# Casio ClassPad II _fx CP400 Graphing Calculator FXCP400 Class Pad UG EN

User Manual: Casio Casio Graphing Calculator FXCP400 FXCP400

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E ClassPad II fx-CP400 User’s Guide CASIO Education website URL http://edu.casio.com Download Free trial software and Support software http://edu.casio.com/dl/ Manuals are available in multi languages at http://world.casio.com/manual/calc Be sure to keep physical records of all important data! Low battery power or incorrect replacement of the batteries that power the ClassPad can cause the data stored in memory to be corrupted or even lost entirely. Stored data can also be affected by strong electrostatic charge or strong impact. It is up to you to keep backup copies of data to protect against its loss. Backing Up Data ClassPad data can be converted to a VCP file or XCP file and transferred to a computer for storage. For details, see “19-2 Performing Data Communication between the ClassPad and a Personal Computer”. • Be sure to keep all user documentation handy for future reference. • The sample screens shown in this manual are for illustrative purposes only, and may not be exactly the same as the screens actually produced by the ClassPad. • The contents of this manual are subject to change without notice. • No part of this manual may be reproduced in any form without the express written consent of the manufacturer. • In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. • Windows® is a registered trademark or trademark of Microsoft Corporation in the United States and/or other countries. • Mac OS, OS X and macOS are registered trademarks or trademarks of Apple Inc. in the United States and/or other countries. • Fugue © 1999 – 2012 Kyoto Software Research, Inc. All rights reserved. • Company and product names used in this manual may be registered trademarks or trademarks of their respective owners. • Note that trademark ™ and registered trademark ® are not used within the text of this manual. 2 Contents About This User’s Guide .......................................................................................................................... 11 Chapter 1: Basics ................................................................................................................ 12 1-1 General Guide .........................................................................................................................12 ClassPad at a Glance............................................................................................................................... 12 Turning Power On or Off .......................................................................................................................... 13 1-2 Power Supply ..........................................................................................................................13 1-3 Built-in Application Basic Operations ..................................................................................14 Using the Application Menu...................................................................................................................... 14 Built-in Applications .................................................................................................................................. 14 Add-in Applications................................................................................................................................... 15 Application Window .................................................................................................................................. 16 Using the O Menu ................................................................................................................................... 17 Interpreting Status Bar Information .......................................................................................................... 17 Pausing and Terminating an Operation.................................................................................................... 17 1-4 Input .........................................................................................................................................18 Using the Soft Keyboard .......................................................................................................................... 18 Soft Keyboard Key Sets ........................................................................................................................... 18 Input Basics .............................................................................................................................................. 19 Various Soft Keyboard Operations ........................................................................................................... 22 1-5 ClassPad Data .........................................................................................................................27 Data Types and Storage Locations (Memory Areas) ............................................................................... 27 Main Memory Data Types ........................................................................................................................ 28 Main Memory Folders............................................................................................................................... 28 Using Variable Manager ........................................................................................................................... 29 Managing Application Files ...................................................................................................................... 32 1-6 Creating and Using Variables ................................................................................................33 Creating a New Variable .......................................................................................................................... 33 Variable Usage Example .......................................................................................................................... 34 “library” Folder Variables .......................................................................................................................... 34 Rules Governing Variable Access ............................................................................................................ 35 1-7 Configuring Application Format Settings.............................................................................36 Application Format Settings ..................................................................................................................... 36 Initializing All Application Format Settings................................................................................................ 42 1-8 When you keep having problems… ......................................................................................43 Chapter 2: Main Application ............................................................................................... 44 Main Application-Specific Menus and Buttons ......................................................................................... 44 2-1 Basic Calculations ..................................................................................................................44 Arithmetic Calculations and Parentheses Calculations ............................................................................ 44 Using the e Key .................................................................................................................................. 45 Omitting the Multiplication Sign ................................................................................................................ 45 Using the Answer Variable (ans) .............................................................................................................. 45 Assigning a Value to a Variable ............................................................................................................... 45 Calculation Priority Sequence .................................................................................................................. 46 Calculation Modes .................................................................................................................................... 46 2-2 Using the Calculation History ................................................................................................48 2-3 Function Calculations ............................................................................................................48 2-4 List Calculations .....................................................................................................................57 Inputting List Data in the Work Area......................................................................................................... 57 LIST Variable Element Operations ........................................................................................................... 57 3 Using a List in a Calculation ..................................................................................................................... 57 Using a List to Assign Different Values to Multiple Variables ................................................................... 57 2-5 Matrix and Vector Calculations .............................................................................................58 Inputting Matrix Data ................................................................................................................................ 58 Performing Matrix Calculations ................................................................................................................ 58 Using a Matrix to Assign Different Values to Multiple Variables............................................................... 59 2-6 Specifying a Number Base ....................................................................................................59 Binary, Octal, Decimal, and Hexadecimal Calculation Ranges ................................................................ 59 Selecting a Number Base......................................................................................................................... 60 Arithmetic Operations ............................................................................................................................... 60 Bitwise Operations ................................................................................................................................... 60 Using the baseConvert Function (Number System Transform) ............................................................... 61 2-7 Using the Action Menu ...........................................................................................................61 Abbreviations and Punctuation Used in This Section............................................................................... 61 Example Screenshots .............................................................................................................................. 62 Using the Transformation Submenu......................................................................................................... 62 Using the Advanced Submenu ................................................................................................................. 64 Using the Calculation Submenu ............................................................................................................... 67 Using the Complex Submenu................................................................................................................... 70 Using the List-Create Submenu ............................................................................................................... 71 Using the List-Statistics and List-Calculation Submenus ......................................................................... 72 Using the Matrix-Create Submenu ........................................................................................................... 75 Using the Matrix-Calculation and Matrix-Row&Column Submenus ......................................................... 76 Using the Vector Submenu ...................................................................................................................... 79 Using the Equation/Inequality Submenu ................................................................................................. 81 Using the Assistant Submenu .................................................................................................................. 84 Using the Distribution/Inv.Dist Submenu .................................................................................................. 85 Using the Financial Submenu .................................................................................................................. 90 Using the Command Submenu ................................................................................................................ 90 2-8 Using the Interactive Menu ...................................................................................................91 Interactive Menu Example ........................................................................................................................ 91 Using the “apply” Command..................................................................................................................... 91 2-9 Using the Main Application in Combination with Other Applications ...............................92 Using Another Application’s Window........................................................................................................ 92 Using the Stat Editor Window................................................................................................................... 93 Using the Geometry Window.................................................................................................................... 93 2-10 Using Verify ...........................................................................................................................94 2-11 Using Probability ..................................................................................................................95 2-12 Running a Program in the Main Application ......................................................................96 Chapter 3: Graph & Table Application ............................................................................... 97 Graph & Table Application-Specific Menus and Buttons.......................................................................... 97 3-1 Storing Functions ...................................................................................................................99 Using Graph Editor Sheets....................................................................................................................... 99 Storing a Function .................................................................................................................................... 99 Graphing a Stored Function ................................................................................................................... 100 Shading the Region Bounded by Two Expressions ............................................................................... 101 Overlaying Two Inequalities in an Intersection Plot / Union Plot ............................................................ 101 Saving Graph Editor Data to Graph Memory ......................................................................................... 102 3-2 Using the Graph Window .....................................................................................................102 Configuring View Window Parameters for the Graph Window ............................................................... 102 Using View Window Memory.................................................................................................................. 104 Panning the Graph Window ................................................................................................................... 104 4 Scrolling the Graph Window ................................................................................................................... 105 Zooming the Graph Window................................................................................................................... 105 Using Quick Zoom .................................................................................................................................. 106 Using Built-in Functions for Graphing..................................................................................................... 106 Saving a Screenshot of a Graph ............................................................................................................ 107 Adjusting the Lightness (Fade I/O) of the Graph Window Background Image ....................................... 107 3-3 Using Table & Graph.............................................................................................................108 Generating a Number Table ................................................................................................................... 108 Showing Linked Displays of Number Table Coordinates and Graph Coordinates (Link Trace)............. 109 Generating Number Table Values from a Graph.................................................................................... 110 Generating a Summary Table ................................................................................................................ 110 3-4 Using Trace ........................................................................................................................... 111 Using Trace to Read Graph Coordinates ............................................................................................... 111 3-5 Using the Sketch Menu ........................................................................................................ 112 Using Sketch Menu Commands ............................................................................................................. 112 3-6 Analyzing a Function Used to Draw a Graph ..................................................................... 114 What You Can Do Using the G-Solve Menu Commands ....................................................................... 114 Using G-Solve Menu Commands ........................................................................................................... 114 3-7 Modifying a Graph ................................................................................................................ 115 Modifying a Single Graph (Direct Modify)............................................................................................... 115 Modifying Multiple Graphs Simultaneously (Dynamic Modify) ............................................................... 115 Chapter 4: Conics Application ..........................................................................................118 Conics Application-Specific Menus and Buttons .................................................................................... 118 4-1 Inputting an Equation ........................................................................................................... 119 4-2 Drawing a Conics Graph ...................................................................................................... 119 Drawing a Parabola ................................................................................................................................ 119 Drawing a Circle ..................................................................................................................................... 120 Drawing an Ellipse.................................................................................................................................. 120 Drawing a Hyperbola .............................................................................................................................. 120 Drawing a General Conics ..................................................................................................................... 120 4-3 Using G-Solve to Analyze a Conics Graph .........................................................................120 What You Can Do Using the G-Solve Menu Commands ....................................................................... 120 Using G-Solve Menu Commands ........................................................................................................... 121 4-4 Modifying a Graph (Dynamic Modify) .................................................................................121 Chapter 5: Differential Equation Graph Application....................................................... 122 Differential Equation Editor Window-Specific Menus and Buttons ......................................................... 122 Differential Equation Graph Window-Specific Menus and Buttons ........................................................ 122 5-1 Graphing a Differential Equation .........................................................................................123 Graphing a First Order Differential Equation .......................................................................................... 123 Graphing a Second Order Differential Equation ..................................................................................... 124 Graphing an Nth-order Differential Equation .......................................................................................... 124 Configuring and Modifying Initial Conditions .......................................................................................... 125 Configuring Differential Equation Graph View Window Parameters ...................................................... 126 5-2 Drawing f (x) Type Function Graphs and Parametric Function Graphs ...........................127 5-3 Using Trace to Read Graph Coordinates ............................................................................127 5-4 Graphing an Expression or Value by Dropping It into the Differential Equation Graph Window ..................................................................................................................................128 Chapter 6: Sequence Application .................................................................................... 129 Sequence Application-Specific Menus and Buttons ............................................................................... 129 6-1 Recursive and Explicit Form of a Sequence ......................................................................130 Generating a Number Table ................................................................................................................... 130 5 Determining the General Term of a Recursion Expression .................................................................... 131 Calculating the Sum of a Sequence ....................................................................................................... 131 6-2 Graphing a Recursion ..........................................................................................................131 Chapter 7: Statistics Application ..................................................................................... 132 7-1 Using Stat Editor ...................................................................................................................132 Basic List Operations ............................................................................................................................. 132 Menus and Buttons Used for List Editing ............................................................................................... 133 Using CSV Files ..................................................................................................................................... 134 7-2 Drawing a Statistical Graph .................................................................................................135 Operation Flow Up to Statistical Graphing ............................................................................................. 135 Graphing Single-Variable Statistical Data .............................................................................................. 136 Graphing Paired-Variable Statistical Data .............................................................................................. 137 Overlaying a Regression Graph on a Scatter Plot ................................................................................. 139 Overlaying a Function Graph on a Statistical Graph .............................................................................. 140 Stat Graph Window Menus and Buttons ................................................................................................ 140 7-3 Performing Basic Statistical Calculations ..........................................................................141 Calculating Statistical Values ................................................................................................................. 141 Performing Regression Calculations ...................................................................................................... 143 Viewing the Results of the Last Statistical Calculation Performed (DispStat) ........................................ 145 7-4 Performing Advanced Statistical Calculations ..................................................................145 Performing Test, Confidence Interval and Distribution Calculations Using the Wizard .......................... 145 Tests....................................................................................................................................................... 146 Confidence Intervals............................................................................................................................... 149 Distributions............................................................................................................................................ 151 Input and Output Terms ......................................................................................................................... 154 Chapter 8: Geometry Application .................................................................................... 156 Geometry Application-Specific Menus and Buttons ............................................................................... 156 Configuring Geometry View Window Settings........................................................................................ 157 About the Geometry Format Dialog Box ................................................................................................ 157 8-1 Drawing Figures ....................................................................................................................157 Drawing a Figure .................................................................................................................................... 157 Inserting Text Strings into the Screen .................................................................................................... 161 Attaching an Angle Measurement to a Figure ........................................................................................ 161 Displaying the Measurements of a Figure .............................................................................................. 161 Displaying the Result of a Calculation that Uses On-screen Measurement Values ............................... 162 Using the Special Polygon Submenu ..................................................................................................... 162 Using the Construct Submenu ............................................................................................................... 163 8-2 Editing Figures ......................................................................................................................167 Selecting and Deselecting Figures ......................................................................................................... 167 Moving and Copying Figures.................................................................................................................. 168 Pinning an Annotation on the Geometry Window................................................................................... 168 Specifying the Number Format of a Measurement................................................................................. 168 Specifying the Color and Line Type of a Displayed Object .................................................................... 169 Changing the Display Priority of Objects ................................................................................................ 169 8-3 Using the Measurement Box ...............................................................................................170 Viewing the Measurements of a Figure .................................................................................................. 170 Specifying and Constraining a Measurement of a Figure ...................................................................... 171 Using Sliders .......................................................................................................................................... 172 Changing a Label or Adding a Name to an Element .............................................................................. 174 8-4 Working with Animations .....................................................................................................174 Using Animation Commands .................................................................................................................. 174 6 8-5 Using the Geometry Application with Other Applications ................................................177 Drag and Drop ........................................................................................................................................ 177 Copy and Paste ...................................................................................................................................... 177 Chapter 9: Numeric Solver Application ........................................................................... 178 Numeric Solver Application-Specific Menus and Buttons ...................................................................... 178 Inputting an Equation ............................................................................................................................. 178 Solving an Equation ............................................................................................................................... 178 Chapter 10: eActivity Application .................................................................................... 180 eActivity Application-Specific Menus and Buttons.................................................................................. 180 10-1 Creating an eActivity ..........................................................................................................180 Basic Steps for Creating an eActivity ..................................................................................................... 180 Inserting Data into an eActivity ............................................................................................................... 181 Inserting an Application Data Strip ......................................................................................................... 182 Inserting a Geometry Link Row .............................................................................................................. 184 10-2 Transferring eActivity Files ................................................................................................185 File Compatibility .................................................................................................................................... 185 Transferring eActivity Files between a ClassPad Unit and a Computer ................................................. 185 Transferring eActivity Files between Two ClassPad Units ..................................................................... 185 Chapter 11: Financial Application .................................................................................... 186 11-1 Financial Application Basic Operations ...........................................................................186 Page Operations .................................................................................................................................... 187 Configuring Financial Application Settings ............................................................................................. 188 11-2 Performing Financial Calculations ....................................................................................189 11-3 Calculation Formulas .........................................................................................................189 Simple Interest ....................................................................................................................................... 189 Compound Interest ................................................................................................................................. 190 Cash Flow .............................................................................................................................................. 190 Amortization ........................................................................................................................................... 191 Interest Conversion ................................................................................................................................ 191 Cost/Sell/Margin ..................................................................................................................................... 192 Depreciation ........................................................................................................................................... 192 Bond Calculation .................................................................................................................................... 192 Break-Even Point ................................................................................................................................... 193 Margin of Safety ..................................................................................................................................... 193 Financial Leverage ................................................................................................................................. 193 Operating Leverage................................................................................................................................ 193 Combined Leverage ............................................................................................................................... 193 Quantity Conversion ............................................................................................................................... 193 11-4 Financial Calculation Functions ........................................................................................194 11-5 Input and Output Field Names ...........................................................................................195 Chapter 12: Program Application .................................................................................... 196 Program Application-Specific Menus and Buttons ................................................................................. 196 12-1 Creating and Running Program ........................................................................................197 Creating a Program ................................................................................................................................ 197 Running a Program ................................................................................................................................ 199 Terminating Program Execution ............................................................................................................. 200 Creating a Text File ................................................................................................................................ 200 Using Text Files...................................................................................................................................... 201 Converting a Text File to a Program File................................................................................................ 201 Converting a Program File to an Executable File ................................................................................... 201 7 12-2 Debugging a Program ........................................................................................................202 Debugging After an Error Message Appears ......................................................................................... 202 Debugging a Program Following Unexpected Results ........................................................................... 202 Editing a Program................................................................................................................................... 202 12-3 User-defined Functions ......................................................................................................203 Creating a New User-defined Function .................................................................................................. 203 Executing a User-defined Function ........................................................................................................ 204 Editing a User-defined Function ............................................................................................................. 204 12-4 Program Command Reference ..........................................................................................205 Using This Reference ............................................................................................................................. 205 Syntax Conventions ............................................................................................................................... 205 Command List ........................................................................................................................................ 206 12-5 Including ClassPad Functions in Programs ....................................................................225 Including Graphing Functions in a Program ........................................................................................... 225 Including Table & Graph Functions in a Program .................................................................................. 225 Including Recursion Table and Recursion Graph Functions in a Program ............................................ 225 Including Statistical Graphing and Calculation Functions in a Program ................................................. 225 Including Financial Calculation Functions in a Program......................................................................... 225 Chapter 13: Spreadsheet Application .............................................................................. 226 Spreadsheet Window-Specific Menus and Buttons ............................................................................... 226 Changing the Width of a Column ........................................................................................................... 227 Option Settings ....................................................................................................................................... 228 13-1 Inputting and Editing Cell Contents ..................................................................................228 Selecting Cells........................................................................................................................................ 228 Inputting Data into a Cell ........................................................................................................................ 229 Inputting a Formula ................................................................................................................................ 229 Inputting a Cell Reference ...................................................................................................................... 230 Cell Data Types (Text Data and Calculation Data) ................................................................................ 231 Inputting a Constant into a Calculation Data Type Cell .......................................................................... 231 Using the Cell Viewer Window ............................................................................................................... 233 Changing the Text Color and Fill Color of Specific Cells........................................................................ 233 Copying or Cutting Cells and Pasting Them to Another Location .......................................................... 234 Recalculating Spreadsheet Expressions ................................................................................................ 234 Transferring Data between a Spreadsheet and CSV Files .................................................................... 235 Importing and Exporting Variable Values ............................................................................................... 235 13-2 Graphing ..............................................................................................................................237 Basic Graphing Steps ............................................................................................................................ 237 Column Series and Row Series ............................................................................................................. 237 Graph Colors and Color Link .................................................................................................................. 238 Spreadsheet Graph Window-Specific Menus and Buttons .................................................................... 239 Graph Menu and Graph Examples......................................................................................................... 239 Regression Graph Operations (Curve Fitting) ........................................................................................ 242 Other Graph Window Operations ........................................................................................................... 243 13-3 Statistical Calculations ......................................................................................................244 Single-variable, Paired-variable and Regression Calculations............................................................... 245 Test and Interval Calculations ................................................................................................................ 246 Distribution Calculations ......................................................................................................................... 248 About DispStat Command ...................................................................................................................... 248 13-4 Cell and List Calculations ..................................................................................................249 Using the Cell Calculation Functions...................................................................................................... 249 Using the List Calculation Functions ...................................................................................................... 249 8 Chapter 14: 3D Graph Application ................................................................................... 250 3D Graph Application-Specific Menus and Buttons ............................................................................... 250 14-1 Inputting an Expression .....................................................................................................251 Using 3D Graph Editor Sheets ............................................................................................................... 251 Storing a Function .................................................................................................................................. 251 Graphing a Stored Function ................................................................................................................... 252 14-2 Using the 3D Graph Window .............................................................................................253 Configuring 3D Graph View Window Parameters .................................................................................. 253 Showing and Hiding Axes and Labels .................................................................................................... 254 Rotating the Graph ................................................................................................................................. 255 3D Graph Example ................................................................................................................................. 255 Using Trace to Read Graph Coordinates ............................................................................................... 255 Inserting Text into a 3D Graph Window ................................................................................................. 256 Calculating a z-value for Particular x - and y -values, or s- and t -values ................................................. 256 Chapter 15: Picture Plot Application ............................................................................... 257 Picture Plot Application-Specific Menus and Buttons............................................................................. 258 15-1 Using the Plot Function .....................................................................................................259 Starting a Picture Plot Operation ............................................................................................................ 259 Plotting Points on a c2p File Image ........................................................................................................ 259 Plotting Points on a c2b File Image ........................................................................................................ 260 Editing Plots on a Background Image .................................................................................................... 261 Overlaying a Graph on Background Image Plots ................................................................................... 261 G-Solve .................................................................................................................................................. 263 Scrolling the Picture Plot Window .......................................................................................................... 263 15-2 Using the Plot List ..............................................................................................................264 Using the Plot List Window to Edit Plots ................................................................................................ 264 Saving Data to and Importing Data from a Spreadsheet........................................................................ 264 Exporting Plot Data to and Importing Plot Data from a Variable ............................................................ 265 15-3 Displaying Plots on t-y or t-x Coordinates........................................................................265 15-4 Picture Plot Application Files ............................................................................................266 Chapter 16: Interactive Differential Calculus Application.............................................. 267 DiffCalc Table Window-Specific Menus and Buttons ............................................................................. 267 16-1 Learning about Tangents Using the [Tangent] Tab .........................................................268 16-2 Deriving the Derivative Using the [Deriv] Tab ..................................................................269 16-3 Generating a Number Table and Graphing the First Derivative and Second Derivative Using the [D Trace] Tab ......................................................................................................271 Chapter 17: Physium Application .................................................................................... 273 Physium Application Menus and Buttons ............................................................................................... 273 17-1 Periodic Table......................................................................................................................274 17-2 Fundamental Physical Constants .....................................................................................275 17-3 Precautions .........................................................................................................................277 Chapter 18: System Application ...................................................................................... 279 18-1 Managing Memory Usage ..................................................................................................279 Using the Storage Sheet ........................................................................................................................ 279 Using the Main Memory Sheet and eActivity Sheet ............................................................................... 280 18-2 Configuring System Settings ............................................................................................281 System Application Menus and Buttons ................................................................................................. 281 Configuring System Settings .................................................................................................................. 281 9 Chapter 19: Performing Data Communication................................................................ 285 19-1 Data Communication Overview .........................................................................................285 Using the ClassPad Communication Application ................................................................................... 285 Select Connection Mode Dialog Box ...................................................................................................... 286 19-2 Performing Data Communication between the ClassPad and a Personal Computer ..286 Connecting and Disconnecting with a Computer in the USB Flash Mode ............................................. 287 Transferring Data between the ClassPad and a Personal Computer .................................................... 288 Installing an Add-in Application .............................................................................................................. 289 Auto Import of VCP Files ........................................................................................................................ 289 Rules for ClassPad Files and Folders .................................................................................................... 289 VCP and XCP File Operations ............................................................................................................... 289 19-3 Performing Data Communication between Two ClassPads ...........................................291 Connecting to Another ClassPad Unit .................................................................................................... 291 Transferring Data between Two ClassPads ........................................................................................... 291 Communication Standby ........................................................................................................................ 293 Interrupting an Ongoing Data Communication Operation ...................................................................... 293 19-4 Connecting the ClassPad to a Data Logger .....................................................................293 Connecting a ClassPad to a Data Logger .............................................................................................. 293 19-5 Connecting the ClassPad to a Projector ..........................................................................294 Projecting ClassPad Screen Contents from a Projector......................................................................... 294 Precautions when Connecting................................................................................................................ 294 Appendix ............................................................................................................................ 295 Character Code Table ..................................................................................................................295 System Variable Table .................................................................................................................299 Graph Types and Executable Functions....................................................................................302 Error and Warning Message Tables ...........................................................................................303 Error Message Table ............................................................................................................................. 303 Warning Message Table ........................................................................................................................ 307 Low Memory Error Processing ............................................................................................................... 307 Resetting and Initializing the ClassPad .....................................................................................307 Number of Digits and Precision .................................................................................................308 Number of Digits..................................................................................................................................... 308 Precision................................................................................................................................................. 308 Display Brightness and Battery Life ..........................................................................................309 Display Brightness.................................................................................................................................. 309 Battery Life ............................................................................................................................................. 309 Specifications ..............................................................................................................................309 Exam Mode..........................................................................................................................311 Communication Application - Exam Mode Menu ................................................................................... 311 Entering the Exam Mode ........................................................................................................................ 311 ClassPad Operation in the Exam Mode ................................................................................................. 312 Exiting the Exam Mode .......................................................................................................................... 313 Displaying Exam Mode Help .................................................................................................................. 314 10 About This User’s Guide • The four digit boldface example numbers (such as 0201 ) that appear in Chapters 2 through 14 indicate operation examples that can be found in the separate “Examples” booklet. You can use the “Examples” booklet in conjunction with this manual by referring to the applicable example numbers. • In this manual, cursor key operations are indicated as f, c, d, e (1-1 General Guide). 11 Chapter 1: Basics This chapter provides a general overview of the ClassPad and application operations, as well as information about input operations, the handling of data (variables and folders), file operations, and how to configure application format settings. 1-1 General Guide ClassPad at a Glance 3-pin data communication port See Chapter 19 for details. 4-pin mini USB port See Chapter 19 for details. Touch screen Stylus Icon panel See “1-3 Built-in Application Basic Operations”. Cursor key*1 k key f key*2 K key c key Keypad *1 In this manual, cursor key operations are indicated as f, c, d, e. *2 Certain functions (cut, paste, undo, etc.) or key input operations can be assigned to key combinations that consist of pressing the f key and a keypad key. For more information, see “18-2 Configuring System Settings”. Chapter 1: Basics 12 Turning Power On or Off While the ClassPad is turned off, press c to turn it on. To turn off the ClassPad, press f and then c. Auto Power Off The ClassPad also has an Auto Power Off feature. This feature automatically turns the ClassPad off when it is idle for a specified amount of time. For details, see “To configure power properties” on page 282. Note Any temporary information in ClassPad RAM (graphs drawn on an application’s graph window, a dialog box displayed, etc.) is retained for approximately 30 seconds whenever power is turned off manually or by Auto Power Off. This means you will be able to restore the temporary information in RAM if you turn ClassPad back on within about 30 seconds after it is turned off. After about 30 seconds, the temporary information in RAM is cleared automatically, so turning ClassPad back on will display the startup screen of the application you were using when you last turned it off, and the previous information in RAM will no longer be available. 