Introduction This graphing calculator can handle many types of mathematical formulas and expressions for you. It is powerful enough to process very complex formulas used in rocket science, but yet so compact that it fits in your coat pocket. The main features of this graphing calculator are as follows: • Graphing Capability to help you visualize what you are working on, • Slide Show Function to help you understand common formulas, prepare for presentations, • Large memory capacity, with fast processing speed, and more. We strongly recommend you read this manual thoroughly. If not, then browse through the very first chapter “Getting Started”, at least. Last, but not least, congratulations on purchasing the Graphing Calculator! NOTICE • The material in this manual is supplied without representation or warranty of any kind. SHARP assumes no responsibility and shall have no liability of any kind, consequential or otherwise, from the use of this material. • SHARP strongly recommends that separate permanent written records be kept of all important data. Data may be lost or altered in virtually any electronic memory product under certain circumstances. Therefore, SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use, repairs, defects, battery replacement, use after the specified battery life has expired, or any other cause. • SHARP assumes no responsibility, directly or indirectly, for financial losses or claims from third persons resulting from the use of this product and any of its functions, the loss of or alteration of stored data, etc. • The information provided in this manual is subject to change without notice. • Screens and keys shown in this manual may differ from the actual ones on the calculator. • Some of the accessories and optional parts described in this manual may not be available at the time you purchase this product. • All company and/or product names are trademarks and/or registered trademarks of their respective holders. 1 Contents Caring for Your Calculator................................................................................................. 7 Chapter 1 Getting Started...............................................................................................................8 Before Use........................................................................................................................ 8 Using the Hard Cover..................................................................................................... 10 Part Names and Functions............................................................................................. 11 Main Unit................................................................................................................ 11 Basic Key Operations..................................................................................................... 15 Quick Run-through......................................................................................................... 16 Chapter 2 Operating the Graphing Calculator.............................................................................18 Basic Key Operations - Standard Calculation Keys........................................................ 18 1. Entering numbers............................................................................................... 18 2. Performing standard math calculations............................................................... 20 Cursor Basics................................................................................................................. 20 Editing Entries................................................................................................................ 22 Second Function Key...................................................................................................... 23 ALPHA Key..................................................................................................................... 24 Math Function Keys ....................................................................................................... 25 MATH, STAT, and PRGM Menu Keys............................................................................. 27 SETUP Menu.................................................................................................................. 28 SETUP Menu Items........................................................................................................ 29 Calculations Using MATH Menu Items........................................................................... 32 Precedence of Calculations............................................................................................ 45 Error Messages.............................................................................................................. 46 Resetting the Calculator................................................................................................. 47 1. Using the reset switch......................................................................................... 47 2. Selecting the RESET within the OPTION menu................................................. 48 Chapter 3 Manual Calculations.....................................................................................................49 1. Try it!........................................................................................................................... 49 2. Try it!........................................................................................................................... 51 3. Arithmetic Keys........................................................................................................... 52 4. Calculations Using Various Function Keys.................................................................. 54 5. More Variables: Single Value Variables and LIST Variables........................................................................................................... 65 6. TOOL Menu................................................................................................................ 65 2 Contents Chapter 4 Graphing Features........................................................................................................68 1. Try it!........................................................................................................................... 68 2. Try it!........................................................................................................................... 71 3. Explanations of Various Graphing Keys...................................................................... 74 4. Graph Modes.............................................................................................................. 79 5. Graphing Parametric Equations.................................................................................. 80 6. Polar Graphing............................................................................................................ 81 7. Graphing Sequences.................................................................................................. 82 8. The CALC Function.................................................................................................... 86 9. Format Setting............................................................................................................ 90 10. Setting a Window...................................................................................................... 92 11. Tables........................................................................................................................ 93 12. The DRAW Function................................................................................................. 96 13. Other Useful Graphing Features............................................................................. 111 Split screen........................................................................................................... 111 Substitution feature............................................................................................... 113 Chapter 5 SLIDE SHOW Feature.................................................................................................116 1. Try it!......................................................................................................................... 116 2. The SLIDE SHOW menu.......................................................................................... 119 Chapter 6 Matrix Features...........................................................................................................121 1. Try it!......................................................................................................................... 121 2. Entering and Viewing a Matrix.................................................................................. 123 Editing keys and functions.................................................................................... 124 3. Normal Matrix Operations......................................................................................... 125 4. Special Matrix Operations......................................................................................... 126 Calculations using OPE menus............................................................................ 126 Calculations using MATH menus.......................................................................... 130 Use of [ ] menus................................................................................................... 131 3 Contents Chapter 7 List Features...............................................................................................................132 1. Try it!......................................................................................................................... 132 2. Creating a list............................................................................................................ 134 3. Normal List Operations............................................................................................. 134 4. Special List Operations............................................................................................. 136 Calculations using the OPE menu functions........................................................ 136 Calculations using MATH Menus.......................................................................... 140 Calculations using VECTOR Menus..................................................................... 143 5. Drawing multiple graphs using the list function......................................................... 144 6. Using L_DATA functions............................................................................................ 144 7. Using List Table to Enter or Edit Lists....................................................................... 145 How to enter the list.............................................................................................. 145 How to edit the list................................................................................................ 146 Chapter 8 Statistics & Regression Calculations.......................................................................147 1. Try it!......................................................................................................................... 147 2. Statistics Features.................................................................................................... 151 1. STAT menus...................................................................................................... 151 2. Statistical evaluations available under the C CALC menu................................ 152 3. Graphing the statistical data..................................................................................... 155 1. Graph Types...................................................................................................... 155 2. Specifying statistical graph and graph functions............................................... 159 3. Statistical plotting on/off function...................................................................... 159 4. Trace function of statistical graphs.................................................................... 160 4. Data list operations................................................................................................... 161 5. Regression Calculations........................................................................................... 162 6. Statistical Hypothesis Testing................................................................................... 167 7. Distribution functions................................................................................................ 179 Chapter 9 Financial Features......................................................................................................185 1. Try it! 1...................................................................................................................... 185 2. Try it! 2...................................................................................................................... 189 3. CALC functions......................................................................................................... 191 4. VARS Menu.............................................................................................................. 195 4 Contents Chapter 10 The SOLVER Feature..................................................................................................196 1. Three Analysis Methods: Equation, Newton & bisection, and Graphic..................... 196 2. Saving/Renaming Equations for Later Use............................................................... 202 3. Recalling a Previously Saved Equation.................................................................... 203 Functions of the SOLVER feature......................................................................... 203 Chapter 11 Programming Features..............................................................................................204 1. Try it!......................................................................................................................... 204 2. Programming Hints................................................................................................... 206 3. Variables................................................................................................................... 207 Setting a variable.................................................................................................. 207 Index of variables in the programs........................................................................ 207 4. Operands.................................................................................................................. 207 Comparison operands.......................................................................................... 207 5. Programming commands.......................................................................................... 208 A PRGM menu P A............................................................................... 208 B BRNCH menu P B............................................................................ 209 C SCRN menu P C............................................................................... 210 D I/O menu P D.................................................................................... 210 E SETUP menu P E............................................................................. 210 F FORMAT menu P F........................................................................... 212 G S_PLOT menu P G........................................................................... 213 6. Flow control tools...................................................................................................... 214 7. Other menus convenient for programming................................................................ 216 H COPY menu P H............................................................................... 216 VARS menu.......................................................................................................... 217 8. Debugging................................................................................................................ 219 9. Preinstalled program................................................................................................. 220 Calculating the area between equations for a given interval................................ 220 Chapter 12 OPTION Menu.............................................................................................................222 Accessing the OPTION Menu...................................................................................... 222 1. Adjusting the screen contrast........................................................................... 222 2. Checking the memory usage............................................................................ 222 3. Deleting files..................................................................................................... 224 4. Linking to another EL-9950 or PC.................................................................... 224 5. Reset function................................................................................................... 227 5 Contents Appendix 1. Replacing Batteries.................................................................................................. 228 2. Troubleshooting Guide.............................................................................................. 231 3. Specifications............................................................................................................ 233 4. Error Codes and Error Messages............................................................................. 235 5. Error Conditions Relating to Specific Tasks.............................................................. 237 1. Financial........................................................................................................... 237 2. Error conditions during financial calculations.................................................... 239 3. Distribution function.......................................................................................... 239 6. Calculation Range.................................................................................................... 241 1. Arithmetic calculation........................................................................................ 241 2. Function calculation.......................................................................................... 241 3. Complex number calculation............................................................................. 246 7. List of Menu/Sub-menu Items................................................................................... 247 6 Caring for Your Calculator Caring for Your Calculator • Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile. • Keep the calculator away from extreme heat such as on a car dashboard or near a heater, and avoid exposing it to excessively humid or dusty environments. • Since this product is not waterproof, do not use it or store it where fluids, for example water, can splash onto it. Raindrops, water spray, juice, coffee, steam, perspiration, etc. will also cause malfunction. • Clean with a soft, dry cloth. Do not use solvents. Avoid using a rough cloth or anything else that may cause scratches. • Do not use a sharp pointed object or exert too much force when pressing keys. • Avoid excessive physical stress. 7 Chapter 1 Getting Started Before Use Inserting batteries resetting the memory 1. Open the battery cover located on the back of the calculator. Pull down the notch, then lift the battery cover up to remove it. 2. Insert the batteries, as indicated. Make sure that the batteries are inserted in the correct directions. 3. Pull off the insulation sheet from the memory backup battery. 4. Place the battery cover back, and make sure that the notch is snapped on. 5. After a few seconds, press O and you will see the following message on the display: PRESS [CL] KEY TO CLEAR ALL DATA PRESS [ON] KEY TO CANCEL 6. Make sure to press C to reset the calculator’s memory. The memory will be initialized and “ALL DATA CLEARED” will be displayed. Press any key to set the calculator ready for normal calculation mode. 8 Chapter 1: Getting Started Note: Adjusting display contrast If the above message does not appear or malfunction occurs, check the direction of the batteries and close the cover again. If this does not solve the problem, remove the battery cover, and then gently push the RESET switch with the tip of a ball-point pen or a similar object while pressing O simultaneously. And then, follow steps 4 to 6 above. DO NOT use a tip of a pencil or mechanical pencil, a broken lead may cause a damage to the button mechanism. Since the display contrast may vary with the ambient temperature and/or remaining battery power, you may want to adjust the contrast accordingly. Here’s how: 1. Press @, then p. 2. Adjust the contrast by using the + and - keys. +: increases the contrast -: decreases the contrast Hold down the key. 3. When done, press C to exit the mode. Turning the calculator OFF Press @ o to turn the calculator off. Automatic power off function • The calculator is automatically turned off when there is no key operation for approximately 10 minutes (The power-off time depends on the conditions.) • The calculator will not automatically power off while it is executing calculations (“■” flashes on the upper right corner of the display.) 9 Chapter 1: Getting Started Using the Hard Cover To open the cover: When in use: When not in use: 10 Chapter 1: Getting Started Part Names and Functions Main Unit 1Display screen 2Power ON/ OFF key 4Graphing keys 5Cursor keys 3Key operation keys 11 Chapter 1: Getting Started 1Display screen: Displays up to 132 pixels wide by 64 pixels tall of graphs and texts. 2Power ON/OFF key: Turns calculator ON. To turn off the calculator, press @, then o. 3Key operation keys: These keys are used to change the key functions. @: Changes the cursor to “2”, and the next keystroke enters the function or mode printed above each key in orange. A: Changes the cursor to “A”, and the next keystroke enters the alphabetical letter printed above each key in green. Note: Press @ . to lock the specific keys in the alphabet entering mode. (ALPHA-LOCK) 4Graphing keys: These keys specify settings for the graphing-related mode. Y: Opens the formula input screen for drawing graphs. G: Draws a graph based on the formulas programmed in the Y window. t: Opens a Table based on the formulas programmed in Y. W: Sets the display ranges for the graph screen. Z: Changes the display range of the graph screen. U: Places the cursor pointer on the graph for tracing, and displays the coordinates. ,: Displays the substitution feature. ": Displays both a graph and a table at the same time. y: Opens the table setup screen. d: Draws items on the graph. Use this key also to save or recall the graph/pixel data. f: Sets the operations of the graph screen. k: Calculates specific values based on formulas programmed in Y. 12 Chapter 1: Getting Started 5Cursor keys: Enables you to move the cursor (appears as _, ■, etc. on the screen) in four directions. Use these keys also to select items in the menu. Reset switch (in the battery compartment): Used when replacing batteries or clear the calculator memory. # key: Returns calculator to calculation screen. p key: Sets or resets the calculator settings, such as LCD contrast and memory usage. n key: Obtains the screen for the slide show. l key: Accesses list features. ] key: Creates your own slide shows. [ key: Sets the statistical plotting. Keyboard Basic Operation keys E: Used when executing calculations or specifying commands. C / q: Clear/Quit key B: Backspace delete key D: Delete key i: Toggle input mode between insert and overwrite (in one-line edit mode). ;: Allows you to set up the basic behavior of this calculator, such as to set answers in scientific or normal notation. 13 Chapter 1: Getting Started Menu keys M: Enter the Math menu with additional mathematical functions. S: Enter the statistics menu. P: Enter the programming menu. V: Converts hexadecimal, decimal, octal and binary numbers or solves systems of linear equations, finds roots for quadratic and cubic equations. m: Enter menu for matrix functions. ': Enter screen and menu for Solver features. z: Enter the menu for calculator specific variables. g: Enter menu for financial solver and functions. Scientific Calculation keys See each chapter for details. 14 Chapter 1: Getting Started Basic Key Operations Since this calculator has more than one function assigned to each key, you will need to follow a few steps to get the function you need. Example F Operation of y @ x : Specify x -1 A F : Specify character F y : Specify x2 • Press “as is” to get the function and number printed on each key. • To access secondary function printed above each key in orange, press @ first, then press the key. Press C to cancel. • To press the key printed above each key in green, press A first, then press the key. When in Menu selection screen however, you do not have to press A to access the characters. Press C to cancel. • If you want enter alphabetical letters (green) sequentially, use @ .. Press A to return to the normal mode. • In this manual, alphanumeric characters to be entered are indicated as they are (without using the key symbols). Use of the key symbol indicates that it is for selecting the menu specified by the character or number. The above example also indicates the key notation rules of this manual. 15 Chapter 1: Getting Started Quick Run-through Here are the major ingredients for 18 doughnuts: 1 cup warm water 4 3 cup warm milk 4 1 cup sugar 3 4 cups all-purpose flour 2 eggs 3 tablespoons butter Based on these values, solve the following problems using the calculator. Question If you make 60 doughnuts according to the above recipe, how many cups of warm milk are required? At first, you may calculate how many cups of warm milk are required for 1 doughnut = 3 ÷ 18 4 As for the ordinary calculator, the answer is 0.041666666. But how much is 0.04166666 of a cup of warm milk? Set up the calculator before calculation 1. Press # to enter the calculation screen. Change answer mode from decimals to fractions 1. Press @ ;. 2. Press C to clear the display. 2. Select F ANSWER and press 2. Press C. 16 Chapter 1: Getting Started Enter fractions 3. Press 3 b 4 '. 4. Press b 18 '. 5. Press E. 1 of a cup of warm milk is required per one Now we have found 24 doughnut, how many cups are required for 60 doughnuts? If you want to use the answer of the previous calculation, press b and you do not have to reenter the value. 6. Press @ b |, or directly | (multiplication). “Ans×” is displayed. ANS is a calculator specific variable which indicates the answer of calculations just before. *When you enter + (addition), – (subtraction), × (multiplication), ÷ (division), it is not required to press b. 7. Press 60. 8. Press E. Answer: 2 1 cups of warm milk are required for making 60 doughnuts. 2 17 Chapter 2 Operating the Graphing Calculator Basic Key Operations - Standard Calculation Keys The standard calculation keys, located at the bottom four rows of the keyboard, enable you to access the basic functions of the calculator. 1. Entering numbers Use the number keys (0 ~ 9), decimal point key (.), and negative number key (_) to enter numbers into the calculator. To clear the screen entry, press C. In the examples and descriptions in this manual, a point is used to provide a Display decimal point to coincide with the display of the computer. Number entry Example Type 10.23456789 onto the Calculation screen. 1. Enter the Calculation screen, then clear the screen entry: #C 2. Enter numbers with the number keys and decimal point key, as follows: 10 . 23456789 18 Chapter 2: Operating the Graphing Calculator Note: $ can be used to enter a value in scientific notation. Example 6.3 × 108 + 4.9 × 107 # C 6.3 $ 8 + 4.9 $ 7 Entering a negative value The negative number key _ can be used to enter numbers, lists, and functions with negative values. Press _ before entering the value. Note: Do not use the - key to specify a negative value. Doing so will result in an error. Example Type -9460.827513 into the Calculation screen. # C _ 9460.827513 19 Chapter 2: Operating the Graphing Calculator 2. Performing standard math calculations By utilizing the + - | and = keys, you can perform the standard arithmetic calculations of addition, subtraction, multiplication, and division. Press E to perform each calculation. Perform an arithmetic calculation Example Obtain the answer to “6 × 5 + 3 – 2”. #C6|5+3 -2E Using parentheses With the ( and ) keys, parentheses (round brackets) can be added to group sections of expressions. Sections within the parentheses will be calculated first. Parentheses can also be used to close the passings of values in various functions, such as “round(1.2459,2)”. Example Obtain the answer to “(9 + 7) × (5 – 3)”. #C(9+7 )|(5-3 )E Note: The multiplication sign “×”, as the one in the above example, can be abbreviated if it proceeds a math function, a parenthesis “(”, or a variable. Please note that the precedence of calculations may be changed (see page 45). And, the multiplication sign "×" after a parenthesis ")" cannot be abbreviated. For examples, Abbreviating “(1 + 2) × 3” to “(1 + 2) 3” will result in an error. Cursor Basics The cursor indicates where the next entry will be placed. The cursor may be placed automatically to different areas by various functions and tools, or can be moved around by using the ; ' { } keys. Use the cursor keys to select a menu item, select a cell item in a matrix, and trace along a graph. 20 Chapter 2: Operating the Graphing Calculator Example Enter “ 65536 × 3 8 ” in the Calculation screen. Then press E to calculate. 4 1. Press #, then C to clear the display. 2. Enter 4 for the root’s depth, then press @ _. The root figure is entered, with the cursor automatically placed below the figure. For detailed instructions of how to use the @ key, refer to “Second Function Key” and “ALPHA Key” in this chapter. 3. Enter 65536. At this moment, the cursor is still placed under the root figure. 4. Press ' to move the cursor out of the area, then enter | at the cursor. 5. Press @ _ again. Notice that the cursor is automatically placed so that you can specify the depth of this root figure. Type 3, }, and 8. 6. Press E to obtain the answer. Cursor appearance and input method The cursor also displays information regarding the calculator’s input method. See the following diagram. Mode Symbol Normal mode When A is pressed When @ is pressed Remarks The appearance of the cursor pointer may vary according to the mode or position. The major shapes and the definitions are as follows: : Insert mode : Overwrite mode * , and appear at the insertion point within the functions such as a/b and a . 21 Chapter 2: Operating the Graphing Calculator Editing Entries Editing modes The calculator has the following two editing modes: equation mode, and one line mode. You can select one from the G EDITOR menu of the SETUP menu. Equation editor One line editor *See page 31 for details. Cursor navigation Use ; ' { } to move the cursor around, and use the D B C keys to edit entries. • D key deletes an entry AT THE CURSOR. • B key erases one BEFORE THE CURSOR. • Use C to clear the entire entry line. About the Insert mode When the editing mode is set to one-line, insert mode needs to be manually specified. Press and release @, then i to set the insert mode. Press @ i again to return to the overwrite mode. The C key clears all screen entries in the Calculation screen, as well as clearing error messages. It also clears a single line equation in the Y screen. Example Type 3096, then change 3 to 4. When done, jump the cursor to the very end of the numbers. #C3096; ;;;D4 ''' 22 Chapter 2: Operating the Graphing Calculator Example Type 4500000, then remove 500. #C4500000; ;;BB B Tips: You can jump the cursor to the beginning or the end of line by using the @ and ; ' keys. Likewise, press @ } to jump the cursor all the way to the bottom. Press @ { to jump the cursor to the top. To learn about how to use the @ key and its functions, refer to the section “Second Function Key” of this chapter. Second Function Key Use @ to call up the calculator’s extended key functions, math functions and figures. All functions associated with @ are color coded orange, and are printed above each key. Example Enter “2π” on the screen. 1. Press # C to clear the screen, then enter “2” by pressing 2. 2. Press @. When the key is released, the cursor on the screen changes, indicating that a second function is now ready to be called up. 3. Press $ (_ key). The entry appears on the screen. 23 Chapter 2: Operating the Graphing Calculator ALPHA Key Use A to enter an alphabet character. All 26 characters accessible, as well as “θ ”, “=”, “ : ”, and space. All functions associated with A are color coded green, and are printed above each key. Note: Do not type out math figures (sin, log, etc.), graph equation names (Y1, Y2, etc.), list names (L1, L2, etc.), or matrix names (mat A, mat B, etc.), etc. with A keys. If “SIN” is entered from A mode, then each alphabet character — “S”, “I” and “N” — will be entered as a variable. Call up the figure and equation names from within the second functions and various menus instead. If a colon (:) is used, data may continue to be entered in more than one term. Entering one Alphabet character Example Enter 2 × A on the screen. 1. Press # C to clear the screen. Enter “2 ×” by pressing 2 |. 2. To enter “A”, press A; the cursor pattern changes to “A _” upon releasing the key. 3. Press A to call “A” at the cursor. After the entry, the cursor pattern changes back to normal. Entering 1 or More Alphabet characters 24 To type more than one alphabet character, use @ then A to apply the “ALPHA-LOCK”. When done, press A to escape from the mode. Chapter 2: Operating the Graphing Calculator Math Function Keys Mathematical functions can be called up quickly with the Math Function keys. s Enters a sine function at the cursor s Enters an arc sine function at the cursor c Enters a cosine function at the cursor c Enters an arc cosine function at the cursor Enters a tangent function at the cursor Enters an arctangent function at the cursor l Enters a logarithm function at the cursor 0 Enters “10 to the xth power”, then sets the cursor at the “x” I Enters a natural logarithm function at the cursor @ Enters “e-constant to the power of x”, then sets the cursor at the “x” y Enters “ 2 ” at the cursor, to raise a number to the second power x Enters “ -1 ” at the cursor, to raise a number to the negative first power d Enters a mixed number. b Enters a fraction. a Enters an exponent. _ By itself enters a “root” figure; the cursor will be set at “a”, the depth. 