EN fx-83GT X fx-85GT X User’s Guide CASIO Worldwide Education Website https://edu.casio.com Manuals are available in multi languages at https://world.casio.com/manual/calc/ Be sure to keep all user documentation handy for future reference.
Table of Contents Before Using the Calculator.................................................... 4 About this Manual.................................................................................... 4 Initializing the Calculator.......................................................................... 4 Precautions.............................................................................................. 4 Safety Precautions..............................................................................
Switching between Improper Fraction and Mixed Fraction Format...............34 Percent Calculations.............................................................................. 34 Degree, Minute, Second (Sexagesimal) Calculations............................36 Inputting Sexagesimal Values....................................................................... 36 Sexagesimal Calculations.............................................................................
Using Calculation Modes.......................................................60 Statistical Calculations........................................................................... 60 Inputting Data with Statistics Editor...............................................................61 Statistical Calculation Screen........................................................................64 Using the Statistical Menu.............................................................................
Before Using the Calculator About this Manual • 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. • Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever by any other party arising out of the use of this product and the items that come with it.
• Use only the type of battery specified for this calculator in this manual. Handling Precautions • fx-83GT X: Even if the calculator is operating normally, replace the battery at least once every two years (R03 (UM-4)). fx-85GT X: Even if the calculator is operating normally, replace the battery at least once every three years (LR44). A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator.
Note • The calculator also will turn off automatically after approximately 10 minutes of nonuse. Press the key to turn the calculator back on. Adjusting Display Contrast (SETUP). 1. Press • This displays the setup menu. 2. Press . 3. Press (Contrast). • This displays the contrast adjustment screen. 4. Use and to adjust display contrast. 5. After the setting is the way you want, press .
• The following shows what the different colors of the alternate function key text mean. If key marking text is this color: It means this: Yellow Press and then the key to access the applicable function. Red Press and then the key to input the applicable variable, constant, function, or symbol. • The following shows an example of how an alternate function operation is represented in this manual. Example: (sin-1*) * Indicates the function that is accessed by the key operation ( ) before it.
Reading the Display (1) Input expression (2) Calculation result (3) Indicators • If a or indicator appears on the right side of either the input expression line (1) or calculation result line (2), it means the displayed line continues to the right. Use and to scroll the line display. Note that if you want to scroll the input expression while both the and indicators are displayed, you will need to press first and then use and to scroll.
The display currently shows an intermediate result of a multi-statement calculation. This indicator is displayed while the calculator is being powered directly by its solar cells, either entirely or in some combination with the battery. (fx-85GT X only) Using Menus Some of the operations of this calculator are performed using menus. or and then (SETUP). Menus are displayed by pressing General menu operation operations are described below.
Calculation Modes and Calculator Setup Calculation Mode The calculation modes of this calculator are described below. Icon: Description: General calculations (Calculate) Statistical and regression calculations (Statistics) Generate a number table based on one or two functions (Table) Ratio calculations (Ratio) Specify the calculation mode that is suitable for the type of calculation you want to perform. 1. Press to display the Main Menu. 2.
Note • You can also enter a mode without highlighting an icon in the Main Menu by inputting the number or letter marked in the lower right corner of the icon. • The initial default calculation mode is the Calculate Mode. Configuring the Calculator Setup Pressing (SETUP) displays the setup menu, which you can use to control how the calculations are executed and displayed. To change the calculator setup 1. Press (SETUP) to display the setup menu. 2.
Input: Linear*2 Output: Converted to decimal value (SETUP) DecimalO) (Input/Output) (LineI/ *1 Decimal output is applied when this format cannot be output for some reason. *2 All calculations, including fractions and functions are input in a single line. Same output format as that for models without Natural Textbook Display (S-V.P.A.M. models, etc.
Grads (SETUP) (Gradian) (Angle Unit) 90°= π/2 radians = 100 grads Number Format Specifies the number of digits for display of a calculation result.
Fraction Result Specifies either mixed fraction or improper fraction for display of fractions in calculation results. To specify this fraction display format: Mixed Improper Perform this key operation: (SETUP) (Fraction Result) (SETUP) (Fraction Result) (ab/c) (d/c)◆ Statistics Specifies whether or not to display a Freq (frequency) column in the Statistics Mode Statistics Editor.
Recurring Dec Specifies whether or not to use recurring decimal form in calculation results. To specify this: Use recurring decimal form Do not use recurring decimal form Perform this key operation: (SETUP) (Recurring Dec) (SETUP) (Recurring Dec) (On)◆ (Off) Decimal Mark Specifies whether to display a dot or a comma for the calculation result decimal mark. A dot is always displayed during input. To specify this decimal point display format: Dot (.
