Efofex Fx Draw 4 Modules 4s731d

FX Draw 4 The Mathematics Teacher's Drawing Program

© 1989-2011 Efofex Software

FX Draw 4 's Guide by Efofex Software

Efofex Software Always check our website for our current postal, phone and fax details Email: [email protected] Web: www.efofex.com

FX Draw 4

© 1989-2011 Efofex Software All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems - without the written permission of the publisher. Products that are referred to in this document may be either trademarks and/or ed trademarks of the respective owners. The publisher and the author make no claim to these trademarks. While every precaution has been taken in the preparation of this document, the publisher and the author assume no responsibility for errors or omissions, or for damages resulting from the use of information contained in this document or from the use of programs and source code that may accompany it. In no event shall the publisher and the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused directly or indirectly by this document.

FX Draw 4

I

Table of Contents Part I Features

1

1 Basic Concept

1

2 New in Version 4

1

3 Upgrading from Version 3

2

Part II Licence Statement

2

1 General Conditions

2

2 Personal Use Perpetual Licence

2

3 Personal Use Subscription

3

4 Full Site Licence / Subscription

3

5 Distribution Licence / Subscription

3

6 Details

4

Part III Installation

5

1 System Requirements

5

2 Installing FX Draw on Your Computer

5

3 Installation Notes

5

Privileges Adding To Word Registration Adobe Acrobat FX Draw and Networks (Advanced) Changes FX Draw Makes (Advanced)

Part IV Basic FX Draw Concepts

5 6 6 6 7 7

8

1 Accessing FX Draw

8

2 Select & Draw

8

3 Drawing With A Mouse

9

4 A First Look

9

5 The Main Drawing Toolbar

10

6 Geometrically Aware Drawing (GAD)

11

7 Using GAD

15

8 Changing the GAD Level

15

9 Overriding GAD

15

10 GAD Links What are GAD Links? Breaking GAD Links

16 16 17

11 Figure Information

20

12 Creating Annotations

21

13 Editing Annotations

22

14 The Toolbars

24 © 1989-2011 Efofex Software

FX Draw 4

II

Standard Toolbar Show Grid Button Isometric Grid Button Autopoint Button Zoom Toolbar Line Type Toolbar Fill Type Toolbar GAD Level Toolbar Break GAD Links Button Lock Button Layout Toolbar Format Painter Toolbar Grouping Toolbar Reflection Toolbar Subscription Toolbar

24 24 24 24 25 25 27 28 29 31 32 33 34 34 34

15 Control Points

35

16 Manipulating Figures

35

Selecting Figures Moving Figures Resizing Figures Rotating Figures

35 36 37 37

17 Sliders

38

18 Editing Properties

38

19 Grid

39

20 Setting Defaults

40

21 Grouping and Ungrouping

40

22 Changing the Drawing Order

41

23 Printing

42

24 Cut / Copy / Paste

42

25 Undo and Redo

42

26 Keyboard Shortcuts

42

27 Exporting to Graphics Files

43

What Formats are Offered? Why no JPG?

Part V Using FX Draw in Word

44 44

44

1 Editing Graphics

45

2 Sizing Graphics

45

3 Zoom Toolbar

45

4 Copying Data out of FX Draw's Statistics Tool

46

5 Copying Statistics out of FX Draw's Statistics Tool

47

Part VI Tools

47

1 Select

47

2 The Lines

47

Line Defined By End Points Line Defined By Mid Point and End Point Line Defined By Three Points (Ray) Line Defined By Start Point, Rise and Run Line Defined By Start Point, Length and Angle

49 50 50 52 53 © 1989-2011 Efofex Software

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III

Arrow Line Tool - A Preset Line.

53

3 Ruler

54

4 The Circles

55

Centre Radius Circle Diameter Circle Three Point Circle Circle in a Square Com Circle

5 The Quadrilaterals Rectangle Angled Rectangle Parallelogram Rhombus Kite 1 and Kite 2 Trapezium Rounded Rectangle Bitmap Tool

56 56 57 57 57

58 58 59 60 62 62 63 63 65

6 Text

67

7 Equations

70

8 Point

70

9 Interactive Whiteboard Tools

72

Freehand Tools Freehand Line Eraser Interactive Whiteboard Mode Onscreen Keyboard Right Click Move Toolbars Transparency

10 Triangles, Polygons and Smoothed Lines Triangles Isosceles Triangles 1 & 2 Equilateral Triangle Right Triangles 1 & 2 Polygons Regular Polygons 1 Regular Polygons 2 Smoothed Line Bezier Curve

72 72 73 73 73 75 75 75

76 76 77 78 79 80 82 83 83 84

11 The Ellipses

85

12 The Arcs / Sectors / Segments

87

End Points & Point on Arc Centre & Two Ends Four Corner (Elliptical) Arcs Com Arc

89 89 91 92

13 Angle Tools - Marks and Protractors

93

One Click Angle Marking Two Click Angle Marking Angle Mark Size Angle Mark Options Marking Angles in Radians

14 The Protractors 180 Degree Protractor 360 Degree Protractor

94 95 96 97 98

100 100 100 © 1989-2011 Efofex Software

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IV

15 Bearings

102

16 Shade Regions

104

17 Specialized Mathematical Tools

108

Function Graphs Quick Entry Screen Function Entry Important Points About Function Entry Types of Functions Overview Cartesian Functions "Multiple Armed" Functions Polar Functions Inverse Cartesian Implicitly Defined Parametric Point Functions (Cartesian & Polar) Groups of Points Vectors First Order Differentials Complex Numbers Greatest Integer Functions, Sgn Functions and Piecewise Defined Functions Piecewise Defined Functions Function Reference Points of Interest Right Clicking Select Mode Moving Around The Plane Using The Keyboard Zooming Zooming with the Keyboard Zooming with the Mouse Zoom Mode Click Zooming Rectangle Zooming Undo Zoom Domains Default Domains Constants Entering Constants Changing Constants Families of Curves Animations Constants Everywhere Inequations & Feasible Regions Entering Inequations Feasible Region Options Half Planes or Feasible Region Solid Shading Derivative Curves Integrals Using Your Mouse to Create Integrals Integral Mode Integration with One Function Graphed Integration with Two (or More) Functions Graphed Integral Between Two Curves Integral to y Axis Editing Integrals With a Mouse

108 109 111 112 113 113 114 115 116 118 119 120 121 123 124 126 129 131 132 133 134 134 134 135 137 137 139 139 139 139 140 140 141 141 141 142 143 145 147 147 147 148 149 152 154 156 156 156 156 159 160 162 162 © 1989-2011 Efofex Software

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V

Editing Integrals Approximations To The Integral Tangent and Secant Lines Using Your Mouse to Create Tangent Lines Tangent / Secant Line Mode Tangent Line on a Curve Secant Line on a Curve Selecting Tangent/Secant Lines Moving a Tangent / Secant Line With Your Mouse Using Your Keyboard Editing a Tangent / Secant Line Tables of Values What are Tables of Values? Tables Mode Adding a Table of Values Moving a Table of Values Horizontal or Vertical? Copying Data to The Clipboard Where Do The Entries Come From? Editing Tables of Values Moving Tables of Values to the Edge Marked Points What is a Marked Point? Marked Point Mode Free Marked Points Marked Points on Functions Marked Points on Slope Fields Editing Marked Points Statistical Graphs Using The Stat Tool The Three Views The Data View Think in Columns! Formulas Work Once! Column Types Column Type Detection Changing Column Types Data Columns Label Columns Using Frequency Columns Entering Grouped Data Entering Formulas Formula Columns Column Titles Fill Down Masking Data Highlighting Data Re Run Formulas Quick Graph Quick Group Quick Sort Quick Statistics Statistics Specific Functions The Statistics View Automatic Statistics Expanding Subsections Extra Columns Copying Statistics to Clipboard

163 165 169 169 169 169 171 172 172 173 173 174 174 174 174 175 175 176 177 177 177 178 178 178 178 179 180 182 182 182 182 183 183 183 183 186 187 188 189 190 191 193 193 194 194 195 196 198 200 200 202 203 204 205 205 207 208 209 © 1989-2011 Efofex Software

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VI

The Graph View Graph Control Buttons Creating A Graph Changing Graph Type Editing Graph Properties Axes Properties Scale Properties Grid Properties Titles Specific Graph Type Properties Bar Graph Stacked Bar Graph Column Graph Stacked Column Graph Box Plots Cumulative Frequency Plot Dot Plot Frequency Polygon Stacked Frequency Polygon Histogram Stacked Histogram Cumulative Histogram Stacked Cumulative Histogram Back-to-Back Histogram Line Graph Pie Graph Residuals Graph Scattergraph Stem & Leaf Plot Triangle Graph Data Box Properties Selecting Data On Graph Modifying Data On Graph Combining Graph Types Data Generators Discrete Equi-Likely Integers Bernoulli Binomial HyperGeometric Geometric Negative Binomial Poisson Continuous Uniform Normal Exponential Log Normal Chi Squared Student t Bivariate Data Time Series Data Dice Customizing FX Stat Setting Defaults System Options Normal Distribution Curve Two Circle Venn

210 210 212 214 216 217 219 225 228 229 229 230 230 231 231 233 234 235 239 240 242 243 243 244 245 251 255 256 259 262 264 268 270 272 276 276 276 276 277 277 277 277 278 278 278 278 278 279 279 279 279 280 281 282 282 283 285 287 © 1989-2011 Efofex Software

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VII

Three Circle Venn Number Line Grids / Dots Unit Circle Tree Diagrams Clocks

18 The Galleries Selecting a Gallery Image Drawing a Gallery Image Saving to Galleries Other Gallery Issues

Part VII Tools and Preferences 1 Grid

288 289 292 292 294 297

298 298 299 300 301

301 301

2 Preferences Graph Axes Background Rectangle Sizes Tick Style Blank Under Scale Add Space for Arrows Expand Grid to Edge Preferences Shade Accept Region Dot Density Domain Size Discontinuity Size Key Zoom Ratio Right Click on Axes Statistics Axes Preferences Equation Fonts Use Text Font Use One Font Fonts and Colours Vectors Column Vectors Automatic Vectors Lowercase Vectors Double Capitals Styles Vertical Spacing Tabs Multiplication Sign Raising The Decimal Point Integrals Mixed Numerals Negative Numbers Lines Units Matrix Shortcuts General Measurement System

302 302 302 303 303 303 304 305 307 307 307 308 309 309 310 310 310 310 311 312 312 312 313 314 315 315 315 316 317 318 318 318 319 319 320 320 321 321 322 323 323 324 324 © 1989-2011 Efofex Software

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VIII

Default File Location Gallery Location Control Point Size Increase Selection Area Show Bounding Rectangle Line Colours Bitmap Resolutions Transparent PNG/GIF Files Screen Adjust Reset All Options

324 325 325 325 325 326 326 326 327 328

328

Part VIII Hints & Tips 1 How Do I Select Figures?