25 Chapter 2: Operating the Graphing Calculator Note: If a number precedes d b a and _, then the number will be set as the first entry of the figure. Else, the first entry is blank and the cursor flashes. Examples 2d3} 4' d ;2'3}4' , Enters “ , ” (a comma) at the cursor + Enters a “root” figure at the cursor R Stores a number or a formula into a variable r Recalls an item stored in a variable X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically determined according to the calculator’s coordinate setup: “x” for rectangular, “θ” for polar, “T” for parametric, “n” for sequential. z Brings up the VARS menu. (See Chapter 6). 26 Chapter 2: Operating the Graphing Calculator MATH, STAT, and PRGM Menu Keys By using the M, S, and P keys, you can access many menu items for complex calculation tasks. The appendix “List of Menu/Sub-menu Items” shows the contents of each, with detailed descriptions of each sub-menu item. Example Round the following number beyond the decimal point: 34.567 1. Press # C, then M. The MATH menu takes over the screen, as shown to the right. MATH menu items are displayed on the left side of the screen. 2. Use the { and } keys to move the cursor up and down the menu. As you scroll, you will see the corresponding submenu contents (shown on the right side of the screen) change. 3. Set the cursor at B NUM. Menu items can also be selected by using shortcut keys (A through H); in this example, simply press B to select B NUM. There is no need to use A for this operation. 4. Press a shortcut key 2 to select 2 round(. The screen now goes back to the calculation screen, as follows: Another way of selecting the sub-menu item is to press ' (or E) on the menu item B NUM. The cursor will be extended into the sub-menu on the right. Now, move the cursor on the sub-menu down to 2 round(, then press E. 5. Type 3 4 . 5 6 7 , 0 ), and press E. 27 Chapter 2: Operating the Graphing Calculator SETUP Menu Use this menu to verify basic configurations, such as to define the calculator’s editing preferences, and scientific and mathematical base units. Checking the calculator’s configuration To check the current configuration of the calculator, press @, then ;. By entering menu items (B DRG through H SIMPLE), various setups can be changed. To exit the SETUP menu, press C. Example Display the calculation result of “10002” in scientific notation. 1. Press @, then ;. Within the SETUP menu, press C, then 3 to select 3 Sci under the C FSE menu. Tips: Using the arrow keys, move the cursor down to the C FSE position, press E, and then move the cursor down to the 3 Sci position. Press E to select the sub-menu item. 2. The display goes back to the SETUP menu’s initial screen. 3. Press C to exit the SETUP menu. 4. Press # C to clear the Calculation screen, type 1 0 0 0 y, then E. 28 Chapter 2: Operating the Graphing Calculator SETUP Menu Items DRG: For trigonometric calculations and coordinate conversions, various angle units can be selected: Please make sure to use the appropriate angle unit when making trigonometric calculations (e.g. sin, cos). Deg Angle values to be set in degrees. (360°) Rad Angle values to be set in radians (default). (2π) Grad Angle values to be set in gradients. (400°) Note: Please use "Degree" (DEG) for angle values and not GRAD because this is used to represent Grads, where one turn comprises 400 Grads. FSE: Various decimal formats can be set: FloatPt Fix Answers are given in decimal form. The decimal point can be set in the TAB menu. Sci Answers are given in “scientific” notation. For example, “3500” is displayed as “3.500000000E3”. The decimal point can be set in the TAB menu. Eng Answers are given in “engineering” notation with exponents set to be multiples of 3. “100000” will be displayed as “100.0000000E3”. The decimal point can be set in the TAB menu. Answers are given in decimal form with a floating decimal point (default). The SETUP in TAB does not have any effect on this setting. (default) If the value of the mantissa does not fit within the range ±0.000000001 to ±9999999999, the display changes to scientific notation. The display mode can be changed according to the purpose of the calculation. TAB: Sets the number of digits beyond the decimal point (0 through 9). The default is “9”. 29 Chapter 2: Operating the Graphing Calculator COORD: Sets the calculator to various graph coordinate systems. Rect Param Polar Seq Rectangular coordinates (default) Parametric equation coordinates Polar coordinates Sequential graph coordinates ANSWER: Sets the answer preference to various number formats. Decimal (Real) Mixed (Real) Improp (Real) x±yi (Complex) 30 r (Complex) Answers will be given in decimal form (default). Answers will be given in mixed fractions, whenever appropriate. Answers will be given in improper fractions, whenever appropriate. (e.g. 2 1 ) 2 Answers will be given in complex rectangular form. Answers will be given in complex polar form. Chapter 2: Operating the Graphing Calculator EDITOR: Sets the editing style to one of two available formats. Equation Formulas can be entered in a "type it as you see it approach" (default setting). One line Formulas will be displayed on one line. Note: Immediately after changing the EDITOR, the calculator will return to the calculation screen and the following data will be cleared. • ENTRY memory • Equations stored in the graph equation window (Y) • Equations temporally stored in the SOLVER window (@ ') • Resetting to the default settings (@ p E 1) will also clear the above data. Expression of up to 114 bytes can be entered in the Equation edit mode. If the expression exceeds the screen width, it is horizontally extended. Expression of up to 160 bytes can be entered in One-line edit mode. if the expression exceed the screen width, it goes to the next line. SIMPLE: Sets the preference for handling reducible fractions. Auto Manual Fractions will automatically be reduced down (default). Fractions will not be reduced before simplifying (Simp). Note: All the procedures in this manual are explained using the default settings unless otherwise specified. 31 Chapter 2: Operating the Graphing Calculator Calculations Using MATH Menu Items The MATH menu contains functions used for more elaborate math concepts such as trigonometry, logarithms, probability, and math unit/format conversions. The MATH menu items may be incorporated into your expressions. A Note about Degrees and Radians The degree and radian systems are two of the basic methods of measuring angles. There are 360 degrees in a circle, and “2pi” radians. 1 degree is equal to pi/180 radians. “Then, what’s this pi?”, you may ask. Pi, or to use its symbol “π”, is the ratio of the circumference of a circle to its diameter. The value of π is the same for any circle “3.14...”, and it is believed to have an infinite number of digits beyond the decimal point. Note: Please use "Degree" (DEG) for angle values and not GRAD because this is used to represent Grads, where one turn comprises 400 Grads. A CALC Contains sub-menu tools for advanced calculations. 01 log2 log2 value Enters a base-2 logarithm (log2). 02 2X2value Raises 2 to a power. Sets the cursor to exponent. 03 fmin( fmin(equation, lower limit of x, upper limit of x) Returns the value of variable x when the equation Y has the minimum value within the specified range of x. 04 fmax( fmax(equation, lower limit of x, upper limit of x) Return the value of variable x when the equation Y has the maximum value within the specified range of x. 05 d/dx( d/dx(equation, value of x [, tolerance]) Returns derivative of equation Y at the specified X value using the tolerance (if not specified, default value is 1E–5). 32 Chapter 2: Operating the Graphing Calculator 06 ∫ ∫ equation, lower limit, upper limit [, tolerance] dx Calculates an integral value of equation Y from the lower limit to the upper limit using the specified tolerance (if not specified, default value is 1E–5). Use in conjunction with the 07 dx sub-menu item. • Press the keys as follows in the Equation edit mode. M A 0 6 2 { 8 ' ( X a 3 ' - 0.5 X y + 6 ) , 0.001 M A 0 7 E 07 dx Enters a differential “dx” in an integration expression. 08 ∑( ∑(expression, initial value, end value [, increment]) Returns the cumulative sum of a given expression from an initial value to an end value in the specified increment value (if not specified, default increment is 1). 09 sec sec value Enters a secant function to be used in a trigonometric expression. 10 csc csc value Enters a cosecant (cosec) function to be used in a trigonometric expression. 11 cot cot value Enters a cotangent (cotan) function to be used in a trigonometric expression. 12 sec-1sec-1 value Enters an inverse secant. 33 Chapter 2: Operating the Graphing Calculator 13 csc-1csc-1 value Enters an inverse cosecant. 14 cot-1cot-1 value Enters an inverse cotangent. 15 sinh sinh value Enters a hyperbolic sine. 16 cosh cosh value Enters a hyperbolic cosine. 17 tanh tanh value Enters a hyperbolic tangent. 18 sinh-1sinh-1 value Enters an inverse hyperbolic sine. 19 cosh-1cosh-1 value Enters an inverse hyperbolic cosine. 20 tanh-1tanh-1 value Enters an inverse hyperbolic tangent. BNUM Use the sub-menu items below to convert a value. 1 abs( abs(value) Returns an absolute value. * A real number, a list, matrix, variable, or equation can be used as values. Example • Find an absolute value of “-40.5”. MB1_ 40.5E 2 round( round(value [, digit number of decimals]) Returns the rounded value of the term in parentheses. A rounding point can be specified. * A real number, a list, matrix, variable, or equation can be used as values. Example 34 • Round off 1.2459 to the nearest hundredth. (= 1.25) MB21.2459,2)E Chapter 2: Operating the Graphing Calculator 3 ipart ipart value Returns only the integer part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values. Example • Discard the fraction part of 42.195. (=42) MB342.195E 4 fpart fpart value Returns only the fraction part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values. Example • Discard the integer part of 32.01. (=0.01) MB432.01E 5 int int value Rounds down a decimal number to the closest integer. Example • Round down 34.56 to the nearest whole number. (= 34) MB534.56E 6 min( min(list) Finds and returns the minimum value within a list of numbers. To define a list of more than two numbers, group the numbers with brackets (@ { and @ }), with each element separated by a comma. Example • Find the smallest value among 4, 5, and -9. [email protected] {4,5,_ [email protected]})E 7 max( max(list) Finds and returns the maximum value within a list of numbers. Example • Find the smallest value among 4, 5, and -9. M B 7 @ { 4 , 5 , _ 9 @})E 35 Chapter 2: Operating the Graphing Calculator 8 lcm( lcm(natural number, natural number) Returns the least common multiple of two integers. Example • Find the least common multiple of 12 and 18. MB812,18)E 9 gcd( gcd(natural number, natural number) Returns the greatest common divisor of two integers. Example • Find the greatest common divisor of 16 and 36. MB916, 36)E C PROB 1randomrandom [(number of trial)] Returns a random decimal number between 0 and 1 (uniform distributed). Example • Make a list with three random numbers. Note: Set the “FSE” to “Fix” and “TAB” to “0”. @ { M C 1 | 100 , M C 1 | 100 , M C 1 | 100 @ } E 2 rndInt( rndInt(minimum value, maximum value [, number of trial]) Returns a specified number of random integers, between a minimum and a maximum value. Example • Produce eight random integers, ranging between values of 1 and 6. M C 2 1 , 6 , 3 ) E *Minimum value: 0 ≤ xmin < 1010 Maximum value: 0 ≤ xmax < 1010 Number of trial: 1 ≤ n ≤ 999 36 Chapter 2: Operating the Graphing Calculator 3 rndNorm( rndNorm(mean, standard deviation [,number of trial] ) Returns a random real number from a specified normal distribution. * Number of trial : 1 ≤ n ≤ 999 (n is an integer.) Standard deviation : 0 < s 4 rndBin( rndBin(number of trial, probability of success [, number of simulations] ) Returns a random real number from a specified binominal distribution. * Number of trial : 1 ≤ n ≤ 9999 Probability of success : 0 ≤ p ≤ 1 Number of simulations : 1 ≤ n ≤ 999 (n is an integer.) Note:The random functions will generate different numbers every time. Therefore, the table values of the random functions will be different every time. When in case of random-based graphing calculations, the tracing values and other parameters of the graph will not match the graph’s visual representation. 5 nPr Returns the total number of different arrangements (permutations) for selecting “r” items out of “n” items. n! nPr = (n – r)! Example • How many different ways can 4 people out of 6 be seated in a car with four seats? 6MC54E 6 nCr Returns the total number of combinations for selecting “r” item out of “n” items. (Binomial distribution) Cr = n n! r!(n – r)! Example • How many different groups of 7 students can be formed with 15 students? 15MC67E 37 Chapter 2: Operating the Graphing Calculator 7 ! Returns a factorial. Example • Calculate 6 × 5 × 4 × 3 × 2 × 1. 6 M C 7 E D CONV These tools deal with conversions between different angle units and between rectangular and polar coordinates. Sexagesimal and Degree System The “base 60” sexagesimal system, as well as the minutes-second measurement system, was invented by the Sumerians, who lived in the Mesopotamia area around the fourth millennium B.C.(!) The notion of a 360 degrees system to measure angles was introduced to the world by Hipparchus (555-514 B.C.) and Ptolemy (2nd cent. A.D.), about 5000 years later. We still use these ancient systems today, and this calculator supports both formats. 1 →deg Takes a number in sexagesimal form, and converts it into a decimal number. To enter a number in sexagesimal form, use items in the “ANGLE” sub-menu, described as described in Chapter 3. Example • Convert 34° 56’ 78” to degrees. 34ME15 6 M278 M 3 MD1 E 2 →dms Takes a number in decimal form (in degrees), and converts it into a sexagesimal number. Example • Show 40.0268 degrees in degrees, minutes, and seconds. 40.0268 M D 2 E 38 Chapter 2: Operating the Graphing Calculator Rectangular/polar coordinate conversion This calculator is equipped with rectangular coordinates and polar coordinates conversion capabilities. x y r θ Rectangular to polar coordinate conversion functions 2 2 1/2 -1 Conversion formulas: r = (x + y ) , θ = tan (y/x) Polar to rectangular coordinate conversion functions Conversion formulas: x = rcosθ, y = rsinθ 3 xy→r( xy→r(x coordinate, y coordinate ) Returns polar coordinate radius value from X-Y rectangular coordinates. 4 xy→θ(xy→θ(x coordinate, y coordinate ) Returns polar coordinate θ value from X-Y rectangular coordinates. The following ranges are used to find θ. Degree mode: 0 ≤ |θ| ≤ 180 Radian mode: 0 ≤ |θ| ≤ 2π Gradient mode: 0 ≤ |θ| ≤ 200 5 rθ→x( rθ→x(r coordinate , θ coordinate ) Returns rectangular coordinate X value from r-θ polar coordinates. 6 rθ→y( rθ→y(r coordinate, θ coordinate) Returns rectangular coordinate Y value from r-θ polar coordinates. 39 Chapter 2: Operating the Graphing Calculator E ANGLE Use these tools to enter the symbols to specify angle units. 1 ° Inserts a degree, and sets the preceding value in degrees. 2 ’ Inserts a minute, and sets the preceding value in minutes. 3 ” Inserts a second, and sets the preceding value in seconds. Example • Enter 34° 56’ 78”. 3 4 M E 1 5 6 M 2 ← “E ANGLE” remains selected; 78M3 type the number to enter the symbols. E 4 r Enters an “r”, to enter a number in radians. Example • Type 2 radian. 2ME4 5 g Enters an “g” symbol, to enter a number in gradients. F INEQ Use the equality/inequality figures to compare two values. These sub-item tools return 1 (true) or 0 (false). 1 = Tests whether a preceding value and a following value are equal. 2 Tests whether a preceding value and a following value are not equal. 3 > Tests whether a preceding value is larger than a following value. 4 Tests whether a preceding value is larger than OR equal to a following value. 5 < Tests whether a preceding value is smaller than a following value. 6 Tests whether a preceding value is smaller than OR equal to a following value. 40 Chapter 2: Operating the Graphing Calculator G LOGIC Use the LOGIC sub-menu items to perform boolean operations. In the N-base calculation mode (binary, octal, decimal and hexadecimal), A LOGIC will directly appear when M is pressed. The following is the truth table of the combination of input A and B: A B A and B A or B A xor B A xnor B A notA 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 The following examples show the answer screen when executing a boolean operation for AND, OR, XOR, XNOR between “1100” and “1010” in binary mode. Compare the results (binary) to the above table. 1. Press # @ V A E to enter the binary, octal, and hexadecimal calculation mode. 2. Press } } } to select the binary mode. 1 and value A and value B Enters an “AND” logic figure. 1100 M 1 1010 E 2 or value A or value B Enters an “OR” logic figure. 1100 M 2 1010 E 3 not not value Enters a “NOT” logic figure. M 3 10 E 41 Chapter 2: Operating the Graphing Calculator 4 neg neg value Enters a “neg” logic figure. M41E Note: “4 neg” menu appears only in the N-base calculation (binary, octal, decimal and hexadecimal) mode. 5 xor value A xor value B Enters an Exclusive-OR (xor) logic figure. 1100 M 5 1010 E 6 xnor value A xnor value B Enters an Exclusive-NOR (xnor) logic figure. 1100 M 6 1010 E H COMPLX In order to use the sub-menu items within the COMPLX menu, the calculator must be set up to handle complex numbers. Otherwise the result will be a data type error. Refer to the section “SETUP Menu Items” in chapter 2 for changing/ verifying the calculator’s setup to enable complex number answers, in either rectangular or polar coordinates. 1 conj( conj(complex number) Returns the complex conjugate of the specified complex number (or list of complex numbers). 2 real( real(complex number) Returns the real part of a complex number (or list of complex numbers). 42 Chapter 2: Operating the Graphing Calculator 3 image( image(complex number) Returns the imaginary part of a complex number (or list of complex numbers). 4 abs( abs(complex number) Returns the absolute value of a complex number (or list of complex numbers). 5 arg( arg(complex number) Takes the coordinates (x + yi), and returns the θ. Calculations using complex numbers To calculate using complex numbers, select the sub-menu item 4 x ± yi or 5 r ANSWER of the SETUP menu items. in the F The initial screen for the complex number calculation mode is the same as for the real number mode. Complex numbers can be noted using either 4 x ± yi (rectangular coordinates) or 5 r (polar coordinates). Example • Calculate (3 + 4i) × (4 – 6i) Note:It is possible to input complex numbers (i) in the real number mode, however an error message will return. 43 Chapter 2: Operating the Graphing Calculator Functions available for complex number calculations The following function keys are available for complex number calculations without the limits existing in the real number calculations. y, x, l, I, 0, @, a, +, _ The following MATH menu functions are also available for complex number calculations. abs(, round(, ipart, fpart, int 44 Chapter 2: Operating the Graphing Calculator Precedence of Calculations When solving a mathematical expression, this calculator internally looks for the following figures and methods (sorted in the order of evaluation): 1) Fractions (1/4, a/b, , etc.) 2) Complex angles (∠) 3) Single calculation functions where the numerical value occurs before the function (X 2, X-1, !, “°”, “ r ”, “ g ”, etc) 4) Exponential functions (ab, a , etc) 5) Multiplications between a value and a stored variable/constant, with “×” abbreviated (2π, 2A, etc.) 6) Single calculation functions where the numerical value occurs after the function (sin, cos, tan, sin-1, cos-1, tan-1, log, 10x, ln, ex, √¯, abs, int, ipart, fpart, (-), not, neg, etc.) 7) Multiplications between a number and a function in #6 (3cos20, etc. “cos20” is evaluated first) 8) Permutations and combinations (nPr, nCr) 9) ×, ÷ 10)+, – 11)and 12)or, xor xnor 13)Equalities and nonequalities (<, ≤, >, ≥, ≠, =, →deg, →dms, etc.) Example The key operation and calculation precedence 5 + 2 | s 30 + 25 | 5 a 3 E 1st 4th 2nd 5th 3rd 6th • If parentheses are used, parenthesized calculations have precedence over any other calculations. 45 Chapter 2: Operating the Graphing Calculator • About the order of precedence of the multiplications, that the multiplication sign "×" before such as "(", π and a variable is abbreviated, are higher than that of the multiplications that the multiplication sign "×" is not abbreviated. Therefore, if there is a division before a multiplication, the order of calculations may be changed and then the calculation results may be changed. Example 48 ÷ 24 × (6 + 2) = 48 = 24 | ( 6 + 2 ) E → 16 [ (48 ÷ 24) × (6 + 2) = ] 48 = 24 ( 6 + 2 ) E → 0.25 [ 48 ÷ (24 × (6 + 2)) = ] Error Messages The calculator will display an error message when a given command is handled incorrectly, or when instructions cannot be handled correctly such that the task cannot be processed further. Various types of error messages are given to inform users the types of situations to be remedied. For example, performing the following key strokes: 5|E will result in an error, and the error message will be displayed. In such a situation, you can go back to the expression to correct its syntax by pressing ; or ', or you can erase the entire line to start over by pressing C. For a list of various error codes and messages, refer to the appendix. 46 Chapter 2: Operating the Graphing Calculator Resetting the Calculator Use the reset when a malfunction occurs, to delete all data, or to set all mode values to the default settings. The resetting can be done by either pressing the reset switch located in the battery compartment, or by selecting the reset in the OPTION menu. Resetting the calculator’s memory will erase all data stored by the user; proceed with caution. 1. Using the reset switch 1. Pull down the notch to open the battery cover located on the back of the calculator. 2. Place the battery cover back until the notch is snapped on. 3. Wait a few seconds and press O. The verification window will appear on the screen. 4. Press C to clear all the stored data. Press O to cancel resetting. After C is pressed, the calculator's memory will be initialized. Press any key to display the calculation screen. Note: If the above verification window does not appear, remove the battery cover and gently push the RESET switch with the tip of a ball-point pen or a similar object while pressing O simultaneously. DO NOT use a tip of a pencil or mechanical pencil, a broken lead may cause a damage to the button mechanism. 47 Chapter 2: Operating the Graphing Calculator • The message on the right may occasionally appear. In this case, repeat the procedure from step 1 to prevent loss of data. 2. Selecting the RESET within the OPTION menu 1. Press @, then p. The OPTION menu appears. 2. While in the OPTION menu, press E to select E RESET; the RESET submenu items should appear on the right side of the screen. 3. The first item 1 default set will initialize only the SETUP and FORMAT settings, while the second item 2 All memory will erase all memory contents and settings. To reset the memory, select 2 All memory by pressing 2. The verification window will appear. 4. Press the C key to clear all data stored on the calculator. Press any key to continue. 48 Chapter 3 Manual Calculations 1. Try it! The speed of light is known to be 186,282 miles (approximately 300,000 kilometers) per second. That means light can go around the earth 7 and a half times within a second! Suppose you are standing at the equator. While the earth rotates over the period of one day, you also rotate around the globe at a certain speed. Knowing the facts above, can you figure out how fast you are traveling, in miles per hour? Since distance traveled = average speed × time taken, the following equation can be formed to find out the circumference of the earth (x miles): x × 7.5 = 186282 Then, x = 186282 ÷ 7.5 Since you know the earth turns around once a day (which means, in 24 hours), divide the above “x” with 24 to get a value in miles per hour. 24 × v = x v= x 24 49 Chapter 3: Manual Calculations CONCEPT 1. Enter a math expression, then perform the calculation. 2. Save a number into a variable, then recall the value later. PROCEDURE 1. First, press #, then C to clear any screen entries. 2. Type 186282 = 7.5, then press E. The circumference of the earth is thus obtained. 3. Store the answer in a variable. A variable is a symbol under which you can store a numerical value. We will use variable A to store the circumference of the earth. Press R to set the “store” mode. Press A A, then E to store the answer. To call up the stored answer, press A A E again. Note: While checking the stored values, you may see “0”; this means that no value is stored in the variable. 4. Now, since the value you have stored under “A” is the distance you will be travelling in 24 hours, divide the number by 24. Press A A = 24, then E. So, you are travelling at 1034.9 miles/hour. That is fast! 50 Chapter 3: Manual Calculations 2. Try it! The Mendocino Tree, a coast redwood growing in Montgomery Woods State Reserve in California, is known to be the tallest living tree in the world. You are to find out how tall the tree is by using the following factors: • The distance from you to the bottom of the tree is exactly 505.8 feet, and the tree stands vertically. • T he angle of elevation between the top and the bottom of the tree is 36 degrees If the base length of the right triangle is 505.8 feet, and the angle of elevation is 36 degrees, then the following expression can be derived: the height of the Mendocino tree (ft.) = 505.8 ft. × tan(36°) CONCEPT 1. Verify/change the calculator’s angle unit. 2. U se the calculator’s trigonometric function key to enter/perform the calculation. PROCEDURE 1. S ince the angle of elevation is measured in degrees, the calculator’s angle setting will need to be matched with that. Press @ ; to bring up the SETUP menu. 2. O n the right side of the SETUP menu, the current setup will be displayed. Make sure that the top line is indicated as Deg (i.e., degrees). If not, then the angle system will need to be changed. Press B to select B DRG, then press 1 to select 1 Deg. 3. N ow, let’s work on the actual calculation part. Press the # key to enter the Calculation screen, and press C to clear 51 any screen entries. Chapter 3: Manual Calculations 4. Press 505.8 | 36. Press E to execute the calculation. 3. Arithmetic Keys Performing addition, subtraction, multiplication and division There are various keys for arithmetic calculations. Use the + - | =, _, ( and ) keys to perform basic arithmetic calculations. Press E to solve an equation. E Executes an expression. Example • Calculate 1 + 2. #C1+2E A Note about expressions An expression is a mathematical statement that may use numbers and/or variables that represent numbers. This works just like a regular word sentence; one may ask “how are you?”, and you may answer “okay.” But what if an incomplete sentence is thrown, such as “how are”? You’ll wonder, “how are... what?”; it just doesn’t make sense. A math expression needs to be complete as well. 1 × 2, 4x, 2sinx × cosx form valid expressions, while “1 ×” and “cos” do not. If an expression is not complete, the calculator will display an error message upon pressing the E key. + Enters a “+” sign for addition. Example • Calculate 12 + 34. # C 1 2 + 3 4 E - Enters a “–” sign for subtraction. Example • Subtract 21 from 43. 52 43-21E Chapter 3: Manual Calculations | Enters a “×” sign for multiplication. Example • Multiply 12 by 34. 12|34E = Enters a “÷” sign for division. Example • Divide 54 by 32. 54=32E When to leave out the “×” sign The multiplication sign can be left out when: a. It is placed in front of an open parenthesis. b. It is followed by a variable or a mathematical constant (π, e, etc.): c. It is followed by a scientific function, such as sin, log, etc.: _ Sets a negative value. Example • Calculate -12 × 4. _ 1 2 | 4 E Note: Do not use the - key to enter a negative value; use the _ key instead. ( ) Enters a closing parenthesis; a parenthesis left open will result in an error. Enters an open parenthesis. Use with “)” as a pair, or the calculation will result in an error. 53 Chapter 3: Manual Calculations Example • Calculate (4 + 6) ÷ 5. ( 4 + 6 ) = 5E Note: Functions, such as “round(”, automatically include an open parentheses. Each of these functions needs to be closed with a closing parenthesis. 4. Calculations Using Various Function Keys Use the calculator’s function keys to simplify various calculation tasks. s Enters a sine function to be used in a trigonometric calculation. Example • Calculate sine π . 2 s @ $ b 2 E c Enters a cosine function to be used in a trigonometric calculation. Example • Calculate cosine π . 3 [email protected]$b3E Enters a tangent function to be used in a trigonometric calculation. Example • Calculate tangent π . 4 E @$b4 s Enters an arcsine function to be used in a trigonometric expression. Example • Calculate arcsine 1. @s1E 54 Chapter 3: Manual Calculations c Enters an arccosine function to be used in a trigonometric expression. Example • Calculate arccosine 0.5. @ c 0.5 E Enters an arctangent function to be used in a trigonometric expression. Example • Calculate arctangent 1. @ 1E Note: Expressions with inverse trigonometric functions evaluate in the following ranges. -1 -1 θ = sin x, θ = tan x Deg:0 ≤ | θ | ≤ 90 Rad: 0 ≤ | θ | ≤ π Rad: 0 ≤ | θ | ≤ π Grad: 0 ≤ | θ | ≤ 100 Grad: 0 ≤ | θ | ≤ 200 2 -1 θ = cos x Deg: 0 ≤ | θ | ≤ 180 l Enters a “log” function for a logarithmic calculation Example • Calculate log 100. l 1 0 0 E 0 Enters a base of 10, setting the cursor at the exponent. Example • Calculate 5 × 105. 5 | @ 0 5 E 55 Chapter 3: Manual Calculations I Enters a natural logarithm function. Example • Calculate In e4. I @ @ 4 E. @ Enters the Euler Number e (2.71…) to a power. The cursor will then be placed at the exponent. Example • Obtain a value of e3. @ @ 3 E. y Squares the preceding number. Example • Obtain the answer to 122. (= 144) 12 y E Note: When no base number is entered, the base number area will be left blank and just the exponent appear. C y ;1 2 E x Enters “x-1”, and returns an inverse by raising a value to the -1 power. The inverse of “5”, for example, is “ 1 ”. 5 Example • Raise 12 to the -1 power. (= 0.083333333) [email protected] Note: When no base number is entered, “x-1” will be entered, with “x” left blank. C @ x ;1 2 E d Enters a mixed number. Example 5 • Enter 4 6 4 d 5 ' 6 56 Chapter 3: Manual Calculations Note: When no value is entered prior to this key, the number areas will be left blank. *If the calculator is set to one-line mode, d enters “ ” (integerfraction separator) only. Use d in combination with b as follows. 5 • Enter 4 6 in one-line mode 4 d 5 b 6 *Integer part of the mixed number must be a natural number. A variable can not be used. Equation or use of parenthesis, such as (1+2) 2¬3 or (5) 2¬3, causes syntax error. *When a numerator or a denominator is negative, the calculator will cause error. b Enters a fraction, setting the preceding number as its numerator. *If the calculator is set to one-line mode, then “¬” will be entered instead. For example, “2¬5” indicates “ 2 ”. 5 Example • Calculate 2 + 3 . 5 4 2b5'+b 3'4'E a Enters an exponent, setting the preceding number as its base. Example • Raise 4 to the 5th power. (= 1024) 4 a 5 E 57 Chapter 3: Manual Calculations Note: When no base value is entered, “ab” will be entered with both number areas left blank. C a ; 4 ' 5 E When calculating x to the power of m-th power of n, enter as follows; 2 • Calculate 23 (= 512) 2 a 3 a 2 E 2 The above calculation is interpreted as 23 = 29. If you wish to calculate (23)2 = 82, press ( 2 a 3 ' ) a 2 E. _ Enters “ a ”. Example • Bring 4 to the 5th root. (= 1.319507911) [email protected]_4E Note: When no depth of power is entered, “ a number areas left blank. ” is entered, with both C @ _ 5 ' 4 E + Enters a square root symbol. Example • Obtain the square root of 64. (= 8) @ + 6 4 E , Enters a comma “ , ” at the cursor. A comma is required in some of the MATH functions. ~ Sets the following value as θ, assuming the preceding value is the radius of the polar coordinates. #Enters i (representing numbers. 58 -1 ), to make imaginary or combination Chapter 3: Manual Calculations R Stores a number in a variable. Example • Let A = 4, and B = 6. Calculate A + B. 4 R A A E 6 R A B E AA+ABE r Recalls a variable. Example • Set C = 8. 8RACE Recall the value of C. @ r A C E X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically determined according to the calculator’s coordinate setup: “x” for rectangular, “θ” for polar, “T” for parametric, “n” for sequential. z Accesses the VARS menu. { } Enter braces to group numbers as a list. b Recalls the previous answer. Use this key to incorporate the answer to the previous calculation into an expression. Example • Perform 3 × 3. 3 | 3 E Subtract the value of the previous answer from “10”. [email protected] Note: b can be considered as a variable; its value is automatically set when E is pressed. If b is not empty, then pressing +, -, |, or = will recall “Ans” and places it at the beginning of an expression. If “1” was the previous answer, then pressing + 4 E will result in “5”. 59 Chapter 3: Manual Calculations e Recalls the previous entry. This is useful when you want to modify the previous entry, rather than reenter the whole expression over. Example • Calculate 4 × 6. 4|6E Next, calculate 4 × 8. @ e B 8 E Note: Executed expressions are stored in a temporary memory in the executed order. If the temporary memory is full, the oldest data is automatically deleted. Be aware that e may not function on these occasions. A maximum of 160 bytes can be stored in the temporary memory. The capacity may vary when there are division codes between expressions. When switching from equation edit mode to one-line edit mode in the SETUP menu, all the numerical and graph equations stored in the temporary memory are cleared and cannot be recalled. $ Enters “pi”. Pi is a mathematical constant, representing the ratio of the circumference of a circle to its diameter. Example • Enter “2π”. (= 6.283185307) [email protected]$E j Calls up the CATALOG menu. From the CATALOG menu, you can directly access various functions in the menus. • Functions are listed in alphabetic order. • Move the cursor using the { / } keys and press E to access or enter the function. • Press A and an appropriate alphabetic key (A to Z) to navigate the catalog. • Press A { / A } to scroll the catalog page by page and press @ { / @ } to jump to the beginning or the end of the catalog. • The functions accessible only from the CATALOG menu are: →a b/c, →A.xxx, →b/c, e, int÷, remain, rndCoin, rndDice, Simp, %. 60 Please refer to the following explanation. Chapter 3: Manual Calculations →a b/c Converts an improper fraction to a mixed number. Example 12 • Change 5 to a mixed number. 12 b 5 ' →a b/c E →A.xxx Converts a fraction to a decimal number. Example 12 • Change 5 to a decimal number. 