MultiLine Font Specifies the display font size when LineI/LineO or LineI/DecimalO is selected for Input/Output. Up to four lines can be displayed while Normal Font is selected, and up to six lines can be displayed with Small Font.
Inputting Expressions and Values Inputting a Calculation Expression Using Values Inputting a Calculation Expression Using 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.
• Normally the input cursor appears as a straight vertical ( ) or horizontal ( ) flashing line on the display screen. When there are 10 or fewer bytes of input remaining in the current expression, the cursor changes shape to to let you know. If the cursor appears, terminate the expression at a convenient point and calculate the result. Correcting an Expression This section explains how to correct an expression as you are inputting it.
Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) 60 Inserting Input into a Calculation Use and to move the cursor to the location where you want to insert the character or function and then input it. Be sure always to use the insert mode if LineI/LineO or LineI/DecimalO is selected. Clearing all of the calculation you are inputting Press .
369 12 Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) 60 Inputting an Expression Using Natural Textbook Format (MathI/ MathO or MathI/DecimalO Only) Formulas and expressions that include fractions and/or special functions such as √ can be input in natural textbook format by using templates that appear when certain keys are pressed. Note • When you press and obtain a calculation result, part of the expression you input may be cut off.
Natural Textbook Format Input Examples • Pay close attention to the location and size of the cursor on the display when you input using natural textbook format.
Example 5: To input 2 + √2 1 + √2 2 2 1 2 Tip: While the input cursor is located within the input area of a template (mixed fractions), pressing jumps to the position immediately following (to the right) of the template, while pressing jumps to the position immediate before (to the left of) it. Undo Operations (UNDO). To undo the last key operation, press To redo a key operation you have just undone, press again.
Displaying Calculation Results in a Form that Includes √2, π, etc. (Irrational Number Form) While MathI/MathO is selected for Input/Output on the setup menu, you can specify whether calculation results should be displayed in a form that includes expressions like √2 and π (irrational number form). • Pressing after inputting a calculation displays the result using irrational number form. • Pressing (≈) after inputting a calculation displays the result using decimal values.
(sin-1) 0.
Basic Calculations Recurring Decimal Calculations Your calculator uses a recurring decimal when you input a value. Calculation results also can be displayed using recurring decimal form whenever applicable. Inputting a Recurring Decimal When inputting a recurrent decimal, press ( ) 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 ( ) 90”.
428571 Example 3: To calculate 1.021 + 2.312 1 ( 2 ) 021 ( ) 312 Calculation result displayed as recurring decimal value: Displaying a Calculation Result as a Recurring Decimal Value Calculation results that can be displayed as recurring decimal values will be displayed as such when On is selected for the Recurring Dec setting on the setup menu. key will cycle between the available calculation result Pressing the formats. Example 1: 1 = 0.142857 = 0.
Return to initial display format (fraction): Example 2: 1 ÷ 7 = 1 = 0.142857 = 0.1428571429 (Number Format: 7 Norm 1) 1 7 (≈) Display as fraction: Display as recurring decimal: Return to initial display format (Norm 1): 1 = 0.142857 = 0.
Decimal value according to Norm 1 setting: Return to initial display format (fraction): Example 4: 1 ÷ 7 = 0.1428571429 (Norm 1) = 0.142857 = 1 7 (LineI/LineO) 1 7 Display as fraction: Display as recurring decimal: Return to initial display format (Norm 1): Conditions for Displaying a Calculation Result as a Recurring Decimal will If a calculation result satisfies the following conditions, pressing display it as a recurring decimal value.
Recurring Decimal Examples Example 1: 0.3 + 0.45 = 0.78 0 0 ( ( )3 ) 45 Example 2: 1.6 + 2.8 = 4.5 1 2 ( )6 ( )8 Example 3: To confirm the following: 0.123 = 0.12345 = 123 1234 , 0.
Toggling Calculation Results While MathI/MathO or MathI/DecimalO is selected for Input/Output on the setup menu, each press of will toggle the currently displayed calculation result between its fraction form and decimal form, its √ form and decimal form, or its π form and decimal form. Example 1: Fraction → Decimal (MathI/MathO) (Recurring Dec: Off) 5 Each press of the 6 key toggles between the two forms.