328

2 How Do I Change a Figure's Properties?

328

3 What Are Sliders?

328

4 What Is The Most Under-utilized FX Draw Feature?

328

5 How Do I Change a Figure's Default Properties?

328

6 Why Is There an Equation Tool?

329

7 How Do I Draw Network Diagrams Easily?

329

8 Why Do I End Up With a Small Mess When I Use The Graph Tool?

329

9 How Do I Draw More Than One Function On A Graph?

329

10 How Do I Draw Polar Graphs?

329

11 How Do I Draw Inverse Graphs?

329

12 How Do I Enter Domains?

329

13 Can FX Draw Draw Piecewise Defined Functions?

330

14 What is the Difference Between Out Of Range Arrows and High/Low End?

330

15 What is a Group?

331

16 How Do I Group Figures?

331

17 How Do I Ungroup Figures?

331

18 What Can Groups Be Used For?

331

19 What Is A Gallery?

331

20 How Do I Use the Galleries?

331

21 How Does the Direction of Drawing Affect the Gallery Images?

332

22 How Do I Save My Own Graphics To a Gallery?

332

23 Can I Edit Gallery Images?

332

24 What Is The Grid?

332

25 How Can I The Greek Letter Codes?

332

26 Does The Equation Tool Balance Brackets?

333

27 Why Are Spaces So Important?

333

28 How Do I Enter An Ordered Pair?

333

29 How Do I Stop the Equation Tool From Formatting Something?

333

30 How Do I Enter A Matrix?

333

31 How Do I Enter a Degrees Sign?

334

Part IX Appendices 1 A - The Equation Tool

334 334 © 1989-2011 Efofex Software

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Entering Equations Symbols Absolute Value Degrees Greek Letters Square Roots nth Roots Fractions Using Brackets Powers Subscripts Integrals Limits Sigma Notation Product Notation Scientific Notation Vector Column Vectors (COPY) Automatic Vectors (COPY) Lowercase Vectors (COPY) Double Capitals (COPY) Matrices Complex Numbers Means and Complements Predictions Dots Preventing Formatting Spaces Decimals Recognized Functions Mixed Numerals Negative Numbers Recurring Decimals Greatest Integer Definite Integral Bounds Logarithms Piecewise Defined Functions Shortcuts Multi-Line Equations International Considerations

2 B - Statistics Function Reference The Statistics Functions CumFreqTable(column) Decile(column) Deviation(column) Fibonacci(first, second number) FreqTable(column) Group(column, number) / GroupN(column, number) GroupE(column) GroupW(column,width) Inc(start,increment,number) MPA(column,cyclelen) Normal(column) / NormP(column) NormPDF(column) NormQ(column) Percentile(column) Predict(column1, column2, regtype) / PredictY() PredictX(column1, column2, regtype)

334 334 335 336 336 337 337 337 338 338 339 339 340 341 341 341 341 342 342 343 344 345 346 346 346 346 347 347 347 347 348 348 349 349 349 349 350 350 351 351

351 351 351 352 352 352 352 353 353 354 354 354 355 355 355 356 356 357 © 1989-2011 Efofex Software

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X

Rand(number) RandBernoulli(probability,number) RandBetween(low,high,number) RandBinomial(attempts,probability,number) RandChiSquared(degrees, number) RandExponential(rate, number) RandGeometric(probability,number) RandHyperGeometric(select,total,success,number) RandNegBinomial(successes, probability, number) RandLognormal(mean, sd, number) RandNormal(mean, sd, number) RandPoisson(successes, number)) RandStudentt(degrees,number) Rank(column) / RankD(column) RankA(column) Residual(column1, column2, regtype) / ResidualY( ) ResidualX(column1, column2, regtype) Round(column, decimalplaces) Row / @ Seasonalise(column, cyclelen) Sort(column) / SortA(column) SortD(column) SortCol(column) / SortColA(column) SortColD(column) Stanine(column) Standardise(column, mean, sd) Triangular(number) Tribonacci(first, second, third, number) ZScore(column) Other Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions Abs(x) Exp(x) Ln(x) Log(x) Sqrt(x) / SR(x)

Index

358 358 358 358 359 359 359 359 360 360 360 361 361 361 362 362 363 363 364 364 364 364 365 365 365 365 366 366 366 366 366 366 366 366 366 367 367 367

368

© 1989-2011 Efofex Software

FX Draw 4

1

Features

1.1

Basic Concept

Features

1

FX Draw is the mathematics teachers' drawing program. The aim is to provide mathematics teachers with a tool that can draw any required mathematical diagram with a minimum amount of input from the teacher. FX Draw provides specialised tools for drawing angles, graphs, normal distribution curves, Venn diagrams and right triangles and also comes supplied with a gallery of over three hundred pre drawn diagrams. FX Draw can integrate with your copy of Word to provide a quick and easy solution to your diagramming needs.

1.2

New in Version 4 FX Draw 4 is FX Draw evolved. Where FX Draw 3 represented a revolutionary step forward, FX Draw 4 is a polished FX Draw. Most tools in FX Draw 4 have been tweaked and improved but the major new features include:

Autopoints FX Draw 4 has the capability of adding points automatically to your geometry diagrams. Every labeled point on this diagram has been generated and labeled automatically.

Text Boxes Equations FX Draw 4 has massively increased the power of its equations and text boxes. You can now mix and match formatting and equations in one line.

Function Graphs The full FX Graph 4 tool set has been included in FX Draw 4. This provides you with a vastly superior set of tools to create exactly the right image.

Statistics Graphs FX Stat 2's dynamic statistics capabilities have been added to FX Draw 4.

New Geometric Shape Tools

© 1989-2011 Efofex Software

FX Draw 4

Features

2

FX Draw 4 adds tools for drawing angled rectangles, parallelograms, rhombi, trapezoids, and kites as well as isosceles, equilateral and right triangles. Don't forget to check out the Moving from FX Draw 3 to FX Draw 4 document available from the Help menu. That summarizes the things you need to know in one concise document.

1.3

Upgrading from Version 3 Easy... 1. Look at the Moving from V3 to V4 document. This summarizes all of the important changes. 2. Load version 4 on to your computer. Version 4 will automatically take over any version 3 diagrams in documents. There is no need to convert anything. Please note: Once you make a change to a version 3 diagram, it becomes a version 4 diagram and cannot be loaded with version 3. Upgrading your images to version 4 is a "one-way" process.

2

Licence Statement

2.1

General Conditions IMPORTANT – Read before installing, copying or using Do not use or load this software and any associated materials (collectively, the "Software") until you have carefully read the following and conditions. By loading or using the Software, you agree to the of this Agreement. If you do not wish to so agree, do not install or use the Software.

General Conditions 1. You may not copy, modify, rent, sell, distribute or transfer any part of the Software except as provided in this Agreement, and you agree to prevent unauthorized copying of the Software. 2. You may not reverse engineer, decompile, or disassemble the Software. 3. The Software may contain the software or other property of third party suppliers, some of which may be identified in, and licensed in accordance with, any enclosed "license.txt" file or other text or file.

2.2

Personal Use Perpetual Licence A personal use perpetual licence permits the nominated person to use the Software where ever they need it. The software can exist on multiple computers but only the nominated person can use the software. Personal use licences MUST be in an actual person's name.

© 1989-2011 Efofex Software

FX Draw 4

2.3

Licence Statement

3

Personal Use Subscription

NOTE: Only applies to FX MathPack Personal Use Subscribers. A personal use subscription permits the person nominated in the subscription to use the Software where ever they need it. The software can exist on multiple computers but only the nominated person can use the software. Personal use subscriptions MUST be in an actual person's name.

2.4

Full Site Licence / Subscription A full site licence or subscription allows the institution to place copies of the software on as many computers as required within ONE SITE of the institution. The software may be in use on all of these computers concurrently. The software may not be distributed to students or customers for use outside ONE SITE of the institution or on a personal computer within the institution. Special Note Efofex considers use, at home, by a teacher employed at an institution holding a Full Site Licence or Subscription to be fair use PROVIDING such use is solely restricted to producing materials for use within the institution.

NOTE: Full Site Subscriptions are only available as part of an FX MathPack Subscription. 2.5

Distribution Licence / Subscription A distribution licence or subscription allows the institution to place copies of the software on as many computers as required within ONE SITE of the institution and allows the institution to distribute the software to persons directly associated with ONE SITE of the school (eg. students, teachers, istration staff, gardeners ...) at no extra charge to the institution. Efofex Software gives a school holding a distribution licence the right to charge a once off fee of not more than $15 (Australian) per copy to cover the costs of distribution Efofex Software gives a school holding a distribution subscription the right to charge a fee of not more than $3 (Australian) per copy, per annum, to cover the costs of distribution Distribution of the registration code must NOT be carried out in a publicly accessible manner. In particular distribution must NOT occur through a web page that is accessible by people not linked to the institution.

NOTE: Distribution Subscriptions are only available as part of an FX MathPack Subscription. © 1989-2011 Efofex Software

FX Draw 4

2.6

Licence Statement

4

Details Ownership of Software and Copyrights Title to all copies of the Software remains with Efofex Software or its suppliers. The Software is copyrighted and protected by the laws of Australia, the United States and other countries, and international treaty provisions. You may not remove any copyright notices from the Software. Efofex Software may make changes to the Software, or to items referenced therein, at any time without notice, but is not obligated to or update the Software. Except as otherwise expressly provided, Efofex Software grants no express or implied right under Efofex Software patents, copyrights, trademarks, or other intellectual property rights. You may transfer the Software only if the recipient agrees to be fully bound by these and if you retain no copies of the Software. Distribution Licences are not transferable without agreement, in writing, from Efofex Software.

Upgrades Upgrades to the software do not constitute a new product and do not purchase a new licence. Old versions of the software cannot be transferred to a new owner.

Limited Media Warranty If

the Software has been delivered by Efofex Software on physical media, Efofex Software warrants the media to be free from material physical defects for a period of ninety (90) days after delivery by Efofex Software. If such a defect is found, return the media to Efofex Software for replacement or alternate delivery of the Software as Efofex Software may select.

Exclusion of Other Warranties EXCEPT AS PROVIDED ABOVE, THE SOFTWARE IS PROVIDED "AS IS" WITHOUT ANY EXPRESS OR IMPLIED WARRANTY OF ANY KIND INCLUDING WARRANTIES OF MERCHANTABILITY, NONINFRINGEMENT, OR FITNESS FOR A PARTICULAR PURPOSE. Efofex Software does not warrant or assume responsibility for the accuracy or completeness of any information, text, graphics, links or other items contained within the Software.

Limitation of Liability IN NO EVENT SHALL EFOFEX SOFTWARE OR ITS SUPPLIERS BE LIABLE FOR ANY DAMAGES WHATSOEVER (INCLUDING, WITHOUT LIMITATION, LOST PROFITS, BUSINESS INTERRUPTION, OR LOST INFORMATION) ARISING OUT OF THE USE OF OR INABILITY TO USE THE SOFTWARE, EVEN IF EFOFEX SOFTWARE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. SOME JURISDICTIONS PROHIBIT EXCLUSION OR LIMITATION OF LIABILITY FOR IMPLIED WARRANTIES OR CONSEQUENTIAL OR INCIDENTAL DAMAGES, SO THE ABOVE LIMITATION MAY NOT APPLY TO YOU. YOU MAY ALSO HAVE OTHER LEGAL RIGHTS THAT VARY FROM JURISDICTION TO JURISDICTION.

Termination of Agreement Efofex Software may terminate this Agreement at any time if you violate its .

© 1989-2011 Efofex Software

FX Draw 4

Licence Statement

5

Upon termination, you will immediately destroy the Software or return all copies of the Software to Efofex Software.

Applicable Laws Claims arising under this Agreement shall be governed by the laws of Western Australia, excluding its principles of conflict of laws and the United Nations Convention on Contracts for the Sale of Goods. You may not export the Software in violation of applicable export laws and regulations. Efofex Software is not obligated under any other agreements unless they are in writing and signed by an authorized representative of Efofex Software.

3

Installation

3.1

System Requirements FX Draw 4 will run on any computer running Windows 2000 or later. FX Draw 4 is compatible with Windows 2000/XP/Vista and 7. A word processor is required to use FX Draw 4 to its greatest potential. Efofex specifically s Microsoft Word 2000 and later. FX Draw is compatible with most networked situations. FX Draw is very computationally intensive and responds well to increases in processor speed.

3.2

Installing FX Draw on Your Computer To install FX Draw onto your system: · · ·

the installation file onto your computer - noting where the file has been saved. Double click on the installation file (FXD400.EXE). The install program will ask you which directory you would like FX Draw to be placed in and will then make all necessary adjustments to your system.

Please note that all of our products are distributed as time-limited, evaluation versions. If you do not enter registration information within 30 days of installation, the product will cease to work as normal. If you have purchased a registration code for FX Draw, you can enter it during installation or later, by choosing FX Draw from the Help menu. FX Draw is designed to be used as an OLE object and this is the preferred way to print a graphic. There is no need to create an icon for FX Draw, it should be accessed as an object through your word processor. Equation Editor and Word Art are other examples of objects in Word for Windows.

3.3

Installation Notes

3.3.1

Privileges FX Draw requires privileges in order to install and save its registration information. We recommend that if you have purchased a registration code, you enter it during installation to combine these two © 1989-2011 Efofex Software

FX Draw 4

Installation

6

procedures. If you are installing the software on a networked computer the software will probably need to be installed by your IT coordinator. You do NOT need privileges to run FX Draw normally.

3.3.2

Adding To Word Adding FX Draw to Word is automatic. You need to know which version of Word you are using and make sure you select the correct option in the setup program. Word should not be running when you install FX Draw.