12 b 5 ' →A.xxx E →b/c Converts a mixed number to an improper fraction. Example 2 • Change 2 5 to an improper fraction. 2d2' 5' →b/c E Note:Above three conversions will not affect the ANSWER settings in the SET UP menu. If a decimal number is not rational, fraction conversion will not function and display the answer in decimal format. About →a b/c and →b/c • Only a value that can be converted to a fraction is displayed in a fraction form. • Only a rational number within 10 digits can be simplified, if Manual is selected in the SETUP menu, item H SIMPLE. (Default setting is Auto for simplifying fractions.) • A List or Matrix format can be used. (The elements of a list and matrix of the calculation results are in one line.) e Enter the euler number. Example e E 61 Chapter 3: Manual Calculations int÷ Executes an integer division and returns its quotient and remainder. Example • Get a quotient and a remainder of 50 ÷ 3. 50 int÷ 3 E * Quotient value is set to Ans memory and remainder is not stored. remain Returns the remainder of a division. Example • Obtain the remainder when 123 is divided by 5. 1 2 3 remain 5 E rndCoin Returns a specified number of random integers to simulate a coin flip: 0 (head) or 1 (tail). The size of the list (i.e., how many times the virtual coin is thrown) can be specified. (The same as rndInt (0, 1, number of times)) Example • Make the calculator flip a virtual coin 4 times. rndCoin ( 4 ) E Returns specified number of random integers (1 to 6) to simulate rndDice rolling dice. The size of the list (i.e., how many times the die is thrown) can be specified. (The same as rndInt (1, 6, number of times)) Example • Make the calculator roll a virtual die 11 times. rndDice ( 11 ) E 62 Note: The random functions, (rndCoin and rndDice)will generate different numbers every time. Chapter 3: Manual Calculations Simp Simplifies a given fraction stored in the ANSWER memory. • Set the ANSWER mode to Mixed(Real) or Improp (Real), and the SIMPLE mode to Manual in the SETUP menu to use this key. Specifying no common factor Simplify the fraction using the lowest common factor other than 1. Example 1 b 12 ' + 5 b 12 E Simp E (Simplified by 2, the lowest common factor of 12 an 6.) Simp E (Simplified by 3, the lowest common factor of 6 and 3.) Specifying a common factor Simplify the fraction using the specified common factor. Example 1 b 12 ' + 5 b 12 E Simp 6 E (Manually specify 6, the Greatest Common Factor of 12 and 6, to simplify the fraction.) Note:If the wrong number is specified for a common factor, an error will occur. Simp is effective in a fraction calculation mode only (when the ANSWER mode is set to Mixed(Real) or Improp(Real) in the SETUP menu). 63 Chapter 3: Manual Calculations % Set the preceding value as a percentage. Example • Get 25% of 1234. 1 2 3 4 | 2 5 % E * Percentage must be a positive value equal to or less than 100. Note : • The CATALOG commands and the equivalent keys: CATALOG command ¬ Equivalent key ^ a 2 y -1 x b R C M C nCr P M C nPr d • Sequen and Simul features can also be accessible from the CATALOG menu. 64 Chapter 3: Manual Calculations 5. More Variables: Single Value Variables and LIST Variables Additional single value variables (from A to Z, and θ) may be accessed. In addition, six LIST variables (from L1 to L6) are readily accessible through the second function. To save a list of numbers, follow the procedure below: 1.On the Calculation screen (#), create a list of numbers (“1, 2, 3”, in this example). Separate numbers with a comma (,), and group the numbers with braces ({ and }). 2.Press R, then select one of the six LIST variables. To store the list in “L1”, press @ 1 to call up the LIST variable. 3.Pressing E will store the list in the LIST variable. Note that this procedure will overwrite the list previously stored in the LIST variable. Refer to Chapter 7 “LIST Features” to learn more about how LIST variables can be utilized. 6. TOOL Menu The TOOL menu contains items to help calculating in different number systems, as well as to help solve both linear and polynomial equation. Press @ V to access the TOOL menu. Press the # key (or @ q) to escape from the menu. A NBASE Calculations can be performed in different number base systems, while simultaneously converting the calculation result into hexadecimal, decimal, octal, and binary systems. 1.While this menu item A NBASE is selected, press the E key. The NBASE tool opens, with the cursor set at HEX: (hexadecimal). 65 Chapter 3: Manual Calculations 2.Type 1B | 9, for example. When entering the hexadecimal B, simply press the B key; using the A key will call up the variable B instead. 3.When done entering the hexadecimal expression, press E. The calculation result will be displayed in three other number base systems, as well as in hexadecimal format. Note :Numerical values in binary, octal, and hexadecimal modes can be expressed in the following number of digits: Binary: 16 digits Octal: 10 digits Hexadecimal: 10 digits If you enter a number exceeding the range specified above for calculations or conversions, the calculator will return an error. If the answer exceeds the above range, the calculator will also return an error. Decimals can be used for DEC mode only (. cannot be used in the other modes). If you convert decimal values to binary, octal, or hexadecimal number, the decimal part is discarded and only the integer part is converted. When numerical values of binary, octal, and hexadecimal modes are negative, the display is switched to complements of 2. B SYSTEM With this tool, linear equations containing up to 6 unknown values (i.e., ax + by + cz + du + ev + fw = g) can be solved. 1.Press B to select B SYSTEM, and select the number of unknown values. For example, press 2 if values x and y are unknown. 2.In the next screen, an equation ax + by = c is displayed, with an entry table for the known values — a, b, and c. 3.Enter 2 sets of the known values, as shown in the figure. Pressing E at each entry will store the value, and sets the cursor at the next entry area. 66 Chapter 3: Manual Calculations 4.When done entering the known values, press @ h. The calculation result will be displayed on the next screen. Pressing C will bring back the previous entry screen. 5.To go back to the TOOL menu to perform another calculation, press @ V. C POLYThis tool is designed so that quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0) equation may be solved. 1.Press C to select C POLY, and select the degree. For example, press 2 if a quadratic equation is desired. 2.In the next screen, an equation ax2 + bx + c = 0 is displayed, with an entry area for the known values — a, b, and c. 3.Enter the values, as shown in the screen to the right. Pressing E at each entry will store the value, and sets the cursor at the next entry area. 4.When done, press @ h to execute the calculation. The results (i.e. the x-intersects) will be displayed. 5.To enter a different set of numbers for a, b, and c, press C to go back to the previous screen. To select a different degree of polynomial, press @ V to go back to the TOOL menu. • If the solution cannot be displayed on the screen, a symbol will appear at the bottom left corner of the screen. Press } to scroll the screen. 67 Chapter 4 Graphing Features 1. Try it! There are two taxi cab companies in your city, Tomato Cab and Orange Cab, with different fare systems. The Tomato Cab charges 2.00 Euro upon entering the taxi cab, and 1.80 Euro for each mile the taxi travels. The Orange Cab, on the other hand, charges 3.50 Euro plus 1.20 Euro per mile. This means that taking the Tomato Cab will initially cost less than going with the Orange Cab, but will be more expensive as you travel longer distances. Suppose you need to go to a place 3 miles away from where you are now. Which cab company should you take to save money? Two math expressions can be derived from the above fare systems. If “y” represents the cost, while “x” represents the mileage, then: y = 2 + 1.8x.................... Tomato Cab’s fare system y = 3.5 + 1.2x................. Orange Cab’s fare system Use the calculator’s graphing capabilities to figure out the approximate point where the Orange Cab gets ahead of the Tomato Cab, in terms of cost performance. CONCEPT 1. By using two linear graphs, the approximate crossing point can be found. 2. The exact crossing point can be found with the TABLE function. 68 Chapter 4: Graphing Features PROCEDURE 1. Press Y to enter the Graph Equation window. Six equation entry areas appear, from “Y1=” to “Y6=”. Since we need only two equations in this exercise, let’s use “Y1=” and “Y2=”. 2. By default, the cursor should be placed on the right side of the “Y1=” equation, next to the equal sign. If this is not so, use the cursor keys to bring the cursor to the “Y1=” line, then press the C key to clear any entries. The cursor will automatically be placed to the right of the equal sign. 3. Enter the first equation, “2 + 1.8X”, to represent the Tomato Cab’s fare system. 2 + 1 . 8 X Use the X key to enter the “x”, representing the distance in miles. 4. When the equation line is complete, press E. The first equation is now stored, and the cursor automatically jumps to the second line, where the second equation can be entered. 5. At the second line, press C to clear any entries, then enter “3.5 + 1.2X” to represent the Orange Cab’s fare system. When done entering the equation, press E. The two equations are now ready to graph. 6. Press G to draw the graphs. To draw a graph, “=” must be highlighted. If not, move the cursor to “=” of the targeted equation and press E to draw a graph, and press E again not to draw a graph. Graph Basics The graph examples in this exercise are called X-Y graphs. An X-Y graph is quite useful for clearly displaying the relationship between two variables. 69 Chapter 4: Graphing Features 7. Let’s take a look at the graph. The vertical axis represents the Y value, while X is represented by the horizontal axis. It appears that the two diagonal lines cross at the point where the X value is somewhere between 2 and 3, indicating that Orange Cab costs less than the other, after 3 miles of traveling. 8. Next, press t to find the values per graph increment. When the traveling distance is 2 miles, the Tomato Cab charges 30 cents less overall than the Orange Cab, but it costs 30 cents more at 3 miles. To make the X increment smaller, press @ y. 9. When the Table setting window appears, move the cursor down to “TBLStep”, type . 5, and press E. Now the Y values will be sampled at every 0.5 mile. 10.Press t to show the table again. It indicates that when the X value is 2.5, both Y1 and Y2 values are 6.5. It is now clear that if you are traveling 2.5 miles or more, the Orange Cab costs less. 70 Chapter 4: Graphing Features 2. Try it! You have just opened your own bank account, with an initial deposit amount of 2000 Euro. Suppose your monthly income is 3000 Euro, and you will spend 60 percent of what you have in the account every month, how much will your balance be after one year? How much will you have in the account, 6 months from now? The example can be expressed as a sequential equation, as follows: un = un–1 × (1 – 0.6) + 3000 where un is the balance of the current month and un–1 is the balance of the previous month, and n is the month. CONCEPT 1. Grasp the idea of sequential equations. 2.Use the graph tracing function to obtain approximate values. 71 Chapter 4: Graphing Features PROCEDURE 1. F irst, let us set the calculator to the appropriate graphing coordinate mode. Press @ ; to enter the SETUP menu, press E to select E COORD, then press 4 to select 4 Seq, and press C. 2. W e will use the “Time” sequential graph type within the FORMAT menu. Press @ f, press G to select G TYPE, and 2 to select 2 TIME. 3.Then press Y. The Graph Equation Entry window will open. 4. E nter a new equation set u(n1) × (1 - 0.6) + 3000 for u(n)=. Press @ u (7) to enter u and press X for n. Press E when done entering. Note: P ress C to clear the previous entry. Using a capitalized “U” or “N” here will result in an error upon pressing the G key. 5. On the second entry row (u(nMin) =), enter 2000, then press E. The figure is automatically enclosed by braces. 6.The v and the w entry sets will not be necessary in this case, so press C to clear, then press E to move one row down. Repeat until the four unnecessary entry rows are cleared. 7. Press G to draw the graph. 8. If the line is outside of the graph’s range, press Z then 1 to select automatic zoom. This will only display a small portion of the graph, so the graph’s range will need to be changed. 72 Chapter 4: Graphing Features 9. Press W. Find nMax= and change the value to 15 (default: 10). Next, find Xmax= and change the value to 15 too (default: 10). 10.Press the G key again. 11.Use the graph trace function by pressing U. As ' is pressed several times, the n value (=X value, since the graph is set to “Time” format) increases, and the Y value (the balance of your account) will change. Find the Y value when the n value is 6 (after 6 months) as well as the value when n=12 (after 12 months = 1 year). You can obtain the value directly from the CALC menu. 1. Press @ k and select 1 VALUE. n= will appear on the bottom line of the screen. 2. Enter the n value of 6, and press E. 3. Follow the procedure 1 to 2 to obtain the Y value for 12. 73 Chapter 4: Graphing Features 3. Explanations of Various Graphing Keys The explanations in this section are based on the rectangular coordinates (COORD RECT). Y: Displays the Graph Equation window. Up to 10 different equations can be entered. After the graph expression is entered, press E to store the equation. = : The expression can be represented as a graph. = : The expression cannot be drawn as a graph. • Move the cursor pointer to the “=” sign and press E to change between to-draw and not-to-draw. Note: To switch the window back to the calculation screen, simply press the # key. G: Draws a full-screen graph based on the equation(s) entered in the Graph Equation window. To cancel the graph drawing, press O. Note: If no equations are entered in the Graph equation window, only the vertical (Y) and horizontal (X) axis will be displayed upon pressing the G key. t: Displays the graph values in a table. The default sample increment value of the graph’s X axis is “1”. See “11. Tables” on page 93. W: Displays the graph window setup. The setup values — the minimum/maximum X/Y values, and X/Y-axis scale — can be changed manually: 1. While the graph is displayed on the screen, press the W key. The following window appears, with the cursor set at “Xmin=”. 2. The required X-minimum value can be entered here. This limits the left boundary of the graph window. For example, if “Xmin=” is set to “0”, then the portion of the graph’s Y-axis to the left will not be displayed. 3. Once the “Xmin=” value is entered (“0”, for example), press E. The left limit of the graph is now set, and the cursor moves to “Xmax=”. 74 4. Now the right boundary of the graph can be set. Enter the required value here (“3”, for example), and press E. Chapter 4: Graphing Features Note: The “Xmax=” value cannot be set equal to or smaller than the value of “Xmin”. If so done, the calculator will display an error message upon attempting to redraw the graph, and the graph will not be displayed. 5. The next item “Xscl=” sets the frequency of the X-axis indices. The default value is “1”. If, for example, the value is set to “0.5”, then indices will be displayed on the X-axis at increments of 0.5. Enter the required “Xscl=” value (“0.5”, for example), and press E. 6. The “Ymin=”, “Ymax=”, and “Yscl=” can be set, as was described for “Xmin=”, “Xmax=”, and “Xscl=” above. 7. When done, press the G key to draw the graph with the newly configured window setup. See “10. Setting a Window” on page 92. Z: Displays the ZOOM menu. Within the ZOOM menu, various preferences can be set for the graph appearance on zooming in/ out. The menu items with each function and the sub-menu items are described below: A ZOOM 1 Auto According to the WINDOW setup, the graph will be zoomed in by adjusting the “Ymin” (the minimum Y value) and “Ymax” (the maximum Y value) according to the “Xmin” (the minimum X value) and “Xmax” (the maximum X value). When this item is selected, the graph will automatically be redrawn. Note: The “Auto” sub-menu item is directly affected by how the WINDOW items are set up. Refer to the W key section in this chapter to learn how to set up the Xmin and Xmax items. 2 Box A box area can be specified with this sub-menu tool so that the area within the box will be displayed full screen. To select a box area to zoom: 1. W hile the ZOOM menu item is selected within the ZOOM window, press 2 to select 2 Box. 2.The graph appears on the screen. Use the cursor keys to position the cursor at a corner of the required box area. Press E to mark the point as an anchor. 75 Chapter 4: Graphing Features 3.Once the initial anchor is set, move the cursor to a diagonal corner to define the box area. When the required area is squared off, press E. If a mistake is made, the anchor can be removed by pressing the C key. 4. The graph will automatically be redrawn. 3 In A zoomed-in view of the graph will be displayed, sized according to the B FACTOR set up under the ZOOM menu. For example, if the vertical and horizontal zoom factors are set to “2”, then the graph will be magnified two times. Refer to the B FACTOR segment of this section for more information. 4 Out The graph image will be zoomed out according to the B FACTOR setup under the ZOOM menu. 5 Default The graph will be displayed with default graph setting (Xmin = -10, Xmax = 10, Xscl = 1, Ymin = -10, Ymax = 10, Yscl = 1) 6 Square Set the same scale for X and Y axes. The Y-axis scale is adjusted to the current X-axis scale. The graph will be redrawn automatically. 7 Dec Sets the screen dot as 0.1 for both axes. The graph will then be redrawn automatically. 8 Int Sets the screen dot as 1.0 for both axes. The graph will then be redrawn automatically. 76 9 Stat Displays all points of statistical data set. Chapter 4: Graphing Features B FACTOR Use this menu to set the vertical and horizontal zooming factor. The factor set under this menu directly affects the zoom rate of the 3 In and 4 Out sub-menu tools under the ZOOM menu, as described above. To set the zooming factor, do the following: 1.Within the B FACTOR menu, press E to activate the setup tool. 2. W hen the “Zoom factor” window appears, the cursor is automatically placed at “X_ Fact=”. The default zoom factor is 4; enter the required value here. 3. P ressing E after entering a value will switch the cursor position to “Y_Fact=”. Enter the required zooming factor, and press E. 4. To go back to the ZOOM menu, press the Z key. C POWER 1 x2 Use this zooming tool when the equation contains a form of “x2”. 2 x–1 Use this zooming tool when the equation contains a form of “x-1”. 3 x Use this tool to zoom correctly when the equation contains a form of “ x ”. D EXP 1 10X Use this tool when the equation contains a form of “10 ”. 2 ex Use this tool when the equation contains a form of “e ”. 3 log X Use this tool when the equation contains a form of “log x”. 4 In X Use this tool when the equation contains a form of “In x”. x x E TRIG 1 sin X Use this when the equation contains a sine function. 77 Chapter 4: Graphing Features 2 cos X Use this when the equation contains a cosine function. 3 tan X Use this when the equation contains a tangent function. 4 sin–1 X Use this when the equation contains an arc sine function. 5 cos–1 X Use this when the equation contains an arc cosine function. 6 tan–1 X Use this when the equation contains an arc tangent function. F HYP 1 sinh X Use this when the equation contains a hyperbolic sine function. 2 cosh X Use this when the equation contains a hyperbolic cosine function. 3 tanh X Use this when the equation contains a hyperbolic tangent function. 4 sinh-1 XUse this when the equation contains an inverse hyperbolic sine function. 5 cosh-1 XUse this when the equation contains an inverse hyperbolic cosine function. 6 tanh-1 XUse this when the equation contains an inverse hyperbolic tangent function. G STO Under this menu item there is one tool that enables the storing of graph window settings. 1 StoWin B y selecting this sub-menu item, the current graph window setup will be stored. Note: The actual graph image will not be stored with this tool. H RCL Under this menu item there are two tools that enable the recalling of the previous graph window setup: 78 1 RclWin O n selecting this sub-menu item, the previously stored window setup will be recalled, and the graph will be redrawn accordingly. If no window setup has been stored previously, the default graph window setup will be used. Chapter 4: Graphing Features 2 PreWin O n selecting this sub-menu item, the window setup prior to the current zoom setup will be recalled, and the graph will be redrawn accordingly. U: Press this button to trace the graph drawn on the screen, to obtain the X-Y coordinates: 1. While the graph is displayed, press the U key. The cursor appears, flashing on the graph line, with the present X-Y coordinates. 2. Trace the graph using the ; or ' keys. The ; key decreases the value of x, while the ' key increases it. 3. Pressing the U key again will redraw the graph, with the cursor at the center of the screen. If the cursor is moved beyond the range of the screen, pressing the U key will redraw the screen centered around the cursor. 4. When done, press the C key to escape the tracing function. If more than one graph is displayed on the screen, use the { or } keys to switch the cursor from one graph to the other. Note: If the U key is not activated, the cursor will not be bound to the graph. Pressing the ;, ', {, or } keys will position the free-moving flashing cursor on the graph display. 4. Graph Modes • This calculator has four graph modes (rectangular coordinate graph, parametric coordinate graph, polar coordinate graph, and sequence graph): • To select a mode, use the SETUP menu (E COORD). Rectangular (X-Y) coordinates Parametric coordinates Polar coordinates Sequence coordinates 79 Chapter 4: Graphing Features 5. Graphing Parametric Equations A two-dimensional parametric equation assumes that both X and Y are represented by functions in a third variable T. When set in parametric graphing mode, the calculator automatically sets up the Graph Equation Entry screen to take one set of X and Y per each graph, with the equation’s right side variable to be set as “T”. Example • Draw a graph: x(t) = 16cos(t), y(t) = 9sin(t). 1. Press @ ; to enter the SETUP menu. 2. Press E to select E COORD, then 2 to select 2 Param. Be sure that the other settings are as shown on the right. To exit the SETUP menu, press C. 3. Press Y to go to the Graph Equation Entry window. 4. Enter 16cos(t) for X1T=. Press E when done entering. 5. Enter 9sin(t) for Y1T=. Press E when done entering. Note: The right side variable is automatically set to “T”. When the X key is pressed within the Graph Equation Entry window, it will enter the variable “T”. 6. Press G to draw the graph. 7. If the graph line extends beyond the screen, press Z and select A ZOOM then 1 AUTO. Use 3 IN or 4 OUT of the A ZOOM to adjust the drawing size. 80 You can also set the drawing size in the WINDOW menu by determining the maximum and minimum values of T, X and Y. Chapter 4: Graphing Features 6. Polar Graphing Polar coordinates are a different method of specifying a point in two dimensions; the location of the point is described by the distance from the X-Y intersect “r”, and its elevation angle “θ”. r θ Example • Draw a graph: r = 16cos(θ)sin(θ). 1. Press @ ;. The SETUP menu appears. 2. Press E to select E COORD, then press 3 to select 3 Polar. Be sure that the other settings are as shown on the right. To exit the SETUP menu, press C. 3. Press Y. The Graph Equation Entry window will appear. 4. At the first entry row R1=, enter 16cos(θ) × sin(θ). Press E. 5. Press G to draw the graph. Press Z, then press 6 to select 6 Square. 81 Chapter 4: Graphing Features 7. Graphing Sequences The Setup setting COORD Seq enables you to input and draw up to three explicit or recursive sequence equations u(n), v(n), w(n) . Variables u, v and w are entered as @ 7, @ 8, and @ 9 respectively. Use X to enter the natural number n. A sequence is an ordered, numbered series of numbers. Sequence equations may be recursive or explicit. In an explicit equation, only the variable n is used to calculate the nth sequence element, and in a recursive equation only the value of u(n-1). Using the sequence {1, 2, 4, 8, 16, 32, …} as an example, this means: n u(n) = 2 (explicit representation) u(n) = 2 u(n-1) (recursive representation) In @ f G (TYPE) five different settings are possible for drawing sequences. The default setting is Time. If the expected graph is not drawn or the error message “Invalid” appears this may be caused by an incorrect setting for TYPE. For base n (Time) The values of n are plotted along the X-axis and the values of the sequence elements along the Y-axis. uv setting u(n) is plotted along the X-axis, and v(n) along the Y-axis. The uw and vw settings are analogous. Web setting Here, the X-axis represents u(n-1) and the Y-axis u(n). When using this setting, a recursive sequence representation is mandatory. 82 Chapter 4: Graphing Features Example 1: Sequence representation when using the Time default setting Draw the sequence u(n) = 2 n First, ensure that the graphic coordinates are set to sequential (See page 72). 1.Use @ f to navigate to the Format menu. 2. Select G (TYPE) 2 (Time). 3. By pressing Y you now enter the input window for sequence equations. The cursor is placed on the first line, u(n); pressing C will delete existing entries and the cursor will be moved to the right side of the equation. n 4.Input 2 . Use the X key to input n. And input 1 for u(nMin). 5. Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically. 6.Using U, you can now read concrete values of the sequence. 83 Chapter 4: Graphing Features Example 2: Representation using the uv setting (n-1) Compare 2 × 0.9 with the sequence previously input. n Sequence 2 is still stored in u(n) from the previous example. Now, sequence v(n) is to be defined and the representation type to be changed. 1. Press @ f G 3 to select uv. 2. Press Y and input the (n-1) equation 2 × 0.9 in the v(n) v(nMin). line. And input 1 for 3. Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically. Using U, you can now read concrete values of both sequences. If a third sequence equation is input in w this can be compared with the first sequence using TYPE setting 4 uw and, using setting 5 vw, with the second sequence. 84 Note: Attempting to compare a sequence with an incomplete entry will result in an error. Chapter 4: Graphing Features Example 3: A representation using the Web TYPE setting View the sequence u(n) = u(n-1) + 100 by comparing the sequence elements u(n) with the predecessor elements u(n-1) . 1. Press @ f G 1 to select Web. 2. Press Y and input the equation in the u(n) line. Because this is a recursive representation, a value for u(nMin) must be input. 3. If the lower four lines still contain entries, move the cursor down and delete them using C. 4. Select Z A 1 for the automatic zoom function in order to set suitable window settings automatically. Using U, you can now read concrete values of the sequence. 85 Chapter 4: Graphing Features 8. The CALC Function The CALC function utilizes the entered graph equation to calculate values. In conjunction with the 4 graph coordinates, it can be called up anywhere. Note however that the CALC function will not do anything if no graph equation has been entered or specified. The following is an example that uses the previously entered polar graph equations above. 1. First, verify the graph coordinate mode by pressing @ ;; check to see if E COORD is set to Polar. If not, this will need to be changed accordingly. Also, make sure the angle unit B DRG is set to Rad. Otherwise the graph will not be drawn correctly. Press @ f, press F to select F CURSOR, and 2 to select 2 PolarCoord. 2. Press Y to verify the previously entered polar graph equation, then press G to draw the graph. Adjust the view by using Z menu items. 3. Press @ k. 4. Press 1 to select 1 Value. The graph is drawn back on the screen again, with the θ= prompt visible at the bottom left side of the screen. 5. Enter the θ value at the prompt. Enter π, for example. Be aware that θ cannot be more than 2π (2π radians = 360 degrees). 6. Upon pressing E, the radian r coordinate will be calculated. 86 Chapter 4: Graphing Features Specific submenus Note: When coordinate system is Polar, Param or Seq, only 1 Value is selectable in the CALC menu. 1 Value With this sub-menu tool, the Y value can be obtained by entering an X value. The flashing graph cursor will then be placed in that position on the graph. If more than one graph equation is set, use the { or } keys to switch to the equation you wish to work with. Note: If the entered X value is incalculable, an error message will be displayed. Also, if the Y value exceeds the calculation range, then “----” will be displayed instead. 2 Intsct With this tool, the intersection(s) of two or more graphs can be found, where the flashing cursor will be placed. When the intersection is found, then the X-Y coordinates of the intersection will be displayed at the bottom of the screen. If there is more than one intersection, the next intersection(s) can be found by selecting the tool again. Note: If there is only one graph equation entered there will be no other graph(s) to form an intersection, so selecting this tool will result in an error. 3 Minimum Finds the minimum of the given graph, and places the flashing cursor at that position. Note: If the given graph has no minimum value, an error message will be displayed. If there are several minimum values, please use this function again. 87 Chapter 4: Graphing Features 4 Maximum Finds the maximum of the given graph, and places the flashing cursor at that position. Note: If the given graph has no maximum value, an error message will be displayed. If there are several maximum values, please use this function again. 5 Y_zero Finds an Y_zero (a intersect point or a contact point of the graph on the X-axis) of the given graph, and places the flashing cursor at that position. If there is more than one Y_zero, the next Y_zero can be found by selecting the tool again. Note: If the graph has no Y_zero, an error message will be displayed. 6 Y_Incpt Finds an Y-intercept of the given graph, and places the flashing cursor at that position. Note: If the graph has no Y-intercept, an error message will be displayed. Note: The result may be different when the ZOOM function is used. 7 Inflec Calculates the inflection point of the given graph and moves the cursor to that point. Example 1. Enter the graph equation Y1 = x3 – 3x2 + 2. 2. Press @ k 7. 88 Chapter 4: Graphing Features 8 ∫ dx Calculates the numerical integral of equation and display it on a graph. Example 1. Enter the graph equation. Y1 = – x2+ 5. 2. Press @ k 8. 3.Move the cursor to the point of lower and press E. • The line is drawn between the point of lower and X axis. 4.Move the cursor to the point of upper and press E. • The calculation result is displayed and shaded on the graph. Note: In the step 3 and 4, it is also possible to input the X value and press E. 89 Chapter 4: Graphing Features 9. Format Setting You can set up the Graph screen format from the FORMAT menu. Press @ f to display the Graph format menu. Specific sub-menus Note: G TYPE appears only when the sequence coordinate graph mode is selected. A – – – – – – Displays the current FORMAT settings. The default setting is: EXPRES ON (for the graph equation to be displayed on the graph) Y’ OFF AXIS ON GRID OFF (for displaying a grid on the graph) CURSOR RectCoord (for displaying the cursor location) (for displaying numeric derivatives on the graph) (for displaying the X/Y axis on the graph) B EXPRES This sets whether or not graph equations are displayed on the graph screen (in the trace mode, etc.). To not display the equations on the graph, select 2 OFF by pressing 2 at this menu item. C Y’ The numeric derivative (dx/dy) can be displayed on the graph screen (in the trace mode, etc.). To activate this function, select 1 ON by pressing 1 at this menu item. D AXIS The graph axis can be set invisible with this menu item. To hide the X/Y axis of the graph, select 2 OFF by pressing 2 at this menu item. E GRID The graph display can be backed with an X-Y grid. To show the grid on the graph, select 1 ON by pressing 1 at this menu item. 90 F CURSOR The coordinate system that indicates the location selected by the trace or other function can be selected from 1 RectCoord (Rectangular coordinates) or 2 PolarCoord (Polar coordinates) (In the parametric system, the T indication is added.) Chapter 4: Graphing Features G TYPE This menu is only active when the sequence coordinate graph mode is selected in the SETUP menu. The G TYPE menu will not appear in the other modes. A web graph plot mode where x = u(n-1) and y = u(n). 1 Web 2 TimeTime graph plot mode where x = n and y = u(n), v(n), w(n). (default) 3 uv A uv mode where x = u(n) and y = v(n). 4 uw A uw mode where x = u(n) and y = w(n). 5 vw A vw mode where x = v(n) and y = w(n). Note: u(n), v(n) and w(n) indicate the n-th term of the sequences. 91 Chapter 4: Graphing Features 10. Setting a Window The W key displays the graph window setup. The display will differ according to the selected coordinate system. Rectangular coordinate system Xmin/Xmax Minimum and maximum values of x-axis, respectively Xscale Scale of x-axis Ymin/Ymax Minimum and maximum values of y-axis, respectively Yscale Scale of y-axis Parametric coordinate system Tmin/Tmax Minimum and maximum values for T, respectively Tscale Cursor pointer step value for tracing Others Same as rectangular coordinate system Polar coordinate system θmin/θmax Minimum and maximum angle for θ, respectively θstep Cursor pointer step value for tracing Others Same as rectangular coordinate system Sequential coordinate system nMin/nMax Minimum and maximum value for n, respectively PlotStart Starting value of sequential variable n PlotStep Increments of sequential variable n 92 Others Same as rectangular coordinate system Chapter 4: Graphing Features 11. Tables The calculator enables you to illustrate the changes using the equation and graph you have input. It also has tables for showing a list of X and Y values. Each column item can display up to 7 digits, including a sign and/or a decimal point. There are four kinds of tables available corresponding to the coordinate system. Rectangular coordinate system • The variable X is displayed in the left end column. • The columns Y1 to Y3 are displayed on the first screen. • Press ; ' to horizontally scroll the table. (The variable X is always displayed in the left end column.) • The 10-digit value in the column where the cursor is currently located is displayed on the bottom line of the screen. • Move the cursor using ; ' { }. • Non-input equation numbers and equations invalid for graphing will not be displayed in the above table. Parametric coordinate system • The variable T is displayed in the left end column. • The columns X1T, Y1T, and X2T are displayed on the first screen. • Press ; ' to horizontally scroll the table. • The 10-digit value in the column where the cursor is currently located is displayed on the bottom line of the screen. • Move the cursor using ; ' { }. • Non-input equation numbers and equations invalid for graphing will not be displayed in the above table. 