While LineI/LineO or LineI/DecimalO is selected for Input/Output on the setup menu, each press of will toggle the currently displayed calculation result between its decimal form and fraction form. Example 4: 1 ÷ 5 = 0.2 = 1 (LineI/LineO) 5 1 5 4 1 = = 0.2 (LineI/LineO) 5 5 Example 5: 1 － 1 4 5 Important! • With certain calculation results, pressing the key will not convert the displayed value.
7 8 4 5 • The calculator automatically judges the calculation priority sequence. Number of Decimal Places and Number of Significant Digits You can specify a fixed number of decimal places and significant digits for the calculation result.
Improper Fraction MathI/MathO MathI/DecimalO ( Mixed Fraction LineI/LineO LineI/DecimalO (7 1 3 ( )2 1 3 ( )2 1 3) 2 7 3 7 3 or 7 3 or 7 3) ( or 3) (2 1 3) Note • Under initial default settings, fractions are displayed as improper fractions. • Mixing fractions and decimal values in a calculation while something other than MathI/ MathO is selected will cause the result to be displayed as a decimal value. • Fractions in calculation results are displayed after being reduced to their lowest terms.
( )1 2 3 1 2 3 (LineI/LineO) 3 Example 3: 4 － 3 1 4 1 1 = (Fraction Result: ab/c) 2 2 (MathI/MathO) 4 ( )3 1 2 3 1 2 (LineI/LineO) 4 Note • If the total number of digits used for a mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10, the value is automatically displayed in decimal format. • The result of a calculation that involves both fraction and decimal values is displayed in decimal format.
2 (%) Example 2: 150 × 20% = 30 (150 × 150 (≈) 20 ) 100 20 (%) Example 3: Calculate what percentage of 880 is 660. (75%) 660 880 (%) Example 4: Increase 2500 by 15%. (2875) 2500 2500 15 (%) Example 5: Discount 3500 by 25%. (2625) 3500 3500 25 (%) Example 6: Discount the sum of 168, 98, and 734 by 20%. (800) 168 98 20 734 (%) Example 7: 300 grams are added to a test sample originally weighing 500 grams, producing a final test sample of 800 grams.
500 300 500 (%) Example 8: What is the percentage change when a value is increased from 40 to 46? How about to 48? (15%, 20%) 46 40 40 (%) 8 Degree, Minute, Second (Sexagesimal) Calculations You can perform calculations using sexagesimal values, and convert values between sexagesimal and decimal. Inputting Sexagesimal Values The following is the syntax for inputting a sexagesimal value.
2 20 30 0 39 30 Converting Values between Sexagesimal and Decimal while a calculation result is displayed toggles the value Pressing between sexagesimal and decimal. Example: Convert 2.255 to its sexagesimal equivalent. 2.255 (≈) Multi-Statements You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press .
(LineI/LineO) 3 “ 3 (:) 3 3 ” indicates this is an intermediate result of a multi-statement. Using Engineering Notation A simple key operation transforms a displayed value to engineering notation. Engineering notation converts the exponent part of a displayed calculation result value to a power of ten that is a multiple of 3, and displays the result. Example 1: Transform the value 1234 to engineering notation, shifting the decimal point to the right.
(←) Prime Factorization In the Calculate Mode, a positive integer no more than 10 digits long can be factored to prime factors. Example: To perform prime factorization on 1014 1014 (FACT) • To re-display the unfactored value, press (FACT) or . Example: To perform prime factorization on 4104676 (= 22 × 10132) 4104676 (FACT) Any one of the following operations will exit prime factorization result display. (FACT) or . - Pressing - Pressing any of the following keys: or .
Calculation History and Replay Calculation History An and/or at the top of the display indicates that there is more calculation history content above and/or below. You can scroll through calculation history contents using and . Note that calculation history can be used in the Calculate Mode only. Example: (MathI/MathO) (1 + 1 = 2) 1 1 2 2 3 3 (2 + 2 = 4) (3 + 3 = 6) (Scrolls back.) (Scrolls back again.
Replay While a calculation result is on the display, you can press edit the expression you used for the previous calculation. or Example: 4 × 3 + 2 = 14 4×3−7=5 4 3 2 7 Note • If you want to edit a calculation when the calculation result display, press indicator is on the right side of a and then use or calculation.
Using Memory Functions Answer Memory (Ans) The last calculation result obtained is stored in Ans (answer) memory. Note • Ans Memory contents are updated whenever you execute a calculation using any one of the following keys: , (≈), , (M−), (RECALL), . • Ans Memory contents are not change if an error occurs during the current calculation.