3.3.3

Registration If you are evaluating the software and wish to purchase: · ·

·

Choose the licence you require. For a full description of the licences available, read the licence information file on this disk. Efofex or your local distributor by post, fax or email for the latest prices. Alternatively the latest prices are available from our web site at www.efofex.com Purchase a registration code from Efofex or your local distributor and use the instructions below to your copy.

To your copy during installation: ·

When offered the opportunity during installation, type in your ed Name and Registration Code EXACTLY as supplied by Efofex. You MUST enter your ed name using the same abbreviations, even the same spelling errors (if we have made any) as the ed name we have supplied.

To your copy after installation: · ·

From the Help menu of FX Draw, choose FX Draw... Type in your ed Name and Registration Code EXACTLY as supplied by Efofex. You MUST enter your ed name using the same abbreviations, even the same spelling errors (if we have made any) as the ed name we have supplied.

FX Draw will now operate correctly past the thirty day evaluation period. 3.3.4

Adobe Acrobat All manuals are provided in Adobe Acrobat PDF format. In order to read and print the manuals you will need to obtain a copy of Acrobat Reader V6.0 or later. The Acrobat reader is available as a free from www.adobe.com.

© 1989-2011 Efofex Software

FX Draw 4

Installation

7

Before ing a copy of the reader, try clicking on the supplied PDF files. You are quite likely to already have a copy of Acrobat Reader installed on your system.

3.3.5

FX Draw and Networks (Advanced) Because FX Draw can operate as an OLE object, it must be located in an always-available location. We recommend, due to speed considerations, that FX Draw is stored locally if possible. FX Draw is extremely compute intensive and running it on a central server with dumb terminals is generally unsatisfactory. The default data file directory and the galleries directory can be explicitly set in the Tools/Customize/Directories screen. This allows you to store the galleries and any data files in a central location.

3.3.6

Changes FX Draw Makes (Advanced) A standard installation of FX Draw makes the following changes to a system. ·

FXDraw4.exe, PDF versions of manuals and quick reference cards, an uninstall program and log are all placed in the installation directory (c:\Program Files\Efofex\FXD by default).

·

FX Draw's uninstall information is included in the Add/Remove Programs section of Control . This can be disabled by removing the uninstall program and log from the installation subdirectory.

·

A Galleries subdirectory is created in the installation directory. This contains all the standard galleries. FX Draw will, BY DEFAULT, look for its galleries in this subdirectory.

·

FX Draw s itself as an OLE object in the registry (HKEY_CLASSES_ROOT).

·

Registration information is stored in an ini file saved to the Efofex program files directory. (c:\Program Files\Efofex is a likely location).

·

Individual s preferences are stored in a .ini file that is saved into their profile. (c:\Documents and Settings\%name%\Application Data\Efofex is a likely location). Copying this file to the Default profile or All s profile can assist in network installations. If FX Draw cannot determine profile information, it will store the ini file in FX Draw's application directory.

·

Word macros and toolbars are stored in FXDraw2.dot. By default, this file is placed in Word's application startup directory (C:\Program Files\Microsoft Office\Office\Startup for example). In networked installations, you may wish to move this file to another startup directory – see below for details. This file has been digitally signed by Efofex

© 1989-2011 Efofex Software

FX Draw 4

Installation

8

Software and must be trusted to install. It is likely that installation of FX Draw will require privileges.

4

Basic FX Draw Concepts

4.1

Accessing FX Draw There are two main ways of using FX Draw – as a standalone program, or as an object from within a word-processor. Standalone Mode If you accept FX Draw's default installation, you can run it as a standalone program by finding FX Draw in the Program Files section of the Start menu. Although this is possible, it is not the best way of using FX Draw. FX Draw is best used from within a word processor. Document Object Mode FX Draw is designed to be inserted as an object into a document. You can insert an FX Draw object into a document by either pushing the FX Draw toolbar button (see the section on using FX Draw in Word) or load your favourite Windows word processor and choose Insert / Object from the menus. You will be given a list of available objects and FX Draw will be on the list. Select it and FX Draw will start. You use it the same way you use FX Draw as a standalone program. The only real difference is how you return to Word.

The green tick will return your image to Word showing all changes you have made. The red cross returns to Word without any changes being updated. When you have finished your image, just "Click the Tick" and your diagram will be inserted into your word document.

4.2

Select & Draw FX Draw operates in the same way as any drawing package you may have already had experience with. First select the tool you wish to draw with, then draw on the canvas.

© 1989-2011 Efofex Software

FX Draw 4

Basic FX Draw Concepts

9

The light blue grid on the canvas will not print in your final graphic, it is a background grid which makes drawing easier.

4.3

Drawing With A Mouse People have described drawing with a mouse as being something akin to drawing with a brick. This is one of the main problems associated with drawing graphics on a computer. FX Draw's Geometrically Aware Drawing system makes drawing mathematical diagrams easy. After you have selected the tool you wish to use on the canvas, drawing is accomplished by holding down the left mouse button while moving the mouse. The desired figure will fill the rectangle created by the starting point of the mouse and the current position. For most people this is natural as long as they that you must hold down the mouse button to draw.

4.4

A First Look FX Draw is a comprehensive mathematical drawing package so it is not surprising that the FX Draw screen is fairly complex.

© 1989-2011 Efofex Software

FX Draw 4

Basic FX Draw Concepts

10

We will be looking at all of the different settings available in later sections of this document. For the moment we want to bring your attention to the main sections of the FX Draw screen. The Main Drawing Toolbar - is the source of all the different tools that you can use to draw in FX Draw. There are over 50 buttons in this toolbar but you can only see 14 at any one time. We will discuss how to access the others in a later section. The Drawing Canvas is where most of the action will occur. Zoom lets you zoom in and out of your drawing. Line style, thickness and colour let you control the lines in your drawing. Fill Style and Colour lets you change the colour of any shading.

4.5

The Main Drawing Toolbar The main drawing toolbar gives you access to all of the different tools FX Draw provides. There are so many tools that we have had to hide some of them! Most tools on this toolbar have other tools hiding behind them.

© 1989-2011 Efofex Software

FX Draw 4

Basic FX Draw Concepts

11

To access the extra tools, hover the mouse pointer over one of the buttons for half a second. A "flyout" toolbar will appear. We will look at the lines flyout bar.

If I move out and select the ruler tool, the main drawing toolbar will change to.

and I can now draw rulers on the drawing canvas.

4.6

Geometrically Aware Drawing (GAD) FX Draw implements Geometrically Aware Drawing (GAD) – but what does it mean? Traditionally, drawing packages had a grid of points that the mouse jumped to while drawing. That allowed you to align figures that were based on lines but made it very difficult to do anything with curves or points of intersection. FX Draw rectifies this problem. While FX Draw still has a grid, it also knows a lot about geometry.

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For example.

Drawing this diagram in most drawing packages is a difficult proposition. Not only do you need to draw a line that is tangential to a circle, but you also need to draw on the correct point of the first circle so that the line is tangential to both! Drawing the diagram with FX Draw is almost trivial: First, draw the two circles.

Second, place the cursor NEAR a point on one circle that would be the end of a line that is tangential to both.

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When you are somewhere close, FX Draw will graphically show you what it has found. It will also add a message to the status bar at the bottom of the screen to tell you what it has found. "Tangent to both circles" If you start to draw the line now, it will automatically begin at the appropriate point.

Finally, move to the other circle, look for the same message and the line is drawn.

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We have drawn in the other three possible tangent lines. All are found automatically by FX Draw. That is the crux of GAD. FX Draw automatically jumps to points which are of geometrical interest. It is "aware" of a wide variety of geometrical points and relationships. The Grid Underneath all drawings there is a grid. In the absence of any other significant points FX Draw will automatically jump to the nearest grid point (unless the grid is disabled.) All Figures FX Draw will automatically jump to a point on a figure in preference to a grid point. This makes it easy to draw something that starts or finishes ON a circle for example. Points of geometrical interest are more "attractive" than points on a figure. Lines FX Draw considers the end points, mid point, third points and quarter points to be important points on a line. FX Draw will also preferentially draw perpendiculars and parallels to existing lines. It will also preferentially make lines the same length or which bisect existing angles. Circles The centre point and points on the circumference are attractive points to FX Draw. FX Draw will also draw lines that through the centre of the circle and are tangential to the circle. FX Draw can also determine tangents to two circles as shown previously. Arcs The end points and centre of arcs as well as the arc's centre of curvature are tracked as geometrically important points. Points of Intersection Points of intersection between figures are attractive to FX Draw. FX Draw can find points of intersection for most figures including lines, circles, arcs, ellipses and Bezier curves. Most figures have geometrically important points. We have not listed all of them here. Most importantly, the points are found automatically for you and the system tells you exactly what it is finding at all times.

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Using GAD This is the easy part. All you have to do is make sure that GAD is turned on and the GAD system will always keep you informed about what it has found.

4.8

Changing the GAD Level Geometrically Aware Drawing is a wonderful tool but it does have some problems. Firstly, sometimes you might not want to use it because it does suit your purpose. You might like to use just the grid or you may even wish to turn off GAD entirely. The second problem with GAD is that it is computationally intensive, so intensive that it can eventually bring even the most powerful computer to a standstill if you have enough figures on the screen. To overcome these problems, FX Draw has four levels of GAD available. No GAD

FX Draw uses the mouse position for all actions

FX Draw draws everything to the underlying grid with no geometric analysis. FX Draw determines geometrically important points and Limited GAD relationships but as the number of figures increases, the (Default) range of things determined is reduced. For example, after there are more than 15 figures, FX Draw does not calculate points of intersection. This option allows for extensive use of GAD without the computational limit problems. "Infinite" GAD Sometimes you will want to use GAD regardless of the computational cost. With this option, FX Draw will calculate all geometrically important points and relationships regardless of the number of figures in the diagram Grid Only

The GAD level is selected using the GAD toolbar

4.9

Overriding GAD Sometimes you will want to override the GAD system for just a moment. Perhaps you wish to use a grid point that is too close to an existing figure and the GAD system will not let you use it. You can override the GAD system at any time by using the Shift or Ctrl key while you are moving the mouse. Shift FX Draw will use a grid point and will ignore any geometrically important points. Ctrl

FX Draw will not use any geometrically important or grid points. It will use the raw mouse position.

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4.10

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GAD Links

4.10.1 What are GAD Links? Your first with GAD Links will occur when you select some figures and the selection squares will be different colours. What is going on? In short, GAD Links give GAD a memory.

The colours represent relationships that the has used when creating the diagram. Line 1 was drawn first. Neither end was linked to anything else - so both ends are green, free to move. Line 2 was drawn second. We started on the mid-point of line one and moved out to a point on the perpendicular. Line 2 is locked onto the midpoint - a fixed point at one end (red = locked to a point) and locked onto a relationship - the perpendicular (amber = restricted to a relationship). In Line 4, the right hand point is restricted to being parallel to line 3. The colours give you some indication of what is going on - but what's the point? When you move the first line, the second line moves too - to maintain the relationship.

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We have moved Line 1 and Line 2 has remained attached to the midpoint and on the perpendicular. GAD Links make FX Draw much "smarter" but also allow you to construct complicated geometric relationships that changed dynamically. Combine this with dynamic annotations (oops, haven't mentioned those yet) and you have a powerful geometry canvas that takes almost no training to use.

4.10.2 Breaking GAD Links Imagine you have drawn the following diagram and FX Draw has created GAD Links for the figures as you have drawn them.

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The second line is linked to the first and will move around with it. You can break this link in two ways. 1.

Move the point. For example, if I pick up the red point and move it, the GAD Link to the midpoint will be broken. FX Draw will not break the link until you have moved the point quite a distance however!

FX Draw keeps the perpendicular relationship but lets you move the end of the line from the midpoint.

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You can move this end point to another geometrically interesting point if you want - the whole time FX Draw will keep the other relationship current. 2. You can also break ALL of the links for a figure without moving it at all. Select the figure

and press the Break GAD Links button

This will break any GAD links for all selected figures.

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Figure Information FX Draw 4 provides much more information about the figures you are drawing. To view this information: draw the figure; click on it to select it and then let your mouse cursor sit near the figure for half a second. Most figures will display a yellow box with relevant information. For example: Below I have drawn a triangle using the triangle tool.

The information presented depends on the figure selected.

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Creating Annotations An annotation is a text box that is attached to a figure and is dynamically updated with the information about that figure.

When you change the figure, the annotation automatically updates.