93 Chapter 4: Graphing Features Polar coordinate system • The variable θ is displayed in the left end column. • The columns θ, R1 to R3 are displayed on the first screen. • Press ; ' to horizontally scroll the table. • The 10-digit value in the column where the cursor is currently located is displayed on the bottom line of the screen. • The cursor can be moved using ; ' { }. • Non-input equation numbers and equations invalid for graphing will not be displayed in the above table. Sequential coordinate system • The variable n is displayed in the left end column. • Tables values u(n), v(n), and w (n) are simultaneously displayed. • The 10-digit value in the column where the cursor is currently located is displayed on the bottom line of the screen. • The cursor can be moved using ; ' { }. • Non-input equation numbers and equations invalid for graphing will not be displayed in the above table. Setting a table • To display the table, press t. • Table setting allows you set how to input data for a table. • Press @ y to enter the table setting screen. • The cursor is initially located at Auto, showing the variable input method. 94 Auto: Automatically creates a table based on the graph equations and given TableStart and TableStep values. User: Displays a blank table. As you input values for variable columns, table values are automatically calculated by the equation. Thus, although TableStart and TableStep inputs can be made when selecting User, set values will be ignored. Chapter 4: Graphing Features • Press ; or ' to switch between Auto and User. • TableStart is a start value of the variable in the table, and TableStep is a step value of the variable. Both are numeric values. Example Automatically create a table starting from -5 with a step of 1 in the X-Y coordinate after equations, based on “Y1 = X”, “Y2 = X2”, and “Y3 = -X2 + 3”. 1. Press @ y and } _ 5 E 1 E. 2. Press t. *If the cursor is on the top or bottom line of the table, { or } can still be used. The table contents will move to become visible in the display area. Example Create a table in the User mode under the above conditions. 1. Press @ y and 'E}0E 1 E. 2. Press t. Blank table will appear. 3. Press 2 E _ 3 E to enter X values. * An automatically created table in the User mode cannot be scrolled vertically. Note: While the table is in the User mode, a selected row can be deleted by pressing D. 95 Chapter 4: Graphing Features 12. The DRAW Function With the DRAW function, lines, circles, graphs, and pixel points can be added to the graph window. The DRAW menu also contains configuration tools for the ordinary graphs entered in the Graph Equation Entry window: line types, shading, and visibility status of each graph. Press @ d to enter the DRAW menu. Note: When entering coordinates, the DRAW function assumes that rectangular coordinates will be entered. The exception to this is for PxlON(, PxlOFF(, PxlCHG(, and PxlTST(, all within the B POINT menu item. A DRAW The tools in this menu add lines, circles, additional graphs and text on the graph screen. The tools below can be accessed from the GRAPH window, or any other windows such as the Graph Equation Entry window and Calculation screen. Most of these tools, such as Line(, can be entered directly onto a graph from the cursor point. 01 ClrDraw Clears all items on the graph window EXCEPT for the graphs entered via the Graph Equation Entry window. 1. From the GRAPH window, press @ d to enter the DRAW menu. 2. Press A to select A DRAW, then press 0 1 to select 1 ClrDraw. or 1. From the Calculation screen, press @ d A 0 1. “ClrDraw” will appear. 2. Press E. 96 All the items on the graph will be deleted and the message “Done” will appear. Chapter 4: Graphing Features 02 Line( Draws a line according to the given X-Y coordinates of a start/end point. Note: This tool can be used with any type of graph. From the Calculation screen Line(x-coordinate of start point, y-coordinate of start point, x-coordinate of end point, y-coordinate of end point [,0]) Example 1. Select the DRAW menu. Select A DRAW in the menu, then select 02 Line(. “Line(” will appear. Suppose you wish to draw a line, starting from an X-Y coordinate (1,2) to end at (8,8). 2. Enter “1,2,8,8” right after the “Line(” object, then close the expression with ). 3. Press E. The GRAPH window will appear with the specified line drawn on the graph. Note: If you enter 0 for the 5th element of Line( function, (e.g. Line(1,2,8,8,0)) and press E, you can clear the specified line. From the GRAPH window Line( 1. Press @ d to enter the DRAW menu. 97 Chapter 4: Graphing Features 2. Press A to select A DRAW, then press 0 2 to select 02 Line(. The GRAPH window reappears, with the coordinate of the cursor showing at the bottom of the screen. Note: To change the cursor coordinate system, use the FORMAT menu. Select F CURSOR, then select the required coordinate system for the cursor. 3. Move the flashing cursor on the screen to set the starting point of the line. Note: The pixel increment can be set within the ZOOM menu. While A ZOOM is selected, choose 7 Dec to set each pixel size to “0.1 × 0.1”, or 8 Int to set to “1 × 1”. 4. When the starting point is set, press E to anchor the location. 5. Move the cursor to indicate the end point of the line. When set, press E to finalize the line drawing. 6. You may draw as many lines as you wish, by repeating the procedure from 4 to 5. When done drawing, press C to exit the entry mode. 98 Chapter 4: Graphing Features 03 H_line From the Calculation screen Draws a horizontal line on the graph window. H_Line y-value Draws a horizontal line (y = value) on the graph window. Example • Draw a horizontal line of y = 5. 1. Press @ dA 0 3 and enter the value 5. From the GRAPH window H_Line Example • Draw a horizontal line manually. 1. Press @ dA 0 3. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3. Press E to draw the line. 99 Chapter 4: Graphing Features 04 V_line From the Calculation screen Draws a vertical line on the graph window V_Line x-value Draws a vertical line (x = value) on the graph window. Example • Draw a horizontal line of x = 3. 1. Press @ d A 0 4 and enter the value 3. From the GRAPH window V_Line Example • Draw a vertical line manually. 1. Press @ d A 0 4. 2. Use the cursor navigation keys ({ } ; ') to move the flashing cursor to the appropriate position. 3. Press E to draw the line. 05 T_line( From the Calculation screen Draws a tangential line at the specified point of a graph curve. T_line(equation, x-value) Example • Draw the tangential line of y = x2 at x = 1. 1. Select T_Line(. 2. Enter “x2, 1)” on the line. 3. Press E. Note: It is also possible to specify a function equation from Y0 to Y9 if stored. (T_ line(Y1, 1)) 100 Chapter 4: Graphing Features From the GRAPH window T_line( Example • Draw a tangential line by manually specifying the point. 1. Select T_Line(. 2.Use ; ' to move the flashing cursor on the targeted graph line. Use { } to select a graph to draw the tangential line. 3. When the point is set at the tangent point, press E. • It is also possible to input the x-value and press E. Note: The equation of the tangent line is displayed temporally. (The equation may include a margin of error.) 06 N_line( From the Calculation screen Draws the normal line at the specified point of a graph curve. Draws the orthogonal line of a tangent at the specified point of a graph curve. N_line(equation, x-value) Example • Draw the normal line of y = x2 at x = 1. 1. Select N_Line(. 2. Enter “x2, 1)” on the line. 3. Press E. Note:It is also possible to specify a function equation from Y0 to Y9 if stored. (N_ line(Y1, 1)) 101 Chapter 4: Graphing Features From the GRAPH window N_line( Example • Draw a normal line by manually specifying the point. 1. Select N_Line(. 2.Use ; ' to move the flashing cursor on the targeted graph line. Use { } to select a graph to draw the orthogonal line. 3. When the point is set at the point, press E. • It is also possible to input the x-value and press E. Note: The equation of the line is displayed temporally. (The equation may include a margin of error.) 07 Draw Draw equation Draws an additional graph based on a given expression. Example • Draw the graph of y = 3x2-4x+2. 1. Select Draw. 2. Enter “3x2–4x+2” on the line. 3. Press E. Note: This tool can be used with rectangular coordinate graphs only. 08 Shade( Shade(equation1, equation2 [, lower value, upper value]) Draws two graphs, and shades the area between the two. If the x range is specified, it shades the area within the specified range. Example • Shade the area enclosed by y = 1 4 x2 – 8 and y = x. 1. Select Shade(. 2. Enter “ 1 x2 – 8, x)” on the line. 4 3. Press E. 102 Chapter 4: Graphing Features Example • Shade the area enclosed by y = 1 x2 – 8 and y = x 4 within the range of –2 ≤ x ≤ 3. Before starting operation, Select ClrDraw to clear the graphs previously drawn. 1. Select Shade(. 2. Enter “ 1 x2 – 8, x, 4 -2, 3)” on the line. 3. Press E. Note: It is also possible to specify a function equation from Y0 to Y9 if stored. 09 DrawInv DrawInv equation Draws an inverse of a given graph expression. Example • Draw the inverse graph of y = 1 x2 – 8. 1. Select DrawInv. 4 2. Enter “ 1 x2 – 8” on 4 the line. 3. Press E. Note: It is also possible to specify a function equation from Y0 to Y9 if stored. 10 Circle( From the Calculation screen Draw a circle on the graph screen. Circle(x-coordinate of center, y-coordinate of center, radius) Example • Draw a circle with center at (2,3) and of radius 7. 1. Select Circle(. 2. Enter “2,3,7)” on the line. 3. Press E. Note: Before drawing a circle, press Z A 6 to set the X-Y coordinates to square. 103 Chapter 4: Graphing Features From the GRAPH window Circle( Example • Draw a circle manually. 1. Select Circle(. 2. Move the cursor to set the center point of the circle. Press E to set the anchor. 3. Move the cursor to determine the radius length of the circle. 4. When done, press E. 11 Text( The circle is drawn at the location. Text(column, row, “strings”) Enters a text string at a given coordinate. Text(column, row, variable) Draw the value of A-Z, θ. Example • Draw “HELLO” on the graph at column 2, row 1. Text(2, 1, “HELLO”) Note:Use M E 3 to enter “ " ” (double quotes). Column and row definitions for text input * Refer to the following diagram to specify the coordinates where you wish to start writing the text. column (0,0) (30,0) (0,9) (30,9) row 104 Chapter 4: Graphing Features Note: Lines, points, and curves drawn by the Draw menu are handled as pictures. Therefore, they cannot be traced. Graphs drawn by the Draw menu are automatically cleared if any screen settings are changed. To save the graph, use the StoPict menu. B POINT Utilize these tools to manage point drawing and deletion on the graph. There are two operation methods. One is to directly move the cursor pointer to the location on the graph screen where you wish to insert the point. The other is to call a relevant command on the Calculation screen and to directly input the coordinates to draw or delete the point. (X and Y coordinates should be separated by a comma.) 1 PntON( PntON(x-coordinate, y-coordinate) Draws a point at a given coordinate. It takes the X-Y coordinate as an argument. This tool can either be accessed from the GRAPH window or other windows. Entering from the GRAPH window enables a graphic entry, while entering from other windows enables text-based entry. 2 PntOFF( PntOFF(x-coordinate, y-coordinate) Erases a pixel point. It takes the X-Y coordinate as an argument. 3 PntCHG( PntCHG(x-coordinate, y-coordinate) Changes the status (i.e., visible/invisible) of a pixel at a given coordinate. Deletes the point when it is displayed and draws the point when it is not displayed. 105 Chapter 4: Graphing Features 4 PxlON( PxlON(column, row) Draws a pixel point at a given screen location indicated by column and row. The column and row definitions are as follows: Column: 0 to 132, Row: 0 to 64. column 132 (0, 0) (126, 0) (0, 62) (126, 62) row 64 This area cannot be specified 5 PxlOFF( PxlOFF(column, row) Erases a pixel point at a given screen location indicated by column and row. 6 PxlCHG( PxlCHG(column, row) Changes the status (i.e., visible/invisible) of a pixel at a given screen location indicated by column and row. 7 PxlTST( PxlTST(column, row) Returns “1” if a pixel point is present at a given screen location indicated by column and row. Returns "0" if no pixel point exists. 106 Chapter 4: Graphing Features C ON/OFF Sets the visibility status of a given graph number (0-9). 1 DrawON 2 DrawOFF DrawON [equation number 1, ....] or DrawON Sets the specified graphs visible. If no argument is given, then all graphs will be set visible. DrawOFF [equation number 1, ....] or DrawOFF Sets the specified graphs invisible. If no argument is given, then all graphs will be set invisible. Example • Set Y1 and Y2 to visible and Y3 to invisible. 1. Press @ d C 1. 2. Enter “1, 2” for equation numbers. 3. Press E. 4. Press @ d C 2. 5. Enter 3 for equation number. 6. Press E. D LINE Sets the line appearance of each graph. Each graph coordinate mode (i.e., rectangular, polar, etc.) can retain a set of line appearance preferences. Solid line, dotted line, bold line, locus and dots can be selected. 1. Press @ d D to select D LINE, then press E. 2. The next window enables you to select the line types of each graph in the set coordinate mode. (The rectangular coordinate mode is selected in this example.) Use the cursor keys to select the required line type, and press E. 107 Chapter 4: Graphing Features E G_DATA All graph data, including the graph equations and window settings, can be stored in 10 graph storage areas (1-9, and 0), which can be called up later. 1 StoGD StoGD number (0-9) Saves the graph data. Example • Store the current graph data in location #1. Note: The lines, graphs and pixels drawn with the A DRAW tools will not be saved here; use StoPict under F PICT instead. 2 RclGD RclGD number (0-9) Recalls the saved graph data. Example • Call back the previously stored graph data from location #1. 108 Note: Attempting to call back graph data from an empty location will result in an error. Chapter 4: Graphing Features F PICT Stores and recalls the displayed pixel data for the graph window. The graph equations will not be saved or recalled with these tools. 1 StoPict StoPict number (0-9) Saves the pixel data. Example • Store the current graph, including the drawings, in location #1. 2 RclPict RclPict number (0-9) Recalls the saved pixel data. Example • Call back the previously stored graph data from location #1. 109 Chapter 4: Graphing Features G SHADE With these sub-menu tools, inequalities, intersections and compliments of multiple graphs can be visualized. 1 SET Sets up the shading area for each graph. Example 1. Set up a simple graph within the Graph Equation window. Enter “X2” for Y1, for example. 2. Press @, and d to enter the DRAW menu, then press G to select G SHADE. The SHADE sub-menu appears. 3. Press 1 to select 1 SET. The “Set shade” window appears. 4. Using the cursor keys, move the cursor pointer to the appropriate position. 5. Press @ z E. 6. Press 1 to select Y1. 7. When the value is set, press the G key. The graph will be redrawn. 8. Let’s add another inequation, so that the area where the two inequality overlap can be shaded. Press the Y key, and enter another simple graph equation such as “X + 4” for “Y2”. 9. Now, return to the SHADE menu by pressing @ d, and G. Press 1 to select “1 SET”. 10.Within the “Set shade” window, add the second equation at the right of the topmost inequation. Use the ' or ; key to position the underscore cursor, then select “Y2” using the VARS menu. 11.Press the G to redraw the graph with the new shading appearance. 110 2 INITIAL Initializes the shading setup, and brings up the shading setup window. Chapter 4: Graphing Features 13. Other Useful Graphing Features Split screen It splits the display vertically, to show the graph on the left side of the screen while showing the X-Y values in a table on the right. The cursor is positioned on the table, and can be scrolled up/down using the { or } keys. Graph and table Graph and equation • When @ " are pressed on the graph screen, the graph and table are displayed on the same screen. • When @ " are pressed on the equation input screen, the graph and equation are displayed on the same screen. 111 Chapter 4: Graphing Features The following illustration shows these relationships. Y G G @" Y Y @" G @" • The split screen is always in the trace mode. Therefore, the cursor pointer appears on the graph. Accordingly, the coordinate values are displayed reverse in the table and in the equation at which the cursor pointer is located is also displayed reversely. • Using ; or ', move the cursor along the graph. (Values displayed reverse in the table are also changed accordingly.) • When two or more graphs are displayed on the screen, the desired graph is selected using { or }. (The table or equation on the right of the screen is also changed accordingly.) • The table on the split screen does not relate to the table settings on the full-screen table. • The table on the split screen is displayed in units of trace movement amount based on the cursor pointer position on the graph screen. When the full-screen table is displayed by pressing t, a different table may appear on the screen. • When the EXPRES or Y’ is set to ON on the FORMAT menu, the equation or coordinates are displayed on the graph screen. • Only equations to be graphed are displayed on the split screen. • Press G or t on the split screen to display the fullscreen of the graph or table. To exit the split screen, press any of other function keys. 112 Chapter 4: Graphing Features Substitution feature • The substitution feature allows you to input an equation using characters and variables, and then substitute numeric values for the characters to draw the graph. • The substitution feature is valid only in the rectangular coordinate system. Using this feature, any number of numeric value sets can be substituted while referring to the graph drawing screen. This clearly shows the changes in the graph depending on numeric values. For example, the graph for “Y1 = AX3 + BX2 + CX2 – D” is drawn by substituting numeric values for variables A, B, C, and D of the equation. • 22 kinds of variables (characters), A to Z except for R, T, X, and Y can be used for the substitution feature. • Up to seven variables (characters) can be used for one equation. (If the equation contains more than seven variables (characters), up to seven characters from the top of the equation are determined as variables and subsequent characters are ignored.) • If you attempt to execute an equation containing no variables, the substitution feature becomes invalid and the error message, “NO VARIABLE”, appears on the screen. • To input the equation, there are the following two methods after Y has been pressed. After the equation has been input, the same operations apply to subsequent steps. Example Substitute numeric values under the conditions that “Y1 = AX2 + BX + C” and “Y2 = AX” have been input. Equation Entry screen The cursor pointer is located at Y1. Drawing of both graphs Y1 and Y2 is valid. 1. Press @ ,. The substitution feature screen will appear. The equation on which the cursor pointer is located and its variables are displayed on the right of the screen. If variables (characters) contain no values, the graph is not drawn. 113 Chapter 4: Graphing Features If independent memories A to C contain any numeric values, the graph is drawn based on these values. * If the equation (in this example, Y1) on which the cursor is located contains no variables, the substitution feature screen will not appear. 2. Press 2 E. (2 is input to A.) The graph for “Y1 = 2X2” is drawn. (Since B and C have no values, they are ignored.) At this time, the graph for Y2 is also drawn. Y2 also uses variable A which is used in Y1. Therefore, the drawing of the graph for Y2 is also valid. * If you need to draw only the graph for Y2, it is necessary to change variables (characters) or make the graph drawing for Y1 invalid. 3. Press 1 E. (1 is input to B.) The graph is changed from “Y1 = 2X2” to “Y1 = 2X2 + 1X”. 4. Press _ 3 E. (-3 is input to C.) Now, the graph for “Y1 = 2X2 + 1X – 3” is drawn on the screen. 114 Chapter 4: Graphing Features Next, change variable A from 2 to 5 and see how the graph changes. Rewrite the equation based on the numeric values input on the substitution feature screen. 1. Press { { 5 E. (The cursor is moved from C to A and 5 is input.) The slope of the graph becomes sharp. * Move the cursor accordingly and substitute other numeric values for variables to view how the graph changes. * The trace function cannot be used in the substitution feature. (When U is pressed, the full-screen graph will appear.) 2. Press @ h to return to the equation display screen. The equation is written based on the last numeric values input on the substitution feature screen. * Once @ h have been pressed, the screen cannot be returned to the previous substitution feature screen. 115 Chapter 5 SLIDE SHOW Feature The SLIDE SHOW feature is especially incorporated to help students understand math concepts utilizing the calculator’s graphing capabilities. With this feature, the calculator’s screen images can be captured, organized, and stored. To enter the SLIDE SHOW, press ]. To exit the SLIDE SHOW feature, press #. 1. Try it! Make a SLIDE SHOW named “CUBIC” to explain how to draw the graph of a factorbase cubic function and explain how to solve cubic equations using factors. Use the following cubic function as a sample. y = (x – 3)(x – 1)(x + 2) Create a new SLIDE SHOW 1. Set up a SLIDE SHOW file. Press ] to enter the SLIDE SHOW menu. 2. Press C E to select C NEW. 3. Name your project (type “CUBIC,” for example), and press E. 116 Chapter 5: SLIDE SHOW Feature Capture images 4. Press Y to enter the graph equation mode. 5.Enter (x – 3)(x – 1)(x + 2) at the first equation. 6. Press @ n. The message “STORE SCREEN: 01” will appear. The image will be stored on page 1 of the SLIDE SHOW “CUBIC,” and the screen will automatically return to the previous screen. Each time you press @ n, the screen image will be captured and stored in the SLIDE SHOW. 7. Press G. Note: • You cannot capture an image while drawing. • If the cursor flashes at the upper right corner of the screen, the calculator is busy processing tasks. The SLIDE SHOW feature cannot capture images during this period. • A captured image cannot be recaptured. 8. After the graph is drawn, press @ n. The image will be stored on page 2 of the SLIDE SHOW “CUBIC”. 9. Press @ " to split the screen between the graph and the table. 10.After drawing is done, press @ n. The screen image is stored on page 3. 11.Press ' once, and press @ n. Continue this operation. 117 Chapter 5: SLIDE SHOW Feature Playing back the newly created SLIDE SHOW 1. Press ] to go to the SLIDE SHOW menu. Press B to select B PLAY. A list of saved SLIDE SHOW projects will be shown. 2. Select the one you want to play back, either by using the shortcut key strokes, or by moving the cursor. (Select the item and press E.) The first page of the SLIDE SHOW will appear. The number appearing at the upper right of the screen is the slide number. 3. Use the } key or E to display the next image; press the { key to show the previous image. Rearranging the captured images Let’s change the last image of the SLIDE SHOW feature to before the third. 1. Press ] to bring up the SLIDE SHOW menu. Select a file 2. Press D to select D SELECT. 3. Choose the project you want to edit from the sub-menu list. 4. Press E to select. Select an image 5. Press ] E to select E EDIT, then press 1 to select 1 MOVE. 118 The target SLIDE SHOW will be selected. The first image of the selected SLIDE SHOW file appears. Chapter 5: SLIDE SHOW Feature 6. Go down to the last captured image using the } key. 7. Press E to mark the image. Specify the insertion point 8. Go up to the page 3 using the { key. 9. Press E. The marked image will be inserted at page 3. 2. The SLIDE SHOW menu This section of the chapter summarizes each item in the SLIDE SHOW feature menu. A CURR Displays the name of the currently selected or working SLIDE SHOW. Press @ n to capture an image. B PLAY Enables you to select a SLIDE SHOW file for playback. C NEW Creates a new SLIDE SHOW file to store screen images. D SELECT Enables you to select a SLIDE SHOW file to be edited and display its name in the A CURR window. E EDIT Enables you to move/delete captured images, or change the file name of the current SLIDE SHOW. Note: If no SLIDE SHOW file is stored, selecting any of the following submenu items will result in an error. 1 MOVE With this sub-menu tool, a selected screen image can be moved, so that the playback order will change. To escape from this mode and go back to the SLIDE SHOW menu, press the ] key. 119 Chapter 5: SLIDE SHOW Feature 1. While in the SLIDE SHOW menu, press E to select E EDIT, then press 1 to select the 1 MOVE sub-menu item. 2. With the { and } cursor keys, select the captured image you wish to move, then press E. 3. Select the position to which you wish to move the previously selected image using the { and } cursor keys. 4. Pressing E will place the selected image at the new location. The selected image will be placed immediately before the current screen. 2 DEL This sub-menu tool deletes the selected image captured in the SLIDE SHOW. 1. While in the SLIDE SHOW menu, press E to select E EDIT, then press 2 to select the 2 DEL sub-menu item. 2. With the { and } cursor keys, select the image you wish to delete. 3. Press E to remove the selected image from the SLIDE SHOW file. 3 RENAME Use this sub-menu tool to rename the SLIDE SHOW. 1. In the SLIDE SHOW menu, press E to select E EDIT, then press 3 to select the 3 RENAME sub-menu item. 2. The following screen enables you to change the SLIDE SHOW name. 3. Type the new name. The default input mode is A-LOCK. If you wish to incorporate numbers, press the A key to enter numbers. To switch back into the ALPHA mode, press A again. 4. Pressing E will store the new SLIDE SHOW name. 120 Chapter 6 Matrix Features Within the Matrix features, up to ten different matrices can be entered. To get to the Matrix features, press @ m. Define and edit the matrices within this mode too. 1. Try it! Three sheaves of the first class crop, two of the second, and one of the third are sold for 39 dollars. Two of the first, three of the second and, one of the third for 34 dollars. And one of the first, two of the second and three of the third for 26 dollars. How much did you receive from each sheaf of the first, second and third class crops? (Chapter VIII of Chiu Chang Suan Shu - Nine Chapters of Arithmetic Arts, 200 B.C., China) Three equations can be derived as follows, containing three unknown quantities: 3x + 2y + z = 39 2x + 3y + z = 34 x + 2y + 3z = 26 x, y and z represent the price for each sheaf of the first, second and third class crops, respectively. You can solve the above system of linear equations by using a matrix. CONCEPT 1. Enter the coefficients as elements in a matrix. 2. Use the rrowEF function to obtain the reduced row echelon form. 121 Chapter 6: Matrix Features PROCEDURE Select a matrix to edit 1. Press @ m to enter the MATRIX menu. 2. Press B to select B EDIT and then 1 to select 1 mat A. Define dimensions 3. Press 3 E 4 E to define the dimensions of the matrix (3 rows × 4 columns). Enter the values 4. Press 3 E 2 E 1 E 3 9 E to enter the first row of 3x + 2y + z = 39. The cursor will automatically position itself at the beginning of the second row. 5. Press 2 E 3 E 1 E 3 4 E to enter the second row of 2x + 3y + z = 34. 6. Press 1 E 2 E 3 E 2 6 E to enter the third row of x + 2y + 3z = 26. 7. Press # to return to the calculation screen. Matrix A is now set. Solve the problem 8. Press @ m to display the MATRIX MENU, and press D to select D MATH and then press 4 to select 4 rrowEF. The reduced row echelon form is now set, as shown: 9. Press @ m, then press A to select A NAME and press 1 to select 1 mat A. The Matrix A is now set and ready to be calculated. 122 Chapter 6: Matrix Features 10.Press E. The reduced row echelon form of the matrix is displayed. Display Solution 1x + 0y + 0z = x = 9.25 0x + 1y + 0z = y = 4.25 0x + 0y + 1z = z = 2.75 2. Entering and Viewing a Matrix Select a matrix 1. Press @ m, then press @ B (select EDIT) and select the matrix you want to define. Note: Up to 10 matrices from 1 matA to 0 matJ can be defined. Define dimensions 2. Enter the row dimension number and press E. Cursor moves to the column dimension. 3. Enter the column dimension number and press E. The matrix will be displayed with null values. (See below.) *It is not required to press E when the dimension number is 2 digits. Matrix name Matrix dimensions (row × column) Element entry field Input field (bottom line) Up to 5 rows by 3 columns of elements can be displayed on the screen. Press ; ' { } to scroll the matrix. Use row and column numbers on the left and upper side of the matrix to check the display location. • If the dimensions of the matrix have previously been defined, the values will be displayed. You can retain or alter the dimensions accordingly. 123 Chapter 6: Matrix Features Enter elements in the matrix 1. Press appropriate number keys to enter numbers at the 1st row and 1st column. The number is displayed at the bottom of the screen. 2. Press E. The cursor moves to the 1st row, 2nd column. 3. Sequentially input the element data. 4. Press # after completion of data input. Note: Elements in Matrix can be specified using the NAME menu of the MATRIX menu such as “mat A (1, 1).” Editing keys and functions ; ' Move the cursor within the current row or scroll horizontally. { } Move the cursor within the current column or scroll vertically. On the top row, { moves the cursor to the dimensions field. E ENTER the number in the cursor position and move the cursor to the next position. C Clear the value of bottom line (input field). 124 # Store all the elements of the matrix and returns to the calculation screen. 124 Chapter 6: Matrix Features 3. Normal Matrix Operations Many functions can be used for calculations of matrices and scalars. Examples of each calculation are as follows: Matrix + Matrix Matrix – Matrix To add or subtract matrices, the dimensions must be the same. Example 1. Press # C. 2. Press @ m A [email protected] A2 3. Press E. Matrix × Matrix To multiply two matrices, the column dimension of the first matrix must match the row dimension of the second matrix. Example 1. Press # C. 2. Press @ m A 1|@m A2 3. Press E. Square of Matrix To obtain the square of a matrix: Example 1. Press # C. 2. Press @ m A 1y 3. Press E. 125 Chapter 6: Matrix Features Inverse of Matrix For the calculation of the inverse of a matrix, please proceed as for the reciprocal of a real number. Example 1. Press # C. 2. Press @ m A 1 @ x E. 4. Special Matrix Operations This calculator has three Matrix calculation menus: OPE, MATH and [ ]. Examples of each calculation are as follows: Calculations using OPE menus 01 dim( dim(matrix name) Returns the dimensions of the specified matrix. Example • Check the dimensions of mat A. • Newly define or change the dimensions to 2 × 3 for Mat C. 02 fill( fill(value, matrix name) Fills each element with a specified value. Example • Enter the value 5 into all the empty elements of matrix C. 126 Chapter 6: Matrix Features 03 cumul cumul matrix name Returns the cumulative matrix. Example • Obtain the cumulative sum of mat A. cumulative sum of aij = ai1 + ai2 + ...... + aij 04 augment( augment(matrix name, matrix name) Appends the second matrix to the first matrix as new columns. The first and second matrices must have the same number of rows. Example • Create a new matrix with matrix A augmented by matrix B. 05 identity identity dimension value Returns the identity matrix with specified value of rows and columns. Example • Create the identity matrix of 3 rows × 3 columns. 06 rnd_mat( rnd_mat(number of row, number of column) Returns a random matrix with specified values of rows and columns. Example • Create a matrix of 2 rows × 3 columns with generated random values. (when TAB = 2 and FSE = “FIX” at SETUP menu) 127 Chapter 6: Matrix Features 07 row_swap( row_swap(matrix name, row number, row number) Returns the matrix with specified rows swapped. Example • Swap the 2nd and 3rd rows in the matrix E. e2j’ = e3j , e3j’ = e2j 08 row_plus( row_plus(matrix name, row number, row number) Adds the first specified row data to the second specified row data. Example • Add the 2nd row data to the first row of matrix E. e1j’ = e1j + e2j 09 row_mult( row_mult(multiplied number, matrix name, row number) Returns the scalar multiplication of elements in a specified row. Example • 3 × each element of 1st row of mat E e1j’ = 3 × e1j 10 row_m.p.( row_m.p.(multiplied number, matrix name, row number, row number) Returns the scalar multiplication of elements in a specified row and adds result to elements in another specified row. Example • 2 × each element of 3rd row and add the result to each element of the 1st row. e1j’ = e1j + 2 × e2j 128 Chapter 6: Matrix Features 11 mat→list( Creates lists with elements from each column in the matrix. If dimensions of columns is greater than the number of lists specified, extra columns are ignored. Also, if it is less than the number of lists specified, extra lists are ignored. mat→list(matrix name, list name 1, ..., list name n) Example • Make List 1 and List 2 by using the 1st and 2nd columns of matrix E, respectively. mat→list(matrix name, column number, list name) Example • Make List 3 by using the 3rd column of matrix E. 12 list→mat(list→mat(list 1, .... list n, matrix name) Creates a matrix using specified lists. This function is the same as list→mat( in the List OPE menu. Note: The list items must be prepared prior to executing this function. Example • Create columns of matrix D by using list items in L1 and L2. 129 Chapter 6: Matrix Features Calculations using MATH menus 1 det det matrix name Returns the determinant of a square matrix. The determinant can only be applied to a matrix which has the same row and column dimensions. Example • Give the determinant of matrix A. 2 trans trans matrix name Returns the matrix with the columns transposed to rows and the rows transposed to columns. Example • Transpose rows and columns of matrix B. 3 rowEF rowEF matrix name Returns the row Echelon Form of the specified matrix. The number of columns must be greater than or equal to the number of rows. Example • Give the row-echelon form of matrix B. 4 rrowEF rrowEF matrix name Returns the reduced row Echelon Form of the specified matrix. The number of columns must be greater than or equal to the number of rows. Example • Give the reduced row-echelon form of matrix B. 130 Chapter 6: Matrix Features Use of [ ] menus Using [ ] menus, you can manually enter a matrix on the calculation screen. 