1-2 Power Supply Your ClassPad is powered by four AAA-size batteries LR03 (AM4), or four nickel-metal hydride batteries. The battery level indicator is displayed in the status bar. full medium low dead Important! • Be sure to replace batteries as soon as possible whenever the battery level indicator shows (low). • Replace batteries immediately whenever the battery level indicator shows (dead). At this level, you will not be able to perform data communication or other functions. • For information about initial setup operations required after replacing batteries, see “Loading Batteries and Setting Up the ClassPad” in the separate Quick Start Guide. • When battery power is very low, your ClassPad may not turn back on when you press its c key. If this happens, immediately replace its batteries. • The following message indicates that batteries are about to go dead. Replace batteries immediately whenever this message appears. If you try to continue using the ClassPad, it will automatically turn off. You will not be able to turn power back on until you replace batteries. • Be sure to replace batteries at least once a year, no matter how much you use the ClassPad during that time. Note: The batteries that come with the ClassPad discharge slightly during shipment and storage. Because of this, they may require replacement sooner than the normal expected battery life. Backing Up Data ClassPad data can be converted to a VCP file or XCP file and transferred to a computer for storage. For details, see “19-2 Performing Data Communication between the ClassPad and a Personal Computer”. Chapter 1: Basics 13 1-3 Built-in Application Basic Operations This section explains basic information and operations that are common to all of the built-in applications. Using the Application Menu Tapping m on the icon panel displays the application menu. You can perform the operations below with the application menu. Tap a button to start up an application. See “Built-in Applications” below. Tap here (or tap s on the icon panel) to display the next menu. VCP file operations. See page 289. Starts touch panel alignment. See page 284. Displays version information. See page 284. Tapping here scrolls between application menu pages. The application menu page can also be changed by swiping the screen left or right with the stylus or your finger. Built-in Applications The table below shows the application icons displayed on the application menu, and explains what you can do with each application. Tap this icon: To start this application: To perform this type of operation: Main • General calculations, including function calculations • Matrix calculations • Computer Algebra System eActivity • Create an eActivity file that can be used for input of formulas, text, and other ClassPad application data Statistics • Create a list • Perform statistical calculations • Draw a statistical graph Spreadsheet • Input data into a spreadsheet • Manipulate and/or graph spreadsheet data • Perform statistical calculations and/or draw a statistical graph Graph & Table • Draw a graph • Register a function and create a table of solutions by substituting different values for the function’s variables 3D Graph • Draw a 3-dimensional graph of an equation in the form z = f (x, y) or of a parametric equation Geometry • Draw geometric figures • Build animated figures Chapter 1: Basics 14 Tap this icon: To start this application: To perform this type of operation: Picture Plot • Plot points (that represent coordinates) on a photograph, illustration, or other graphic and perform various types of analysis based on the plotted data (coordinate values) Interactive Differential Calculus • Learn about the differential coefficients and/or derivative formulas that are the foundation of differentiation Conics • Draw the graph of a conics section Differential Equation Graph • Draw vector fields and solution curves to explore differential equations Numeric Solver • Obtain the value of any variable in an equation, without transforming or simplifying the equation Sequence • Perform sequence calculations • Solve recursion expressions Financial • Perform simple interest, compound interest, and other financial calculations Program • Input a program or run a program • Create a user-defined function E-CON3 • Control the optionally available Data Logger (See the separate E-CON3 User’s Guide.) Communication • Exchange data with another ClassPad, a computer, or another device System • Manage ClassPad memory (main memory, eActivity area, storage area) • Configure system settings Tip: You can also start up the Main application by tapping M on the icon panel. Add-in Applications You can download add-in applications (as c2a files) from the CASIO website, install them on your ClassPad, and use them the same way you use built-in applications. The table below shows the add-in applications that are currently available. Icon Application Description Physium • Find elements and display the atomic number, chemical symbol, atomic weight and other information from the periodic table of elements • Display various physical constants Note You can delete all add-in applications using one of the procedures below. • Reset - Storage Memory or Reset - All (“To batch delete specific data (Reset)”, page 281) • Initialize (“To initialize your ClassPad”, page 282) After deleting add-in applications, you can use the procedure under “Installing an Add-in Application” (page 289) to re-install them. Chapter 1: Basics 15 Application Window The following shows the basic configuration of a built-in application window. Menu bar Tool bar Upper window Application window(s) Lower window Soft keyboard See page 18. Status bar See page 17. Many applications split the display between an upper window and a lower window, each of which shows different information. When using two windows, the currently selected window (the one where you can perform operations) is called the “active window”. The menu bar, toolbar, and status bar contents are all applicable to the active window. The active window is indicated by a thick boundary around it. You can perform the operations below on an Application window. To do this: Perform this operation: Switch the active window While a dual window is on the display, tap anywhere inside the window that does not have a thick boundary around it to make it the active window. Note that you cannot switch the active window while an operation is being performed in the current active window. Resize the active window so it fills the display While a dual window is on the display, tap r. This causes the active window to fill the display. To return to the dual window display, tap r again. Swap the upper and lower windows While a dual window is on the display, tap S. This causes the upper window to become the lower window, and vice versa. Swapping windows does not have any effect on their active status. If the upper window is active when you tap S for example, that window will remain active after it becomes the lower window. Close the active windows While a dual window is on the display, tap C at the top right corner of the window to close the active window. This will cause the other (inactive) window to fill the display. Tip: When you tap the r icon while a dual window is on the display, the currently active window will fill the display, but the other (inactive) window does not close. It remains open, hidden behind the active window. This means you can tap S to bring the hidden window forward and make it the active window, and send the current active window to the background. u Changing the Display Orientation (Application Menu and Some Applications Only) You can change the display orientation to horizontal while any one of the following is displayed: application menu, or the Main, Graph & Table, Conics, or Physium application. Tap g to switch to horizontal (landscape) display orientation. To return to vertical (portrait) display orientation, tap g again. Chapter 1: Basics 16 Using the O Menu The O menu appears at the top left of the window of each application, except for the System application. You can access the O menu by tapping m on the icon panel, or by tapping the menu bar’s O menu. The following describes all of the items that appear on the O menu. 1 Tapping [Variable Manager] starts up Variable Manager. See “Using Variable Manager” (page 29) for details. 1 2 2 Tapping [View Window] displays a dialog box for configuring the display range and other graph settings. For details, see the explanations for the various applications with graphing capabilities (Graph & Table, Differential Equation Graph, Statistics, etc.) 3 3 Tapping a menu selection displays a dialog box for configuring the corresponding setup settings. See “1-7 Configuring Application Format Settings” for details. 4 Tapping [Default Setup] returns all settings to their initial defaults (except for the current folder setting). See “1-7 Configuring Application Format Settings” for details. 4 5 6 7 5 Tapping [Window] displays a list of all of the windows that can be accessed from the current application (Statistics application in this example). Tapping a menu selection displays the corresponding window and makes it active. 6 Tap [Keyboard] to toggle display of the soft keyboard on or off. 7 Tapping [Close] closes the currently active window, except in the following cases. • When only one window is on the display • When the currently active window cannot be closed by the application being used You cannot, for example, close the Graph Editor window from the Graph & Table application. Interpreting Status Bar Information The status bar appears along the bottom of the window of each application. 1 2 3 1 Information about the currently running application You can change the configuration of a setting indicated in the status bar by tapping it. Tapping “Cplx” (indicating complex number calculations) while the Main application is running will toggle the setting to “Real” (indicating real number calculations). Tapping again will toggle back to “Cplx”. For more details about the current application information, see “1-7 Configuring Application Format Settings”. 2 This indicator rotates while processing in progress. appears here to indicate when an operation is paused. 3 Battery level indicator (See “1-2 Power Supply”.) Pausing and Terminating an Operation Many of the built-in applications provide operations to pause and terminate (break) expression processing, graphing, and other operations. u To pause an operation Pressing the K key while an expression processing, graphing, or other operation is being performed pauses the operation. appears on the right side of the status bar to indicate when an operation is paused. Pressing K again resumes the operation. Chapter 1: Basics 17 u To terminate an operation Pressing the c key while an expression processing, graphing, or other operation is being performed terminates the operation and displays a “Break” dialog box like the one shown nearby. Tap the [OK] button on the dialog box to exit the Break state. 1-4 Input You can input data on the ClassPad using its keypad or by using the on-screen soft keyboard. Virtually all data input required by your ClassPad can be performed using the soft keyboard. The keypad keys are used for input of frequently used data like numbers, arithmetic operators, etc. Using the Soft Keyboard The soft keyboard is displayed in the lower part of the touch screen. u To display the soft keyboard When the soft keyboard is not on the touch screen, press the k key, or tap the O menu and then tap [Keyboard]. This causes the soft keyboard to appear. • The soft keyboard has a number of different key sets such as [Math1], [abc], and [Catalog], which you can use to input of functions and text. To select a key set, tap one of the tabs along the left side of the soft keyboard. • Pressing the k key or tapping the O menu, and then [Keyboard] again hides the soft keyboard. Soft keyboard Soft Keyboard Key Sets The soft keyboard has a variety of different key sets that support various data input needs. Each of the available key sets is shown below. [Math1], [Math2], [Math3], [Trig] (trigonometric), [Advance] key sets These key sets include keys for inputting functions, operators, and symbols required for numerical formulas. Math1 Math2 Math3 Chapter 1: Basics 18 Trig Advance For details above the above key sets, see “Using Math, Trig, and Advance Key Sets” (page 23). [Var] (variable) key set This key set includes only keys for the input of single-character variables. For more information, see “Using Single-character Variables” (page 25). [abc] key set Use this key set to input alphabetic characters. Tap one of the tabs along the top of the keyboard (along the right when using horizontal display orientation) to see additional characters, for example, tap [Math]. For more information, see “Using the Alphabet Keyboard” (page 26). [Catalog] key set This key set provides a scrollable list that can be used to input built-in functions, built-in commands, system variables, and user-defined functions. Tap a command to select it and then tap it again to insert it. Selecting an item from the Form list changes the available commands. For more information, see “Using the Catalog Keyboard” (page 27). [Number] key set This key set provides the same keys as those on the keypad. Use this key set when you want to use only the touch screen for input or in place of the keypad while using horizontal (landscape) display orientation. Input Basics This section includes a number of examples that illustrate how to perform basic input procedures. All of the procedures assume the following. • The Main application is running. See “Built-in Applications” (page 14). • The soft keyboard is displayed. See “Using the Soft Keyboard” (page 18). Chapter 1: Basics 19 k Inputting a Calculation Expression You can input a calculation expression just as it is written, and press the E key to execute it. The ClassPad automatically determines the priority sequence of addition, subtraction, multiplication, division, and parenthetical expressions. Example: To simplify −2 + 3 − 4 + 10 u Using the keypad keys cz2+3-4+10E If the line where you want to input the calculation expression already contains input, be sure to press c to clear it. u Using the soft keyboard Tap the keys of the [Number] keyboard to input the calculation expression. c4-c+d-e+baw As shown in the above Example, you can input simple arithmetic calculations using either the keypad keys or the soft keyboard. Input using the soft keyboard is required to input higher level calculation expressions, functions, variables, etc. See Chapter 2 for more information about inputting expressions. Tip: In some cases, the input expression and output expression (result) may not fit in the display area. If this happens, tap the left or right arrows that appear on the display to scroll the expression screen and view the part that does not fit. You can also change the display orientation to horizontal (landscape) for easier-to-read display of long input formulas and calculation results. See “Changing the Display Orientation” (page 16). k Editing Input u To delete a single character Move the cursor so it is directly to the right of the character you want to delete, and then press K. Each press of K deletes one character to the left of the cursor. Example: To change the expression 369 × × 2 to 369 × 2 1. c369**2 2. dK After you make all of the changes you want, press E to calculate the result. To add more characters to the calculation, press e to move the cursor to the end of the calculation, and input what you want. Tip: You can move the cursor without using the cursor key by tapping at the destination with the stylus. This causes the cursor to jump to the location where you tap. u To insert new input into the middle of an existing calculation expression Use d or e to move the cursor to the location where you want to insert new input, and then input what you want. Chapter 1: Basics 20 Example: To change 302 to sin(30)2 (For input, use the keypad and the [Math1] soft keyboard set.) 1. c30x 2. dddds 3. ee) u To replace a range of input with new input After you drag the stylus across the range of input that you want to replace, enter the new input. Example: To change “1234567” to “10567” 1. c1234567 2. Drag the stylus across “234” to select it. 3. 0 k Using the Clipboard for Copy and Paste You can copy (or cut) a function, command, or other input to the ClassPad’s clipboard, and then paste the clipboard contents at another location. Performing a copy or cut operation causes the current clipboard contents to be replaced by the newly copied or cut characters. u To copy characters 1. Drag the stylus across the characters you want to copy to select them. 2. On the soft keyboard, tap p. Or tap the [Edit] menu and then tap [Copy]. • This puts a copy of the selected characters onto the clipboard. u To cut characters 1. Drag the stylus across the characters you want to cut to select them. 2. Tap the [Edit] menu and then tap [Cut]. • This causes the selected characters to be deleted, and moves them onto the clipboard. u To paste the clipboard contents 1. Move the cursor to the location where you want to paste the clipboard contents. 2. On the soft keyboard, tap q. Or tap the [Edit] menu and then tap [Paste]. • This pastes the clipboard contents at the current cursor location. Tip: The clipboard contents remain on the clipboard after you paste them. This means you can paste the current contents as many times as you like. Copying and pasting in the message box The “message box” is a 1-line input and display area under the Graph window (see Chapter 3). You can use the two buttons to the right of the message box to copy the message box contents (p button), or to paste the clipboard contents to the message box (q button). Copy and paste are performed the same way as the copy and paste operations using the soft keyboard. Message box Chapter 1: Basics 21 k Copying with Drag and Drop You can also copy a string of text by simply selecting it and then dragging it to another location that allows text input. Example 1: To use the Main application to perform the calculation 15 + 6 × 2, edit to (15 + 6) × 2, and then re-calculate 1. In the Main application work area, perform the calculation below. c15+6*2E 2. Drag across the 15 + 6 × 2 expression to select it, and then drag the expression to the . • This will copy 15 + 6 × 2 to the location where you dropped it. 3. Add parentheses before and after 15 + 6 and then press E. Tip: You can use drag and drop to copy both input formulas and calculation results. Example 2: To copy an expression you input with the Main application to the Graph Editor window 1. In the Main application work area, input: 2x^2 + 2x − 1. c2x{2+2x-1E 2. On the right end of the toolbar, tap the down arrow button. On the button palette that appears, tap !. • This will display the Graph Editor window in the bottom half of the screen. 3. Select the 2x^2 + 2x − 1 expression you input with the Main application by dragging across it, and then drag the expression to the located to the right of y1: on the Graph Editor window. • This will copy 2x^2 + 2x − 1 to the location where you dropped it. Tip • An expression you copy using the operation above is registered to the Graph Editor window of the Graph & Table application. For information about Graph Editor window operations, see Chapter 3. • Depending on the destination to which you drag a character string or an expression, the drop operation may cause it to be converted automatically to a graph or a figure. For example, dropping the expression in Example 2 into the Graph window will graph the expression. Refer to the locations provided below to see examples using drag and drop. - “2-9 Using the Main Application in Combination with Other Applications” (Chapter 2, page 92) - “5-4 Graphing an Expression or Value by Dropping It into the Differential Equation Graph Window” (Chapter 5, page 128) - “8-5 Using the Geometry Application with Other Applications” (Chapter 8, page 177) - “13-1 Inputting and Editing Cell Contents” (Chapter 13, page 228), “13-2 Graphing” (Chapter 13, page 237) Various Soft Keyboard Operations This section explains how to use each of the soft keyboard key sets. For information about key set types and a general overview of key sets, see “Soft Keyboard Key Sets” (page 18). All of the examples in this section assume the following conditions. • The Main application is running. See “Built-in Applications” (page 14). • The soft keyboard is displayed. See “Using the Soft Keyboard” (page 18). Chapter 1: Basics 22 k Using Math, Trig, and Advance Key Sets The [Math1], [Math2], [Math3], [Trig] (trigonometric), and [Advance] key sets contain keys for inputting numeric expressions. The L key in the upper left corner and all of the keys in the bottom row are common to all key sets. Their functions are described below. L Switches between template input and line input. See “Template Input and Line Input” (page 24). h Performs the same operation as the keypad’s K key. Deletes the character to the left of the current cursor position. pq See “Using the Clipboard for Copy and Paste” (page 21). D Inputs “ans”. See “Using the Answer Variable (ans)” (page 45). w Performs the same operation as the keypad’s E key, which executes calculations. The keys in the following table are found on different key sets and are used to input functions and commands for performing particular calculations and operations. Key set Key N5 Math1, Math2, Math3, Trig Math1, Math2, Trig Description “Template Input and Line Input” (page 24), “Other Functions” (page 50) p Inputs pi (π). W Inputs the substitution symbol (⇒). “Creating a New Variable” (page 33) m “Logarithmic Functions and Exponential Functions” (page 49) sct “Trigonometric and Inverse Trigonometric Functions” (page 49) Math1, Math2 QI Math1, Math2 4 Inputs the absolute value symbol (| |) or function (abs(). Math1, Math3 . “solve [Action][Equation/Inequality][solve]” (page 81) Math1, Math3 ( Inputs parentheses (( )). Math1, Math3 ) Inputs brackets ({ }). “2-4 List Calculations” (page 57) Math1, Trig *R “Logarithmic Functions and Exponential Functions” (page 49) “Angle Conversion (°, r)” (page 48) Math1 V"% Math1 wE Math1 / “dms [Action][Transformation][DMS][dms]” (page 64) Math1 a “toDMS [Action][Transformation][DMS][toDMS]” (page 64) Math1 # “solve [Action][Equation/Inequality][solve]” (page 81) i Inputs the imaginary unit (i). e Inputs the infinity symbol (∞). Math2, Trig 8 Inputs the θ variable. Math2, Trig [ Inputs the single-character variable (page 25) t. Math2, Math3, Trig “Logarithmic Functions and Exponential Functions” (page 49) “Other Functions” (page 50) Chapter 1: Basics 23 Key set Key Description Math2 `*7 ]_) “Using the Calculation Submenu” (page 67) Math2 678 “2-5 Matrix and Vector Calculations” (page 58) Math3 d Math3 fg Math3 ' “Derivative Symbol (’)” (page 54) Math3 + “dSolve [Action][Equation/Inequality][dSolve]” (page 82) Math3 1 “piecewise Function” (page 54) Math3 U “with Operator ( | )” (page 55) Math3 [ Inputs square brackets ([ ]). “2-5 Matrix and Vector Calculations” (page 58) Math3 <>;:=/ Math3 ~ “To create a user-defined function using the Define command” (page 203) Inputs the “f” of f(x), or the “g” of g(x). “Equal Symbols and Unequal Symbols” (page 55) “Angle Symbol (∠)” (page 54) Trig SCT “Trigonometric and Inverse Trigonometric Functions” (page 49) Trig 123 !@# “Hyperbolic and Inverse Hyperbolic Functions” (page 49) Advance :! “Other Functions” (page 50) Advance PN “Permutation (nPr) and Combination (nCr)” (page 53) Advance NM< hin Advance r Advance 5%(^ Advance 7 “Gamma Function” (page 57) Advance 6 “Dirac Delta Function” (page 56) Advance l “nth-Delta Function” (page 56) Advance ' “Heaviside Unit Step Function” (page 56) “Chapter 6: Sequence Application” “About rSolve” (page 131) “Using the Advanced Submenu” (page 64) k Template Input and Line Input ClassPad supports two different input methods: template input and line input. Template input lets you input fractions, powers, and other functions using formats that are the same as those in textbooks. Line input uses a linear format for inputting expressions. 2+ ( 2' 2 ' 2+ 1 2 ) Template Input 2+ (2 (2) / ( (2) + 1))^2 Line Input Chapter 1: Basics 24 u Switching between Template Input and Line Input Tap the L key. Each toggles the key color between white (L) and light blue ( ). A white key indicates the template input mode, while a light blue key indicates the line input mode. In the template input mode, you can perform template input using keys with or marked on their key tops, such as N and !. Other keys input the same functions or commands as they do in the line mode. 2' 2 ' 2+ 1 1. Tap the [Math1] tab and then enter the template input mode (white L key). ( Example 1: To use the template input mode to input 2+ 2 ) 2. Perform the key operation below: 2+(N2!2c!2e+1 eem2E Example 2: To use the line input mode to input the same expression as in Example 1 (2+ (2 (2) / ( (2) + 1))^2) 1. Tap the [Math1] tab and then enter the line input mode (light blue key). 2. Perform the key operation below: 2+(d2!2)N (!2)+1)ewE Example 3: To use the template input mode to input Y() 1. Tap the [Math2] tab and then enter the template input mode (white L key). 2. Perform the key operation below: Oxe1f10exE Example 4: To use the template input mode to input ∫ 0 1 (1 − 2) 1. Tap the [Math2] tab and then enter the template input mode (white L key). 2. Perform the key operation below: 7(1-xm2e)Qxeex 3. Tap the upper right input box of ∫ and then press 1. Next, tap the lower right input box of ∫ and then press 0. 4. To execute the calculation, press E. Tip: For information about the contents and input formats of the functions in Example 3 and Example 4, see “2-7 Using the Action Menu” (page 61). k Using Single-character Variables As its name suggests, a single-character variable is a variable name that consists of a single character like “a” or “x”. Input of single-character variable names is subject to different rules than input of a series of multiple characters (like “abc”). Chapter 1: Basics 25 u To input a single-character variable name Any character you input using any one of the following techniques is always treated as a single-character variable. • Tapping any key in the [Var] (variable) key set (page 19) • Tapping the X, Y, or Z key of the [Number] key set • Tapping the [ key of the [Math2] key set • Pressing the x, y, or Z keypad key If you use the above key operations to input a series of characters, each one is treated as a single-character variable. Inputting A, B, C using the [Var] key set, for example, is treated as the mathematical expression a × b × c, and not as the characters “abc”. Tip: The single-character variables described above make it possible for you to perform calculations as they appear in your textbook. Example 1: ABCw Example 2: 2xyE Tip: When you input a single-character variable, its name appears on the display as an italicized character. This is simply to let you know that the letter is a single-character variable name. u To input a series of multiple characters A series of multiple characters (like “list1”) can be used for variable names, program commands, comment text, etc. Always use the [abc] key set when you want to input a series of characters. Example: abcE You can also use the [abc] key set to input single-character variable names. To do so, simply input a single character, or follow a single character with a mathematical operator. Example: a*b+cE Tip: A single-character variable you input using the [abc] key set is identical to a single-character variable you input using the [Var] key set. k Using the Alphabet Keyboard Tap the [abc] tab to the left of the soft keyboard to display the alphabet keyboard [abc] key set. In addition to the [abc] key set, you can also select from among three other key sets named [αβγ] (character symbols), [Math] (mathematics symbols), and [Symbol] (extra symbols). Use the tabs above the alphabet keyboard (to the right of the keyboard when using horizontal screen orientation) to select a key set. To return to the [Math1] key set from the alphabet keyboard, tap the I key in the lower left corner. Chapter 1: Basics 26 k Using the Catalog Keyboard The “Form” menu of the catalog keyboard lets you select one of the five categories described below. Func ........ built-in functions (pages 48 and 61) Cmd ........ built-in commands and operators (page 206) Sys .......... system variables (page 299) User ........ user-defined functions (page 203) All ............ all commands, functions, etc. After selecting a category, you can choose the item you want from the alphabetized list that appears on the catalog keyboard. Tip: Note that user-defined variables and user-defined programs cannot be input using the catalog keyboard. Use Variable Manager (page 29) instead. Catalog keyboard configuration Tapping a letter button displays the commands, functions, or other items that begin with that letter. This is an alphabetized list of commands, functions, and other items available in the category currently selected with “Form”. Tap the down arrow button and then select the category you want ([Func], [Cmd], [Sys], [User], or [All]) from the list that appears. Tap this key to input the item that is currently selected in the alphabetized list. u To use the catalog keyboard Example: To input the built-in command “Plot” 1. On the catalog keyboard, tap the “Form” down arrow button and then select [Cmd] from the list of categories that appears. 2. Tap the + button in the upper right corner until the P button is visible. 3. Tap P. 4. In the alphabetized list, tap “Plot” and then tap [INPUT] to input the command. • Instead of tapping [INPUT], you could also tap the command a second time to input the command. 1-5 ClassPad Data This section provides information about the various types of data that can be stored in ClassPad memory, and the location where each type of data is stored. It also explains how to use Variable Manager, which is a tool for managing stored data, as well as file operations (file save, recall, delete, rename, etc.) that are common to a number of different applications. Data Types and Storage Locations (Memory Areas) ClassPad uses a “main memory” memory area to store various types of data. Examples: • Executing “10⇒x” (which assigns a value of 10 to variable x) in the Main application or eActivity application causes variable x to be stored in main memory as “EXPR” (expression) type data. • Creating a user-defined function (page 203) causes the function to be stored in main memory as “FUNC” (function) type data. Chapter 1: Basics 27 • Saving a spreadsheet to a file (by executing [File] - [Save] with the Spreadsheet application) saves the file in main memory as “MEM” (memory) type data. An eActivity file created with the eActivity is stored in a separate eActivity memory area in order to keep it separate from other application data. Accessing Data Besides the application that originally created it, data in main memory can also be accessed by any other application. It can also be deleted, renamed, copied, moved and otherwise accessed using Variable Manager (page 29). eActivity files can be accessed from the eActivity application only. Main Memory Data Types Data stored in main memory has a data type attribute that is assigned in accordance with the application that created the data and the actual content of the data. The data type is indicated by a data type name. Data type names are shown on the Variable Manager variable list, and on the Select Data dialog box that appears when you are specifying a variable in any ClassPad application. The following table lists all of the data type names and explains the meaning of each. Data Type Name Data Type EXPR Real number, complex number or expression data STR String data LIST List data created using the Statistics application, Main application, etc. MAT Matrix data created using the Main application, etc. PRGM* General program EXE* Edit prohibited program TEXT* Text data FUNC* User-defined function GMEM* Graph memory data saved using the Graph & Table application For more information, see “Saving Graph Editor Data to Graph Memory” (page 102). GEO* Geometry application data MEM* Data saved to a file using one of the following applications: Spreadsheet, Geometry, Verify (page 94), Probability (page 95). OTHR Data other than that described above Protected variable types Some data types are protected. A variable whose data type is protected cannot be overwritten with another variable, which protects variable contents from being inadvertently altered. Data types whose names are marked with an asterisk in the above table are protected. Note that whether or not a data type is protected is determined by the system. You cannot change the protection status of a data type. Tip: Even when a variable is a protected data type, you can rename, delete, or move it. To disable these operations, you need to lock the variable. See “Variable Manager operations” on page 30. Main Memory Folders Your ClassPad stores data in one of the following types of folders described below. “main” folder: The “main” folder is a ClassPad reserved folder, and acts as the default current folder (see “Current Folder” below). “library” folder: Also a ClassPad reserved folder, the “library” folder can be used for storing user-created data (variables, programs, user functions, etc.). Data stored in the “library” folder can be accessed without specifying a path, regardless of the current folder setting. Chapter 1: Basics 28 User folder: This is a folder created and named by you. You can make a user folder the current folder, move data to a user folder, etc. You can also delete and rename a user folder as required. You can have up to 87 user folders in main memory at one time. Tip: You cannot put a folder inside of another folder. Current Folder The current folder is the folder where the data (excluding eActivity files) created by applications are stored and from which such data can be accessed. The initial default current folder is the “main” folder. You can also select a user folder you created as the current folder. For more information about how to do this, see “Variable Manager operations” on page 30. Using Variable Manager Variable Manager is a tool for managing user variables, programs, user functions, and other types of data. Though this section uses only the term “variables”, the explanations provided here also refer to the other types of data that can be managed by Variable Manager. With Variable Manager you can: • Create, delete, rename, lock, and unlock folders, and configure current folder settings. • Delete, copy, rename, move, lock, unlock, search for variables, and view the contents of variables. About Variable Types A variable with a letter name like x and y can be a user-created user variable, a system variable, or a local variable. • System variables are pre-defined reserved variables, and cannot be renamed. For the names of and detailed information about system variables, see the “System Variable Table” on page 299. • A local variable is a variable that is temporarily created by a defining function, program, or other operation for a particular purpose. For more information about local variables, see the “Local” command under the “12-4 Program Command Reference”. u To start up Variable Manager 1. While any application (except for the System application) is running, tap O and then tap [Variable Manager]. • This displays the folder list. The folder list always appears first whenever you start up Variable Manager. Folder name Number of variables contained in the folder Folder list Number of variables contained in the folder 2. Tap a folder name twice to open the folder contents; a variable list. Folder name Variable name Data types (page 28) and sizes (bytes) • To close the variable list and return to the folder list, tap [Close]. Variable list 3. To exit Variable Manager, tap [Close] on the folder list. Chapter 1: Basics 29 u Variable Manager operations The operations described in the table below can be performed while Variable Manager is displayed. To do this: Do this: Specify the current folder On the folder list, tap the [Current] down arrow button. On the list that appears, select the folder that you want to specify as the current folder. Create a folder On the folder list, tap [Edit] - [Create Folder]. On the dialog box that appears, enter the name you want to assign to the folder and then tap [OK]. Open a folder On the folder list, tap the name of the folder you want to open so it is highlighted, and then tap it again. Open the “library” folder Tap [View] and then [“library” Folder]. This opens the “library” folder and displays a variable list showing its contents. Select a folder or variable Select the check box next to the folder or variable name. To select all the folders or variables in the list, tap [All] and then [Select All]. Deselect a folder or variable Clear the check box next to the folder or variable name. To deselect all the folders or variables in the list, tap [All] and then [Deselect All]. Delete a folder See “To delete a folder” (page 31). Delete a variable Select the check box next to the variable you want to delete, and then tap [Edit] - [Delete]. In response to the confirmation dialog box that appears, tap [OK] to delete the selected variable. Rename a folder or variable Highlight the folder or variable you want to rename and then tap [File] [Rename]. On the dialog box that appears, enter the name you want to assign to it and then tap [OK]. Lock a folder or variable Select the check box next to the folder or variable you want to lock, and then tap [Edit] - [Lock]. This locks the currently selected folder or variable, and adds a b icon to the left of its name to indicate that it is locked. Unlock a folder or variable Select the check box next to the folder or variable you want to unlock, and then tap [Edit] - [Unlock]. Display a list of a particular type of variable On the variable list, tap [View] - [Variable Type]. On the dialog box that appears, tap the down arrow button and then select the data type from the list that appears and then tap [OK]. Copy or move a variable On the variable list, tap [Edit] and then [Copy] or [Move]. On the dialog box that appears, tap the down arrow button and then select the destination folder from the list that appears and then tap [OK]. Tip • If a variable with the same name already exists in the destination folder, the variable in the destination folder is replaced with the one that you are copying or moving. • A variable that is locked cannot be moved. View the contents of a variable On the variable list, tap the name of the variable whose contents you want to view so it is highlighted, and then tap it again. This displays a dialog box that shows the contents of the variable. Input a folder name or variable name into an application See “To input a folder name or variable name into an application” (page 31). Search for a variable On the folder list, tap [Search]. On the dialog box that appears, enter the variable name you want to find and then tap [OK]. An exclamation point (!) appears in front of all folders containing a variable name that matches the name in your search. Note: You can use the above procedure to search the “main” folder or a user defined folder for a particular variable name. Note that you cannot search the “library” folder. Chapter 1: Basics 30 Selecting a Folder • If no check box is selected on the folder list, any folder operation that is performed affects the folder whose name is currently highlighted on the list. If any folder check box is selected, only that folder is affected by a folder operation, and the folder whose name is highlighted on the list is not affected. • Selecting the check box of a folder causes the check boxes of all of the variables inside of it also to become selected. • When renaming a folder, only the folder whose name is highlighted on the folder list is renamed. Other folders whose check boxes are selected are not affected. Selecting a Variable • If no check box is selected on the variable list, any variable operation that is performed affects the variable whose name is currently highlighted on the list. If any variable check box is selected, only that variable is affected by a variable operation, and the variable whose name is highlighted on the list is not affected. • When renaming a variable, only the variable whose name is highlighted on the variable list is renamed. If other variables are selected (checked), they will not be affected. Folder and Variable Name Rules The following are the rules that apply to folder and variable names. • Folder or variable names can be up to 8 bytes long. • The following characters are allowed in a folder or variable name: Upper-case and lower-case characters, subscript characters, numbers, underscore (_). • Folder or variable names are case-sensitive. For example, each of the following is treated as a different folder/variable name: abc, Abc, aBc, ABC. • A reserved word (system variable names, built-in function names, command names, etc.) cannot be used as a folder or variable name. • A number, subscript characters or the underscore (_) cannot be used as the first character of a folder or variable name. u To delete a folder Important! Before deleting a folder, make sure you no longer need any of the variables contained inside it. It is probably a good idea to first delete the variables you don’t need, move the variables you do need to another folder, and then delete the empty folder. 1. Open the folder you want to delete and check its contents. • Make sure you no longer need any of the variables in the folder. If any of the variables are locked, unlock them. • After checking the contents of the folder, close it to return to the folder list. 2. Select the check box next to the folder you want to delete. • You can select and delete multiple folders, if you want. 3. On the folder list, tap [Edit] and then [Delete]. 4. In response to the confirmation dialog box that appears, tap [OK] to delete the folder. Tip: You cannot delete the “library” folder or the “main” folder. u To input a folder name or variable name into an application 1. In the Main application, Graph & Table application, or some other application, move the cursor to the location where you want to input the variable name. 2. Start up Variable Manager to display the folder list. 3. If you want to input a variable name, double-tap the folder that includes the variable whose name you want to input. If you want to input a folder name, advance to the next step. Chapter 1: Basics 31 4. Tap the folder or variable whose name you want to input, so its name is highlighted. 5. Tap [INPUT]. • This exits Variable Manager and inputs the name of the folder or variable you selected in step 4 into the application at the current cursor position. Managing Application Files The applications below can save data to files. Geometry (Chapter 8), eActivity (Chapter 10), Spreadsheet (Chapter 13), Verify (page 94), Probability (page 95), Picture Plot (Chapter 15) This section explains the common operations that can be performed on data files created with these applications. Tip: The eActivity file save dialog box is slightly different from the save dialog box of the other applications, but operations are basically the same. u To save a file 1. Tap [File] and then [Save]. 2. On the dialog box that appears, tap the name of the folder where you want to save the file so it is selected. 3. Input up to 8 bytes for the file name in the file name edit box, and then tap [Save]. u To open an existing file 1. Tap [File] and then [Open]. 2. On the dialog box that appears, open the folder that contains the file you want to open. 3. Tap the name of the file you want to open so it is selected, and then tap [Open]. u To search for a file 1. Tap [File] and then [Open]. 2. On the dialog box that appears, tap [Search]. This displays the Search dialog box. 3. Enter the file name you want to find and then tap [Search]. • File names that match the one you enter become highlighted on the display. Tapping [Open] opens the highlighted file. • To search for the next occurrence of the file name, tap [Search] again and then tap [Next] on the Search dialog box. u To delete a folder or file Important! Deleting a folder also deletes all files inside of it. Please double-check to make sure you no longer need the contents of a folder before deleting it. 1. Tap [File] and then [Open]. 2. On the dialog box that appears, select the check box next to the folder or file you want to delete. • You can select multiple folders/files for deletion, if you want. • Selecting a check box next to a folder name automatically checks the boxes for all files inside that folder. 3. Tap [File] and then [Delete]. 4. In response to the confirmation dialog box that appears, tap [OK] to delete the folder(s) or file(s). Tip: Selecting a folder in the above procedure deletes the folder and all of its contents. Note, however, that the “main” folder cannot be deleted, even if you check it. Chapter 1: Basics 32 u To rename a folder or file 1. Tap [File] and then [Open]. 2. On the dialog box that appears, tap the name of the folder or file you want to rename so it is selected. 3. Tap [File] and then [Rename]. This displays the Rename dialog box. 4. Enter the name you want to assign to it and then tap [OK]. u To move a file to another folder 1. Tap [File] and then [Open]. 2. On the dialog box that appears, select the check box next to the file you want to move. • To move multiple files, select all of their check boxes. 3. Tap [File] and then [Move]. • This causes a dialog box for selecting the destination folder to appear. 4. On the dialog box, tap the down arrow button and then select the destination folder from the list that appears. 5. Tap [OK] to move the files. u To switch the file menu view between List View and Detail View (eActivity application only) 1. Tap [File] and then [Open]. 2. On the dialog box that appears, open the folder that contains the files you want to list. 3. To display both the file name and file size, tap [View] - [Detail View]. To display file names only, tap [View] [List View]. u To create a new folder 1. Tap [File] and then [Open]. 2. On the dialog box that appears, tap [File] and then [Create Folder], or tap {. • This displays the Create Folder dialog box. 3. Enter up to 8 bytes for the folder name, and then tap [OK] to create a folder. 1-6 Creating and Using Variables This section explains how to create a new variable (user variable), and provides a simple sample calculation that illustrates how to use a variable. Creating a New Variable The most common way to create a new variable is assigning a value or expression to the applicable variable name. Use the variable assignment key (W) to assign data to a variable. The following is an example of assignment to a variable while “main” is specified as the current folder. Example: To create a new variable named “eq1” and assign the expression 2x + 1 to it The following assumes that there are no variables named “eq1” or “x” currently in the “main” folder. u ClassPad Operation 1. Start the Main application. 2. Press k to display the soft keyboard, and then perform the following key operation. 2x+11W0eqbw Chapter 1: Basics 33 • This creates a variable named “eq1” in the current folder (the “main” folder in this example), and assigns the expression 2x + 1 to it. Tip • If a variable with the specified name already exists in the current folder, the contents of the existing variable are replaced with the newly assigned data, unless the existing variable is locked or protected. For more information, see “Variable Manager operations” (page 30) and “Protected variable types” (page 28). • To store the newly created variable in a folder other than the current folder, specify the variable name as follows:\ . • You can use Variable Manager to view the contents of a variable you create. For more information, see “Variable Manager operations” (page 30). • For information about rules for naming variables, see “Folder and Variable Name Rules” (page 31). Variable Usage Example The following example uses the variable we created in the example under “Creating a New Variable” above. Example: To assign values of 5 and 10 to x and check the results of eq1 (= 2x + 1) u ClassPad Operation 1. Assign 5 to x. 51WxE 2. Check the contents of variable “eq1”. 0eqbw • This displays the calculation result of 2x + 1 when x = 5. 3. Assign 10 to x. 101WxE 4. Check the contents of variable “eq1”. 0eqbw “library” Folder Variables Variables in the “library” folder can be accessed without specifying a path name, regardless of the current folder. Example: To create and access two variables, one located in the “library” folder and one located in another folder u ClassPad Operation 1. With “main” specified as the current folder, perform the following operation to create a variable named “eq1” and assign the indicated list data to it. {1, 2, 3} W eq1w 2. Keeping “main” specified as the current folder, perform the following operation to create a variable named “eq2” in the “library” folder, and assign the indicated list data to it. {4, 5, 6} W library\eq2w 3. Check the contents of the two variables. eq1w eq2w (Since variable “eq2” is stored in the “library” folder, you do not need to indicate a path to access it.) Chapter 1: Basics 34 4. Change the current folder specification to “Test”. • Use Variable Manager (page 29) to create a folder named “Test” and change the current folder specification. 5. Perform the following operations to view the contents of variables “eq1” and “eq2”. eq1E (Since this key operation does not access the “main” folder, the variable name (“eq1”) is displayed without showing the variable contents.) main\eq1E (Specifying the path to the “main” folder where “eq1” is located displays the contents of the variable.) eq2E (Since variable “eq2” is stored in the “library” folder, you do not need to indicate a path to access it.) Tip: Specifying a variable name that exists in both the current folder and the “library” folder causes the variable in the current folder to be accessed. For details about the variable access priority sequence and how to access variables in particular folders, see “Rules Governing Variable Access” below. Rules Governing Variable Access Normally, you access a variable by specifying its variable name. The rules in this section apply when you need to reference a variable that is not located in the current folder or to access a variable that has the same name as one or more variables located in other folders. k Variable Search Priority Sequence Specifying a variable name to access a variable causes variables to be searched in the sequence below. (1) Local variables (2) Current folder variables (3) “library” folder variables • Multiple variables with the same name can exist simultaneously as a local variable, as a variable in the current folder, and as a variable in the “library” folder. In this case, the ClassPad searches folders according to the sequence shown above and accesses the first instance of the variable that it finds. If you want to access such a variable when it occurs lower in the above sequence, you need to specify the folder name along with the variable name as shown in “Specifying a Variable in a Particular Folder” below. • If a variable you specify cannot be found, it is treated as an “undefined variable”. • Note that “system” variables are not included in the above variable search. When accessing a system variable, you need to specify the variable name only, without specifying the folder name. Tip: Only local variables and current folder variables are searched in the case of an operation that stores variable data or a command that performs an operation on a variable (like “DelVar”). Normally, “library” folder variables are not searched. If you want to include “library” folders in the search, you need to specify the “library” folder as the variable location as explained below. k Specifying a Variable in a Particular Folder You can access a variable located inside the “main” folder, “library” folder, or a particular user folder by specifying the folder name along with the variable name. Use the following syntax when specifying a folder name: \ Example: To specify variable “abc” located in the “main” folder main\abc Chapter 1: Basics 35 1-7 Configuring Application Format Settings The O menu includes format settings for configuring the number of calculation result display digits and the angle unit, as well as application-specific commands. The following describes each of the settings and commands that are available on the O menu. Select this O menu command: To do this: Specify folder for variables, and to configure number format, angle, and other basic settings for all built-in applications Basic Format Configure Graph window and graph drawing settings for Graph & Table, Conics, and other graphing applications Graph Format Configure number format, angle, and other settings for Geometry application Geometry Format Configure Fourier transform and FFT settings Advanced Format Configure Financial application settings Financial Format Return all the above menu settings to their initial default values (except for the current folder setting specified on Basic Format dialog box) Default Setup u To configure application format settings 1. Open any application (except the System application). 2. Tap O. Next, tap the menu command you want: Basic Format, Graph Format, Geometry Format, Advanced Format, or Financial Format. 3. Use the dialog box to configure the settings you want. • For details about the settings you can configure on each of the dialog boxes, see “Application Format Settings” below. 4. To close a dialog box and apply its settings, tap [Set]. To close a dialog box without applying its settings, tap [Cancel] or the C button in the upper right corner of the dialog box. Application Format Settings This section provides details about all of the settings you can configure using the application format settings. Settings marked with an asterisk (*) in the following explanations are ClassPad initial default settings. k Basic Format Dialog Box Use the Basic Format dialog box to configure basic settings for calculations, cells, and other parameters. 1 2 3 To specify the current folder Tap 1 and then tap the name of the folder (main*) you want. To specify the numeric value display format Tap 2 and then tap one of the settings described below. Normal 1*: Automatically uses exponential display format when calculation result x is: 10−2 > |x| or |x| t 1010. Normal 2: Automatically uses exponential display format when calculation result x is: 10−9 > |x| or |x| t 1010. Fix 0 – Fix 9: Fixed number of decimal places Sci 0 – Sci 9: Fixed number of significant digits To specify the angle unit Tap 3, and then tap “Radian*”, “Degree”, or “Grad”. Chapter 1: Basics 36 To do this: Do this: Switch between complex number calculations (Complex mode) and real number calculations (Real mode) Select the “Complex Format” check box to enter the Complex mode, or clear the check box* to enter the Real mode*. Display results as a decimal value (Decimal mode) or leave calculation results as expressions (Standard mode) Select the “Decimal Calculation” check box to enter the Decimal mode, or clear the check box* to enter the Standard mode. Turn auto simplification of expressions on (Algebra mode) or off (Assistant mode) Select the “Assistant” check box to enter the Assistant mode, or clear the check box* to enter the Algebra mode. See page 47 for details. Specify descending order or ascending order for the calculation result expression Select the “Descending Order” check box* to display calculation result expressions in descending order (like x2 + x + 1), or clear the check box to display in ascending order (like 1 + x + x2). Specify whether variables in Complex Mode calculation should be treated as real numbers or complex numbers Select the “Variable is Real” check box to treat variables as real numbers, or clear the check box* to treat variables as complex numbers. Tip: For information about the “Q1, Q3 on Data” check box, see “Calculation Methods for Q1, Q3 and Median” (page 141). Using Status Bar to Change Application Format Settings With the applications listed in the table below, you can use the status bar to check and modify a number of Basic Format dialog box settings. For this application: You can check and change these settings: Main, eActivity Algebra mode/Assistant mode setting, Standard mode/Decimal mode setting, Complex mode/Real mode setting, angle unit setting Statistics Standard mode/Decimal mode setting, angle unit setting Graph & Table, Conics, Differential Equation Graph, Numeric Solver, Sequence Complex mode/Real mode setting, angle unit setting u To use the status bar to change application format settings On the status bar, tap the text of the setting you want to change. Main application Graph & Table application Each tap changes the tapped item as described below. • • • • “Alg” ↔ “Assist” ... Toggles between the Algebra mode and Assistant mode. “Standard” ↔ “Decimal” ... Toggles between the Standard mode and Decimal mode. “Real” ↔ “Cplx” ... Toggles between the Real mode and Complex mode. “Rad” → “Deg” → “Gra” ... Cycles the angle unit setting between Radian, Degree, and Grad. Tip: Changing a setting using the status bar has the same effect as changing the corresponding setting on the Basic Format dialog box. This means the setting will be changed for all applications. Chapter 1: Basics 37 k Graph Format Dialog Box Use the Graph Format dialog box to configure settings for the Graph window and for drawing graphs. [Basic] tab 1 2 3 4 To specify display of Graph window axes Tap 1 and then tap one of the settings described below. On: show axis Off: hide axis Number*: show axis along with maximum and minimum value of each axis To specify display of Graph window grid Tap 2 and then tap one of the settings described below. On: show grid as dots Off: hide grid Line*: show grid as lines To select inequality fill specification (Inequality Plot) Tap 3 and then tap one of the settings described below. Union*: fill areas where all inequality conditions are satisfied when graphing multiple inequalities Intersection: fill areas where each inequality condition is satisfied when graphing multiple inequalities To specify the color of figures and graphs drawn with the Sketch function (page 112) Tap 4. On the dialog box that appears, select the color you want and then tap [OK]. To do this: Do this: Turn display of Graph window axis labels on or off Select the “Labels” check box* to show labels, or clear the check box to hide labels. Tip: Regardless of the “Labels” setting, labels are never displayed on the Sequence application Graph window. Also, labels are not displayed for the following types of graph drawn with the Statistics application: NPPlot, Histogram, MedBox, NDist Broken. Turn display of graph controller arrows on or off Select the “G-Controller” check box to show graph controller arrows (page 105), or clear the check box* to hide graph controller arrows. Specify plotted points or solid lines for graph drawing Select the “Draw Plot” check box to specify plotted points, or clear the check box* to specify solid lines for graphing. Turn display of the function name and function on or off Select the “Graph Function” check box* to show the function name and function on the graph, or clear the check box to hide the function name and function. Turn display of Graph window pointer coordinates on or off Select the “Coordinates” check box* to show Graph window pointer coordinates, or clear the check box to hide the coordinates. Turn display of the leading cursor during graphing on or off Select the “Leading Cursor” check box to show the leading cursor, or clear the check box* to hide the leading cursor. Specify the draw method when drawing multiple graphs Select the “Simultaneous Graphs” check box to draw multiple graphs simultaneously, or clear the check box* to draw graphs in sequence, one at a time. Show or hide derivative values on the Graph window and Table window Select the “Derivative/Slope” check box to show derivative values in the Graph window and Table window, or clear the check box* to hide derivative values. For details about display contents, see “Using Trace to Read Graph Coordinates” (page 111) and “Generating a Number Table” (page 108). Chapter 1: Basics 38 [Special] tab 1 2 3 To specify the row width for Stat Editor and data table displays Tap 1 and then select a cell width pattern: 2 Cells, 3 Cells*, or 4 Cells for vertical display orientation, or 4 Cells, 5 Cells*, or 6 Cells for horizontal orientation (see “Changing the Display Orientation” on page 16). To specify a source for table data Tap 2 and then tap one of the settings described below. Table Input*: Uses the data input in a Table Input dialog box as the source for number table generation. list1 through list6: Uses list data in list1 through list6 as the source for number table generation. : Uses the list data in a selected list as the source for number table generation. For details about how to generate a number table using each setting, see “Generating a Number Table” (page 108). To specify a source for summary table data Tap 3 and then tap one of the settings described below. View Window*: Uses View Window settings as the source for summary table generation. list1 through list6: Uses list data in list1 through list6 as the source for summary table generation.