Annotations are based on the figure information we discussed in the previous lesson. Whatever is displayed as figure information will be added as an annotation. Creating an annotation is easy. 1. 2. 3. 4.

Draw the figure Select just the figure you wish to annotate. Let the mouse hover over the figure until figure information is displayed. Right click.

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Normally, when you right click you will edit the properties of the currently selected figure. If the figure is displaying its information, you will instead be offered the choice of either adding an annotation or editing the properties.

Choose Add Annotation and an annotation will automatically be attached to the figure.

4.13

Editing Annotations Editing annotations is just like editing any other figure in FX Draw - you right click on them. The Annotation Properties dialog box will pop up.

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Most of these options are obvious but the two areas marked in red require some explanation. Area 1 allows you to control the text in the annotation. This information produces this annotation

Annotations are dynamic so FX Draw uses parameters rather than just raw text. The parameters available for the current figure are listed in area 2. All parameters start with a $ sign and each figure has its own parameters. There are often more parameters than are displayed in the figure information. $u, $su and $cu are standard parameters available for all figures. They allow you to add linear units, square units and cubic units to any annotation. The last thing we need to look at is the column of check boxes on the left hand side of area 1. These allow you to tell FX Draw to interpret the line as an equation and use its equation technology to render the line. This allows you to include equations into annotations.

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4.14

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The Toolbars

4.14.1 Standard Toolbar The standard toolbar contains standard tools that are common with most other products. Two extra buttons are added, the tick and the cross. These are used to return to a document and are explained fully in the Using FX Draw in Word section of this guide.

4.14.2 Show Grid Button

The show grid button determines whether FX Draw shows the background grid. It does not have any effect on whether FX Draw uses the grid. FX Draw automatically removes the background grid when some figures (a function graph for example) are drawn. This is to prevent confusion between the grid of graph and the background grid. 4.14.3 Isometric Grid Button

Pushing the Isometric Grid button has three effects: 1. 2. 3.

The background grid is switched from Cartesian to isometric. The size of the background grid is doubled (usually from 5 mm to 10mm) GAD is turned off so that the background grid is dominant.

These three changes put FX Draw into a state that is ideal for drawing isometric diagrams. 4.14.4 Autopoint Button

FX Draw has the ability to automatically add points to geometric diagrams. The points are automatically generated as you draw geometric figures such as lines and circles. Obviously this is not always what is required. The Autopoint button controls this feature of FX Draw.

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Autopoint On

Autopoint Off

4.14.5 Zoom Toolbar

The zoom toolbar controls the level of zoom used by FX Draw. Most s find leaving the zoom level at about 200% allows to to create diagrams for Word that are not too big.

4.14.6 Line Type Toolbar The line type toolbar lets you control the style, thickness and colour of lines that make up your image.

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The first drop down menu lets you pick the style of line you wish to use. You can choose between solid, dotted, dashed and a mixture of dashes and dots.

The second drop down menu allows you to set the thickness of the line drawn. The line tool uses points as its standard measurement. A point is one 72th of an inch.

You can enter ANY measurement in the line thickness using any of FX Draw's ed units (cm, mm, pt and ")

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The final button allows you to choose the colour of the line.

If a figure is selected, the line type toolbar will show the line settings for that figure and allows you to change them. If there are no figures selected then the line type toolbar will show the current default line settings that any NEW figure will be created with. 4.14.7 Fill Type Toolbar You can change the type and colour of the fill used to draw a figure using the fill type toolbar. When you first draw a figure, it will be drawn using the currently selected fill type and colour. You can also change the fill type of the currently selected figure using the same toolbar. You have the choice of solid colour or six types of hatching. You can select a figure's fill colour by pushing the colour button. You can choose one of forty basic colours or define a colour of your own.

The transparency/opacity slider allows you to control the transparency of some shading - in particular shading of closed shapes such as circles, rectangles and polygons. The following diagrams show the effects of different transparencies using the same colours each time.

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4.14.8 GAD Level Toolbar The GAD Level Toolbar allows you to control the Geometrically Aware Drawing calculations performed by FX Draw ranging from none up to full GAD regardless of the number of figures. Most of the time you will leave it set to the default level (shown).

© 1989-2011 Efofex Software

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No GAD

Basic FX Draw Concepts

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FX Draw uses the mouse position for all actions

FX Draw draws everything to the underlying grid with no geometric analysis. FX Draw determines geometrically important points and Limited GAD relationships but as the number of figures increases, the (Default) range of things determined is reduced. For example, after there are more than 15 figures, FX Draw does not calculate points of intersection. This option allows for extensive use of GAD without the computational limit problems. "Infinite" GAD Sometimes you will want to use GAD regardless of the computational cost. With this option, FX Draw will calculate all geometrically important points and relationships regardless of the number of figures in the diagram Grid Only

4.14.9 Break GAD Links Button

The first button breaks any GAD links for the selected figure - this means that it is no longer dependent on other figures. For example, in the diagram below, the selected line starts at the midpoint of the other line and is locked to the perpendicular. That is why its selection squares are red (locked to point) and amber (locked to a relationship).

If I select and move the first line, the linked line will automatically moved to

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maintain its dependencies.

This behaviour is great but sometimes you will want the line to stay where it is. To do this, select the line and push the break links button.

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Note that the line's end points have turned green - they are now totally unlinked and moving the first line will not affect the selected line.

4.14.10 Lock Button

The lock button lets you lock figures in place so that they cannot be moved accidentally. If you have spent ages carefully placing a figure in exactly the right spot and want to make absolutely sure that you don't move it accidentally, you now have the option of locking it. Draw your diagram and select any figures you want to lock.

Now press the lock button and the figure will be locked in place. FX Draw 3 will change the squares to grey to show you that they are locked.

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This line is now locked in place and you will not be able to move it at all apart from one important exception - it will still and use any GAD Links that were used. Even though you will not be able to directly move the line, it you change the circle, the line will remain tangential.

You can unlock any locked figures by selecting them and clicking on the lock button.

4.14.11 Layout Toolbar FX Draw draws the figures in the diagram in the same order you initially created them. If you have overlapping figures this means that one figure will be drawn over the top of the other. The layout toolbar allows you to change the drawing order of the figures so that different figures appear on "top of the pile". Each button represents the currently selected figure in green and shows what will happen when the button is pushed. · · · ·

Bring the currently selected figure to the front. Send the currently selected figure to the back. Move the currently selected figure one forward in the drawing order. Move the currently selected figure one back in the drawing order. © 1989-2011 Efofex Software

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4.14.12 Format Painter Toolbar The format painter allows you to format one figure exactly as you want and then copy the formatting over to other figures. Format painting is available in a lot of products (such as Word) and ours works in exactly the same way.

To use the format painter, first format a figure and then select it as shown above. When the SOURCE figure is selected, press the format painter button

Then click on a DESTINATION figure that you would like the formatting copied on to.

To format more figures, keep clicking the format painter button and the next figure.

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The format painter will always copy the line style, line thickness, line colour, fill style and fill colour. The more similar the source and destination figures, the more information is painted across.

4.14.13 Grouping Toolbar Allows you to group the currently selected figures or ungroup the currently selected group. A group is just a collection of figures that is treated as one.

4.14.14 Reflection Toolbar Allows you to reflect the currently selected figures.

4.14.15 Subscription Toolbar The subscription toolbar will only appear if you have subscribed to FX Draw as part of an FX MathPack subscription.

The subscription toolbar gives the date that the current subscription expires.

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Control Points All figures have control points. They are the crucial points that are used to define it. If a figure is selected, its control points will be show as small red, amber or green squares. Control points allow you to control a figure's shape, size and structure.

For example, the diagram above shows a circle defined by three control points. By moving the points, the circle will be redrawn to through the three new points. If you have GAD active while you are drawing, you will find that your control points have different colours. This is explained more fully in What Are GAD Links?

4.16

Manipulating Figures

4.16.1 Selecting Figures To select figures you must first select the selection tool.

Selecting an individual figure You can select an individual figure by clicking on it once. With most figures you must click on the LINES that figure is comprised of. FX Draw does not usually allow you to select a figure by clicking on the filled areas. Selecting a number of figures A group of figures can be selected by sweeping out a selection rectangle. Any figure whose control points are within the rectangle will be selected.

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All of the figures except the tangent on the left will be selected by the (dotted) selection rectangle. Adding or subtracting a figure from your selection You can add and subtract figures from an existing selection by holding the Ctrl key whilst clicking on a figure. If the figure is not already selected it will be added to the selection. If the figure is already selected, it will be subtracted from the selection. The use of the Ctrl key whilst clicking the mouse allows you to select exactly the figures you require.

If you wish to move a figure, click and hold anywhere within the select region and you can then move the figure anywhere on the canvas. It is important that you become proficient in selecting, resizing and moving figures and it is worthwhile practising the skill.

4.16.2 Moving Figures You must have the selection tool selected to move figures Moving figures with the mouse If you click on a figure, it will be selected and will then move with the mouse. If a number of figures are selected and you click on one of them, all of the selected figures will move with the mouse. Moving figures with the keyboard Any figures currently selected can be moved with the keyboard. The arrow keys will move the figures in the selected direction. · ·

Holding down an arrow key will move figures 0.25 mm. Holding down Ctrl and an arrow key will move figures 1 mm. © 1989-2011 Efofex Software

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Holding down Shift and an arrow key will move figures 0.05 mm.

4.16.3 Resizing Figures If you move a figure's control point, the figure will be redrawn to fit the new control points. The result of moving control points depends on the figure.

4.16.4 Rotating Figures You can rotate currently selected figures using the keyboard or free rotate using the mouse. Rotating figures with the keyboard Ctrl + Pg Up Rotates 15° anti-clockwise Ctrl + Pg Dn Rotates 15° clockwise Shift + Ctrl + Pg Up Rotates 1° anti-clockwise Shift + Ctrl + Pg Dn Rotates 1° clockwise Rotating figures with the mouse When you select figures, you will usually see a rotate point.

Grabbing and moving this will rotate the selected figures. Not All Figures Are Rotatable! Sometimes you will notice that the rotate point will not appear. This means that the selected figure is NOT rotatable.

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Sliders

Some of the more complicated figures include "sliders" – little grey dots - which appear when the figure is selected. A slider is a convenient way of manipulating some of the properties of a figure. The diagram shows a normal distribution curve. The sliders allow you to visually adjust the shading on the curve. The function of the sliders depend on the figure they are attached to so if you ever see a slider move it (by clicking and holding the mouse button as you move the mouse) and look at the changes. You will find that sliders make many drawing jobs easier.

4.18

Editing Properties Most of the figures you will be drawing have many properties that can be changed. Properties such as the line type and fill type can be changed using the line and fill toolbars. Some properties may be changed by using the sliders attached to the figure. Mostly, however, you will change a figure's properties by right clicking on the figure. Most figures, when right-clicked, will create a dialog box that allows you to adjust the properties of the figure. Below is an example of one of those dialogs.

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This shows the available properties for an arc. They will be discussed later in the guide.

4.19

Grid The grid, shown as a very light grid on the screen, can assist you when drawing figures. FX Draw will preferentially jump to a grid point unless a geometrically important point is nearby. The grid can help you construct accurate figures. You can override the GAD system by holding down the Shift key whilst drawing. You can override the GAD system and the grid by holding down the Ctrl key whilst drawing.

The Tools / Preferences / Grid menu allows you to adjust the properties of the grid. You can choose to display the grid (the default) or to remove the dots from the canvas. You can set the size of the grid and most importantly you can set to grid to Cartesian or isometric. An isometric grid, although a little harder to work with, makes drawing isometric diagrams easy. You can also set the colour and opacity of the grid. Increase the opacity if you find the grid hard to see. © 1989-2011 Efofex Software

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If the GAD toolbar is set to No GAD, the grid is ignored. This is equivalent to holding down the Ctrl key whilst drawing.

4.20

Setting Defaults Many of the tools come set with defaults. Perhaps the tool that you are most likely to want to set using defaults is the arrow line tool.