Variables (A, B, C, D, E, F, M, x, y) Your calculator has nine preset variables named A, B, C, D, E, F, M, x, and y. You can assign values to variables and use the variables in calculations. • You can assign a specific value or a calculation result to a variable. Example: To assign the result of 3 + 5 to variable A. 3 5 (A) Example: To assign the result of 4 × 6 to variable x. 4 6 (x) • Use the following procedure when you want to check the contents of a variable.
*2 Input a variable as shown here: press and then press the key that corresponds to the desired variable name. To input x as the variable (x). name, you can press Example: 9×6+3 = 1.425 5×8 9 (B) 6 3 (B) 5 8 (C) (C) (≈) Clearing the Contents of a Specific Variable Press 0 and then press the key for the name of the variable whose contents you want to clear.
Subtract the displayed value or result of the expression from independent memory (M−) Recall current independent memory contents (RECALL) (M) • Variable M is used for independent memory. • You can also insert the M variable into a calculation, which tells the calculator to use the current independent memory contents at that location. The following is the key operation for inserting the M variable.
(RECALL) (M) Clearing Independent Memory Press 0 (M). This clears independent memory and causes the “M” indicator to disappear from the display. 0 (M) Clearing the Contents of All Memories Ans memory, independent memory, and variable contents are retained , change the calculation mode, or turn off the even if you press calculator. Perform the procedure below when you want to clear the contents of all memories.
Function Calculations Pi (π), Natural Logarithm Base e Pi (π) You can input pi (π) into a calculation. The following shows the required key operations and the values this calculator uses for pi (π). π = 3.14159265358980 ( (π)) π is displayed as 3.141592654, but π = 3.14159265358980 is used for internal calculations. Natural Logarithm Base e You can input natural logarithm base e into a calculation. The following shows the required key operations and the values this calculator uses for e. e = 2.
Example: sin-1 0.5 = 30 (Angle Unit: Degree) (sin-1) 0.5 Hyperbolic Functions, Inverse Hyperbolic Functions Hyperbolic Functions • Input a function from the menu that appears when you press (Hyperbolic Func)*. * Depending on the calculation mode, you should press . Example 1: sinh 1 = 1.175201194 (Hyperbolic Func) (sinh) 1 Example 2: cosh 0 = 1 (Hyperbolic Func) (cosh) 0 Inverse Hyperbolic Functions • Input a function from the menu that appears when you press (Hyperbolic Func)*.
(cosh-1) 1 Converting an Input Value to the Calculator’s Default Angle Unit After inputting a value, press (Angle Unit)* 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. * Depending on the calculation mode, you should press .
Example 3: cos-1(-1) = 180 (Angle Unit: Degree), cos-1(-1) = π (Angle Unit: Radian) (Angle Unit: Degree) (cos-1) 1 (cos-1) 1 (Angle Unit: Radian) Exponential Functions, Logarithmic Functions Exponential Functions Example 1: e5 × 2 = 296.8263182 (MathI/MathO) ( )5 2 ( )5 2 (LineI/LineO) Example 2: 1.2 × 103 = 1200 (MathI/MathO) 1.2 ( )3 (LineI/LineO) 1.
Logarithmic Functions • For the logarithmic function “log(”, you can specify base m using the syntax “log (m, n)”. If you input only a single value, a base of 10 is used for the calculation. • “ln(” is a natural logarithm function with base e. • You can also use the key when inputting an expression with the form of “logmn” while using MathI/MathO or MathI/DecimalO format. For details, see Example 1. Note that you must input the base (base m) key for input.
Power Functions and Power Root Functions Example 1: (1 + 1)2+2 = 16 1 1 2 2 Example 2: (52)3 = 15625 5 Example 3: (√2 + 1)(√2 － 1) = 1 (MathI/MathO) 2 1 2 1 1 2 1 (LineI/LineO) 2 Example 4: 5√32 = 2 (MathI/MathO) ( )5 (LineI/LineO) 5 ( ) 32 2 Example 5: (-2) 3 = 1.
2 2 3 (LineI/LineO) 2 2 3 Example 6: 3√5 + 3√-27 = -1.290024053 (MathI/MathO) ( )5 ( ) 27 (LineI/LineO) ( ( Example 7: )5 27 ) = 12 (MathI/MathO) 3 4 Rectangular-Polar Coordinate Conversion • Coordinate conversion can be performed in the Calculate and Statistics calculation modes.
• Pol converts rectangular coordinates to polar coordinates, while Rec converts polar coordinates to rectangular coordinates. • Specify the angle unit before performing calculations. Converting to Polar Coordinates (Pol) Pol(X, Y) X: Specifies the rectangular coordinate X value Y: Specifies the rectangular coordinate Y value • Calculation result θ is displayed in the range of -180° < θ < 180°. • Calculation result θ is displayed using the calculator’s angle unit.