1. Press @ m E 1 ( [ ) at the beginning of the matrix. 2. Press @ m 1 ( [ ) to indicate the beginning of the first row. 3. Enter a number or expression for each element. Separate each element with commas. 4. Press @ m 2 ( ] ) to indicate the end of the first row. 5. Repeat above steps 2 to 4 to enter all the rows. 6. Press @ m 2 ( ] ) to indicate the end of the matrix. 7. Press E. The matrix will be displayed. Using a Matrix in an expression To use a matrix in an expression, you can do any of the followings: • Select a matrix from the m NAME menu. • Enter the matrix directly using the [ ] function menus. 131 Chapter 7 List Features 1. Try it! By analyzing years of data, we found that it takes the driver of a car approximately 0.75 seconds to react to a situation before actually applying the brakes. Once the brake pedal is depressed, it takes additional time for the car to come to a complete stop. Here is the equation used to compute total stopping distance on dry, level concrete: The reaction time distance (in feet) = 1.1 times the speed (in miles per hour); The braking distance = 0.06 times the speed squared; y = 1.1 × v + 0.06 × v2, where y represents the total stopping distance (in feet), and v represents the speed (miles/hour) Calculate the total stopping distances at the speeds of 30, 40, 50, 60, 70, 80 miles per hour. CONCEPT 1. You can calculate all answers individually, but if you use list, you can obtain the results with one calculation. PROCEDURE Enter each speed value in the list 2. Press # C to enter the calculation screen. 3. Press @ { 30 , 40 , 50 , 60 , 70 , 80 @ } The calculator displays the set of data. 132 Chapter 7: List Features Store the list in L1 4. Press R @ 1. 5. Press E to store the list in L1. 6. Press 1.1 | @ Enter the equation using L1 1 + 0.06 | @1y 7. Press E. 8. List {87, 140, 205, 282, 371, 472} will appear. So the solutions are: Car speed Stopping distance 30 miles/hour 87 feet 40 miles/hour 140 feet 50 miles/hour 205 feet 60 miles/hour 282 feet 70 miles/hour 371 feet 80 miles/hour 472 feet Note: • You can also perform the above calculation using the direct list input method (using braces). 1.1 | {30, 40, 50, 60, 70, 80} + 0.06 | {30, 40, 50, 60, 70, 80} y and press E. 133 Chapter 7: List Features 2. Creating a list A list is a series of values enclosed by braces, and is treated as a single value in calculations or an equations. The calculator has 6 storage areas for lists from L1 to L6. You can edit or access lists by pressing @ 1 to 6 (numeric keys from 1 to 6). Using @ l (L_DATA) menus, you can store up to 10 sets (L_DATA 0 to L_ DATA 9) of lists (L1 to L6) in a memory and recall any of the stored sets as required. Store a series of data 1, 3, 2, and 9 in the list L1, and 5, 4, 6, 3 in L2 1. Press # C to enter the calculation screen. 2. Press @ { 1 , 3,2,[email protected] } 3. Press R @ 1. 4. Press E to store the list in L1. 5. Press @ { 5 , 4,6,[email protected] }[email protected] E for L2. Tips: To view a specific list, press @ 1 to 6, then E at the calculation screen. 3. Normal List Operations • Lists can contain real and complex numbers. • Lists can be used as values (or variables) in calculations or equations. • Calculations between lists are also possible. (Both lists must contain the same number of elements.) • The following examples use the L1 and L2 values stored in the previous section. 134 Chapter 7: List Features Calculate 10 × L1 and store the results in L3 1. Press 10 | @ 1 R @ 3 E. Calculate the sine of L3 2. Press s @ 3 E. “...” shows that results extend beyond the display to the right. Use ;, ' to scroll left or right, respectively. Calculate L1 + L2 3. Press @ 1 + @ 2 E. Change the 3rd element of L1 to –3 4. Press _ 3 R @ 1(3)A / @ 1 E. Append the new value 7 to L1 as the 5th element 5. Press 7 R @ 1 (5)A/ @ 1 E. Note: Separated by a colon (:), two or more commands can be entered in one line. Calculate the root of L2 6. Press @ + @ 2 E. 135 Chapter 7: List Features 4. Special List Operations This calculator has four list calculation menus: OPE, MATH, L_DATA and VECTOR. Calculations using the OPE menu functions 1 sortA( sortA(list name) Sorts lists in ascending order. Example • Store list {2, 7, 4} in L1, and sort L1 in ascending order. 2 sortD( sortD(list name) Sorts lists in descending order. Example • Sort the above list L1 in descending order. Note:sortA(list name 1, list name 2,...) If two or more lists are entered separated by commas, a sort is performed on the first list as a key, and the following lists are sorted in the order corresponding to the elements in first list (key list). Example • Store lists {2, 7, 4} and {-3, -4, -1} in L1 and L2 respectively, and sort L1 and L2 in ascending order using list L1 as a key list. 136 Chapter 7: List Features 3 dim( dim(list) Returns the number of items (dimension) in the list. Example • Display the dimension of list L1. natural number ⇒ dim(list name) Set the number of items (dimension) of specified list to the specified number. Example • Set the dimension of list L6 to 4. All the elements are initially 0. This operation overwrites the existing list dimensions. The existing values within the new dimensions remain as they are. 4 fill( fill(value, list) Enter the specified value for all the items in the specified list. *The dimension of the list must be set beforehand. Example • Set the dimension of list L6 to 4 and substitute 5 for all the items of list L6. 137 Chapter 7: List Features 5 seq( seq(equation, start value, end value[, increments]) target list name Makes a list using the specified equation, range (start value and end value) and increments. Example • Fill the list using the equation y = x2 – 8, where x increases from -4 to 4 by increments of 2. Additional examples • The 1st command displays all number from 0 to 10, the 2nd all odd numbers from 1 to 21, the 3rd all even numbers from 0 to 10. *If increment is omitted, the default value 1 is used. 6 cumul cumul list Sequentially cumulates each item in the list. li’ = l1 + l2 + ... + li , where li is the i-th item of the list. Example • Set the list L1 to {4, 2, 7}, and obtain the cumulated list L1. • Cumulate the above result. 7 df_list df_list list Returns a new list using the difference between adjacent items in the list. li’ = li+1 – li, where li is the i-th item of the list. Example • Set the list L1 to {4, 2, 7}, and calculate the difference between adjacent items. 138 Chapter 7: List Features 8 augment( augment(list 1, list 2) Returns a list appending the specified lists. Example • Obtain the list appending L1 ({4, 2, 7}) and L2 ({-1, -3, -4}). • Press b R 1 to store the list. 9 list→mat(list→mat(list 1, ..., list n, matrix name) Makes a matrix using the specified list as column data, stored under the specified matrix name. Example • Make a matrix mat A using list L1 as the first column and list L2 as the second column. *The dimensions of the two lists must be the same. *Complex numbers cannot be used with this function. *This function is the same as list→mat of the OPE menu in the MATRIX function. 0 mat→list(mat→list(matrix name, list name 1, ..., list name n) mat→list(matrix name, column number, list name) Makes lists from the matrix. This function is the same as “mat→list” of the OPE menu in the MATRIX function. See page 129 for details. 139 Chapter 7: List Features Calculations using MATH Menus During the following explanations, the values of lists, L1 and L2 will be assumed to be: L1 = {2, 8, -4} L2 = {-3, -4, -1} 1 min( min(list) Returns the minimum value in the list. Example • Calculate the minimum value of the list L1. 2 max( max(list) Returns the maximum value in the list. Example • Calculate the maximum value of the specified list L2. Note: min(list 1, list 2) max(list 1, list 2) If two lists are specified in parenthesis separated by a comma, then a list consisting of minimum (or maximum) values is returned. 3 mean( mean(list [, frequency list]) Returns the mean value of items in the specified list. Example • Calculate the mean value of list L1. 140 Chapter 7: List Features 4 median( median(list [, frequency list]) Returns the median value of items in the specified list. Example • Calculate the median value of the list L2. 5 sum( sum(list [, start number, end number]) Returns the sum of items in the specified list. Example • Calculated the sum of the list items of L1. *You can specify the range of items in the list to sum. sum(L1,1,2) means sum the 1st to 2nd items of the list L1. sum(L1,2) means sum all items from the second to the last of the list L1. 6 prod( prod(list [, start number, end number]) Returns the multiplication of items in the specified list. Example • Calculate the multiplication of items in the list L1. *You can specify the range of items in the list to multiply. prod(L1,1,2) means multiply the 1st to 2nd items of the list L1. prod(L1,2) means multiplication of all items from the second to the last of the list L1. 141 Chapter 7: List Features 7 stdDv( stdDv(list [, frequency list]) Returns the standard deviation of the specified list items. Example • Calculate the standard deviation using the list items of list L2. Note: If relative frequencies or probabilities are stored in the frequency list, please use P_stdDv. 8 varian( varian(list [, frequency list]) Returns the variance of the specified list items. Example • Calculate the variance using the list items of list L2. 9 P_stdDv( P_stdDv(list [, frequency list]) Returns the population standard deviation of the specified list items. Example • Calculate the population standard deviation using the list items of list L2. Standard deviation and variance Standard deviation: s = (Estimation) n 2 Variance = kΣ= 1 (lk – m) (Estimation) n–1 Variance n Population standard deviation: σ= (Variance in case of complete survey) where n = number of list items lk = list item value m = mean value of the list 142 Σ (lk – m)2 k=1 n Chapter 7: List Features Calculations using VECTOR Menus During the following explanations, the values of lists, L1 and L2 will be assumed to be: L1 = {2, 8, -4} L2 = {-3, -4, -1} These functions use lists as vectors. 1 CrossPro( CrossPro(list name1, list name2) Calculate the cross product (vector product) of two lists. Example • Calculate the cross product of L1 and L2. Note: Calculation range: up to 3-dimensional vector. The dimensions of the vectors have to be identical. 2 DotPro( DotPro(list name1, list name2) Calculate the dot product. Example • Calculate the dot product of L1 and L2. Note: Calculation range: up to 9-dimensional vector. The dimensions of the vectors have to be identical. 143 Chapter 7: List Features 5. Drawing families of curves using the list function Using list items as coordinates, you can simultaneously draw families of curves. 1. Press Y. 2. Enter the equation; Y1 = {3, -2}x2 + {5, 3}x + {2, 4} 3. Press G. Two graphs are drawn as shown on the right. In this case, the first one represents the equation y = 3x2 + 5x + 2 and the second y = -2x2 + 3x + 4. You can also use L1 to L6 to enter the equation; 1. Set the lists L1 to L3 as follows; {3, -2} ⇒ L1, {5, 3} ⇒ L2, {2, 4} ⇒ L3, and then 2. Enter the equation as follows. Y1 = L1x2 + L2x + L3 6. Using L_DATA functions The calculator can store up to 10 list groups in memory (L_DATA 0 to L_DATA 9). You may store or recall any one of these list groups. Each list group can contain up to 6 lists. 1 StoLD StoLD natural number (0-9) Stores the current group of lists (L1 to L6) in L_DATA 0 to 9. Example 1. Press @ l and select C 1. 2. Enter the preferred number from 0 to 9 and press E. 144 “Done” will appear and the current lists will be stored in L_DATA #. Chapter 7: List Features 2 RclLD RclLD natural number (0-9) Recall the stored group of lists for use. Any current list data (not stored in L_DATA) is overwritten. Example 1. Press @ l and select C 2. 2. Enter the number to recall and press E. “Done” will appear and the current lists will be overwritten by the recalled list group. 7. Using List Table to Enter or Edit Lists You can use List Table in the STAT menu to easily access the contents of the lists. Though the STAT menu was originally designed for Statistics function calculations, the List Table is very useful for entering or editing list items. How to enter the list 1. Press S A E. The list table will appear. The first column indicates the order number of each list, and the 2nd column corresponds to the list L1, the 3rd to the L2, and so on. 2. Move the cursor to the target cell and enter the appropriate value. The value will appear on the bottom line. 3. Press E. The value will enter the cell and the cursor move down to the next cell. *“--------” indicates the end of the list. When you enter the value, “--------” goes down to the next cell. 145 Chapter 7: List Features How to edit the list 1. Press S and select A EDIT, then press E. 2. Use the cursor keys to move the cursor to the target cell. 3. Enter the new value and press E. The new value will be stored in the target cell. *The display on the bottom line relates to the cell where the cursor pointer is located. Though any number can be entered in a cell, the bottom line of the screen can display up to a maximum of 10 digits excluding exponents, and the cell can display up to a maximum of 8 digits including exponents. 146 Chapter 8: Statistics & Regression Calculations Chapter 8 Statistics & Regression Calculations The following statistical and regression features are available: • Statistical calculations such as means and standard deviations • Graphing statistical data • Plotting regression curves • Statistical tests • Estimation • Obtaining coefficients from regressions • Distribution functions 1. Try it! The following table shows the access counts (per hour) of a certain web site from Sunday midnight to Monday midnight. Hours 0102 030405 060708 09 10111213 141516 1718 1920 212223 24 Sunday 9872 55 3 6 241530 59 72554321 1015015113510820425323225175 30 Monday328 122 4 1932729591123 201 1841089572453875111153908435 Let’s input these data into the calculator (List function) and plot a histogram. Opening the list table to enter data 1. Press S. The Stat menu will appear. 147 Chapter 8: Statistics & Regression Calculations 2. Select A EDIT and press E. The List table will appear. Initially, all elements are blank and the cursor pointer is located at L1-1 (top left). Entering hours (index value) 3. Input 1 for hour. 4. 1 will be displayed at the bottom line of the display. 5. Press E to input the index value. 6. Continue the procedure to input 2 to 24. Entering the data for Sunday 7. Press ' to move the cursor to the top line of L2. 8. Input 98 for hour 01. 98 will be displayed at the bottom line of the display. 9. Press E to input the data. 98 will appear in position L2-1 and the cursor will move to the second row. 10.Input 72 for hour 02 and press E. Continue the procedure to the end of the data. Entering the data for Monday 11.Press ' to move the cursor to the top line of L3. 12.Input 32 for hour 01 and press E. 13.Continue the procedure to the end of the data. If you enter the wrong data 1. Press ;, ', {, or } to move the cursor pointer to the target cell. 2. Input the correct number and press E. Graphing the statistical data (Histogram) Now we can plot the data to make histograms, broken line graphs and other statistical graphs. 1. Press [. 2. Select A PLOT1 and press E. The following screen will appear. 148 Chapter 8: Statistics & Regression Calculations Setting the graph drawing “on” 3. The first line shows if the graph drawing is on or off. Initially, the graph drawing is off. With the cursor pointer at the “on” position, press E to set the graph drawing on. 4. Press } to move the cursor to the next line (DATA). Selecting whether 5. Select X for 1-variable plotting and press E. 1-variable plotting or 2-variable plotting Select the list number used for graphing Determining ListX and Freq Frequency relates to the number of times access occurred (L2) at the ListX stage. You can refer that the Access of ListX (L1) hour occurred Freq (L2) number of times. 6. Press } to move the cursor to the next line (ListX). 7. The default list name for ListX is L1. If another list name is set, press @ 1 to enter L1. 8. L1 is set to be used for x-axis items. Setting the frequency 9. Press } to move the cursor to the next line (Freq). 10.Press @ 2 to enter L2. Selecting the graph 11.Press } to move the cursor to the next line (GRAPH). Making a graph 13.Press Z, and then select A ZOOM. 12.The graph format defaults to histogram, so if that is what is required, this does not need to be changed. 14.Press ' to move the cursor right and then press } several times. 9 Stat will appear. 149 Chapter 8: Statistics & Regression Calculations 15.Select 9 Stat and press E. You can directly press 9 at step 13 to select 9 Stat. The histogram will appear on the display. Set the WINDOW settings When you draw the graph using the automatic statistics zoom function (9 Stat), the division number is automatically set to Xmax –Xmin (default value: 10). If you wish to show the graph Xscl hour by hour, change the value in the Window menu. 1. Press W. Window (Rect) setting menu will appear. 2. Enter the values as shown in the diagram to the right. Ymax is determined by the maximum access number (253 at 20:00 on Sunday). Compare the access rates on Sunday and Monday 3. Press G. You can compare up to 3 statistical data by setting PLOT2/PLOT3 to on. Set the statistical 1. Press [ A E and move the cursor to GRAPH. plotting of PLOT1 2. Press [ again. (Sunday data) to 3. Press B and 1 a broken line (broken line with circle dots). 4. Press G. The histogram is now changed to a broken line graph. 5. Press @ q to clear the screen. 6. Press [ and select B PLOT2. 7. Set as follows. PLOT: on, DATA: X, ListX: L1, and Freq: L3. 150 Chapter 8: Statistics & Regression Calculations 8. Move the cursor to GRAPH and press [. 9. Press B 2 (broken line with cross points). 10.Press G. Now you can compare the difference in web site access counts between Sunday and Monday. Press @ q. 2. Statistics Features 1. STAT menus Press the S key to access the statistical calculation menus. The menus are as follows: A EDIT Provides the entry or edit mode and displays a list table. B OPE Calculation menu for operations such as ascending or descending sort. C CALC Obtains statistical values. D REG Calculates regression curves. E TEST Statistical hypothesis tests F DISTRI Distribution menu items Data Entry Use a list table to enter the statistical data (press S to access). Up to 999 elements can be used for each list, though the amount of data able to be entered will vary according to the memory usage. Calculating statistic values (CALC menu) Use the CALC menu under the STAT menu to obtain statistic values. Press S C to access the CALC menu. 151 Chapter 8: Statistics & Regression Calculations 2. Statistical evaluations available under the C CALC menu 1_Stats 1-variable (x) statistical a calculations _ x Mean of sample (x) sx Standard deviation of sample (x) sx = Σx2 − nx2 n−1 σx Population standard deviation of sample (x) σx = Σx2 − nx2 n Σx 2 Sum of sample (x) Σx n xmin Q1 Med Q3 Third quartile of sample (x) xmax Largest value of sample (x) Sum of squares of sample (x) Sample number Smallest value of sample (x) First quartile of sample (x) Median of sample (x) 2_Stats 2-variable (x, y) statistical calculations The following values are added to the 1-variable statistic calculations _ y Mean of sample (y) sy Standard deviation of sample (y) σy Population standard deviation of sample (y) Σy Sum of sample (y) 2 Σy Sum of squares of sample (y) Σxy Sum of product of sample (x, y) ymin Smallest value of sample (y) ymax Largest value of sample (y) 152 Chapter 8: Statistics & Regression Calculations The web site access counts example on page 147 will be used again to demonstrate the calculation of statistical values. Hours 0102 030405 060708 09 10111213 141516 1718 1920 212223 24 Sunday 9872 55 3 6 241530 59 72554321 1015015113510820425323225175 30 Monday328 122 4 1932729591123 201 1841089572453875111153908435 * If you did not previously enter the above values in the list table, press S and select A EDIT to display the list entry mode and enter the values. Calculating one-variable statistics using web site access counts for Sunday (L2) and Monday (L3). Statistical 1. Press # C and S to display the statistics menu. calculations 2. Press C and then 1. using the Sunday 1_Stats will be displayed on the top line of the screen followed data (L2) by the cursor. 3. Press @ 2 to enter L2 and press E. All the statistical values will be displayed on the screen. 4. Press } or { to scroll the screen. 5. Press S to display the statistics menu. Statistical calculations 6. Press C and then 1. using the Monday 1_Stats will be displayed on the bottom line of the screen data (L3) followed by the cursor. 7. Press @ 3 to enter L3 and press E. 153 Chapter 8: Statistics & Regression Calculations Calculating the previous two-variable statistical values can be performed in a single operation. Use a “ , ” (comma) to separate the two variables. 1. Press # C and S to display the statistics menu. 2. Press C and then 2. 2_Stats will be displayed on the top line of the screen followed by the cursor. 3. Press @ 2 , @ 3 to enter L2 and L3, and press E. All the statistical values will be displayed on the screen. 4. Press } or { to scroll the screen. ANOVA( The ANOVA( feature performs an analysis of variance to compare up to six population means. 1. Press # C and S to display the statistics menu. 2. Press C and then 3. ANOVA(_ will display on the top line of the screen. 3. Press @ 2 , @ 3 ). 4. Press E. The answer will appear on the screen. Each character represents the following variables. 154 F p df SS MS sxp The F statistic for the analysis The p value for the analysis Degrees of freedom Sum of squares Mean Square Pooled standard deviation Chapter 8: Statistics & Regression Calculations 3. Graphing the statistical data Press [ to access the statistical graphing mode. The calculator can plot statistical data on up to 3 types of graph (PLOT1 to PLOT3) to check the state of distribution. The graph types can be selected from histogram, broken line plot, normal probability plot, normal distribution plot, box plot, modified box plot, pie chart, scatter diagram and XY line. Broken line plot, normal probability plot, modified box plot, scatter diagram and XY line can use 3 different types of points — circle, cross, and square. Statistical graph types overview (chart) Histogram Broken line plot PLOT1 PLOT2 PLOT3 Normal probability plot Normal distribution plot Box plot Modified box plot Pie chart POINT: ° POINT: + POINT: Scatter diagram XY line 1. Graph Types Histogram (HIST) A bar graph of sample (x) The width of the bars is set by the Xscl*. The Y-axis shows the frequency. *The Xscl can be changed to between 1 and 64. Use the Window Setting Menu to change the Xscl. (See page 74.) 155 Chapter 8: Statistics & Regression Calculations Broken line plot (B.L.) A broken line graph for the frequency distribution of sample (x) Three types of points can be selected from circle, cross and square. The broken line is displayed by connecting the upper left points of the bars of the histogram, as the upper left point of each bar represents each class value in the histogram. The calculator can draw both a histogram and a broken line plot at the same time. Normal probability plot (N.P.) Plots the variance of the standardized normal distribution with the statistical data (x) on the X axis or Y axis. If the points plot almost linearly, it indicates that the data is of normal distribution. The distance between the dots is set by the Xscl. • The Xscl can be changed between 1 and 64. Use the Window Setting Menu to change the figure. (See page 74) • You cannot set the frequency in the Normal probability plot. The statistical data must be created using only one list without splitting into the data and frequency. Normal distribution plot (N.D.) 156 A normal distribution curve of sample(x) The x-axis is in the range of Xmin to Xmax. Chapter 8: Statistics & Regression Calculations Box plot (Box) A box plot graph of sample (x) A. The minimum value (xmin) of the sample (x) B. The first quartile (Q1) A B C D E C. Median (Med) of the sample (x) D. The third quartile (Q3) E. The maximum value (xmax) of the sample (x) Modified box plot (MBox) A modified box plot graph of sample (x) A. The minimum value (xmin) of the sample (x) B. The tip of extension which is defined by (Q3 – Q1) x 1.5 A B CD E F G C. The first quartile (Q1) D. Median (Med) of the sample (x) E. The third quartile (Q3) F. The tip of extension which is defined by (Q3 – Q1) x 1.5 G. The maximum value (xmax) of the sample (x) • Statistical data on the outside of the extension are indicated by points, selectable from circle, cross, or square. • The length of the extension from the box is determined by Q1 and Q3. 157 Chapter 8: Statistics & Regression Calculations Pie chart (PIE) Pie graph of sample (x) • Maximum number of division is 8. • Calculation range: 0 ≤ x < 10100 • Data can be displayed in two modes: • Value display: 8 digits • Percentage display: Fixed decimal (2 digits decimal) *Pie graphs are drawn in the same order as on the specifying list. *Pie graphs cannot be displayed simultaneously with other graphs and X/Y axis, though lines or dots can be drawn. The coordinates of the free-moving cursor depend on the Window settings. • The values are stored in variables A to H. • As all the displayed values are rounded down in the percentage display mode, the total percentage may not be 100. Scatter diagram (S.D.) A two-dimensional plot graph using two samples (x, y) Two sets of statistical data are required for the scatter diagram. • Three types of points are selectable from circle, cross and square. • Two statistical data lists can be set to either x- or y-axis according to your requirements. XY Line (XYLINE) • Displays a graph that connects each point of the scatter diagram. • Each point is connected in the sequence (rows) of the statistical data. 158 Chapter 8: Statistics & Regression Calculations 2. Specifying statistical graph and graph functions • Up to three graphs can be plotted per sample data. Specifying type of statistics graphing 1. Press [. 2. Select from A PLOT1, B PLOT2 or C PLOT3 and press E to set the statistical graphing specifications. Press @ q before step #3. • You may just press A to C to select. • You can overlap 3 plotting graphs (from PLOT1 to PLOT3) on a single screen. Choose on or off at the top line to determine whether each graph is displayed or not. Limit settings (x value) 3. Press [ D (D Limit) to specify the graphing range. The D Limit menu is used to set the upper and lower limit lines of sample (x) of the statistical graph. Displaying the upper and lower limit lines 4. Press 1 (1 SET). Displaying the mean value line of sample (x) 7. Press [ D (D Limit) and press 2 (2 LimON) E to display a line that indicates the mean value of sample (x), as well as the upper and lower limit lines. 5. Enter the appropriate value for Lower limit and press E. 6. Enter the appropriate value for Upper limit and press E. 8. Press [ D 3 (3 LimOFF) and E not to display the lines. • Upper and lower limit values are displayed using short broken lines. • The default value of the upper/lower limit is 1. *The mean value line is indicated by a long broken line. 3. Statistical plotting on/off function • You can set the statistical plotting of PLOT 1 to 3 at once. 1. Press [. 2. Press E. 159 Chapter 8: Statistics & Regression Calculations 3. • To set the all plotting ON: Press 1 (1 PlotON). • To set the all plotting OFF: Press 2 (2 PlotOFF). * You can control the plotting of PLOT1 to PLOT3 separately by pressing 1 ~ 3 after PlotON (or PlotOFF). 4. Press E to set. 4. Trace function of statistical graphs • The trace feature is available in statistical graphing and can be used to trace the curves of graphs with the cursor. Tracing the graph 1. Press U. Histogram How tracing is done 2.Use ; or ' to move the cursor pointer to trace the graph curve. • After pressing U, the cursor pointer will appear on the top left corner of the first bar. • If you press ; or ', the cursor pointer sequentially jumps between top left corners of the bars. • X and Y values are displayed at the bottom line of the screen. • Use { or } to change between graphs to trace. Box plots and modified box plots • After pressing U, the cursor pointer will appear on the Med value of sample (x). • If you press ; or ', the cursor pointer sequentially jumps among specific values, such as Q1, Q3, min, max. • The value of cursor pointer position is displayed at the bottom line of the screen. Pie chart 160 • If you press ; or ', the cursor pointer sequentially trace the chart. The cursor is displayed at the outside the graph, and the selected chart is highlighted. Chapter 8: Statistics & Regression Calculations 4. Data list operations Descending sort, ascending sort, changing the list order and deleting the lists can be done in the Operation menu. Press S B OPE to access the data list operations. 1 sortA( sortA(list) Sorts the list in ascending order. This function is the same as the sortA( menu item in List functions. See page 136 for details. 2 sortD( sortD(list) Sorts the list in descending order. This function is the same as the sortD( menu item in List functions. See page 136 for details. 3 SetList SetList list name 1 [, list name 2 ...] Changes the list order as specified. Example To change the order of lists in order of L2, L3, L1. Press E to execute. Each list must be separated by a “ , ” (comma). • If only a single list name is specified, the specified list moves to the left end of the table. • After changing the list order, execute SetList with no argument. The list names are redefined according to the changing order. 4 ClrList ClrList list name 1 [, list name 2 ...] Deletes all the data from the specified list(s). Example To delete the data of L1 and L2. Press E to execute. Each list must be separated by a “ , ” (comma). 161 Chapter 8: Statistics & Regression Calculations 5. Regression Calculations Accessing the regression menu 1. Press S D REG. The Regression menu is displayed. 01 Med_Med Med_Med (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line using the median-median method. (linear regression) Formula: y = ax + b Parameters: a, b 02 Rg_ax+b Rg_ax+b (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line. (linear regression) Formula: y = ax + b Parameters: a, b, r, r2 03 Rg_ax Rg_ax (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line. (linear regression) Formula: y = ax Parameters: a, r2 04 Rg_a+bx Rg_a+bx (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line. (linear regression) Formula: y = a + bx Parameters: a, b, r, r2 05 Rg_x2Rg_x2 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line using the second degree polynomial. (quadratic regression) Formula: y = ax2 + bx + c Parameters: a, b, c, R2 162 Chapter 8: Statistics & Regression Calculations 06 Rg_x3Rg_x3 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression line using the third degree polynomial. (cubic regression) Formula: y = ax3 + bx2 + cx + d Parameters: a, b, c, d, R2 07 Rg_x4Rg_x4 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the fourth degree polynomial. (quartic regression) Formula: y = ax4 + bx3 + cx2 + dx + e Parameters: a, b, c, d, e, R2 08 Rg_ln Rg_ln (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the natural logarithm. (natural logarithm regression) Formula: y = a + b ln x Parameters: a, b, r, r2 09 Rg_log Rg_log (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the common logarithm. (common logarithm regression) Formula: y = a + b log x Parameters: a, b, r, r2 10 Rg_abxRg_abx (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the exponential function. (exponential regression) Formula: y = abx Parameters: a, b, r, r2 11 Rg_aebxRg_aebx (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the Euler exponential function. (Euler exponential regression) Formula: y = aebx Parameters: a, b, r, r2 163 Chapter 8: Statistics & Regression Calculations 12 Rg_x–1Rg_x–1 (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the reciprocal function. (reciprocal regression) Formula: y = a + bx-1 Parameters: a, b, r, r2 13 Rg_axbRg_axb (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the power function. (power regression) Formula: y = axb Parameters: a, b, r, r2 14 Rg_logistic Rg_logistic (list name for x, list name for y [, frequency list] [, equation name to store]) Finds the regression curve using the logistic function. (logistic regression) Formula: y = c ÷ (1 + ae-bx) Parameters: a, b, c 15 Rg_sin Rg_sin ([iterations,] list name for x, list name for y [, frequency list] [, period] [, equation name to store]) Finds the regression curve using the sine function. The calculator will fit a sine curve for unequal and equal spacing. Formula: y = a sin(bx + c) + d Parameters: a, b, c, d Note: The default iterations value is 3. The user may specify the value up to 25. To raise the accuracy, set the iterations value to 25 and enter 2π/b to the period, where b = result obtained from the calculation beforehand. 164 Chapter 8: Statistics & Regression Calculations 16 x’ value or list x’ Finds the estimated value of x for a given value of y by applying the function determined by the regression. Example When the following is entered as statistical data: x 1020304050 y 20406080100 Find estimated value of x given y = 140. 1. Enter the above data into L1 (x) and L2 (y) and execute Rg_ax+b (L1, L2). 2. Press # 140 S D 1 6 E. 17 y’ value or list y’ Find the estimated value of y for a given value of x by applying the function determined by the regression formula. Example Using above data, find the estimated value for y given x = 80, 100. 1. Press # @ { 80 , 100 @ } SD17 E. • 16 x’ and 17 y’ will be valid after executing a regression calculation excluding 2nd, 3rd, 4th, degree polynomial, logistic, and sine regressions. Using the regression functions The following table shows the relationship between the time and temperature of water, when heating a beaker filled with water. Time (min) 23 456 78910 10.5 11 11.5 12 12.5 Temperature 38.446.4 54.462.569.6 76.182.488.6 93.494.9 96.598.299.1 100 (°C) 165 Chapter 8: Statistics & Regression Calculations Enter a data in a list table 1. Press S A E. 2. Enter the time into list 1 (L1). 3. Enter the temperature into list 2 (L2). Plotting the data 1. Press [ A E. 2. Press E to turn on the plotting. 3. Press } and ' to select XY of DATA menu and press E. Freq will change to ListY and set L2 to ListY. Selecting the graph type 1. Press } to move the cursor to GRAPH. 2. Press [ G and 2 (2 Scattr+) to set the graph type to scatter and point type to “+”. 