If you wish to draw this network diagram,

you have to create eleven lines and make the start and end points filled in white circles. Because the arrow line defaults to a line with a triangular arrow head, this means drawing eleven lines, selecting them individually and editing their properties to add the white circles OR set the default for the arrow line. To set a default, you set a line to the desired type and then press the Set to Default button. Your selected defaults will be saved and used whenever you create another arrow line. In the example above, the default arrow line was set to

4.21

Grouping and Ungrouping When you draw a complicated shape, you will often want to group the figures together to form a single figure. For example, if you have drawn an icosahedron, it is useful to move all components of the graphic as a group rather than individually. The easiest way to achieve this is to "group" the components together. To create a group you should:

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· Select all figures you wish to group together. · Choose Group from the Draw Menu OR type Ctrl + G OR push the Group button. Once grouped together, the group figure behaves in much the same way as any other graphics figure, it can be selected, moved or resized. All the gallery figures that you can select are in fact "groups" of lines, arcs, rectangles etc. If for some reason you wish to access the individual figures within a group, you can "ungroup" a figure. To do this you should: · Select the figure to be ungrouped. · Choose Ungroup from the Draw Menu OR type Ctrl + H OR push the Ungroup button. Because the gallery figures are groups, this gives you the ability to load a gallery figure and modify it to suit your needs. Simply select the figure, ungroup it, and make the modifications you need.

4.22

Changing the Drawing Order As you create figures, they are added to a list of figures to be drawn. Every time FX Draw redraws your graphic, it draws them in this drawing order. The diagram below shows the result of different drawing orders.

The Layout Toolbar allows you to change the order figures are drawn and get exactly the result you want.

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4.23

Basic FX Draw Concepts

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Printing FX Draw has in-built print routines but you will usually use some other application to actually print your graphic. All Windows word processors (including Write) have the ability to use and print FX Draw graphics. Although FX Draw is designed to be used in word processor documents, many other packages can use FX Draw graphics (for example, Microsoft Excel and Powerpoint)

4.24

Cut / Copy / Paste Cut / Copy / Paste works the same way in FX Draw as in any other Windows program. If you wish to cut out a figure and place it on the clipboard or to copy a figure onto the clipboard, all you need to do is to select the figure(s) you wish to operate on, and choose Edit / Cut (Ctrl + X) or Edit / Copy (Ctrl + C). The selected items are then placed on the clipboard. All items placed onto the clipboard in this way can later be Pasted into FX Draw. To Paste from the clipboard you can choose Edit / Paste (or Ctrl + V) and a copy of the clipboard contents will be pasted onto the canvas. This copy can then be moved to the required location. If you simply wish to delete the selected figures, without placing them onto the clipboard, press Del. You can copy an image to the clipboard and then paste it into another application (eg Word) but this IS NOT the best way of using FX Draw. Make sure you read the section on using FX Draw in Word.

4.25

Undo and Redo All actions except grouping and ungrouping can be undone. You can undo the last action by choosing Undo from the Edit menu or by typing Ctrl + Z. You can redo the last undone action by choosing Redo from the Edit menu or by typing Ctrl + Y. FX Draw's undo system is limited only by the available memory. For most editing, you will not find the limits of the undo system and should be able to undo actions indefinitely.

4.26

Keyboard Shortcuts Keyboard shortcuts can make using FX Draw a quicker experience. Overriding GAD Shift to Ctrl Alt Points.

Ignores Geometrically Important Points and instead jumps the grid. Ignores grid and any Geometrically Important Points. Ignores grid and jumps to any Geometrically Important

Returning to Word © 1989-2011 Efofex Software

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Returns to Word and updates diagram.

Editing Ctrl + X Ctrl + C Ctrl + V Ctrl + D Ctrl + Z Ctrl + Y

Cuts selected figures and places them on the clipboard. Copies the selected figures to the clipboard Pastes figures from the clipboard Copies and pastes selected figures Undo last action Redo last undone action

Rotating Ctrl + Pg Up Ctrl + Pg Dn Shift + Ctrl + Pg Up Shift + Ctrl + Pg Dn

Rotates selected figures 15° anti-clockwise Rotates selected figures 15° clockwise Rotates selected figures 1° anti-clockwise Rotates selected figures 1° clockwise

Grouping Ctrl + G Ctrl + H

Collects all selected figures into a group figure Ungroups the selected figure

Drawing Order (Layout) F6 Shift + F6

Brings selection to the front Sends selection to the back

Nudging Up Arrow Down Arrow Left Arrow Right Arrow

Nudges selected figures upward Nudges selected figures downward Nudges selected figures to the left Nudges selected figures to the right

Holding the Shift key decreases the amount the figures are nudged. Holding the Ctrl key increases the amount the figures are nudged.

Resizing Groups Holding the Shift key whilst resizing a group forces the group to maintain its aspect ratio (ratio of width to height) so that the group is not distorted.

Drawing Gallery Images Holding the Shift key whilst drawing a gallery image forces the gallery image to maintain the aspect ratio it was created with. This again ensures that the gallery image is not distorted.

Drawing Figures Based on Rectangles Many of the figures which are based on rectangles (rectangles, rounded rectangles, Venn diagrams, graphs, grids etc) can be forced to a square by holding the Shift key when creating them.

4.27

Exporting to Graphics Files FX Draw can save its images to a variety of graphics formats. 1. 2. 3. 4.

Draw your diagram Choose File / Save As from the menus Select a filename and a location to save your graphic (see below) Select whether you want your graphic saved as a PNG file, GIF file or a BMP

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file (see below) 5. Push OK.

4.27.1 What Formats are Offered? FX Draw can create PNG, GIF and BMP format bitmaps. You should normally use the PNG or GIF format. BMP bitmaps are very large and should only be used if a third party product you need cannot handle GIF style bitmaps. 4.27.2 Why no JPG? JPG (also known as JPEG) files are not suitable for the type of graphics FX Draw produces. The JPG format was designed for photographs and, when used on solid colour graphics, such as FX Draw's, produces unsightly extra dots when displayed. While they excel at reproducing photographs, they are simply the wrong tool for the job in this application.

5

Using FX Draw in Word FX Draw is designed to be used in Word to generate publication quality graphics for tests, examinations, worksheets and assignment. The easiest way to insert graphics into Word is to use fxdraw.doc (or fxd695.doc) to add a toolbar button to your Word toolbars (see Adding FX Draw to Word). Alternatively you can use Insert Object from the Insert menu in Word and select FX Draw V2 Diagram. When you insert an FX Draw object into your document, FX Draw will start and © 1989-2011 Efofex Software

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you can use it in the same way you use FX Draw as a standalone program. The only real difference is how you return to Word.

The green tick will return your image to Word showing all changes you have made. The red cross returns to Word without any changes being updated. Once you have finished drawing your graphic, push the appropriate button to return to Word.

5.1

Editing Graphics Once you have returned to Word, you can edit a graphic by double-clicking on it. FX Draw will restart and you will be able to edit your graphic.

5.2

Sizing Graphics There are two ways of sizing graphics for your document; inside FX Draw and inside Word. When you return to Word, the graphic will be inserted into your word document the same size as you have drawn it in FX Draw. The sizing is very accurate (all points are located to within one hundredth of a millimetre) and a line that is 92.5mm in FX Draw will be 92.5mm when returned to Word and should be 92.5mm long when printed. Once you have returned to Word, you can resize the graphic inside Word. This can causes problems. Once Word resizes a graphic, there is no way for FX Draw to guarantee lengths of lines or the regularity of circles. For many diagrams this is a not a problem but it can be a problem if you are relying on a particular measurement or if you do not wish your circles to become ellipses. You might also find that fonts become distorted or the spacing of text is incorrect. This is especially the case if you change the aspect ratio of the graphic (the ratio of height to width) Generally, it is better draw the diagram to size in FX Draw and not resize it in Word. If you must resize in Word, you will get the best results if you maintain the graphic's aspect ratio.

5.3

Zoom Toolbar Zoom operates in the same way as in other products but it has a use that may not be immediately obvious. When people used FX Draw 2 to draw diagrams, they would often complain that the diagram was too big when it was returned to Word. This seemed to be a © 1989-2011 Efofex Software

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problem of perception - the diagram looked bigger in Word because it was no longer the "only" thing on the page. We suggest that you use FX Draw 3's zoom function to overcome this perception problem. Set your zoom to about 140% in FX Draw 3. This allows you to focus on the diagram and include the detail you need - but when you return to Word the diagram will not appear too large.

5.4

Copying Data out of FX Draw's Statistics Tool If you need to copy your data out of FX Draw's Statistics Tool and into a word processor or spreadsheet, you have two options available Data in Columns FX Draw's Statistics Tool always works in columns. If your want your data copied into your word processor in columns, you can achieve this easily by selecting your data in FX Draw's Statistics Tool, copying it to the clipboard (using the Edit menu, Ctrl+C or the copy toolbar button) and then pasting it into your word processor.

Sheet with data selected 1 2 2 5 3 6 4 7 5 7 6 9 7 12 8 13 9 15 10 18 Pasted into the word processor Data in Rows If you wish your data to be copied into your word processor in rows, rather than columns, FX Draw has a special function especially for this purpose. Select the same data as shown above but this time select Copy As Rows from the right click menu. When you paste the data into your word processor, it will be in rows. 1 2

2 5

3 6

4 7

5 7

6 9

7 12

8 13

9 15

10 18

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Copying Statistics out of FX Draw's Statistics Tool Right click on a column of statistics to get the Copy menu

6

Tools

6.1

Select The select tool allows you to select figures or collections of figures.

If you wish to select a single figure, make sure that the select tool is pushed and click once on the desired figure. It is important to that the select region is built around the LINES that make up the figure and not the fill. The selected figure will show its handles so that you can move, resize, cut or copy it. Sometimes you will want to select a collection of figures so that you can move them as a collection, delete them as a collection or actually group them together (see Grouping / Ungrouping). To select a collection, hold down the mouse button while moving the mouse and a dotted rectangle will appear. Any figure that is totally contained within the dotted rectangle will become part of the collection. You can add a figure to your selection or subtract a figure from your selection by holding down the Ctrl key while clicking on the figure you wish to add or subtract.

6.2

The Lines Why so many lines??

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Simply so you will always have the right tool for the job. The first six buttons on this toolbar all produce lines. Once drawn, they all have the same options. If you right click on an existing line you be able to access all of the lines properties - and there are lots.

You have a choice of nineteen arrow types for the start, middle and stop arrow. You can also set the size of the arrows, the position of the middle arrow. All of this is shown dynamically on the line at the base of the dialog box. You can have FX Draw show the length of the line automatically (shown) with or without units. Alternatively you can attach text to the line. Normal text will be angled with the line. You can also ask FX Draw to interpret the text as an equation using its FX Equation technology. This can be used to good effect when drawing networks or to indicate measurements.

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See the Appendix A on how to enter equations into FX Draw. All lines have these options. Available Parameters for Lines $start $stop $length $angle $mid 6.2.1

- start point - stop point - midpoint

Line Defined By End Points

The simplest line. The line is defined by its end points.

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Line Defined By Mid Point and End Point

This line is defined by starting on the midpoint of the line and then moving out to and end point. You might use it to draw the perpendicular bisector of another line for example.

6.2.3

Line Defined By Three Points (Ray)

The ray tool is mostly used during constructions. You would use it in situations where the line you are drawing is determined by a point that is NOT one of the end points.

When drawing in the angle bisector, you are likely to want to extend the line past the intersection which is a little difficult with the standard line tools. This is a great time to use the ray tool. The ray tool is easier to use than to describe. To begin with, you draw a line to the intersection. This defines the angle of the line.

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Now that you have defined the angle, if you move the mouse you should notice that the line changes length. It is always on the same angle - just the length has changed.

The line does not even need to be in the same direction.

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Click again and your ray will appear. If we select the ray you will see three selection squares.

6.2.4

Line Defined By Start Point, Rise and Run

To use this tool, draw a line normally. Once you have released the mouse button, FX Draw will show this dialog box which will show the current rise and run, and allows you to set the exact rise and run you desire.

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Enter the rise and run and FX Draw will automatically adjust the line. 6.2.5

Line Defined By Start Point, Length and Angle

To use this tool, draw a line normally. Once you have released the mouse button, FX Draw will show this dialog box which will show the current length and angle, and allows you to set the exact length and angle you desire.

Enter the length and angle and FX Draw will automatically adjust the line. 6.2.6

Arrow Line Tool - A Preset Line.

An arrow line is exactly the same figure as a line, the only difference is that its properties can be pre-set to your requirements. When FX Draw is first started, the arrow line is pre-set to a line with a solid arrow at the stop end of the line. This line, when drawn, can be edited to include any of the properties discussed above. Sometimes you will wish to set different defaults for the arrow line so that any future arrow lines will be created to suit your purposes.

