Converting Values between Sexagesimal and Decimal Pressing e while a calculation result is displayed toggles the value...
  • Page 26: Replay Function

    Example: LINE • Note that calculation history memory contents are cleared whenever you turn off the calculator, press the O key, change to the calculation mode or the input/output format, or perform any reset operation. • Calculation history memory is limited. When the calculation you...
  • Page 27: Answer Memory (Ans)

    • Answer Memory contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. • If a CMPLX Mode calculation produces a complex number result, both the real part and imaginary part are stored in Answer Memory.
  • Page 28: Independent Memory (M)

    • Independent memory contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. 789 – 579 = 210 Perform this key operation: 1m(M–)
  • Page 29: Clearing The Contents Of All Memories

    B Sy(A)*Se(B)= • Variable contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. Appendix <#015> Clearing the Contents of a Specific Variable Press 01t(STO) and then press the key for the name of the variable whose contents you want to clear.
  • Page 30: Using Calc

    Using CALC The CALC feature lets you input a calculation expression that contains variables, and then assign values to the variables and perform the calculation. You can use CALC in the COMP Mode (N1) and in the CMPLX Mode (N2). k Expressions Supported by CALC The following describes the types of expressions that can be used with CALC.
  • Page 31: Using Solve

    • To exit CALC, press A. • If the expression you are using contains more than one variable, an input prompt appears for each one. Appendix <#016> Calculate an from a = 21) *1 Assigns 1 to a *3 Value of a *5 Assigns 2 to *7 Value of a Using SOLVE...
  • Page 32 • An error (Variable ERROR) occurs when the solution variable is not included in the expression being solved. k Example SOLVE Operation Example: To solve MATH Sf(Y)Ss(=)Sy(A) S)(X)w+Se(B) 1)(,)S)(X) • To interrupt an ongoing SOLVE operation, press A. Precautions when Using SOLVE •...
  • Page 33 • SOLVE uses Newton’s Method, so even if there are multiple solutions, only one of them will be returned. • Newton’s Method can have problems obtaining solutions for the following types of functions. - A periodic function ( - A function whose graph includes a steep slope , etc.) - A discontinuous function ( Solution Screen Contents...
  • Page 34: Function Calculations

    Function Calculations This section explains how to use the calculator’s built-in functions. The functions available to you depends on the calculation mode you are in. The explanations in this section are mainly about the functions that are available in all calculation modes. All of the examples in this section show operation in the COMP Mode (N1).
  • Page 35: Converting Input Value To Default Angle

    After inputting a value, press 1G(DRG') to display the angle unit specification menu shown below. Press the number key that corresponds to the angle unit of the input value. The calculator will automatically convert it to the calculator’s default angle unit.
  • Page 36: Power Functions/Power Root Functions

    • A “Time Out” error occurs when an integration calculation ends without the ending condition being fulfilled. • When performing an integration calculation involving trigonometric functions, specify Rad as the calculator’s default angle unit. • Integration calculations can take considerable time to complete. • A smaller value provides better precision, but it also causes the calculation to take more time.
  • Page 37: Improving Integration Value Accuracy

    Tips on Improving Integration Value Accuracy • When a periodic function or integration interval results in positive and negative ) function values Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results. Positive ∫...
  • Page 38: Differential Calculations

    • Differential calculations can be performed in the COMP Mode only. • When performing a differential calculation involving trigonometric functions, specify Rad as the calculator’s default angle unit. • A “Time Out” error occurs when a differential calculation ends without the ending condition being fulfilled.
  • Page 39: Rectangular-Polar Coordinate Conversion

    Σ (X + 1, 1, 5) = 20 θ is displayed in the range of –180° < θ is displayed using the calculator’s default angle is assigned to variable X, while value of polar coordinate θ value of polar coordinate...
  • Page 40: Other Functions

    The random 3 digit decimal values are converted to 3-digit integer values by multiplying by 1000. Note that the values shown here are examples only. Values actually generated by your calculator will be different. Permutation ( These functions make it possible to perform permutation and combination calculations.
  • Page 41 Rounding Function (Rnd) This function rounds the value or the result of the expression in the function’s argument to the number of significant digits specified by the number of display digits setting. Display Digits Setting: Norm1 or Norm2 The mantissa is rounded to 10 digits. Display Digits Setting: Fix or Sci The value is rounded to the specified number of digits.
  • Page 42: Practical Examples

    (Check rounded result.) k Practical Examples Appendix π ∫ <#042> (sin + cos <#043> Confirm that the two sides of the following equation are equal: Transforming Displayed Values You can use the procedures in this section to transform a displayed value to engineering notation, or to transform between standard form and decimal form.
  • Page 43: Examples Of S-D Transformation