: Uses the list data in a selected list as the source for summary table generation. For details about how to generate a summary table using each setting, see “Generating a Summary Table” (page 110). To show or hide the second derivative for summary tables Select the On button* under “Summary Table f (x)” to show the second derivative, or the Off button to hide it. To specify auto setting or manual setting of Statistics application View Window settings Select the “Stat Window Auto” check box* to specify automatic setting configuration, or clear the check box for manual settings. [3D Format] tab 1 2 3 To specify display of coordinate values Tap 1, and then select “Rectangular*” (display rectangular coordinate values), “Polar” (display polar coordinate values), or “Off” (turn off display of coordinates). To specify display of axes Tap 2 and then select “On” (display axes normally), “Box” (display box type coordinate axes), or “Off*” (turn off display of axes). To turn display of Graph window axis labels on or off Tap 3 and then select “On” or “Off*”. Chapter 1: Basics 39 k Geometry Format Dialog Box Use the Geometry Format dialog box to configure settings for the Geometry application. Tip: The information that appears in the preview area at the bottom of the dialog box shows a preview of the Geometry application window, based on the settings configured in upper part of the dialog box. 1 2 3 4 5 6 To specify the Geometry window numeric value display format Tap 1 and then select the format you want. The initial default Number Format setting is Fix2. For more information, see “To specify the numeric value display format” (page 36). To specify the unit of the displayed length value Tap 2 and then tap one of the settings described below. Off*: Length value unit not displayed. mm, cm, m, km, in, ft, yd, mi: Displays the length value in the selected unit. To specify the angle unit for the measurement box Tap 3, and then tap “Radian”, “Degree*”, or “Grad”. To specify the angle unit for graphing Tap 4, and then tap “Radian*”, “Degree”, or “Grad”. To specify the initial status of Graph window axes when the Geometry application is started up Tap 5 and then tap one of the settings described below. On: Show the axes Off*: Hide the axes Number: Show the axes along with the maximum and minimum value of each To specify the initial status of the grid when the Geometry application is started up Tap 6 and then tap one of the settings described below. On: Show the grid as dots Off*: Hide the grid Line: Show the grid as lines k Advanced Format Dialog Box Use the Advanced Format dialog box to configure settings for Fourier transform and FFT settings. 1 2 To specify the Fourier transform formula Tap 1 and then tap “Modern Physics”, “Pure Math*”, “Probability”, “Classical Physics”, or “Signal Processing”. To specify the FFT scaling constant Tap 2 and then tap “Pure Math”, “Signal Processing*”, or “Data Analysis”. To specify how Fourier calculation variables are treated Select the “Assume positive real” check box* to specify that Fourier calculation variables should be treated as positive reals only. Clear the check box to specify that complex numbers are allowed for Fourier calculation variables. Chapter 1: Basics 40 k Financial Format Dialog Box Use the Financial Format dialog box to configure settings for the Financial application. [Basic] tab To specify the number of days in a year Tap 1, and then tap “360 days” or “365 days*”. 1 2 3 To specify the beginning or the period or the end of the period as the payment date Tap 2 and then tap “Beginning of period” or “End of period*”. To specify the date format Tap 3 and then tap one of the settings described below. MM/DD/YYYY*: month/day/year DD/MM/YYYY: day/month/year YYYY/MM/DD: year/month/day To specify the status of input fields when starting a new calculation To do this: Do this: When changing to another calculation type, automatically copy the contents of all fields in the current calculation whose names match the names of fields in the new calculation. Select the [Automatically copy common fields to new calculation] check box*. When changing to another calculation type, clear all fields. Clear the [Automatically copy common fields to new calculation] check box. Chapter 1: Basics 41 [Special] tab 1 2 3 4 5 To specify odd period handling Tap 1 and then tap one of the settings described below. Compound (CI): Apply compound interest to the odd period when performing a Compound Interest calculation Simple (SI): Apply simple interest to the odd period when performing a Compound Interest calculation Off*: Apply no interest to the odd period when performing a Compound Interest calculation To specify the compounding frequency Tap 2, and then tap “Annual*” (once a year) or “Semi-annual” (twice a year). To specify the bond interval Tap 3 and then tap one of the settings described below. Term*: Specifies use of the number of payments as the duration for bond calculation. Date: Specifies use of a date as the duration for bond calculation. To specify whether to use the amount (PRF) or profit ratio (r%) when performing break-even point calculations Tap 4, and then tap “Amount (PRF)*” or “Ratio (r%)”. To specify whether to calculate sales quantity ([QBE]) or sales amount ([SBE]) first when performing break-even point calculations Tap 5, and then tap “Quantity*” or “Sales”. When “Quantity” is selected, sales quantity can be calculated before calculating the sales amount. When “Sales” is selected, sales amount can be calculated before calculating the sales quantity. Tip: When performing a financial calculation, you can change settings using the Financial application status bar and [Format] tab. For more information, see “Configuring Financial Application Settings” (page 188). Initializing All Application Format Settings Perform the following procedure when you want to return all application format settings to their initial defaults. u ClassPad Operation 1. Tap O and then tap [Default Setup]. 2. In response to the “Reset Setup Data?” message that appears, tap [OK] to initialize all settings. • The settings are initialized except for the current folder setting specified on Basic Format dialog box. Chapter 1: Basics 42 1-8 When you keep having problems… If you keep having problems when you are trying to perform operations, try the following before assuming that there is something wrong with the ClassPad. 1. Initialize all application format settings. Perform the procedure under “Initializing All Application Format Settings” (page 42). 2. Perform the RAM reset (RESTART) operation. Perform RAM reset when the ClassPad freezes up or otherwise fails to perform as expected for some reason. To perform the RAM reset operation Important! • The RAM reset operation deletes all data that is temporarily stored in ClassPad RAM. Performing the RAM reset operation while a calculation is in progress will cause any data stored in RAM by the calculation to be lost. • Perform the RAM reset operation only when your ClassPad freezes up or when it begins to operate abnormally for some reason. 1. Use the stylus to press the RESTART button on the back of the ClassPad. • Following the RAM reset operation, the ClassPad restarts automatically. RESTART Button 2. After the ClassPad restarts, perform the ClassPad setup operation. For more information about the procedures you need to perform here, see “Loading Batteries and Setting Up the ClassPad” in the separate Quick Start Guide. • The application menu appears after you finish the setup operation. 3. Reset the ClassPad. Before performing the reset operation, first make a written copy of all important data. For details, see “To batch delete specific data (Reset)” (page 281). Chapter 1: Basics 43 Chapter 2: Main Application The Main application is a general-purpose numerical and mathematical calculation application that you can use to study mathematics and solve mathematical problems. You can use the Main application to perform general operations from basic arithmetic calculations, to calculations that involve lists, matrices, etc. Starting up the Main application displays a large white work area. Use this area for inputting operations and commands. ClassPad also uses this area to output calculation results. Input expression Basic Main application operations consist of inputting a calculation expression into the work area and pressing E. This performs the calculation and then displays its result on the right side of the work area. Calculation result Work area Main Application-Specific Menus and Buttons • Clear variables that contain numbers, list and matrices ...........................................Edit - Clear All Variables • Insert a command into the work area (page 61) ....................................................................................Action • Execute an Interactive command for the expression selected in the work area (page 91)............. Interactive • Toggle calculation result display between the Standard mode and Decimal mode ....................................u • Recalculate the equation just for the current line where the cursor is currently located .............................7 • Output an input expression as-is ................................................................................................................0 • Insert and execute the Simplify command ..................................................................................................S • Switch between binary, octal, decimal or hexadecimal number bases during normal calculation (page 60).......................................................................................................< • Access ClassPad application windows from the Main application (page 92) .............................................$ 2-1 Basic Calculations This section explains how to perform basic mathematical operations in the Main application. Arithmetic Calculations and Parentheses Calculations You can perform arithmetic calculations by inputting expressions as they are written. The ClassPad automatically judges the calculation priority sequence for addition, subtraction, multiplication, and division, functions, and parentheses. 0201 Calculation examples Chapter 2: Main Application 44 • All of the example calculations shown in 0201 are performed using the keypad or the soft keyboard [Number] key set, unless noted otherwise. • The example calculations are all performed using the Decimal mode (page 46). Using the e Key Use the e key to input exponential values. You can also input exponential values using the E key on the soft keyboard [Number] key set. 0202 Calculation examples Omitting the Multiplication Sign You can omit the multiplication sign in any of the following cases. • In front of a function… 2sin (30), 10log (1.2), etc. • In front of a constant or variable… aπ, 2ab, 3ans, etc. • In front of an open parenthesis… 3(5 + 6), (a + 1)(b – 1), etc. Note that you must use a multiplication sign when the expression directly in front of the open parenthesis is a literal variable. Example: ab (3 + b) must be written ab × (3 + b). Otherwise, your input is considered to be in function notation ( f (x)). • In front of the e key or E key (See “Using the e Key” above.) • In front of a matrix or list… a {1, 2, 3}, 3 [[1, 2] [3, 4]], etc. Using the Answer Variable (ans) Any time you execute a calculation in the Main application work area, the last result is assigned automatically to a variable named “ans” (answer). You can even recall current “ans” variable contents and input them into another calculation by tapping the D key on the soft keyboard. 0203 Calculation examples Tip: Starting a calculation expression with +, −, ×, ÷, or ^ operator will cause the “ans” variable to be inserted automatically to the left of the operator, even if you do not tap the D key. Assigning a Value to a Variable Besides using the variable assignment key (W, page 33), you can also use the syntax shown below in the Main application and eActivity application to assign a value to a variable. Syntax: Variable: = value 0204 Assign 123 to variable x Important! “:=” can be used only in Main and eActivity. It can NOT be used in a program. In the Program application, you must use W to store a value to a variable. Chapter 2: Main Application 45 Calculation Priority Sequence Your ClassPad automatically performs calculations in the following sequence. 1 Commands with parentheses (sin(, diff(, etc.) 5 +, –, (–) 2 Factorials (x!), degree specifications (o, r ), percents (%) 6 Relational operators (=, , <, >, s, t) 7 and 3 Powers 4 π, memory, variable multiplication operations that omit the multiplication sign (2π, 5A, etc.), command with parentheses multiplication operations that omit the multiplication sign (2' 3, etc.), ×, ÷ 8 or, xor 9 with ( | ) Tip • Expressions in parentheses are given priority. • In cases where a series of calculations in the same expression includes more than one of the operators 4 through 9 that are the same priority sequence level, the same level operations are performed from left to right. A series of power calculations 3 (example: 5^2^3) is performed from right to left (5^(2^3)). Example: 2 + 3 × (log (sin( 2 π2 )) + 6.8) = 22.07101691 (In Algebra mode, Decimal mode, Radian mode) Calculation Modes All of the following calculation examples are shown using the Algebra mode only. Standard Mode and Decimal Mode The Standard mode displays calculation results in mathematical expression format whenever possible, while the Decimal mode converts calculation results to a decimal form. Expression Decimal Mode Result Standard Mode Result 12.5 25 2 3.414213562 2+ 2 π = 3.1415926535... 3.141592654 π sin (2.1π) × 5 = 1.5450849718... 1.545084972 5 · ( 5 − 1) 4 50 ÷ 4 = 12.5 2 + 2 = 3.414213562... • The Decimal mode results in the above table show what would appear on the display when “Normal 1” is selected for the [Number Format] setting on the Basic Format dialog box. u Using the u Button to Toggle between the Standard Mode and Decimal Mode You can tap u to toggle a displayed value between Standard mode and Decimal mode format. Note that tapping u toggles the format of a displayed value. It does not change the current Standard mode and Decimal mode setting. 0205 Tapping u while the ClassPad is configured for Standard mode (Normal 1) display 0206 Tapping u while the ClassPad is configured for Decimal mode (Normal 1) display Chapter 2: Main Application 46 u Number of Decimal Places, Number of Significant Digits, Normal Display Settings The [Number Format] settings on the Basic Format dialog box specify the number of decimal places, the number of significant digits, and the normal display setting for Main application Decimal mode calculation results. The following shows how calculation results appear under each setting. Expression Normal 1 Normal 2 Fix 3 Sci 3 12.5 12.5 12.500 1.25E + 1 100 ÷ 6 = 16.6666666... 16.66666667 16.66666667 16.667 1.67E + 1 1 ÷ 600 = 0.00166666... 1.666666667E –3 0.00166666666 0.002 1.67E – 3 2.5E + 10 2.5E + 10 2.5E + 10 2.50E + 10 50 ÷ 4 = 12.5 11 10 ÷ 4 = 2.5E + 10 The allowable range for the number of decimal places is Fix 0 to Fix 9, and the range for the number of significant digits is Sci 0 to Sci 9. For details about the [Number Format] settings, see “Basic Format Dialog Box” on page 36. Complex Mode and Real Mode The Complex mode is for complex number calculations, while the Real mode is limited to calculations within the range of real numbers. Performing a calculation in the Real mode that produces a result that is outside the range of real numbers causes an error (Non-Real in Calc). 0207 (Complex mode and Real mode calculation results) Tip • You can select “ i ” or “ j ” for the imaginary unit. See “To specify the complex number imaginary unit” on page 283. • If the expression includes ⬔(r,), calculation results should be ⬔(r,) form. Radian Mode, Degree Mode and Grad Mode You can specify radians, degrees or grads as the angle unit for display of trigonometric calculation results. u Examples of Radian mode, Degree mode and Grad mode calculation results Expression Radian Mode Degree Mode Grad Mode sin (π/4) ' sin (45) sin (45) ' sin (45) sin (50) sin (50) sin (50) ' sin ( 4π ) sin ( 4π ) Important! Regardless of the currently selected angle unit setting, a calculation that includes an imaginary number power exponent (such as: eπi) is performed using radians as the angle unit (eπi = −1). Assistant Mode and Algebra Mode The Algebra mode automatically simplifies mathematical expressions produced by calculations. No simplification is performed in the Assistant mode. In the Assistant mode, you can view intermediate results as well, which allows you to see the steps that lead to a particular result as shown in 0208 (see the “expand” example). 0208 (Assistant mode and Algebra mode calculation results) Important! The Assistant mode is available in the Main application and eActivity application only. Chapter 2: Main Application 47 2-2 Using the Calculation History The Main application work area calculation history can contain up to 30 expression/result pairs. You can look up a previous calculation, edit, and then re-calculate it, if you want. • Use the scroll bar or scroll buttons to scroll the work area window up and down. This brings current calculation history contents into view. • You can edit a calculation expression in the calculation history and then re-calculate the resulting expression. Pressing E re-calculates the expression where the cursor is currently located, and also re-calculates all of the expressions below the current cursor location. 0209 To change the expression “ans × 2” to “ans × 3” in the example, and then re-calculate Tip • To re-calculate only a single specific line, tap 7. Tapping 7 re-calculates the calculation where the cursor is currently located only. It does not affect anything in calculation history that comes before or after the line. • To re-calculate all of the expressions in the calculation history, locate the cursor in the top line, and then press E. u To delete part of the calculation history contents 1. Move the cursor to the expression line or result line of the two-line unit you want to delete. 2. Tap [Edit] and then [Delete]. Important! Even if the result of the deleted two-line unit has an effect on subsequent calculations, the affected calculations are not updated automatically following the deletion. When you want to update everything in the calculation history following the deleted unit, move the cursor to a line that is above the one you deleted and then press E. u To clear all calculation history contents Tap [Edit] and then [Clear All]. In response to the confirmation message that appears, tap [OK]. 2-3 Function Calculations This section explains how to perform function calculations in the Main application work area. • You do not need to input the closing parenthesis that comes immediately before an E key operation. All of the calculation examples in this section omit the closing parentheses before E. • The following example calculations are all performed using the Decimal mode. Using the Standard mode causes results to be displayed as fractions. Angle Conversion (°, r) The first two examples use “Degree” (indicated by “Deg” in the status bar) as the angle unit setting. The final example uses “Radian” (indicated by “Rad” in the status bar) as the angle unit setting. Note that using the wrong angle unit setting will make it impossible to produce correct calculation results. u To change the angle unit setting 1. On the O menu, tap [Basic Format]. 2. Tap the [Angle] down arrow button, and then select [Radian], [Degree] or [Grad]. • You can also change the angle unit setting by tapping the current setting (Rad, Deg, or Gra) on the status bar. Each tap will cycle through the available settings. Chapter 2: Main Application 48 Problem Operation Convert 4.25 radians to degrees. = 243.5070629 4.25 Rw 47.3° + 82.5rad = 4774.20181° 47.3 + 82.5 Rw How many radians is 243.5070629°? = 4.249999999 Change the [Angle] setting to “Radian”, and then input 243.5070629 *w. Trigonometric and Inverse Trigonometric Functions Problem Operation cos(( π ) rad) = 0.5 3 Change the [Angle] setting to “Radian”. 2 · sin45° × cos65° = 0.5976724775 Change the [Angle] setting to “Degree”. 2*s 45 )*c 65 w c7/ 3 w or cN7c 3 w Can be omitted. sin–10.5 =30° (Determine x for sinx = 0.5.) S 0.5 w “.5” can also be used. Logarithmic Functions and Exponential Functions Problem Operation log1.23 (log101.23) = 0.08990511144 " 1.23 w or V 10 e 1.23 w ln90 (loge90) = 4.49980967 I 90 w or V`e 90 w log39 = 2 V 3 e 9 w or LV 3 , 9 w e = 90.0171313 Q 4.5 w (–3)4 = (–3) × (–3) × (–3) × (–3) = 81 (- 3 ){ 4 w 4.5 7 1 7 123 (= 123 ) = 1.988647795 123 {( 1 / 7 w or % 7 e 123 w Hyperbolic and Inverse Hyperbolic Functions Problem Operation sinh3.6 = 18.28545536 1 3.6 w cosh–1 ( ) = 0.7953654612 @ 20 / 15 w or @N 20 c15 w Chapter 2: Main Application 49 Other Functions (%, ', x2, x –1, x!, abs, ⬔, signum, int, frac, intg, fRound, sRound) Problem What is 12% of 1500? Operation 1500 * 12 &w (180) What percent of 880 is 660? 660 / 880 &w (75%) What value is 15% greater than 2500? What value is 25% less than 3500? (2875) (2625) ' 2+' 5 = 3.65028154 2500 *( 1 + 15 & 3500 *( 1 - 25 & 5 2 e+5 5 w (3 + i) = 1.755317302 + 0.2848487846i Change to the Complex mode (“Cplx” indicated on the status bar). 5 3 +0w (–3)2 = (–3) × (–3) = 9 (- 3 )xw –3 = –(3 × 3) = –9 - 3 xw 2 ( 3 X- 4 X)Xw or 1 = 12 1 – 1 4 3 N 1 cN 1 c 3 e-N 1 c 4 w 8! (= 1 × 2 × 3 × … × 8) = 40320 8 !w What is the absolute value of the common 3 ? logarithm of 4 3 ⎜log ( )⎟ = 0.1249387366 4 4V 10 eN 3 c 4 w or L4V 3 / 4 w 8⬔40° × 5⬔35° ⬔(8,40) × ⬔(5,35) = ⬔(40,75) Change to the Degree mode (“Deg” indicated on the status bar). ~ 8 , 40 )*~ 5 , 35 )w What is the sign of –3.4567? (–1) (signum returns –1 for a negative value, 1 for a $ for an positive value, “Undefined” for 0, and ²$´ imaginary number.) [signum] - 3.4567 w What is the integer part of –3.4567? :- 3.4567 w (–3) (–0.4567) [frac] - 3.4567 w What is the greatest integer less than or equal to –3.4567? (–4) [intg] - 3.4567 w What is –3.4567 rounded to two decimal places? (–3.46) [fRound] - 3.4567 , 2 w What is –34567 rounded to four significant digits? (–34570) [sRound] - 34567 , 4 w* What is the decimal part of –3.4567? * To round to 10 digits, specify “0” for the second argument. Random Number Generator (rand, randList, randNorm, randBin, RandSeed) The ClassPad random number generator can generate truly random numbers (non-sequential random numbers) and random numbers that follow a particular pattern (sequential random numbers). u To switch between non-sequential and sequential random number generation 1. Use the “RandSeed” command to configure random number generation settings. See “RandSeed Command” on page 52. 2. Use the “rand”, “randList”, “randNorm”, or “randBin” function to generate the random numbers. Chapter 2: Main Application 50 u “rand” Function The “rand” function generates random numbers. If you do not specify an argument, “rand” generates 10-digit decimal values 0 or greater and less than 1. Specifying two integer values for the argument generates random numbers between them. Problem Operation Generate random numbers between 0 and 1. [rand] w Generate random integers between 1 and 6. [rand] 1 , 6 w u “randList” Function Syntax: randList(n [, a, b]) Function: • Omitting arguments “a” and “b” returns a list of n elements that contain decimal random values. • Specifying arguments “a” and “b” returns a list of n elements that contain integer random values in the range of “a” through “b”. Description: • “n” must be a positive integer. • The random numbers of each element are generated in accordance with “RandSeed” specifications, as with the “rand” function. Problem Operation Generate a list of three elements that contain decimal random values. [randList] 3 w Generate a list of five elements that contain random values in the range of 1 through 6. [randList] 5 , 1 , 6 w u “randNorm” Function The “randNorm” function generates a 10-digit normal random number based on a specified mean and standard deviation values. Syntax: randNorm(, [, n]) Function: • Omitting a value for “n” (or specifying 1 for “n”) returns the generated random number as-is. • Specifying a value for “n” returns the specified number of random values in list format. Description: • “n” must be a positive integer, and “ ” must be greater than 0. Problem Operation Randomly produce a body length value obtained in accordance with the normal distribution of a group of infants less than one year old with a mean body length of 68 cm and standard deviation of 8. [randNorm] 8 , 68 w Randomly produce the body lengths of five infants in the above example, and display them in a list. [randNorm] 8 , 68 , 5 w u “randBin” Function The “randBin” function generates binomial random numbers based on values specified for the number of trials n and probability P. Syntax: randBin(n, P [, m]) Chapter 2: Main Application 51 Function: • Omitting a value for “m” (or specifying 1 for “m”) returns the generated random number as-is. • Specifying a value for “m” returns the specified number of random values in list format. Description: • “n” and “m” must be positive integers. Problem Operation Randomly produce the number of heads that can be expected in accordance with binomial distribution for five coin tosses where the probability of heads is 0.5. [randBin] 5 , 0.5 w Perform the same coin toss sequence described above three times and display the results in a list. [randBin] 5 , 0.5 , 3 w u “RandSeed” Command • You can specify an integer from 0 to 9 for the argument of this command. 0 specifies non-sequential random number generation. An integer from 1 to 9 uses the specified value as a seed for specification of sequential random numbers. The initial default argument for this command is 0. • The numbers generated by the ClassPad immediately after you specify sequential random number generation always follow the same random pattern. Problem Operation Generate sequential random numbers using 3 as the seed value. [RandSeed] 3 w Generate the first value. Generate the second value. Generate the third value. [rand] w [rand] w [rand] w Tip • Random values generated by these commands are pseudo random values. • The arguments a and b of “rand(a,b)” and “randList(n,a,b)” must be integers, subject to the following conditions. a

,, [ ) ] or piecewise( , , , [ ) ] Use the soft keyboard (1) to input “piecewise” function according to the syntax shown below. , or , , Problem Operation For the expression 0 t x (x = variable), return 1 when x is 0 or less, and 2 when x is greater than 0 or undefined. [piecewise] 0 :X, 1 , 2 w or 1 1 c 2 ef 0 :X w For the expression 1 t x (x = variable), return 1 when x is 1 or less, and 2 when x is greater than 1. 1 1 c 2 ef 1 :X c 1 , s, t) You can use these symbols to perform a number of different basic calculations. Problem Operation To add 3 to both sides of x = 3. x+3=6 (X= 3 )+ 3 w Subtract 2 from both sides of y s 5. y–2s3 (Y; 5 )- 2 w Tip • In the “Syntax” explanations of each command under “2-7 Using the Action Menu”, the following operators are indicated as “Eq/Ineq”: =, ≠, <, >, s, t. Whether or not the “Eq/Ineq” operators include the “≠” operator is specified for each command by a separate note. • An expression that contains multiple equation or inequality operators cannot be input as a single expression. For output expressions, an expression can be output with multiple operators only in the case of inequality operators that are facing in the same direction (example: –1 < x < 1). Example: solve(x2 – 1 < 0, x) w {–1 < x < 1} “with” Operator ( | ) The “with” ( I ) operator temporarily assigns a value to a variable. You can use the “with” operator in the following cases. • To assign the value specified on the right side of | to the variable on the left side of | • To limit or restrict the range of a variable on the left side of | in accordance with conditions provided on the right side of | The following is the syntax for the “with” ( I ) operator. Exp/Eq/Ineq/List/Mat|Eq/Ineq/List/(and operator) You can put plural conditions in a list or connected with the “and” operator on the right side. “” can be used on the left side or the right side of |. Problem Evaluate x2 + x + 1 when x = 3. Operation 13 X{ 2 +X+ 1 UX= 3 w For x – 1 = 0, determine the value of x when x > 0. {x = 1} .X{ 2 - 1 = 0 ,X)UX> 0 w Determine the value of abs (x) when x > 0. 4XeUX> 0 w 2 x Chapter 2: Main Application 55 Solutions Supported by ClassPad (TRUE, FALSE, Undefined, No Solution, ∞, const, constn) Solution Description Example TRUE Output when a solution is true. judge (1 = 1) w FALSE Output when a solution is false. judge (1 < 0) w Undefined Output when a solution is undefined. 1/0 w No Solution Output when there is no solution. solve (abs (x) = –1, x) w ∞ Infinity lim (1/x2, x, 0) w const Constant displayed as const(1) when any value that is a constant is included in the solution. In the case of multiple constants, they are indicated as const(1), const(2), and so on. dSolve ( y = x, x, y) w { y = 0.5·x2 + const (1)} constn Constant displayed as constn(1) when the solution includes any integer value that is a constant. In the case of multiple constants, they are indicated as constn(1), constn(2), and so on. Change the [Angle] setting to “Degree”. solve (sin (x) = 0, x) w {x = 180·constn (1)} Dirac Delta Function “delta” is the Dirac Delta function. The delta function evaluates numerically as shown below. ^ b b Non-numeric expressions passed to the delta function are left unevaluated. The integral of a linear delta function is a Heaviside function. Syntax: delta(x) x : variable or number 0210 (Calculation example screenshot) nth-Delta Function The nth-delta function is the nth differential of the delta function. Syntax: delta(x, n) x : variable or number n : number of differentials 0211 (Calculation example screenshot) Heaviside Unit Step Function “heaviside” is the command for the Heaviside function, which evaluates only to numeric expressions as shown below. H ! Any non-numeric expression passed to the Heaviside function will not be evaluated, and any numeric expression containing complex numbers will return undefined. The derivative of the Heaviside function is the Delta function. Syntax: heaviside(x) x : variable or number 0212 (Calculation example screenshot) Chapter 2: Main Application 56 Gamma Function The Gamma function is called “gamma” on the ClassPad. +∞ ∫0 Γ(x) = t x–1e–t dt For an integer n the gamma is evaluated as shown below. K ^ ² ! s The gamma is defined for all real numbers excluding zero and negative integers. It is also defined for all complex numbers where either the real or imaginary part of the complex number is not an integer. Gamma of a symbolic expression returns unevaluated. Syntax: gamma(x) x : variable or number 0213 (Calculation and graph example screenshots) 2-4 List Calculations This section explains how to input list data, and how to perform basic list calculations. Inputting List Data in the Work Area 0214 To input the list {1, 2, 3} and assign it to LIST variable “lista” in the Main application work area LIST Variable Element Operations You can recall the value of any element of a LIST variable. You can also assign a value to any element in a list. 0215 To recall the second element of the “lista” list variable of example 0214 0216 To assign 5 to the second element of “lista” Using a List in a Calculation You can perform arithmetic operations between two lists, between a list and a numeric value, or between a list and an expression, equation, or inequality. Important! • When you perform an arithmetic operation between two lists, both of the lists need to have the same number of cells. An error will occur if they do not. • An error will also occur whenever an operation between any two cells of the two lists results in an error. 0217 Perform the operation list3 × {6, 0, 4} when list3 contains {41, 65, 22} Using a List to Assign Different Values to Multiple Variables Use the procedure in this section when you want to use a list to assign various different values to multiple variables. Syntax: List with Numbers S List with Variables 0218 Assign the values 10, 20, and 30, to variables x, y, and z respectively Chapter 2: Main Application 57 2-5 Matrix and Vector Calculations This section explains how to create matrices, and how to perform basic matrix calculations. Tip: Since a vector can be viewed as 1-row by n-column matrix or n-row by 1-column matrix, this section does not include explanations specifically about vectors. For more information about vector-specific calculations, see the explanations about the applicable [Action] menu items in “2-7 Using the Action Menu”. Inputting Matrix Data You can input matrix values in a single line in the work area, or input matrix values using an actual on-screen matrix. Inputting Matrix Values in a Single Line 0219 1 3 To input the matrix 2 4 and assign it to the variable “mat1” in the Main application work area Matrix Variable Element Operations You can recall the value of any element of a matrix variable. You can also assign a value to any element in a matrix. 0220 To recall the value in row 2, column 1 of the matrix variable “mat1” of example 0219 0221 To assign 5 to the element at row 1, column 2 of “mat1” Inputting Matrix Values Using an Actual On-Screen Matrix • Create a new 1-row × 2-column matrix ...................................................................................................... 6 • Create a new 2-row × 1-column matrix ...................................................................................................... 7 • Create a new 2-row × 2-column matrix ..................................................................................................... 8 • Add a column to the currently displayed matrix ......................................................................................... 6 • Add a row to the currently displayed matrix ............................................................................................... 7 • Add both a row and column to the currently displayed matrix ................................................................... 8 0222 1 4 To input the matrix 2 5 3 6 and assign it to the variable “mat2” Performing Matrix Calculations This section provides examples of how to perform the most basic types of matrix calculations. Matrix Addition, Subtraction, Multiplication, and Division 0223 To calculate 1 2 1 1 + 2 2 3 1 in a single line 0224 To calculate 1 2 1 1 × 2 2 3 1 using an actual on-screen matrix 0225 To multiply the matrix 1 3 2 4 by 5 Chapter 2: Main Application 58 Raising a Matrix to a Specific Power Example: To raise 1 3 2 4 to the power of 3 0226 Input in a single line 0227 Input using an actual on-screen matrix Tip: You can raise only a square matrix to a specific power. An error occurs when you try to raise a non-square matrix to a specific power. Using a Matrix to Assign Different Values to Multiple Variables Use the procedure in this section when you want to use a matrix to assign various different values to multiple variables. Syntax: Matrix with Numbers ⇒ Matrix with Variables (The matrix can be one line with multiple columns, or multiple lines with one column.) 0228 Assign the values 10, 20, and 30, to variables x, y, and z respectively 2-6 Specifying a Number Base While using the Main application, you can specify a default number base (binary, octal, decimal, hexadecimal). You can also convert between number bases and perform bitwise operations using logical operators (not, and, or, xor). Note the following limitations, which all apply while a default number base (binary, octal, decimal, hexadecimal) is specified in the Main application. • You cannot use scientific functions, or [Action] or [Interactive] menu commands. • Except for Ans (Answer Memory variable), you cannot use variables. • You can input integers only. An error (Invalid Syntax) will occur if you try to input a non-integer value (like 1.5 or ' 2 ). • If a calculation produces a non-integer result (with a decimal part), the ClassPad will cut off the decimal part automatically. For example, the calculation 5 ÷ 2 while decimal is selected as the number base is 2. • An error message is displayed if you try to enter a value that is invalid for the speicfied number base. The following shows the numerals that can be used in each number system. Binary: 0, 1 Octal: 0 to 7 Decimal: 0 to 9 Hexadecimal: 0 to 9, A, B, C, D, E, F Binary, Octal, Decimal, and Hexadecimal Calculation Ranges • The following are the display capacities and calculation ranges for each of the number bases. Number Base Display Capacity Calculation Range (Positive ; Negative) Binary 32 digits 0 s x s 01111111111111111111111111111111 ; 10000000000000000000000000000000 s x s 11111111111111111111111111111111 Octal 11 digits 0 s x s 17777777777 ; 20000000000 s x s 37777777777 Decimal 10 digits 0 s x s 2147483647 ; −2147483648 s x s −1 Hexadecimal 8 digits 0 s x s 7FFFFFFF ; 80000000 s x s FFFFFFFF • Negative binary, octal, and hexadecimal values are produced using the two’s complement of the original value. Chapter 2: Main Application 59 Selecting a Number Base Specifying a default number base in the Main application will apply to the current line (expression/result pair), and to all subsequent lines until you change the default number base setting. u To select the number base for the line where the cursor is located 1. Tap the down arrow button next to the < button. 2. Tap the button that corresponds to the number base you want to use: 1 (binary), 2 (octal), 3 (decimal), 4 (hexadecimal). • The currently selected number base is indicated in the status bar. 3. Execute the calculation. Important! • A line for which a number base is not specified is called a “normal calculation line”. To return a line to a normal calculation line, tap < in step 2 of the above procedure. • Calculation results produced by a line for which a number base is specified are followed by one of the suffixes listed below, to indicate its number system. Number System Binary Octal Decimal Hexadecimal b o d h Suffix u To specify a number base for an input value You can input the following suffixes to specify the number base of a value as you input it: [b] (binary), [o] (octal), [d] (decimal), and [h] (hexadecimal). You can specify a number base for an input value only when a default number base (besides normal) is selected Arithmetic Operations You can use the following operators when performing binary, octal, decimal and hexadecimal values: +, −, ×, ÷, ^. You can also use parenthetical expressions. 0229 To calculate 101112 + 110102 0230 To calculate (118 + 78)2 0231 Perform the calculation 12310 + 10102 so it produces a hexadecimal result Bitwise Operations The logical operators (and, or, xor, not) can be used in calculations. and ...Returns the result of a bitwise product. or ......Returns the result of a bitwise sum. xor ....Returns the result of a bitwise exclusive logical sum. not ....Returns the result of a complement (bitwise inversion). 0232 Calculation examples Chapter 2: Main Application 60 Using the baseConvert Function (Number System Transform) The baseConvert function lets you convert a number in one base (number system) to its equivalent in another base. Important! • The baseConvert function works for positive integers only. • The baseConvert function cannot be used in a line for which a particular number base is specified. It can be used in a normal calculation line only. Syntax: baseConvert (Number, Current base, Expected base) • Number must be a positive integer consisting of digits 0 to 9 and/or A to F. • The current base and expected base can be any whole number from 2 to 16. 0233 Calculation examples 2-7 Using the Action Menu The [Action] menu helps to make transformation and expansion functions, calculus functions, statistical functions, and other frequently used mathematical menu operations easier to use. Simply select the function you want, and then enter expressions or variables in accordance with the syntax of the function. Tip • Unless specifically indicated otherwise, all of the explanations in this section are performed using the following modes: Algebra mode, Standard mode, Complex mode, Radian mode, Descending Order. • You can use the [Interactive] menu to select most of the commands that are included on the [Action] menu. For details about using the [Interactive] menu, see page 91. Abbreviations and Punctuation Used in This Section The following are the meanings of the abbreviations and punctuation used in the syntax descriptions in this section. Exp: Eq: Expression (Value, Variable, etc.) Equation Ineq: Ineqⴝ: [ ]: { }: All types of inequalities (a>b, atb, a 0, and the limit from both sides (left and right) when “direction” = 0 or when the direction is omitted. Chapter 2: Main Application 67 u Σ [Action][Calculation][Σ] Function: Evaluates an expression at discrete variable values within a range, and then calculates a sum. Syntax: Σ(Exp/List, variable, lower value, upper value [ ) ] Example: To calculate the sum of x2 as the value of x changes from x = 1 through x =10 u Π [Action][Calculation][Π] Function: Evaluates an expression at discrete variable values within a range, and then calculates a product. Syntax: Π(Exp/List, variable, lower value, upper value [ ) ] Example: To calculate the product of x2 as the value of x changes from x = 1 through x = 5 u rangeAppoint [Action][Calculation][rangeAppoint] Function: Finds an expression or value that satisfies a condition in a specified range. Syntax: rangeAppoint (Exp/Eq/List, start value, end value [ ) ] • When using an equation (Eq) for the first argument, input the equation using the syntax Var = Exp. Evaluation will not be possible if any other syntax is used. Example: To find the expression(s) in the list {x = π, x = 2π, x = 3π} that belong(s) to the closed range 0 s x s 5 u mod [Action][Calculation][mod] Function: Returns the remainder when one expression is divided by another expression. Syntax: mod ({Exp/List} -1, {Exp/List} -2 [ ) ] Example: To determine the remainder when 26 is divided by 3 (26mod3) u tanLine [Action][Calculation][line][tanLine] Function: Returns the right side of the equation for the tangent line (y = ‘expression’) to the curve at the specified point. Syntax: tanLine (Exp/List, variable, variable value at point of tangency [ ) ] Example: To determine the function of the line tangent to y = x 3 at x = 2 u normal [Action][Calculation][line][normal] Function: Returns the right side of the equation for the line normal (y = ‘expression’) to the curve at the specified point. Syntax: normal (Exp/List, variable, variable value at point of normal [ ) ] Example: To determine the function of the line normal to y = x3 at x = 2 u arcLen [Action][Calculation][line][arcLen] Function: Returns the arc length of an expression from a start value to an end value with respect to a specified variable. Syntax: arcLen (Exp/List, variable, start value, end value [ ) ] 3 2 Example: To determine the arc length for y = x from x = 0 to x = 4 Chapter 2: Main Application 68 u fMin [Action][Calculation][fMin/fMax][fMin], fMax [Action][Calculation][fMin/fMax][fMax] Function: Returns the minimum (fMin) / the maximum (fMax) point in a specific range of a function. Syntax: fMin(Exp[,variable] [ ) ] fMin(Exp, variable, start value, end value[,n] [ ) ] fMax(Exp[,variable] [ ) ] fMax(Exp, variable, start value, end value[,n] [ ) ] • “x” is the default when you omit “[,variable]”. • Negative infinity and positive infinity are the default when the syntax fMin(Exp[,variable] [ ) ] or fMax(Exp[,variable] [ ) ] is used. • “n” is calculation precision, which you can specify as an integer in the range of 1 to 9. Using any value outside this range causes an error. • This command returns an approximate value when calculation precision is specified for “n”. • This command returns a true value when nothing is specified for “n”. If the true value cannot be obtained, however, this command returns an approximate value along with n = 4. • Discontinuous points or sections that fluctuate widely can adversely affect precision or even cause an error. • Inputting a larger number for “n” increases the precision of the calculation, but it also increases the amount of time required to perform the calculation. • The value you input for the end point of the interval must be greater than the value you input for the start point. Otherwise an error occurs. Example: To find the minimum point of x2 – 1 with respect to x Example: To find the maximum point of –x2 + 1 with respect to x u gcd [Action][Calculation][gcd/lcm][gcd] Function: Returns the greatest common denominator of two expressions. Syntax: gcd (Exp/List-1, Exp/List-2 [ ) ] Example: To obtain the greatest common denominator of x + 1 and x2 – 3x – 4 u lcm [Action][Calculation][gcd/lcm][lcm] Function: Returns the least common multiple of two expressions. Syntax: lcm (Exp/List-1, Exp/List-2 [ ) ] Example: To obtain the least common multiple of x 2 – 1 and x2 + 2x – 3 u denominator [Action][Calculation][fraction][denominator] Function: Extracts the denominator of a fraction. Syntax: denominator (Exp/List [ ) ] Example: To extract the denominator of the fraction (y – 2)/(x + 1) u numerator [Action][Calculation][fraction][numerator] Function: Extracts the numerator of a fraction. Syntax: numerator (Exp/List [ ) ] Example: To extract the numerator of the fraction (y – 2)/(x + 1) Chapter 2: Main Application 69 Using the Complex Submenu The [Complex] submenu contains commands that relate to calculations that involve complex numbers. u arg [Action][Complex][arg] Function: Returns the argument of a complex number. Syntax: arg (Exp/Eq/List/Mat [ ) ] Example: To obtain the argument of complex 2 + i (in the Radian mode) u conjg [Action][Complex][conjg] Function: Returns the conjugate complex number. Syntax: conjg (Exp/Eq/Ineq/List/Mat [ ) ] (Ineq: Real mode only) Example: To obtain the conjugate of complex number 1 + i u re [Action][Complex][re] Function: Returns the real part of a complex number. Syntax: re (Exp/Eq/Ineq/List/Mat [ ) ] (Ineq: Real mode only) Example: To obtain the real part of complex number 3 – 4i u im [Action][Complex][im] Function: Returns the imaginary part of a complex number. Syntax: im (Exp/Eq/Ineq/List/Mat [ ) ] (Ineq: Real mode only) Example: To obtain the imaginary part of complex number 3 – 4i u cExpand [Action][Complex][cExpand] Function: Expands a complex expression to rectangular form (a + bi). Syntax: cExpand (Exp/Eq/List/Mat [ ) ] • The variables are regarded as real numbers. Example: To expand cos–1(2) (in the Radian mode) u compToPol [Action][Complex][compToPol] Function: Transforms a complex number into its polar form. Syntax: compToPol (Exp/Eq/List/Mat [ ) ] • When the argument is Mat (Matrices), calculation can be performed using the Radian angle unit only. Example: To transform 1 + i into its polar form Radian mode Degree mode Grad mode u compToTrig [Action][Complex][compToTrig] Function: Transforms a complex number into its trigonometric/hyperbolic form. Syntax: compToTrig (Exp/Eq/List/Mat [ ) ] Example: To transform 1 + i into its trigonometric form (in the Radian mode) Chapter 2: Main Application 70 u compToRect [Action][Complex][compToRect] Function: Transforms a complex number into its rectangular form. Syntax: compToRect (⬔(r,) or r · e^( · i) form [ ) ] Example: To transform a complex number into its rectangular form Using the List-Create Submenu The [List][Create] submenu contains commands that are related to creating lists. u seq [Action][List][Create][seq] Function: Generates a list in accordance with a numeric sequence expression. Syntax: seq (Exp, variable, start value, end value [,step size] [ ) ] Example: To generate a list in accordance with the expression x2 + 2x when the start value is 1, the end value is 5, and the step size is 2 • “1” is the default when you omit “[,step size]”. • The step size must be a factor of the difference between the start value and the end value. u augment [Action][List][Create][augment] Function: Creates a new list by appending one list to another. Syntax: augment (List-1, List-2 [ ) ] Example: To combine list {1, 2} and list {3, 4} u fill [Action][List][Create][fill] Function: Replaces the elements of a list with a specified value or expression. This command can also be used to create a new list whose elements all contain the same value or expression, or a new list in which the frequency of each element in the first list is determined by the corresponding element in the second list. Syntax: fill (Exp/Eq/Ineq, number of elements [ ) ] fill (Exp/Eq/Ineq, List [ ) ] fill (List, List [ ) ] Example: To create a list consisting of four identical elements (2) u subList [Action][List][Create][subList] Function: Extracts a specific section of a list into a new list. Syntax: subList (List [,start number] [,end number] [ ) ] Example: To extract the second through the fourth elements of the list {1, 2, 3, 4, 5} • The leftmost element is the default when you omit “[,start number]”, and the rightmost element is the default when you omit “[,end number]”. u shift [Action][List][Create][shift] Function: Returns a list in which elements have been shifted to the right or left by a specific amount. Syntax: shift (List [,number of shifts] [ ) ] • Specifying a negative value for “[,number of shifts]” shifts to the right, while a positive value shifts to the left. • Right shift by one (–1) is the default when you omit “[,number of shifts]”. Example: To shift the elements of the list {1, 2, 3, 4, 5, 6} to the left by three Chapter 2: Main Application 71 u rotate [Action][List][Create][rotate] Function: Returns a list in which the elements have been rotated to the right or to the left by a specific amount. Syntax: rotate (List [,number of rotations] [ ) ] • Specifying a negative value for “[,number of rotations]” rotates to the right, while a positive value rotates to the left. Example: To rotate the elements of the list {1, 2, 3, 4, 5, 6} to the left by two • Right rotation by one (–1) is the default when you omit “[,number of rotations]”. u sortA [Action][List][Create][sortA] Function: Sorts the elements of the list into ascending order. Syntax: sortA (List [ ) ] Example: To sort the elements of the list {1, 5, 3} into ascending order u sortD [Action][List][Create][sortD] Function: Sorts the elements of the list into descending order. Syntax: sortD (List [ ) ] Example: To sort the elements of the list {1, 5, 3} into descending order u listToMat [Action][List][Create][listToMat] Function: Transforms lists into a matrix. Syntax: listToMat (List-1 [, List-2, ..., List-N] [ ) ] Example: To transform the lists {3, 5} and {2, 4} into a matrix u matToList [Action][List][Create][matToList] • For information about matToList, see page 76. Using the List-Statistics and List-Calculation Submenus The [List][Statistics] and [List][Calculation] submenus contain commands related to list calculations. u min [Action][List][Statistics][min] Function: Returns the minimum value of an expression or the elements in a list. Syntax: min (Exp/List-1[, Exp/List-2] [ ) ] Example: To determine the minimum values of the elements in list {1, 2, 3} u max [Action][List][Statistics][max] Function: Returns the maximum value of an expression or the elements of a list. Syntax: max (Exp/List-1[, Exp/List-2] [ ) ] Example: To determine the maximum value of the elements in list {1, 2, 3} u mean [Action][List][Statistics][mean] Function: Returns the mean of the elements in a list. Syntax: mean (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the mean of the elements in list {1, 2, 3} Chapter 2: Main Application 72 u median [Action][List][Statistics][median] Function: Returns the median of the elements in a list. Syntax: median (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the median of the elements in the list {1, 2, 3} u mode [Action][List][Statistics][mode] Function: Returns the mode of the elements in a list. If there are multiple modes, they are returned in a list. Syntax: mode (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the mode of the elements in the list {1, 1, 2, 2, 2} u Q1 [Action][List][Statistics][Q1] Function: Returns the first quartile of the elements in a list. Syntax: Q1 (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the first quartile of the elements in the list {1, 2, 3, 4, 5} u Q3 [Action][List][Statistics][Q3] Function: Returns the third quartile of the elements in a list. Syntax: Q3 (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the third quartile of the elements in the list {1, 2, 3, 4, 5} u percentile [Action][List][Statistics][percentile] Function: Finds the nth percentile point in a list. Syntax: percentile (list, number) u stdDev [Action][List][Statistics][stdDev] Function: Returns the sample standard deviation of the elements in a list. Syntax: stdDev (List [ ) ] Example: To determine the sample standard deviation of the elements in the list {1, 2, 4} u variance [Action][List][Statistics][variance] Function: Returns the sample variance of the elements in a list. Syntax: variance (List [ ) ] Example: To determine the sample variance of the elements in the list {1, 2, 4} u dim [Action][List][Calculation][dim] Function: Returns the dimension of a list. Syntax: dim (List [ ) ] Example: To determine the dimension of the list {1, 2, 3} u sum [Action][List][Calculation][sum] Function: Returns the sum of the elements in a list. Syntax: sum (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the