Setting your default line is easy. Draw a line and then change its properties to your desired default. When you are happy, push the Set to Default button. All future arrow lines will be drawn with your defaults. It is important to that arrow lines are exactly the same as lines, just pre-set to your choice.

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Ruler

The ruler tool lets you quick draw a ruler to demonstrate measurement.

The ruler is slightly offset from the line that defines it. This is so that you can use the ruler to measure a line without the ruler covering up what you are trying to measure. The amount of offset can be changed by right clicking on the ruler and editing its properties.

Height is the height of the ruler. You can set the height of the ruler as low as zero and just use the scale.

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Margin controls how much space there is between the edge of the ruler and the beginning of the scale. Offset controls the amount the ruler is offset from the line it is measuring. Reversing the scale lets you draw "left-handed" rulers. Starting the scale at a number apart from 0 allows you to construct number line like rulers.

FX Draw will produce rulers marked in mm, cm, inches and points. The rulers will be true to scale unless you change the scale factor. The scale factor lets you create rulers that are not true to scale if you need to.

6.4

The Circles

There are five different types of circles available in FX Draw. Each of the circle figures has been created to solve a different drawing problem. What makes them different is how the circle's control points are used to define the circle.

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When you draw a circle it will be drawn with a default centre mark. You have a choice of seven centre marks and these can be changed by right clicking on the circle. These are the same marks that you can choose as points for the point tool. Circles can be filled using the fill palette (see Setting Fill Type). The centre mark for the circle can be set as a default. When you are drawing diagrams including circles, your choice of circle tool can make a large difference to the ease with which you will draw your diagram. Available Parameters for Circles $centre $radius $diameter $circumference $area

6.4.1

Centre Radius Circle

The centre & radius circle is defined by the centre of the circle and any point on the circumference. This is the circle tool to use if you know the location of the centre of the circle. To draw a centre & radius circle, you mark the centre of the circle with your initial click and the point on the circumference when you release the button. Your Centre & Radius circle could extend beyond the bounds of the drawing area. If this occurs, FX Draw will draw as much of the circle as possible.

6.4.2

Diameter Circle

When you are drawing a diameter circle, the two points you define will form a diameter of the circle To draw a diameter circle, you click and hold the left mouse button – move the mouse to the other end of the diameter and release the mouse button.

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Three Point Circle

Three-point circles are defined by ANY three points on their circumference. They are ideal for drawing, for example, the circum-circle of a triangle. To draw a three point circle, just click once on each of the three points. 6.4.4

Circle in a Square

The four corner circle will draw a circle inscribed in a square region defined by four control points. This is how FX Draw V1 defined circles and any FX Draw 1 files will load with this type of circle. To draw a four corner circle, you click and hold the left mouse button – move the mouse to the diagonally opposite corner and release the mouse button.

6.4.5

Com Circle

When you use a com to draw a circle, you place the point on the centre, set the radius and draw - just like the centre/radius circle that is the first circle tool on our list. The thing that IS different ing a com is that with a com you can keep the same radius to draw more circles. That is what the Com Circle tool does. It is a Centre/Radius circle that re the radius. The first time you use the com circle tool it operates in exactly the same way as the centre/radius tool. The second and subsequent times, you just click on the centre of the new circle. The com circle tool re the radius and marks the circle.

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The com circle tool will the radius for as long as it is selected. You can force the com circle tool to reset its radius by: a) b)

6.5

Selecting another tool and then reselecting the com circle tool. Right clicking on a blank part of the drawing canvas.

The Quadrilaterals

The quadrilateral tools contain a normal rectangle, an angled rectangle, parallelogram, rhombus, two ways to draw a kit, a trapezium, rounded rectangles and the bitmap tool. 6.5.1

Rectangle

Right-clicking on one of the sides of a rectangle will allow you to add arrowheads to the middle of the line.

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Available Parameters for Rectangles $height $width $perimeter $area

6.5.2

Angled Rectangle

The angled rectangle tool is very similar to the normal rectangle, the only difference is how it is defined. Angled rectangles are defined by drawing one of the sides (which can be at any angle) and they moving to a third point that defines the height of the rectangle. The third point need not be on the rectangle.

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Right-clicking on one of the sides of a rectangle will allow you to add arrowheads to the middle of the line.

Available Parameters for Rectangles $height $width $perimeter $area

6.5.3

Parallelogram

The parallelogram tool makes drawing parallelograms easy. The first line can be any length and direction. The third point defines the parallelogram.

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Right-clicking on one of the sides of a parallelogram will allow you to add arrowheads to the middle of the line.

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Rhombus

The rhombus tool allows you to draw a rhombus quickly and easily. 6.5.5

Kite 1 and Kite 2 The two kite tools provide two slightly different ways of drawing kites.

When using the first kite tool, the first line drawn is one of the sides of the kite. The third point defines the kite.

When using the second kite tool, the first line defines the major axis of the kite.

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Right-clicking on one of the sides of a kite will allow you to add marks to the middle of the line.

6.5.6

Trapezium

The trapezium tool allows you to quickly draw a trapezium. Right-clicking on one of the sides of a trapezium will allow you to add marks to the middle of the line.

6.5.7

Rounded Rectangle

The rounded rectangle tool draws unshaded rounded rectangles. The shaded rounded rectangle will draw a rounded rectangle using the currently selected

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shading. When a rounded rectangle is selected, you will be able to see a grey, round slider that controls the radius of the rounded corners.

Alternatively you can right click on the rounded rectangle and control the radius explicitly.

Available Parameters for Rounded Rectangles $height $width $perimeter $area $radius

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Bitmap Tool

The bitmap tool allows you to place any bitmap into an FX Draw diagram - but you have to supply the bitmap. In FX Draw 4, you can also add a bitmap to your diagram by copying and pasting from another application. 1.

Sketch out a rectangle that the bitmap will be placed into.

2.

FX Draw will display a dialog box so you can choose a bitmap.

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Select a file and click on Open

By right clicking on the bitmap, you can change its properties.

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Available Parameters for Bitmaps $height $width $xpixels $ypixels

6.6

- width of original bitmap in pixels - height of original bitmap in pixels

Text

The text tool creates a multi-line text box where text can be entered. The text can be left justified, right justified or centred. The entered text can be interpreted as an equation if you wish. Drawing a text box: Sweep out a rectangular box the desired size. Once drawn, you can edit the text.

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In FX Draw 4, the text can be fully formatted. Here we have formatted the word equation as bold Tahoma. Equations: The text window includes an equation button. Any text formatted with this button will be show as underlined.

and when you exit the text box, it will be formatted using FX Equation technology

This allows you to include equations into any text box. Editing text: Either DOUBLE-CLICK on the text box – you will now be able to edit the text in its current location.

OR Right click on the text box. The following dialog box will appear.

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Here you have slightly more control over how the text box is displayed and also have the option of setting the current font as the default.

Text boxes that do not contain equations can be rotated like any other figure. Often this is not what you really want to happen. By removing the Rotatable check mark, the text box will NOT rotate with any other selected figures. It will maintain its location relative to other figures but the text will remain horizontal. Text boxes automatically resize themselves after editing the text. The margin setting determines the size of the margin around the text.

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Equations

The Text tool and the Equation tool are identical. They only difference is that when you choose the equation tool, the equation option is already turned on when you start.

You can still mix and match fonts, colours and equations. Why have two tools – one for text and one for equations? Because often you will require a quick equation for a diagram and the equation tool makes this a one step process. Entering equations into an equation box uses our FX Equation technology. This is fully described in Appendix A.

6.8

Point

FX Draw has a tool that allows you to mark and label points in one step. There are two ways of using the labelled point tool. Mark a Point Without Using a Label. Clicking the left mouse button anywhere on the drawing canvas will mark a point without adding a label. Mark a Point and Attach a Label Click and hold the left mouse button on the point you wish to mark and then move the mouse to the location you wish the label to appear. © 1989-2011 Efofex Software

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If you add more than one labelled point, the labels will automatically increment.

Editing the Properties of a Labelled Point Right clicking on a labelled point allows you to edit a point's properties.

Here you can change the style and size of the point mark, as well as changing label and formatting. If you change any label, the automatic increment will start from your new text. For example, if we change the label from E to P', the next automatically generated labels will automatically be Q', R' and so on.

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Labelled points are GAD aware and will automatically move with any underlying geometry.

6.9

Interactive Whiteboard Tools

6.9.1

Freehand Tools

6.9.1.1

Freehand Line

The first tool is a freehand drawing tool - the second is an eraser that can erase freehand drawn lines. The freehand drawing tool can be used to annotate any FX Draw image.

Here we have used a red pen to mark some intercepts. The freehand lines are normal FX Draw figures. If I click on one, FX Draw will select it and it can be deleted or moved in the same manner as any other figure.

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Eraser

The freehand eraser tool allows you to erase parts of the freehand line. It will not erase any other figures on the screen.

If you "erase" while holding down the right button, FX Draw will redraw the erased line.

6.9.2

Interactive Whiteboard Mode FX Draw has a number of features that are only available in Interactive Whiteboard mode. You can enter the interactive whiteboard mode by pushing this button.

Interactive whiteboard mode changes FX Draw's behaviour in a number of subtle but important ways and displays a new, Interactive Whiteboard, toolbar.

6.9.2.1

Onscreen Keyboard

The onscreen keyboard lets you use your computer's keyboard while standing at © 1989-2011 Efofex Software

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the interactive whiteboard. Pushing the onscreen keyboard button will display one of four available keyboards. The orange keys on each keyboard let you select the other keyboards available. Mini Keyboard Gives you access to the basic control keys on the keyboard

Full Keyboard Recreates a full QWERTY keyboard on your screen.

Numeric Keyboard Useful for data entry.

Equation Keyboard Quick entry of functions and equations

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Right Click

Pushing this button makes FX Draw interpret the NEXT click on the screen as a right click. This is useful if your interactive whiteboard makes right-clicking difficult. 6.9.2.3

Move Toolbars

Pushing the Move Toolbars button moves all of FX Draw's toolbars to the bottom of the FX Draw screen. This makes life a little easier for shorter teachers.

6.9.2.4

Transparency

The transparency control controls how transparent the FX Draw screen is. This allows you to use FX Draw over the top of some other screen or image.

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Triangles, Polygons and Smoothed Lines

6.10.1 Triangles

The triangle tool allows you to draw any triangle. Right-clicking on one of the sides of a triangle will allow you to add marks to the middle of the line.

Available Parameters for Triangles $area $aalt $balt $calt $perimeter $a

Altitudes

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Angle sizes Side lengths

6.10.2 Isosceles Triangles 1 & 2 The isosceles triangles tools provide slightly different ways of drawing isosceles triangles.

When using the first isosceles triangle tool, the first line you draw is the base of the isosceles triangle.

When using the second isosceles triangle tool, the first line draw is one of the two congruent sides.

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Right-clicking on one of the sides of a triangle will allow you to add marks to the middle of the line.

6.10.3 Equilateral Triangle

The equilateral triangle tool allows you to quickly draw equilateral triangles. Right-clicking on one of the sides of a triangle will allow you to add marks to the middle of the line.

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6.10.4 Right Triangles 1 & 2 The right triangles tools provide slightly different ways of drawing right triangles.

When using the first right triangle tool, the first line you draw is one of the shorter sides of the right triangle.

When using the second right triangle tool, the first line draw is the hypotenuse.

Right-clicking on one of the sides of a triangle will allow you to add marks to the middle of the line.

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6.10.5 Polygons

The polygon tool allows you to draw polygons that may be filled if desired. When drawing a polygon, click the mouse button at the position you want each vertex to fall. You should hold down the mouse button while moving the mouse, so you will be able to see the side of the polygon being drawn. When you have completed the polygon, right click to end the polygon drawing process. This is most important, a polygon is NOT completed until you RIGHT CLICK.

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Editing a polygon is different to most other figures. If you right-click on a polygon, FX Draw will add or delete a vertex. If you right click in the middle of a side of the polygon, FX Draw will display a dialog box that allows you to add a vertex – increasing the number of sides - or to add an arrow to the side.

If you click on an existing vertex, FX Draw will offer to delete that vertex – reducing the number of sides. Available Parameters for Polygons $area $centroid $perimeter $anglesum $s1 $s2 $s3 ...