    Note • When you transform from decimal form to standard form, the calculator automatically decides the standard form to use. You cannot specify the standard form. Fraction: The current fraction display format setting determines whether the result is an improper fraction or mixed fraction.
  • Page 44: Complex Number Calculations

    Your calculator can display complex number calculation results in rectangular coordinate or polar coordinate format. You can select the coordinate format by configuring the calculator’s setup. For more information, see “Specifying the Complex Number Display Format”. Examples of Calculation Results Using Rectangular Coordinate Format ( Example 1: 2 ×...
  • Page 45: Conjugate Complex Number (Conjg)

    • With Linear format, the real part and imaginary part are shown in two different lines. Example 2: ' 2 ∠ 45 = 1 + MATH !2e1y(∠)45= Examples of Calculation Results Using Polar Coordinate Format ( Example 1: 2 × (' 3 + MATH 2*(!3e+i)= •...
  • Page 46: Absolute Value And Argument (Abs, Arg)

    k Absolute Value and Argument (Abs, arg) You can use the following procedure to obtain the absolute value (|Z|) and argument (arg) on the Gaussian plane for a complex number of the format Z = 1w(Abs); 12(CMPLX)1(arg) Appendix <#051> Obtain the absolute value and argument of 2 + 2 *1 Absolute Value Statistical Calculation All calculations in this section are performed in the STAT Mode...
  • Page 47 • The first line of the STAT editor screen shows the value for the first sample or the values for their first pair of samples. FREQ (Frequency) Column If you turn on the Statistical Display item on the calculator’s setup screen, a column labeled “FREQ” will also be included on the STAT editor screen.
  • Page 48 STAT Editor Screen Input Precautions • The number of lines in STAT editor screen (the number of sample data values you can input) depends on the type of statistical data you selected, and on the Statistical Display setting of the calculator’s setup screen. Statistical...
  • Page 49 A key while the STAT editor screen is displayed switches to the STAT calculation screen. The STAT calculation screen also uses Linear format, regardless of the current input/output format setting on the calculator’s setup screen. k Using the STAT Menu While the STAT editor screen or STAT calculation screen is on the display, press 11(STAT) to display the STAT menu.
  • Page 50 Single-variable Menu Item Select this When you want to do this: menu item: Display the Distr sub-menu of commands for 7Distr normal distribution calculations • For more information, see “Distr Sub-menu”. Paired-variable Menu Item Select this When you want to do this: menu item: Display the Reg sub-menu of commands for regression calculations...
  • Page 51 Distr Sub-menu (11(STAT)7(Distr)) 1 P( 2 Q( This menu can be used to calculate the probability of standard normal distribution. Normalized variate shown below, using the mean value ( xσ deviation value ( screen. Standard Normal Distribution Appendix Single-variable Statistical Calculation <#053>...
  • Page 52 Commands when Linear Regression Calculation (A+BX) Is Selected With linear regression, regression is performed in accordance with the following model equation. The following are the commands that appear on the sub-menus that appear when you select 4(Sum), 5(Var), 6(MinMax), or 7(Reg) on the STAT menu while linear regression is selected as the statistical calculation type.
  • Page 53 Reg Sub-menu (11(STAT)7(Reg)) Select this When you want to obtain this: menu item: Regression coefficient constant term A Regression coefficient B Correlation coefficient Estimated value of Estimated value of Appendix Linear Regression Calculation: <#061> to <#064> • Examples <#062> through <#064> all use the data input in Example <#061>.
  • Page 54 Comments for Other Types of Regression For details about the calculation formula of the command included in each regression type, refer to the indicated calculation formulas ( Appendix <#069> to <#073>). Statistical Calculation Type Logarithmic Regression (ln X) Exponential Regression Exponential Regression (A•B^X) Power Regression (A•X^B)
  • Page 55: Inputting Values

    k Number Base Setting and Value Input Use the keys listed below to specify the number base. The key markings used in this section are the ones that are above each key, on the right. Number Base Hexadecimal • The current number base setting is indicated in the second line of the display.
  • Page 56 Specifying the Base during Input The BASE-N Mode lets you override the current default number base setting and input a particular value using a different base. When inputting the value, press 13(BASE) c to display page two of the BASE menu, and then press the number key that corresponds to the base you want to specify.
  • Page 57: Equation Calculations