sum of the elements in the list {1, 2, 3} Chapter 2: Main Application 73 u prod [Action][List][Calculation][prod] Function: Returns the product of the elements in a list. Syntax: prod (List-1[, List-2] [ ) ] (List-1: Data, List-2: Freq) Example: To determine the product of the elements in the list {1, 2, 3} u cuml [Action][List][Calculation][cuml] Function: Returns the cumulative sums of the elements in a list. Syntax: cuml (List [ ) ] Example: To determine the cumulative sums of the elements in the list {1, 2, 3} u Alist [Action][List][Calculation][Alist] Function: Returns a list whose elements are the differences between two adjacent elements in another list. Syntax: Alist (List [ ) ] Example: To generate a list whose elements are the differences between two adjacent elements in the list {1, 2, 4} u percent [Action][List][Calculation][percent] Function: Returns the percentage of each element in a list, the sum of which is assumed to be 100. Syntax: percent (List [ ) ] Example: To determine the percentage of each element in the list {1, 2, 3} u polyEval [Action][List][Calculation][polyEval] Function: Returns a polynomial arranged in the descending order of powers, so coefficients correspond sequentially to each element in the input list. Syntax: polyEval (List [,Exp/List] [ ) ] • “x” is the default when you omit “[,Exp/List]”. Example: To create a second degree polynomial with the coefficients {1, 2, 3} u sequence [Action][List][Calculation][sequence] Function: Returns the lowest-degree polynomial that represents the sequence expressed by the input list. When there are two lists, this command returns a polynomial that maps each element in the first list to its corresponding element in the second list. Syntax: sequence (List-1[, List-2] [,variable] [ ) ] • “x” is the default when you omit “[,variable]”. Example: To determine a polynomial for a sequence expressed by the list {3, 5, 7, 9} u sumSeq [Action][List][Calculation][sumSeq] Function: Finds the lowest-degree polynomial that represents the sequence expressed by the input list and returns the sum of the polynomial. When there are two lists, this command returns a polynomial that maps each element in the first list to its corresponding element in the second list, and returns the sum of the polynomial. Chapter 2: Main Application 74 Syntax: sumSeq (List-1[, List-2] [,variable] [ ) ] • “x” is the default when you omit “[,variable]”. Example: To determine the sum of a polynomial for a sequence expressed by the list {3, 5, 7, 9} Using the Matrix-Create Submenu The [Matrix][Create] submenu contains commands related to creation of matrices. u trn [Action][Matrix][Create][trn] Function: Returns a transposed matrix. Syntax: trn (Mat [ ) ] Example: To transpose the matrix [[1, 2] [3, 4]] u augment [Action][Matrix][Create][augment] Function: Returns a matrix that combines two other matrices. Syntax: augment (Mat-1, Mat-2 [ ) ] Example: To combine the two matrices [[1, 2] [3, 4]] and [[5, 6] [7, 8]] u ident [Action][Matrix][Create][ident] Function: Creates an identity matrix. Syntax: ident (natural number [ ) ] Example: To create a 2 × 2 identity matrix u fill [Action][Matrix][Create][fill] Function: Creates a matrix with a specific number of rows and columns, or replaces the elements of a matrix with a specific expression. Syntax: fill (Exp, number of rows, number of columns [ ) ] fill (Exp, Mat [ ) ] Example: To create a 2 × 3 matrix, all whose elements are 2 u subMat [Action][Matrix][Create][subMat] Function: Extracts a specific section of a matrix into a new matrix. Syntax: subMat (Mat [,start row] [,start column] [,end row] [,end column] [ ) ] • “1” is the default when you omit “[, start row]” and “[, start column]”. • The last row number is the default when you omit “[, end row]”. • The last column number is the default when you omit “[, end column]”. Example: To extract the section from row 2, column 2, to row 3, column 3 from the matrix [[1, 4, 7] [2, 5, 8] [3, 6, 9]] u diag [Action][Matrix][Create][diag] Function: Returns a one-row matrix containing the elements from the main diagonal of a square matrix. Syntax: diag (Mat[ ) ] Example: To extract the diagonal elements of the matrix [[1, 2] [3, 4]] Chapter 2: Main Application 75 u listToMat [Action][Matrix][Create][listToMat] • For information about listToMat, see page 72. u matToList [Action][Matrix][Create][matToList] Function: Transforms a specific column of a matrix into a list. Syntax: matToList (Mat, column number [ ) ] Example: To transform column 2 of the matrix [[1, 2] [3, 4]] into a list Using the Matrix-Calculation and Matrix-Row&Column Submenus The [Matrix][Calculation] and [Matrix][Row&Column] submenus contain commands that are related to matrix calculations. u dim [Action][Matrix][Calculation][dim] Function: Returns the dimensions of a matrix as a two-element list {number of rows, number of columns}. Syntax: dim (Mat [ ) ] Example: To determine the dimensions of the matrix [[1, 2, 3] [4, 5, 6]] u det [Action][Matrix][Calculation][det] Function: Returns the determinant of a square matrix. Syntax: det (Mat [ ) ] Example: To obtain the determinant of the matrix [[1, 2] [4, 5]] u norm [Action][Matrix][Calculation][norm] Function: Returns the Frobenius norm of the matrix. Syntax: norm (Mat [ ) ] Example: To determine the norm of the matrix [[1, 2] [4, 5]] u rank [Action][Matrix][Calculation][rank] Function: Finds the rank of matrix. The rank function computes the rank of a matrix by performing Gaussian elimination on the rows of the given matrix. The rank of matrix A is the number of non-zero rows in the resulting matrix. Syntax: rank (Matrix) u ref [Action][Matrix][Calculation][ref] Function: Returns the row echelon form of a matrix. Syntax: ref (Mat [ ) ] Example: To obtain the row echelon form of the matrix [[1, 2, 3] [4, 5, 6]] u rref [Action][Matrix][Calculation][rref] Function: Returns the reduced row echelon form of a matrix. Syntax: rref (Mat [ ) ] Example: To obtain the reduced row echelon form of the matrix [[2, –1, 3, 19] [1, 1, –5, –21] [0, 4, 3, 0]] Chapter 2: Main Application 76 u eigVl [Action][Matrix][Calculation][eigVl] Function: Returns a list that contains the eigenvalue(s) of a square matrix. Syntax: eigVl (Mat [ ) ] Example: To obtain the eigenvalue(s) of the matrix [[3, 4] [1, 3]] u eigVc [Action][Matrix][Calculation][eigVc] Function: Returns a matrix in which each column represents an eigenvector of a square matrix. • Since an eigenvector usually cannot be determined uniquely, it is standardized as follows to its norm, which is 1: When V = [x1, x2, ..., xn], (⎥ x1⎥ 2 + ⎥ x2⎥ 2 + .... + ⎥ xn⎥ 2 ) = 1. Syntax: eigVc (Mat [ ) ] Example: To obtain the eigenvector(s) of the matrix [[3, 4] [1, 3]] u LU [Action][Matrix][Calculation][LU] Function: Returns the LU decomposition of a square matrix. Syntax: LU (Mat, lVariableMem, uVariableMem [ ) ] Example: To obtain the LU decomposition of the matrix [[1, 2, 3] [4, 5, 6] [7, 8, 9]] • The lower matrix is assigned to the first variable L, while the upper matrix is assigned to the second variable U. To display the lower matrix To display the upper matrix Lw Uw u QR [Action][Matrix][Calculation][QR] Function: Returns the QR decomposition of a square matrix. Syntax: QR (Mat, qVariableMem, rVariableMem [ ) ] Example: To obtain the QR decomposition of the matrix [[1, 2] [3, 4]] • The unitary matrix is assigned to variable Q, while the upper triangular matrix is assigned to variable R. To display the unitary matrix To display the upper triangular matrix Qw Rw u swap [Action][Matrix][Row&Column][swap] Function: Swaps two rows of a matrix. Syntax: swap (Mat, row number-1, row number-2 [ ) ] Example: To swap row 1 with row 2 of the matrix [[1, 2] [3, 4]] Chapter 2: Main Application 77 u mRow [Action][Matrix][Row&Column][mRow] Function: Multiplies the elements of a specific row in a matrix by a specific expression. Syntax: mRow (Exp, Mat, row number [ ) ] Example: To multiply row 1 of the matrix [[1, 2] [3, 4]] by x u mRowAdd [Action][Matrix][Row&Column][mRowAdd] Function: Multiplies the elements of a specific row in a matrix by a specific expression, and then adds the result to another row. Syntax: mRowAdd (Exp, Mat, row number-1, row number-2 [ ) ] Example: To multiply row 1 of the matrix [[1, 2] [3, 4]] by x, and then add the result to row 2 u rowAdd [Action][Matrix][Row&Column][rowAdd] Function: Adds a specific matrix row to another row. Syntax: rowAdd (Mat, row number-1, row number-2 [ ) ] Example: To add row 1 of the matrix [[1, 2] [3, 4]] to row 2 u rowDim [Action][Matrix][Row&Column][rowDim] Function: Returns the number in rows in a matrix. Syntax: rowDim (Mat [ ) ] Example: To obtain the number of rows in the matrix [[1, 2, 3] [4, 5, 6]] u rowNorm [Action][Matrix][Row&Column][rowNorm] Function: Calculates the sums of the absolute values of the elements of each row of a matrix, and returns the maximum value of the sums. Syntax: rowNorm (Mat [ ) ] Example: To calculate the sums of the absolute values of the elements in each row of the matrix [[1, –2, 3] [4, –5, –6]], and obtain the maximum value of the sums u colDim [Action][Matrix][Row&Column][colDim] Function: Returns the number of columns in a matrix. Syntax: colDim (Mat [ ) ] Example: To obtain the number of columns in the matrix [[1, 2] [3, 4] [5, 6]] u colNorm [Action][Matrix][Row&Column][colNorm] Function: Calculates the sums of the absolute values of the elements of each column of a matrix, and returns the maximum value of the sums. Syntax: colNorm (Mat [ ) ] Example: To calculate the sums of the absolute values of the elements in each column of the matrix [[1, –2, 3][4, –5, –6][–7, 8, 9]], and obtain the maximum value of the sums Chapter 2: Main Application 78 Using the Vector Submenu The [Vector] submenu contains commands that are related to vector calculations. • A vector is handled as a 1 × N matrix or N × 1 matrix. • A vector in the form of 1 × N can be entered as [……] or [[……]]. Example: [1, 2], [[1, 2]] • Vectors are considered to be in rectangular form unless ∠() is used to indicate an angle measure. u augment [Action][Vector][augment] Function: Returns an augmented vector [Mat-1 Mat-2]. Syntax: augment (Mat-1, Mat-2 [ ) ] Example: To augment vectors [1, 2] and [3, 4] u fill [Action][Vector][fill] Function: Creates a vector that contains a specific number of elements, or replaces the elements of a vector with a specific expression. Syntax: fill (Exp, Mat [ ) ] fill (Exp, 1, number of columns [ ) ] Example: To replace the elements of the vector [1, 2] with x Example: To create a 1 × 3 (1 row, 3 columns) vector, all of whose elements are “3” u dim [Action][Vector][dim] Function: Returns the dimension of a vector. Syntax: dim (Mat [ ) ] Example: To determine the dimension of the vector [1, 2, 3] • The vector [1, 2, 3] is handled as a 1 × 3 matrix. u unitV [Action][Vector][unitV] Function: Normalizes a vector. Syntax: unitV (Mat [ ) ] • This command can be used with a 1 × N or N × 1 matrix only. Example: To normalize the vector [1, 3, 5] u angle [Action][Vector][angle] Function: Returns the angle formed by two vectors. Syntax: angle (Mat-1, Mat-2 [ ) ] • This command can be used with a 1 × N or N × 1 matrix only. Example: To determine the angle formed by vectors [1, 2] and [3, 4] (in the Radian mode) Chapter 2: Main Application 79 u norm [Action][Vector][norm] Function: Returns the norm of a vector. Syntax: norm (Mat [ ) ] Example: To obtain the norm of the vector [1, 2, 3] u crossP [Action][Vector][crossP] Function: Returns the cross product of two vectors. Syntax: crossP (Mat-1, Mat-2 [ ) ] • This command can be used with a 1 × N or N × 1 matrix only (N = 2, 3). • A two-element matrix [a, b] or [[a], [b]] is automatically converted into a three-element matrix [a, b, 0] or [[a], [b], [0]]. Example: To obtain the cross product of the two vectors [1, 3, 5] and [2, 4, 6] u dotP [Action][Vector][dotP] Function: Returns the dot product of two vectors. Syntax: dotP (Mat-1, Mat-2 [ ) ] • This command can be used with a 1 × N or N × 1 matrix only. Example: To obtain the dot product of the two vectors [1, 3, 5] and [2, 4, 6] u toRect [Action][Vector][toRect] Function: Returns an equivalent rectangular form [x y] or [x y z]. Syntax: toRect (Mat [,natural number] [ ) ] • This command can be used with a 1 × N or N × 1 matrix only (N = 2, 3). • This command returns “x” when “natural number” is 1, “y” when “natural number” is 2, and “z” when “natural number” is 3. • This command returns a rectangular form when you omit “natural number”. Example: To transform the polar form [' 2 , ∠(π/4)] into an equivalent rectangular form (in the Radian mode) u toPol [Action][Vector][toPol] Function: Returns an equivalent polar form [r∠]. Syntax: toPol (Mat [,natural number] [ ) ] • This command can be used with a 1 × 2 or 2 × 1 matrix only. • This command returns “r” when “natural number” is 1, and “ ” when “natural number” is 2. • This command returns a polar form when you omit “natural number”. Example: To transform the rectangular form [1, 2] into its equivalent polar form u toSph [Action][Vector][toSph] Function: Returns an equivalent spherical form [ ρ ∠ ∠φ]. Syntax: toSph (Mat [,natural number] [ ) ] • This command can be used with a 1 × 3 or 3 × 1 matrix only. • This command returns “ρ” when “natural number” is 1, “ ” when “natural number” is 2, and “φ” when “natural number” is 3. • This command returns a spherical form when you omit “natural number”. Chapter 2: Main Application 80 Example: To transform the rectangular form [1, 1, 1] into its equivalent spherical form (in the Radian mode) u toCyl [Action][Vector][toCyl] Function: Returns an equivalent cylindrical form [r∠ z]. Syntax: toCyl (Mat [,natural number] [ ) ] • This command can be used with a 1 × 3 or 3 × 1 matrix only. • This command returns “r” when “natural number” is 1, “ ” when “natural number” is 2, and “z” when “natural number” is 3. • This command returns a cylindrical form when you omit “natural number”. Example: To transform the rectangular form [1, 1, 1] into an equivalent cylindrical form (in the Radian mode) Using the Equation/Inequality Submenu The [Equation/Inequality] submenu contains commands that are related to equations and inequalities. u solve [Action][Equation/Inequality][solve] Function: Returns the solution of an equation or inequality. Syntax 1: solve(Exp/Eq/Ineq [,variable] [ ) ] • “x” is the default when you omit “[,variable]”. Example: To solve ax + b = 0 for x Syntax 2: solve(Exp/Eq/Ineq,variable[, value, lower limit, upper limit] [ ) ] • “value” is an initially estimated value. • This command is valid only for equations and expressions when “value” and the items following it are included. In that case, this command returns an approximate value. • A true value is returned when you omit “value” and the items following it. When, however, a true value cannot be obtained, an approximate value is returned for equations only based on the assumption that value = 0, lower limit = – ∞, and upper limit = ∞. Syntax 3: solve({Exp-1/Eq-1, ..., Exp-N/Eq-N}, {variable-1, ..., variable-N} [ ) ] • When “Exp” is the first argument, the equation Exp = 0 is presumed. Example: To solve simultaneous linear equations 3x + 4y = 5, 2x – 3y = –8 You also could input the simultaneous equations shown in this example using the soft keyboard # key. The following shows the required input syntax. Exp-1/Eq-1 Exp-N/Eq-N variable-1, ..., variable-N • The following shows the required key operation to input this example using the # key. #dX+eY=fccX-dY=-ieX,Yw • To input simultaneous equations with three or more unknowns, tap the # key when the cursor is in the Exp-N/Eq-N input field. Each tap of # will add one more line for input of an equation. Chapter 2: Main Application 81 Syntax 4: You can solve for the relationship between two points, straight lines, planes, or spheres by entering a vector equation inside the solve( command. Here we will present four typical syntaxes for solving a vector equation using the solve( command. In the syntaxes below, Vct-1 through Vct-6 are column vectors with three (or two) elements, and s, t, u and v are parameters. solve(Vct-1 + s * Vct-2 [= Vct-3, {variable-1}]) • If the right side of the equation (= Vct-3) is omitted in the above syntax, it is assumed that all of the elements on the right side are 0 vectors. solve(Vct-1 + s * Vct-2 = Vct-3 + t * Vct-4, {variable-1, variable-2}) solve(Vct-1 + s * Vct-2 + t * Vct-3 = Vct-4 – u * Vct-5, {variable-1, variable-2, variable-3}) solve(Vct-1 + s * Vct-2 + t * Vct-3 = Vct-4 – u * Vct-5 + v * Vct-6, {variable-1, variable-2, variable-3, variable-4}) • Variables (variable 1 through variable 4) can be input into the elements of each vector (Vct-1 through Vct-6) in the above four syntaxes to solve for those variables. 0234 To prove whether point P (5, 7, 9) and point Q (5, 7, 8) each exist on straight line l, which is an orientation vector (4, 5, 6) that passes through point A (1, 2, 3) Note For the solution, the solve function returns an expression or value for the expression (Exp/Eq) input as its argument. The message “More solutions may exist” will appear on the display when a value is returned as the solution, because there may be multiple solutions. The solve function can return a maximum of 10 solutions in the case of values. Example: To solve cos (x) = 0.5 for x (initial value: 0) (Angle unit setting: Deg) u dSolve [Action][Equation/Inequality][dSolve] Function: Solves first, second or third order ordinary differential equations, or a system of first order differential equations. Syntax: dSolve(Eq, independent variable, dependent variable [, initial condition-1, initial condition-2][, initial condition-3, initial condition-4][, initial condition-5, initial condition-6] [ ) ] dSolve({Eq-1, Eq-2}, independent variable, {dependent variable-1, dependent variable-2} [, initial condition-1, initial condition-2, initial condition-3, initial condition-4] [ ) ] • If you omit the initial conditions, the solution will include arbitrary constants. • Input all initial conditions equations using the syntax Var = Exp. Any initial condition that uses any other syntax will be ignored. Example: To solve a differential equation y’ = x, where y = 1 when x = 0 Example: To solve the system of first order differential equations y’ = y + z, z’ = y – z, where “x” is the independent variable, “y” and “z” are the dependent variables, and the initial conditions are y = 3 when x = 0, and z = ' 2 – 3 when x = 0 Chapter 2: Main Application 82 u rewrite [Action][Equation/Inequality][rewrite] Function: Moves the right side elements of an equation or inequality to the left side. Syntax: rewrite(Eq/Ineq/List [ ) ] Example: To move the right side elements of x + 3 = 5x – x2 to the left side u exchange [Action][Equation/Inequality][exchange] Function: Swaps the right-side and left-side elements of an equation or inequality. Syntax: exchange(Eq/Ineq/List [ ) ] Example: To swap the left-side and right-side elements of 3 > 5x – 2y u eliminate [Action][Equation/Inequality][eliminate] Function: Solves one equation with respect to a variable, and then replaces the same variable in another expression with the obtained result. Syntax: eliminate(Eq/Ineq/List-1, variable, Eq-2 [ ) ] Example: To transform y = 2x + 3 to x =, and substitute the result into 2x + 3y = 5 u absExpand [Action][Equation/Inequality][absExpand] Function: Divides an absolute value expression into formulas without absolute value. Syntax: absExpand(Eq/Ineq [ ) ] Example: To remove the absolute value from ⎜2x – 3 ⎜ = 9 u andConnect [Action][Equation/Inequality][andConnect] Function: Combines two equations or inequalities into a single expression. Syntax: andConnect(Eq/Ineq-1, Eq/Ineq-2 [ ) ] Example: To rewrite x > –1 and x < 3 into a single inequality u getRight [Action][Equation/Inequality][getRight] Function: Extracts the right-side elements of an equation or inequality. Syntax: getRight(Eq/Ineq/List [ ) ] Example: To extract the right side elements of y = 2x2 + 3x + 5 u getLeft [Action][Equation/Inequality][getLeft] Function: Extracts the left-side elements of an equation or inequality. Syntax: getLeft(Eq/Ineq/List [ ) ] Example: To extract the left side elements of y = 2x2 + 3x + 5 u and [Action][Equation/Inequality][Logic][and] Function: Returns the result of the logical AND of two expressions. Syntax: Exp/Eq/Ineq/List-1 and Exp/Eq/Ineq/List-2 Example: To obtain the result of the logical AND of x2 > 1 and x < 0 Chapter 2: Main Application 83 u or [Action][Equation/Inequality][Logic][or] Function: Returns the result of the logical OR of two expressions. Syntax: Exp/Eq/Ineq/List-1 or Exp/Eq/Ineq/List-2 Example: To obtain the result of the logical OR of x = 3 or x > 2 u xor [Action][Equation/Inequality][Logic][xor] Function: Returns the logical exclusive OR of two expressions. Syntax: Exp/Eq/Ineq/List-1 xor Exp/Eq/Ineq/List-2 Example: To obtain the logical exclusive OR of x < 2 xor x < 3 u not [Action][Equation/Inequality][Logic][not] Function: Returns the logical NOT of an expression. Syntax: not(Exp/Eq/Ineq/List [ ) ] Example: To obtain the logical NOT of x = 1 Using the Assistant Submenu The [Assistant] submenu contains four commands related to the Assistant mode. Note that the following commands are valid in the Assistant mode only. For more information on the Assistant mode see “Assistant Mode and Algebra Mode” on page 47. u arrange [Action][Assistant][arrange] Function: Collects like terms and arranges them in descending order, starting with the term that contains the smallest coefficient. Syntax: arrange (Exp/Eq/Ineq/List/Mat [ ) ] Example: To arrange 2x + 3 – 5x + 8y in the sequence of its variables u replace [Action][Assistant][replace] Function: Replaces the variable in an expression, equation or inequality with the value assigned to a variable using the “store” command. Syntax: replace (Exp/Eq/Ineq/List/Mat [ ) ] Example: To replace s in the expression 3x + 2s, when the expression 2x + 1 is assigned to s u invert [Action][Assistant][invert] Function: Inverts two variables in an expression. Syntax: invert (Exp/Eq/Ineq/List [,variable-1, variable-2] [ ) ] • x and y are inverted when variables are not specified. Example: To invert x and y in the expression 2x = y u Clear_a_z Function: Clears all single-character variable names (a–z and A–Z) in the current folder. Chapter 2: Main Application 84 Using the Distribution/Inv.Dist Submenu The [Distribution/Inv.Dist] submenu includes functions related to each type of statistical calculation distribution probability. The functions on this submenu perform the same calculations as the Distribution commands that are available in the Statistics application and the Main, eActivity, and Program applications. For information about the numeric expressions used in calculations, see “Distributions” on page 151. For information about the meanings of the variables used in the syntaxes of the functions presented in this section, and the system variables that store the values obtained as calculation results, see “Input and Output Terms” on page 154. Specifying Arguments within the Distribution Function You can specify either values or list data for any of the arguments within the Distribution function. The normPDf function (page 85) syntax (normPDf(x, , )) that returns normal probability density can be used to perform the calculations shown below. The “Number Format” setting is “Fix 2” for all calculation results. normPDf(1, 1, 0) = 0.24 normPDf({1, 2}, 1, 0) = {0.24, 0.05} normPDf(1, {1, 2}, 0) = {0.24, 0.18} normPDf({1, 2},{1, 2}, 0) = {0.24, 0.12} normPDf({1, 2},{1, 2},{1, 0}) = {0.40, 0.12} The following explains how to specify list data in arguments and how calculation results are output. (a) Specifying list data for a single argument • Basically, you can specify any list you like, but the each of the elements in the list must be in accordance with the conditions required by the argument of the function being used. • Calculation is performed on each element within the list and results are output as shown below. normPDf(x, {1, 2}, ) = {, } (b) Specifying list data for multiple arguments • In this case, all of the lists must have the same number of elements. Otherwise an Invalid Dimension error will occur. • Calculation is performed on each element within the list and results are output as shown below. normPDf({x1, x2}, {1, 2}, ) = { , } Assignment of List Data Calculation Results to Variables Using the list data in the argument of the Distribution function causes calculation results to be output as list data, which is assigned as-is to the “ans” variable. In addition to the “ans” variable, calculations that use the Distribution function causes calculation results also to be assigned to certain system variables. For example, the normal probability density variable returned by normPDf is assigned to system variable prob. Only the last element of the list data will be assigned to a system variable as a calculation result. In the distribution function explanations below, the names of the functions to which calculation results are assigned are shown under “Calculation Result Output”. u normPDf [Action][Distribution/Inv.Dist][Continuous][normPDf] Function: Returns the normal probability density for a specified value. Syntax: normPDf(x[,σ , μ)] • When σ and μ are skipped, σ = 1 and μ = 0 are used. Calculation Result Output: prob Example: To determine the normal probability density when x = 37.5, σ = 2, μ = 35 Chapter 2: Main Application 85 u normCDf [Action][Distribution/Inv.Dist][Continuous][normCDf] Function: Returns the cumulative probability of a normal distribution between a lower bound and an upper bound. Syntax: normCDf(lower value, upper value[,σ , μ)] • When σ and μ are skipped, σ = 1 and μ = 0 are used. Calculation Result Output: prob, zLow, zUp Example: To determine the normal probability density when lower bound value = −∞, upper bound value = 36, σ = 2, μ = 35 u invNormCDf [Action][Distribution/Inv.Dist][Inverse][invNormCDf] Function: Returns the boundary value(s) of a normal cumulative distribution probability for specified values. Syntax: invNormCDf([tail setting, ]area value[,σ , μ)] • When σ and μ are skipped, σ = 1 and μ = 0 are used. • “tail setting” displays the probability value tail specification, and Left, Right, or Center can be specified. Enter the following values or letters to specify: Left: −1, “L”, or “l” Center: 0, “C”, or “c” Right: 1, “R”, or “r” • • • • When input is skipped, “Left” is used. When one argument is omitted (resulting in three arguments), Tail=Left. When two arguments are omitted (resulting in two arguments), Tail=Left, μ =0. When three arguments are omitted (resulting in one argument), Tail=Left, σ =1, μ =0. When “tail setting” is Center, the lower bound value is returned. Calculation Result Output: x1InvN, x2InvN Example: To determine the upper bound value when tail setting = Left, area value = 0.7, σ = 2, μ = 35 u tPDf [Action][Distribution/Inv.Dist][Continuous][tPDf] Function: Returns the Student’s t probability density for a specified value. Syntax: tPDf(x, df [ ) ] Calculation Result Output: prob Example: To determine the Student’s t probability density when x = 2, df = 5 u tCDf [Action][Distribution/Inv.Dist][Continuous][tCDf] Function: Returns the cumulative probability of a Student’s t distribution between a lower bound and an upper bound. Syntax: tCDf(lower value, upper value, df [ ) ] Calculation Result Output: prob, tLow, tUp Example: To determine the Student’s t distribution probability when lower value = 1.5, upper value = ∞, df = 18 Chapter 2: Main Application 86 u invTCDf [Action][Distribution/Inv.Dist][Inverse][invTCDf] Function: Returns the lower bound value of a Student’s t cumulative distribution probability for specified values. Syntax: invTCDf(prob, df [ ) ] Calculation Result Output: xInv Example: To determine the lower bound value when prob = 0.0754752, df = 18 u chiPDf [Action][Distribution/Inv.Dist][Continuous][chiPDf] Function: Returns the χ2 probability density for specified values. Syntax: chiPDf(x, df [ ) ] Calculation Result Output: prob Example: To determine the χ2 probability density when x = 2, df = 4 u chiCDf [Action][Distribution/Inv.Dist][Continuous][chiCDf] Function: Returns the cumulative probability of a χ2 distribution between a lower bound and an upper bound. Syntax: chiCDf(lower value, upper value, df [ ) ] Calculation Result Output: prob Example: To determine the χ2 probability when lower value = 2.7, upper value = ∞, df = 4 u invChiCDf [Action][Distribution/Inv.Dist][Inverse][invChiCDf] Function: Returns the lower bound value of a χ2 cumulative distribution probability for specified values. Syntax: invChiCDf(prob, df [ ) ] Calculation Result Output: xInv Example: To determine the lower bound value when prob = 0.6092146, df = 4 u fPDf [Action][Distribution/Inv.Dist][Continuous][fPDf] Function: Returns the F probability density for a specified value. Syntax: fPDf(x, n:df, d:df [ ) ] Calculation Result Output: prob Example: To determine the F probability density when x = 1.5, n:df = 24, d:df = 19 u fCDf [Action][Distribution/Inv.Dist][Continuous][fCDf] Function: Returns the cumulative probability of an F distribution between a lower bound and an upper bound. Syntax: fCDf(lower value, upper value, n:df, d:df [ ) ] Calculation Result Output: prob Example: To determine the F distribution probability when lower value = 1.5, upper value = ∞, n:df = 24, d:df = 19 Chapter 2: Main Application 87 u invFCDf [Action][Distribution/Inv.Dist][Inverse][invFCDf] Function: Returns the lower bound value of an F cumulative distribution probability for specified values. Syntax: invFCDf(prob, n:df, d:df [ ) ] Calculation Result Output: xInv Example: To determine the lower bound value when prob = 0.1852, n:df = 24, d:df = 19 u binomialPDf [Action][Distribution/Inv.Dist][Discrete][binomialPDf] Function: Returns the probability in a binomial distribution that the success will occur on a specified trial. Syntax: binomialPDf(x, numtrial value, pos [ ) ] Calculation Result Output: prob Example: To determine the binomial probability when x = 5, numtrial value = 3, pos = 0.63 u binomialCDf [Action][Distribution/Inv.Dist][Discrete][binomialCDf] Function: Returns the cumulative probability in a binomial distribution that the success will occur between specified lower value and upper value. Syntax: binomialCDf(lower value, upper value, numtrial value, pos [ ) ] Calculation Result Output: prob Example: To determine the binomial cumulative probability when lower value = 2, upper value = 5, numtrial value = 3, pos = 0.63 u invBinomialCDf [Action][Distribution/Inv.Dist][Inverse][invBinomialCDf] Function: Returns the minimum number of trials of a binomial cumulative probability distribution for specified values. Syntax: invBinomialCDf(prob, numtrial value, pos [ ) ] Calculation Result Output: xInv, ½xInv Important! When executing the invBinomialCDf, invPoissonCDf, invGeoCDf, or invHypergeoCDf function, the ClassPad uses the specified prob value and the value that is one less the prob value minimum number of significant digits (½prob value) to calculate minimum number of trials values. The results are assigned to the system variables xInv (calculation result using prob) and ½xInv (calculation result using ½prob). The function always returns the xInv value only. However, when the xInv and ½xInv values are different, the warning message shown nearby appears showing both values. The calculation results of the function are integers. Accuracy may be reduced when the first argument has 10 or more digits. Note that even a slight difference in calculation accuracy affects calculation results. If a warning message appears, check the displayed values. Example: To determine the minimum number of trials when prob = 0.609, numtrial value = 5, pos = 0.63 u poissonPDf [Action][Distribution/Inv.Dist][Discrete][poissonPDf] Function: Returns the probability in a Poisson distribution that the success will occur on a specified trial. Syntax: poissonPDf(x, [ ) ] Calculation Result Output: prob Example: To determine the Poisson probability when x = 10, = 6 Chapter 2: Main Application 88 u poissonCDf [Action][Distribution/Inv.Dist][Discrete][poissonCDf] Function: Returns the cumulative probability in a Poisson distribution that the success will occur between specified lower value and upper value. Syntax: poissonCDf(lower value, upper value, [ ) ] Calculation Result Output: prob Example: To determine the Poisson cumulative probability when lower value = 2, upper value = 3, = 2.26 u invPoissonCDf [Action][Distribution/Inv.Dist][Inverse][invPoissonCDf] Function: Returns the minimum number of trials of a Poisson cumulative probability distribution for specified values. Syntax: invPoissonCDf(prob, [ ) ] Calculation Result Output: xInv, ½xInv Important! See “Important!” under “invBinomialCDf” on page 88. Example: To determine the minimum number of trials when prob = 0.8074, = 2.26 u geoPDf [Action][Distribution/Inv.Dist][Discrete][geoPDf] Function: Returns the probability in a geometric distribution that the success will occur on a specified trial. Syntax: geoPDf(x, pos [ ) ] Calculation Result Output: prob Example: To determine the geometric probability when x = 6, pos = 0.4 u geoCDf [Action][Distribution/Inv.Dist][Discrete][geoCDf] Function: Returns the cumulative probability in a geometric distribution that the success will occur between specified lower value and upper value. Syntax: geoCDf(lower value, upper value, pos [ ) ] Calculation Result Output: prob Example: To determine the geometric probability when lower value = 2, upper value = 3, pos = 0.5 u invGeoCDf [Action][Distribution/Inv.Dist][Inverse][invGeoCDf] Function: Returns the minimum number of trials of a geometric cumulative probability distribution for specified values. Syntax: invGeoCDf(prob, pos [ ) ] Calculation Result Output: xInv, ½xInv Important! See “Important!” under “invBinomialCDf” on page 88. Example: To determine the minimum number of trials when prob = 0.875, pos = 0.5 Chapter 2: Main Application 89 u hypergeoPDf [Action][Distribution/Inv.Dist][Discrete][hypergeoPDf] Function: Returns the probability in a hypergeometric distribution that the success will occur on a specified trial. Syntax: hypergeoPDf(x, n, M, N [ ) ] Calculation Result Output: prob Example: Determine the hypergeometric probability when x = 1, n = 5, M = 10, N = 20. u hypergeoCDf [Action][Distribution/Inv.Dist][Discrete][hypergeoCDf] Function: Returns the cumulative probability in a hypergeometric distribution that the success will occur between specified lower value and upper value. Syntax: hypergeoCDf(lower value, upper value, n, M, N [ ) ] Calculation Result Output: prob Example: Determine the hypergeometric cumulative distribution when lower value = 0, upper value = 1, n = 5, M = 10, N = 20. u invHypergeoCDf [Action][Distribution/Inv.Dist][Inverse][invHypergeoCDf] Function: Returns the minimum number of trials of a hypergeometric cumulative distribution for specified values. Syntax: invHypergeoCDf(prob, n, M, N [ ) ] Calculation Result Output: xInv, ½xInv Important! See “Important!” under “invBinomialCDf” on page 88. Example: To determine the minimum number of trials when prob = 0.3, n = 5, M = 10, N = 20 Using the Financial Submenu The [Financial] submenu contains commands that are related to financial calculations. For information about the functions included in this submenu, see “11-4 Financial Calculation Functions”. Using the Command Submenu u Define Function 1: Defines function and registers it with Graph Editor. Syntax 1: Define { y1(x) − y100(x) ; x1(y) − x100(y) ; yt1(t) − yt100(t) ; xt1(t) − xt100(t) ; r1() − r100()} = Example: To define the function y = sin(x) and assign it to line “y3” of the Graph Editor Function 2: Creates a user-defined function. For more information, see “12-3 User-defined Functions”. u DispStat Function: Displays previous statistical calculation results. For more information, see “DispStat” on page 209 and the examples 1208 through 1210 under “Including Statistical Graphing and Calculation Functions in a Program” on page 225. Chapter 2: Main Application 90 u Clear_a_z Function: Clears all single-character variables. For more information, see “Clear_a_z” on page 84. u DelVar Function: Deletes a specified variable. For more information, see “DelVar” on page 208. u Clear All Variables Function: Clear variables that contain numbers, list and matrices. 2-8 Using the Interactive Menu The [Interactive] menu includes most of the commands that are on the [Action] menu. Selecting a command on the [Action] menu will simply input the command. With the [Interactive] menu, you drag the stylus across existing input in the work area and then select a command. This encloses the highlighted expression with the command and opens a dialog box if more arguments are needed. When you select an [Interactive] menu item without highlighting an expression first, a dialog box will open prompting you for the necessary arguments. Tip • Operation of the following [Interactive] menu commands is identical to the same commands on the [Action] menu. For information about using these commands, see “2-7 Using the Action Menu”. [Transformation], [Advanced], [Calculation], [Complex], [List]-[Create], [List]-[Statistics], [List]-[Calculation], [Matrix][Create], [Matrix]-[Calculation], [Matrix]-[Row&Column], [Vector], [Equation/Inequality], [Assistant], [Distribution/Inv.Dist], [Financial], Define • The “DispStat”, “Clear_a_z,” and “DelVar” commands of the [Action] menu’s [Command] submenu are not included on the [Interactive] menu. Interactive Menu Example [Interactive] menu operations come in handy in the following cases. • When you want to use a command on an expression you are calculating • When you want to use a command that requires multiple arguments 0235 To factorize the expression x3 – 3x2 + 3x – 1 0236 To obtain the definite integral of x2 + 2x, 1 s x s 2 Using the “apply” Command The “apply” command is included on the [Interactive] menu only. You can use this command to execute only a specific part of an expression and display its result. 0237 To calculate the result of diff(sin(x),x) × cos(x) + sin(x) × diff(cos(x),x), and then calculate only part of the expression Note: This example assumes that your ClassPad is configured with the following mode settings: Algebra, Complex, Radian, Descending Order. Chapter 2: Main Application 91 2-9 Using the Main Application in Combination with Other Applications You can access the windows of other ClassPad applications from the Main application and perform copy, paste, drag and drop, and other operations between them. Tip • Copying data that includes color information from another application and pasting it into the Main application will cause the color information to be disregarded, and the pasted data will become black. This is also true when dragging data from another application to the Main application. • Copying data in the Main application and pasting it into another application will cause the pasted data to be displayed in accordance with the other application’s color settings. This is also true when dragging data from the Main application to another application. Using Another Application’s Window u To open another application’s window 1. Tap the right most toolbar down arrow button. • This displays a palette of application icons. Graph 3D Graph Editor Conics Graph Differential Equation Editor Numeric Solver Graph Editor 3D Graph Geometry Spreadsheet Stat Editor Conics Editor Probability Financial Verify Sequence Editor 2. Tap the button that corresponds to the window you want to display. • This causes the window that corresponds to the button you tap to appear in the lower window. u To close another application’s window 1. Tap anywhere inside of the window you would like to close. 2. Tap the C button in the upper right corner, or tap O and then [Close]. • The Main application work area expands to fill the entire display. Tip • Even if you used the icon panel r icon to expand the lower window to fill the entire display, tapping O and then [Close] closes it and returns to the work area window. • Nothing happens if you tap O and then [Close] while the work area window is active. u To copy an expression in the work area and paste it into the Graph Editor window 0238 To copy “x2 – 1” in the work area and paste it into the Graph Editor window • For more information about the Graph Editor window, see Chapter 3. u To graph a function by dragging it from the work area to the Graph window 0239 To graph the expression “x2 – 1”, which has already been input into the work area Chapter 2: Main Application 92 • As can be seen in this example, a graph can be drawn by dropping an expression in the form of f (x) into the Graph window. • When dropping a formula into the 3D Graph window instead of the Graph window, the formula must be in form f (x, y) (such as x^2+y^2). Using the Stat Editor Window You can use the Stat Editor window to create new LIST variables and edit existing LIST variables. You can also use the Stat Editor window to specify a LIST variable’s name and display its contents. u To use a LIST variable with data input using Stat Editor to perform a calculation in the work area 0240 To input data into “list1” and “list2” using Stat Editor, and then perform the calculation list1+list2 in the work area • list1 through list6 are LIST type system variables. For more information, see “Main Memory Data Types” (page 28). • For information about inputting and editing list data using the Stat Editor, see Chapter 7. u To use Stat Editor to recall a LIST variable created in the work area 0241 Continuing from example 0240 , to use Stat Editor to recall list variable “test”, which was created in the work area Using the Geometry Window When there is a Geometry window on the display, you can drag values and expressions to the Geometry window to draw the graph or figure of the value or expression. You can also drag a figure from the Geometry window to the work area, which displays the corresponding expression or value. u To drag an expression from the work area to the Geometry window 0242 To input the expression x2/52 + y2/22 = 1 in the work area, and then drag it to the Geometry window Tip: The following table shows the types of expressions you can drop into the Geometry window. When the expression is not recognized, Geometry displays it as text. Dropping this into the Geometry window: Displays this: Linear equation in x and y An infinite line Equation of circle in x and y A circle Equation of ellipse in x and y An ellipse Equation of hyperbola in x and y A hyperbola 2-dimensional vector (2 rows × 1 column format) A point Equation y = f (x) A curve 2 × n matrix, n t 3 A polygon (each column represents a vertex of the polygon) n × 2 matrix, n t 3 An open polygon u To drag a figure from the Geometry window to the work area 0243 To drag a point, circle, point and its image from the Geometry window to the work area • For details about Geometry window operations, see Chapter 8. Chapter 2: Main Application 93 Tip: The following shows what happens when you drag a figure from the Geometry window to the work area. Dropping this into the work area: Displays this: Point Coordinates as a vector (2 × 1 matrix) Line Equation of the line Vector An ordered pair (head of vector assuming the tail is at the origin) Circle, Arc, Ellipse, Function, or Curve Corresponding equation Polygon 2 × n matrix Open Polygon (Created by Animation) n × 2 matrix Line Pair Simultaneous equations for the pair A point and its image under a transformation Matrix expression for the transformation 2-10 Using Verify Verify provides you with a powerful tool to check whether your numeric or algebraic manipulations are correct. Verify will assist you in simplifying an expression by verifying whether or not the expression you entered is equivalent to your original expression. If it is, you will get a pleasant response; if not, you will need to correct your mistake before continuing. u To start up Verify 1. On the work area window, tap the right most toolbar down arrow button. 2. On the icon palette that appears, tap W. Left-side expression Right-side expression u Verify window menus and buttons • Clear the Verify window ............................................................................... File - New, Edit - Clear All or O • Open or save a file ............................................................................................File - Open, File - Save or { • Specify the complex number calculation range for Verify ...........................................................................T • Specify the real number calculation range for Verify ..................................................................................Y • Specify the positive real number calculation range for Verify .....................................................................U • Verify the equation starting from the first line..............................................................................................! • Verify the equation starting from the current line ........................................................................................" 0244 To factor 50 completely 0245 Continuing from example 0244 , to rewrite x2 + 1 in factored form Chapter 2: Main Application 94 2-11 Using Probability You can use Probability to simulate the following. • The die faces that will appear when a single die is thrown a specified number of times (1 Die) • The sum of the data of dice faces that will appear when a pair of dice is thrown a specified number of times (2 Dice +) • The product of the data of dice faces that will appear when a pair of dice is thrown a specified number of times (2 Dice ½) • When any number of balls labeled A, B, C, D, E, and F are placed into a box, data about how many times each ball will be drawn within a specified number of draws (Container) You can specify any integer from 1 to 20 as the number of die faces. Probability window (Trial information and result) Probability dialog box u To start up Probability 1. On the work area window, tap the right most toolbar down arrow button. 2. On the icon palette that appears, tap P. This will display an initial Probability dialog box. u Probability window menus and buttons • Clear the Probability window (and display the Probability dialog box) ......... File - New, Edit - Clear All or O • Display the Probability dialog box and try the probability emulation (the trial result will be added to the end of the current file) ...............................................Edit - Add or P • Open or save a file ............................................................................................File - Open, File - Save or { • Delete the currently selected trial data......................................................................................... Edit - Delete • Show the selected result as a frequency distribution table (in matrix form) ....................Display - Distribution • Show the selected result as sample data (in list form)................................................. Display - Sample Data 0246 To obtain the sum data when a two six-sided die are thrown 50 times 0247 After putting 10 A-balls, 20 B-balls, and 30 C-balls into a box, determine how many times each type of ball will be drawn when there is a total of 50 draws. Each time a ball is drawn, it should be replaced into the box before the next draw. Tip: Under initial default settings, trial results are shown as a frequency distribution table in matrix form. Selecting distribution table results and selecting [Sample Data] on the [Display] menu will change them to sample data in list form. Conversely, selecting sample data results and selecting [Distribution] on the [Display] menu will change them to distribution table results. Distribution table (matrix form) Sample data (list form) Chapter 2: Main Application 95 2-12 Running a Program in the Main Application You can run a program in the Main application or the eActivity application. Syntax: Folder name\Program name(parameter) • You do not need to specify the folder name if the program you want to run is in the current folder. If you leave ClassPad configured with its initial default settings, the current folder for both the Program application and the Main application is the “main” folder, so you normally do not need to specify a folder name. • Unless you change it, the current folder of the eActivity application is the “eAct” folder, so you always need to specify the folder name. If you want to run a program that is in the “main” folder, input “main\Program name(parameter)”. Important! If the program command “Pause” is used in a program, it is ignored when the program is called from Main or eActivity. Program 0248 Main application eActivity application To run the program named OCTA that we created and stored under “Creating a Program” (page 197) from the Main application, and determine the surface area and volume of a regular octahedron with a side length of 20 cm Chapter 2: Main Application 96 Chapter 3: Graph & Table Application The Graph & Table application allows you to input and graph rectangular coordinate equations (or inequalities), polar coordinate equations, and parametric expressions. After you graph an expression, you can perform various graph-based analytical operations, such as determining the points of intersection of two graphs, point of inflection, and definite integral for a particular range of a parabola or other figure. When you start up the Graph & Table application, two windows appear on the display: 1 the Graph Editor window and 2 the Graph window. • A Graph Editor sheet can contain up to 20 functions. You can have up to 100 functions stored in the Graph Editor at one time. Functions stored in the Graph Editor can be graphed on the Graph window. 1 • You can also use a function on the Graph Editor window to generate a number table or a summary table. Number tables and summary tables are displayed in a Table window. • The Graph window and Table window have a message box along the bottom that can display expressions and values, or they can be used for input and editing. 2 Message box Graph & Table Application-Specific Menus and Buttons Graph Editor window • Open batch saved data in the Graph Editor window............................................. File - Open Graph Memory • Save all of the expressions on the Graph Editor window.......................................File - Save Graph Memory • Select the entire expression you are editing ........................................................................... Edit - Select All • Clear all of the expressions from the Graph Editor window ......................................................Edit - Clear All • Input a rectangular coordinate type function ...................................................................Type - y=Type or d • Input a polar coordinate type function .............................................................................Type - r=Type or f • Input a parametric function ......................................................................................Type - ParamType or g • Input an x equality ...........................................................................................................Type - x=Type or h • Input a rectangular coordinate type inequality ............................................... Type - Inequality - y>Type, y Type, x Type], [y Type], [x , x<, xt, xs) or y-type (y=, y>, y<, yt, ys, Shade Type) expression after you input it. Simply tap the current equality/inequality sign. On the Type dialog box that appears, select the sign you want and then tap [OK]. Graphing a Stored Function You can select multiple functions and graph them simultaneously, as long as all of the functions are on the same sheet. You can turn graphing of each function on or off, and even specify the line style and color to be used for each function. u To graph a specified function 1. Tap the tab of the sheet that contains the functions you want to graph to make it active. 2. Select the check boxes of all the functions you want to graph, and clear the check boxes of all the functions you do not want to graph. 3. You can tap the current line style and color to specify another style, if you want. • See “To specify the graph line style and color” below. 4. Tap $ to graph. u To specify the graph line style and color 1. Tap the style area next to the function whose line style and color you want to specify. This displays the Style Settings dialog box. Style area Chapter 3: Graph & Table Application 100 2. Configure the dialog box with the following settings. To specify this: Perform this operation: Line type Tap “Graph Plot” and then tap the desired line type. Line color Tap “Line Color” and then tap the desired color. 3. To apply the settings, return to the dialog box in step 2 of this procedure and then tap [OK]. Shading the Region Bounded by Two Expressions You can shade the region bounded by two expressions by specifying [ShadeType] as the function type and then inputting the expressions in the syntax shown below. {lower function f(x), upper function g(x)} | A < x < B Note: A < x < B can be omitted. A < x < B can be replaced with x > A or x < B. u To shade the region bounded by two expressions 1. Tap [Type] - [ShadeType]. 2. Use the above syntax to input two x-variable expressions, specify the x-value range, and then press E. Example: {x2 – 1, –x2 + 1} | –1 < x < 1 3. Tap $ to graph. 0301 To use the draw shade dialog box to shade the region bounded by x2 – 1 and –x2 + 1 Overlaying Two Inequalities in an Intersection Plot / Union Plot Use the following procedure to overlay two inequalities in an Intersection Plot or Union Plot, which are described below. Intersection Plot: Only the parts of the inequalities that overlap are shaded. Union Plot: The inequalities are overlaid as they are. u To overlay two inequalities y < x2, y s x + 1 1. Store y < x2 in line y1 and y s x + 1 in line y2. 2. On the O menu, tap [Graph Format]. 3. On the Graph Format dialog box that appears, tap the [Inequality Plot] down arrow and then select [Intersection] or [Union]. 4. Tap $ to graph. Intersection Plot Union Plot Chapter 3: Graph & Table Application 101 Saving Graph Editor Data to Graph Memory Graph memory lets you store all of the expressions and their related information to a file for later recall. Each graph memory file contains the following data: • Functions on all five Graph Editor sheets (up to 100 functions) • Whether the check box next to each function is selected (checked) or cleared (unchecked) • The line style and color of each function • The graph type of each function • Which sheet is currently active • The View Window settings • Sheet names u To open a graph memory file 1. Tap [File] and then [Open Graph Memory]. This displays a list of names of graph memory files you have stored in memory. 2. Select the name of the graph memory file you want, and then tap [OK]. u To save Graph Editor data to graph memory 1. On the Graph Editor window, tap [File] and then [Save Graph Memory]. This displays a dialog box for inputting a name for the graph memory file. 2. Enter the name and then tap [OK]. 3-2 Using the Graph Window This section explains Graph window operations, including configuring display settings, scrolling, zooming the image, and more. Configuring View Window Parameters for the Graph Window The View Window dialog box lets you specify the maximum and minimum values for each axis, the space between the marks on each axis (the scale), and other graph display parameters. Before drawing a graph, be sure to first configure View Window parameters to ensure proper display of the graph. u To configure View Window parameters Note: Steps 2 and 3 of the procedure below can be performed in reverse, if you want, as long as step 4 is performed next. 1. Tap 6, or tap O and then [View Window] to display the View Window dialog box. Chapter 3: Graph & Table Application 102 2. If you want to configure settings using preset ClassPad View Window parameters, perform the operations described below. To configure this setting: Do this: ClassPad initial defaults On the [Memory] menu select [Initial], or tap the [Default] button. Configure settings optimized for trigonometric function graphing On the [Memory] menu, select [Trigonometric]. Display both the x-axis and y-axis in a range of –10 to 10 On the [Memory] menu, select [Standard]. Configure View Window settings that maintain the current background image On the [Memory] menu, select [Picture]. Configure parameters automatically optimized for a graph On the [Memory] menu, select [Auto]. • For details about each preset parameter, see “View Window Preset Parameters” (page 103). 3. Configure View Window parameters required for the type of graph you want to draw. Rectangular Coordinates Use this item: To configure this View Window parameter: xmin/ymin xmax/ymax xscale/yscale xdot/ydot x-axis/y-axis minimum value x-axis/y-axis maximum value (Specify a value greater than xmin/ymin.) x-axis/y-axis marker spacing Value of each dot on the x-axis/y-axis • Selecting the x-log and/or y-log check box at the top of the display will switch the applicable axis to logarithmic scale. Selecting one of the check boxes results in a semi-log graph, while selecting both check boxes results in a log-log graph. Polar Coordinates and Parametric Coordinates Use this item: To configure this View Window parameter: t min/t max t step Minimum/maximum value of t Step size of t (Specify a non-zero value.) 