(LineI/LineO) (Pol) 3 (,) 1 Example 3: (r, θ) = (√2, 45) → (X, Y) (Angle Unit: Degree) (MathI/MathO) (Rec) 2 (,) 45 (Rec) 2 (,) 45 (LineI/LineO) Example 4: (r, θ) = (2, π ) → (X, Y) (Angle Unit: Radian) 6 (MathI/MathO) (Rec) 2 (,) (π) 6 (LineI/LineO) (Rec) 2 (,) (π) 6 Factorial (!) This function obtains the factorials of a value that is zero or a positive integer.
Absolute Value Calculation (Abs) When you are performing a real number calculation, this function simply obtains the absolute value. Example: Abs(2 － 7) = |2 － 7| = 5 (MathI/MathO) 2 7 (LineI/LineO) 2 7 Random Number (Ran#), Random Integer (RanInt#) Random Number (Ran#) Function that generates a pseudo random number in the range of 0.000 to 0.999. The result is displayed as a fraction when MathI/MathO is selected for Input/Output on the setup menu. Example: Generate three 3-digit random numbers.
Random Integer (RanInt#) For input of the function of the form RanInt#(a, b), which generates a random integer within the range of a to b. Example: To generate random integers in the range of 1 to 6. Note that the values shown here are examples only. Values actually generated by your calculator will be different. (RanInt) 1 (,) 6 Permutation (nPr) and Combination (nCr) These functions make it possible to perform permutation and combination calculations.
Rounding Function (Rnd) Using the Rnd function causes decimal fraction values of the argument to be rounded in accordance with the current Number Format setting. Number Format: Norm 1 or Norm 2 The argument is rounded off to 10 digits. Number Format: Fix or Sci The argument is rounded off to the specified digit. When Fix 3 is the Number Format setting, for example, the result of 10 ÷ 3 is displayed as 3.333, while the calculator maintains a value of 3.33333333333333 (15 digits) internally for calculation.
(Check rounded result.
Using Calculation Modes Statistical Calculations Perform the steps below to start a statistical calculation. 1. Press , select the Statistics Mode icon, and then press . 2. On the Select Type screen that appears, press one of the keys below to select a statistical calculation type.
Inputting Data with Statistics Editor Statistics Editor There are two Statistics Editor formats, depending on the type of statistical calculation you selected. Single-variable Paired-variable • The first line of the Statistics Editor shows the value for the first sample or the values for their first pair of samples. Freq (Frequency) Column If you turn on the Statistics setting on the setup menu, a column labeled “Freq” will also be included on the Statistics Editor.
Rules for Inputting Sample Data on the Statistics Editor • Data you input is inserted into the cell where the cursor is located. Use the cursor keys to move the cursor between cells. • After inputting a value, press . This registers the value and displays up to six of its digits in the currently selected cell. Example 1: To input the value 1234 in cell X1 (Move the cursor to cell X1.) 1234 The value you input appears in the formula area. Registering a value causes the cursor to move down one cell.
Statistics setting Off (No Freq column) On (Freq column) Single-variable 160 lines 80 lines Paired-variable 80 lines 53 lines calculation type • Pressing the key while the Statistics Editor is on the screen will display a statistical calculation screen for performing calculations based on the input data. What you need to do to return to the Statistics Editor from the statistical calculation screen depends on the (Data) if you selected calculation type you selected.
Important! • Note that the insert operation will not work if the maximum number of lines allowed for the Statistics Editor are already used. To delete all Statistics Editor contents 1. On the Statistics Editor, press 2. Press (Delete All). (Editor). Statistical Calculation Screen The statistical calculation screen is for performing statistical calculations key with the data you input with the Statistics Editor.
(Statistics Calc) Display the statistical calculation screen Statistics Editor: Paired-variable Select this menu item: When you want to do this: (Select Type) Display the statistical calculation type selection screen (Editor) Display the Editor sub-menu for editing Statistics Editor contents (2-Variable Calc) Display statistical values based on input data (Regression Calc) Display regression calculation results based on input data (Statistics Calc) Display the statistical calculation screen S
Select this menu item: When you want to do this: (Select Type) Display the statistical calculation type selection screen (1-Variable Calc) Display statistical values based on input data (Data) Display the Statistics Editor (Summation) Display the Summation sub-menu of commands for calculating sums (Variable) Display the Variable sub-menu of commands for calculating the mean, standard deviation, etc.