Side lengths

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6.10.6 Regular Polygons 1

This regular polygon tool permits you to draw a regular polygon defined by its centroid and one of its vertices.

Right clicking on the polygon lets you change the number of sides and add arrow heads.

You can draw any regular polygon up to a 30-gon

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Available Parameters for Regular Polygons $sides $sidelen $perimeter $area $anglesum

side length

6.10.7 Regular Polygons 2

The second regular polygon tool defines a polygon by one of its sides.

This tool shares all of its options with the first regular polygon tool. Available Parameters for Regular Polygons $sides $sidelen $perimeter $area $anglesum

side length

6.10.8 Smoothed Line

The smoothed line tool will smooth a mouse drawn line for you.

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Most people have a great deal of difficulty drawing a smooth line with a mouse. The smoothed line tool allows you to produce a smooth line without any mouse drawing skills! Simply select the smoothed line tool and begin drawing. FX Draw will automatically smooth the line for you. The smoothed line options are shown in the dialog box below.

You can add arrows to the start, middle and end of the smooth line. You can leave the line as a single line or make it double (like a road) or triple. You can also close the curve. If the curve is closed, it can be filled. Please note: Finding the middle of the smoothed line is computationally intensive. Having a large number of smoothed lines with middle arrows can dramatically slow down FX Draw's response. Available Parameters for Smoothed Lines $length 6.10.9 Bezier Curve

A Bezier curve is defined by its two end points and two other points which determine the direction the curve approaches its end points. Mathematically speaking, it is a parametric function where both the x and y functions are cubic polynomials.

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Drawing Bezier curves: · · · · · · ·

Click AND HOLD the left mouse button. This will define End Point 1. Move the mouse (while holding the button) to End Point 2. Release the button. Click AND HOLD the left mouse button. Move the mouse (while holding the button) until you are at Tangent Point 1. Release the button. Click AND HOLD the left mouse button. Move the mouse (while holding the button) until you are at Tangent Point 2. Release the button.

Bezier curves have almost the same properties as a smoothed line. The only difference is that you cannot close the curve. Available Parameters for Bezier Curves $length

6.11

The Ellipses

FX Draw provides three ellipse tools. As with circles, the tool you choose to draw a particular ellipse depends on what you know about the ellipse you wish to draw. Choosing the correct tool can make your job much easier.

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An Axis and a Point on the Ellipse

This form of ellipse is defined by one of its axes (either major or minor) and one other point on the ellipse. Drawing the ellipse: · ·

·

Click AND HOLD the left mouse button – this defines one end of the axis. Move the mouse (while holding the button) to the other end of the axis. While you are moving the mouse, FX Draw will synthesize a third point and show you an ellipse. Release the button when you are at the second point. Click AND HOLD the left mouse button and move the mouse to the point on the ellipse. As you move the mouse, FX Draw will draw an ellipse through your points. Release the button when you are at the third point.

Foci and a Point on the Ellipse

This form of ellipse is defined by its foci and one other point on the ellipse. Drawing the ellipse: · ·

·

Click AND HOLD the left mouse button – this defines one focus. Move the mouse (while holding the button) to the other focus. While you are moving the mouse, FX Draw will synthesize a third point and show you an ellipse. Release the button when you are at the second point. Click AND HOLD the left mouse button and move the mouse to the point on the ellipse. As you move the mouse, FX Draw will draw an ellipse through your points. Release the button when you are at the third point. © 1989-2011 Efofex Software

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Four Corners

The four corner circle will draw an ellipse inscribed in a rectangular region defined by four control points. This is how FX Draw V1 defined ellipses and any FX Draw 1 files will load with this type of ellipse. To draw a four corner ellipse, you click and hold the left mouse button – move the mouse to the diagonally opposite corner and release the mouse button. Available Parameters for Ellipses $centre $majoraxis $minoraxis $focus1 $focus2 $circumference $area $eccentricity

6.12

- length of major axis - length of minor axis

The Arcs / Sectors / Segments

FX Draw provides 4 arc tools - end points and point on the arc; centre and end points, four corner (elliptical) arcs and com arcs. Arcs, sectors and segments are all drawn with the same tool. Any arc can be made into a sector or a segment by selecting the options in the properties. As with circles and ellipses, there is more than one way to draw an arc. Once drawn, all arcs share the same properties.

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Every arc can have an arrowhead drawn at each end and one in the middle. You can select a mark to show the centre of curvature. On most arcs you can set the rotation and central angle of the arc explicitly. You can choose to draw the arc or its associated sector or segment. Finally, on most arcs you can choose to draw the major or minor arc defined by your control points. Rotation is measured anti-clockwise from a horizontal line pointing to the right. Negative rotations rotate the arc clockwise. The central angle is the angle between the two arms of the arc.

One final major difference between the arc tools is that the four corner tool is the ONLY arc tool that can draw elliptical arcs. The other three tools will always draw circular arcs. Available Parameters for Arcs $centre $start $stop

- centre of curvature

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- area of sector defined by arc - area of segment defined by arc - central angle

Available Parameters for Elliptical Arcs $centre $start $stop $length $minoraxis $majoraxis $angle $eccentricity

- centre of curvature

- length of minor axis - length of major axis - central angle

6.12.1 End Points & Point on Arc

This arc is defined by its two end points and any other point on the arc. You can draw this arc in two ways. · Click AND HOLD the left mouse button – this determines one end of the arc. · Move the mouse (while holding the button) to the other end of your arc. While you are moving the mouse, FX Draw will synthesize a third point and show you an arc. Release the button when you are at the second point. · Click AND HOLD the left mouse button and move the mouse to a third point on your arc. As you move the mouse, FX Draw will draw an arc defined by your points. Release the button when you are at the third point. Alternatively you can click three times - once on each point.

6.12.2 Centre & Two Ends

This arc is defined by its centre of curvature and its two end points. Drawing The Arc · ·

Click AND HOLD the left mouse button – this defines the centre of curvature. Move the mouse (while holding the button) to one end of your arc. While you are moving the mouse, FX Draw will draw a light grey circle showing the current radius of the arc.

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· Release the mouse button when you are on one end of the arc. · Move the mouse - FX Draw will draw the current arc in a darker grey.

· Click the mouse button when you are at the other end of the arc. Minor and Major Arcs If you select a centre/two ends arc, you will notice that there is an extra point on the arc. A point you didn't define.

FX Draw automatically generates this point so it can be sure about which side of the arc to shade - the minor or major side. You can move this point and change the side to suit yourself.

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6.12.3 Four Corner (Elliptical) Arcs

The four corner arc tool is the ONLY way to draw elliptical arcs. When you first draw a four corner arc, you can force the tool to draw a circular arc by holding down the Shift key as you sweep out the rectangle. In common with many FX Draw tools, holding down the Shift key forces the rectangle you sweep to a square. As you sweep out a rectangle, FX Draw will show you a light grey ellipse that your arc will fit on.

Release the mouse button and move the cursor to one of the end points of the arc you require. Click and hold the mouse button while moving the mouse button to the other end point.

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Release the mouse button to define the arc.

Minor and Major Arcs If you select a four corner arc, you will notice that there is an extra point on the arc. A point you didn't define.

FX Draw automatically generates this point so it can be sure about which side of the arc to shade - the minor or major side. You can move this point and change the side to suit yourself.

6.12.4 Com Arc

When you use a com to draw an arc, you place the point on the centre, set the radius and draw - just like the centre/end points arc tool. The thing that IS different ing a com is that with a com you can keep the same radius to draw more arcs. That is what the Com Arc tool does. It is a Centre/End Points circle that re the radius.

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The first time you use the com arc tool it operates in exactly the same way as the centre/end points tool. The second and subsequent times, you just click on the centre of the new arc. The com arc tool re the radius and marks the circle so you can set the end points. The com arc tool will the radius for as long as it is selected. You can force the com arc tool to reset its radius by: a) b)

6.13

Selecting another tool and then reselecting the com arc tool. Right clicking on a blank part of the drawing canvas.

Angle Tools - Marks and Protractors

FX Draw provides versatile and efficient angle marking tools. The two tools provided are "One Click" angle marking and "Two Click" angle marking. One click marking is highly efficient and flexible and will be the tool of choice in most situations. Two click marking is more tedious but can mark some angles that are not accessible using one click marking. Angle Marks can be drawn between any two intersecting line segments. You can indicate the angle using points, arcs, the actual angle in degrees, radians or grads, or you can add any text to the angle. Importantly...

GAD MUST BE TURNED ON TO USE ANGLE MARKS! FX Draw needs to detect the lines you are using for your angle so you must have GAD on to use this feature. If GAD is turned off, the angle marking tools will be greyed out. One common misconception is that the angle tools will draw a complete angle including the two rays that define the angle. They will not. They will only add an angle mark to an EXISTING angle. Depending on your current default setting, FX Draw will mark the angle with either a point, arc(s) or some text. The angles are dynamic – they will adjust themselves as you move the line segments – they will disappear if the line segments no longer cross and reappear if you later move them so that they cross again.

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6.13.1 One Click Angle Marking

First, draw a diagram that includes some angles. Second, make sure that you have picked the one-click angle tool. As you move your mouse pointer around, FX Draw will automatically sense close angles and show you where it would mark it.

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One click and the angle will be marked using the current defaults.

6.13.2 Two Click Angle Marking

Two click angle marking harks from FX Draw 2. It is a little tricky but allows you to mark some angles that One click marking misses - for example the 60 degree angle marked below.

To draw a two click angle mark... · · ·

Move the mouse to one of the "arms" of your angle. Wait until FX Draw has found the line and put a red dot on it. Click AND HOLD the mouse button. Move the mouse (while holding the button) to the other arm of the angle. © 1989-2011 Efofex Software

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Release the mouse button when the OTHER arm is detected .

You do not need to be too near to the intersection to draw an angle. Once FX Draw has detected your two lines, it will work back to the intersection automatically.

6.13.3 Angle Mark Size Changing the size of an angle mark is easy. Click on an angle mark to select it. You will see a control point.

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Moving this control point changes the size of the angle mark. Some angle marks have two components (an arc and an angle for example). These components can be controlled individually.

6.13.4 Angle Mark Options Angle marks will initially be drawn using the current default settings. Right clicking on an angle mark will give you access to other angle options.

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Most of the angle mark properties are self explanatory. The last style is useful for marking 90 degree angles in 3D diagrams. Notice that we have used FX Equation's standard ` character (next to the 1 button on your keyboard) to indicate degrees.

The "Angled" setting changes how an angle is written – either horizontally or angled along the bisector of the angle as shown above. Text formatted as an equation cannot be angled.

6.13.5 Marking Angles in Radians If you have chosen to mark angles in radians, the style of the mark will depend on the number of decimal places you have selected. Selecting 0 decimal places allows FX Draw to mark the angles in multiples of pi.

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If you increase the number of decimal places, FX Draw will show the angle as decimal radians.

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The Protractors

6.14.1 180 Degree Protractor

The 180 degree protractor is drawn in the same manner as a centre radius circle. This makes it extremely easy to place the protractor onto an angle to show the measurement.

Protractors have no options so right clicking on them has no effect. By default they are unshaded but they can be shaded by selecting them and then using the fill toolbar.

6.14.2 360 Degree Protractor

The 360 degree protractor is drawn in the same manner as a centre radius circle. This makes it extremely easy to place the protractor onto an angle to show the © 1989-2011 Efofex Software

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measurement.

Right-clicking on the 360 degree protractor allows you to reverse the scale.

By default they are unshaded but they can be shaded by selecting them and then using the fill toolbar.

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Bearings

There are two quite distinct ways of using the bearings tool.

Drawing in the Bearing Line By default, FX Draw draws in the bearing line (or the "course"). This means that, if you are drawing in a bearing between A and B it will appear like this.

Using the bearings tool in this way is a bit like drawing lines. You simply draw your course and FX Draw will add a little bearings set at the start point of each line. It is quick but you don't have a lot of control over how the lines are drawn.

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If you select one of the lines and then hover over it with your mouse, FX Draw will show you the value of the indicated bearing. You can make this permanent by right-clicking and Adding an Annotation.

Right - clicking on a bearing allows you set the bearing properties and optionally saving those settings as the default.

Most settings are self-explanatory. One important point to note is that you can enter your own value for the bearing (using common notations like 048, 48, N48E, E42N, NE) and FX Draw will adjust your diagrams to suit.