3. Press Z A 9 (9 Stat) to plot the scatter diagram for this data. • Selecting A 9 in the ZOOM mode allows for quick graphing in an optimum range since window setting values of the graph plotting screen are automatically set using the list data. Drawing a regression curve using quadratic regression 1. Press # C S D 0 5 (05 Rg_x2). 2. Press ( @ 1 , @ 2 , @ z A E A 1 ). If you enter Y1 as the last variable, the obtained formula will automatically be set to the formula Y1. 3. Press E. The regression formula and parameters will be displayed on the screen. 4. Press G. The calculator will draw the scatter diagram using the determined parameter values. 5. If there is a large difference between the regression curve and plotted dots, change the regression curve and repeat the above procedures. 166 Chapter 8: Statistics & Regression Calculations About the residual list • There are residuals between regression curves and actual values. • The residual list stores these residuals automatically. • The resid list can be found in B REGEQN of the STAT VARS menu (@ z H E B 0). • Use the following key operation to recall the residual list from the calculation screen. #[email protected] • Press E to display the residual list on-screen. • To show the residual list in the form of a graph, first store as a list, then follow the graphing operation. *resid cannot be graphed when specified independently. 6. Statistical Hypothesis Testing • The calculator performs hypothesis tests on statistical data. Start a statistical test 1. Press S E (E TEST). The statistics test menu will appear. 2. There are 17 options in the statistics test menu. Press ' to navigate between pages, and press { or } to scroll the window. 3. Press the appropriate number to access a specific test. The statistics test window will appear. 4. Input appropriate information in the test window. • There are two types of input, from a statistics data list or inputting numerical values. • Some tests may not allow for inputting from the statistics data lists. 167 Chapter 8: Statistics & Regression Calculations • 16 InputList and 17 InputStats specify the above input methods. 16 InputList: 17 InputStats: Sets the input mode to the value input mode Sets the input mode to the statistic data list method For example, press S E 1 6 E to set to the list input mode. 5. Press @ h to execute the hypothesis test. Note: • Either list input or parameter input may be used for tests other than 01 χ2test, 05 TtestLinreg, 10 Ztest1prop, 11Ztest2prop, 14 Zint1prop and 15 Zint2prop. • To clear the contents entered in Freq, move the cursor to the list name then press D E. 01 χ2 test Uses the sample data from a two-dimensional table represented by a matrix. Example If mat A = 3254 6138 2351 execute the χ2test and store the obtaining results in mat B. 1. Press S E 0 1. 2. Enter mat A as the Observed Matrix, and mat B as the Expected Matrix. Press @ m A [email protected] A 2. 3. Press @ h to execute the χ2 test. The result is entered in mat B. 2 χ :χ-squared statistic for the test p: p value for the test df:degrees of freedom 168 Chapter 8: Statistics & Regression Calculations 02 Ftest2samp Two samples data are tested for equality of standard deviation σ1 and σ2. Example Test when population standard deviation σ1 < σ2, n1 = 20, standard deviation sx1 = 5.6, n2 = 50, and standard deviation sx2 = 6.2 Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 0 2. The parameter input screen will appear. 3. Press ' E } to select σ1 < σ2. 4. Enter the values into the parameter fields. 5.6 E 20 E 6.2 E 50 E. 5. Press @ h to execute the test. 03 Ttest1samp F: Statistics p: Probability Tests the hypothesis of population mean µ. Example Test the population mean µ0 = 65 with the sample data of {65.6, 62.8, 66.0, 64.5, 65.1, 65.3, 63.8, 64.2, 63.5, 64.4}, from a given population (alternate hypothesis of µ < µ0) 1. Enter the above statistical data into L1. Press S E 1 6 E to set the list input mode. 2. Press S E 0 3. The parameter input screen will appear. 169 Chapter 8: Statistics & Regression Calculations 3. Press ' E } to select µ < µ0 and press E. 4. Move the cursor pointer to µ0 and input 65 and press E. 5. Set the List to L1 and press E. 6. Press @ h. Answers are displayed on the screen, where t is the t statistic for the test, p is the p value for the test and sx indicates sample standard deviation. • If there is no weight list, the Freq field can remain empty. 04 Ttest2samp Tests two sample means, µ1 and µ2. Example Test the following two samples; List 1 {2.37, 2.51, 2.43, 2.28, 2.46, 2.55, 2.49} List 2 {2.63, 2.71, 2.56, 2.61, 2.55, 2.68, 2.42, 2.48, 2.51, 2.65} 1. Enter the above data into lists L1 and L2, respectively. 2. Press S E 0 4. The parameter input screen will appear. 3. Enter the appropriate value into each field. If no Freq specification data is input, an initial Freq value of 1 is used. * Pooled is prediction for unknown σ1, σ2. Select “No” if σ1, σ2, are subjectively unequal. Select “Yes” if σ1, σ2, are equal. Calculation is executed using this prediction as the basis. 170 Chapter 8: Statistics & Regression Calculations 4. Press @ h. 05 TtestLinreg Tests the significance of the slope for the linear regression and its correlation coefficient ρ. Example The test is for the slope β, and correlation coefficient ρ obtained from statistical data X {65, 56, 78, 86, 92, 71, 68} and Y {95, 59, 88, 78, 75, 68, 80} are not equal to zero (β & ρ ≠ 0.) 1. Input the above lists X and Y into lists L1 and L2, respectively. 2. Press S E 0 5. The parameter input screen will appear. 3. Enter the appropriate value into each field. • Equation items may not be required. • If a linear regression calculation has been executed using the data, and the function equation has been stored in Y0 to Y9, input that equation number for the equation items. 4. Press @ h. Answers are displayed on the screen, where a, b indicate regression coefficients, s indicates standard deviation, r indicates the correlation coefficient, and r2 indicates the coefficient of determination. 171 Chapter 8: Statistics & Regression Calculations 06 Tint1samp Finds the confidence interval for the population mean µ. Example Find the confidence interval for the statistical data of {65.6, 62.8, 66.0, 64.5, 65.1, 65.3, 63.8, 64.2, 63.5, 64.4}, from a given population and the level of confidence is 0.99. 1. Enter the above statistical data into list L1. 2. Press S E 0 6. The parameter input screen will appear. 3. Enter the C-level value of 0.99. 4. Set the List to L1 and press E. 5. Press @ h. Answers are displayed on the screen, where sx indicates the sample standard deviation. • If you enter a value from 1 to 100 for the C-level, it will be changed to the % input mode. • In the numerical value input mode, n is a positive integer. 07 Tint2samp Finds the confidence interval for the difference of two sample means, µ1 and µ2. Example Use the following two sample data (used for example 04); List 1 {2.37, 2.51, 2.43, 2.28, 2.46, 2.55, 2.49} List 2 {2.63, 2.71, 2.56, 2.61, 2.55, 2.68, 2.42, 2.48, 2.51, 2.65}, with the level of confidence of 0.99. 172 Chapter 8: Statistics & Regression Calculations 1. Enter the above data in to lists L1 and L2. 2. Press S E 0 7. The parameter input screen will appear. 3. Enter the appropriate value in each field. 4. Press @ h. Answers are displayed on the screen, where the numerical value within () indicates the confidence interval for the differences between µ1 and µ2 when the level of confidence is 99%. In the numerical value input mode, “n1”, “n2” are positive integers. 08 Ztest1samp Tests the hypothesis of population mean µ. Example The average weight of a newly developed product is known to be 53.4 g and standard deviation (σ) is 4.5. Judge the validity when the average weight of 20 units is 52.4 g (x). Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 0 8. The parameter input screen will appear. 3. Set the alternate hypothesis to µ ≠ µ0, µ < µ0 and µ > µ0 (two-tail test, one-tail test settings). In this case, choose µ ≠ µ0 (two-tail test). 173 Chapter 8: Statistics & Regression Calculations • µ0 indicates the hypothesis mean, σ indicates the population standard deviation, x indicates the sample mean and n indicates the sample size. (“n” is a positive integer.) 4. Enter the appropriate value in each field. 5. Press @ h. Answers will be displayed on the screen, where z indicates the test statistic and p indicates the p value of the test. 09 Ztest2samp Tests the equality of two sample means, µ1 and µ2. Example _ _ Test µ1 > µ2 where x1 = 77.3, σ1 = 3.4, n1 = 30, and x2 = 75.2, σ2 = 2.8, n2 = 20. Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 0 9. The parameter input screen will appear. 3. Enter the appropriate value into each field. 4. Press @ h. Answers will be displayed on the screen. 174 Chapter 8: Statistics & Regression Calculations 10 Ztest1prop Tests the success probability P0 of a population. Example A coin was tossed 100 times and landed head side up 42 times. Normally, the probability of head facing up is 0.5. Test to see if the coin is fair. 1. Press S E 1 0. The parameter input screen will appear. • prop is the hypothesis probability. The test will be conducted using hypothesis prop ≠ P0. • x is the number of successes observed and n is the number of trials (where n is a positive integer.) 2. Enter the appropriate value into each field. 3. Press @ h. ^: Success probability p obtained from the sample data. 11 Ztest2prop Executes a comparative test for two success probabilities, (P1, P2). Example Test the equality of P1 and P2 given the sample data n1 = 50, x1 = 16 and n2 = 20, x2 = 5, where the hypothesis is P1 < P2. 1. Press S E 1 1. The parameter input screen will appear. 2. Enter the appropriate value into each field. 175 Chapter 8: Statistics & Regression Calculations 3. Press @ h. Answers will be displayed on ^ the screen, where P indicates the calculated success rate of the data combined with sample data 1 and 2, and ^ ^ P1 and P2 show the success rates of sample data 1 and 2, respectively. n1 and n2 are positive integers. 12 Zint1samp Finds the confidence interval of a population mean, µ. Example The average weight of a newly developed product is known to be 52.4 g and standard deviation (σ) is 4.5. Given the average weight of 20 units is 53.4 g (x), find the confidence interval of the data where the level of confidence (C-level) is 0.95. Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 1 2. The parameter input screen will appear. 3. Enter the appropriate value into each field. 4. Press @ h. Answers will be displayed on the screen, where the numerical value within () indicates the confidence interval with the level of confidence at 0.95, that is, the confidence interval of this sample data with the confidence level of 95% is between 51.427… and 55.372…. C-level indicates the level of confidence and n is a positive integer. 176 Chapter 8: Statistics & Regression Calculations 13 Zint2samp Finds the confidence bound of two sample means µ1 and µ2. Example Find the confidence interval of µ1 and µ2 of sample data with the _ _ confidence level of 0.9, where x1 = 77.3, σ1 = 3.4, n1 = 30 and x2 _ _ = 75.2, σ2 = 2.8, n2 = 20 (x1 and x2 indicate sample means of two data.) Set the input method to value input mode 1. Press # S E 1 7 E. 2. Press S E 1 3. Parameter input screen will appear. 3. Enter the appropriate value into each field. 4. Press @ h. Answers will be displayed on the screen, where the numeric value within () indicates the confidence interval of µ1 and µ2 at a confidence level of 90%. *n1 and n2 are positive integers. 14 Zint1prop Finds the confidence interval of the success probability of a population from the success probability obtained from sample data collected from a population. Example A coin was tossed 100 times and landed head side up 42 times. Normally, the probability of head facing up is 0.5. Find the confidence interval of the success probability at a confidence level of 0.95. 1. Press S E 1 4. The parameter input screen will appear. 177 Chapter 8: Statistics & Regression Calculations 2. Enter the appropriate value into each field. 3. Press @ h. Answers will be displayed on the screen, where the numerical value within () indicates the confidence interval of the success probability at a confidence level of 95%. * n is a positive integer. 15 Zint2prop Finds the confidence interval of the difference (P1-P2) of the success probability obtained from the two sets of sample data collected from two different populations. Example Find the confidence interval of the success probability (P1, P2) at a confidence level of 0.9 for the two sets of sample data n1 = 50, x1 = 16 and n2 = 20, x2 = 5. 1. Press S E 1 5. The parameter input screen will appear. 2. Enter the appropriate value into each field. 3. Press @ h. 4. Answers will be displayed on the screen, where the numerical value within () indicates the confidence interval of the success probability P1-P2 at a confidence level of 90%. *n1 and n2 are positive integers. 178 Chapter 8: Statistics & Regression Calculations 7. Distribution functions The calculator has distribution features to find statistical calculations. To enter the distribution menu, 1. Press S F (F DISTRI). The distribution menu will appear. 2. There are 15 options in the distribution menu. Press ' to navigate between pages, and press { or } to scroll the window. 3. Press E to select the function. 4. Input the specified values. 5. Press E to solve. Note: All functions of the distribution feature can be displayed as a graph by using the graphing feature. 01 pdfnorm( pdfnorm(value [, mean, standard deviation]) Finds the probability density of the specified value x for the normal distribution N(µ, σ2). A list cannot be used. *When mean (µ) and standard deviation (σ) are omitted, µ = 0 and σ = 1 are applied. Example Find the nominal distribution probability density for x = 65 when the normal distribution of the test score averages is 60 with a standard deviation of 6. 02 cdfnorm( cdfnorm(lower limit, upper limit [, mean, standard deviation]) Calculates the normal distribution probability of a specified range x for the normal distribution N(µ, σ2). A list cannot be used. *When mean (µ) and standard deviation (σ) are omitted, µ = 0 and σ = 1 are applied. Example Calculate the probability of range x = 54 to 66 in the above sample. 179 Chapter 8: Statistics & Regression Calculations 03 InvNorm( InvNorm(probability [, mean, standard deviation]) Finds the value of x of a given normal distribution probability. A list cannot be used. *When mean (µ) and standard deviation (σ) are omitted, µ = 0 and σ = 1 are applied. Example Find the value of x for the probability of 0.8 in the above sample. 04 pdfT( pdfT(value, degree of freedom) Finds the probability density of a specified value x for the T distribution with n degrees of freedom. A list cannot be used. Limitations: Degree of freedom ≤ 140 • Degrees of freedom is a positive real number. If decimal values are used for the degrees of freedom, the calculator uses the closest integer of the given degree of freedom. • An error may occur when an extremely large number is entered for degree of freedom. Example Find the probability density of the T distribution with 9 degrees of freedom when x = 2.5. 180 Chapter 8: Statistics & Regression Calculations 05 cdfT( cdfT(lower limit, upper limit, degree of freedom) Finds the T distribution probability within the specified range of x for the T distribution with n degrees of freedom. A list cannot be used. Limitations: Degree of freedom ≤ 670 • Degrees of freedom is a positive real number. Example Find the probability of range X = 0.5 to 3.2 for T distribution with 9 degrees of freedom. 06 pdfχ2(pdfχ2(value, degree of freedom) Finds the probability density of a specified value x for the χ2 distribution with n degrees of freedom. A list cannot be used. Limitations: Degree of freedom ≤ 141 • Degree of freedom is a positive real number. Example Find the probability density of χ2 distribution with 15 degrees of freedom when x = 6.5. 07 cdfχ2(cdfχ2(lower limit, upper limit, degree of freedom) Finds the χ2 distribution probability of a specified range of x for the 2 χ distribution with n degrees of freedom. A list cannot be used. • Degree of freedom is a positive real number. Example Find the probability of range x = 3 to 15 for the χ2 distribution with 10 degrees of freedom. 181 Chapter 8: Statistics & Regression Calculations 08 pdfF( pdfF(value, degree of freedom of numerator, degree of freedom of denominator) Finds the probability density of a specified value x for the F distribution that possesses two independent degrees of freedom, m and n. A list cannot be used. Limitations: Degree of freedom ≤ 70 • Degree of freedom is a positive real number. • An error may occur when an extremely large number is entered for degrees of freedom. Example Find the probability density for the F distribution generated with degrees of freedom 15 and 10 when x = 3. 09 cdfF( cdfF(lower limit, upper limit, degree of freedom of numerator, degree of freedom of denominator) Finds the F distribution probability of a specified range x for the F distribution with two independent degrees of freedom, m and n. A list cannot be used. Limitations: Degree of freedom ≤ 670 • Degree of freedom is a positive real number. • An error may occur when an extremely large number is entered for degree of freedom. Example Find the probability of the range x = 0 to 2.5 for the F distribution generated with degrees of freedom 15 and 10. 182 Chapter 8: Statistics & Regression Calculations 10 pdfbin( pdfbin(trial number, success probability [, success number])) Finds the probability density of a specified value x for the binomial distribution. A list cannot be used except for success numbers. When the success number is not specified, the calculation is executed by entering values from 0 to the trial number and displays the list. Limitations: Success probability is 0 ≤ p ≤ 1. Example Find the probability density for 15 trials with x = 7, for the binomial distribution with success probability of 30%. 11 cdfbin( cdfbin(trial number, success probability [, success number])) Finds the probability of a specified range x for the binomial distribution. A list cannot be used except for success numbers. When the success number is not specified, the calculation is executed by entering values from 0 to the trial number and displays the list. Example Find the probability of range up to x = 7 for the F distribution generated with degrees of freedom 15 and 10. Note for When using function terms, please note that values for the number 10 pdfbin(, 11 cdfbin(: of trials and for the success number must be integer(i.e. must be rounded). E.g. inputting Y1=pdfbin(X, 0.5, 0) provides a value table, but no graph is drawn. If X is replaced by „intX“, the expected graph is displayed. 12 pdfpoi( pdfpoi(mean, value) Finds the probability density of a specified value x for a Poisson distribution of mean µ. Limitations: Mean of Poisson distribution ≤ 230 Example Find the probability density of x = 4, for the mean of a Poisson distribution of 3.6. 183 Chapter 8: Statistics & Regression Calculations 13 cdfpoi( cdfpoi(mean, value) Finds the probability of a specified range x for a Poisson distribution of mean mu. Example Find the probability within the range up to x = 4. 14 pdfgeo( pdfgeo(success probability, value) Finds the probability density of a specified value x for the geometric distribution. Limitations: Success probability is 0 ≤ p ≤ 1. Example Find the probability density of a geometric distribution of success at the 26th time with success probability of 5.6%. 15 cdfgeo( cdfgeo(success probability, value) Finds the probability of a specified range of x for the geometric distribution. Limitations: Success probability is 0 ≤ p ≤ 1 Example Find the probability for the range up to x = 26 with success probability of 5.6%. 184 Chapter 9 Financial Features The financial calculation features include capabilities for compound interest calculations. Press @ g. The financial menu screen will appear. • Specifies the TVM-SOLVER mode. • Selects a financial calculation function • Specifies payment due (to pay at the beginning or end of period) • Determines individual settings (in TVM-SOLVER mode) 1. Try it! 1 You plan to purchase a house for a price of $300,000. The down payment is $100,000. Calculate the monthly payments for a 30year loan at an annual interest rate of 5% for the remaining $200,000. Draw a cash flow diagram on paper 1. Draw the following cash flow diagram to simplify the problem. (+) Present Value (PV) = 300,000 – 100,000 = 200,000 I = 5% Cash flow (–) 1 2 3 Time flow PMT = ? Future Value (FV) = 0 358 359 N = 12 × 30 = 360 • A horizontal line indicates a time flow (left to right) divided into even sections — months in this case. Each section indicates a compound period and the total number of sections indicates the total number of periods for payment. 185 Chapter 9: Financial Features • Vertical arrows along the horizontal line indicate the cash flow. An UP arrow indicates inflow (+) and a DOWN arrow indicates outflow (–). • The calculator considers the cash inflow for each period is constant. (Even payment.) 2. Determine the time each payment is due. For deposits and loan payments, the time each payment is due (paid at the beginning or the end of the period) makes for a different cash flow diagram. Payment due at the end of the period (+) PV I% FV Cash flow 1 (–) 2 Time flow N–1 N PMT Payment due at the beginning of the period (+) PV I% FV Cash flow (–) 1 2 Time flow PMT N–1 N In this case payment is due at the end of the period. 3. Determine the inflow and outflow and place the present value (PV = $200,000) on the diagram. We can consider the present value (PV) as a loan and thus inflow (revenue) from the customer’s point of view. So, place the PV at the top left end of the diagram. We also can consider the principal interest total (Future value) as outflow (payment). Draw a vertical line with a DOWN arrow on the top of the diagram. 4. Complete the diagram with interest (I%), number of payment periods (N), future value (FV), and other required numbers. 186 Chapter 9: Financial Features Starting the calculation Setting the payment due time 5. Press @ g. 6. Press C (C PERIOD). 7. Press 1 (1 PmtEnd) and press E. Enter the value using the SOLVER function Payment due time is now set to the end of the period. 8. Press @ g. 9. Press A E. 10.The following TVM-SOLVER screen will appear. The payment due time is set to the end of the period. The payment due time is set to the end of period. Payment due settings Number of payment periods Interest Present value (principal sum) Payment or received amount Future value (principal interest total) Number of payments per year Cumulative interest per year 11.Input 360 for N (number of payment periods) and press E. The cursor moves to “I%”. 12.Input 5 for I% (annual interest) and press E. 13.Input 200000 for PV (present value) and press E. 14.Press E. Since the payment amount is to be calculated from the other values, no value must be entered for PMT (payment or received amount). 15.Press E again. Since FV (future value) is “0” at the end, no value must be entered for FV. 16.Press 12 for P/Y (number of payments per year) and press E. 187 Chapter 9: Financial Features 17.Press E. Usually C/Y (cumulative interest per year) is the same value as P/Y. If not, enter the value instead. 18.Press { 3 times to move the cursor to PMT (payment amount). 19.Press @ h. The result will appear as follows. 20.Payment amount per month PMT = -1073.643246 (Negative value indicates payment.) The numerical value input format and display format in the FINANCE mode comply to that of SETUP. The above answer is given when the FSE setting in SET UP menu is set to FloatPT. If you wish to display 2 digit decimal point format, set TAB to 2 and FSE to FIX. Answer: You have to pay $1,073.64 per month for 30 years. Simple interest and compound interest There are two ways to calculate interest: simple and compound. In the FINANCE mode, the calculator can execute compound interest calculations. Example of depositing $10,000 in a bank for 3 years at an annual interest rate of 3% Period Simple interest First year Receive $10,000 x 0.03 = $300 Second year Receive $300 (constantly) Third year Receive $300 (constantly) Compound interest Receive $10,000 x 0.03 = $300 Receive $10,300 x 0.03 = $309 Receive $10,609 x 0.03 = $318.27 With compound interest, the amount in the bank is increased by receiving interest on the interest gained during each calculated period. 188 Chapter 9: Financial Features 2. Try it! 2 If the monthly payments in the first example is limit to a fixed $800, how much must be the present value (PV) and the required amount of down payment. (+) PV = 300,000 – down payment I = 5% FV = 0 Cash flow 1 (–) Set the TAB and FSE (2 and FIX respectively) 2 3 Time flow PMT = 800 358 359 N = 360 1. Press @ ; C 2 D 2 TAB is set to 2 and FSE is set to FIX. 2. Press C @ g A and E. The previous TVM-SOLVER screen will appear with the cursor flashing on N. 3. Press } three times to move the cursor to PMT. 4. Press _ 800 and E. Be sure to enter the minus sign to indicate payment. 5. Move the cursor to PV. 6. Press @ h. 7. PV will change to 149025.29 • This indicates that the total amount over 30 years will be $149,025.29 if the maximum monthly payment is limited to $800. 189 Chapter 9: Financial Features • So, the required amount of down payment is $300,000 – $149,025.29 = $150,974.71. Using the TVM-SOLVER screen, you can obtain various results by inputting the known variables and then moving the cursor to the unknown variable and pressing @ h. The value where the cursor pointer is placed will be calculated from the known variables. Example Compare the principal interest total when accumulating an interest of 2.18% monthly on $100 for 5 years with payment due at the beginning of the period and at the end of the period. 1. Payment due at the beginning of the period 1. Press @ g C 2 and press E. 2. Press @ g A E. Payment due is now set to the beginning of the period. 3. Enter the values. 4. Move the cursor to FV and press @ h. 2. Payment due at the end of the period. 1. Press @ g C 1 and press E. 2. Press @ g A E. Payment due is now set to the beginning of the period. 3. Enter the values. 4. Move the cursor to FV and press @ h. 190 Chapter 9: Financial Features 3. CALC functions Press @ g B to access the CALC functions. The CALC functions 01 to 05 calculate any of the following variables from the other variables. (The same calculations are possible as the SOLVER functions.) N: I%: PV: PMT: FV: P/Y: C/Y: Number of payment periods Interest Present value (principal sum) Payment or received amount Future value (principal interest total) Number of payments per year Cumulative interest per year • The contents calculated on the calculation screen do not affect the variable values in the TVM-SOLVER. 01 slv_pmt solv_pmt [(N, I%, PV, FV, P/Y, C/Y)] Calculates monthly payment (PMT) 02 slv_I% slv_I% [(N, PV, PMT, FV, P/Y, C/Y)] Calculates annual interest 03 slv_PV slv_PV [(N, I%, PMT, FV, P/Y, C/Y)] Calculates present value (PV) 04 slv_N slv_N [(I%, PV, PMT, FV, P/Y, C/Y)] Calculates the number of payment periods (N) 05 slv_FV slv_FV [(N, I%, PV, PMT, P/Y, C/Y)] Calculates future value (FV) 191 Chapter 9: Financial Features 06 Npv ( Npv (Interest rate, initial investment, list of following collected investment [, frequency list]) Calculates the net present value and evaluates the validity of the investment. You can enter unequal cash flows in the list of following collected investment. Example The initial investment is $25,000 planning to achieve the profits each year as shown on the right, Evaluate whether annual revenue of 18% is achieved. $11K $9K $7K 1 $25,000 $8K $5K 2 3 4 5 Year *You can execute the calculation by using a list or a frequency list calculation. 07 Irr ( Irr (initial investment, list of following collected investment [, frequency list] [, assumed revenue rate]) Calculates the investment revenue rate where the net present value is 0. Example If the investment for the sales plan in the previous example is $28,000, how much is the investment revenue rate? • 12.42 is obtained as the answer, thus, the investment revenue rate for the above condition is 12.42%. * In the previous example, revenues following the investment value (input using minus sign) were assumed to be positive. However, when the assumed revenue is set to minus (in other words, more than two inverse symbols), the assumed revenue rate must be entered at the end. Otherwise an error may occur. 192 Chapter 9: Financial Features The following CALC functions, 08 Bal, 09 ΣPrn and 10 ΣInt require the values of I%, PV and PMT variables. Enter the values beforehand in the TVMSOLVER function. Example using the 08 and 10 calculations You plan to purchase a house for the price of $300,000. The down payment is $100,000. Calculate the monthly payments for a 30-year loan at an annual interest rate of 5% for the remaining $200,000. 08 Bal ( Bal (number of payments [, decimal place to round]) Calculates loan balance. Calculate the loan balance after 15 years (180 months). 09 ΣPrn ( ΣPrn (initial number of payments, end number of payments [, decimal place to round]). Calculates the principal amount of the total payments. Compare the principal amount of the total payments after 5 (1 to 60 months) and 10 years (61 to 120 months). 10 ΣInt ( ΣInt (Initial number of payments, end number of payments [, decimal place to round]) Calculates the sum of the interest on the payments. Compare the sum of the interest on the payment sum after 5 years and 10 years. 193 Chapter 9: Financial Features Conversion functions 11 →Apr ( →Apr (effective interest rate, number of settlements) Converts effective interest rate to nominal interest rate Example If the effective interest rate is 12.55%, how much is the nominal interest rate for the quarterly compound interest? If the monthly compound interest rate is 10.5%, how much is the nominal interest rate? 12 →Eff ( →Eff (nominal interest rate, number of settlements) Converts nominal interest rate to effective interest rate Example If the annual (nominal) interest rate is 8%, how much is the effective interest rate for monthly compound interest? How much is it over half a year? 13 days ( days (start month.day year, end month.day year) days (day month.year, day month.year) Calculates the number of days between dates entered (within the range of 1950 to 2049) Year, month, and day must be entered in 2-digit form. For example, enter 02 for 2002. Calculate the number of days from September 1, 2012 to December 31, 2019. 194 Chapter 9: Financial Features 4. VARS Menu The VARS menu consist of a list of the variables used for the TVM-SOLVER functions. • The VARS menu can be used to enter values in the sub-menu within the Finance menu. 1. Press @ g D. 2. The VARS sub-menu will appear. 3. Select the appropriate variable to use. The variables in the VARS sub-menu are the same as those of the TVM-SOLVER feature. How to recall the content of N 1. Press # @ g D 1 E. How to recall the content of I% 2. Press @ g D 2 E. How to recall the content of PV 3. Press @ g D 3 E. How to reenter the value • Each variable of the TVM-SOLVER can be recalled and then reentered. Reenter 400 for N instead of 360 1. Press 400 R. 2. Press @ g D 1 E. 195 Chapter 10 The SOLVER Feature The SOLVER feature is one of the calculator’s most powerful and distinctive features, and helps you solve math problems with various analysis methods. Using this feature, problems from linear equations to complex formulas can be solved with ease. To access the SOLVER feature, press @ '; to exit, press #. Note: The SOLVER feature shares variables with other calculator features. These variables can be called up or defined within the SOLVER feature or any other features. For example, solving/ defining a value of “A” within the SOLVER feature will also change the global value of “A”. 1. Three Analysis Methods: Equation, Newton & bisection, and Graphic To switch your preferred analysis style: 1. Go into the SOLVER menu by pressing @ ' within the SOLVER window. The SOLVER menu appears with four menu items. 2.While A METHOD item is selected on the left, select your preferred method by pressing 1, 2, or 3. Equation method Note: When you enter an equation, you can use graph equations variables (Y1 - Y0) which are defined in the Graph Equation window. The Equation method is useful when there is only one unknown variable. For example, if you know the values of B and C for an expression “A + B = C”, use the Equation method. Example Determine the value of “C” in “A = 2B2 + 4C”, when A = 4, and B = 5. 196 Chapter 10: The SOLVER Feature 1. Enter SOLVER by pressing @ '. The word SOLVER will flash on the screen, indicating that you are now in the SOLVER feature mode. 2. Enter the equation “A = 2B2 + 4C”. Press A A A = 2ABy+4 A C. 3.Press E. The screen above right appears, indicating that there are 3 variables to be assigned. Note: If values were assigned to those variables prior to this operation, then the previously set values will be shown here. For example, “C = 57” may show up in this window; this simply indicates the value of “C” was previously set to “57”. 4. Enter “4” for variable “A”, and “5” for variable “B”. Press 4 E 5 E. 5. When the two known values have been specified, make sure that the cursor is at the value yet to be determined (in this case, the value of “C”). 6.Press @ h to execute the SOLVER. The value of “C” will be obtained. *After the solution has been found, press C to return to the variable input screen. You may change the numeric values for the variables and select another unknown variable to solve. *To edit the equation, press C on the variable input screen. The equation input screen allows you to correct or edit the previously input equation. 197 Chapter 10: The SOLVER Feature Newton& bisection method Newton&bisection method is a technique of finding approximate solutions to a math problem via calculus, when conventional algebraic techniques just cannot work. If the Equation method fails, the calculator will automatically switch to Newton&bisection method. Example Solve “X2 + 4X – 2 = 0”. 1. Enter SOLVER by pressing @ '. If you have items left on the screen, clear the entries by pressing the C key several times. 2. Enter “X2 + 4X – 2”. When the expression is entered as a non-equation format, then “=0” is automatically assumed at the end. When done, press E. 3. The next screen indicates the variable “X” and its previously set value. This value will be assumed as the starting point of the calculation segments, and the Newton&bisection SOLVER will find the closest approximation to the starting point. Enter “0”, and press E. 4. Now, press @ h to execute the SOLVER. Since this cannot be solved using the Equation method, the calculator automatically switches analysis to Newton&bisection method. 