Select this menu item: When you want to do this: (Select Type) Display the statistical calculation type selection screen (2-Variable Calc) Display statistical values based on input data (Regression Calc) Display regression calculation results based on input data (Data) Display the Statistics Editor (Summation) Display the Summation sub-menu of commands for calculating sums (Variable) Display the Variable sub-menu of commands for calculating the mean, standard deviation, etc.
Single-variable Statistical Calculation Commands The following are the commands that appear on the sub-menus that appear when you select Summation, Variable, or Min/Max on the statistical menu while a single-variable statistical calculation type is selected. The following is the calculation formula used for each command.
(n) Number of items Min/Max Sub-menu ( (Min/Max)) Select this menu item: When you want to obtain this: (min(x)) Minimum value (Q1) First quartile (Med) Median (Q3) Third quartile (max(x)) Maximum value Single-variable Statistical Calculation Examples Select single-variable and input the following data: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (Statistics: On) (Select Type) 1 2 3 4 5 6 7 (1-Variable) 8 9 10 Edit the data to the following, using insert and delete: {0, 1, 2, 3, 4, 5, 6, 7, 9
(Editor) (Insert Row) Edit the Freq data to the following: {1, 2, 1, 2, 2, 2, 3, 4, 2, 1} (Data) 2 2 2 2 3 4 2 Display statistical values based on input data.
Calculate sum of squares of the sample data and sum of the sample data. (Summation) (Σx2) (Summation) (Σx) Calculate number of samples, mean, and population standard deviation. (Variable) (n) (Variable) (x) (Variable) (σx) Calculate minimum value and maximum value.
Linear Regression Calculation (y=a+bx) Commands With linear regression, regression is performed in accordance with the following model equation. y = a + bx The following is the calculation formula used for each command.
(Σxy) Sum of products of the x-data and y-data (Σx3) Sum of cubes of the x-data (Σx2y) Sum of (x-data squares × y-data) (Σx4) Sum of biquadrate of the x-data Variable Sub-menu ( Select this menu item: (Variable)) When you want to obtain this: (x) Mean of the x-data (σ2x) Population variance of the x-data (σx) Population standard deviation of the x-data (s2x) Sample variance of the x-data (sx) Sample standard deviation of the x-data (n) Number of items (y) Mean of the y-data (σ2y)
Select this menu item: When you want to obtain this: (min(x)) Minimum value of the x-data (max(x)) Maximum value of the x-data (min(y)) Minimum value of the y-data (max(y)) Maximum value of the y-data Regression Sub-menu ( Select this menu item: (Regression)) When you want to obtain this: (a) Regression coefficient constant term a (b) Regression coefficient b (r) Correlation coefficient r (x̂) Estimated value of x (ŷ) Estimated value of y Linear Regression Calculation Examples Selec
(Select Type) (y=a+bx) 1 1.2 1.5 1.6 1.9 2.1 2.4 2.5 2.7 3 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 Display statistical values based on input data. (2-Variable Calc) Display regression calculation results based on input data. (Regression Calc) Calculate sum of products of the x-data and y-data, Population standard deviation of the x-data, and maximum value of the y-data.
(Σxy) (Variable) (σx) (Min/Max) (max(y)) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r. (Regression) (a) (Regression) (b) (Regression) (r) Calculate estimated values.
(x̂) (x=2 → ŷ=?) 2 (Regression) (ŷ) Quadratic Regression Calculation (y=a+bx+cx2) Commands With quadratic regression, regression is performed in accordance with the following model equation. y = a + bx + cx2 The following is the calculation formula used for each command. • Summation Sub-menu, Variable Sub-menu, and Min/Max Sub-menu operations are the same those for linear regression calculations.
Select this menu item: When you want to obtain this: (a) Regression coefficient constant term a (b) Linear coefficient b of the regression coefficients (c) Quadratic coefficient c of the regression coefficients (x̂1) Estimated value of x1 (x̂2) Estimated value of x2 (ŷ) Estimated value of y Quadratic Regression Calculation Examples Select quadratic regression and input the following data (Statistics: Off) x y x y 1.0 1.0 2.1 1.5 1.2 1.1 2.4 1.6 1.5 1.2 2.5 1.7 1.6 1.3 2.
Display statistical values based on input data. (2-Variable Calc) Display regression calculation results based on input data. (Regression Calc) Calculate regression coefficient constant term a, linear coefficient b, and quadratic coefficient c.