4. After all the parameters are the way you want, tap [OK]. • When you tap [OK] after changing View Window dialog box settings, the graph is redrawn automatically using the new View Window settings. View Window Preset Parameters Selecting preset View Window parameters configures the settings shown in the table below. Note • The values in the explanations below apply during the vertical half-size view of the Graph window (which is the initial default setting of the Graph & Table application). Tapping r on the icon panel will switch to the full-screen view and change the View Window settings. • The View Window settings will different from those shown below when the Graph window is displayed using the horizontal view. Parameter Name Description Initial (Default) • Both xscale and yscale are set to 1. The x-axis direction is displayed from –7.7 (xmin) to 7.7 (xmax), while the y-axis direction is from –4.6 (ymin) to 4.6 (ymax). • The following settings are configured: tmin = 0, tmax = 2π* radian = 360 degree = 400 grad, tstep = (tmax – tmin)/120*. The values depend on the Basic Format Angle setting. Chapter 3: Graph & Table Application 103 Parameter Name Description Trigonometric • xscale is set to π/2* radian = 90 degree = 100 grad. The values depend on the Basic Format Angle setting. This xscale is used as the basis to display an x-axis direction in the range of xscale × –7.7 (xmin) to xscale × 7.7 (xmax). For example, when the Angle setting is Degree, xmin = –693, xmax = 693. • y-axis settings are fixed as follows, regardless of the Angle setting: yscale = 1, ymin = –2.1, ymax = 2.1. • tmin, tmax, tstep settings are the same as Initial Default. Standard Both xscale and yscale are set to 1. Both the x-axis and y-axis directions are displayed in the range of –10 (xmin, ymin) to 10 (xmax, ymax). Picture View Window settings that maintain the current background image are applied. Auto View Window settings are automatically optimized for the expression (the last expression selected in the case of multiple expressions) selected for graphing on the Graph Editor window. * These values are displayed as decimal format values. View Window parameter precautions • When the View Window setting produces an axis that does not fit on the display, the scale of the axis is indicated on the edge of the display closest to the origin. • Changing the xmin (ymin) or xmax (ymax) value automatically changes the xdot (ydot) value, while changing the xdot (ydot) value automatically changes the xmax (ymax) value. Using View Window Memory You can save your View Window setup for later use. u To save the current View Window setup 1. Tap 6, or tap O and then [View Window] to display the View Window dialog box. 2. Change parameters as required (see “To configure View Window parameters” on page 102). 3. Tap [File] and then [Save File]. This displays a dialog box for inputting a name for the View Window setup. 4. Enter the name and then tap [OK]. u To recall a setup from View Window memory 1. Tap 6, or tap O and then [View Window] to display the View Window dialog box. 2. Tap [File] and then [Open File]. This displays a list of names of View Window setups stored in ClassPad memory. 3. Select the name of the setup you want, and then tap [OK]. • This causes the current View Window parameters to be replaced by the parameters of the recalled setup. Panning the Graph Window You can drag the Graph window screen to scroll (pan) its contents. u ClassPad Operation 1. Holding the stylus anywhere against the Graph window, drag it in the direction you want. • This causes the Graph window to scroll automatically in accordance with the dragging. 2. When the Graph window shows the area you want, remove the stylus from the display. • This causes the graph to be redrawn on the Graph window. Chapter 3: Graph & Table Application 104 Tip • Graph window panning cannot be performed while any one of the following functions is being used: Modify, Trace, Sketch, G-Solve, box zoom. • While a panning operation is in progress on the Graph window, the coordinates of the point where the stylus is held against the display is displayed in the status bar. Scrolling the Graph Window You can use either of the two operations to scroll the Graph window up, down, left, or right. • Tapping the graph controller arrows at the edges of the Graph window. • Using the cursor key. Display of the graph controller arrows is turned off under initial default settings. Use the Graph Format dialog box to turn them on, if you want. For more information, see “Graph Format Dialog Box” on page 38. Graph controller arrows Zooming the Graph Window You can zoom in on the Graph window image by holding two fingers against the screen while moving them apart from each other. Moving two fingers closer to each other in a pinching action will zoom out. Your ClassPad also provides you with a wide selection of zoom commands that you can use to enlarge or reduce an entire graph or a specific area of a graph. To perform this type of zoom: Do this: To enlarge the area enclosed in a boundary 1. Tap [Zoom] and then [Box], or tap Q. 2. On the Graph window, drag the stylus to draw a selection boundary around the area you want to enlarge. 3. Remove the stylus from the display. • The area within the selection boundary will expand to fill the entire Graph window. To enlarge or reduce to a specified numeric factor 1. Tap [Zoom] and then [Factor]. 2. On the dialog box that appears, input the x- and y-axis zoom factor, and then tap [OK]. 3. Tap [Zoom] - [Zoom In] to enlarge to the specified factor, or [Zoom] - [Zoom Out] to reduce. To do this on the Graph window: Do this: Automatically configure settings so the Graph screen fills the entire screen in accordance with the graph being drawn Tap [Zoom] and then [Auto], or tap R. Return a graph to its original View Window settings Tap [Zoom] and then [Original]. Adjust View Window x-axis values so that they are identical to the y-axis values Tap [Zoom] and then [Square]. Round View Window settings (xmin, xmax, xdot) to an appropriate number of decimal places and redraw the graph Tap [Zoom] and then [Round]. Make the value of each dot equal 1, which makes all coordinate values integers Tap [Zoom] and then [Integer]. Return View Window parameters to their settings prior to the last zoom operation Tap [Zoom] and then [Previous]. Return View Window parameters to their initial default (see “Initial (Default)” under “View Window Preset Parameters” on page 103) Tap [Zoom] and then [Initialize]. Redraw graphs using preset View Window parameter values See “Using Quick Zoom” below. Chapter 3: Graph & Table Application 105 Using Quick Zoom The quick zoom commands on the [Zoom] menu draw a graph using preset built-in View Window parameter values. Note • The values in the explanations below apply during the vertical half-size view of the Graph window (which is the initial default setting of the Graph & Table application). Tapping r on the icon panel will switch to the full-screen view and change the View Window settings. • The View Window settings will different from those shown below when the Graph window is displayed using the horizontal view. Command View Window Parameter Values*1 xmin 2 xmax xscale 2 * ymin ymax yscale 2 –2.1 2.1 1 Quick Trig * * Quick log (x) –2 13.4 2 –4.6 4.6 1 Quick e^x –2.2 2.2 1 –1.4 9 1 Quick x^2 –7.7 7.7 2 –12 80 5 Quick –x^2 –7.7 7.7 2 –80 12 5 Quick Standard –10 10 1 –10 10 1 *1 Any View Window parameter that is not shown in the above table is unchanged when you execute a quick zoom command. *2 Depending on the Basic Format Angle setting, executing Quick Trig changes the xscale setting to π/2 (for Radian), 90 (for Degree), or 100 (for Grad). The following settings are applied based on the xscale value: xmin = –7.7 × xscale, xmax = 7.7 × xscale. Using Built-in Functions for Graphing Your ClassPad is pre-programmed with the commonly used functions listed below. y = aⴢx + b y = aⴢx^2 + bⴢx + c y = aⴢx^3 + bⴢx^2 + cⴢx + d y = aⴢsin (bⴢx + c) + d y = aⴢcos (bⴢx + c) + d y = aⴢtan (bⴢx + c) + d y = aⴢlog (bⴢx + c) + d y = aⴢln (bⴢx + c) + d y = aⴢe^(bⴢx + c) + d y = a^(bⴢx + c) + d y = a /(bⴢx + c) + d You can recall a built-in function and register it as-is into the Graph Editor window. You can then replace the parameters in the function with values and graph the results, or you can leave the literal parameter names unchanged and use Dynamic Modify (page 115) to modify the form of the graph. u ClassPad Operation 1. Tap [Type] - [ y =Type]. 2. On the Graph Editor window, tap a and then [Built-In]. 3. On the menu that appears, tap the built-in function you want to select. • The selected built-in function is input as-is on the Graph Editor window. Input values for each parameter as required. • You can leave some or all of the literal parameter names unchanged and use Dynamic Modify (page 115) to modify the form of the graph. Chapter 3: Graph & Table Application 106 Saving a Screenshot of a Graph Use the following procedures to save a screenshot of a graph as image data for later recall. u To open a screenshot of a graph 1. On the Graph window, tap a and then [Open Picture]. This displays a list of names of graph images you have stored in memory. 2. Select the name of the image you want, and then tap [OK]. • The image you select is displayed as the Graph window background. u To save a screenshot of a graph 1. Draw the graph you want to save. 2. Tap a and then [Save Picture]. This displays a dialog box for inputting a name for the screenshot. 3. Enter the name and then tap [OK]. u To clear the current screenshot of a graph On the Graph window, tap a and then [Clear Picture]. Adjusting the Lightness (Fade I/O) of the Graph Window Background Image You can adjust the lightness of the graph window background image within a range of 0% (as-is) to 100% (all white). A higher setting value makes the image lighter, and a setting of 100% displays an all white background. You can use this setting to adjust the background image to a level that makes the graph easier to see. u To adjust the lightness (Fade I/O) of the graph window background image 1. On the Graph window, tap a and then [Fade I/O]. • This causes a slider for adjusting image lightness to appear on the toolbar. 2. Use d and e to adjust the lightness value. • Each press of d and e changes the setting value in steps of 5%. 3. After the setting is the way you want, tap [OK]. Chapter 3: Graph & Table Application 107 3-3 Using Table & Graph The Graph & Table application includes a “Table window” for displaying number tables and summary tables generated with the functions you input on the Graph Editor window. Generating a Number Table A number table can be created for one or more y=Type, r=Type, or ParamType (Parametric Type) functions registered on the Graph Editor window. y=Type: (x, y) number table r=Type: (, r) number table ParamType: (t, xt, yt) number table The following are the two methods that can be used to create a number table using the Graph & Table application. • Specifying the value range of x, , or t using the Table Input dialog box • Specifying the value range of x, , or t using a list stored in ClassPad memory Tip • The derivative is also included in the number table when the Graph Format “Derivative/Slope” check box is selected. • You can specify the width of table cells using the [Cell Width Pattern] on the Graph Format dialog box (page 38). u To generate a number table by specifying a range of values for x, , or t using the Table Input dialog box 1. On the Graph Editor window, input the function(s) you want to use for number table creation, and select the check box(es) to the left of the function(s) you want to use. 2. Tap the [Type] menu, and then select the type ([y=Type], [r=Type], or [ParamType]) of the function(s) you want to use for number table creation. 3. Tap 8 to display the Table Input dialog box. 4. Input the values for the x-, -, or t -values of your table, and then tap [OK]. 5. Tap # to generate the number table and display it on the Table window. Tip: The above operation is possible only when “Table Input” (which is the initial default) is selected for the Graph Format dialog box [Table Variable] item. Chapter 3: Graph & Table Application 108 u To generate a number table by assigning list values to x, , or t 1. Tap O and then [Graph Format] to display the Graph Format dialog box. 2. Tap [Special] tab, and then select a list option (list1 through list6 or a list variable created by you) for the [Table Variable] item. • By way of example, here we will select “list1”. 3. Tap [Set] to apply the settings and close the dialog box. 4. Tap O, [Window] and then [Stat Editor] to display the Stat Editor window. 5. In the list you selected in step 2 (list1 in this example), input the values you want to assign to x, , or t. • For information about Stat Editor window operations, see Chapter 7. 6. On the Graph Editor window, input the function(s) you want to use for number table creation, and select the check box(es) to the left of the function(s) you want to use. 7. Tap the [Type] menu, and then select the type ([y=Type], [r=Type], or [ParamType]) of the function(s) you want to use for number table creation. 8. Tap # to generate the number table and display it on the Table window. u To draw a graph using a number table Perform either of the operations below. Tap [Graph] - [G-Plot] or tap !. • This will draw a graph that plots the coordinates in the number table. Tap [Graph] - [G-Connect] or $. • This graphs the expression used to create the number table and plots the coordinates in the table. u To save a number table to a list 1. On the Table window, select any cell in the column you want to save to a LIST variable. • To save column y1, for example, select any cell in column y1. 2. Tap a and then [Table to List]. • This displays a dialog box for specifying a variable name. 3. Enter the name you want to give to the variable, and then tap [OK]. • This assigns the list of data you selected to a variable with the name you specified. Showing Linked Displays of Number Table Coordinates and Graph Coordinates (Link Trace) With Link Trace, selecting a value in a number table created using a function causes a crosshair pointer (trace pointer) to appear at the corresponding coordinates on the graph. 0302 To create a number table of y = 3log(x+5), graph the values, and perform link trace Chapter 3: Graph & Table Application 109 Generating Number Table Values from a Graph You can input the coordinate values where the pointer is currently located on a graph into a table by simply pressing E. 0303 To generate number table values from the y = x3 – 3x graph Generating a Summary Table A summary table can be created from a y=Type function registered on the Graph Editor window. The figure below shows an example of the summary graph and table of y = x3 – 3x. The following are the two methods that can be used to create a summary table using the Graph & Table application. • Creating a summary table with the View Window settings xmin as the lower limit value and xmax as upper limit value With this method, the x within the range of xmin and xmax where f (x) = 0 is automatically calculated and added to the table. You can specify xmin and xmax values, or you can use auto settings ([Memory] - [Auto] View Window settings). • Specifying the range of x-values for creating a summary table using a list stored in ClassPad memory This method generates a summary table by looking up data stored in a list. A LIST variable is used to specify the x-values. When using this method, it is up to you specify all of the correct x-values required to generate the summary table. The summary table will not be generated correctly if you provide incorrect x-values. Tip • You can control whether or not the summary table should include an f (x) line (second derivative component) using the [Summary Table f (x)] setting on the [Special] tab of the Graph Format dialog box (page 38). Turning on the [Summary Table f (x)] option causes both first derivative components and second derivative components to be displayed in the summary table. Turning it off shows first derivative components only. • Some functions may not be solvable by the ClassPad’s internal summary table calculation. When this happens, the “Can’t Solve!” error message appears on the display. u To generate a summary table using View Window 1. On the Graph Editor window, register the function you want to use to create the summary table. • Make sure that only the check box of the function to be used for summary table creation is selected. Clear the check boxes of all other functions on the Graph Editor window. 2. Tap 6 to display the View Window dialog box. 3. Perform any one of the operations below. • Tap [Memory] and then [Auto]. This causes all settings on the View Window dialog box to change to “Auto”. • Specify the x-values for the summary table by specifying values for the [xmin] and [xmax] settings. Chapter 3: Graph & Table Application 110 4. Tap [OK] to close the View Window dialog box. • Tapping $ here graphs the function using the View Window settings. 5. Tap 4. • This starts summary table generation, and displays the result on the Table window. Note that generation of a summary table can take a bit of time. Tip • The above operation is possible only when “View Window” (which is the initial default) is selected for the Graph Format dialog box [Summary Table] item. • A monotone increasing function or other special function may not be solvable by the ClassPad’s internal summary table calculation. If this happens, use the procedure below. u To generate a summary table by specifying all of the values for x 1. Tap O and then [Graph Format] to display the Graph Format dialog box. 2. Tap the [Special] tab, and then select a list option (list1 through list6 or a list variable created by you) for the [Summary Table] item. • By way of example, here we will select “list1”. 3. Tap [Set] to apply the settings and close the dialog box. 4. Tap O, [Window] and then [Stat Editor] to display the Stat Editor window. 5. In the list you selected in step 2 (list1 in this example), input the values you want to assign to x. 6. Tap the Graph Editor window to make it active. 7. On the Graph Editor window, register the function you want to use to create the summary table. • Make sure that only the check box of the function to be used for summary table creation is selected. Clear the check boxes of all other functions on the Graph Editor window. 8. Tap 4. • This starts summary table generation using the x-values you input in step 5, and displays the result on the Table window. 3-4 Using Trace Trace lets you move a point along a graph and displays the coordinates for the current pointer location. You can also link the trace operation to the number table used to draw a graph, so the pointer jumps to the coordinates that are currently selected in the table. Using Trace to Read Graph Coordinates Starting the trace operation causes a crosshair pointer to appear on the graph. You can then press the cursor key or tap the graph controller arrows to move the pointer. The coordinates are displayed as you move the pointer. u To perform a trace operation 1. On the Graph Editor window, input and store a function, and then tap $ to graph it. • Here, input y = x2 – 3 into line y1. Chapter 3: Graph & Table Application 111 2. Tap [Analysis], [Trace], or tap =. • This will display the pointer at the coordinates where x = 0. The pointer will not be visible when it is located at a point outside the graph display area. • If “Undefined” appears in place of the xc or yc coordinate, it means that the current point is undefined. Press the left or right cursor key to move to a point that is defined. 3. Press the left or right cursor key, or tap the left or right graph controller arrow. • This moves the pointer along the graph, and displays the coordinates of the current pointer location. • You can also move the pointer to a particular point by inputting coordinates. Pressing a number key displays a dialog box for inputting coordinates. Input the values you want and then tap [OK]. • When there are multiple graphs on the Graph window, you can use the up and down cursor keys or the up and down graph controller arrows to move the pointer between graphs. 4. To quit the trace operation, tap l on the icon panel. Tip • While the trace pointer is on the window, tapping the displayed coordinate values causes the coordinate values to appear in the message box. You can then copy the coordinates to the clipboard. • Selecting the [Derivative/Slope] check box on the Graph Format Dialog Box will show the derivative along with coordinates while the trace pointer is on the display. Clearing the [Coordinates] check box will hide the coordinate display while the trace pointer is on the display. For more information, see “Graph Format Dialog Box” on page 38. 3-5 Using the Sketch Menu The [Sketch] menu lets you add points, lines, figures, and text after you draw a graph. You can also add tangent and normal lines to your graph. Using Sketch Menu Commands This section describes how to use each of the commands on the [Sketch] menu. u To clear figures inserted using the Sketch menu To clear plots, lines, text, or other figures inserted using the [Sketch] menu, tap [Analysis], [Sketch], and then [Cls]. This redraws the graph to what is stored on the Graph Editor window. u To plot a point on the Graph window 1. While the Graph window is active, tap [Analysis], [Sketch], and then [Plot]. 2. Tap the location on the Graph window where you want to plot a point. • Instead of tapping the Graph window, you could also use the keypad to specify the coordinates of the point. Press a number key on the keypad. On the dialog box that appears, input x- and y-coordinate values, and then tap [OK]. u To draw a line on the Graph window 1. While the Graph window is active, tap [Analysis], [Sketch], and then [Line]. 2. Tap the start point of the line and then tap the end point. This causes a straight line to be drawn between the two points. The message box shows the equation of the line. • Instead of tapping the Graph window, you can use the keypad to specify the coordinates of the start point and end point. Press a number key on the keypad. On the dialog box that appears, input the coordinates for the start point (x1, y1) and the end point (x2, y2), and then tap [OK]. Chapter 3: Graph & Table Application 112 u To write text on the Graph window 1. While the Graph window is active, tap [Analysis], [Sketch], and then [Text]. 2. On the dialog box that appears, enter the text you want and then tap [OK]. • This displays the word “Text” in the lower right corner of the Graph window. 3. Place the stylus on the screen and hold it there. • This causes the text you input in step 2 to appear at the location where you are pointing with the stylus. 4. Drag the text to the location you want, and then lift the stylus from the screen. Tip: You cannot edit text after inputting it into the Graph window. u To draw a line tangent to a graph 1. On the Graph Editor window, register the function you want to graph. • By way of example, here we will register the following function: y = x2 – x – 2. 2. Tap $ to draw the graph. Next, tap [Analysis], [Sketch], and then [Tangent]. • This displays the crosshair pointer along with its corresponding coordinate values. 3. Press 1. 4. The x-value specification dialog box will have x = 1 input, so tap [OK]. • This draws the tangent to y = x2 – x – 2 at x = 1. Tip: Instead of inputting coordinate values in steps 3 and 4, you can use the cursor key or the graph controller arrows to move the pointer to the point of tangency on the Graph window. u To draw a line that is normal to a graph The procedure for drawing a line that is normal to a graph is virtually identical to the procedure “To draw a line tangent to a graph”, above. The only difference is in step 2, where you need to tap [Analysis], [Sketch], and then [Normal] instead of [Tangent]. u To graph the inverse of a function 0304 To graph y = x2 – x – 2 and then overlay it with x = y2 – y – 2 u To draw a circle 0305 To draw a circle u To draw a vertical or horizontal line 0306 To draw a vertical line at x = 2 Chapter 3: Graph & Table Application 113 3-6 Analyzing a Function Used to Draw a Graph Your ClassPad includes a G-Solve feature that lets you perform a variety of different analytical processes on an existing graph. What You Can Do Using the G-Solve Menu Commands While there is a graph on the Graph window, you can use a [G-Solve] menu command to obtain the following information. • x-coordinate for a given y-coordinate .................................................Analysis - G-Solve - x-Cal/y-Cal - x-Cal • y-coordinate for a given x-coordinate .................................................Analysis - G-Solve - x-Cal/y-Cal - y-Cal • Root (the x-intercept) .................................................................................... Analysis - G-Solve - Root or Y • Minimum value ................................................................................................ Analysis - G-Solve - Min or I • Maximum value .............................................................................................. Analysis - G-Solve - Max or U • Minimum value in the range displayed on the Graph window................................. Analysis - G-Solve - f Min • Maximum value in the range displayed on the Graph window............................... Analysis - G-Solve - f Max • y-intercept ...................................................................................................... Analysis - G-Solve - y-Intercept • Point of intersection for two graphs.............................................................. Analysis - G-Solve - Intersection • Integration value for a specified range ........................................................ Analysis - G-Solve - Integral - ∫dx • Integration value between the two or more of the graph’s roots .............. Analysis - G-Solve - Integral - Root • Integration value between the two or more intersections of two graphs ............................................. Analysis - G-Solve - Integral - Intersection • Point of inflection...............................................................................................Analysis - G-Solve - Inflection • Distance between two points ............................................................................ Analysis - G-Solve - Distance • Volume of a solid of revolution ......................................................................... Analysis - G-Solve - π ∫ f(x)2dx Tip: See “Graph Types and Executable Functions” (page 302) for information about graph types and executable G-Solve functions. Using G-Solve Menu Commands When multiple solutions are obtained by a G-Solve command, only one solution is displayed at a time. For example, executing [Analysis] - [G-Solve] - [Root] for a cubic function that has two roots will display only one root at a time. In a case such as this, use the left and right cursor keys (or tap the left and right graph controller arrows) to cycle between the available solutions. u To obtain the root of a function 1. On the Graph Editor window, input and store a function, and then tap $ to graph it. • Here, input y = x(x + 2)(x – 2) into line y1. 2. Tap [Analysis], [G-Solve], and then [Root], or tap Y. • This displays “Root” on the Graph window, and locates a pointer at the first solution of the root (root for smallest value of x). The x- and y-coordinates at the current pointer location are also shown on the Graph window. Chapter 3: Graph & Table Application 114 3. To obtain other roots, press the left or right cursor key, or tap the left or right graph controller arrows. • If there is only one solution, the pointer does not move when you press the cursor key or tap the graph controller arrow. The following are examples for other G-Solve commands. 0307 To obtain the point of intersection for two graphs y = x + 1 and y = x2 0308 To determine coordinates at a particular point on a graph 0309 To graph the function y = x(x + 2)(x – 2) and obtain its definite integral in the domain of 1 s x s 2 0310 To graph the function y = x3 – 1 and determine its inflection point 0311 To graph the function y = x2 – x – 2 and obtain the volume of a solid of revolution as the line segment from x = 1 to x = 2 is rotated on the x-axis 3-7 Modifying a Graph A graph can be modified in real time as you change its parameters and/or variable values. The Graph & Table application provides you with two methods for modifying a graph - “Direct Modify” and “Dynamic Modify”. Modifying a Single Graph (Direct Modify) “Direct Modify” changes the parameter in the equation of the original graph. This method can be used when you are modifying a single graph. 0312 To graph the functions y = 2x2 + 3x – 1 and y = 2x + 1, and then find out how a change in the parameters of each function affects the shape and position of the graphs Modifying Multiple Graphs Simultaneously (Dynamic Modify) “Dynamic Modify” changes the values assigned to common parameters of multiple functions. Use Dynamic Modify when you want to modify multiple graphs at the same time. u Inputting a Graph Formula for Use with Dynamic Modify Example: To input the following formula with two common parameters (a, b): y = ax2 – bx and y = ax + b 1. On the Graph Editor window, tap [Type] - [ y =Type]. 2. Perform any one of the operations below. - Input using built-in functions (1) Tap a - [Built-In] - [ y = a · x^2+b · x+c] to input y = ax2 + bx + c. (2) Edit the function you input (y = ax2 + bx + c) to it becomes y = ax2 – bx, and then press E. (3) Tap the line below the function. (4) Tap a - [Built-In] - [ y=a · x+b] to input y = ax + b and then press E. Chapter 3: Graph & Table Application 115 - Input using the soft keyboard and keyboard (1) Display the soft keyboard and use it to perform the key operation below. a*x{c-b*xw (2) Tap the line below the formula you input and then perform the key operation below. a*x+bw u To run Dynamic Modify 1. On the Graph Editor window, input at least one formula that contains a parameter. 2. Select the check box next to the graph formula(s) you want to use with Dynamic Modify and clear the check boxes of all of the other graphs. • In the explanation below, there are two formulas registered on the Graph Editor window: y = ax2 – bx and y = ax + b. The Sliders check boxes of both of these formulas are selected for use with Dynamic Modify. 3. To run Dynamic Modify, tap a and then [Dynamic Graph] or tap 4. • This will display sliders for changing values assigned to parameters a and b. 4. Tap the arrow buttons at either end of the a and b sliders. • Each tap will change the values assigned to the applicable parameter (a or b) and redraw the graph accordingly. • The operations described below are supported while Dynamic Modify is running. To do this: Do this: Change the current value, minimum value, maximum value and step value. (1) Tap the upper left corner of the slider display box. On the menu that appears, tap [Settings]. • This displays the Slider Settings dialog box. The number of tabs on the dialog box will match the number of parameters in your graph formula(s). (2) Use the tabs to specify the current value, minimum value, maximum value, and step value for each of the parameters. (3) To close the dialog box and save your changes, tap [OK]. Automatically modify the form of a graph (by changing the value of a specific parameter between specified minimum and maximum values) (1) Tap the upper left corner of the slider display box. (2) On the menu that appears, tap [Auto Play]. • This starts an operation that automatically changes the value of the applicable parameter between the minimum value and maximum value, and then from the maximum value back to the minimum value. This cycle will stop automatically after a few cycles from the minimum value to the maximum value are complete. To stop a cycle part way through, tap l on the icon panel or press c. (Simultaneous Auto Play execution for multiple parameters is not supported.) Temporarily hide sliders (1) Tap the upper left corner of the slider display box. On the menu that appears, tap [Minimize]. • This hides all currently displayed sliders and causes the slider icon (a) to appear in the status bar. (2) To unhide the sliders, tap the slider icon (a) in the status bar. Chapter 3: Graph & Table Application 116 u To exit Dynamic Modify Tap the close button (C) in the upper right corner of the slider display box. Note • While Dynamic Modify is running, up to three sliders can be displayed for the parameters included in the graph formulas whose check boxes are selected. If there are more than three parameters in the selected graph formulas, the three parameters are automatically assigned to sliders in accordance with the rules below. In the case of one graph formula, parameters are assigned to sliders from left to right until three are assigned. In the case of multiple graph formulas, parameters are assigned to sliders in the chronological order that the graph formulas were registered (from left to right in each formula) until three are assigned. • To change slider allocations from those applied automatically, perform the steps below. 1. Tap the upper left corner of the slider display box. 2. On the menu that appears, tap [Settings]. 3. On the Slider Settings dialog box that appears, tap the “Parameter” line button. 4. On the parameter list that appears, tap the parameter you want to assign to the slider. • If you use the above procedure to assign a different parameter to a slider, the parameter that was previously assigned to the slider will retain the value it was set at when you changed the slider assignment. Also, the minimum value, maximum value and step value will automatically change in accordance with the parameter value. The automatically generated values will be applied if you later assign the parameter to a slider. 0313 To graph the functions y = ax2 – bx and y = ax + b, and then find out how a change in parameter a from 1 to 4 and a change in parameter b from –2 to 2 affect the shape and position of each graph Chapter 3: Graph & Table Application 117 Chapter 4: Conics Application The Conics application provides you with the capability to graph circular, parabolic, elliptic, and hyperbolic functions. You can also use the Conics application to quickly and easily determine the proper focal point, vertex, directrix, and other information about each type of conics. Starting up the Conics application displays two windows: 1 the Conics Editor window and 2 the Conics Graph window. 1 A function input on the Conics Editor window is graphed on the Conics Graph window. 2 Conics Application-Specific Menus and Buttons Conics Editor window • Draw a graph ..............................................................................................................................................^ • Start modifying a graph (Dynamic Modify, page 121) .................................................................................4 • Insert a Conics Form....................................................................................Form - Insert Conics Form or q • Adjust the equation so it fits a Conics Form................................................... Fit - Fit into Conics Form or w Conics Graph window • Make the Conics Editor window active .......................................................................................................* • Perform a G-Solve operation (page 120) ........................................................................... Analysis - G-Solve Tip: The Conics application uses many of the same commands (Zoom, Trace, Sketch, etc.) as the Graph & Table application. Chapter 4: Conics Application 118 4-1 Inputting an Equation You can select one of the preset Conics Forms or input a conics equation manually. You can also transform a manually input equation to a Conics Form. u To input an equation using a Conics Form 1. On the Conics Editor window, tap q to displays the Select Conics Form dialog box. Horizontal Parabola 1 Horizontal Parabola 2 Vertical Parabola 1 Vertical Parabola 2 Circle 1 Circle 2 Ellipse Horizontal Hyperbola Vertical Hyperbola General Form 2. Select the Conics Form of the type of equation you want to graph, and then tap [OK]. • This displays the Conics Editor window, which will contain the selected Conics Form. 3. Change the parameters of the equation as required. 0401 To use a Conics Form to input the equation for a parabola with a horizontal axis (principal axis parallel with x-axis) u To input an equation manually Make the Conics Editor window active, and then use the soft keyboard for input. u To transform a manually input equation to a Conics Form ( − 1)2 2 to the standard Conics Form x = Ay2 + By + C 0402 To transform the equation + ( − 2)2 = 22 4 Tip • If the equation you input cannot be transformed into the standard Conics Form you selected, the message “Can’t Transform into This Type” appears. • An input equation may not transform correctly if it includes a square root calculation or some other function. 4-2 Drawing a Conics Graph Tip: You can drag the Conics Graph window screen to scroll (pan) its contents (except for Trace, Sketch, G-Solve, box zoom, and certain other functions). Drawing a Parabola A parabola can be drawn with either a horizontal or vertical orientation. The parabola type is determined by the direction of its principal axis. • A parabola with a horizontal axis is one whose principal axis is parallel to the x-axis. There are two possible equations for a parabola with a horizontal axis: x = A(y – K)2 + H and x = Ay2 + By + C. 0401 To draw the parabola x = 2(y – 1)2 – 2 • A parabola with a vertical axis is one whose principal axis is parallel to the y-axis. There are two possible equations for a parabola with a vertical axis: y = A(x – H)2 + K and y = Ax2 + Bx + C. Chapter 4: Conics Application 119 Drawing a Circle There are two forms that you can use to draw a circle. • One form is the standard form, which allows you to specify the center point and radius: (x – H)2 + (y – K)2 = R2 • The other form is the general form, which allows you to specify the parameters of each term: Ax2 + Ay2 + Bx + Cy + D = 0 Drawing an Ellipse You can use the standard equation ( − H)2 ( − K)2 + = 1 to draw an ellipse. A2 B2 Drawing a Hyperbola A hyperbola can be drawn with either a horizontal or vertical orientation. The hyperbola type is determined by the direction of its principal axis. ( − H)2 ( − K)2 • The standard form of a hyperbola with a horizontal axis is: – =1 A2 B2 ( − K)2 ( − H)2 • The standard form of a hyperbola with a vertical axis is: – =1 A2 B2 Drawing a General Conics Using the conics general equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, you can draw a parabola or hyperbola whose principal axis is not parallel either to the x-axis or the y-axis, a slanted ellipse, etc. 4-3 Using G-Solve to Analyze a Conics Graph What You Can Do Using the G-Solve Menu Commands While there is a graph on the Conics Graph window, you can use a command on the [Analysis] - [G-Solve] menu to obtain the following information. • x-coordinate for a given y-coordinate ................................................................. G-Solve - x-Cal/y-Cal - x-Cal • y-coordinate for a given x-coordinate ................................................................. G-Solve - x-Cal/y-Cal - y-Cal • Focus of a parabola, ellipse, or hyperbola .............................................................................G-Solve - Focus • Vertex of a parabola, ellipse, or hyperbola ........................................................................... G-Solve - Vertex • Directrix of a parabola ........................................................................................................ G-Solve - Directrix • Axis of symmetry of a parabola....................................................................................... G-Solve - Symmetry • Length of the latus rectum of a parabola ...................................................... G-Solve - Latus Rectum Length • Center point of a circle, ellipse, or hyperbola ........................................................................G-Solve - Center • Radius of a circle ................................................................................................................. G-Solve - Radius • Asymptotes of a hyperbola ...........................................................................................G-Solve - Asymptotes • Eccentricity of a parabola, ellipse, or hyperbola ........................................................... G-Solve - Eccentricity • x-intercept / y-intercept ...............................................................G-Solve - x-Intercept / G-Solve - y-Intercept Tip: The color of Directrix, Symmetry, Asymptotes lines drawn using G-Solve is the color specified by the Graph Format Sketch Color. For more information about Graph Format, see “Graph Format Dialog Box” (page 38). Chapter 4: Conics Application 120 Using G-Solve Menu Commands When multiple solutions are obtained by a G-Solve command, only one solution is displayed at a time. For example, executing [Analysis] - [G-Solve] - [Focus] for an ellipse that has two foci will display only one focus at a time. In a case such as this, use the left and right cursor keys (or tap the left and right graph controller arrows) to cycle between the available solutions. u To determine the focus of the parabola x = 2(y – 1)2 – 2 1. On the Conics Editor window, input the conics equation and then tap ^ to graph it. • Here, input the parabolic equation x = 2(y – 1)2 – 2. 2. Tap [Analysis] and then [G-Solve]. Next, on the submenu that appears, select the command you want. To determine the focus for this example, select [Focus]. • Press the left and right cursor keys to toggle the display between the two foci. The following are examples for other G-Solve commands. 0403 To determine the axis of symmetry of the parabola x = 2(y – 1)2 – 2 0404 To determine the center point of the circle x2 + y2 + 4x – 6y + 9 = 0 0405 To determine the radius of the circle x2 + y2 + 4x – 6y + 9 = 0 0406 To determine the asymptotes of the hyperbola 0407 To determine the eccentricity of the ellipse 0408 To determine the x-intercept of the parabola x = 2(y – 1)2 – 2 ( − 1)2 ( − 2)2 − =1 22 32 ( − 1)2 ( − 2)2 + =1 22 32 4-4 Modifying a Graph (Dynamic Modify) A graph can be modified in real time as you change its parameter values. u To modify a graph 0409 To observe the form and position of the graph of the parabola x = ay2 + by + c as parameters a, b, and c are each changed within a range of –2 to 2 Chapter 4: Conics Application 121 Chapter 5: Differential Equation Graph Application This chapter explains how to use the Differential Equation Graph application, which you can use to investigate families of solutions to ordinary differential equations. The Differential Equation Graph application has the following two types of windows. 1 1 Differential Equation Editor window Use this window to input expressions ([DiffEq] tab) and initial conditions ([IC] tab) for graphing. You also can input f (x) type functions ([Graphs] tab). 2 Differential Equation Graph window 2 This window shows the graph of the expression that you input into the Editor window. Differential Equation Editor Window-Specific Menus and Buttons [DiffEq] tab, [IC] tab, [Graphs] tab • Graph the selected function(s) ....................................................................................................................O • Display the View Window dialog box to configure Differential Equation Graph window settings ................6 • Display the Main application window ..........................................................................................................~ • Delete the line of data at the current cursor location ..................................................................................q [DiffEq] tab only • Input a single first order differential equation ................................................... Type - 1st (Slope Field) or A • Input a single second order differential equation or a set of two first order differential equations ........................................................ Type - 2nd (Phase Plane) or B • Input a higher order differential equation or a set of multiple differential equations ..................................................................................... Type - Nth (No Field) or 9 [Graphs] tab only • Input f(x) type functions.........................................................................................................Type - f (x) or d • Input parametric functions......................................................................................... Type - Parametric or g [IC] tab and [Graphs] tab only • Change graph line thickness to normal (1-dot line) or thick (2-dot line) ..............................................F, G Differential Equation Graph Window-Specific Menus and Buttons • Toggle arrows on or off to indicate the direction of slope field or phase plane vectors ............................................................................................................... Edit - Arrows Chapter 5: Differential Equation Graph Application 122 • Toggle the use of unit vectors on or off for slope field or phase plane graphing ...............................................................................................................Edit - Unit Vectors • Display the Differential Equation Editor window [DiffEq] tab........................Edit - Editor - DiffEqGraph Editor • Display the Differential Equation Editor window [IC] tab ..............................................Edit - Editor - IC Editor • Display the Differential Equation Editor window [Graphs] tab............................... Edit - Editor - Graph Editor • Clear all currently registered initial conditions (and, as a result, all solution curves) ...................................................................................Edit - Clear All • Pan the graph window ....................................................................................................Analysis - Pan or T • Select and move the initial condition point .................................................................. Analysis - Select or G • Register the coordinates at the location you tap on the Differential Equation Graph window as the initial condition, and graph the solution curve based on that initial condition ........................................................ Analysis - Modify or J • Make the Differential Equation Editor window active ..................................................................................A • Display the View Window dialog box to configure Differential Equation Graph window settings...........................................................................................................................6 • Display a trace cursor that can be positioned on any x, y coordinate .........................................................K • Display a trace cursor that can be positioned on any grid point that has a field line ..................................L • Display a trace cursor that can be positioned on any solution curve or general graph ..........................................................................................................Analysis - Trace or = • Turn display of axes and coordinate values on or off .................................................................................q 5-1 Graphing a Differential Equation You can use the Differential Equation Graph application to graph a first order, a second order, or an nth-order differential equation. Graphing a First Order Differential Equation This section explains how to input a first order differential equation, draw a slope field, and graph the solution curve(s). • A slope field is the family of solutions of a single, first order differential equation of the form y’= f (x, y). It is a grid of solution lines where each line has the slope y’ for a given grid value of x and y. It is often referred to as a “slope field” or “direction field” because only the direction of the field at any given point in known, not the magnitude. • You can overlay, onto the slope field, solution curves of the first order differential equation input for given initial conditions on the [DiffEq] tab. u To input a first order differential equation and draw a slope field 0501 To input y’ = y2 − x and draw its slope field u To input initial conditions and graph the solution curves 0502 After performing the operation under example 0501 , to graph three solution curves for the initial conditions (xi, yi) = (0, 0), (0, 0.5), (0, 1) Tip: You can specify whether or not a solution curve should be drawn for each initial condition input on the initial condition editor. Use the initial condition editor to select the check box to the left of each initial condition input box (Initial Condition 1, Initial Condition 2, etc.) whose solution curve you want to graph. The solution curve of any initial condition whose check box is not selected will not be graphed. Chapter 5: Differential Equation Graph Application 123 Graphing a Second Order Differential Equation This section explains how to input a second order differential equation, draw a phase plane, and graph the solution curve(s). With this application, a second order differential equation is input in the form of a set of two first order differential equations. • A phase plane is the family of solutions of either a second order differential equation or two first order differential equations of the form x’ = dx/dt = f (x, y) and y’ = dy/dt = g(x, y). A single second order differential equation can also be graphed, but it must be written as two first order differential equations. • You can overlay, onto the phase plane, solution curves of the second order differential equation input on the [DiffEq] tab for given initial conditions. u To input a second order differential equation and draw a phase plane 0503 To input {x’ = x, y’ = −y} and draw its phase plane u To input initial conditions and graph the solution curves 0504 After performing the operation under example 0503 , to graph the solution curve of the initial condition (xi, yi) = (1, 1) Independent variable minimum value (tmin) = −7.7, maximum value (tmax) = 7.7, and initial value (t0) = 0 Graphing an Nth-order Differential Equation This section explains how to graph the solution curve(s) for an nth-order (higher order) differential equation based on specified initial conditions. With this application, an nth-order differential equation is input in the form of a set of multiple first order differential equations. Note: For nth-order differential equations, only solution curves are drawn. u To input an nth-order differential equation and initial conditions, and then graph the solution curves 0505 To specify the three initial conditions (xi, y1i, y2i) = (0, −1, 0), (0, 0, 0), (0, 1, 0) for the differential equation y” = x − y, and graph its solution curves Chapter 5: Differential Equation Graph Application 124 Configuring and Modifying Initial Conditions You can modify an existing initial condition on the Differential Equation Graph window by dragging it. You can also configure a new initial condition on the Differential Equation Graph window by tapping the coordinates you want to specify as the new initial condition. u To modify an initial condition on the Differential Equation Graph window 1. Perform the operation under example 0505 , which will produce a graph like the one shown below to appear on the Differential Equation Graph window. These dots are the currently configured initial conditions. 2. Tap [Analysis] - [Select] or G. 3. Tap one of the initial condition dots to select it, and then use the stylus to drag the dot to another location. • Here we will drag the bottom dot, which is the Initial Condition 1 setting (xi, y1i, y2i) = (0, −1, 0). The applicable initial condition will change to the coordinates of the location where you release the stylus after dragging the dot, and the solution curve will be redrawn accordingly. u To configure new initial conditions on the Differential Equation Graph window 1. Perform the operation under example 0501 to produce a slope field on the Differential Equation Graph window. 2. Tap [Analysis] - [Modify] or J. Chapter 5: Differential Equation Graph Application 125 3. On the Differential Equation Graph window, tap the coordinates that you want to specify as the new initial condition. • This will set the coordinates as the new initial condition and draw a solution curve. • The newly configured initial condition is added to the initial condition editor. To view it, tap the [IC] tab. Configuring Differential Equation Graph View Window Parameters You can set a number of graphing parameters on the View Window dialog box. This dialog box contains two tabs. The [Window] tab lets you set the window values and steps used for graphing a field. The [Solutions] tab contains parameters used for graphing solution curves. u To configure differential equation graph View Window settings 1. Tap 6 to display the View Window dialog box. 2. Input the required parameters on the [Window] and [Solutions] tabs. • See “Differential equation graph View Window parameters” below. 3. After the settings are the way you want, tap [OK]. Differential equation graph View Window parameters [Window] tab Setting Description xmin, xmax ymin, ymax Minimum/maximum value along the (horizontal) x-axis Field Specifies display of arrow, line or nothing. Steps Number of steps or field lines used for graphing a field Minimum/maximum value along the (vertical) y-axis [Solutions] tab The variable assignments available on the [Solutions] tab vary depending on the graph type selected with the Graph Editor. Some graph types have preset assignments for the independent, x-axis, and y-axis variables. If a value is preset for the current graph type the value will still be displayed on the Solutions tab, but you will not be able to change it. Chapter 5: Differential Equation Graph Application 126 Setting Description Solution Dir. A solution curve is graphed starting at the initial condition value t0 and continues until it reaches a target value, which can be either tmin or tmax. The solution direction determines the target values. Forward will graph the solution curve from t0 to tmax. Backward will graph the solution curve from t0 to tmin. Both will graph the solution curve from t0 to tmin, and then t0 to tmax. Independent Assignment of the independent variable for differential equations 1st-order, Nth-order: x or t 2nd-order: t (fixed) t0 (or x0) If the independent variable is different from the x-axis variable, you can enter the initial value for the independent variable (2nd-order and Nth-order only). tmin (or xmin), tmax (or xmax) x-Axis If the independent variable is different from the x-axis variable, you can enter the minimum/maximum value for the independent variable (2nd-order and Nth-order only). y-Axis Variable assignment for the (vertical) y-axis 1st-order, 2nd-order: y (fixed) Nth-order: independent variable or y1 through y10 Variable assignment for the (horizontal) x-axis 1st-order: same as independent variable 2nd-order: x (fixed) Nth-order: independent variable or y1 through y10 5-2 Drawing f (x) Type Function Graphs and Parametric Function Graphs f (x) type function graphs and parametric function graphs can be overlaid on differential equation graphs. u To draw an f (x) type function graph 0506 To overlay a differential equation graph with the graphs of y = x2 and y = −x2 u To draw a parametric function graph 0507 To graph {xt = 3sin(t) + 1, yt = 3cos(t) + 1} (Angle unit setting: radian, 0 s t s 2π) 5-3 Using Trace to Read Graph Coordinates The trace function let you read the coordinates on graphs drawn with the Differential Equation Graph application. There are three types of trace: “point trace” (shows the coordinates of any point), “field trace” (shows the coordinates of center of each field line), and “graph/curve trace” (shows the coordinates of points on a graph or solution curve). u To start a point trace On the Differential Equation Graph window, tap K. u To start a field trace Draw a slope field (page 123) or a phase plane (page 124), and then tap L. Chapter 5: Differential Equation Graph Application 127 u To start a graph/curve trace 1. Draw a solution curve (pages 123 through 124) or function graph (page 127). 2. Tap = or [Analysis] - [Trace]. 5-4 Graphing an Expression or Value by Dropping It into the Differential Equation Graph Window You can use the procedures in this section to graph an expression or value by dragging it from the eActivity application window or the Main application window, and dropping it into the Differential Equation Graph window. To draw this type of graph: Drop this type of expression or value into the Differential Equation Graph window: Slope field 1st-order differential equation in the form of y’ = f (x, y) Solution curve(s) of a 1storder differential equation Matrix of initial conditions in the following form: [[x1, y(x1)][x2, y(x2)] .... [xn, y(xn)]] • Note that the Slope field should already be graphed on the Differential Equation Graph window before the matrix is dropped in. If it isn’t, dropping in the matrix will simply plot points at the coordinates indicated by each (x, y) pair. • Regardless of whether or not the Slope field is already graphed, values in the dropped in matrix will be registered to the [IC] tab of the Differential Equation Editor. Solution curve(s) of an nthorder differential equation f (x) type function graph 1) nth-order differential equation such as y” + y’ + y = sin(x), followed by 2) Matrix of initial conditions in the following form: [[x1, y1(x1)][x2, y1(x2)] .... [xn, y1(xn)]] or [[x1, y1(x1), y2(x1)][x2, y1(x2), y2(x2)] .... [xn, y1(xn), y2(xn)]] Function in the form y = f (x) 0508 To drag the 1st-order differential equation y’ = exp(x) + x2 and then the initial condition matrix [0, 1] from the eActivity application window to the Differential Equation Graph window, and graph the applicable slope field and solution curve 0509 To drag the nth-order differential equation y” + y’ = exp(x) and then the initial condition matrix [[0, 1, 0] [0, 2, 0]] from the eActivity application window to the Differential Equation Graph window, and graph the applicable solution curves Tip: An nth-order differential equation of the form f (y’, y”…, x) dropped into the Differential Equation Graph window will be treated as f (y’, y”…, x) = 0. Chapter 5: Differential Equation Graph Application 128 Chapter 6: Sequence Application The Sequence application provides you with the tools you need to work with explicit sequences and recursive type sequences. Starting up the Sequence application displays two windows. 