5. The next window confirms the starting point of the analysis (set to “X = 0” from step #3), and the size of each step (default is set to “0.001”). Press @ h. 198 Chapter 10: The SOLVER Feature 6. The following window shows the approximate value of X (0.449489742), the right side value of the equation (assumed as “0”, at step #2), the left side value (which the entered expression results to this value when the value X is entered), and the difference between the left and the right side. 7. Since the L-R difference above indicates a margin of error, try entering smaller steps. Press C to go back to step #3. Enter the value of X, then press @ h to execute the SOLVER again. When the next window appears, try entering smaller step value (“0.00001”, for example). 8. Press E to register the step value change, then @ h. Although the value of X appears to be unchanged, the margin of error will have become small enough (“0”, in this example), to be as close to zero as possible. Note: As you may well know, there may be more than one solution to the equation. To obtain the value of the other solutions, set the starting point of Newton&bisection method lower (“-10”, for example) or execute the SOLVER again with the current solution as a starting point. 199 Chapter 10: The SOLVER Feature Graphic method The Graphic method is another way of approximating solutions, using graphical representations. This method is particularly useful when finding more than one solution on a graph axis. Example Obtain values for “Y = X3 – 3X2 + 1”, when Y = 0. 1. Press @ ' to enter SOLVER. Clear screen entries by pressing C several times. 2. Enter “Y = X3 – 3X2 + 1” into the initial window, and press E. 3. In the next window, set the Y value as “0”, and press E. The right side value of the equation is now set. Note: Unlike in the Newton&bisection method, the X value will not be assumed as the starting point for the Graphic method. 4. Before proceeding further, you will need to set the SOLVER to the Graphic method. Press @ ' to call up the SOLVER menu, and press A (for A METHOD), then 3 (for 3 Graphic). The Graphic method is now set. 5. Press @ h to proceed. 6. Next in the following window, specify the range of analysis that will incorporate all possible solution. In this example, we will set the beginning point at “-1”, and the end point at “3”. Press E at each variable entry. 200 Chapter 10: The SOLVER Feature Note: The analysis will be limited to the range specified; a solution outside of the analysis range will not be detected. If no crossing point is found in the range, then a message “No solution found” will show at the bottom of the screen. 7. Pressing @ h at this point will engage the analysis, as well as the graphical representation of the equation. Note that while the cursor flashes at the upper right corners of the screen, the calculator is busy processing tasks. 8. When the processing is complete, you will get the first value of X (the smallest), with a flashing star on the graph at the crossing point. To obtain the next X value, press @ k. Note: To enlarge a part of graph after the solution has been found, you may use the ZOOM Box function. Press Z and use the cursor for defining the box area. 201 Chapter 10: The SOLVER Feature 2. Saving/Renaming Equations for Later Use The expressions you have entered in the SOLVER can be named and stored: 1. Go to the SOLVER menu by pressing @ '. 2. Press C to select the C SAVE menu, and press E. 3. When the next screen appears, ALPHA LOCK mode is automatically set and the cursor is changed to “A”, indicating that alphabet characters can be entered. To enter numbers, press A. The equation name should consist of 8 characters/numbers or less. 4. When done, press E. The screen goes back to the SOLVER function screen. Saved SOLVER expressions can also be renamed: 1. Go to the SOLVER menu by pressing @ ', and press D to select the D RENAME sub-menu. 2. A list of saved equation names appears in the submenu. Select the equation name you wish to change. For example, press 0 1 to select the first item of the list. 3. When renaming is complete, press E to save the change. 202 The screen goes back to the SOLVER function screen. Chapter 10: The SOLVER Feature 3. Recalling a Previously Saved Equation To recall a stored SOLVER equation: 1. Go to the SOLVER menu, and press B to select the B EQTN sub-menu. 2. A list of saved equation names appears in the submenu. Select the equation you wish to call back. 3. Press E. The stored equation is called back. Note: Any changes unsaved prior to recalling will be lost. Also be aware that any changes to the recalled equation will not be retained unless saved manually. Functions of the SOLVER feature Functions of the SOLVER feature are as follows: (–), (, ), =, +, –, ×, ÷, a b/c, a/b, x2, x–1, ab, , a , log, ln, log2, 10x, ex, 2x, sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1, cosh –1, tanh –1, sec, csc, cot, sec–1, csc –1, cot –1, int, pdfnorm(, pdfT(, pdfχ2(, pdfF(, pdfbin(, pdfpoi(, pdfgeo(, cdfnorm(, cdfT(, cdfχ2, cdfF(, cdfbin(, cdfpoi(, cdfgeo(, InvNorm(. 203 Chapter 11 Programming Features The calculator has programming features that enable automatic processing of a series of calculations any number of times. Almost all the calculation and graphing language can be used in programs as well as the usual control flow statements such as If, For, While and Goto (with Label). Please note that complex numbers cannot be used in programming. 1. Try it! Display a message “HELLO WORLD” on the display. Creating a new program 1. Press P. The program menu screen will appear. A EXEC Executes the selected program B EDIT Opens a stored program file. C NEW Creates a new program file D V_INDX Show variables which are used in the programs. 2. Press C E. A new program window will open. 3. Input the program name (HELLO) on the top line of the screen. Up to 8 characters can be used for the title. 4. Press E. 5. The cursor will move to the program input field just under the title. 204 Chapter 11: Programming Features Starting programming 6. Press P. The program menu will open. The commands and other statements are preinstalled in the calculator. Do not directly type in commands using the Alphabetical mode, select each command from the program menu. Note: Press @ j, and you can access all the available commands at once. Entering a command 7. Select A 1. 8. Press P. 9. Select A 2. Entering the alphabetical input lock mode Store the program line by line The characters following a double quotation mark can be manipulated as text. No double quotation mark is required to close the text. 10.Press @ . to enter the alphabetic lock mode. 11.Type HELLO WORLD. Up to 160 alphanumeric characters can be input per line. (Strings of up to 158 characters maximum can be entered per line excluding commands, because each command is regarded as a single character. When a line exceeds the width of the screen, the display will shift to the left. 12.Press E. The cursor will move to the next line and the data input will be stored. Store the program line by line by pressing E, { or }. 13.Press @ q to exit the program edit screen. Execute the program 14.Press P A. A list of stored programs will appear. Select a program by using { }, and press E. 205 Chapter 11: Programming Features 2. Programming Hints Editing the program Press P B and then the appropriate numbers to open the stored program. Press @ i to enter the insert type mode. Adding commands, strings or Press E to go to the next line. Be sure to press @ i command lines again to turn off the insert type mode and return to type over mode. to the program Press E twice to insert a blank line. Entering alphabetical characters (uppercase only) Press A to enter characters. Press @ . to use an ALPHA-LOCK mode to input a series of alphabetical characters. Inputting commands In general, only a single command can be input per line. Storing a program line by line After pressing E, } or {, the line will be stored in memory. Otherwise, it is not stored. Be sure to store the all lines by pressing E ({ or }) before quitting editing (pressing @ q). Blank line Blank lines are ignored during execution. You can include blank lines to gain better readability. Deleting a line Move the cursor to the line you wish to delete and press C. Deleting command or strings Move the cursor to on or after the letter you wish to delete and press D or B, respectively. Deleting an entire program Press @ p and use C DEL. (See Chapter 12 OPTION Menu). Copying a line to another location Press P H in the program edit mode. (See page 216 for details) Changing the program name Press { to move the cursor to the program name field. Enter the new name and press E or }. Re-executing the program Pressing E again after execution of the program completes. Break the execution process Press O or @ q to break the execution process. 206 Chapter 11: Programming Features 3. Variables • Single letters (uppercase letter from A to Z and θ) can be used as variables. • Defined once in one program, a variable is set as a global variable across all other stored programs unless redefined. Hence results calculated in one program can be used by another. • Only value (numbers) can be set as variables. • Strings cannot be set as variables. Setting a variable Use R to input a specific value or the value of formula into the variable. Do not use = (comparison operands) to set the values into variable. 5 ⇒ X The variable X is set to the value 5. MX + B ⇒ Y The variable Y is set to the value of formula MX + B. Index of variables in the programs Programs can overwrite variables that you are using, e.g., in the calculation screen. Here, you can check for which variable names this is the case. Press P D, and then select the program title. The index of variables which are used in the selected program is displayed. • The subjects of the index are as follows ; A~Z, θ, L1~L6, mat A~ mat J • Press { or } to display the previous or next program's variables. • Press @ q to exit. 4. Operands • Almost all the calculation operands can be used in a program. • Input an operand directly from the keys (+, –, ×, ÷, sin, cos, log and others) or using MATH, STAT, LIST, MATRIX and other menus. Comparison operands • The calculator has 6 comparison operands. • Press M F and select an appropriate comparison operand. =Equal ≠ Not equal > Greater than ≥ Greater than or equal < Less than ≤ Less than or equal 207 Chapter 11: Programming Features 5. Programming commands • Print, Input, Wait, Rem, End and other commands can be used in a program. Screen settings, data input/output, graph settings and others can be controlled from a program. • Press P in the program edit mode to input the command. A PRGM menu P A 1 Print Print variable Print “character strings [“] Displays the value of the variable on the screen. The display format may vary according to the SET UP menu settings. Character strings displayed by the print command will break at the edge of the screen. 2 “ command “ strings Characters enclosed by double-quote marks are considered to be strings. The closing double-quote can be omitted when it would appear at the end of a line. 3 Input Input [“prompt strings”,] variable Enables the user to input a value (list, etc.) for the specified variable during execution. A message “variable = ?” or “prompt strings?” will appear on the screen while the calculator waits for data input. Prompt strings include alphabetical words, numbers, and other character strings that can be entered by keys and menus. 208 Chapter 11: Programming Features 4 Wait Wait [natural number (1 to 255)] Interrupts execution for the (natural number) of seconds. If no value is specified, interruption continues until any key is pressed. • A symbol will flash at the upper right corner of the screen during the wait. • This command can be used for displaying intermediate results or other information. 5 Rem Rem comments Comments start with Rem and extend to the end of the line. These lines are ignored at execution. Comments should be entered as notes for future reference, though it should be noted that they do occupy some memory space. 6 End End Indicates the end of a program. End is not necessary at the last line of the program. 7 Key Key variable If a numeric key or one of the cursor keys is pressed, the variable is set to the corresponding numeric value as specified in the following table. Keys and Corresponding Numbers keys Numbers keys Numbers keys Numbers 00 55 '10 11 66 ;11 22 77 {12 33 88 }13 44 99 B BRNCH menu P B See 6. Flow control tools on page 214. 209 Chapter 11: Programming Features C SCRN menu P C C SCRN menu commands are used to display or clear the screen. 1 ClrT ClrT Clears the program text screen without affecting the plotted graph. 2 ClrG ClrG Clears the graph screen without affecting the specified graph. After the graph screen is cleared, the specified graph statement is drawn. 3 DispT DispT Displays the program text screen. 4 DispG DispG Displays the graph screen. D I/O menu P D This menu is used to send or receive data from externally connected devices. 1 Get Get variable Receives data from externally connected devices. 2 Send Send variable Sends data to externally connected devices. E SETUP menu P E SETUP menu commands are used to set the various settings used in graphing and calculations. 01 Rect Rect Sets the graph coordinates as X and Y coordinates. 02 Param Param Sets the graph coordinates as parametric coordinates. 210 03 Polar Polar Sets the graph coordinates as polar coordinates. Chapter 11: Programming Features 04 Web Web Sets the graph coordinates as axes in sequence graphs. u(n – 1) is set to the X axis and u(n) is set to the Y axis. 05 Time Time Sets the graph coordinates as axes in sequence graphs. n is set to the X axis and u(n), v(n) and w(n) is set to the Y axis. 06 uv uv Sets the graph coordinates as the axes of sequence graphs. u(n) is set to the X axis and v(n) is set to the Y axis. 07 uw uw Sets the graph coordinates as the axes of sequence graphs. u(n) is set to the X axis and w(n) is set to the Y axis. 08 vw vw Sets the graph coordinates as the axes of sequence graphs. v(n) is set to the X axis and w(n) is set to the Y axis. 09 Deg Deg 10 Rad Rad 11 Grad Grad Sets the angle mode to degree, radian and gradient, respectively. 12 FloatPt FloatPt 13 Fix Fix 14 Sci Sci 15 Eng Eng 16 Tab Tab integer (0 to 9) Sets the number display mode to floating point, fixed decimal, scientific and engineering, respectively. 17 Decimal Decimal 18 Mixed Mixed 19 Improp Improp 20 x±yi x±yi 21 r r Sets the answering mode to the one specified. 211 Chapter 11: Programming Features F FORMAT menu P F F FORMAT menu commands are used to set the graph format. 01 RectCursor RectCursor Sets the graph coordinate display format to X - Y axes. 02 PolarCursor PolarCursor Sets the graph coordinates display format to polar coordinates. 03 ExprON 04 ExprOFF 05 Y’ ON Y’ON Sets the derived function (Y’) to be displayed on the graph screen. 06 Y’ OFF Y’OFF Sets the derived function (Y’) to not be displayed on the graph screen. 07 AxisON 08 AxisOFF 09 GridON 10 GridOFF ExprON Sets the graph equation to be displayed on the graph screen. ExprOFF Sets the graph equation to not be displayed on the graph screen. AxisON Sets the specified axis to be displayed on the graph screen. AxisOFF Sets the specified axis to not be displayed on the graph screen. GridON Sets the grid lines to be displayed on the graph screen. GridOFF Sets the grid lines to not be displayed on the graph screen. 11 Connect Connect Draws a graph with connected lines. 12 Dot Dot Draws a graph with dots. 13 Sequen Sequen Draws the graphs in sequential order. 14 Simul Simul Draws the graphs simultaneously. 212 Chapter 11: Programming Features G S_PLOT menu P G S_PLOT menu commands are used for statistics plotting. 1 Plt 1( Sets the statistical graph settings for plot 1. 2 Plt 2( Sets the statistical graph settings for plot 2. 3 Plt 3( Sets the statistical graph settings for plot 3. The above menu commands have the same usage as the following: Plt1(graph type, X list name [, Y list name, frequency list]) Press [ to specify a graph type. 4 PlotON PlotON [number] Sets drawing of the specified statistical graph to on. If no number is specified, this command turns on all of the statistical graphs. 5 PlotOFF PlotOFF [number] Sets drawing of the specified statistical graph to off. If no number is specified, this command turns off all of the statistical graphs. 6 LimON LimON This commands turns on the limit lines for upper, lower, and mean values. 7 LimOFF LimOFF This commands turns off the limit lines for upper, lower, and mean values. 213 Chapter 11: Programming Features 6. Flow control tools The calculator has the common flow control tools such as Goto - Label loop structures, and If-, For- and While-statement clauses for enhancing a program’s efficiency. It also has the capability for subroutines. It is recommended to use If, For or While statements rather than Goto-Label loop structures. To access the flow control tools, use the P B BRNCH menu. 01 Label Label label name Specifies a branch destination for Goto or Gosub. The same Label name cannot be used in two places within the same program. Up to 10 characters can be used for a Label name. Up to 50 Labels can be used in a single program. 02 Goto Goto label name To shift the program execution to a label. 03 If If conditional statements Goto label name or If conditional statements Then commands or multiple statements * [Else commands or multiple statements] EndIf • Multiple statements mean a group of statement lines separated by colons(:) that are evaluated as a single line. Within a second structure it is possible to use the following menu items. 04 Then 05 Else 06 EndIf • Use a comparison operand in a condition statement. • Up to 115 If clauses can be nested, though if combined with other types of loops, the maximum nested loop number may vary due to the memory capacity. 214 Chapter 11: Programming Features 07 For For variable, initial value, end value [, increment] 08 Next commands or multiple statements Next • The increment value can be omitted. The default value is 1. • For and Next statements must be placed at the beginning of the line. • If the comparisons variable > end value (positive) or variable < end value (negative) are satisfied, the program will end the loop and go to the line indicated by the Next command. • Up to 5 For loops can be nested, though if combined with other types of loops, the maximum nested loop number may vary due to the memory capacity. • It is highly recommended that Label and Goto statements are not used in For loop structures. While 09 While conditional statements 10 WEnd commands or multiple statements WEnd • While and WEnd statements must be placed at the beginning of the line. • Multiple While loops can be nested to within the memory capacity. • Conditional statements are evaluated before entering the While clause. • It is highly recommended that Label and Goto statements are not used in While loop structures. • Up to 8 while loops can be nested, though if combined with other types of loops, the maximum nested loop number may vary due to the memory capacity. Note: Else clause cannot be omitted when the matching If clause is contained in a For or a While loop. label name Gosub 11 Gosub ..................... 12 Return End 215 Chapter 11: Programming Features [Rem start of the subroutine (label name)] Label label name Statements Return Subroutine structures can be used for programming. • The Gosub label name must be the same as the Label starting the subroutine. • A Return statement is necessary at the end of the subroutine. When the Return statement is executed, the calculator executes the next line after the Gosub statement. • Up to 10 subroutines can be nested. 7. Other menus convenient for programming H COPY menu P H You can copy and paste line by line using the COPY menu commands. 1. Move the cursor to the line that you wish to copy. 2. Press P H. 3. Select 1 StoLine and press E. The selected line will be stored in the memory. 4. Move the cursor to the line where you wish to paste the stored line. 5. Press P H, select 2 RclLine and press E. The stored line will be inserted at the targeted position. • Please note that only a single line can be stored in the memory. 216 Chapter 11: Programming Features VARS menu • Functions that control the graph screen can be selected from the VARS menu. • Press @ z to display the VARS menu (shown to the right). A EQVARS Specifies the graph equation (Y1 to Y9, and Y0, X1T•Y1T to X6T•Y6T, R1 to R6). B WINDOW Specifies the functions that set the graph display screen size (Xmin, Ymax, Tstep, etc.). C STOWIN Specifies the stored zoom (window) setting value (Zm_Xmin, Zm_ Ymax, etc.). D L_DATA Specifies list data (L_Data1 to L_Data9, and L_Data0). E G_DATA Specifies the graph data (G_Data1 to G_Data9, and G_Data0). F PICTUR Specifies picture data (Pict1 to Pict9, and Pict0). G TABLE Specifies table setting values (Table Start, Table Step, Table List). _ _ H STAT Specifies statistics, functions ( x , Σx, y … ), regression expressions, points and statistical verification functions. • The commands and functions in the VARS menu can be displayed on the screen. Current setting data can also be reset. • The results of arithmetic functions can also be displayed. • The ZOOM command is selected directly from the ZOOM menu. Names of some ZOOM commands change when inserted into programs. These are [A ZOOM], [C POWER], [D EXP], [E TRIG], and [F HYP] of the ZOOM menu. “Zm_” is automatically added to each of these functions when inserted into programs. Example Zm_Auto, Zm_x2, Zm_sin, etc. 217 Chapter 11: Programming Features • Always enter the argument for functions requiring an argument at the end of the command, such as the CALC function (@ k). An error will be returned for commands not accompanied by an argument. Example Value 5 Example Set Xmin = -3, Xmax = 10, Xscl = 1, Ymin = -5, Ymax = 5, Yscl = 1 in the WINDOW screen. Use R to input the settings. Expression Operational sequence -3 ⇒ Xmin [email protected] 10 ⇒ Xmax 10 R @ z E 2 E 1 ⇒ Xscl [email protected] -5 ⇒ Ymin [email protected] 5 ⇒ Ymax [email protected] 1 ⇒ Yscl [email protected] E6E *Operation to input a function equation (for example, x2 + 2) to the graphic equation “Y1” is also made using R in the same manner as described above. “X2 + 2” ⇒ Y1: P A 2 X y + 2 P [email protected] Note: Function equations cannot be assigned in the graphic equations, such as Y1, if the EDITOR mode under SET UP is set to Equation. Switch the EDITOR to One line mode prior to assigning such graphic equations. Example The following data are included in list L1. L1: 165, 182.5, 173.8, 166.5, 185.3 A one-variable calculation was executed based on this data. After returning to the calculation screen, average values can be viewed by using the following procedure. 218 Chapter 11: Programming Features • Press @ z H E A 0 2 to _ display “x ” on the screen. • Press E to obtain the average value of X as determined in the previous calculation. • In this way, the contents of an immediately preceding statistical calculation can be stored as statistical values. • These contents remain valid until the next statistical calculation is executed, even if the power is turned off. • The same is true even for regression calculations and verification calculations. 8. Debugging After programming, it is required to debug the program. 1. Press P A and select the program to debug. If any bugs are present, error messages will appear. The following example indicates that the same label name has been used two or more times. 2. Press ; or ' to display the line where the error exists and correct the mistake. When an infinite loop occurs Execution can be interrupted by pressing O. Use this command if the program enters an infinite loop. Press ; or ' to display the program source with the cursor on the line where interrupted. *Refer to Appendix 4 “Error Codes and Error Messages” on page 235. *It is highly recommended that goto-Label statements are not used in If, While and For loop structures. *Multiple statements cannot be used in a command line such as Else, EndIf, Next, While and WEnd. It is recommended not to use multiple statements. 219 Chapter 11: Programming Features Chapter 13: Programming Features 9. Preinstalled program There is one preinstalled program ("integral"). Calculating the area between graphs for a given interval Integral • Enter necessary equations before executing this program. 1. Press P A 0 1. 2. Press 1 to select “∫Y1dx”, 2 to select “∫Y1-Y2dx” or 3 to select "AREA BETWEEN Y1-Y2" to avoid the surface cancel each other. 3. Press 1 ~ 3 to select the first equation, and then press 1 ~ 3 to select the second equation, if need. 4. Input a lower value while “LOWER=?” is displayed, then press E. 5. Input an upper value while “UPPER=?” is displayed, then press E. The calculation result is displayed with highlighted graph. 6. Press E to display the calculation result without the graph. Errors and calculation ranges • If “ERROR” is displayed instead of a calculation result, press E, then enter the numeric values again. •If a screen like the one shown on the right is displayed during calculation or after you exit the program, press C. 220 Please do not press ; or ' instead of C. The editing screen will be displayed if you press ; or '. Press # at this time to exit the editing screen. Chapter 11: Programming Features Calculation ranges are illustrated below. Program name integral Calculation range Note Xmin and Xmax are in the windows settings. Xmin ≤ LOWER ≤ Xmax Xmin ≤ UPPER ≤ Xmax Storage locations of the calculation result This program calculate by using the variables below. Therefore, please note that some numbers are stored in these variables if you execute the program. Program name Variable integral A, B, C, D, E, M, S, T Storage location of the calculation result C Note: This program will not be deleted by resetting the calculator. To delete a program, please refer to “Deleting an entire program” on page 206 in this operation manual. Note that the program will be retrieved if you reset the calculator, even if you have deleted it previously. 221 Chapter 12 OPTION Menu The optional products (CE-451L and CE-LK4) are not available in some regions. The calculator is equipped with OPTION menu for adjusting the display contrast, checking memory usage, deleting stored data, transferring data, and resetting the calculator’s memory. Accessing the OPTION Menu Press @ p. The OPTION Menu will appear. A: Adjusts the display contrast B: Checks the memory usage C: Deletes files D: Link command to use with another calculator or PC. E: Resets the calculator 1. Adjusting the screen contrast 1. Press @ p. The screen contrast setting window will appear. 2. Press + to darken or - to lighten the screen. 2. Checking the memory usage The memory usage window enables you to check how much memory you have used. If the memory is nearly full, delete files or reset the calculator to operate safely. 1. Press @ p. 2. Press B. The memory check window will appear. The remaining number of bytes of user memory will be shown on the display. Software version The user memory is used to store data for graph equations, graph screens, matrices, lists and so on. The memory window shows the software version of the calculator as well. If a new software version will be released, it can be uploaded to EL-9950 by the PC link software. 222 Chapter 12: OPTION Menu 3. If you want check the details, press E. The detailed memory usage window will appear. The total remaining memory will appear on the bottom line of the screen. 4. Press } to scroll the window. List: The amount of memory (bytes) used by lists Matrix: The amount of memory (bytes) used by matrices Graph Eqn: The amount of memory (bytes) used by graph equations Solver Eqn: The amount of memory (bytes) used by solver equations Program: The amount of memory (bytes) used by program files Picture: The amount of memory (bytes) used by graph pictures G_Data: The amount of memory (bytes) used by stored graph data L_Data: The amount of memory (bytes) used by stored list data Slide: The amount of memory (bytes) used by slide shows the user has created 223 Chapter 12: OPTION Menu 3. Deleting files Press @ p C to enter the delete menu. The sub-menu items are the same as those of the Memory Check menu (List, Matrix, Graph Eqn, Solver Eqn, Program, Picture, G_Data, L_Data and Slide). Deletions can be executed entry by entry. To delete the matrix mat C 1. Press @ p C 2. The matrix deletion window will appear with the cursor pointer at the top (mat A). 2. Move the cursor pointer to mat C using { / }. 3. Press E. mat C will disappear and the mat C line will become empty. • Press @ q to cancel the delete option. • Above procedures and displays are only an example. Displayed items may vary according to data input and use. *Press @ p C 0 to delete the memories previously entered. 4. Linking to another EL-9950 or PC The optional products (CE-451L and CE-LK4) are not available in some regions. Using the optional CE-451L or CE-LK4, the EL-9950 can be linked to another EL-9950. To transfer data, press @ p D to open the Link option window. Press 1 to send data and press 2 to receive data. Transmission between EL9950's 1. Connect the calculators securely using the optional CE-451L communication cable. • Make sure the communication cable is firmly inserted into the ports of both calculators. *Use the communication cable only for linking two EL-9950’s. The EL-9950 can only be linked to another EL-9950. 224 Chapter 12: OPTION Menu 2. Press @ p D on both calculators. 3. Press 2 on the receiving machine. The receive mode screen will appear on the display. 4. Press 1 on the sending machine. 5. The send menu will appear on the display. Specify the data to send from the following categories. A SELECT Displays the menu window to send the data specified as follows: 01 ALL Displays a list of all the stored files category by category. 02 List Displays a list of all the stored list files. 03 Matirx 04 Graph Eqn Displays a list of all the stored graph equations. 05 Solver Eqn Displays a list of all the stored solver equations. 06 Program 07 G_Data Displays a list of all the stored graph data files. 08 L_Data Displays a list of all the stored list data files. 09 Picture Displays a list of all the stored picture files. 10 Slide 11 A - Z, θ Displays a list of all the stored matrix files. Displays a list of all the stored program files. Displays a list of all the user-made slide show data. Displays a list of variables A to Z and θ. B BACKUP Send all the data stored in the calculator memory. 225 Chapter 12: OPTION Menu 6. Select the item to send using { / } and pressing E. A “✱” will be placed by the selected item. 7. Press @ E to send. 8. Transmission begins and a busy message will appear on the displays of the both calculators. • An data in the same memory locations in the receiver will be automatically overwritten. • Up to 10 files can be selected to send at once. Example If you wish to send the list L1, matrices mat A and mat B and graph equation Y2 to the other calculator. 1. Prepare the receiving calculator by pressing @ p D 2. 2. Press @ p D 1 on the sending calculator. The send menu will appear. 3. Press 0 1. A list of all the data stored will be are displayed and the cursor positioned on the top line. • You can also select 02 List for “L1”, 03 Matrix for “mat A” and “mat B”, and 04 Graph Eqn for “Y2”, for example, and send the data category by category. 4. Move the cursor to L1 and press E. A “✱” mark will flash to the left of “L1”, indicating that the item has been selected to be sent. Press E again to deselect. 5. Select the other files you wish to send in the same manner. 6. Press @ E to start transmission. 226 Chapter 12: OPTION Menu Transmission between the EL9950 and PC • The optional kit CE-LK4 (cable and Windows software) is required for calculator to data communication with PC. And “SHARP CE-LK4 for EL-9950” (PC-Link software) must be installed on your Windows PC. • Refer to the CE-LK4 operation manual for details. • During communications between calculator and PC, no operation of the calculator is required. Just connect the cable and press the power on key, and the entire operation can be controlled from the PC. • CE-LK4 can also be utilized to update the calculator’s software. 5. Reset function If a problem occurs after replacing batteries, or the calculator does not function correctly, use the RESET option. 1. Press @ p E. 2. Press 1 to return the calculator’s SETUP and FORMAT settings to the default value, or 2 to delete all the stored data. See “Resetting the Calculator” on page 47 for details. 227 Appendix 1. Replacing Batteries The calculator uses two different kinds of batteries: manganese (AAA) for unit operation, and lithium (CR2032) for memory backup. Compatible battery types Type (use) Manganese battery (for unit operation) Lithium battery (for memory backup) Model AAA Quantity 4 CR2032 1 Note: • To prevent loss of stored data, DO NOT remove both the unit operation and memory backup batteries at the same time. • Please do not use rechargeable battery. This can lead to a malfunction of the device. • Batteries are factory-installed before shipment, and may be exhausted before they reach the service life stated in the specifications. Precautions for • Fluid from a leaking battery accidentally entering an eye could handling batteries result in serious injury. Should this occur, wash with clean water and immediately consult a doctor. • Should fluid from a leaking battery come into contact with your skin or clothes, immediately wash with clean water. • If the product is not to be used for some time, to avoid damage to the unit from leaking batteries, remove them and store in a safe place. • Do not leave exhausted batteries inside the product. • Do not fit partially used batteries, and be sure not to mix different batteries types. • Keep batteries out of the reach of children. • Do not allow batteries to become completely exhausted; doing so may cause the batteries to leak, and may damage the calculator’s hardware. • Do not throw batteries into a fire or water, as this may cause them to explode. 228 Appendix Procedures for replacing unit operation batteries When battery power becomes low, a message will show indicating that a new set of batteries are needed. 1. Turn off the calculator’s power (@ o). 2. Turn over the calculator. Locate the battery compartment cover, and open the cover as illustrated. 3. Replace all four AAA batteries as illustrated. Note: Do not remove the lithium battery while the unit operation batteries are removed; otherwise all the calculator's stored memory will be lost. 4. Replace the battery compartment cover. 5. After a few seconds, press O. The following message will appear. If the message does not appear, repeat the procedures from step 2. 6. Press O. Replacing the memory backup battery Do not press C. This will clear all the data. Once every 5 years, the lithium battery will need to be replaced. The lithium battery is used to maintain the memory of the calculator. 229 Appendix 1. Perform procedures 1 and 2, as shown above. Do not remove the unit operation batteries. 2. Remove the screw and the lithium battery cover, as shown. 3. Use a pen to lift the lithium battery out of the battery compartment. 