Logarithmic Regression Calculation (y=a+b･ln(x)) Commands With logarithmic regression, regression is performed in accordance with the following model equation. y = a + blnx The following is the calculation formula used for each command. • Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and Regression Sub-menu operations are the same those for linear regression calculations.
1.6 23.5 38 46.4 48.9 Display statistical values based on input data. (2-Variable Calc) Display regression calculation results based on input data. (Regression Calc) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r.
(Regression) (r) Calculate estimated values. (y=73 → x̂=?) 73 (Regression) (x̂) (x=80 → ŷ=?) 80 (Regression) (ŷ) e Exponential Regression Calculation (y=a･e^(bx)) Commands With e exponential regression, regression is performed in accordance with the following model equation. y = aebx The following is the calculation formula used for each command. • Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and Regression Sub-menu operations are the same those for linear regression calculations.
x y 6.9 21.4 12.9 15.7 19.8 12.1 26.7 8.5 35.1 5.2 (Select Type) 6.9 21.4 12.9 15.7 19.8 12.1 (y=a･e^(bx)) 26.7 8.5 35.1 5.2 Display statistical values based on input data. (2-Variable Calc) Display regression calculation results based on input data.
(Regression Calc) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r. (Regression) (a) (Regression) (b) (Regression) (r) Calculate estimated values. (y=20 → x̂=?) 20 (Regression) (x̂) (x=16 → ŷ=?) 16 (Regression) (ŷ) ab Exponential Regression Calculation (y=a･b^x) Commands With ab exponential regression, regression is performed in accordance with the following model equation.
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and Regression Sub-menu operations are the same those for linear regression calculations. ab Exponential Regression Calculation Examples Select ab exponential regression and input the following data (Statistics: Off) x y -1 0.24 3 4 5 16.2 10 513 (Select Type) 0.24 (y=a･b^x) 1 3 5 4 16.2 10 513 Display statistical values based on input data.
(2-Variable Calc) Display regression calculation results based on input data. (Regression Calc) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r. (Regression) (a) (Regression) (b) (Regression) (r) Calculate estimated values. (y=1.02 → x̂=?) 1.
(x̂) (x=15 → ŷ=?) 15 (Regression) (ŷ) Power Regression Calculation (y=a･x^b) Commands With power regression, regression is performed in accordance with the following model equation. y = axb The following is the calculation formula used for each command. • Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and Regression Sub-menu operations are the same those for linear regression calculations.
(Select Type) 28 2410 3033 30 3895 (y=a･x^b) 33 35 4491 38 5717 Display statistical values based on input data. (2-Variable Calc) Display regression calculation results based on input data. (Regression Calc) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r.
(a) (Regression) (b) (Regression) (r) Calculate estimated values. (y=1000 → x̂=?) 1000 (Regression) (x̂) (x=40 → ŷ=?) 40 (Regression) (ŷ) Inverse Regression Calculation (y=a+b/x) Commands With inverse regression, regression is performed in accordance with the following model equation. y=a+ b x The following is the calculation formula used for each command.
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and Regression Sub-menu operations are the same those for linear regression calculations. Inverse Regression Calculation Examples Select inverse regression and input the following data (Statistics: Off) x y 1.1 18.3 2.1 9.7 2.9 6.8 4.0 4.9 4.9 4.1 (Select Type) 1.1 18.3 2.1 9.7 2.9 6.8 (y=a+b/x) 4 4.9 4.9 4.1 Display statistical values based on input data.
Display regression calculation results based on input data. (Regression Calc) Calculate regression coefficient constant term a, regression coefficient b, and correlation coefficient r. (Regression) (a) (Regression) (b) (Regression) (r) Calculate estimated values.
(x=3.5 → ŷ=?) 3.5 (Regression) (ŷ) Creating a Number Table The Table Mode 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). Configuring a Number Table Generation Function Perform the following steps to generate a number table. , select the Table Mode icon, and then press 1. Press • This displays the function input screen. . 2. Use the x variable to input two functions, one in the format f(x) and the other in the format g(x).
Input the increment step (Default = 1). Note: The Step specifies by how much the Start value should be sequentially incremented as the number table is generated. If you specify Start = 1 and Step = 1, x Step sequentially will be assigned the values 1, 2, 3, 4, and so on to generate the number table until the End value is reached. • Pressing generates and displays the number table in accordance with the Table Range dialog box.
Tip: • In the number table, you can change the value in the currently highlighted x cell. Changing the x value causes the f(x) and g(x) values in the same line to be updated accordingly. • If there is value in the x cell above the currently highlighted x cell, or automatically inputs into the highlighted cell the pressing value equal to the value of the cell above it plus the step value. So also, pressing automatically inputs the value equal to the value of the cell above less the step value.