    Press this key: When you want to input this: 5(Not) 6(Neg) • Negative binary, octal, and hexadecimal values are produced by taking the binary two’s complement and then returning the result to the original number base. With the decimal number base, negative values are displayed with a minus sign.
  • Page 58 k Inputting Coefficients Use the coefficient editor screen to input the coefficients of an equation. The coefficient editor screen shows input cells for each of the coefficients required by the currently selected equation type. Simultaneous linear equations with two unknowns Rules for Inputting and Editing Coefficients •...
  • Page 59: Matrix Calculations

    • The display format of solutions is in accordance with the input/ output format and complex number display format settings of the calculator’s setup screen. • Note that you cannot transform values to engineering notation while an equation solution is displayed.
  • Page 60: Performing Matrix Calculations

    (3) Press a number key (1 through 6) to specify the matrix dimension you want to use. • Pressing a number key to specify the matrix dimension causes the matrix editor screen to appear. (4) Use the matrix editor screen to input each of the elements into the matrix.
  • Page 61: Matrix Menu Items

    • You cannot edit the contents of a cell. • To switch to the matrix calculation screen, press A. • While the MatAns screen is on the display, you can press an arithmetic operator key (like + or -) and use the screen contents in a subsequent calculation, just as with Answer Memory contents.
  • Page 62 <#104> Obtain the absolute value (Abs(MatB)) of each element of Matrix B. • Use 1w(Abs). <#105> Determine the square (MatA • Use w to specify squaring, and 1w( cubing. Note that you cannot use 6 for this input. Generating a Number Table from a Function All calculations in this section are performed in the TABLE Mode (N7).
  • Page 63: Supported Function Types

    (4) After specifying the start value, press =. • This displays the end value input screen. • Specify the end value. (5) After specifying the end value, press =. • This displays the step value input screen. • Specify the step value. •...
  • Page 64: Vector Calculations

    • Pressing the A key returns to the function editor screen. k TABLE Mode Precautions Note that changing the input/output format settings (Math format or Linear format) on the calculator’s setup screen while in the TABLE Mode clears the number table generation function. Vector Calculations You can save vectors under the names “VctA”, “VctB”, and “VctC”...
  • Page 65 (4) Use the vector editor screen to input each element. • Input is subject to the same rules as those that govern the coefficient editor screen in the EQN Mode. For more information, see “Rules for Inputting and Editing Coefficients”. •...
  • Page 66: Scientific Constants

    *2 Size 1 vector perpendicular to both A and B = Scientific Constants Your calculator comes with 40 built-in constants that are commonly used in scientific calculations. You can use the scientific constants in any calculation mode except for BASE-N.
  • Page 67: Metric Conversion

    Perform all of these examples in the COMP Mode (N1). Technical Information k Calculation Priority Sequence The calculator performs calculations according to a calculation priority sequence. • Basically, calculations are performed from left to right. • Expressions within parentheses have the highest priority.
  • Page 68: Stack Limitations

    1/(2i)= k Stack Limitations This calculator uses memory areas called stacks to temporarily store lower calculation priority sequence values, commands, and functions. The numeric stack has 10 levels and the command stack has 24 levels, as shown in the illustration below.
  • Page 69 A Stack ERROR occurs when the calculation you are performing causes the capacity of either stack to be exceeded. Stack Issues to Keep in Mind for Each Mode • In the CMPLX Mode, each input value uses two levels of the numeric stack, regardless of whether the input value is a real number or a complex number.
  • Page 70 Functions tanh tanh – 0 9.999999999 10 –9.999999999 10 –9.999999999 10  1  1  1  1  1 10  1 10 !  1 10 Pol( 9.999999999 10 Rec( θ: Same as sin a , b, c °’...
  • Page 71: Error Messages

    Error Messages The calculator will display an error message when a result exceeds the calculation range, when you attempt an illegal input, or whenever any other similar problem occurs. When an error message appears... The following are general operations you can use when any error message appears.
  • Page 72 Can’t Solve Error (SOLVE feature only) • Cause • The calculator could not obtain a solution. • Action • Check for errors in the equation that you input. • Input a value for the solution variable that is close to the expected solution and try again.
  • Page 73: Power Requirements And Battery

    Note that you will not be able to use the calculator if its button battery is dead. When any of these symptoms occur, replace the button battery.
  • Page 74: Specifications

    • Make sure you perform the above key operation. Do not skip it. Auto Power Off Your calculator will turn off automatically if you do not perform any operation for about six minutes. If this happens, press the O key to turn the calculator back on.
  • Page 75 CASIO COMPUTER CO., LTD. 6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan SA0411-B Printed in China...

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