4. Insert the new battery with the PLUS (+) side facing up. 5. Replace the lithium battery cover and fasten the screw. 6. Replace the battery compartment cover, wait a few seconds and then press O. The following message will appear. 7. Press O. Do not press C. This will clear all the data. 230 Appendix 2. Troubleshooting Guide Refer to the list of possible symptoms, and solutions may be found here. The calculator’s power won’t turn on! • The operation batteries may not be installed, may be exhausted, or may be inserted incorrectly. Check the operation batteries in the battery compartment. • Place the battery cover securely or the calculator will not turn on. The saved calculator configurations are not retained! • Both the lithium battery and the operation batteries may need to be replaced. The power seems to be on, but the characters and numbers cannot be seen clearly on the display! • Press @ p, then press A to enter A CTRST; the screen contrast can be adjusted by using the + or the key. The calculator won’t take the minus (-) sign; calculation results in a syntax error! • To set a negative value, use the _ key instead of the key. The calculation results are very different from what is usually expected! • The angle unit and other configurations may be incorrectly set. Check the configuration under the @ ;. The graph cannot be seen! • Check the zoom configuration. Try selecting the automatic zoom tool, by pressing Z, then A 1. • The graph line may be set differently; check the line configuration under @ d menu. • The calculator may not be set to display graphs. Check the “=” sign in Y= screen. • Graphs drawings may be interrupted in rare cases when equations of Graphs have a list format. 231 Appendix The screen images cannot be stored (SLIDE SHOW) • The available memory may be too small to store the screen image. Select “B MEMCHK” under @ p menu. Select and delete unnecessary items under “C DEL”. The calculator is not responding; the software appears to have crashed! • Press O. If this does not work, then press @, then O to tell the running application to quit. If everything fails, then the calculator’s memory may need to be reset. Resetting the calculator’s memory will clear all the stored information, such as programs, lists, and variables. To reset the unit’s memory, open and close the battery compartment cover, wait a few seconds, and then press O to open the verification window. To prevent data loss, try O first. If it does not work, repeat the reset operation and press C when prompted. 232 Appendix 3. Specifications Model EL-9950 Product name Graphing Calculator Display 132 x 64 dot matrix liquid crystal display Number of digits: mantissa 10 digits, exponents 2 digits (standard screen); 7 digit display (including negatives, decimals) for table screen, split screen, etc. Mantissa of 10 digits in the complex number mode Display method: Numerical value, calculation equation input (direct algebraic logic input / one-line input method), fraction, and complex number display method specification. Calculation method D.A.L. (Direct Algebraic Logic) Calculation features Manual calculation (arithmetic, parentheses calculation, memory calculation, function calculation, integral calculation, coordinate conversion), binary/octal/decimal/hexadecimal calculation, Boolean operation, matrix calculation, complex number calculation, complex function calculation, statistic calculation, regression calculation, statistic authorization calculation, financial calculation, etc. Input method Manual key entry Graphic features Rectangular/polar/parametric/sequence coordinate graph Graph range specification, graph window mode automatic specification, graph plotting, trace, calculation function, zoom, picture input, paint, graph database register split-screen, etc. Statistic features 1-/2-variable statistical data input/calculation, register, edit and frequency input, regression calculation function, and estimated statistic/authorization function, etc. Solver features Equation solver: numerical syntax analysis, Newton&bisection method, graph analysis, and solver equation register. 233 Appendix List features Direct data entry/edit to list, calculation function for various lists, and list/matrix conversion. Substitution features Graph drawing, numerical input from split-screen Slide Show features Screen image capture, play function The maximum number of pages to be captured: Approx. 250 pages (pages equivalent to the Y = X2 graph screen) Program features Condition statement command, subroutine, graph, various function commands Option menu Screen contrast adjustment, memory usage check, data delete, data link (between EL-9950 and PC or another EL-9950) Memory size 64 KB (user area: approx. 47.4 KB) Power supply — AAA manganese battery (R03) × 4 Operation: 6 V DC... — Lithium battery (CR2032) × 1 Memory backup: 3 V DC... Automatic power-off Approx. 10 minutes Operating temperature range 0 °C to 40 °C (32 °F to 104 °F) Battery life Operation battery set: approx. 150 hours (with 5 minutes of continual use and 55 minutes in the display state for every hour at a temperature of approx. 20 °C/68 °F) Memory backup: approx. 5 years (at a temperature of approx. 20 °C/68 °F, and when the operation batteries are replaced frequently) Note: The life span may differ according to battery brand, type, usage, and ambient temperature. External dimensions 86 mm (W) × 183 mm (D) × 20 mm (H) 3-3/8” (W) × 7-7/32” (D) × 25/32” (H) Weight Approx. 202 g (0.45 lb) (with batteries, without the hard cover) Accessories 4 AAA manganese batteries (included), 1 lithium battery (installed), hard cover, operation manual 234 Appendix 4. Error Codes and Error Messages Error Code Error Message 01 02 Syntax Calculate 03 Nesting Description Syntax error found in equation/program Calculation-related error found (division by 0, calculation beyond range, etc.) Cannot nest more than 14 numerical values, or 32 functions during execution. Graph equation variables (Y1, etc.) includes other graph equation variables (Solver features). 04 Invalid Matrix definition error or entering an invalid value. 05 Dimension Matrix dimension, or STAT list dimension, inconsistent. 07 08 Invalid DIM Argument Size of list/matrix exceeds calculation range. Inconsistency found in argument of the structured function. 09 Data Type Invalid data type used in calculation. 10 No Sign Change Financial calculation error found. 11 No define Undefined list/matrix used in calculation. Undefined graph equation variables used in Solver features. 12 Domain Argument definition outside of domain. 13 Increment Increment error found. 16 Irr Calc More than two inflection points for Irr calculation. 17 Stat Med Med-Med law (statistic) error found. 20 No Argument Argument missing. 21 Not pair ∫ dx ∫ and dx are not used in a pair. 22 Not pair [ ] Brackets are not used in a pair. 23 Not pair ( ) Parentheses are not used in a pair. 24 Not pair { } Braces are not used in a pair. 25 Line over Line is over the capacity. 26 Not delete Unable to delete a selected item. 27 Buffer over Input/equation exceeds buffer capability. 30 Editor type Invalid editor type found.* 31 Continue = “ = ” exists in equation that has been recalled (RCL). 32 No data Data does not exist. 33 Graph Type Graph type setting incorrect. 34 Too many var. Too many variables assigned in the SOLVER. 35 No variable No variable specified in the SOLVER. 235 Appendix Error Code Error Message Description 36 No solution No solution found. 37 No title No title entered. 38 Too many obj More than 30 objects selected. 40 Lbl duplicate Labels with identical name found in program. 41 Lbl undefined Goto/Gosub encountered with no defined label. 42 Lbl over More than 50 labels found in program. 43 Gosub stack Nesting of more than 10 subroutines found. 44 Line too long Line contains more than 160 characters. 45 Can’t return Return used without jumping from subroutine. 46 Storage full Cannot create more than 99 files. 47 Coord type Invalid coordinate system for command. 48 Without For For is missing corresponding to the Next command. 49 Without WEnd WEnd is missing corresponding to the While command. 50 Without While While is missing corresponding to the WEnd command. 51 Without Then Then is missing corresponding to the If command. 52 Without EndIf EndIf is missing corresponding to the If command. 53 Without If If is missing corresponding to the EndIf command. 70 I/O device Communication error found among devices. 71 Wrong Mode Wrong communication mode set. 90 Memory over Memory is full; cannot store data as requested. 99 System error System error found; user memory space is insecure. Low battery Operation interrupted due to low battery power. BREAK!! Operation break specified. * The following operations may cause Editor type error. Correct the Editor type to continue. • Recall the SOLVER equations (EQTN) or Graph data (G_DATA) stored in a different EDITOR mode than currently in use. • Receive the Graph equation (Y1 and others) entered in a different EDITOR mode than currently in use. 236 Appendix 5. Error Conditions Relating to Specific Tasks 1. Financial * Define constants “r” and “s” as used in the equation below. r= ( I (%) C/Y 100 +1 ) C/Y P/Y –1, { SS == 10 (Pmt_Begin) (Pmt_End) } 1. I% calculation 1 If PMT = 0 ( r= - PV FV ) - 1n –1 2 If PMT ≠ 0 -n f (r) = PV + (1 + r × s) × PMT × 1 – (1 + r) + FV (1 + r)-n: (r ≠ 0) f (r) = PV + PMT × n + FV: (r = 0) r calculate the following for r solved in 1 and 2 P/Y I (%) = 100 × C/Y × ((r + 1)C/Y –1) 2. PV calculation 1 If r ≠ 0, r > -1 -n PV = - (1 + r × s) × 1 – (1 + r) × PMT – FV × (1 + r)-n r 2 If r = 0 PV = -n × PMT – FV 3 If r ≤ -1 Error 237 Appendix 3. FV calculation 1 If r ≠ 0, r > -1 FV = – 1 – (1 + r)-n × PMT r -n (1 + r) PV + (1 + r × s) × 2 If r = 0 FV = -n × PMT – PV 3 If r ≤ -1 Error 4. PMT calculation 1 If r ≠ 0, r > -1 PMT = – PV + FV × (1 + r)-n 1 – (1 + r)-n (1 + r × s) × r 2 If r = 0 PMT = – PV + FV n 3 If r ≤ -1 Error 5. N calculation 1 If r ≠ 0, r > -1 log N=– { PV + 1 × (1 + r × s) × PMT – FV r log (1 + r) 2 If r = 0 N = – FV + PV PMT 3 If r ≤ -1 238 Error 1 × (1 + r × s) × PMT r } Appendix 2. Error conditions during financial calculations • r ≤ -1 • N = 0 in PMT calculations • I% = 0 and PMT = 0, or I% ≠ 0 and FV = (1/r) (1 + r × s) × PMT, in N calculations. s = 1 (Pmt_Begin) s = 0 (Pmt_End) In I% calculations If PMT > 0: Pmt_End mode: PV ≥ 0 and FV + PMT ≥ 0 PV < 0 and FV + PMT < 0 Pmt_Begin mode: PV + PMT ≥ 0 and FV ≥ 0 PV + PMT < 0 and FV < 0 If PMT < 0: Pmt_End mode: PV > 0 and FV + PMT > 0 PV ≤ 0 and FV + PMT ≤ 0 Pmt_Begin mode: PV + PMT > 0 and FV > 0 PV + PMT ≤ 0 and FV ≤ 0 If PMT = 0: PV ÷ FV ≥ 0 • FV, N × PMT, PV ≥ 0 or FV, N × PMT, PV ≤ 0 • Irr calculation: all cash flows have the same sign. 3. Distribution function 1 pdfnorm( f (x) = 1 2πσ exp (– (x – µ)2 ) 2σ2 Calculation result→Xreg μ:Mean σ: Standard deviation 2 pdfT( 2 - df + 1 Γ ( df + 1 ) (1 + x ) 2 2 df f (x) = Γ ( df ) πdf 2 ∞ However: Γ(s) = ∫ 0 xs–1 e-x dx Calculation result→Xreg 239 Appendix 3 pdfχ2( f (χ2, df) = 1 2Γ ( df ) 2 df χ2 2 – 1 (- χ ) e 2 ) 2 2 ( ∞ However: Γ(s) = ∫ 0 xs–1 e-x dx df: Degree of freedom 4 pdfF( f (x) = Γ (m + n) m m –1 2 ( m ) 2 x 2 (1 n n m Γ( ) Γ( ) 2 2 + mx ) n - m 2+ n ∞ However: Γ(s) = ∫ 0 xs–1 e-x dx m: Degree of freedom of numerator n: Degree of freedom of denominator 5 pdfbin( P (x = 0) = (1 – p)n P (x = c + 1) = (n – c) p P (x = c) (c + 1)(1 – p) (c = 0, 1, ..., n – 1) n: Trial number (integers greater than 0) p: Success probability (0 ≤ p ≤ 1) c: Success number 6 pdfpoi( x -µ f (x) = e µ x! (x = 0, 1, 2, ...) 7 pdfgeo( f (x) = p (1 – p)x - 1 240 x: First successful trial number Appendix 6. Calculation Range 1. Arithmetic calculation The results for dividend, multiplicand and operand are: -1 × 10100 < x ≤ -1 × 10-99, 1 × 10-99 < x ≤ 1 × 10100 or x = 0 (valid within the range of display capability) Note: Calculation results and input values less than 1 × 10-99 are considered equal to 0. 2. Function calculation Calculation accuracy In principle, calculation errors are ±1 of the last digit. (In case of exponential display, the calculation errors are ±1 of the last digit of the mantissa display.) However, a calculation error increases in continuous calculations due to x accumulation of each calculation error. (This is the same for ab, b , n!, e , In, etc. where continuous calculations are performed internally.) Additionally, a calculation error will accumulate and become larger in the vicinity of inflection points and singular points of functions. (for example, calculating sinh X or tanh X at X = 0) Function sin x Calculation range DEG : |x| < 1 × 10 RAD : |x| < 180 × 1010 Notes 10 π 10 cos x GRAD : |x| < 9 × 1010 However, the following are excluded for tan x tan x DEG : |x| = 90 (2n – 1) RAD : |x| = π (2n – 1) 2 “n” is an integer GRAD : |x| = 100 (2n – 1) -1 sin x cos-1 x tan-1 x -1 ≤ x ≤ 1 |x| < 1 × 10100 sinh x cosh x -230.2585093 ≤ x ≤ 230.2585092 tanh x sinh-1 x |x| < 1 × 1050 cosh-1 x 1 ≤ x ≤ 1 × 1050 tanh-1 x |x| < 1 241 Appendix Function ln x log x ex x 10 x-1 x2 x n! Calculation range Notes ln x = loge x 1 × 10-99 ≤ x < 1 × 10100 e.=. 2.71828... -1 × 10100 < x ≤ 230.2585092 -1 × 10100 < x < 100 |x| < 1 × 10100 |x| < 1 × 1050 0 ≤ x < 1 × 10100 x≠0 -0.5 ≤ n ≤ 69.5 n is an integer or integer + 0.5 When a > 0: -1 × 10100 < b log a < 100 When a = 0: b a (^) ab = 10b·log a 0 < b < 1 × 10100 When a < 0: b is an integer, or 1 is an odd number (b ≠ 0) b However, -1 × 10100 < b log |a| < 100 When b > 0: -1 × 10100 < When b = 0: a b 1 log b < 100, a ≠ 0 a 0 < a < 1 × 10100 a When b < 0: 1 b = 10 a log b a is an odd number, or 1 is an integer (a ≠ 0) a However, -1 × 10100 < 1 log |b| < 100 a nPr nCr 0 ≤ r ≤ n ≤ 9999999999 100 n _n!_ When r < _ 2 : (r-1)! (n-r)! < 10 _n!_ 100 n When _ 2 ≤ r : r!(n- r-1)! < 10 0 ≤ r ≤ n ≤ 9999999999 _n!_ < 10100 (n- r)! 242 n and r are positive integers Appendix Function Calculation range Notes Decimal:|x| ≤ 9999999999 Binary: 1000000000000000 ≤ x ≤ 1111111111111111 dec bin 0 ≤ x ≤ 0111111111111111 oct Octal: hex 0 ≤ x ≤ 3777777777 4000000000 ≤ x ≤ 7777777777 x is an integer Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FF →dms →deg xy → r xy → θ |x| < 1 × 10100 |x| < 1 × 10100, |y| < 1 × 10100 x2 + y2 r = x2 + y2 < 1 × 10100 -1 θ = tan y y | x | < 1 × 10100 x x = r cosθ rθ → x rθ → y y = r sinθ |r| < 1 × 10100 Binary: The range of θ is the same as x of sin x and cos x 1000000000000000 ≤ x ≤ 1111111111111111 0 ≤ x ≤ 0111111111111111 not Octal: 4000000000 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FE Binary: 1000000000000001 ≤ x ≤ 1111111111111111 Other Boolean operations are the same as not and neg 0 ≤ x ≤ 0111111111111111 neg Octal: 4000000001 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FF 243 Appendix Function Calculation range Notes |x| < 1 × 1050 |y| < 1 × 1050 |Σx| < 1 × 10100 2 100 Statistic Σx < 1 × 10 calculations |Σy| < 1 × 10100 2 100 Σy < 1 × 10 |Σxy| < 1 × 10100 |n| < 1 × 10100 _ x n ≠ 0 n>1 sx |Σx| < 1 × 1050 0≤ (Σx)2 n <1 n–1 Σx2 – × 10100 _ Same for y, sy and σy n>0 σx |Σx| < 1 × 1050 (Σx)2 Σx2 – n < 1 × 10100 0≤ n n>0 |Σx| < 1 × 1050 r |Σy| < 1 × 1050 (Σy)2 (Σx)2 0 < (Σx2 – ) (Σy2 – ) <1 × 10100 n n |Σxy – ΣxΣy | < 1 × 10100 n < 1 × 10100 n > 0 |Σx| < 1 × 1050 b |(Σx) (Σy)| < 1 × 10100 (Σx)2 0 < |Σx2 – | < 1 × 10100 n |Σxy – ΣxΣy | < 1 × 10100 n < 1 × 10100 244 Regression calculations excluding 2nd, 3rd, and 4th degree polynomials. Appendix Function a y’ Calculation range _ |bx| < 1 × 10100 _ _ |y – bx | < 1 × 10100 |bx| < 1 × 10 Same as b for other. |a + bx| < 1 × 10100 |y – a| < 1 × 10100 y–a | b | < 1 × 10100 int÷ 0 ≤ x < 1010 remain 0 ≤ x < 1010 % |x| < 10100 → a b/c |x| < 1010 → b/c Matrix Same as above. 100 x’ List Notes Error is returned when the number of elements exceeds 1000. A number with 10 or less decimal places, or the 1010-th or above decimal places are 0. This is the same when the result of a list function specifies 1000 or more elements. Error is returned when specifying columns or rows that exceed 100. mat An : n ≤ 255 245 Appendix 3. Complex number calculation In a complex number calculation, a calculation error may occur and increase due to inner continuous calculations. Function 1 x + yi Calculation range |x| < 10 |y| < 1050 |x| < 1050 (x + yi)2 |y| < 1050 |xy| < 5 × 1099 In (x + yi) |x| < 1050 50 log (x + yi) |y| < 10 x + yi e(x + yi) 10(x + yi) y | x | < 10100 |x| < 230 |y| < 230 |x| < 100 |y| < 100 |x| < 1050 (x + yi)(a + bi) |y| < 1050 |a| < 10100 |b| < 10100 246 Notes 50 x + yi ≠ 0 Appendix 7. List of Menu/Sub-menu Items CATALOG function lets you access almost all the functions and commands. Square brackets indicate that the value or variable is optional. 1. MATH menus Functions Commands Syntax Keystrokes Page M CALC log2 log2 value A01 32 2X 2 value A02 32 fmin( fmin(equation, lower limit of x, upper limit of x) A03 32 fmax( fmax(equation, lower limit of x, upper limit of x) A04 32 d/dx( d/dx(equation, value of x [, tolerance]) A05 32 ∫ ∫ equation, lower limit, upper limit [, tolerance] dx A06 33 dx ∫ equation, lower limit, upper limit [, tolerance] dx A07 33 ∑( ∑ (expression, initial value, end value [, increment]) A08 33 sec sec value A09 33 csc csc value A10 33 cot cot value A11 33 sec–1 sec–1 value A12 33 csc–1 csc–1 value A13 34 cot–1 cot–1 value A14 34 sinh sinh value A15 34 cosh cosh value A16 34 tanh tanh value A17 34 sinh–1 sinh–1 value A18 34 cosh–1 cosh–1 value A19 34 tanh–1 tanh–1 value A20 34 247 Appendix Functions Commands Syntax Keystrokes Page M NUM abs( abs(value) B1 34 round( round(value [, digit number of decimals]) B2 34 ipart ipart value B3 35 fpart fpart value B4 35 int int value B5 35 min( min(value A, value B) or min(list) B6 35 max( max(value A, value B) or max(list) B7 35 lcm( lcm(natural number, natural number) B8 36 gcd( gcd(natural number, natural number) B9 36 M PROB random random [(number of trial)] C1 36 rndInt( rndInt(minimum value, maximum value [, number of trial]) C2 36 rndNorm( rndNorm(mean, mean, standard deviation [, number of trial]) C 3 37 rndBin( rndBin(number number of trial, probability of success [, number of simulatins]) C4 37 nPr value A nPr value B C5 37 nCr value A nCr value B C6 37 ! value ! C7 38 M CONV →deg value →deg D1 38 →dms value →dms D2 38 xy→r( xy→r(x-coordinate, y-coordinate) D3 39 xy→θ( xy→θ(x-coordinate, y-coordinate) D4 39 rθ→x( rθ→x(r-coordinate, θ-coordinate) D5 39 rθ→y( rθ→y(r-coordinate, θ-coordinate) D6 39 M ANGLE ° value ° [value ’ value "] E1 40 ’ value ° value ’ [value "] E2 40 " value ° value ’ value " Print "character strings["] E3 40 r value r E4 40 248 Appendix Functions Commands g Syntax value g Keystrokes Page E5 40 M INEQ = value A = value B F1 40 ≠ value A ≠ value B F2 40 > value A > value B F3 40 ≥ value A ≥ value B F4 40 < value A < value B F5 40 ≤ value A ≤ value B F6 40 M LOGIC and value A and value B G1 41 or value A or value B G2 41 not not value G3 41 xor value A xor value B G4 42 xnor value A xnor value B G5 42 conj(complex number) H1 42 real( real(complex number) H2 42 image( image(complex number) H3 43 abs( abs(complex number) H4 43 arg( arg(complex number) H5 43 M COMPLEX conj( M (in the N-base calculation mode) LOGIC and value A and value B A1 41 or value A or value B A2 41 not not value A3 41 neg neg value A4 42 xor value A xor value B A5 42 xnor value A xnor value B A6 42 249 Appendix 2. LIST menus Functions Commands Syntax Keystrokes Page @ l OPE sortA( sortA(list name [, subordinate list name1, ... , subordinate list name n]) A1 136 sortD( sortD(list name [, subordinate list name1, ... ,, subordinate list name n]) A2 136 dim( dim(list) A3 137 fill( fill(value, list) A4 137 seq( seq(equation, start value, end value [, increment]) A5 138 cumul cumul list A6 138 df_list df_list list A7 138 augment( augment(list 1, list 2) A8 139 list→mat( list→mat(list 1, ... , list n, matrix name) A9 139 mat→list( mat→list(matrix name, list name1, ... , list name n) mat→list(matrix name, column number, list name) A0 139 @ l MATH min( min(value A, value B) or min(list) B1 140 max( max(value A, value B) or max(list) B2 140 mean( mean(list [, frequency list]) B3 140 median( median(list [, frequency list]) B4 141 sum( sum(list [, start number, end number]) B5 141 prod( prod(list [, start number, end number]) B6 141 stdDv( stdDv(list [, frequency list]) B7 142 varian( varian(list [, frequency list]) B8 142 P_stdDv( P_stdDv(list [, frequency list] ) B9 142 @ l L_DATA StoLD StoLD natural number (0-9) C1 144 RclLD RclLD natural number (0-9) C2 145 @ l VECTOR CrossPro( CrossPro(list name 1, list name 2) D1 143 DotPro( DotPro(list name 1, list name 2) D2 143 * “list” in the above table means a list or a list name. 250 Appendix 3. STAT menus Functions Commands Keystrokes Syntax Page S EDIT/OPE EDIT No arguments AE 151 sortA( sortA(list [, subordinate list 1, ... , subordinate list n]) B1 161 sortD( sortD(list [, subordinate list 1, ... , subordinate list n]) B2 161 SetList SetList [list name 1, list name 2, list name 3, ... ] B3 161 ClrList ClrList list name1 [, list name 2, ... ] B4 161 S CALC 1_Stats 1_Stats [x list name [, frequency list]] C1 152 2_Stats 2_Stats [x list name, y list name [, frequency list]] C2 152 ANOVA( ANOVA(list name 1, list name 2 [, ... ]) C3 154 S REG Med_Med Med_Med (list name for x, list name for y [, frequency list] [, equation name to store]) D01 162 Rg_ax+b Rg_a+bx (list name for x, list name for y [, frequency list] [, equation name to store]) D02 162 Rg_ax Rg_ax (list name for x, list name for y [, frequency list] [, equation name to store]) D03 162 Rg_a+bx Rg_ax+b (list name for x, list name for y [, frequency list] [, equation name to store]) D04 162 Rg_x2 Rg_x2 (list name for x, list name for y [, frequency list] [, equation name to store]) D05 162 Rg_x3 Rg_x3 (list name for x, list name for y [, frequency list] [, equation name to store]) D06 163 Rg_x4 Rg_x4 (list name for x, list name for y [, frequency list] [, equation name to store]) D07 163 Rg_ln Rg_ln (list name for x, list name for y [, frequency list] [, equation name to store]) D08 163 Rg_log Rg_log (list name for x, list name for y [, frequency list] [, equation name to store]) D09 163 * “list” in the above table means a list or a list name. 251 Appendix Functions Commands Syntax Keystrokes Page Rg_abx Rg_abx (list name for x, list name for y [, frequency list] [, equation name to store]) D10 163 Rg_aebx Rg_aebx (list name for x, list name for y [, frequency list] [, equation name to store]) D11 163 Rg_x-1 Rg_x-1 (list name for x, list name for y [, frequency list] [, equation name to store]) D12 164 Rg_axb Rg_axb (list name for x, list name for y [, frequency list] [, equation name to store]) D13 164 Rg_logistic Rg_logistic (list name for x, list name for y [, frequency list] [, equation name to store]) D14 164 Rg_sin Rg_sin ([iterations,] list name for x, list name for y [, frequency list] [, period] [, equation name to store]) D15 164 x' value or list x' D16 165 y' value or list y' D17 165 S TEST χ2 test No arguments E01 168 Ftest2samp No arguments E02 169 Ttest1samp No arguments E03 169 Ttest2samp No arguments E04 170 TtestLinreg No arguments E05 171 Tint1samp No arguments E06 172 Tint2samp No arguments E07 172 Ztest1samp No arguments E08 173 Ztest2samp No arguments E09 174 Ztest1prop No arguments E10 175 Ztest2prop No arguments E11 175 Zint1samp No arguments E12 176 Zint2samp No arguments E13 177 Zint1prop No arguments E14 177 Zint2prop No arguments E15 178 InputList No arguments E16 168 InputStats No arguments E17 168 F01 179 S DISTRI pdfnorm( 252 pdfnorm(value [, mean, standard deviation]) Appendix Functions Commands Syntax Keystrokes Page cdfnorm( cdfnorm(lower limit, upper limit [,mean, standard deviation]) F02 179 InvNorm( InvNorm(probability [, mean, standard deviation]) F03 180 pdfT( pdfT(value, degree of freedom) F04 180 cdfT( cdfT(lower limit, upper limit, degree of freedom) F05 181 pdfχ2( pdfχ2(value, degree of freedom) F06 181 cdfχ2( cdfχ2(lower limit, upper limit, degree of freedom) F07 181 pdfF( pdfF(value, degree of freedom of numerator, degree of freedom of denominator) F08 182 cdfF( cdfF(lower limit, upper limit, degree of freedom of numerator, degree of freedom of denominator) F09 182 pdfbin( pdfbin(number of trial, success probability [, success numbers]) F10 183 cdfbin( cdfbin(number of trial, success probability [, success numbers]) F11 183 pdfpoi( pdfpoi(mean, value) F12 183 cdfpoi( cdfpoi(mean, value) F13 184 pdfgeo( pdfgeo(success probability, value) F14 184 cdfgeo( cdfgeo(success probability, value) F15 184 4. STAT PLOT menus Functions Commands Keystrokes Syntax Page [ PLOT1/PLOT2/PLOT3/LIMIT/ON/OFF PLOT1 No arguments AE 159 PLOT2 No arguments BE 159 PLOT3 No arguments CE 159 SET No arguments D1 159 LimON No arguments D2 159 LimOFF No arguments D3 159 PlotON PlotON [number] E1 160 PlotOFF PlotOFF [number] E2 160 [ (in STAT PLOT mode) HIST/B.L./N.P./N.D./BOX/PIE/S.D./XYLINE Hist No arguments A1 155 Broken • No arguments B1 156 253 Appendix Functions Commands Keystrokes Syntax Page Broken + No arguments B2 156 Broken No arguments B3 156 Norm •_X No arguments C1 156 Norm+_X No arguments C2 156 Norm _X No arguments C3 156 Norm •_Y No arguments C4 156 Norm+_Y No arguments C5 156 Norm _Y No arguments C6 156 NormDis No arguments D1 156 Box No arguments E1 157 MBox • No arguments E2 157 MBox+ No arguments E3 157 MBox No arguments E4 157 Pie No arguments F1 158 Pie% No arguments F2 158 Scattr • No arguments G1 158 Scattr+ No arguments G2 158 Scattr No arguments G3 158 xyLine• No arguments H1 158 xyLine+ No arguments H2 158 xyLine No arguments H3 158 5. DRAW menus Functions Commands Syntax Keystrokes Page @ d DRAW ClrDraw No arguments A01 96 Line( Line(x-coordinate of start point, y-coordinate of start point, x-coordinate of end point, y-coordinate of end point [,0]) A02 97 H_line H_line y-value A03 99 V_line V_line x-value A04 100 T_line( T_line(equation, x-value) A05 100 N_line( N_line(equation, x-value) A06 101 254 Appendix Functions Commands Syntax Keystrokes Page Draw Draw equation A 07 102 Shade( Shade(equation 1, equation 2 [, begin, end]) A 08 102 DrawInv DrawInv equation A 09 103 Circle( Circle(x-coordinate of center, y-coordinate of center, radius) A 10 103 Text( Text(column, row, “character strings”) Text(column, row, variable) A 11 104 @ d POINT PntON( PntON(x-coordinate, y-coordinate) B1 105 PntOFF( PntOFF(x-coordinate, y-coordinate) B2 105 PntCHG( PntCHG(x-coordinate, y-coordinate) B3 105 PxlON( PxlON(column, row) B4 106 PxlOFF( PxlOFF(column, row) B5 106 PxlCHG( PxlCHG(column, row) B6 106 PxlTST( PxlTST(column, row) B7 106 @ d ON/OFF/LINE/G_DATA/PICT/SHADE DrawON DrawON [equation number 1, equation number 2, …] C1 107 DrawOFF DrawOFF [equation number 1, equation number 2, …] C2 107 LINE No arguments DE 107 StoGD StoGD number E1 108 RclGD RclGD number E2 108 StoPict StoPict number F1 109 RclPict RclPict number F2 109 SET No arguments G1 110 INITIAL No arguments G2 110 6. ZOOM menus Functions Commands Syntax Keystrokes Page Z ZOOM Auto Zm_Auto No arguments A1 75 Box Zm_Box No arguments A2 75 255 Appendix Functions Commands Syntax Keystrokes Page In Zm_In No arguments A3 76 Out Zm_Out No arguments A4 76 Default Zm_Default No arguments A5 76 Square Zm_Square No arguments A6 76 Dec Zm_Dec No arguments A7 76 Int Zm_Int No arguments A8 76 Stat Zm_Stat No arguments A9 76 No arguments BE 77 Zm_x2 No arguments C1 77 x-1 Zm_x-1 No arguments C2 77 No arguments C3 77 Z FACTOR/POWER FACTOR x2 x Zm_ x Z EXP 10x Zm_10x No arguments D1 77 ex Zm_ex No arguments D2 77 log x Zm_log No arguments D3 77 ln x Zm_ln No arguments D4 77 Z TRIG sin x Zm_sin No arguments E1 77 cos x Zm_cos No arguments E2 78 tan x Zm_tan No arguments E3 78 256 Appendix Functions Commands Syntax Keystrokes Page sin-1 x Zm_sin-1 No arguments E4 78 cos-1 x Zm_cos-1 No arguments E5 78 tan-1 x Zm_tan-1 No arguments E6 78 Z HYP/STO/RCL sinh x Zm_sinh No arguments F1 78 cosh x Zm_cosh No arguments F2 78 tanh x Zm_tanh No arguments F3 78 sinh-1 x Zm_sinh-1 No arguments F4 78 cosh-1 x Zm_cosh-1 No arguments F5 78 tanh-1 x Zm_tanh-1 No arguments F6 78 StoWin No arguments G1 78 RclWin No arguments H1 78 PreWin No arguments H2 79 7. CALC menus Functions Commands Syntax Keystrokes Page @ k CALC Value Value x A1 87 Intsct No arguments A2 87 Minimum No arguments A3 87 Maximum No arguments A4 88 Y_zero No arguments A5 88 Y_Incpt No arguments A6 88 Inflec No arguments A7 88 dx No arguments A8 89 257 Appendix 8. SLIDE SHOW menus Functions Commands Syntax Keystrokes Page ] CURR/PLAY/NEW/SELECT/EDIT CURR No arguments AE 119 PLAY No arguments B 119 NEW No arguments CE 119 SELECT No arguments D 119 MOVE No arguments E1 119 DEL No arguments E2 120 RENAME No arguments E3 120 9. PRGM menus Functions Commands Keystrokes Syntax Page P EXEC No arguments A 204 EDIT No arguments B 204 NEW No arguments CE 204 V_INDX No arguments D 204 P (in the the Programming Prgramming mode) PRGM PRGM Print Print variable Print "character strings ["] A1 208 " "characters ["] A2 208 Input Input ["prompt strings", ] variable A3 208 Wait Wait [natural number] A4 209 Rem Rem comments A5 209 End No arguments A6 209 Key Key variable A7 209 P (in the the Programming Prgramming mode) BRNCH BRNCH Label Label label name B01 214 Goto Goto label name B02 214 If If conditional statements Then commands [Else commands] EndIf B03 214 B04 214 B05 214 B06 214 Then Else EndIf 258 Appendix Functions Commands For Syntax Keystrokes Page For variable, start value, end value [, increment] commands Next B07 215 B08 215 B09 215 WEnd While conditional statements commands WEnd B10 215 Gosub Gosub label name B11 215 Return No arguments B12 215 Next While mode) SCRN P (in (in the the Programming Prgramming mode) SCRN ClrT No arguments C1 210 ClrG No arguments C2 210 DispT No arguments C3 210 DispG No arguments C4 210 mode) I/O P (in (in the the Programming Prgramming mode) I/O Get Get variable D1 210 Send Send variable D2 210 mode) SETUP P (in (in the the Programming Prgramming mode) SETUP Rect No arguments E01 210 Param No arguments E02 210 Polar No arguments E03 210 Web No arguments E04 211 Time No arguments E05 211 uv No arguments E06 211 uw No arguments E07 211 vw No arguments E08 211 Deg No arguments E09 211 Rad No arguments E10 211 Grad No arguments E11 211 FloatPt No arguments E12 211 Fix No arguments E13 211 Sci No arguments E14 211 Eng No arguments E15 211 Tab Tab integer E16 211 259 Appendix Functions Commands Syntax Keystrokes Page Decimal No arguments E17 211 Mixed No arguments E18 211 Improp No arguments E19 211 x ± yi No arguments E20 211 r∠θ No arguments E21 211 P (in the mode) FORMAT the Programming Prgramming mode) FORMAT RectCursor No arguments F01 212 PolarCursor No arguments F02 212 ExprON No arguments F03 212 ExprOFF No arguments F04 212 Y'ON No arguments F05 212 Y'OFF No arguments F06 212 AxisON No arguments F07 212 AxisOFF No arguments F08 212 GridON No arguments F09 212 GridOFF No arguments F10 212 Connect No arguments F11 212 Dot No arguments F12 212 Sequen No arguments F13 212 Simul No arguments F14 212 P (in the mode) S_PLOT the Programming Prgramming mode) S_PLOT Plt1( Plt1(graph type, X list name [, Y list name, frequency list]) G1 213 Plt2( Plt2(graph type, X list name [, Y list name, frequency list]) G2 213 Plt3( Plt3(graph type, X list name [, Y list name, frequency list]) G3 213 PlotON PlotON [number] G4 213 PlotOFF PlotOFF [number] G5 213 LimON No arguments G6 213 LimOFF No arguments G7 213 260 Appendix Functions Commands Keystrokes Syntax Page P (in mode) COPY (in the the Programming Prgramming mode) COPY StoLine No arguments H1 216 RclLine No arguments H2 216 10. MATRIX menus Functions Commands Keystrokes Syntax Page @ m NAME mat A [(row, column)] A1 131 mat B [(row, column)] A2 131 mat C [(row, column)] A3 131 mat D [(row, column)] A4 131 mat E [(row, column)] A5 131 mat F [(row, column)] A6 131 mat G [(row, column)] A7 131 mat H [(row, column)] A8 131 mat I [(row, column)] A9 131 mat J [(row, column)] A0 131 @ m EDIT mat A No arguments B1 123 mat B No arguments B2 123 mat C No arguments B3 123 mat D No arguments B4 123 mat E No arguments B5 123 mat F No arguments B6 123 mat G No arguments B7 123 mat H No arguments B8 123 mat I No arguments B9 123 mat J No arguments B0 123 dim(matrix name) C01 126 fill( fill(value, matrix name) C02 126 cumul cumul matrix name C03 127 @ m OPE dim( 261 Appendix Functions Commands Keystrokes Syntax Page augment( augment(matrix name A, matrix name B) C04 127 identity identity dimension value C05 127 rnd_mat( rnd_mat(number of row, number of column) C06 127 row_swap( row_swap(matrix name, row number, row number) C07 128 row_plus( row_plus(matrix name, row number, row number) C08 128 row_mult( row_mult(multiplied number, matrix name, row number) C09 128 row_m.p.( row_m.p.(multiplied number, matrix name, row number, row number) C10 128 mat→list( mat→list(matrix name, list name 1, …, list name n) mat→list(matrix name, column number, list name) C11 129 list→mat( list→mat(list 1, …, list n, matrix name) C12 129 @ m MATH/[ ] det det matrix name D1 130 trans trans matrix name D2 130 rowEF rowEF matrix name D3 130 rrowEF rrowEF matrix name D4 130 [ No arguments E1 131 ] No arguments E2 131 11. FINANCE menus Functions Commands Syntax Keystrokes Page @ g SOLVER/CALC SOLVER (TVM SOLVER screen appears) AE 187 slv_pmt slv_pmt [(N, I%, PV, FV, P/Y, C/Y)] B01 191 slv_I% slv_I% [(N, PV, PMT, FV, P/Y, C/Y)] B02 191 slv_PV slv_PV [(N, I%, PMT, FV, P/Y, C/Y)] B03 191 slv_N slv_N [(I%, PV, PMT, FV, P/Y, C/Y)] B04 191 slv_FV slv_FV [(N, I%, PV, PMT, P/Y, C/Y)] B05 191 Npv( Npv(interest rate, initial investment, list of following collected investment [, frequency list]) B06 192 262 Appendix Functions Commands Syntax Keystrokes Page Irr( Irr(initial investment, list of following collected investment [, frequency list] [, assumed revenue rate]) B07 192 Bal( Bal(number of payments [, decimal place to round]) B08 193 ∑Prn( ∑Prn(initial number of payments, end number of payments [, decimal place to round]) B09 193 ∑Int( ∑Int(initial number of payments, end number of payments [, decimal place to round]) B10 193 →Apr( →Apr(effective interest rate, number of settlements) B11 194 →Eff( →Eff(nominal interest rate, number of settlements) B12 194 days( days(start month. day year, end month. day year) days(day month. year, day month. year) B13 194 @ g PERIOD PmtEnd No arguments C1 190 PmtBegin No arguments C2 190 @ g VARS N No arguments D1 195 I% No arguments D2 195 PV No arguments D3 195 PMT No arguments D4 195 FV No arguments D5 195 P/Y No arguments D6 195 C/Y No arguments D7 195 12. TOOL menus Functions Commands Syntax Keystrokes Page @ V NBASE/SYSTEM/POLY NBASE No arguments AE 65 2 No arguments B2 66 3 No arguments B3 66 4 No arguments B4 66 5 No arguments B5 66 263 Appendix Functions Commands Syntax Keystrokes Page 6 No arguments B6 66 2 No arguments C2 67 3 No arguments C3 67 13. SOLVER menus Functions Commands Syntax Keystrokes Page @ ' (in the Solver mode) METHOD/EQTN/SAVE/RENAME Equation No arguments A1 196 Newton&Bisect No arguments A2 198 Graphic No arguments A3 200 EQTN No arguments B 203 SAVE No arguments CE 202 RENAME No arguments D 202 264

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