• Pressing will reset all of the coefficients to one. 4. After all the values are the way you want, press . • This displays the solution (value of X). • Pressing again will return to the Coefficient Editor. Important! • A Math ERROR will occur if you perform a calculation while 0 is input for a coefficient. Changing the Ratio Expression Type (Select Type) and then select the ratio expression type you Press want from the menu that appears.
Technical Information Errors The calculator will display an error message whenever an error occurs for any reason during a calculation. Displaying the Location of an Error While an error message is displayed, press or 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 again. Example: When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2 =.
Action: • Check the input values, reduce the number of digits, and try again. • When using independent memory or a variable as the argument of a function, make sure that the memory or variable value is within the allowable range for the function. Stack ERROR Cause: • The calculation you are performing has caused the capacity of the numeric stack or the command stack to be exceeded. Action: • Simplify the calculation expression so it does not exceed the capacity of the stack.
Before Assuming Malfunction of the Calculator... Perform the following steps whenever an error occurs during a calculation or when calculation results are not what you expected. If one step does not correct the problem, move on to the next step. Note that you should make separate copies of important data before performing these steps. 1. Check the calculation expression to make sure that it does not contain any errors. 2.
3. Remove the battery, and then load a new battery with its plus (+) and minus (−) ends facing correctly. 4. Replace the cover. 5. Initialize the calculator: (RESET) (Initialize All) (Yes). • Do not skip the above step! 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.
10 Addition (+), subtraction (−) If a calculation contains a negative value, you may need to enclose the negative value in parentheses. If you want to square the value -2, for example, you need to input: (-2)2. This is because x2 is a function preceded by a value (Priority 3, above), whose priority is greater than the negative sign, which is a prefix symbol (Priority 5).
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 calculation. Precision for exponential display is ±1 at the least significant digit. Errors are cumulative in the case of consecutive calculations. Function Calculation Input Ranges and Precision Functions sinx cosx Input Range Degree 0 ≦ |x| < 9 × 109 Radian 0 ≦ |x| < 157079632.
logx, lnx 0 < x ≦ 9.999999999 × 1099 10x -9.999999999 × 1099 ≦ x ≦ 99.99999999 ex -9.999999999 × 1099 ≦ x ≦ 230.2585092 √x 0 ≦ x < 1 × 10100 x2 |x| < 1 × 1050 x-1 |x| < 1 × 10100; x ≠ 0 √x 3 |x| < 1 × 10100 x! 0 ≦ x ≦ 69 (x is an integer) nPr 0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r are integers) 1 ≦ {n!/(n−r)!} < 1 × 10100 nCr 0 ≦ n < 1 × 1010, 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.
√y y > 0: x ≠ 0, -1 × 10100< 1/x logy < 100 y = 0: x > 0 2n + 1 y < 0: x = 2n+1, (m ≠ 0; m, n are m integers) However: -1 × 10100 < 1/x log |y| < 100 a b/c Total of integer, numerator, and denominator must be 10 digits or less (including separator symbol). RanInt#(a, b) a < b; |a|, |b| < 1 × 1010; b − a < 1 × 1010 x • Precision is basically the same as that described under “Calculation Range and Precision”, above.
Dimensions: 13.8 (H) × 77 (W) × 165.5 (D) mm ½" (H) × 3" (W) × 61⁄2" (D) Approximate Weight: 100 g (3.5 oz) including the battery fx-85GT X Power Requirements: Built-in solar cell; button battery LR44 × 1 Approximate Battery Life: 2 years (based on one hour of operation per day) Operating Temperature: 0°C to 40°C (32°F to 104°F) Dimensions: 11.1 (H) × 77 (W) × 165.5 (D) mm ⅜" (H) × 3" (W) × 61⁄2" (D) Approximate Weight: 90 g (3.
Frequently Asked Questions Frequently Asked Questions ■ How can I perform input and display results the same way I did on a model that does not have Natural Textbook Format? → Perform the following key operation: (SETUP) (Input/Output) (LineI/LineO), or (SETUP) (Input/Output) (LineI/DecimalO). ■ How can I change a fraction form result produced by a division operation to decimal form? → While a fraction calculation result is displayed, press .
Example: (sin 30) + 15 (Angle Unit: Degree) Older (S-V.P.A.M.) Model: 30 15 15.5 Natural Textbook Display Model: (LineI/LineO) 30 15 15.5 Failure to press here as shown below will result in calculation of sin 45. 30 15 0.
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