1 Sequence Editor window 1 Use this window to input expressions for creating a sequence table. 2 Table window Use this window to create and display table. (a) Title: Shows the equation used in the calculations. The title is not displayed when an item in column n is selected. (a) (b) 2 (b) Column names Sequence Application-Specific Menus and Buttons Sequence Editor window • Specify the recursion type ([Recursive] tab only)................................................. Type menu or ^&*( • Turn display of sequence table subtotals on or off ....................................................... a - Σdisplay - On/Off • Show (On) in the message box or hide (Off) the expression used to draw a figure with Sketch, or show the expression only when E is pressed (StepDisp)...................................................................... a - Set Sequence - On/Off/StepDisp • Clear the contents of the currently active tab sheet .............................................................. a - Clear Sheet • Delete the recursion expression in the current active line ..........................................................................w Sequence Table window • Draw a connect type graph ......................................................................................... Graph - Connect or $ • Draw a plot type graph ................................................................................................... Graph - G-Plot or ! • Save the contents of a table to a list .....................................................................................a - Table to List • Regenerate the currently displayed table ...................................................................................a - ReTable • Delete the currently displayed table ..................................................................................... a - Delete Table • Execute a table and graph link trace..................................................................................................a - Link • To input a recursion term, tap the [n, an] menu and then tap the term you want. If the [Explicit] tab is displayed, you can also use the toolbar’s B to input a term-n. Sequence RUN window • Input the “rSolve” function ........................................................................................................... Calc - rSolve • Input the “Σ” function ........................................................................................................................... Calc - Σ • Use the [n, an] menu to input recursion expression terms. You can also use the [a0, a1] menu to input system variables ranging from a0 to c2. Chapter 6: Sequence Application 129 Buttons common to multiple windows • Create an ordered pair table (Editor/Graph/RUN) ......................................................................................# • Create a sequence table with column(s) that determine if a sequence is an arithmetic sequence, geometric sequence, progression of difference, or Fibonacci sequence (Editor/Graph/RUN) ..........................) (arithmetic), _ (geometric), + (progression of difference), ` (Fibonacci) • Display the Sequence Table Input dialog box (Editor/Table/Graph/RUN) ..................................................8 • Draw a cobweb diagram on a graph (Editor/Table) ....................................................................................w • Display the Sequence RUN window (Editor/Table/Graph) .........................................................................` • Display the Sequence Editor window (Table/Graph/RUN) .........................................................................& 6-1 Recursive and Explicit Form of a Sequence ClassPad supports use of three types of sequence expressions: an+1=, an+2= and anE. Generating a Number Table In addition to an ordered pair table, you can create a sequence table with column(s). This helps you determine if the sequence is an arithmetic sequence, geometric sequence, progression of difference, or Fibonacci sequence. 3=2+1 3=7−4 Fibonacci Sequence Table Ordered Pair Table Arithmetic Sequence Table 5=8−3 3 = 18 ÷ 6 Geometric Sequence Table 0601 2 = 20 ÷ 10 Progression of Difference Table To create a number table (Fibonacci sequence table) to check the Fibonacci sequence expressed by the recursion formula an+2 = an+1 + an, a1 = 1, a2 = 1 Chapter 6: Sequence Application 130 Determining the General Term of a Recursion Expression You can use the rSolve function to convert the sequence expressed by a recursion expression to the general term format an = f (n). 0602 To determine the general term of the recursion expression an+1 = an + 2, a1 = 1 About rSolve The rSolve function returns the explicit formula of a sequence that is defined in relation to one or two previous terms, or a system of recursive formulas. Syntax: rSolve (Eq, initial condition-1[, initial condition-2] [ ) ] rSolve ({Eq-1, Eq-2}, {initial condition-1, initial condition-2} [ ) ] (Eq: Equation) Example: To obtain the n-th term of a recursion formula an+1 = 3an – 1 with the initial conditions a1 = 1 Calculating the Sum of a Sequence Perform the following steps when you want to determine the sum of a specific range of the sequence of a recursion expression or a general term expression. 0603 To calculate the sum of the general term expression anE = n2 + 2n – 1 in the range of 2 s n s 10 6-2 Graphing a Recursion ClassPad lets you graph the values in a number table you create, and draw a cobweb diagram from the recursion expression. 0604 To input the expression an+1 = 2an + 1, a1 = 1, create a number table, and graph the values in the table 0605 To input the expression an+1 = − 1, a1 = 0.5 and draw a cobweb diagram About LinkTrace While the Table and Graph windows are on the display, you can activate LinkTrace. To do this, tap in the Table window to make it active. Next, tap a and then [Link]. While LinkTrace is active, the pointer on the Graph window jumps automatically to the point indicated by the coordinates in the currently selected table cell. Note that LinkTrace does not work when the selected cell is in the first column (column n). Chapter 6: Sequence Application 131 Chapter 7: Statistics Application The Statistics application provides you with the tools you need to perform the operations below. Statistical data input (as list variables) Statistical graph drawing: Single-variable statistical graphs and paired-variable statistical graphs Statistical calculations: Single-variable, paired-variable, regression, test, confidence interval, and distribution calculations Tip: Performing a statistical calculation, graphing operation or other operation causes calculation results to be assigned to pre-determined system variables. For more information, see the “System Variable Table” on page 299. 7-1 Using Stat Editor When you start up the Statistics application, the Stat Editor window shown to the right appears on the display. List name Stat Editor is a tool for creating and maintaining lists (list variables), and it plays a very important role in ClassPad statistical calculations. ClassPad uses lists as data sources for statistical calculations and for statistical graphing. You can specify data by its list name. The list name is located in the cell at the top of each list. The initial default Stat Editor window shows six lists (columns), named list1 through list6. Basic List Operations You can use the Stat Editor window to input and edit the data in the initially displayed list1 through list6. You can also recall list variables you created with the Main application* and create new list variables. * See 0240 and 0241 in the separate “Examples” booklet. u To input data into a list 1. On the Stat Editor window, select the cell where you want to input the data item. • Use the cursor key to move the highlighting, or tap the cell with the stylus. “Cal'” line (see Tip on the next page) Number of line where data is being input Cell where data is being input Input data Chapter 7: Statistics Application 132 2. Input the data you want. • You can input values, formulas, or variable names. If you input a formula, the value of the calculation result will be input into the list. If you input a variable name, the value currently assigned to the variable (or the variable name itself in the case of an undefined variable) will be input into the list. • After you input a formula into a cell, the calculation result will be displayed as a decimal value or a fraction in accordance with the “Decimal Calculation” setting of the Basic Format dialog box (page 36). 3. Press E to store the data in the cell. Tip • Inputting a formula that includes a list (page 57) into a “Cal'” line and then pressing E will cause the calculation result list data to replace the contents currently in the list being input. For example, inputting {1,2,3}^2 into the “Cal'” line of list1 and then pressing E will cause list1 to be overwritten with {1,4,9}. Any data previously in list1 is lost. • A list can contain up to 9,999 rows. • A locked variable (page 30) causes the b icon to be displayed in the “Cal'” line, which cannot be edited. u To create a list 1. On the Stat Editor window, tap a list name cell to select it. 2. Enter up to eight bytes for the list name you want, and then press E. • This creates a list variable with the name you specified. After that, you can input data using the procedure under “To input data into a list”. • If you enter a list name that is already used for another list, pressing E displays the contents of that list. u To open an existing list 1. On the Stat Editor window, select the list name cell of the column where you want the list you will open to appear. • Instead of the above operation, you could also select any cell in the column where you want the list you will open to appear and then tap [Edit] - [Open List]. 2. Enter the variable name of the list you want to open, and then press E. • If you enter a variable name that does not match the names of any of the existing lists in step 1, a new list will be created using the name you entered. u To close a list Select the list name cell of the column of the list you want to close, and then press KE. Or, select any cell of the list you want to close, and then tap [Edit] - [Close List]. • This operation clears the list from the display only. The list is still stored as a list variable in memory, and can be opened when you need it again. Menus and Buttons Used for List Editing • Jump to line 1 of the current list ........................................................................................... Edit - Jump - Top • Jump to the line after the last line of the current list........................................................ Edit - Jump - Bottom • Sort list data ascending......................................................................................Edit - Sort - Ascending or L • Sort list data descending................................................................................. Edit - Sort - Descending or : • Delete a cell ............................................................................................................. Edit - Delete - Cell or H • Delete all of the data in a list .............................................................................. Edit - Delete - Column or J • Delete a list from memory ..................................................................................... Edit - Delete - List Variable • Insert a cell into a list ................................................................................................... Edit - Insert Cell or K • Select all the text in the currently selected cell ....................................................................... Edit - Select All Chapter 7: Statistics Application 133 • Clear list variable data from list1 through list6 and initialize Stat Editor window contents ..................................................................................................................Edit - Clear All • Convert a mathematical expression in the currently selected cell to a decimal value ................................9 • Display two, three, or four columns in the Stat Editor window*...................................................S / D / F * You can also specify the number of display columns using the [Cell Width Pattern] setting on the [Special] tab of the Graph Format dialog box (page 38). Using CSV Files You can import the contents of a CSV file stored with the ClassPad or transferred from a computer into the Stat Editor. You also can save the contents of all the list data in the Stat Editor as a CSV file. Import CSV File Requirements A CSV file that has been output from the Stat Editor or Spreadsheet (Chapter 13), or a CSV file transferred from a computer to storage memory can be used for import. The following types of CSV files are supported for import. • A CSV file that uses the comma (,) or semi-colon (;) as its separator, and the period (.) or comma (,) as its decimal symbol. A CSV file that uses the tab as its separator is not supported. • CR, LF and CRLF are supported for the line break code. For information about transferring files from a computer to the calculator, see “19-2 Performing Data Communication between the ClassPad and a Personal Computer”. Stat Editor Display and List Data Overwriting Following CSV File Import When you import a CSV file into Stat Editor, everything displayed on the Stat Editor screen is cleared and replaced with the imported CSV file data. The first column of the CSV file data is imported into the Stat Editor column 1 list (list 1), the second column of file data is imported into Stat Editor column 2 list (list 2), and so on. List data is created for each of the CSV file columns. Any data previously stored in a list is overwritten by the imported data. Except for data that is overwritten by the CSV file import, current list data cleared from the Stat Editor screen by the import operation is retained in ClassPad memory. u To import the contents of a CSV file to the Stat Editor 1. Prepare the CSV file you want to import. • See “Import CSV File Requirements” described above. 2. While the Stat Editor is on the display, tap [Edit] - [CSV] - [Open CSV]. 3. On the dialog box that appears, select the CSV file you want to import and then tap [Open]. Important! • Importing a CSV file that has a large number of rows and/or columns may cause an insufficient memory error. If this happens, reduce the number of rows and/or columns in the CSV file. • Following import, the contents of all cells that contain character strings are automatically replaced with 0. u To save the contents of all the list data in the Stat Editor as a single CSV file 1. While the Stat Editor is on the display, tap [Edit] - [CSV] - [Save CSV]. 2. On the dialog box that appears, specify the export destination folder and then input a name for the export file. 3. Tap [Save]. Important! The list name line and Cal' line are not output to the CSV file. Chapter 7: Statistics Application 134 u To specify the CSV file separator and decimal symbol 1. While the Stat Editor is on the display, tap [Edit] - [CSV] - [CSV Format]. 2. On the dialog box that appears, specify the desired settings for “CSV Separator” and “CSV Decimal Symbol”. 3. To save the settings, tap [OK]. 7-2 Drawing a Statistical Graph Up to nine graphs, including single-variable data and paired-variable data statistical graphs can be drawn simultaneously ([SetGraph] - [StatGraph1] to [StatGraph9]). In addition to graphs that can be drawn using [Set Graph], the graphs below can also be drawn at the same time. • Regression graphs (using [Linear Reg] and other regression commands on the [Calc] - [Regression] menu) • Function graphs (using the Graph & Table application’s Graph Editor window) Operation Flow Up to Statistical Graphing Drawing a statistical graph requires the following basic steps: (1) preparation of the list data to be used; (2) selection of the graph type and other graph settings; (3) drawing of the graph. u To prepare list data for statistical graphing Prepare the list data using one of the patterns shown below. Single Variable Paired Variable Without frequency With frequency Without frequency With frequency Single list Two lists Two lists Three lists Data Data Frequency Paired data Paired data Frequency Tip • Single-variable data is data that consists of a single value. If you are trying to obtain the average height of the members of a single class, for example, the single-variable would be height. With paired-variable statistical data there are two values for each data item. An example of paired-variable statistical data would be the change in size of an iron bar as its temperature changes. One variable would be temperature, and the other variable is the corresponding bar size. • If you created user list data with another application, open it in the Stat Editor window. For more information, see “To open an existing list” (page 133). You can specify a list displayed in the Stat Editor window as data to be used for statistical graphing. • You can display up to 99 lists on the Stat Editor window. Chapter 7: Statistics Application 135 u To configure statistical graph settings 1. On the Stat Editor window, tap [SetGraph] - [Setting…] or tap G. • This displays the Set StatGraphs dialog box. There are tabs named 1 through 9 that correspond to StatGraph1 through StatGraph9. • Each tab is assigned a color. Tabs [1] and [6]: Blue; Tabs [2] and [7]: Red; Tabs [3] and [8]: Green; Tabs [4] and [9]: Magenta; Tab [5]: Black 2. Tap the tab for the StatGraph setup whose configuration you want to change. 3. Configure the StatGraph setup settings you want as described below. Draw: Select the On setting if you want to draw the tab’s graph, or Off if you do not want to draw it. After closing the dialog box, tap y on the toolbar to execute the graph draw operation. Type: Selects the type of graph to be drawn. The types of graphs available for selection depend on whether the graph data is single-variable or paired-variable. Single-variable NPPlot, Histogram, MedBox, NDist, Broken Paired-variable Scatter, xyLine, LinearR, MedMed, QuadR, CubicR, QuartR, LogR, ExpR, abExpR, PowerR, SinR, LogisticR For details about each graph type, see “Graphing Single-Variable Statistical Data” (page 136) and “Graphing Paired-Variable Statistical Data” (page 137). XList, YList, Freq: Specifies the list data to be used for graphing. If you prepared frequency list data, use Freq to specify the frequency list. Mark: This setting is supported only when Scatter, xyLine, or NPPlot is specified for “Type”. Select square (q), cross (w), large dot (;) or dot (') as the shape for graph lot points. 4. Tap [Set] to apply the settings for the tab you selected in step 2. u To draw a statistical graph 1. On the Stat Editor window, tap [SetGraph], and then confirm that there is at least one item from [StatGraph1] to [StatGraph9] whose check box is selected. • If no check box is selected, select at least one check box. Selecting multiple check boxes will cause the corresponding graphs to be drawn simultaneously. 2. Configure the a - [Stat Window Auto] - [On] / [Off] setting as required. • Selecting [On] for this setting configures View Window settings for drawing statistical graphs automatically. See “Graph Format Dialog Box” (page 38) for details. 3. Tap y to display the Stat Graph window and draw the statistical graphs. 0701 To input the paired-variable data shown below and then plot the data on a scatter plot list1 = 0.5, 1.2, 2.4, 4.0, 5.2 list2 = −2.1, 0.3, 1.5, 2.0, 2.4 Graphing Single-Variable Statistical Data You can produce any of the graphs described below using single-variable data. The text in the parentheses of the graph names below shows text that appears on the Type menu of the Set StatGraphs dialog box. Normal Probability Plot (NPPlot) The normal probability plot plots data against a theoretical normal distribution using a scatter plot. If the scatter plot is close to a straight line, then the data is approximately normal. A departure from the straight line indicates a departure from normality. Chapter 7: Statistics Application 136 Med-Box Plot (MedBox) This type of graph is often called a “Box and Whisker” graph. It lets you see how a large number of data items are grouped within specific ranges. The lines from minX to Q1, and from Q3 to maxX are called “whiskers”. If [Show Outliers] box is checked on the Set StatGraphs dialog box (page 136), “outlier” square symbols are shown instead of “whisker” lines where a data value is relatively large or small compared to the other data values. minX Q1 Med Q3 maxX Normal Distribution Curve (NDist) The normal distribution curve is graphed using the following normal distribution function. 2 y= 1 2πσ e – (x–x) 2σ 2 Histogram Bar Graph (Histogram), Broken Line Graph (Broken) A histogram shows the frequency (frequency distribution) of each data class as a rectangular bar. Classes are on the horizontal axis, while frequency is on the vertical axis. In the broken line graph, lines connect the pointers that fall at the center of each histogram bar. The Set Interval dialog box appears before the graph is drawn. You can use this dialog box to change the start value (HStart) and step value (HStep) of the histogram, if you want. Graphing Paired-Variable Statistical Data You can produce any of the graphs described below using paired-variable data. The text in the parentheses of the graph names below shows text that appears in the Type menu of the Set StatGraphs dialog box (page 136). k Plot graphs Draws graphs by plotting paired-variable points with x data on the horizontal axis and y data on the vertical axis. Scatter plot (Scatter) xy line graph (xyLine) Chapter 7: Statistics Application 137 k Regression graphs Regression graphs of each of the paired-variable data can be drawn according to the model formulas under “Regression types” below. Linear regression graph Quadratic regression graph Logistic regression graph Regression types: Linear regression (LinearR) [Linear Reg] .............................................................. y = aⴢx + b, y = a + bⴢx Linear regression uses the method of least squares to determine the equation that best fits your data points, and returns values for the slope and y-intercept. The graphic representation of this relationship is a linear regression graph. Med-Med line (MedMed) [MedMed Line] ................................................................................... y = aⴢx + b When you suspect that the data contains extreme values, you should use the Med-Med graph (which is based on medians) in place of the linear regression graph. Med-Med graph is similar to the linear regression graph, but it also minimizes the effects of extreme values. Quadratic regression (QuadR) [Quadratic Reg] ............................................................. y = aⴢx2 + bⴢx + c Cubic regression (CubicR) [Cubic Reg]................................................................ y = aⴢx3 + bⴢx2 + cⴢx + d Quartic regression (QuartR) [Quartic Reg] ................................................. y = aⴢx4 + bⴢx3 + cⴢx2 + dⴢx + e Quadratic, cubic, and quartic regression graphs use the method of least squares to draw a curve that passes the vicinity of as many data points as possible. These graphs can be expressed as quadratic, cubic, and quartic regression expressions. Logarithmic regression (LogR) [Logarithmic Reg] .................................................................... a + bⴢln(x) Logarithmic regression expresses y as a logarithmic function of x. The normal logarithmic regression formula is y = a + bⴢln(x). If we say that X = ln(x), then this formula corresponds to the linear regression formula y = a + bⴢX. aⴢebx Exponential regression (ExpR) [Exponential Reg]............................................................. y = aⴢebⴢx Exponential regression can be used when y is proportional to the exponential function of x. The normal exponential regression formula is y = aⴢebⴢx. If we obtain the logarithms of both sides, we get ln(y) = ln(a) + bⴢx. Next, if we say that Y = ln(y) and A = In(a), the formula corresponds to the linear regression formula Y = A + bⴢx. aⴢb x Exponential regression (abExpR) [abExponential Reg] ........................................................ y = aⴢbx Exponential regression can be used when y is proportional to the exponential function of x. The normal exponential regression formula in this case is y = aⴢbx. If we take the natural logarithms of both sides, we get ln(y) = ln(a) + (ln(b))ⴢx. Next, if we say that Y = ln(y), A = ln(a) and B = ln(b), the formula corresponds to the linear regression formula Y = A + Bⴢx. Power regression (PowerR) [Power Reg] ...................................................................................... y = aⴢxb Power regression can be used when y is proportional to the power of x. The normal power regression formula is y = aⴢxb. If we obtain the logarithms of both sides, we get ln(y) = ln(a) + bⴢln(x). Next, if we say that X = ln(x), Y = ln(y), and A = ln(a), the formula corresponds to the linear regression formula Y = A + bⴢX. Sinusoidal regression (SinR) [Sinusoidal Reg] ........................................................ y = aⴢsin(bⴢx + c) + d Sinusoidal regression is best for data that repeats at a regular fixed interval over time. Chapter 7: Statistics Application 138 Logistic regression (LogisticR) [Logistic Reg] .................................................................... y = c 1 + aⴢe–bⴢx Logistic regression is best for data whose values continually increase over time, until a saturation point is reached. Tip: Though ClassPad internally performs regression calculations after drawing a regression graph using the settings of the Set StatGraphs dialog box (page 136), the calculation results (regression formula coefficients and other values) cannot be displayed. To display regression calculation results, use the commands on the [Calc] - [Regression] menu, which are shown in square brackets ([ ]) above. Overlaying a Regression Graph on a Scatter Plot You can use the Set StatGraphs dialog box (page 136) to plot a scatter plot* from paired-variable data and then overlay a regression graph on it. This means you can visually determine which regression formula is closest to the scatter plot. * You can also overlay on other graph types as well. u ClassPad Operation 1. Draw the scatter plot. Here we will use the operation under 0701 in the separate “Examples” booklet. 2. On the [Calc] - [Regression] menu, select one of the regression calculation commands (from [Linear Reg] to [Logistic Reg]). • Here we will select [Logarithmic Reg]. This displays the Set Calculation dialog box. 3. Here, we want to overlay on a scatter plot, so we specify XList, YList, and Freq the same as in step 1 of the procedure for drawing a scatter plot. 4. Tap [OK]. • This displays the Stat Calculation dialog box. For information about this dialog box’s contents, see “Performing Regression Calculations” (page 143). 5. Tap [OK]. • This draws the regression calculation graph over the scatter plot. This regression graph is always drawn in blue. • You can perform trace (page 111) on a regression graph. Trace scroll, however, is not supported when a scatter plot is displayed. Tip • When performing Sinusoidal regression, make sure that “Radian” is selected for the [Angle] setting on the Basic Format dialog box (page 36). The graph cannot be drawn correctly when the [Angle] setting is anything other than “Radian”. • When performing Sinusoidal regression or Logistic regression, certain types of data may cause calculation to take a long time. This is normal and does not indicate malfunction. Chapter 7: Statistics Application 139 • Whenever you perform a regression calculation from the [Calc] - [Regression] menu, the [Previous Reg] check box on the [SetGraph] menu is selected automatically. This tells ClassPad to remember the calculation results produced by the last executed regression calculation command (the menu command selected in step 2 of the above procedure). As long as the [Previous Reg] check box is selected, any time you draw a new graph, it is drawn based on the last regression calculation results. To cancel drawing of this regression graph, clear the check box next to [Previous Reg] before re-drawing the graph. Overlaying a Function Graph on a Statistical Graph You can overlay an existing statistical graph with any type of function graph. Function graphs that can be overlaid are graphs of functions registered on the Graph Editor window of the Graph & Table application (Chapter 3). The Graph Editor window can also be accessed from the Statistics application. u ClassPad Operation 1. Draw a statistical graph as described under “Operation Flow Up to Statistical Graphing” (page 135). 2. Tap ! to display the Graph Editor window. 3. Input the function. 4. Select the check boxes of all the functions you want to graph, and clear the check boxes of all the functions you do not want to graph. 5. Tap y on the Graph Editor window. • This draws the function graph on the statistical graph. • To close the Graph Editor window, Tap ! to make it active, and then tap C. Tip: While the Stat Editor window [SetGraph] - [Graph Function] check box (or the Stat Graph window a - [Graph Function] check box) is selected, each tap of y on the Stat Editor window will draw the statistical graph along with a graph of the function registered by the Graph Editor window of the Graph & Table application. Stat Graph Window Menus and Buttons • Display the Stat Editor window ...................................................................................................................( • Display the Graph Editor window ................................................................................................................! • Redraw the displayed graph ............................................................................................. a - ReDraw or " • Display the View Window dialog box ........................................................................O - View Window or 6 • Start a trace operation .................................................................................................Analysis - Trace or = • Display the Set StatGraphs dialog box .......................................................................................................G • Display the Main application work area window .........................................................................................~ • Pan the window...........................................................................................................................................T • Toggle the [Stat Window Auto] setting between auto and manual .............................................................s Note • For details about the commands included on the Calc menu, see sections 7-3 and 7-4 of this manual. • For information about Zoom, Analysis - Trace, Analysis - Sketch, and the commands included in the a menu, see “Chapter 3: Graph & Table Application”. Chapter 7: Statistics Application 140 7-3 Performing Basic Statistical Calculations Mean, standard deviation, and other statistical values can be obtained from single-variable data and pairedvariable data. Regression calculation can also be performed on paired-variable data. All of these calculations are performed using [Calc] menu commands. Calculating Statistical Values You can use the procedure below to display a lists of various single-variable and paired-variable statistical values. u To display single-variable calculation results 1. On the Stat Editor window or Stat Graph window, tap [Calc] - [One-Variable]. 2. On the dialog box that appears, specify the [XList] name, select the [Freq] setting, and then tap [OK]. • This displays the dialog box with the single-variable statistical calculation results described below. o: sample mean Q1: first quartile Σx: sum of data Med: median Σx2: sum of squares Q3: third quartile σx: population standard deviation maxX: maximum sx: sample standard deviation Mode: n: sample size ModeN: number of data mode items minX: minimum mode* ModeF: data mode frequency * If “Mode = 'ModeStat” is displayed, it means that solutions are stored in the “ModeStat” system variable. To view the “ModeStat” contents, tap any list name cell on the Stat Editor window, input “ModeStat”, and then press E. Calculation Methods for Q1, Q3 and Median Q1 and Q3 can be calculated in accordance with the [Q1, Q3 on Data] setting on the Basic Format dialog box (page 36) as described below. [Q1, Q3 on Data] unchecked (default): (a) When all Frequency values are integers With this calculation method, processing depends on whether the number of elements n in the population is an even number or odd number. Example: n = 8 Example: n = 9 Lower half group 1 2 3 Upper half group 4 5 6 7 Lower half group 8 1 2 3 Q1 Median Q3 Q1 2+3 2 4+5 2 6+7 2 2+3 2 4 Upper half group 5 Median 6 7 8 9 Q3 7+8 2 When n is an even number, using the center point of the total population as the reference, the population elements are divided into two groups: a lower half group and an upper half group. Q1 and Q3 then become the values described below. Q1 = {median of the group of n/2 items from the bottom of the population} Q3 = {median of the group of n/2 items from the top of the population} Median = {center point of the total population} Chapter 7: Statistics Application 141 When n is an odd number, using the median of the total population as the reference, the population elements are divided into two groups: values less than the median and values greater than the median. The median value is excluded. Q1 and Q3 then become the values described below. Q1 = {median of the group of (n − 1)/2 items from the bottom of the population} Q3 = {median of the group of (n − 1)/2 items from the top of the population} Median = {center point of the total population} When n = 1, Q1 = Q3 = Median = population center point. (b) When Frequency includes decimal fraction values The Q1, Q3 and Median values for this calculation method are described below. Q1 = {value of element whose cumulative frequency ratio is greater than 1/4 and nearest to 1/4} When the cumulative frequency ratio for some data value is exactly 0.25, Q1 is the average of that data value and the next data value. Q3 = {value of element whose cumulative frequency ratio is greater than 3/4 and nearest to 3/4} When the cumulative frequency ratio for some data value is exactly 0.75, Q3 is the average of that data value and the next data value. Median = {value of element whose cumulative frequency ratio is greater than 1/2 and nearest to 1/2} When the cumulative frequency ratio for some data value is exactly 0.5, Median is the average of that data value and the next data value. The following shows an actual example of the above. Data Value Frequency Cumulative Frequency Cumulative Frequency Ratio 1 0.1 0.1 0.1/1.0 = 0.1 2 0.1 0.2 0.2/1.0 = 0.2 3 0.2 0.4 0.4/1.0 = 0.4 4 0.3 0.7 0.7/1.0 = 0.7 5 0.1 0.8 0.8/1.0 = 0.8 6 0.1 0.9 0.9/1.0 = 0.9 7 0.1 1.0 1.0/1.0 = 1.0 • 3 is the value whose cumulative frequency ratio is greater than 1/4 and nearest to 1/4, so Q1 = 3. • 5 is the value whose cumulative frequency ratio is greater than 3/4 and nearest to 3/4, so Q3 = 5. • 4 is the value whose cumulative frequency ratio is greater than 1/2 and nearest to 1/2, so Median = 4. [Q1, Q3 on Data] checked: The Q1, Q3 and Median values for this calculation method are described below. Q1 = {value of element whose cumulative frequency ratio is greater than or equal to 1/4 and nearest to 1/4} Q3 = {value of element whose cumulative frequency ratio is greater than or equal to 3/4 and nearest to 3/4} The following shows an actual example of the above. (Number of Elements: 10) Data Value Frequency Cumulative Frequency Cumulative Frequency Ratio 1 1 1 1/10 = 0.1 2 1 2 2/10 = 0.2 3 2 4 4/10 = 0.4 4 3 7 7/10 = 0.7 5 1 8 8/10 = 0.8 6 1 9 9/10 = 0.9 7 1 10 10/10 = 1.0 Chapter 7: Statistics Application 142 3 is the value whose cumulative frequency ratio is greater than or equal to 1/4 and nearest to 1/4, so Q1 = 3. 5 is the value whose cumulative frequency ratio is greater than or equal to 3/4 and nearest to 3/4, so Q3 = 5. Reference Point (0.25) 0.1 0.2 1 2 Reference Point (0.75) 0.4 3 3 4 Q1 4 0.7 0.8 0.9 1.0 4 5 6 7 Q3 • Median is calculated using the same method as that used when the [Q1, Q3 on Data] check box is unchecked. • It makes no different whether frequency values are all integers or include decimal fraction values when the [Q1, Q3 on Data] check box is selected. u To display paired-variable calculation results 1. On the Stat Editor window or Stat Graph window, tap [Calc] - [Two-Variable]. 2. On the dialog box that appears, specify the [XList] and [YList] names, select the [Freq] setting, and then tap [OK]. • This displays the dialog box with the paired-variable statistical calculation results described below. o, p : sample mean Σx, Σy : sum of data n: sample size Σxy : sum of products of XList and YList data Σx2, Σy2 : sum of squares σx, σy : sx, sy : population standard deviation minX, minY : minimum maxX, maxY : maximum sample standard deviation Performing Regression Calculations You can use the procedures under “Overlaying a Regression Graph on a Scatter Plot” (page 139) to specify a model formula, and determine and graph the regression formula for paired-variable data. The dialog box that appears when performing these operations provides the coefficients, constant term, and other values for the regression formula. You can also copy the regression formula to the Graph Editor window and perform residual calculation (which calculates the distance between the regression model and an actual plotted point during regression calculations). u To view regression calculation results 1. On the [Calc] - [Regression] menu, select one of the regression calculation commands (from [Linear Reg] to [Logistic Reg]). • For information about regression calculation characteristics, see “Regression graphs” (page 138). Model formula 2. On the dialog box that appears, specify the [XList] and [YList] names, and select the [Freq] setting. Chapter 7: Statistics Application 143 3. Tap [OK]. • This displays the dialog box with the regression calculation results described below. a, b, c, d, e : coefficients of the model formula (shown at the top of the dialog box) corresponding to the regression calculation r: correlation coefficient (linear regression, logarithmic regression, exponential regression, and power regression only) r2 : coefficient of determination (except for Med-Med, sinusoidal regression, and logistic regression) MSe : mean square error (except for Med-Med) MSe Formulas Depending on the regression calculation type, mean square error (MSe) is obtained using the following formulas. Linear: Quadratic: Quartic: 1 n–3 1 n–5 Sinusoidal: 2 i i i 2 i i=1 ; i 4 i + bxi3 + cxi2 + dxi + e))2 i=1 n Σ (ln y – (ln a + bx )) i 2 i i=1 ; 1 aⴢbx: n – 2 n Σ (ln y – (ln a + b ln x )) i i n Σ (y – (a + bx )) i 2 Logistic: i=1 i 2 i=1 Cubic: n Σ (y – (ax 1 y = a + bⴢx: n – 2 1 n–4 1 Logarithmic: n – 2 + bxi + c))2 i=1 1 1 n–2 1 n–2 Σ (y – (ax + b)) n Σ (y – (ax Exponential: aⴢebⴢx: n – 2 Power: n 1 y = aⴢx+b: n – 2 n Σ (y – (ax i 3 i + bxi2 + cxi + d ))2 i=1 n Σ (y – (a + b ln x )) i 2 i i=1 n Σ (ln y – (ln a + (ln b)ⴢ x )) i i 2 i=1 1 n–2 n Σ yi – i=1 C 1 + ae–bxi 2 n Σ (y – (a·sin (bx i i 2 + c) + d )) i=1 u To copy a regression formula to the Graph & Table application 1. Perform steps 1 and 2 under “To view regression calculation results” (page 143). 2. On the dialog box that appears, tap the [Copy Formula] down arrow button, and then select the Graph & Table line number (y1 through y20) to which you want to copy the formula. 3. Tap [OK]. • This copies the calculated regression expression to the line (y1 through y20) you selected. u To perform residual calculation 1. Perform steps 1 and 2 under “To view regression calculation results” (page 143). 2. On the dialog box that appears, tap the [Copy Residual] down arrow button, and then select [On] or the list into which you want to copy the residual values. 3. Tap [OK]. • This assigns residual data to a system variable named “residual” (and also to the list if you specify a list in step 2). • Values assigned to the “residual” system variable shows the vertical distances between actually plotted points and the regression model. A positive value indicates a plot that is higher than the regression model, while a negative value indicates a plot that is lower. You can use the following procedure to view the current “residual” system variable values. 1. On the Stat Editor window, select any cell in the column where you want the list you will open to appear and then tap [Edit] - [Open List]. 2. Enter “residual”, and then press E. Chapter 7: Statistics Application 144 Viewing the Results of the Last Statistical Calculation Performed (DispStat) To view the results of the last statistical calculation performed using a [Calc] menu command*, tap [Calc] [DispStat]. * Including test, confidence interval and distribution calculations. 7-4 Performing Advanced Statistical Calculations You can perform test, confidence interval and distribution calculations using the wizard that you launch by tapping [Calc] on the menu bar. Performing Test, Confidence Interval and Distribution Calculations Using the Wizard ClassPad includes built-in commands* for performing test, confidence interval, and distribution calculations. The Statistics application lets you perform these types of calculations by simply inputting values and specifying required information in accordance with instructions displayed by a wizard. This eliminates the need to input commands and their arguments directly. * For information about command syntax, see “12-4 Program Command Reference”. u ClassPad Operation 1. On the Stat Editor window, tap [Calc] and then tap [Test], [Interval], [Distribution] or [Inv. Distribution]. • This displays the Wizard window in the lower half of the screen. • Selecting the [Help] check box causes the Wizard window to fill the display, and displays the description of the command. 2. On the Command menu, select the command you want to execute. • For information about what is calculated Type menu by each command, see “Tests” (page Command menu 146), “Confidence Intervals” (page 149), and “Distributions” (page 151). 3. Select “List” to use list data for calculation, or “Variable” to directly input values using a wizard. • Certain commands require data of a specific type (list, variable, or matrix) for calculation. For such commands, you will not be provided with a choice of data type options. Help text Displayed when the [Help] check box is selected. Chapter 7: Statistics Application 145 4. Tap [Next >>]. • This displays a screen for specifying conditions and inputting values. • Initially, the top item on the screen will be selected, with help text about the top item shown at the bottom of the screen. Tapping another item will select it and display help text about it. 5. Input values and configure settings for each of the items on the screen. 6. Tap [Next >>]. • This displays the calculation results. 7. Tap $ to graph the results. • You cannot graph interval calculations and inverse distribution calculations. Tip: You can back-step through the wizard by tapping [<< Back]. After returning to a previous screen you can change settings and values and recalculate results. Closing the wizard screen clears all settings and values. Tests The Z Test provides a variety of different tests based on standard deviation based tests. They make it possible to test whether or not a sample accurately represents the population when the standard deviation of a population (such as the entire population of a country) is known from previous tests. The t Test is used instead of the Z Test when the population standard deviation is unknown. You can also perform χ2 Test, ANOVA (analysis of variance), and other test calculations. The following describes the ClassPad commands for executing each type of statistical test calculation. It includes the calculation formula used and a general overview of each command. n) 1-Sample Z Test .... [Test] - [One-Sample Z-Test] ..... z = (o – μ0)/(σ/' Tests a single sample mean against the known mean of the null hypothesis when the population standard deviation is known. The normal distribution is used for the 1-Sample Z test. 0702 To specify ≠ 0, σ = 3 for n (sample size) = 48, o (sample mean) = 24.5 data and perform a 1-Sample Z Test Chapter 7: Statistics Application 146 0703 To specify > 120, σ = 19 for the data in lists to the right (list1 = data, list2 = frequency) and perform a 1-Sample Z Test 2-Sample Z Test .... [Test] - [Two-Sample Z-Test] ..... Tests the difference between two means when the standard deviations of the two populations are known. The normal distribution is used for the 2-Sample Z test. 1-Proportion Z Test .... [Test] - [One-Prop Z-Test] ..... z = (x/n – p0)/ p0(1 – p0)/n Tests a single sample proportion against the known proportion of the null hypothesis. The normal distribution is used for the 1-Proportion Z test. 2-Proportion Z Test .... [Test] - [Two-Prop Z-Test] ..... z = (x1/n1 – x2/n2)/ p̂ (1 – p̂ )(1/n1 + 1/n2) Tests the difference between two sample proportions. The normal distribution is used for the 2-Proportion Z test. n) 1-Sample t Test .... [Test] - [One-Sample t-Test] ..... t = (o – μ0)/(sx/' Tests a single sample mean against the known mean of the null hypothesis when the population standard deviation is unknown. The t distribution is used for the 1-Sample t test. 2-Sample t Test .... [Test] - [Two-Sample t-Test] Tests the difference between two means when the standard deviations of the two populations are unknown. The t distribution is used for the 2-Sample t test. When the two population standard deviations are equal (pooled) = (o1 − o2)/ s2(1/ = 1+ 2−2 s = (( When the two population standard deviations are not equal (not pooled) 1 − 1)s12 + ( + 1/ 2) 2 − 1)s22)/( 1 + 2 − 2) = (o1 − o2)/ s12/ 1 + s22/ 2 = 1/(2/( 1 − 1) + (1 − )2/( 2 − 1)) = (s12/ 1)/(s12/ 1 + s22/ 2) Linear Regression t Test .... [Test] - [Linear Reg t-Test] ..... = ( − 2)/(1 − = Y ( − o)( − p)/ Y( − o)2 1 2 ) = p − o n: sample size (nt3) Tests the linear relationship between the paired variables (x, y). The method of least squares is used to determine a and b, which are the coefficients of the regression formula y = a + bx. The p-value is the probability of the sample regression slope (b) provided that the null hypothesis is true, = 0. The t distribution is used for the linear regression t test. Chapter 7: Statistics Application 147 R 2 χ2 Test (Chi-square Test) .... [Test] - [χ2 Test] .... χ = ' ( ' − ')2 ' R R ' ' , ' = ' × ' / ' Tests the independence of two categorical variables arranged in matrix form. The χ2 test for independence compares the observed matrix to the expected theoretical matrix. The χ2 distribution is used for the χ2 test. • The minimum size of the matrix is 1 × 2. An error occurs if the matrix has only one column. • The result of the expected frequency calculation is stored in the system variable named “Expected”. 0704 To specify observed matrix: a = 11 68 3 and perform a χ2 test 9 23 5 χ2 GOF Test (Chi-square Goodness-of-Fit Test) .... [Test] - [χ2 GOF Test] χ2 = Y (" − # )2 # $ = ("% − #% )2 ("& − #& )2 (" − # )2 #% #& # Oi: The i-th element of the observed list, Ei: The i-th element of the expected list Tests whether the observed count of sample data fits a certain distribution. For example, it can be used to determine conformance with normal distribution or binomial distribution. Tip: The calculation results χ2, p, df, and Contrib are stored in the system variables named “χ2value”, “prob”, “df”, and “Contrib” respectively. 0705 To specify observed list: list1 = {1,2,3}, expected list: list2 = {4,5,6}, and df = 1, and then perform a χ2 test 2-Sample F Test .... [Test] - [Two-Sample F-Test] ..... = s12 /s22 Tests the ratio between sample variances of two independent random samples. The F distribution is used for the 2-Sample F test. One-Way ANOVA (analysis of variance) .... [Test] - [One-Way ANOVA] Tests the hypothesis that the population means of multiple populations are equal. It compares the mean of one or more groups based on one independent variable or factor. 0706 To use Factor A data of list1 = {7,4,6,6,5}, list2 = {6,5,5,8,7}, and list3 = {4,7,6,7,6}, and perform OneWay ANOVA Tip • To perform One-Way ANOVA using the wizard, you need to create up to six sets of list data (Factor A level 1 data, level 2 data, etc.). Specify the list data on the wizard screen and perform the calculation. • One-Way ANOVA can also be performed using a program command (see the example 1209 under “Including Statistical Graphing and Calculation Functions in a Program” on page 225). To perform One-Way ANOVA using a program command, you need to create a “DependentList” that includes all Factor A level data (level1, level2, etc.) and a “FactorList(A)” that specifies the levels for each of the blocks of data in the DependentList. If you use the program command to perform the same test as shown in the example above, the two lists would be as shown below. DependentList: {7,4,6,6,5,6,5,5,8,7,4,7,6,7,6} ... (All level 1, level 2, and level 3 data) FactorList(A): {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3} ... (Levels of each block of data) Chapter 7: Statistics Application 148 Two-Way ANOVA .... [Test] - [Two-Way ANOVA] Tests the hypothesis that the population means of multiple populations are equal. It examines the effect of each variable independently as well as their interaction with each other based on a dependent variable. 0707 The values in the table below are measurement results that show how the durability of a metal product is affected by changes in heat treatment time (A) and temperature (B). Experiments were conducted twice under each condition. Temperature B1 Temperature B2 Time A1 113, 116 139, 132 Time A2 133, 131 126, 122 Perform analysis of variance on the null hypotheses listed below, using a 5% level of significance. H0: Change in time does not affect durability. H0: Change in treatment temperature does not affect durability. H0: Changes in time and treatment temperature do not affect durability. Use the Two-Way ANOVA test to test the above hypotheses. Input the following measurement data into the indicated lists. This data is from the table above. list1 = {113, 116} … (Factor A1 × B1), list2 = {139, 132} … (Factor A1 × B2) list3 = {133, 131} … (Factor A2 × B1), list4 = {126, 122} … (Factor A2 × B2) Tip • To perform Two-Way ANOVA using the wizard, you need to create list data in the quantity of data table vertical (number of Factor A levels) × horizontal (number of Factor B levels). Specify the list data on the wizard screen and perform the calculation. The dimensions that can be specified for Factor A × Factor B are shown in the screen to the right. • Two-Way ANOVA can also be performed using a program command (see the example 1210 under “Including Statistical Graphing and Calculation Functions in a Program” on page 225). To perform Two-Way ANOVA using a program command, create a “DependentList” that includes all Factor A × Factor B level data, and “FactorList(A)” and “FactorList(B)” lists that specify the levels for each of the blocks of data in the DependentList. If you use the program command to perform the same test as shown in the example above, the three lists would be as shown below. DependentList = {113,116,139,132,133,131,126,122} FactorList(A) = { 1, 1, 1, 1, 2, 2, 2, 2 } FactorList(B) = { 1, 1, 2, 2, 1, 1, 2, 2 } Confidence Intervals A confidence interval is a range of values that has a specified probability of containing the parameter being estimated. A confidence interval that is too broad makes it difficult to get an idea of where the parameter (actual value) is located. A narrow confidence interval, on the other hand, limits the parameter range and makes it possible to obtain highly accurate results. The commonly used confidence levels are 68%, 95% and 99%. With a confidence interval of 95%, for example, there is a 5% probability that a parameter will not be within the interval. The following describes the ClassPad commands for executing each type of confidence interval calculation. It includes an overview of each command and the formulas to obtain the confidence interval lower limit (Lower) and upper limit (Upper). Chapter 7: Statistics Application 149 Lower, Upper = o Z α σ 1-Sample Z Interval .... [Interval] - [One-Sample Z Int] 2 Calculates the confidence interval for the population mean based on a sample mean and known population standard deviation. 0708 n To specify the data below and perform a 1-Sample Z Interval calculation list1: {299.4, 297.7, 301, 298.9, 300.2, 297} Population standard deviation: 3 Significance level: 5% ( = confidence level: 95%) 2-Sample Z Interval .... [Interval] - [Two-Sample Z Int] Lower, Upper = (o1 – o2) Z α 2 Calculates the confidence interval for the difference between population means based on the difference between sample means when the population standard deviations are known. 1-Proportion Z Interval .... [Interval] - [One-Prop Z Int] Lower, Upper = nx Z α 2-Proportion Z Interval .... [Interval] - [Two-Prop Z Int] Lower, Upper = σ12 σ22 + n1 n2 1 x 1– x n 2 n n Calculates the confidence interval for the population proportion based on a single sample proportion. Calculates the confidence interval for the difference between population proportions based on the difference between two sample proportions. x1 x2 x2 x1 n1 1– n1 n2 1– n2 + n1 n2 x1 x2 α n1 – n2 Z 2 Lower, Upper = o tn –1 α sx 1-Sample t Interval .... [Interval] - [One-Sample t Int] 2 Calculates the confidence interval for the population mean based on a sample mean and a sample standard deviation when the population standard deviation is not known. n 2-Sample t Interval .... [Interval] - [Two-Sample t Int] Calculates the confidence interval for the difference between population means based on the difference between sample means and sample standard deviations when the population standard deviations are not known. When the two population standard deviations are equal (pooled) Lower, Upper = oo s= (( When the two population standard deviations are not equal (not pooled) 2 1 – 1)s1 + ( 2 – 1)s2 )/( α 2 Lower, Upper = (o1 – o2) tdf 2 df = 1/(C 2/(n1 – 1) + (1 – C)2/(n2 – 1)) s 1 + 2 – 2) sx12 sx22 n1 + n2 C = (sx12/n1)/(sx12/n1 + sx22/n2) General Confidence Interval Precautions If you input a C-Level (confidence level) value in the range of 0 s C-Level < 1, the value you input is used. To specify a C-Level of 95%, for example, input “0.95”. Chapter 7: Statistics Application 150 Distributions There is a variety of different types of distribution, but the most well-known is “normal distribution”, which is essential for performing statistical calculations. Normal distribution is a symmetrical distribution centered on the greatest occurrences of mean data (highest frequency), with the frequency decreasing as you move away from the center. Poisson distribution, geometric distribution, and various other distribution shapes are also used, depending on the data type. Tip: Though list data can be used within the argument of a Distribution function (page 85), list data cannot be used in the argument of the Statistics Wizard operations described here. The following describes the ClassPad commands for executing each type of distribution calculation. It includes the calculation formula used and a general overview of each command. Normal Probability Density .... [Distribution] - [Normal PD] f (x) = Calculates the normal probability density for a specified value. Specifying σ = 1 and = 0 produces standard normal distribution. 0709 1 e– 2π σ (x – μμ)2 ( σ > 0) 2σ 2 To calculate normal probability density for the data below and graph the result Data: 37.5 Population standard deviation: 2 Population mean: 35 Normal Cumulative Distribution .... [Distribution] - [Normal CD] dx Calculates the cumulative probability of a normal distribution between a lower bound (a) and an upper bound (b). 0710 To calculate normal cumulative distribution for the data below and graph the result Lower bound: −∞ Population standard deviation: 2 Upper bound: 36 Population mean: 35 Inverse Normal Cumulative Distribution .... [Inv. Distribution] - [Inverse Normal CD] Calculates the boundary value(s) of a normal cumulative probability distribution for specified values. Tail: Left Tail: Right Tail: Center (+ 2 = Upper bound ( is returned. 0711 Lower bound ( is returned. Lower bound ( and upper bound are returned. To calculate inverse normal cumulative distribution for the data below and graph the result Tail: Left Population mean: 35 Probability: 0.7 Population standard deviation: 2 Student’s t Probability Density .... [Distribution] - [Student’s t PD] – x2 df + 1 1+ Γ 2 df f (x) = × π .df df Γ 2 Calculates the Student’s t probability density for a specified value. Student’s t Cumulative Distribution …. [Distribution] - [Student’s t CD] Calculates the cumulative probability of a Student’s t distribution between a lower bound (a) and an upper bound (b). df + 1 2 p= df Γ 2 π .df Γ b a x2 1+ df Chapter 7: Statistics Application – df+1 2 df+1 2 dx 151 ∞ Inverse Student’s t Cumulative Distribution .... [Inv. Distribution] - [Inverse t CD] Calculates the lower bound value of a Student’s t cumulative probability distribution for specified values. χ2 Probability Density .... [Distribution] - [χ2 PD] f (x) = Calculates the χ2 probability density for a specified value. χ2 Cumulative Distribution .... [Distribution] - [χ2 CD] 1 df Γ 2 p= 1 df Γ 2 Calculates the cumulative probability of a χ distribution between a lower bound and an upper bound. 2 df 2 1 2 1 2 df 2 b df –1 – x2 e df –1 – x2 e x 2 x 2 dx a Inverse χ2 Cumulative Distribution .... [Inv. Distribution] - [Inverse χ2 CD] ∞ Calculates the lower bound value of a χ2 cumulative probability distribution for specified values. F Probability Density .... [Distribution] - [F PD] n+d 2 f (x) = n d Γ Γ 2 2 Γ Calculates the F probability density for a specified value. F Cumulative Distribution .... [Distribution] - [F CD] Calculates the cumulative probability of an F distribution between a lower bound and an upper bound. n 2 n d x n –1 2 . 1 +n x d × × – n+d 2 * ∞ Inverse F Cumulative Distribution .... [Inv. Distribution] - [Inverse F CD] Calculates the lower bound value of an F cumulative probability distribution for specified values. Binomial Distribution Probability .... [Distribution] - [Binomial PD] Calculates the probability in a binomial distribution that success will occur on a specified trial. p: probability of success (0 s p s 1) n: number of trials Binomial Cumulative Distribution .... [Distribution] - [Binomial CD] Calculates the cumulative probability in a binomial distribution that success will occur on or before a specified trial. Inverse Binomial Cumulative Distribution .... [Inv. Distribution] - [Inverse Binomial CD] Calculates the minimum number of trials of a binomial cumulative probability distribution for specified values. Poisson Distribution Probability .... [Distribution] - [Poisson PD] Calculates the probability in a Poisson distribution that success will occur on a specified trial. 0712 To calculate Poisson probability for the data below and graph the result Specified trial: 10 - t 0 / (x = 0, 1, 2, ...) ): mean (0 < )) Mean: 6 Chapter 7: Statistics Application 152 Poisson Cumulative Distribution .... [Distribution] - [Poisson CD] Calculates the cumulative probability in a Poisson distribution that success will occur on or before a specified trial. 0713 To calculate Poisson cumulative probability for the data below and graph the result Lower bound: 2 Upper bound: 3 Mean: 2.26 Inverse Poisson Cumulative Distribution .... [Inv. Distribution] - [Inverse Poisson CD] - Calculates the minimum number of trials of a Poisson cumulative probability distribution for specified values. 0714 t To calculate inverse Poisson cumulative distribution for the data below and graph the result Poisson cumulative probability: 0.8074 Mean: 2.26 Geometric Distribution Probability .... [Distribution] - [Geometric PD] Calculates the probability in a geometric distribution that the success will occur on a specified trial. (x = 1, 2, 3, ...) p: probability of success (0 s p s 1) Geometric Cumulative Distribution .... [Distribution] - [Geometric CD] Calculates the cumulative probability in a geometric distribution that the success will occur on or before a specified trial. Inverse Geometric Cumulative Distribution .... [Inv. Distribution] - [Inverse Geo CD] m Σ Calculates the minimum number of trials of a geometric cumulative probability distribution for specified values. Hypergeometric Distribution Probability .... [Distribution] - [Hypergeometric PD] Calculates the probability in a hypergeometric distribution that the success will occur on a specified trial. Hypergeometric Cumulative Distribution .... [Distribution] - [Hypergeometric CD] Calculates the cumulative probability in a hypergeometric distribution that the success will occur on or before a specified trial. t x =1 $ = 2 ×102 0 1 3 $ = ∑ 45$6 2 ×102 0 1 Inverse Hypergeometric Cumulative Distribution .... [Inv. Distribution] - [Inverse Hypergeometric] Calculates the minimum number of trials of a hypergeometric cumulative probability distribution for specified values. 7 $ s ∑ 48 ×102 0 1 2 Chapter 7: Statistics Application 153 Input and Output Terms k Input Terms C-Level: confidence level (0 s C-Level < 1) sx: sample standard deviation (0 < sx) Contrib: name of list specifying the contribution of each observed count sx1 / sx2: sample standard deviation of {sample 1 / sample 2} (0 < sx1, 0 < sx2) df : degrees of freedom Upper (Distribution): upper bound Expected: name of list that is for saving expected frequency x (1-Proportion Z Test): sample value*1 Freq, Freq(1), Freq(2): frequency (1 or list name) x (Binomial PD): specified trial (integer, 0 s x s n) List, List(1), List(2): list where sample data is located x (Poisson PD, Geometric PD, Hypergeometric PD): Lower (Distribution): lower bound M: number of success in population*1 Matrix (χ2 Test): name of matrix containing observed values*2 n (Hypergeometric Distribution): number of trials from population* 1 x (1-Proportion Z Interval): data value*1 specified trial*1 x (Other than the above): data value _ x : sample mean _ _ x 1 / x 2: sample mean of {sample 1 data / sample 2 data} n: sample size*1 x1 / x2 (1-Proportion Z Interval): data value of {sample 1 / sample 2} (integer, 0 s x1, 0 s x2) n1 / n2: size of {sample 1 / sample 2}*1 XList / YList: x-data list / y-data list N: population size (integer, n s N, M s N) & ρ condition (LinearReg t Test): and ρ-value Numtrial: number of trials n*1 Observed (χ2 GOF Test): name of list containing observed counts (all cells positive integers) test conditions*4 λ : mean (0 < )) (Distribution): population mean Observed (χ2 Test): name of matrix containing observed values*2 condition (1-Sample Z Test, 1-Sample t Test): p0: expected sample proportion (0 < p0 < 1) 0: assumed population mean p1 condition (2-Proportion Z Test): sample proportion 1 (2-Sample Z Test): population mean value test test conditions*3 Pooled: pooling On or Off pos: probability of success p (0 s p s 1) prob (Inv. Distribution): cumulative probability value (0 s prob s 1) Prop condition (1-Proportion Z Test): sample proportion test conditions*4 population mean value test conditions*4 conditions*3 1 (2-Sample t Test): sample mean value test conditions*3 σ: population standard deviation (0 < σ) σ1 condition (2-Sample F Test): population standard deviation test conditions*3 σ1 / σ2: population standard deviation of {sample 1 / sample 2} (0 < σ1 / 0 < σ2) *1 positive integer *2 positive integers in all cells for 2 × 2 and larger matrices; positive real numbers for one row matrices *3 “” specifies two-tail test, “<” specifies one-tail test where sample 1 is smaller than sample 2, “>” specifies one-tail test where sample 1 is greater than sample 2. *4 “” specifies two-tail test, “<” specifies lower one-tail test, “>” specifies upper one-tail test. Chapter 7: Statistics Application 154 k Output Terms a: regression constant term (y-intercept) A df : df * of Factor A 5 A F: F value of Factor A A MS: MS*6 of Factor A A p: p-value of Factor A prob (Binomial CD, Poisson CD, Geometric CD, Hypergeometric CD): cumulative probability prob (Normal PD, Student’s t PD, χ2 PD, F PD): probability density prob (Normal CD, Student’s t CD, χ2 CD, F CD): distribution probability A SS: SS* of Factor A prob (Test): p value AB df * : df * of Factor A × Factor B r: correlation coefficient AB F*8: F value of Factor A × Factor B r 2: coefficient of determination AB MS*8: MS*6 of Factor A × Factor B sx: sample standard deviation AB p*8: p-value of Factor A × Factor B sx1 / sx2: sample standard deviation of {sample 1 / sample 2} (Displayed only for list format.) 7 8 5 AB SS* : SS* of Factor A × Factor B 8 7 b: regression coefficient (slope) sp: pooled sample standard deviation B df : df *5 of Factor B se: standard error of estimation B F: F value of Factor B SEb: standard error of the least squares slope B MS: MS*6 of Factor B B p: p-value of Factor B B SS: SS*7 of Factor B d:df : degrees of freedom of denominator (positive integer) df : degrees of freedom Errdf : df *5 of error ErrMS: MS*6 of error ErrSS: SS*7 of error F: F value Lower: confidence interval lower limit n:df : degrees of freedom of numerator (positive integer) p : estimated sample proportion t: t value t Low: lower bound value you input t Up: upper bound value you input Upper: confidence interval upper limit x1InvN: Upper bound when Tail:Left, Lower bound when Tail:Right or Tail:Center x2InvN: Upper bound when Tail:Center xInv: inverse cumulative distribution ½xInv: recalculation value of inverse cumulative distribution*9 z: z value z Low: standardized lower limit z value z Up: standardized upper limit z value χ2: χ2 value p 1 / p 2: estimated proportion of {sample 1 / sample 2} prob (Binomial PD, Poisson PD, Geometric PD, Hypergeometric PD): probability *5 *6 *7 *8 degrees of freedom mean square sum of squares Note that “AB df ”, “AB MS ”, “AB SS ”, “AB F ”, and “AB p” are not displayed in the calculation result window if there are no repeated data pairs. *9 In the calculation result window for certain distributions, “½xInv” is displayed only when there may be a possibility of rounding error. To account for possible rounding error, ClassPad additionally obtains the result using the probability that is next lowest for the least significant digit. For example, if the probability is 0.61, ClassPad would recalculate using 0.60. The recalculation result is only shown if it is different from the original one. Chapter 7: Statistics Application 155 Chapter 8: Geometry Application The Geometry application allows you to draw and analyze geometric figures. For example, you can draw a circle and then draw a line that is tangent to a particular point on the circle. The Geometry application also includes an animation feature that lets you watch how a figure changes in accordance with conditions you define. Starting up the Geometry application displays a large white Geometry window. Use this window to draw the figures you want. If you left figures on the Geometry window the last time you exited the Geometry application, those figures will appear the next time you start it up. Geometry Application-Specific Menus and Buttons • Clear all settings fixed with the measurement box......................................................Edit - Clear Constraints • Show hidden objects ................................................................................................................ Edit - Show All • Specify the color of the currently selected object........................................................................... Edit - Style • Hide the currently selected object ............................................................................... Edit - Properties - Hide • Show hidden names ....................................................................................... Edit - Properties - Show Name • Hide the selected name ....................................................................................Edit - Properties - Hide Name • Move the selected object to the front or to the back ...................Edit - Properties - To the front / To the back • Move all text to the front..........................................................................................Edit - Properties - All Text • Pin an annotation position on the Geometry window .....................................................Edit - Properties - Pin • Unpin an annotation on the Geometry window ......................................................... Edit - Properties - Unpin • Specify the number format for each measurement used in the Geometry window ...........................................................................Edit - Properties - Number Format • Display the Animate submenu (page 174) ................................................................................ Edit - Animate • Select a segment, line, or part of a figure (page 167) .......................................................View - Select or G • Activate the pan function for dragging the Geometry window with the stylus ...................... View - Pan or T • Adjust the size of the display image so it fills the display......................................... View - Zoom to Fit or R • Turn display of axes, coordinate values and grid on or off .....................................View - Toggle Axes or q • Show grid points (On) or hide the grid (Off) ................................................................... View - Grid - On / Off • Show grid lines..................................................................................................................... View - Grid - Line • Turn the Animation toolbar on or off ................................................................................ View - Animation UI • Display a submenu for plotting points, and drawing lines and other basic figures (pages 157 through 159) .............................................................. Draw - Basic Object Chapter 8: Geometry Application 156 • Display a submenu for drawing a figure of specially shaped figures such as triangles and rectangles (page 162) ............................................ Draw - Special Polygon • Display a submenu for drawing functions (page 160) ............................................................ Draw - Function • Insert a value or text connected with a displayed figure into the display (pages 161 through 162) .............. Draw - Text / Attached Angle / Measurement / Expression • Display a slider (page 172) for the currently selected object. ..................................................... Draw - Slider • Display a submenu for geometric constructions (page 163) .................................................Draw - Construct • Activate Toggle Select (page 167) .....................................................................Tap i and then tap a figure Tip: The View menu Zoom Box (Q), Zoom In (W), and Zoom Out (E) commands are the same as the Graph & Table application Box, Zoom In, and Zoom Out commands on the Zoom menu. For more information about these commands, see “Chapter 3: Graph & Table Application”. Configuring Geometry View Window Settings You can use the following procedures to configure settings that control the appearance of the Geometry application window. Tap O, and then [View Window] to display the View Window dialog box. The View Window dialog box allows you to configure the x-axis range of values. The ymid value is used to center the Geometry window vertically. For example, if we set ymid = 2, the y-axis will appear 2 units below the center of the Geometry window. The following are the allowable ranges for the indicated View Window parameters. −1 × 106 s xmin s 1 × 106 −1 × 106 s xmax s 1 × 106 −1 × 106 s ymid s 1 × 106 xmax − xmin t 1 × 10−4 About the Geometry Format Dialog Box Settings for the Geometry application can be configured on the Geometry Format dialog box which appears when you tap O and then [Geometry Format]. See “1-7 Configuring Application Format Settings” for more information. 8-1 Drawing Figures This section explains how to use the Geometry application to draw various types of figures. It also explains how to use the geometric construction tools to investigate theorems and properties in Geometry. Drawing a Figure u To plot a point 1. Tap [Draw] - [Basic Object] - [Point], or tap [. 2. Tap the location on the screen where you want to plot a point. Chapter 8: Geometry Application 157 u To draw a line segment 1. Tap [Draw] - [Basic Object] - [Line Segment], or tap y. 2. Tap the screen where you want the line segment to begin, and a point will be drawn, and then tap the point where you want it to end. u To add a labeled point to an existing line 1. Tap [Draw] - [Basic Object] - [Point], or tap [. 2. Drag the stylus to the location on the line where you want to add a labeled point, and then lift the stylus from the screen. u To draw an infinite line 1. Tap [Draw] - [Basic Object] - [Infinite Line], or tap w. 2. Tap two points on the screen through which you want the infinite line to pass. u To draw a ray 1. Tap [Draw] - [Basic Object] - [Ray], or tap b. 2. Tap two points on the screen, or tap one point and then drag to the second point. u To draw a vector 1. Tap [Draw] - [Basic Object] - [Vector], or tap H. 2. Tap the point where you want the vector to start, and then its end point. u To draw a circle 1. Tap [Draw] - [Basic Object] - [Circle], or tap U. 2. Tap the point where you want the center of the circle to be, and then tap a second point anywhere on the circle’s circumference. u To draw an arc 1. Tap [Draw] - [Basic Object] - [Arc], or tap P. 2. Tap the point where you want the center of the arc to be, and then tap a second point to designate where you want the arc to start. 3. Tap a third point, which is where you want the arc to end. Chapter 8: Geometry Application 158 u To draw an ellipse 1. Tap [Draw] - [Basic Object] - [Ellipse] - [Axes], or tap I. 2. Tap the point you want to specify as the center point. 3. Tap or drag to the point you want to specify as minor axis (nearest point on the edge from the center point). 4. Tap or drag to the point you want to specify as major axis (farthest point on the edge from the center point). (Or) 1. Tap [Draw] - [Basic Object] - [Ellipse] - [Foci], or tap z. 2. Tap the two points that you want to specify as the foci of the ellipse (point 1 and point 2). • This causes a line to appear between point 1 and point 2. 3. Tap the point you want to specify as a point anywhere on the ellipse (point 3). • This draws an ellipse whose line passes through point 3, using point 1 and point 2 as foci. u To draw a hyperbola 1. Tap [Draw] - [Basic Object] - [Hyperbola], or tap x. 2. Tap the two points that you want to specify as the foci of the hyperbola (point 1 and point 2). • This causes a line to appear between point 1 and point 2. 3. Tap the point you want to specify as a point anywhere on the hyperbola (point 3). • This draws a hyperbola whose line passes through point 3, using point 1 and point 2 as foci. u To draw a parabola 1. Tap [Draw] - [Basic Object] - [Parabola], or tap c. 2. Tap the two points that you want to specify the directrix (point 1 and point 2). • This causes a line to appear between point 1 and point 2. 3. Tap the point you want to specify as the focus (point 3). • This draws a parabola using the straight line that passes through point 1 and point 2 as the directrix, and point 3 as the focus. u To draw a polygon 1. Tap [Draw] - [Basic Object] - [Polygon], or tap 0. 2. Tap the point from which you want the polygon to start. 3. Sequentially tap each of the vertices of the polygon. 4. Finally, tap the start point again to complete the polygon. Chapter 8: Geometry Application 159 u To draw a function 1. Tap [Draw] - [Function] - [ f (x)]. • Or you could tap { on the tool bar. Next on the Function dialog box that appears, use the Type box to select “f (x)”. 2. On the Function dialog box, input the function and then tap [OK] to draw it. u To draw a polar equation graph* 1. Tap [Draw] - [Function] - [Polar]. • Or you could tap { on the tool bar. Next on the Function dialog box that appears, use the Type box to select “Polar”. 2. On the Function dialog box, input an expression in the syntax of r = f (), the lower limit of (min) and its upper limit (max). 3. Tap [OK] to draw the polar equation graph. * In this example, the [Function Angle] setting of the Geometry Format dialog box (page 40) is set to “Radian”. u To draw a parametric equation graph* 1. Tap [Draw] - [Function] - [Parametric]. • Or you could tap { on the tool bar. Next on the Function dialog box that appears, use the Type box to select “Parametric”. 2. On the Function dialog box, input expressions and values. 3. Tap [OK] to draw the parametric equation graph. * In this example, the [Function Angle] setting of the Geometry Format dialog box (page 40) is set to “Radian”. Chapter 8: Geometry Application 160 Inserting Text Strings into the Screen You can insert text strings into the screen while working on the Geometry application window. To do so, tap [Text] on the [Draw] menu. On the dialog box that appears, input the text you want, and then tap [OK]. Attaching an Angle Measurement to a Figure The measurement of an angle formed by two sides of a figure can be attached to the figure as shown here. To do so, tap [Attached Angle] on the [Draw] menu. u To attach an angle measurement to a figure Example: To attach the measurement of angle A in triangle ABC 1. Draw the triangle. 2. Tap G. Next, tap side AB and then side AC to select them. 3. Tap [Draw] and then [Attached Angle]. • This attaches the angle measurement to the figure. Tip: The two sides of the figure actually form four angles in the illustration shown here. After attaching an angle measurement using the [Attached Angle] command, you can drag it to the position of any one of the other three angles as shown in the example below. Example: To drag the angle measurement attached to interior angle A of triangle ABC to its exterior supplementary angle Displaying the Measurements of a Figure You can display measurements on the Geometry application window. The measurements change dynamically as you manipulate the figure. u To display a measurement of a figure 1. What you should select (point, line, figure, etc.) depends on the type of measurement you want to display. To display this type of measurement: Select this: Angle between two lines Two lines (Any two of the following: line segment, infinite line, ray, or vector, one side of a polygon) Supplementary angle of extended lines Area of selected figure Circumference or perimeter of selected figure • All the sides or all the apexes of a polygon • The circumference of a circle, ellipse, or arc • Three points Chapter 8: Geometry Application 161 To display this type of measurement: Select this: Coordinates of selected point Any single point (including the apex of a polygon) Direction of line or vector A single line (line segment, infinite line, ray, vector, or any side of a polygon) Equation of selected curve Any line or curve Distance between two points, or length of line Any two points, a line segment, or any side of a polygon Radius of circle or arc The radius of the circle or arc Slope of line or vector A single line (line segment, infinite line, ray, vector, or any side of a polygon) 2. Perform any one of the following operations. - Tap [Draw] - [Measurement]. On the submenu that appears, select the measurement type you want to display on the screen. - Select the value in the measurement box and drop it directly into the Geometry application window. - Tap the measurement icon button to the left of the measurement box. Tip: For information about the measurement box, see “8-3 Using the Measurement Box”. 0801 To display the interior angle formed by two sides of a triangle Displaying the Result of a Calculation that Uses On-screen Measurement Values You can use the [Expression] command and the commands on the [Measurement] submenu to perform calculations using the angle value, line length, surface area, and other measurement values attached to a figure, and display the result on the Geometry window. u To display the result of a calculation that uses on-screen measurement values 0802 To display the sum of the interior angles of triangle ABC (⬔A+⬔B+⬔C) Using the Special Polygon Submenu The [Special Polygon] submenu allows you to draw specially shaped figures automatically. Simply select the type of figure you want from the menu, and then touch the screen with the stylus to draw it. Or, touch the screen with your stylus and drag to create a box indicating the size of the figure you would like to draw. Each of the [Special Polygon] submenu figures is also available on the toolbar. [Special Polygon] submenu Triangle Equilateral Triangle Kite Rectangle Square Isosceles Triangle Trapezoid Parallelogram Rhombus Regular n-gon Chapter 8: Geometry Application 162 u To draw a triangle 1. Tap [Draw], [Special Polygon], and then [Triangle]. 2. Place the stylus on the screen and drag diagonally in any direction. • This causes a selection boundary to appear, indicating the size of the triangle that will be drawn. The triangle is drawn when you release the stylus. • In place of the above step 2, you can achieve the same result by simply tapping the screen. This automatically draws the acute triangle you selected. 0803 To draw a regular polygon Using the Construct Submenu The [Construct] submenu provides you with the means to study various geometric theorems. Each of the [Construct] submenu figures is also available on the toolbar. Perpendicular Bisector Midpoint Angle Bisector Tangent to Curve Translation Dilation Perpendicular Intersection Parallel Reflection Rotation General Transform [Construct] submenu The following procedures include steps that require selection of a line segment or other figures. For details about selecting figures, see “8-2 Editing Figures”. u To construct a perpendicular bisector 1. Draw a line segment. 2. Tap G, and then select the line segment. 3. Tap [Draw], [Construct], and then [Perp. Bisector]. This draws a perpendicular bisector through your line segment. Chapter 8: Geometry Application 163 u To construct a perpendicular line that passes through a specified point on a line 1. Draw an infinite line, and then draw a point on the line through which you want the perpendicular line to pass. 2. Select the line and the point. 3. Tap [Draw], [Construct], and then [Perpendicular]. This draws a line through the point you selected, which is perpendicular to the line where the point is located. u To construct a midpoint 1. Draw a line segment and then select it. 2. Tap [Draw], [Construct], and then [Midpoint]. This adds a midpoint to the segment. u To construct the point of intersection of two lines 1. Draw two lines that intersect, and then select both lines. 2. Tap [Draw], [Construct], and then [Intersection]. • This adds the point of intersection. The point(s) of intersection of two circles or of a line and a circle can be constructed in the same manner. u To construct an angle bisector 1. Draw two line segments so they form an angle, and then select both line segments. 2. Tap [Draw], [Construct], and then [Angle Bisector]. This bisects the angle. u To construct a line parallel to another line through a specified point 1. Draw a line and a point that is not on the line. 2. Select the line and the point. 3. Tap [Draw], [Construct], and then [Parallel]. This draws an infinite line that passes through the selected point and is parallel to the selected line. Chapter 8: Geometry Application 164 u To construct a tangent to a curve through a specified point 1. Draw a curve, such as an ellipse. 2. Tap [Draw], [Construct], and then [Tangent to Curve]. • This highlights K on the toolbar. 3. Tap the point of tangency on the curve. This draws the tangent. u To reflect a line segment with respect to a specified line of symmetry 1. Draw a line segment and a line to use as the line of symmetry, and then select the line segment. 2. Tap [Draw], [Construct], and then [Reflection]. • This highlights S on the toolbar. 3. Tap the line of symmetry. This reflects the line segment you drew in step 1 about the line of symmetry. u To translate a line segment by inputting a vector 1. Draw a line segment (AB), and then select it. 2. Tap [Draw], [Construct], and then [Translation] to display the Translation dialog box. 3. Enter the vector for the translation. • Vector values indicate the amount of movement in the x-axis direction and in the y-axis direction. In the nearby screen, for example, the figure selected in step 1 moves parallel to the x-axis by three. 4. Tap [OK]. This translates line segment AB in accordance with the vector value you input, and draws line segment A’B’. u To translate a line segment by selecting a vector 1. Draw a line segment (AB), and a vector to use in the translation. Next, select the line segment. 2. Tap [Draw], [Construct], and then [Translation] to display the Translation dialog box. 3. Tap [Select Vector]. 4. Tap the vector on the screen. This translates line segment AB in accordance with the vector you selected, and draws line segment A’B’. Chapter 8: Geometry Application 165 u To rotate a line segment 1. Draw a line segment, and then select it. 2. Tap [Draw], [Construct], and then [Rotation]. • This highlights F on the toolbar. 3. Tap the screen once to select the center of rotation. • This displays the Rotation dialog box. 4. Specify the angle of rotation in degrees, and then tap [OK]. u To dilate a line segment toward a specified center point 1. Draw a line segment, and then select it. 2. Tap [Draw], [Construct], and then [Dilation]. • This highlights 2 on the toolbar. 3. Tap the center of dilation. • This displays the Dilation dialog box. 4. Specify the dilation scale factor, and then tap [OK]. u To transform a triangle using a matrix or vector (general transform) 1. Tap q to turn on coordinate display in the Geometry window. 2. Draw triangle ABC, and then select its three sides. 3. Tap [Draw], [Construct], and then [General Transform]. This displays the Transform dialog box. 4. Enter the matrix for the transform. • In this example, let’s input [[1, 0], [0, −1]]. 5. Tap [OK]. This draws triangle A’B’C’, which is symmetrical to triangle ABC about the x-axis. 6. Tap anywhere outside of the triangles to deselect the currently selected triangle. Next, select triangle A’B’C’. 7. Tap [Draw], [Construct], and then [General Transform]. 8. Enter the vector to perform parallel displacement. • In this example, let’s input [1, 1]. Chapter 8: Geometry Application 166 9. Tap [OK]. This performs the parallel displacement and draws triangle A’’B’’C’’. Tip: In the above example, we performed the transformation and the parallel displacement operations separately. You could also perform both operations at the same time, if you want. To do so, input both the matrix [[1, 0], [0, −1]] and the vector [1, 1] in step 4, and then tap [OK]. This will produce the result shown in step 9. 8-2 Editing Figures This section explains how to move, copy, change the color of, and perform other editing operations on Geometry application figures. Selecting and Deselecting Figures Before you can execute certain editing commands, you must first select the figure you want to edit. There are two figure selection modes: Select and Toggle Select, each of which is described below. u Using Select Tap G on the toolbar. This causes the button to become highlighted, indicating that Select is enabled. Select allows you to select as many figures as you would like, and then move, copy, paste, or perform other operations on the selection as a single entity. • Tap G on the toolbar. • To select side BC of the triangle, tap it. • Tapping point D selects it, leaving side BC of the triangle selected, too. • To deselect all of the figures, tap anywhere on the screen where there are no figures. u Using Toggle Select Tap i on the toolbar. This causes the button to become highlighted, indicating that Toggle Select is enabled. Toggle Select allows you to select and deselect figures. For example, if you have multiple figures selected, Toggle Select will allow you to deselect a single part of the selection. Tapping the part again will turn the selection back on. Chapter 8: Geometry Application 167 Moving and Copying Figures u To move a figure 1. Draw a figure, and then select it. 2. Drag the figure to move it to the location you want. • A selection boundary appears around the figure when you drag it. 3. Remove the stylus from the screen. u To copy a figure 1. Draw a figure, and then select it. 2. Tap [Edit] - [Copy], and then [Edit] - [Paste]. 3. Drag the pasted figure to the location you want. Pinning an Annotation on the Geometry Window You can pin an annotation on the Geometry window using the Pin function. By default, annotations are ‘Unpinned’, so they pan or zoom along with the Geometry window. Pinning an annotation fixes its position on the screen so it is always displayed in the same location on the Geometry window. u To pin or unpin an annotation on the Geometry window 1. Select (highlight) the text on the Geometry window. 2. Tap [Edit], [Properties], and then [Pin] or [Unpin]. • When text is pinned, it maintains its position as shown here even when the window is panned. Specifying the Number Format of a Measurement You can specify the number format for each measurement value or all the measurement values on the Geometry window. The initial default number format setting for measurement values is “Fix 2”. u To specify the number format for selected measurement value(s) 1. Select (highlight) the measurement(s) you want to specify the number format. 2. Tap the [Edit], [Properties], and then [Number Format]. 3. On the dialog box that appears, select the number format you want by tapping it. • For the meaning of each number format name, see “To specify the numeric value display format” on page 36. 4. Tap [OK]. • This will display the measurement value(s) you selected in the step 1 using the specified number format. u To specify the number format for all the measurement values on the Geometry window 1. Tap anywhere on the screen where there are no figures to deselect all of the figures. 2. Perform the procedure from step 2 under “To specify the number format for selected measurement value(s)”. • This will display all the measurement values on the Geometry window using the specified number format. Chapter 8: Geometry Application 168 Specifying the Color and Line Type of a Displayed Object You can use the procedure below to specify the color and line type for the outline of a figure, the fill color inside a figure, or the color of text, labels, and other non-figure objects. u To specify the color and line type of a particular object 1. Use the procedure under “Selecting and Deselecting Figures” (page 167) to select the object whose color and/or line type you want to specify. 2. Tap [Edit] and then [Style] to display the dialog box shown to the right. • The dialog box will show only supported settings, which depend on the composition of the selected object. 3. Configure the dialog box with the following settings. To specify this: Perform this operation: Specify the text color Tap “Character Color” and then tap the desired color. Specify the line type Tap “Graph Plot” and then tap the desired line type. Specify the line color Tap “Line Color” and then tap the desired color. Specify the figure fill color Tap “Area Color” and then tap the desired color. To specify no fill color, tap “Clear”. 4. To apply the settings you configure, return to the dialog box in step 2 of this procedure and then tap [OK]. u To specify the color and line type of all the objects on the Geometry window 1. Tap anywhere on the screen where there are no figures to deselect all of the figures. 2. Perform the procedure from step 2 under “To specify the color and line type of a particular object”. Changing the Display Priority of Objects Basically, objects you draw on the Geometry window are stacked in the order they are drawn (newest drawing on top). You can use the operations in this section to move a drawn object to the top or the bottom of the stack. You also can move all text to the front, if you want. • To move a particular object to the front, select it and then tap [Edit] - [Properties] - [To the front]. • To move a particular object to the back, select it and then tap [Edit] - [Properties] - [To the back]. • To move all text to the front, tap [Edit], [Properties] and then [All Text]. Chapter 8: Geometry Application 169 8-3 Using the Measurement Box Tapping the u button to the right of the toolbar displays the measurement box. Tap t to return to the normal toolbar. Normal toolbar Measurement box You can use the measurement box to view the measurements of a figure, to specify a measurement of a figure, to fix a measurement of a figure, or to name a figure. Viewing the Measurements of a Figure The type of information that can be displayed in the measurement box depends on the figure currently selected on the screen. The nearby screen shows an example when a line segment is selected. You can change the display information type by tapping one of the icons. The following table describes the information that appears when you tap each icon, and explains when each icon is available for selection. Icon Icon Name This icon appears when this is selected: Tapping this icon displays: T Coordinates A single point Coordinates of the point Yes t Distance/length Two points on one figure or two different figures, or a single line segment or a vector Distance between two points, length of a line segment or vector Yes Q Slope Single line, line segment, or vector Slope of the line, line segment or vector Yes Y Direction Single line, line segment, or vector Direction angle of the line (angle of inclination) Yes O Equation Any single line or line segment, vector, circle, arc, ellipse or any other figure (parabola, etc.) drawn by a function Function of the figure (using rectangular coordinates) Yes 5 Equation edit Single parabola or any other figure drawn by a function Equation of the figure in the function editing dialog box. No ] Radius Single circle or arc Radius of circle or arc Yes 3 Circumference Single circle Length of the circumference Yes v Perimeter Single polygon Sum of the lengths of the sides No E Area Any three points, an arc, ellipse, or polygon Area No Single circle Area Yes Two line segments Angle and its supplement formed by the line segments Yes Q t Angle Lockable Chapter 8: Geometry Application 170 Icon Name This icon appears when this is selected: Tapping this icon displays: K Tangency Two circles or arcs, or a line and circle Whether two items are tangent Yes e Congruence Two line segments Whether line segments are the same length Yes Incidence Point and a line, arc, circle or vector Whether a point is on the line/ curve Yes Point on curve Point and a function, curve, or ellipse F Rotation angle Two points created by [Rotation] Angle of rotation *1 2 Scale of dilation Two points (like point A and point A’) on a figure created by [Dilation] Scale of dilation *1 u Text icon An object that includes text or an object that can be named Editable text used to name the selected image No Icon 6 Lockable *1 The value in the measurement box is always locked while this tool is selected. u To view the measurements of a line segment 1. Draw a line segment. 2. Tap u on the toolbar to display the measurement box. 3. Select the line segment. • This displays the length of the line segment. 4. Tap the down arrow next to the measurement box to cycle through other measurements. • In the case of the line segment, for example, you can view its length, slope, direction, and equation. Specifying and Constraining a Measurement of a Figure The following example shows how to specify and constrain (fix) an angle of a triangle. By “constraining a measurement” we mean that it becomes fixed. For example, constraining (fixing) angle B of triangle ABC at 90 degrees will cause angle B to remain at 90 degrees regardless of where the apex is moved. u To specify and constrain the measure of an angle of a triangle* 1. Draw the triangle, and then select its side AB and side BC. 2. Tap u on the toolbar to display the measurement box. • This displays the measure of angle B in the measurement box. Chapter 8: Geometry Application 171 3. Input 90 into the measurement box and press E. • This specifies and constrains the measure of angle B at 90 degrees. A highlighted check box indicates the measurement is constrained (fixed). * In this example, the [Measure Angle] setting of the Geometry Format dialog box (page 40) is set to “Degree”. Tip: To cancel the constraint of a measurement value fixed using the above operation, tap the check box to the right of the measurement box to unhighlight it. Each tap of the check box toggles the measurement value between fixed and unfixed. u To clear all settings constrained with the measurement box Tap [Edit] and then [Clear Constraints]. Using Sliders Sliders can be displayed and used to change the settings of the objects in the table below. Select the desired object and then display its slider using the procedure following the table. For this type of selected object(s): This type of slider can be displayed: Any two sides of a polygon or two line segments Angle, supplementary angle Two points on one figure or two different figures, or a single line segment or a vector Length Single circle or arc Radius u To display a slider 1. Select the required object(s), as described in the table above. 2. Tap [Draw] - [Slider]. On the sub-menu that appears, select the type of measurement ([Angle], [Supplementary Angle], [Length], [Radius]) you want to perform with the slider. • The items that appear on the sub-menu depend on the object you select in step 1 of this procedure. Note: Instead of step 2 in the above procedure, you could also perform the steps below to display a slider. (1) Tap u on the toolbar to display the measurement box. (2) Tap the down arrow to the right of icon palette on measurement box and then a. Chapter 8: Geometry Application 172 u To specify the measurement minimum value, maximum value, and step value for a slider 1. Perform the operation under “To display a slider” to display a slider. 2. Tap the upper left corner of the slider display box. 3. On the menu that appears, tap [Settings]. 4. On the Slider Settings dialog box that appears, display the tab for the measurement you want to change. • The dialog box has four tabs: [Angle], [SuppAngl] (supplementary angle), [Length], and [Radius]. You can select any of the tabs and change its settings, regardless of the measurement controlled by the slider you selected in step 1 of this procedure. 5. Input values for Min (minimum value), Max (maximum value), and Step (step value). • For the Angle and SuppAngl tabs, you should input a value in the angle unit (degrees, radians, or grads) currently specified by the “Measure Angle” setting on the Geometry Format dialog box. The input range depends on the current angle unit setting: 0 to 180 for degrees, 0 to π for radians, and 0 to 200 for grads. Attempting to input a value that is outside the current allowable range will automatically change the input value so it is within range. • On the Length and Radius tab, input a value that is greater than zero. • To return the setting values on the currently displayed tab to their initial values, tap the [Default] button. Refer to the “Initial Defaults” table for information about default settings. 6. After configuring the settings you want, tap [OK] to save them. • This closes the Slider Settings dialog box. Initial Defaults Measurement Min Max Step Degree 30 150 30 Radian π/6 5π/6 π/6 Grad 100/3 500/3 100/3 Length 1 10 1 Radius 1 5 1 Angle, Supplementary Angle u To use a slider to seamlessly change an angle and/or length 0804 Angle B of triangle ABC is fixed at 90°, and the length of side AC is also fixed. Confirm the movement of vertex B along the circumference of a circle that has side AC as its diameter as angle A changes. Here, angle A changes at 10° increments within a range of 10° to 80°. Chapter 8: Geometry Application 173 Changing a Label or Adding a Name to an Element You can change the name of a point, or add a name to each element as explained in the following example. u To change the label name of the center of a circle from “B” to “Center” 1. Draw the circle, and then select its center point. 2. Tap the down arrow to the right of icon palette on measurement box and then u. • This displays the current name of the point in the measurement box. The displayed name is highlighted so it can be edited. 3. Input a new name (“Center”) in the measurement box. 4. Press E or the check box to the right side of measurement box. • This displays the changed name on the screen as shown here. 8-4 Working with Animations An animation consists of one or more point/curve pairs, in which the curve can be a line segment, circle, ellipse, or function. You build an animation by selecting a point/curve pair, and then adding it to an animation. Using Animation Commands You can build and run an animation either by executing menu commands or by using the animation toolbar that appears when you tap [View] and then [Animation UI]. [Edit] – [Animate] [View] – [Animation UI] Animation toolbar Add Animation Replace Animation Trace Go (once) Go (repeat) Go (to and fro) Stop • Most of the procedures in this section are performed using the [Animate] submenu. • All of the [Animate] menu commands can be accessed from the animation toolbar, except for [Edit] - [Animate] - [Edit Animations]. • To close the animation toolbar and return to the normal toolbar, tap the = button on the right side of the animation toolbar, or tap [View] and then [Animation UI]. Chapter 8: Geometry Application 174 u To add an animation and run it 1. Plot a point and draw a figure (here we draw a parallelogram). Or, you could draw a circle, arc, ellipse, line segment, or function instead of a figure. 2. Select the point and a side of the parallelogram. 3. Tap [Edit], [Animate], and then [Add Animation]. • The point selected in step 2 moves along the side of the parallelogram. 4. Tap [Edit], [Animate], and then [Go (once)], [Go (repeat)], or [Go (to and fro)]. Point A moves along side CD. 5. Tap [Edit], [Animate], and then [Stop] to stop the animation. • You can also stop the animation by tapping l on the icon panel. u To replace the current animation with a new one 1. Select the point and curve for the new animation. 2. Tap [Edit], [Animate], and then [Replace Animation]. • This discards the currently set animation and sets up an animation for a new point and curve set. Tap [Edit], [Animate], and then [Go (once)] to see your new animation. u To trace a locus of points Note: Using trace leaves a trail of points when the animation is run. The procedure below is a continuation of the procedure under “To add an animation and run it”. 1. Draw a line segment that connects point A with apex B. 2. Draw the center point of line segment AB. • Select line segment and then tap [Draw] - [Construct] - [Midpoint]. 3. Select the center point of line segment AB (point F) and then tap [Edit] [Animate] - [Trace]. 4. Tap [Edit], [Animate], and then [Go (once)]. • This draws a line using point F as the locus, that is parallel to and whose length is half that of side CD of the parallelogram. 0805 To create an animation that traces the locus of specific points Chapter 8: Geometry Application 175 u To edit an animation Note: The steps below continue from the procedure under “To trace a locus of points”. 1. While the animation you want to edit is on the display, tap [Edit], [Animate], and then [Edit Animations]. • This displays the animation editing window in the lower window. The upper window contains the animation that we just completed in “To trace a locus of points”. 2. Edit the animation following the procedure below. Steps: This setting specifies how many steps point A takes to move along side CD. The initial default value is 20, which can be changed to value from 2 to 100. Animations: The “A” under “Animations” indicates that point A is the point moved by the animation. When you are building multiple animations, a list of all applicable points appears here. Tapping [Remove] deletes the applicable animation. “t0” and “t1” specify the range of movement of point A on side CD. The initial default values are t0 = 0 and t1 = 1. During animation, the length of CD is considered to be one unit. The default values specify that movement of point A is from start point C (point where length equals 0) up to end point D (point where length equals 1). Changing the value of t0 to 0.5, for example, causes point A to move from the middle of side CD to point D. Changing the value of t0 to −1, causes point A to begin at a point outside side CD (in this case, at a point a distance equivalent to the length of side CD) and ending with point D. Traces: This item shows the specified trace point. Tapping [Remove] cancels the trace point setting. 3. While the lower window is active, tap C to close the animation editing window. u To view an animation table Note: The steps below continue from the procedure under “To trace a locus of points”. 1. Tap line segment AB, which connects point A with apex B, to select it. 2. Tap u on the toolbar to display the measurement box. • This displays the measurement of line segment AB in the measurement box. 3. Tap # next to the measurement box. • This displays a table showing the length of line segment AB for each animation step in the bottom half of the screen. Chapter 8: Geometry Application 176 4. Next, let’s add a column to the table that shows the area of triangle ABE at each step. Perform the steps below. (1) Draw a line segment that connects point A with apex E. (2) Select line segment AB, line segment AE, and side BE. (3) Tap # next to the measurement box. This adds a column that shows the area of triangle ABE at each step. (As can be seen, the area of triangle ABE does not change even when point A moves.) 8-5 Using the Geometry Application with Other Applications You can display the Geometry application from within the eActivity or Main application. This feature allows you to visualize the relationship between Algebra and Geometry. You can, for example, drag a figure from the Geometry window to the eActivity window to see its corresponding mathematical expression. Drag and Drop When you open Geometry within another application, you can drag and drop information between the two application windows. You can see an actual example ( 0243 ) of how this is done using the Main application in Chapter 2 of this manual. The information that appears when you drop a figure into another application depends on the figure you are dragging. Many of the possible outcomes are listed in the table below. Geometric Figure Drag and drop into another application transforms to: *1 Point Ordered pair Yes Line Segment, Infinite Line, Ray Linear equation Yes Vector Ordered pair (head of vector, assuming the tail is at the origin) No Circle, Arc Equation of a circle Yes Ellipse Equation of an ellipse Yes Function ( y = f (x)) Equation of the function Yes Two Lines System of equations No Polygon, or open polygon created by animation Matrix containing each vertex point No Pairs of points related by a transformation Expression showing point relationship No *1 Support for drag and drop into a Geometry Link row in an eActivity. For details about a Geometry Link row, see “Inserting a Geometry Link Row” on page 184. Copy and Paste In addition to drag and drop, you can also copy figures or columns from an animation table and paste them into another application. Chapter 8: Geometry Application 177 Chapter 9: Numeric Solver Application Numeric Solver application lets you obtain the value of any variable in an equation without transforming or simplifying the equation. Starting up the Numeric Solver displays the Numeric Solver window. The screen to the right shows an example of the window with a sample equation input. 1 1 Equation input area. Inputting an equation that includes variables and then pressing E will cause 2 and 3 to appear. 2 2 Equation variables. Input the initial value of each variable to the right of the equals sign (=). Specify the variable you want to solve for by selecting the option button to the left of it. 3 3 Solution lower limit and upper limit input area* 4 Current convergence range setting* * Values shown in the sample screen are initial defaults. 4 Numeric Solver Application-Specific Menus and Buttons • Solve the input equation for the specified variable ...................................................... Solve - Execute or 1 • Clear all single-character variables (a through z)* .................................................................... a - Clear a–z • Initialize the upper boundary and lower boundary ........................................................... a - Initialize Bound • Change the convergence range.......................................................................................... a - Convergence * Performing the “Clear a–z” operation clears all single-character variables, regardless of variable data type. Programs and functions with file names from “a” through “z” are also cleared. Inputting an Equation On the Numeric Solver window, input a single equation into the area under “Equation”. • Use the soft keyboard to input an equation that contains at least one variable. • If you do not input an equals sign, the ClassPad assumes that the expression is to the left of the equals sign, and there is a zero to the right. Solving an Equation Numeric Solver solves equations by calculating approximations based on Newton’s method. Because of this, you should keep the following points in mind about its solutions. • Even if an equation has multiple solutions, only one solution is obtained for a particular Numeric Solver operation. For example, x2−1 = 0 has the two solutions 1 and −1. Numeric Solver will display either of the solutions first, depending on the value specified by “Lower” and “Upper”. • Solutions may include errors that are not actual solutions. The accuracy of solutions can be determined by viewing the [Left–Right] value in the Result dialog box. The closer the [Left–Right] value is to zero, the more accurate the results. Chapter 9: Numeric Solver Application 178 u To solve an equation 1. On the Numeric Solver window, input an equation. • Here, we will input the equation y = x2 − 2, and solve for x when y = 0 and y = 2. 2. Press E. 3. Input 2 as the values for variable y (to the right of y=). 4. Since we want to solve for x, select the option button to the left of variable x (so the button next to the variable becomes ). 5. Tap 1. • This displays the Result dialog box with the calculation result. Tap [OK] to close the dialog box. 6. Input 0 as the values for variable y (to the right of y=). 7. Tap 1. • Though the solution of x2 − 2 = 0 is x = ± 2, here the value that is displayed is the decimal form of 2, which is near the last solution obtained (x = 2). To obtain the other solution, change the Upper value (to 0, for example) and then tap 1. 0901 t is the time it would take for an object thrown straight up with initial velocity v to reach height h. Use the formula h = vt − 1/2 gt2 to calculate the initial velocity v for a height of h = 14 meters and a time of t = 2 seconds. Gravitational acceleration is g = 9.8 m/s2. Tip • If ClassPad judges that the displayed results are not converging sufficiently, it displays the message “Did not converge. Do you wish to continue the calculation?” Tap [Yes] to continue, or [No] to cancel the calculation. • If the message “Can’t solve!” appears on the display, perform either (or both) of the operations below and then tap 1 again. - Tap a - [Initialize Bound], or manually change the “Lower” and “Upper” values. - Change the convergence range. See “To change the convergence range” below. u To change the convergence range 1. Tap a - [Convergence] to display the Convergence dialog box. 2. Enter an integer in the range of 1 to 13. • A smaller value increases the allowable error range, and lessens the chance of a “Can’t solve!” error. If a calculation causes a “Can’t solve!” error, try changing this setting to a smaller value. 3. Tap [OK] to apply the setting and close the dialog box. • The new setting value will be shown in the status bar (page 178). Chapter 9: Numeric Solver Application 179 Chapter 10: eActivity Application The eActivity application lets you input and edit text, mathematical expressions, and ClassPad application data, and save your input in a file called an “eActivity”. A basic eActivity can contain text along with application data, which is embedded as a row or a strip. A row can be a “Text Row”, a “Calculation Row”, or a “Geometry Link”. A strip can be an “application data strip” (Main, Graph & Table, Geometry, and so on). Example eActivity windows 2 3 1 1 eActivity window 2 Graph strip 3 Expand button 4 Expanded graph window 4 Tip: A variety of eActivity files are available for download at the CASIO Website. http://edu.casio.com/products/classpad/ After you download an eActivity file, you will need to transfer it from your computer to your ClassPad. See the instructions provided at the CASIO Website for more information. eActivity Application-Specific Menus and Buttons • Clear variables that contain numbers, list and matrices ...........................................Edit - Clear All Variables • Insert a row or strip .............................................Insert - Calculation Row (page 182); Text Row (page 181); Geometry Link (page 184); Strip(1) or Strip(2) (page 182) • Add help text to the currently selected strip ................................................................. Insert - Add Strip Help • Insert a command ................................................................................................................. Action (page 61) • Open or save a file ......................................................................................................................................{ • Bold the text that is currently selected (Text Input mode only) ...................................................................B • Convert a text row to a calculation row or a calculation row to a text row ..........................................u / < 10-1 Creating an eActivity Basic Steps for Creating an eActivity 1. Start the eActivity application. • This displays the eActivity window as it appeared the last time it was used. • If you are already in the eActivity application and there is data on the display, tap [File] and then [New]. Note that [New] clears data from the display without saving it. Chapter 10: eActivity Application 180 2. On the eActivity window, insert the text, expressions, application data, and other data you want to include in the eActivity. For details, see “Inserting Data into an eActivity” below. 3. After the eActivity is the way you want, tap [File] and then [Save]. 4. On the dialog box that appears, enter a file name and then tap [Save] to save the eActivity. Tip: eActivity files are stored in a memory area that is separate from that used for storing other types of data (variable data, Geometry data, Spreadsheet data, etc.). Because of this, you cannot access eActivity files data using the Variable Manager. You have to use the eActivity application to perform eActivity file operations. Inserting Data into an eActivity The following describes the four types of data you can insert into an eActivity. Text row A text row can be used to insert text data and mathematical expression text in natural format. You can also bold the text in a text row. Calculation row Use the calculation row to insert any of the calculation operations that are available in the Main application. Application data strip The application data strip lets you display a window from a ClassPad application (Main, Graph & Table, Geometry, etc.) and use the window to create data, which is inserted into the eActivity. Geometry Link row Use this row to insert data that is linked with a Geometry window figure. u To insert a text row 1. On the eActivity window toolbar, check to make sure that u is displayed. If it isn’t, tap < to toggle it to u. • u indicates the Text Input mode is selected. • If the cursor is located in a line that already contains input data, place the cursor at the end of the line, tap [Insert] and then [Text Row]. This inserts a text row on the next line. 2. Use the soft keyboard or keypad keys to input the text you want. • Pressing E will advance you to the next line without displaying results. • Standard text (words separated by spaces) is automatically wrapped to the next line as required. A continuous text or number string (one that does not include any spaces) will not be wrapped to the next line if it does not fit within the width of the window. • Note that any mathematical expressions or commands you input into a text row are treated as text. They are not executed. Tip • Text can be changed to bold by dragging to select it and then tapping B. However, note that you cannot bold numeric expressions of a natural display expression that you input with the template input mode (page 24). • You can select a range of characters with the left and right cursor keys. Simply press the ClassPad f key and then press e or d. Each press of the cursor key will select (highlight) the next character in the applicable direction. Chapter 10: eActivity Application 181 u To insert a calculation row 1. On the eActivity window toolbar, check to make sure that < is displayed. If it isn’t, tap u to toggle it to <. • < indicates the Calculation Input mode is selected. • If the cursor is located in a line that already contains input data, place the cursor at the end of the line, tap [Insert] and then [Calculation Row]. This inserts a calculation row on the next line. 2. Use the soft keyboard or keypad keys to input the mathematical expression you want. 3. Press E after inputting an expression to display its result. Tip • If the input expression of a calculation row is not a valid expression, the row will contain only the input expression, without an output expression. • If you edit the expression in an existing calculation row and then press E, all of the expressions following the line you edited are re-calculated and their results are refreshed. Expression you input Result Inserting an Application Data Strip An application data strip can be used to embed data from other ClassPad applications into an eActivity. An application data strip contains the elements shown to the right. Title You can enter a title, if you want. Expand button Tap here to display the application data in the lower window. u To insert an application data strip 1. On the eActivity window, tap [Insert] and then [Strip(1)] or [Strip(2)]. Next, tap a menu item based on the type of application data you want to insert. See “Application data strip list” below for details about application data types. • This inserts the data strip into the eActivity window, opens a data strip window in the lower half of the display, and makes the data strip window active. 2. Perform the required input procedure in accordance with the type of window that is opened. For details, see the examples, below. 3. After completing all the data strip window operations, tap C to close the window. • This makes the eActivity window active, with the cursor in the strip you inserted in step 1. 4. Enter the title you want. 1001 To insert a Graph strip 1002 To insert a Notes strip Chapter 10: eActivity Application 182 Application data strip list Or tap this button: To insert this type of application data: Select this [Insert] menu item: Graph window data (Graph & Table) Strip(1) - Graph $ Graph Editor window data (Graph & Table) Strip(1) - Graph Editor ! 3D Graph window data Strip(1) - 3D Graph 7 3D Graph Editor window data Strip(1) - 3D Graph Editor Z Geometry window data Strip(1) - Geometry 3 Spreadsheet window data Strip(1) - Spreadsheet Q Stat Graph window data Strip(1) - Stat Graph y Stat Editor window data Strip(1) - Stat Editor ( Notes window* Strip(1) - Notes _ Main work area window data Strip(1) - Main ~ Conics Graph window data Strip(2) - Conics Graph ^ Conics Editor window data Strip(2) - Conics Editor * Differential Equation Graph window data Strip(2) - DiffEqGraph O Differential Equation Graph Editor window data Strip(2) - DiffEqGraph Editor A Financial window data Strip(2) - Financial I Probability window* data Strip(2) - Probability P Numeric Solver window data Strip(2) - NumSolve 1 Sequence Editor window data Strip(2) - Sequence Editor & Verify window* data Strip(2) - Verify W Picture Plot window data Strip(2) - Picture Plot 5 1 2 2 *1 The Notes window can be used with the eActivity application only. *2 The Probability window and Verify window can be used with the eActivity application and Main application. For more information see “2-10 Using Verify” and “2-11 Using Probability”. u To add help text to a strip 1. Tap the title box of the strip to which you want to add help text. 2. Tap [Insert] - [Add Strip Help]. • A help window appears in the upper half of the display, while the window that was called from the strip appears in the lower half of the display. 3. Input the help text into the help window. 4. After inputting all the text you want, tap C to close the help window. • The strip will now have a ? button. Tapping ? will display the help window along with the application window. Tip: To delete help text from a strip, tap the title box of the strip whose help text you want to delete, and then tap [Insert] [Remove Strip Help]. Chapter 10: eActivity Application 183 Inserting a Geometry Link Row A mathematical expression in a Geometry Link row in an eActivity dynamically links to figure(s) in the Geometry window. Dragging a line or figure from the Geometry window to a Geometry Link row in an eActivity converts the line or figure to its mathematical expression. Conversely, dragging an expression from a Geometry Link row to the Geometry window converts the expression to its graphical form (line, curve, circle, etc.). This expression is interlinked with its Geometry window figure, so modifying one causes a corresponding change in the other. u To use a Geometry Link row Example: To drag one side of a triangle drawn on the Geometry window and link it to an eActivity 1. From the eActivity menu, tap [Insert], [Strip(1)], and then [Geometry] to insert a Geometry strip. 2. On the Geometry window that appears in the lower half of the screen, draw a triangle. 3. Tap the eActivity window to make it active. 4. Tap [Insert] and then [Geometry Link]. • This inserts a Geometry Link row in the next line. Geometry Link row Link symbol 5. Tap the Geometry window to make it active. 6. Tap one side of the triangle to select it, and then drag it to the right of the link symbol in the eActivity window. • This inputs the equation of the line that represents the side of the triangle into the link. • Modifying the equation in the Geometry Link row and pressing E causes a corresponding change in the Geometry window. Chapter 10: eActivity Application 184 • The example above shows how the isosceles triangle ABC (CA = BC) changes when the equation in the Geometry Link row is changed from y = 2x + 1.581 to y = x + 2. Tip • Pressing E after changing data in a Geometry Link updates the corresponding figure in the Geometry window. • Changing the figure in the Geometry window will cause the linked data in an eActivity to update accordingly. 10-2 Transferring eActivity Files File Compatibility Note the following precautions when using the ClassPad’s data communication function to transfer eActivity files with another ClassPad unit or a computer. • The ClassPad II supports only eActivity files created with a ClassPad II unit or with ClassPad Manager. eActivity files created with another ClassPad model cannot be opened by the ClassPad II. • You may not be able to open an eActivity file created using a newer version ClassPad II using an older version ClassPad II. Transferring eActivity Files between a ClassPad Unit and a Computer You can transfer eActivity files between ClassPad and a computer. For details, see “19-2 Performing Data Communication between the ClassPad and a Personal Computer”. Transferring eActivity Files between Two ClassPad Units You can connect two ClassPad II units to each other and transfer eActivity files between them. For details about how to do this, see “19-3 Performing Data Communication between Two ClassPads”. Chapter 10: eActivity Application 185 Chapter 11: Financial Application You can use the Financial application to perform a variety of financial calculations. Important! Financial calculation rules and practices can differ according to country, geographic area, or financial institution. It is up to you to determine whether the calculation results produced by this calculator are compatible with the financial calculation rules that apply to you. 11-1 Financial Application Basic Operations • Each time you select a calculation from the Financial application menu, a new page is added for that calculation. • Each page has input boxes for inputting values and input/calculation boxes that can be used both to input values and display calculation results. The examples below explain basic operations using the Financial application page. Example: What is the final value after two years (730 days) of a $3,000 investment earning 5.0% simple interest? Also calculate the final value during the same period for the same investment when the simple interest rate is 3%. 1. On the application menu, tap to start the Financial application. • If this is the first time the application is being started up, the Financial menu window will appear. 2. Tap [Calc(1)] and then [Simple Interest] (or, on the Financial menu window, tap “Simple Interest”). • This will add a new page for performing the calculation (page 1) and display the “Simple Interest” page. Financial menu window 3. Input the following information: Days = 730; I% (annual interest rate) = 5; PV (present value) = −3000. 4. Tap [SI] and then [SFV]. • This will display the calculation results for simple interest (SI) and simple future value (SFV = principal + interest). Input box Input values in the box. Input/calculation box Input values when required. For calculation, tap the button to the left of the box. Chapter 11: Financial Application 186 5. Tap [Calc(1)] and then [Simple Interest] again. • This adds a new page (page 2). The new page will inherit value input on the previous page (under initial settings). 6. Change the I% value to 3, tap [SI], and then [SFV]. • The SI and SFV values are updated in accordance with the new I% value. Tip • If the cursor is in an input/calculation box, “Solve” will appear on the left side of the status bar. You can tap this to complete the calculation instead of tapping the box to the left of the input/calculation box. • Financial application pages remain in memory even if you exit the Financial application. The next time you start up the Financial application, the page that was displayed the last time you exited the application will appear first. Page Operations As shown in the sample operation above, each time you select a calculation from the Financial application menu, a new page is added for that calculation. The following types of operations can be performed on a page. • Display the previous page or following page*1 ..............................Tap , / . • Display help about the currently selected field on the page....... Tap [Help] tab • Change the settings of the displayed page’s calculation ....... Tap [Format] tab • Delete the currently displayed Financial application page*2 ........................................................................................Edit - Delete Page • Clear all the values from the displayed Financial application page ..........................................................................................Edit - Clear Page • Delete all the Financial application pages and display the Financial application initial screen*3 ..................................................... Edit - Clear All *1 , and/or . on the toolbar indicates that there is a page before and/or after the current page. < and/or > indicates there is no page before and/ or after the current page. In this case, tapping < or > will not change to another page. *2 Executing this operation when there is only one page will display the Financial menu window. *3 Executing this operation will display the Financial menu window. Note: If the currently displayed page is part way through a series of pages that are in memory, selecting a calculation from the [Calc(1)] or [Calc(2)] menu will create a new page in the series and delete everything after it. If you select a new calculation while page 3 of 5 is displayed, for example, the newly created page will become 4 of 4. Chapter 11: Financial Application 187 Configuring Financial Application Settings Most financial calculations require that you define certain general parameters that affect the results they produce. For example, you need to specify whether you use a 360-day or 365-day year, whether payments are made at the beginning of a period or end of a period, etc. The following are settings required by the Financial application. Default settings Configure default settings using the Financial Format dialog box. These settings are applied whenever you add a new page with the Financial application. Local settings Configure local settings on the Format tab of each page, or by tapping the status bar. Local settings are applied to the currently displayed page only. Local settings are generally applied to the currently displayed page only. Note, however, that if you have one page displayed (Page A) and then add a new page (Page B), the initial settings of any Page B local setting items that are also on Page A will be those inherited from Page A. Default settings will be applied as the initial settings of items on Page B that are not also included on Page A. The table below shows setting items for each type of Financial calculation. Financial Calculation Setting Items Simple Interest Days in Year Yes Payment Date Compound Interest Yes Amortization Odd Period Yes Yes Bond Calculation Yes Yes Yes Yes Yes Yes Break-even Point Yes Date Format Automatically copy common fields to new calculation Day Count Yes Yes Yes Compounding Frequency Yes Bond Interval Yes Profit Amount/Ratio Yes Break-Even Value Yes • The “Date Format” and “Automatically copy common fields to new calculation” setting items in the above table can be configured on the Financial Format dialog box only. • The “Automatically copy common fields to new calculation” option is automatically applied (and is the only option available) for any setting item that is not included in the above table. • For details about each of the setting items, see “Financial Format Dialog Box” (page 41). Chapter 11: Financial Application 188 11-2 Performing Financial Calculations The calculations in the table below can be performed with the Financial application. For actual calculation examples, refer to the sections of this manual or the separate “Examples” booklet shown in the “Example” column. To perform this type of calculation: Select this menu item: Example Interest without compounding based on the number of days money is invested Calc(1) - Simple Interest Page 186 Interest based on compounding parameters specified by you Calc(1) - Compound Interest 1101 Value of money paid out or received in varying amounts over time Calc(1) - Cash Flow 1102 Interest and principal portions of a payment or payments Calc(1) - Amortization 1103 Effective or nominal interest rate for interest compounded multiple times during a year Calc(1) - Interest Conversion 1104 Cost, selling price, or margin of profit on an item given the other two values Calc(1) - Cost/Sell/ Margin 1105 Number of days between two dates, or the date that is a specified number of days from another date Calc(1) - Day Count 1106 Amount that a business expense can be offset by income (depreciated) over a given year Calc(1) - Depreciation 1107 Purchase price or annual yield of a bond Calc(1) - Bond Calculation 1108 Amount you must sell to break even or to obtain a specified profit, as well as amount of profit or loss on particular sales Calc(2) - Break-Even Point 1109 How much sales can be reduced before incurring losses Calc(2) - Margin of Safety 1110 Degree of change in net earnings arising from a change in sales amount Calc(2) - Operating Leverage 1111 Degree of change in net earning arising from a change in interest paid Calc(2) - Financial Leverage 1112 Calc(2) - Combined Leverage 1113 Calc(2) - Quantity Conversion 1114 Combined effects of operating and financial leverages Number of items sold, selling price, or sales amount given other two values; number of items manufactured, unit variable cost, or total variable cost given other two values 11-3 Calculation Formulas For information about terms used in formulas that are not explained in detail below, refer to “11-5 Input and Output Field Names”. Simple Interest 365-day Mode: SI' = Days × PV × i 365 Days × PV × i 360-day Mode: SI' = 360 SI = –SI' SFV = –(PV + SI') i = I% 100 Chapter 11: Financial Application 189 Compound Interest u When calculating PV, PMT, FV, n I% 0 – α × PMT – β × FV PV = PMT = FV = I% = 0 PV = – (PMT × n + FV ) γ PMT = – – PV – FV – PV – FV = – (PMT × n + PV ) PMT n=– log n= α = (1 + i × S) × { (1 + iS ) × PMT – FV × i (1 + iS ) × PMT + PV × i } PV + FV PMT log (1 + i) 1–β i When “Odd Period” is “Off” = ;= PV + FV n (1 + i) When “Odd Period” is “CI” –n When “Odd Period” is “SI” (1 + i) (1 + i) 1 –Intg (n) Frac (n) 1 + i × Frac (n) When “Payment Date” is “End” When “Payment Date” is “Begin” 0 1 When P/Y = C/Y = 1 When P/Y 1 and/or C/Y 1 I% 100 P/Y I% (1 + ) –1 100 × [C/Y ] S= i= C/Y u When calculating I% i (effective interest rate) is calculated using Newton’s Method. ; × PV + ( × PMT + × FV = 0 I% is calculated from i using the formulas below: When P/Y 1 and/or C/Y 1 When P/Y = C/Y = 1 ( i × 100 I% = (1 + i ) P/Y C/Y ) –1 × C/Y × 100 Interest (I%) calculations are performed using Newton’s Method, which produces approximate values whose precision can be affected by various calculation conditions. Interest calculation results produced by this application should be used keeping the above in mind, or results should be confirmed separately. Cash Flow NPV = CF0 + CF2 CF3 CFn CF1 + + +…+ (1+ i) (1+ i)2 (1+ i)3 (1+ i)n ( = =% 100 , n: natural number up to 80) NFV = NPV × (1 + i )n IRR is calculated using Newton’s Method. 0 = CF0 + CF2 CF3 CFn CF1 + + +…+ (1+ i) (1+ i) 2 (1+ i) 3 (1+ i) n Chapter 11: Financial Application 190 In this formula, NPV = 0, and the value of IRR is equivalent to i × 100. It should be noted, however, that minute fractional values tend to accumulate during the subsequent calculations performed automatically by the ClassPad, so NPV never actually reaches exactly zero. IRR becomes more accurate the closer that NPV approaches to zero. 0 .................................. (CF0 t 0) PBP = { NPVn = Σ k n– n =0 NPVn ... (Other than those above) NPVn+1 – NPVn n: smallest positive integer that satisfies the conditions NPVn s 0, 0 s NPVn+1, or 0 CFk (1 + i)k Amortization e a 1 payment 1 payment c d b 1............. PM1................ PM2 ............. Last 1 ............ PM1 ................... PM2 .......... Last Number of payments Number of payments a: interest portion of payment PM1 (INT) b: principal portion of payment PM1 (PRN) c: principal balance upon completion of payment PM2 (BAL) d: total principal paid from payment PM1 to payment PM2 (ΣPRN) =1@PM1=I DG5PM1–1 × I × (H2@) HJ1PM1=H2@+DG5PM1–1 × DG5PM2=DG5PM2–1 +HJ1PM2 Σ HJ1=HJ1 PM2 PM1 +HJ1PM1+1 + … + HJ1PM2 PM1 e: total interest paid from payment PM1 to payment PM2 (ΣINT) a + b = one repayment (PMT) Σ =1@==1@ PM2 PM1 +=1@PM1+1 + … + =1@PM2 PM1 BAL0 = PV (when “Payment Date” is “End”) INT1 = 0, PRN1 = PMT (when “Payment Date” is “Begin”) Converting between the Nominal Interest Rate and Effective Interest Rate The nominal interest rate (I % value input by user) is converted to an effective interest rate (I %' ) for installment loans where the number of annual payments is different from the number of annual compound calculation periods. [C/Y ] { } [P/Y ] I% I%' = (1 + ) – 1 × 100 100 × [C/Y ] The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations. i = I%' ÷ 100 Interest Conversion n APR/100 EFF = 1 + – 1 × 100 n 1 EFF n APR = 1 + – 1 × n × 100 100 Chapter 11: Financial Application 191 Cost/Sell/Margin CST = SEL 1 – MRG 100 SEL = CST MRG 1– 100 MRG(%) = 1 – CST SEL × 100 Depreciation u Straight-Line Method SL1 = (PV – FV ) YR1 × n 12 SLj = (PV – FV ) n SLn+1 = (PV – FV ) 12 – YR1 × n 12 (YR112) u Fixed-Percentage Method YR1 I% FP1 = PV × 100 × 12 FPj = (RDVj–1 + FV ) × RDV1 = PV – FV – FP1 RDVj = RDVj–1 – FPj I% 100 FPn+1 = RDVn (YR112) RDVn+1 = 0 (YR112) u Sum-of-the-Years’-Digits Method Z= n (n + 1) 2 SYD1 = n' = n – YR1 12 n YR1 × (PV – FV ) Z 12 SYDn+1 = ( SYDj = ( n' – j + 2 )(PV – FV – SYD1) Z' n' – (n + 1) + 2 12 – YR1 )(PV – FV – SYD1) × Z' 12 RDV1 = PV – FV – SYD1 (Intg (n' ) + 1)(Intg (n' ) + 2 × Frac (n' ) ) 2 Z' = ( j1) (YR112) RDVj = RDVj –1 – SYDj u Declining-Balance Method DB1 = PV × I% YR1 × 100n 12 RDVj = RDVj–1 – DBj RDV1 = PV – FV – DB1 DBj = (RDVj–1 + FV ) × DBn +1 = RDVn RDVn+1 = 0 (YR112) I% 100n (YR112) Bond Calculation u Terms in the formulas PRC: price per $100 of face value D RDV: redemption price per $100 of face value CPN: coupon rate (%) A YLD: annual yield (%) B Redemption date (d2) M: number of coupon payments per year (1 = Annual, 2 = Semi-annual) Issue date N: number of coupon payments until maturity (n is used when “Term” is specified for “Bond Interval”.) INT: accrued interest Purchase date (d1) Coupon payment dates CST: price including interest A: accrued days D: number of days in coupon period where settlement occurs B: number of days from purchase date until next coupon payment date = D – A Chapter 11: Financial Application 192 u PRC when “Date” is specified for “Bond Interval” For one or fewer coupon period to redemption: RDV + CPN/M PRC = − + A/D × CPN/M 1 + (B/D × (YLD /100)/M) For more than one coupon period to redemption: RDV PRC = − N (N–1+B/D ) (1 + (YLD/100)/M) INT = −A/D × CPN/M –Σ k=1 ( CPN/M (k–1+B/D ) (1 + (YLD /100) /M) ) + A/D × CPN/M CST = PRC × INT u PRC when “Term” is specified for “Bond Interval” PRC = − RDV n n (1 + (YLD/100)/M) –Σ k=1 ( CPN/M k (1 + (YLD/100)/M) ) CST = PRC INT = 0 u YLD The Financial application performs annual yield (YLD) calculations using Newton’s Method, which produces approximate values whose precision can be affected by various calculation conditions. Because of this, annual yield calculation results produced by this application should be used keeping the above in mind, or results should be confirmed separately. Break-Even Point u Profit (Profit Amount/Ratio Setting: Amount (PRF)) QBE = FC + PRF PRC – VCU SBE = FC + PRF × PRC PRC – VCU u Profit Ratio (Profit Amount/Ratio Setting: Ratio (r%)) FC QBE = PRC × 1– r% – VCU 100 Margin of Safety MOS = PRC × 1– r% 100 × PRC – VCU Financial Leverage SAL – SBE SAL DFL = Operating Leverage DOL = FC SBE = SAL – VC SAL – VC – FC EBIT EBIT – ITR Combined Leverage DCL = SAL – VC SAL – VC – FC – ITR Quantity Conversion SAL = PRC × QTY VC = VCU × QTY Chapter 11: Financial Application 193 11-4 Financial Calculation Functions ClassPad mathematical functions can be used to perform some Financial application calculations. ClassPad mathematical functions can be selected on the [Financial] submenu of the [Action] menu of the Main application or eActivity application. The table below shows a list of mathematical functions that perform financial calculations. For descriptions of the arguments shown in each syntax and the values returned by each function, refer to “11-5 Input and Output Field Names”. Financial Calculation Simple Interest Function Syntax This function returns: simpInt simpInt(Days,I%,PV) SI simpFV(Days,I%,PV) SFV cmpdFV* cmpdFV(N,I%,PV,PMT,P/Y,C/Y) FV 1 cmpdIR(N,PV,PMT,FV,P/Y,C/Y) I% simpFV 1 cmpdIR* Compound Interest Cash Flow Amortization Interest Conversion Cost/Sell/ Margin Day Count Bond Calculation 1 cmpdN(I%,PV,PMT,FV,P/Y,C/Y) N cmpdPmt*1 cmpdPmt(N,I%,PV,FV,P/Y,C/Y) PMT cmpdPV*1 cmpdPV(N,I%,PMT,FV,P/Y,C/Y) PV cashIRR cashIRR(Cash) IRR cashNFV cashNFV(I%,Cash) NFV cashNPV cashNPV(I%,Cash) NPV cashPBP cashPBP(I%,Cash) PBP amortBal amortBal(PM1,PM2,I%,PV,PMT,P/Y,C/Y) BAL amortInt amortInt(PM1,PM2,I%,PV,PMT,P/Y,C/Y) INT amortPrn amortPrn(PM1,PM2,I%,PV,PMT,P/Y,C/Y) PRN amortSumInt amortSumInt(PM1,PM2,I%,PV,PMT,P/Y,C/Y) ΣINT amortSumPrn amortSumPrn(PM1,PM2,I%,PV,PMT,P/Y,C/Y) ΣPRN convEff convEff(N,I%) EFF convNom convNom(N,I%) APR priceCost priceCost(Sell,Margin) Cost priceSell priceSell(Cost,Margin) Sell priceMargin priceMargin(Cost,Sell) Margin dayCount dayCount(MM1,DD1,YYYY1,MM2,DD2,YYYY2) Days bondPriceDate*2 bondPriceDate(MM1,DD1,YYYY1,MM2,DD2, YYYY2,RDV,CPN,YLD) {PRC,INT,CST} bondPriceTerm*3 bondPriceTerm(N,RDV,CPN,YLD) {PRC,INT,CST} bondYieldDate*2 bondYieldDate(MM1,DD1,YYYY1,MM2,DD2, YYYY2,RDV,CPN,PRC) YLD bondYieldTerm*3 bondYieldTerm(N,RDV,CPN,PRC) YLD cmpdN* *1 P/Y and C/Y can be omitted. When they are omitted, calculations are performed using P/Y=1 and C/Y=1. *2 “Date” must be specified for the Financial Format “Bond Interval”. *3 “Term” must be specified for the Financial Format “Bond Interval”. Chapter 11: Financial Application 194 11-5 Input and Output Field Names The list below shows the names of the input and output fields displayed on the various Financial application pages. When performing a calculation on your ClassPad, you can also get information using the [Help] tab. APR: Nominal interest rate (as a percent) NFV: Net future value BAL: Balance of principal after PM2 NPV: Net present value C/Y: Number of times interest is compounded per year P/Y: Number of installment periods per year Cash: List of income or expenses (up to 80 entries) Cost (Cost/Sell/Margin): Production cost PM1: Number of first installment period in interval under consideration Cost (Bond Calculation): Cost of bond (price plus partial year interest) PM2: Number of last installment period in interval under consideration CPN: Annual coupon rate PMT: Amount paid each period d1: Month (1-12); Day (1-31); Year (1902-2097) PRC (Bond Calculation): Price of bond d2: Month (1-12); Day (1-31); Year (1902-2097) PRC (Break-Even Point, Quantity Conversion): Selling price per unit Days (Day Count): Number of days from d1 to d2 PBP: Payback period Days (Simple Interest): Number of days in investment period PRF: Profit DB: Depreciation for year j calculated using the declining-balance method PV: Present value (initial investment) DCL: Degree of combined leverage QTY (Manufacturing): Number of units manufactured DFL: Degree of financial leverage QTY (Sales): Number of units sold DOL: Degree of operating leverage r%: Proportion of sales amount retained as a profit EBIT: Earnings before interest and taxes PRN: Principal portion of PM1 QBE: Number of units to be sold (as a percent) EFF: Effective interest rate (as a percent) RDV (Bond Calculation): Redemption value FC: Fixed costs RDV (Depreciation): Residual value after depreciation for year j FP: Depreciation for year j using the fixed-percentage method FV: Future value I%: Annual interest rate (as a percent) INT (Amortization): Interest portion of PM1 INT (Bond Calculation): Interest accumulated during partial year portion of investment period INT (Financial Leverage, Combined Leverage): Interest to be paid to bondholders IRR: Interest rate of return j: Year for which depreciation is being calculated Margin: Margin of profit (portion of selling price not absorbed by cost of production) MOS: Margin of safety (portion of sales amount above break-even point) N (Bond Calculation): Number of periods N (Compound Interest): Number of installment periods N (Depreciation): Number of years over which depreciation occurs N (Interest Conversion): Number of times interest is compounded per year SAL: Amount obtained from sales SAL (Operating Leverage): Amount currently obtained from sales SBE (Break-Even Point): Amount that must be obtained from sales to break even SBE (Margin of Safety): Break-even sales (amount that must be obtained from sales to break even) Sell: Selling price SFV: Simple future value (principal + interest) SI: Simple interest SL: Depreciation for year j using the straight-line method sumINT: Total interest paid from PM1 to PM2 (inclusive) sumPRN: Total principal paid from PM1 to PM2 (inclusive) SYD: Depreciation for year j using the sum-of-theyears’-digits method VC: Variable cost for a certain level of production VCU: Variable cost per unit YLD: Yield to maturity (as a percent) YR1: Number of depreciable months in first year Chapter 11: Financial Application 195 Chapter 12: Program Application The Program application comes in handy when you need to perform the same calculation a number of times. You can create programs that automate graphing and other operations. The Program application consists of a Program Editor for inputting and editing programs, and a Program Loader for loading and executing existing programs. • The Program Loader window appears when you start up the Program application. • To display the Program Editor window, tap P on the Program Loader window, or tap O, [Window] and then [Program Editor]. File name File type N: Program file T: Text file F: User-defined function file Program Loader window Program Editor window Program Application-Specific Menus and Buttons Program Loader window • Display the Program Editor window .........................O - Window - Program Editor, Edit - Open Editor or P • Run a program ....................................................................................................... Run - Run Program or . Program Editor window • Display the Program Loader window ................................................... O - Window - Program Loader or ) • Save a file ..........................................................................................................Edit - Save File - Save or { • Save a file under a new name ................................................................................Edit - Save File - Save As • Close a file ............................................................................................................................. Edit - Close File • Convert a file to a program file .......................................................................Edit - Mode Change - 'Normal • Convert a file to a text file .................................................................................. Edit - Mode Change - 'Text • Convert a file to an edit prohibited program file ..................................................................... Edit - Compress • Search for a newly specified text string ..................................................... Edit - Search - New Search or e • Search again for a previously specified text string.....................................Edit - Search - Search Next or r • Jump to the beginning/end of a program .................................Edit - Search - Jump to Top / Jump to Bottom Chapter 12: Program Application 196 • Input a command (see “12-4 Program Command Reference”) ................................................. Ctrl, I/O, Misc Program Loader window and Program Editor window common commands • Display the Program Output window.....................................................O - Window - Program Output or _ • Display the Text File Contents window ....................................................... O - Window - Text File Contents • Display the Main application work area window .................................................... O - Window - Main or ~ • Create a new file ............................................................................................................ Edit - New File or O • Open an existing file .....................................................................................................Edit - Open File or ~ 12-1 Creating and Running Program This section explains the steps you need to perform in order to create and run a program. Creating a Program Example: To create a program named “OCTA” that uses the formulas below determines the surface area (S) and volume (V) of a regular octahedron S = 2 3 A2, V= 2 3 A 3 A u To create and save a new program 1. On the Program Loader or Program Editor window, tap O. 2. On the dialog box that appears, configure the settings for the new file as described below. • Leave the [Type] setting as “Program(Normal)”. • Tap the [Folder] down arrow button and then select the folder where you want to save the program file. • In the [Name] box, input up to eight bytes for the program file name. Here, we will input “OCTA”. 3. Tap [OK]. This displays a blank Program Editor window. 4. Input the necessary expressions and commands. Here, we will input the program shown in the nearby screenshot. • Each mathematical expression and command must be followed either by a carriage return or colon (:). • Use the menus shown below to input the “SetDecimal”, “Input”, and “Print” commands. [Misc] - [Setup(1)] - [SetDecimal] [I/O] - [Input] - [Input] [I/O] - [Output] - [Print] For information about the menus, syntax, operation, and other details about commands, see “12-4 Program Command Reference”. • Calculation results of arguments that are input using the “approx(” function are displayed using rounded decimal parts. Use the soft keyboard for input. Chapter 12: Program Application 197 5. After the program is the way you want, tap {, or tap [Edit], [Save File] and then [Save] to save it. • To run this program see “Running a Program” on page 199. • If a message appears when you try to save the program, make the necessary corrections and try again. For details about making corrections to a program, see “12-2 Debugging a Program”. Tip • The file name you input in step 2 of the above procedure is subject to the same rules as folder and variable names. For more information, see “Folder and Variable Name Rules” on page 31. • To input a program and save it without running it, perform the above procedure up to step 5, and then tap [Edit] and then [Close File]. • If you want to use the calculation results produced by program execution in another calculation, include a line in the program that uses the “⇒” command to assign the calculation result to a variable. For example, you could add the line below to the above example program to assign the calculated surface area to variable S and the volume to variable V. 2× (3) × A^2 ⇒ S: (2)/3 × A^3 ⇒ V Note that calculation results produced within programs are not stored in Ans memory. Pausing Program Execution You can specify where execution of a program should pause by including either a Pause command or a Wait command inside the program. For details about each command, see “12-4 Program Command Reference”. Configuring Parameter Variables and Inputting Their Values When Creating a Program If you input the names of variables used in a program into the parameter variable box when creating a program on the Program Editor window, you will be able to input values for the variables on the Program Loader window when you run the program. Example: Parameter variable box Indicates variables named “A” and “B” are used within the program. Parameter value input box Inputting 1, 2 before running the program assigns A = 1 and B = 2. Executing the program produces the result A + B = 1 + 2 = 3. Tip: Variables that are specified as parameter variables within a program are automatically treated as local variables. For information about local variables, see “Local” in the “Command List” (page 214). Using a Subroutine to Call another Program Including the name of another program file inside of a program causes execution to jump to the specified program file. Syntax: ({ , , ... }) The program that execution jumps from is called the “main program”, while the program to which execution jumps is called a “subroutine”. Chapter 12: Program Application 198 When program execution returns to the main program, it resumes from the point immediately after the command that jumped to the subroutine. Example 1: Main Program: Subroutine: “Sub1” Jumps to subroutine program “Sub1” Example 2: Main Program: Subroutine: “Sub2” Assigns the values of main program variables “A” and “B” to the parameter variables (D and E) in subroutine “Sub2”, and then jumps to subroutine “Sub2”. Using Strings in a Program A string is a series of characters inside of quotation marks. In a program, strings are used to specify display text. A string made up of numbers (like “123”) or an expression (like “x–1”) cannot be processed as a calculation. Tip: To include quotation marks (") or a backslash (\) in a string, put a backslash (\) in front of the quotation marks (") or backslash (\). Examples: To include Japan: “Tokyo” in a string Print "Japan:\"Tokyo\"" To include main\abc in a string Print "main\\abc" Running a Program Example: To run the “OCTA” program created under “Creating a Program” (page 197) to calculate the surface areas and volumes of three regular octahedrons, the lengths of whose sides are 7, 10, and 15 u To run a program 1. On the Program Loader window, specify the program you want to run. (1) Tap the [Folder] down arrow button, and then select the folder you want. (2) Tap the [Name] down arrow button, and then tap the name of the file. Here, we will tap “OCTA”. • In this example, the “Parameter” input box is left blank. For information about using the “Parameter” input box, see “Configuring Parameter Variables and Inputting Their Values When Creating a Program” (page 198). 2. Tap ., or tap [Run] and then [Run Program] to run the program. • This runs the program and displays a dialog box prompting for input of a value for variable A (length of one side). Chapter 12: Program Application 199 3. Input a side length of 7 and tap [OK]. • A Program Output window, showing the execution results of the program, will appear in the lower half of the screen. • On the “Done” dialog box that appears after program execution is complete, tap [OK]. 4. Tap the Program Loader window and repeat steps 2 and 3 for sides of length 10 and 15. Calculation results when A = 7 Calculation results when A = 10 Calculation results when A = 15 Tip • The Program Output window can be displayed by tapping O, [Window] and then [Program Output], or by tapping _ on the Program Loader window. The Program Output window also appears whenever the DispText command is executed in a program. • Program Output window contents will remain displayed even if you run a different program. To clear the current contents, tap [Edit] - [Clear All] while the Program Output window is displayed. Executing the ClrText command also clears the currently stored Program Output window. • You can run a program from the Main application or the eActivity application. For more information, see “2-12 Running a Program in the Main Application”. Terminating Program Execution Pressing c while a program is running terminates the program. Tip: Pressing c does not terminate the program if program execution is already paused by the Pause command (see “12-4 Program Command Reference”). In this case, tap X on the status bar to resume program execution, and then press c. Creating a Text File Use the procedure below to create a text file using the Program Editor window. You can also convert a previously saved program file to a text file. u To create and save a new text file 1. On the Program Loader or Program Editor window, tap O. 2. On the dialog box that appears, configure the settings for the new file as described below. • Tap the [Type] down arrow button and then select “Program(Text)”. • Tap the [Folder] down arrow button and then select the folder where you want to save the text file. • In the [Name] box, input up to eight bytes for the text file name. 3. Tap [OK]. This displays a blank Program Editor window. 4. Input the text you want. 5. After input is complete, tap {, or tap [Edit], [Save File] and then [Save] to save it. u To change a program file to a text file While a program file is open, tap [Edit], [Mode Change], and then ['Text]. Chapter 12: Program Application 200 Tip: Note that the above operation is not possible while a user-defined function (page 203) is open. Using Text Files • Running a text file from the Program Loader window displays the contents of the file in the Text File Contents window. • Inserting a text file name followed by “()” inside a program causes the contents of the text file to be displayed in the Text File Contents window when execution reaches the name. Example: File Name: “CAUTION” Program that displays contents of “CAUTION” file Converting a Text File to a Program File You can convert a text file created on the ClassPad to a program file. You also can transfer a text file created on your computer to a ClassPad unit, and then convert it to a program file. u To change a text file to a program file While a text file is open, tap [Edit], [Mode Change], and then ['Normal]. Tip • Note that the above operation is not possible while a user-defined function (page 203) is open. • For information about transferring data between a computer and a ClassPad unit, see Chapter 19 of this manual. Converting a Program File to an Executable File You can use the procedure below to change a program file (PRGM file type) to an executable file (EXE file type). • An EXE file is about half the size as its corresponding PRGM file. • An EXE file can only be executed. It cannot be edited. Because of this, converting a PRGM file to an EXE file also generates an editable PRGM file as a backup. u To convert a program file (PRGM) to an executable file (EXE) 1. Open the PRGM file that you want to convert and display it in the Program Editor window. 2. Tap [Edit] and then [Compress]. • This displays a dialog box for inputting the backup file name. 3. Enter the backup file name and then tap [OK]. • This saves two copies of the file. One is an EXE file under the name of the original PRGM file. The other is a backup file, which is created under the name you specify here. Original File: OCTA (type: PRGM) Specified File Name: OCTA2 Resulting Files: OCTA (type: EXE), OCTA2 (type: PRGM) Chapter 12: Program Application 201 12-2 Debugging a Program A programming error that causes a program to behave in a manner not intended by the writer of the program is called a “bug”. Finding and eliminating such errors is called “debugging the program”. Any of the following conditions can indicate that your program has a bug and requires debugging. • If an error message appears when you try to save the program • If an error message appears when you try to run the program • If a program produces some abnormal or unexpected result Debugging After an Error Message Appears When an error occurs, a dialog box appears to explain the cause of the error. Carefully read the text of the error message and then tap its [OK] button. This closes the dialog box, opens the Program Editor window, and positions the cursor at the location where the error occurred. Make the necessary corrections in accordance with the explanation provided by the error message. Tip: EXE type files (page 201) cannot be edited. Tapping the [OK] button on the error dialog box will simply close the dialog box without displaying the Program Editor window. Open the backup PRGM file that was generated when you created the EXE file by converting it from a PRGM file, and use it for debugging. Debugging a Program Following Unexpected Results If execution of a program produces unexpected or abnormal results, carefully read through the program and correct errors as required. Editing a Program u To edit a program 1. On the Program Loader window, tap ~, or tap [Edit] and then [Open File]. 2. On the dialog box that appears, select the program you want to edit, as described below. • Tap the [Type] down arrow button and then select “Program(Normal)”. • Tap the [Folder] down arrow button and then select the folder that contains the program you want to edit. • Tap the [Name] down arrow button, and then select the name of the program you want to edit. 3. Tap [OK]. 4. Edit expressions and commands as required. 5. To overwrite the currently saved program with the edited version tap {, or tap [Edit], [Save File] and then [Save]. • To save the edited version of the program as a different program, use [Edit] - [Save File] - [Save As]. u To rename or delete a program Programs are saved as variables, so you can rename and delete them using Variable Manager. For details, see “Using Variable Manager” (page 29). Chapter 12: Program Application 202 12-3 User-defined Functions ClassPad lets you configure calculation operations as user-defined functions, which can then be used inside of numeric expressions just like its built-in functions. User-defined functions can also be called up in other applications. Note • User-defined functions are stored in ClassPad memory as “FUNC” (Function) type variables. Naming, storage, and folder rules are identical to those for user variables. • A user-defined function can contain only a single mathematical expression. • A user-defined function cannot contain any command. Creating a New User-defined Function You can use either of the methods below to create user-defined functions. • Using the Program application’s Program Editor window. • Using the Main application’s Define command. u To create and save a new user-defined function using the Program Editor window Example: To create a user-defined function named “f4” that calculates the following: x × (x + 1) × (x – 2) 1. On the Program Loader or Program Editor window, tap O. 2. On the dialog box that appears, configure the settings for the new file as described below. • Tap the [Type] down arrow button and then select “Function”. • Tap the [Folder] down arrow button and then select the folder where you want to save the user-defined function. • In the [Name] box, input up to eight bytes for the user-defined function name. Here, we will input “f4”. 3. Tap [OK]. This displays a blank Program Editor window. Parameter variable box 4. Input user-defined function arguments into the parameter variable box. Here, we will input “x”. 5. Input the expression you want. Here, we will input “x × (x + 1) × (x – 2)”. 6. After the function is the way you want, tap {, or tap [Edit], [Save File] and then [Save] to save it. u To create a user-defined function using the Define command Example: To create a user-defined function named “f2” that calculates the following: 2 x + 3y + 1 1. On the Program Loader window, tap ~, or tap O, [Window] and then [Main] to display the Main application window. • You could also tap M on the icon panel to start up the Main application. 2. Tap [Interactive] and then [Define]. 3. On the dialog box that appears, input the following. • [Func name]: “f2” • [Variable/s]: “x, y” • [Expression]: 2x + 3y + 1 Chapter 12: Program Application 203 4. Tap [OK]. • This will cause the Define command to be executed in accordance with your specifications, which will save user-defined function “f2”. Tip: For information about the syntax of the Define command, see “Define” in the “Command List” (page 208). Executing a User-defined Function Example: To use the Main application to execute user-defined functions “f4” and “f2” that were created under “Creating a New User-defined Function” As shown in the nearby screenshot, input the required arguments for each variable name and then press E to execute. Tip: User-defined functions are displayed on the catalog keyboard. You can change the keyboard view to show only userdefined functions by tapping the catalog keyboard [Form] down arrow button and then selecting [User]. Editing a User-defined Function u To edit a user-defined function 1. On the Program Loader window, tap ~, or tap [Edit] and then [Open File]. 2. On the dialog box that appears, select the function you want to edit, as described below. • Tap the [Type] down arrow button and then select “Function”. • Tap the [Folder] down arrow button and then select the folder that contains the function you want to edit. • Tap the [Name] down arrow button, and then select the name of the function you want to edit. 3. Tap [OK]. 4. Edit the expression and/or parameter variables as required. 5. To overwrite the currently saved function with the edited version tap {, or tap [Edit], [Save File] and then [Save]. • To save the edited version of the function as a different program, use [Edit] - [Save File] - [Save As]. u To rename or delete a user-defined function User-defined functions are saved as variables, so you can rename and delete them using Variable Manager. For details, see “Using Variable Manager” (page 29). Chapter 12: Program Application 204 12-4 Program Command Reference Using This Reference • This reference lists ClassPad commands in alphabetical order. Commands that do not use alphabetic characters (such as ⇒ and #) are at the top of the list. • To the right of each command name is shown the Program Editor window menu sequence that you need to use to input the command. For example, to input the “Break” command you would tap [Ctrl], then [Control], then [Break]. Command name Break Ctrl - Control Syntax: Break Function: This command terminates a loop and Menu If a command has k to the right, it means that the command can be input from the soft keyboard only. • Command names inside of explanation text are shown in bold. Syntax Conventions The table below explains each of the symbols that are used inside of command syntax. Symbol Meaning This indicates a space. Always make sure you input one space between a command and its parameters. Example: GetKey { } You need to select one of the multiple options enclosed inside the braces ({ }). Example: {On ; Off ; Number} When inputting the command, do not include the braces or semicolons. [ ] Anything inside brackets ([ ]) is optional. You can input the item inside the brackets or omit it. When inputting the command, do not include the brackets. … The term to the left of ellipsis (…) can be input more than once or repeated. " " Characters inside of parentheses (" ") are a character string. < > You should input what is described inside the angle brackets (< >). When inputting the command, do not include the angle brackets. Example: , , , Chapter 12: Program Application 205 Command List Symbols (Carriage Return) k Function: Performs a carriage return operation. Description: In Program Editor, press the E key to input a carriage return. • The carriage return can be used in a user program. It cannot, however, be used in a manual calculation performed in the Main application. : (Multi-statement Command) Ctrl Function: Use this command to link a series of statements into a multi-statement (on a single line). Description: The multi-statement command can be used in a user program. It cannot, however, be used in a manual calculation performed in the Main application. ⇒ Ctrl Syntax 1: { ; " "} ⇒ Syntax 2: { ; " "} ⇒ Syntax 3:

⇒ Function: The content of the expression on the left is evaluated, and the result is assigned to the item on the right. ’ (Comment) Ctrl - Misc Function: Any text following this symbol is not executed. You can use this command to include comment text in your program. Description: Any line that starts with the comment symbol (’) is treated as comment text, which is skipped during program execution. " (quotation mark) Ctrl - Misc Function: Any text inside of quotation marks is treated as a string. = Ctrl - Logic Syntax: = Function: Returns true when and are equal, and returns false when they are not. ≠ Ctrl - Logic Syntax: ≠ Function: Returns true when and are not equal, and returns false when they are. < Ctrl - Logic Syntax: < Function: Returns true when is less than , and returns false when is equal to or greater than . > Ctrl - Logic Syntax: > Function: Returns true when is greater than , and returns false when is equal to or less than . s Ctrl - Logic Syntax: s Function: Returns true when is less than or equal to , and returns false when is greater than . t Ctrl - Logic Syntax: t Function: Returns true when is greater than or equal to , and returns false when is less than . # Misc - String(2) Syntax: # Function: This command specifies a string variable whose string is a variable name. Example 1: When the content of variable exp1 is π and the content of variable str1 is “exp1”, sin(#str1) calculates sin(π). Example 2: To cause a folder to be created during program execution: InputStrname, "Foldername" : NewFolder#name A abExpReg (abExpR) Misc - Statistics(1) - Regression Syntax: abExpReg xList, yList[,[FreqList (or 1)] [, [ ] [,{On ; Off}]]] Function: Performs y = a·bx regression. Description: See SinReg. and See “Bitwise Operations” (page 60). Ctrl - Logic B BinomialPD k Syntax: BinomialPD x value, Numtrial value, pos value Function: See “Binomial Distribution Probability” (page 152). Chapter 12: Program Application 206 BinomialCD k Syntax: BinomialCDLower value, Upper value, Numtrial value, pos value Function: See “Binomial Cumulative Distribution” (page 152). Break Ctrl - Control Syntax: Break Function: This command terminates a loop and causes execution to advance to the next command following the loop process. Description: • Break terminates a loop and causes execution to advance to the next command following the loop process. • Break can be used inside of a For, Do, While, or Switch process. Broken Misc - Statistics(1) - Graph Function: Used as a StatGraph command argument to specify an option. See StatGraph. C CallUndef Misc - Graph&Table(1) Function: Used as a ViewWindow command argument to specify an option. See ViewWindow. Case Ctrl - Switch See Switch~Case~Default~SwitchEnd. ChiCD k Syntax: ChiCDLower value, Upper value, df value Function: See “χ2 Cumulative Distribution” (page 152). ChiPD k Syntax: ChiPD x value, df value Function: See “χ2 Probability Density” (page 152). ChiGOFTest k Syntax: ChiGOFTest , , df value Function: See “χ2 GOF Test” (page 148). ChiTest k Syntax: ChiTest Function: See “χ2 Test” (page 148). ChrToNum Misc - String(1) Syntax: ChrToNum" ", [,n] Function: Converts the characters up to the nth character of a string to their character code values and assigns the string to the specified variable. Description: Omitting “n” starts conversion from the first character of the string. For information about character codes, see “Character Code Table” on page 295. Circle I/O - Sketch Syntax: Circle , , radius[, ] Function: Draws a circle. Clear_a_z Misc - Variable Syntax: Clear_a_z[ ] Function: Deletes all single letter lower-case named variables from a through z from the specified folder. Description: • If you don’t specify a folder name, the variables of the current folder are cleared. • Deletes all variables from a through z, regardless of type (program, etc.). See GetType for information about variable types. • Keep in mind that this command clears all data types, including programs, functions, etc. ClearSheet Misc - Graph&Table(1) - Sheet Syntax: ClearSheet [{ ; " "}] Function: Deletes the sheet name and expressions on the sheet, and returns its settings to their default values. Omitting the argument causes all sheets to be cleared. CloseComPort38k I/O - Communication Syntax: CloseComPort38k Function: Closes the 3-pin COM port. ClrGraph I/O - Clear Syntax: ClrGraph Function: Clears the Graph window and returns View Window parameters to their initial default settings. ClrPict Misc - Graph&Table(2) Syntax: ClrPict Function: Clears an image recalled by the RclPict command. ClrText I/O - Clear Syntax: ClrText Function: Clears text from the Program Output window. Cls I/O - Clear Syntax: Cls Function: Clears sketch elements (lines and other figures sketched on the Graph window), and graphs drawn using drag and drop. Chapter 12: Program Application 207 ColorBlack, ColorBlue, ColorRed, ColorMagenta, ColorGreen, ColorCyan, ColorYellow I/O - Color Function: Used as arguments of certain commands to specify colors. Description: The following commands use these arguments: DrawShade, DrawGraph, TangentLine, NormalLine, Inverse, Plot, PlotOn, PlotChg, Line, Circle, Vertical, Horizontal, Text, PxlOn, PxlChg, Print, Locate, SetGraphColor, SetSketchColor Example: Text 10, 10, "CASIO", ColorBlue CopyVar Misc - Variable Syntax: CopyVar