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Also note the option to Show the Bearing line (in the first example, the line from A to B). Turning this off and setting this as a new default causes the bearing tool to behave in a slightly different way.

No Bearing Line Sometimes you will want to add bearings to an existing diagram or you will want more control over how the bearing line is drawn. If this is the case, turn off Show Bearing Line in the properties and Set the Default. When you add the bearing to an existing line, start where you want the bearing to display and release the mouse when you are anywhere on the existing line. The bearing will attach to the line but the tool will not try to draw its own line over your existing one.

6.16

Shade Regions

Shading regions is a great new addition to FX Draw's tool set but you need to that it is different to the normal "floodfill" that you might find in a painting program. To shade region, select the shade region tool and click once in the region to be shaded.

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Notice that a light cross is drawn where you clicked. Shading Is Attached to A Click The first difference between FX Draw and a normal paint program is that the shading is an "object" that can be selected and moved. Selecting a shaded region is a little difficult because it can only be done in the spot of the original click. The easiest way to click on the light cross

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Now that the region is selected, you can delete it, or pick up the green square and move it.

You will see the shading jump to the other side as the square is moved. The Drawing Order Another major difference is that the shading is in the "drawing order". So far, the drawing order for this image is 1. 2. 3. 4.

Circle Line Rectangle Shading

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The shading will shade up to anything that has already been drawn. If we now draw a second line, the drawing order will be 1. 2. 3. 4. 5.

Circle Line Rectangle Shading Line

The shading occurs before the second line is drawn and just ignores it.

We can change the drawing order using the drawing order toolbar. If we push the "Bring Forward" button, the selected shading will be brought forward in the diagram (drawn later) and the second line will affect the shading.

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Changing Colours Suppose you wish to change the colour of an already shaded region. If you are used to normal, bitmap painting programs you will probably select a new colour and shade again. FX Draw will not let you do this - you can only shade regions which are blank. To change the colour of your shading, you need to select the existing shading and change its colour.

6.17

Specialized Mathematical Tools

6.17.1 Function Graphs

The graph tool allows you to draw graphs of Cartesian, polar, parametric, implicitly defined and inverse functions. Up to ten functions may be combined onto one set of axes. If you have used FX Graph, you will find FX Draw's function graphing tool very similar. Available Parameters for Function Graphs $f1 $point

- definition of function - coordinates of point of interest

when annotating a point of intersection $f2 - definition of second function in intersection when annotating an integral $integral - definite integral $equation - definition of integral function $area - area of definite integral $upper - upper bound of integral $lower - lower bound of integral when annotating a tangent line $slope - gradient of tangent line $equation - definition of derivative function $tangentline - equation of tangent line $at - point at which tangent line touches function $intercept - y intercept of tangent line

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6.17.1.1 Quick Entry Screen

The Quick Entry screen gives you access to most of the capabilities of the graph tool in one location. You can achieve much greater control over the graph tool's output using its other interfaces but you will spend most of your time using this screen.

Function Entry Area Enter your functions - one per line - in this area. the graph tool's function entry utilizes our equation technology which is discussed in more detail later in this manual. You do not need to tell the graph tool what type of function or relationship you are entering, the graph tool will automatically determine this from the structure of the information you enter. Function Display Area Displays the currently selected function using our equation technology. Notice how the x2+y2=7 that we typed has been converted to a formatted equation. The Function Display Area allows you to ensure that the graph tool has correctly interpreted what you have typed. Axis Control Provides basic, extremely fast, control over the axis settings for the graph tool. Setting the axes using this system is a two stage process. 1. Set the SHAPE you require using the two sliders. 2. Set the MAXIMUM x and y values. The graph tool does everything else automatically (unless you override its automatic selections on the Axes, Scale, Grid and Function Properties pages).

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The three buttons allow you to select three default axes types. The first is a free set of axes from -10 to 10. The second is a equal aspect set from -10 to 10 (equal aspect means that x units and y units are the same size). The third button sets y from -1 to 1 and x from 0 to 360 or 2 pi (depending on the angle setting). Current Function Display Options Functions and relationships are rendered on screen as lines and points. This section allows you to set the style, weight, colour and size of the lines and points used to display the currently selected function. To change the properties of another function, move the cursor to another function in the Function Entry Area . More Control The Axes, Scale, Grid and Function Properties pages give you much greater control over the output of the graph tool. the graph tool will automatically produce great results on most occasions but, inevitably, there will be times when the graph tool's output will not be exactly what you desire. The other pages allow you to achieve what you are after.

This diagram shows the Quick Entry screen with the More >> button depressed. Notice that we have set the axes to a different shape and set the x Max to 2pi. This forces the graph tool to mark the x scale in fractional parts of pi.

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Axis Annotations By default, the graph tool marks the axes as x and y. You can change these annotations here. Show Grid Turns the grid on and off. The grid can also be turned on and off on the Grid page (see More Control) Feasible Region Options These settings are discussed in the Inequations & Feasible Regions section of the manual. Angles The graph tool can use Degree and Radian angle measurement. Set As Default The Quick Entry screen, as with most the graph tool screens, has a Set As Default button. This button makes the graph tool your current settings and use them for all future graphs.

6.17.1.2 Function Entry

The graph tool uses the equation engine from FX Equation so entering functions is extremely easy AND you can see a fully formatted version of your function as you type. Functions are entered into the graph tool by typing what you see WITHOUT any formatting. On most occasions the graph tool will automatically format your function for you. For example. If you want to graph the function 3x3 + 2x2 - 7 simply enter 3x3+2x2-7 into the function entry area. the graph tool automatically recognizes and formats the powers and displays the formatted function for you to check your entry. Simple fractions are also entered as you see them. In other words if you want to graph

you enter 3x3/2x4 and the graph tool will automatically build the appropriate fraction. Most simple functions can be entered this way, with NO formatting on your part. More complicated functions will require some limited extra input on your part. Regional Issues: The graph tool automatically detects which style of decimal point you use (3.2 or 3,2). If you use a , as a decimal point, you must use a semi colon to separate coordinates in points and vectors (eg (3,2; 1,7) ) and a colon to separate domains from functions or the two components of parametric functions.

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6.17.1.3 Important Points About Function Entry

Because of the restrictions of a computer interface, there are some special points you will need to understand to enter all functions. Special Symbols Because mathematicians use many symbols not normally found on a computer keyboard, the graph tool uses a small number of special symbols, codes and abbreviations in order to allow you to enter functions.

Multiplication Exponentiation (Powers)

Normal Symbol ´ none (eg 2x)

Division

¸

Pi

p

Theta Greater than or equal to Less than or equal to Plus Minus

q ³

the graph Notes tool * ^ (eg 2^x) Only needed when the graph tool fails to automatically recognise the power. / (followed by The / character is more often a space) used (without the space) to enter fractions. pi Can be used in both functions and axes. th Used in polar functions >=

£

<=

±

+-

the graph tool will automatically graph both arms of the function.

Most of these symbols are in common use in computer based mathematics. Brackets Many functions, especially fractions, contain assumed brackets. The graph tool will sometimes require you to enter these brackets even though you cannot see them. For example, if you enter y = 3/x+3 does this mean

To graph the second function you need to add logical brackets to your function and type y = 3/(x+3). These brackets will not be displayed but will influence how your function is interpreted. As a general rule, if the function is not shown formatted correctly by the graph tool, add some brackets to make your meaning clear. A very important use of brackets is to logically identify the numerator and denominator in complicated fractions. For example: (x+2)/(x-3) needs the brackets to be interpreted as

rather than

.

Brackets are also used to logically identify powers and ensure that the graph tool interprets your function correctly. © 1989-2011 Efofex Software

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All three bracket types {, [ and ( may be used interchangeably in the graph tool and the graph tool makes no distinction between them. the graph tool does not even check to see if brackets are paired. You are responsible for this. If there is a fraction inside a bracket, the bracket is automatically resized. Example: is entered as 3[(x-2)2+1/2] Powers Most powers will be automatically recognized by the graph tool. The graph tool will not automatically recognize powers if · · · ·

you require a variable as a power you require a function as a power you require a power of a number you require a complicated power.

In these cases you need to explicitly indicate the power using the ^ symbol. As with fractions, complicated powers need to be surrounded with brackets. These brackets will not be displayed. Examples: is entered as e^(sinth)

is entered as x^(2y+3) Spaces Spaces change the way a particular equation is formatted and therefore interpreted. This can best be illustrated using these examples. is entered as sin2 th is entered as sin 2th The only difference between the two equations is the location of a space.

6.17.1.4 Types of Functions 6.17.1.4.1 Overview

The graph tool is capable of graphing a wide variety of functions and relations. Uniquely, you do not have to "tell" the graph tool what sort of function to graph, the graph tool automatically determines this for itself based on what you type. For example: If you type a function which only includes the variable x, the graph tool will graph a Cartesian function. If you include y' in the expression, it will automatically graph a direction field. Functions defined implicitly will automatically be rearranged into Cartesian or inverse Cartesian functions if this is possible. You only have to worry about what to graph rather than how to graph it. © 1989-2011 Efofex Software

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The next sections discuss the different types of things that the graph tool can graph and how to enter them.

6.17.1.4.2 Cartesian Functions

Normal Cartesian functions (y = ...) can be entered into the graph tool with or without the y=. y = 3x - 7 OR 3x - 7 The graph tool is optimised for normal Cartesian functions. Some of the graph tool's are only available for Cartesian functions. The graph tool will always attempt to rearrange functions into normal Cartesian functions to ensure that the most options are available. For example: 3x2 + y = 3x + 2 will be internally rearranged by the graph tool into: y = (3x(1 - x)) + 2 and all features will be available.

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In the diagram above, notice how we entered the function as 3x2 + y = 3x + 2 but the graph tool has rearranged the function when finding the integral.

6.17.1.4.3 "Multiple Armed" Functions

The graph tool s the use of ± in functions. The graph tool s the use of up to ten sets of +- in one equation.

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6.17.1.4.4 Polar Functions

Polar functions are entered in of r and q. Because there is no q key on a computer keyboard, the graph tool uses th to represent q. You can enter a normal polar equation such as r = 5 sin 3q by typing r = 5 sin 3th or 5 sin 3th The r = is optional and will be assumed if you do not enter it.

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the graph tool can also draw inverse Polar functions - just enter them in of r. th = 3r th = 1/r th = pi/4

As shown above, the graph tool can draw polar grids. Go to the Grid page and check Polar Grid © 1989-2011 Efofex Software

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Default Domains Cartesian and Inverse Cartesian functions have an "implied domain" - the bounds of the axes you have drawn the function on. If you have not explicitly set a domain, the graph tool can automatically determine a suitable domain from the axes it is using. For Polar graphs, there is not a natural domain that can be easily determined. To counter this problem, the graph tool uses some default domains for polar graphs. Polar graphs

0 £ q £ 360 (degrees mode) 0 £ q £ 2p (radian mode)

In most cases these default domains produce acceptable results. Sometimes you may need to override the default domains in order to create the result you are after. See Domains for more details on how to explicitly define the domain of your function.

6.17.1.4.5 Inverse Cartesian

Inverse Cartesian functions (x = ) can be entered as x = 3y2+3y-4

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or 3y2+3y-4 the x = is optional

The graph tool will rearrange functions if possible. 3xy + y = 4x will be internally rearranged into y = 4x/(3x+1) to provide access to more of the graph tool's features.

6.17.1.4.6 Implicitly Defined

Implicitly defined functions are treated in two stages. 1. The graph tool tries to rearrange the function to be in of x or y and will then graph the function. 2.

If the graph tool cannot rearrange the function, it uses a more generalized approach to graphing. For example, (x2+2y2-2)(2x2+y2-2)+1/20=0

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This approach basic looks for equality between the two sides of the equation. When using this form of graphing, the graph tool cannot perform detailed analysis of the curve. 6.17.1.4.7 Parametric

Parametric curves are entered as two equations in of t - separated by a semicolon (see regional issues). x = 6cos t ; y = 6sin 3t

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Default Domains Cartesian and Inverse Cartesian functions have an "implied domain" - the bounds of the axes you have drawn the function on. If you have not explicitly set a domain, the graph tool can automatically determine a suitable domain from the axes it is using. For parametric graphs, there is not a natural domain that can be easily determined. To counter this problem, the graph tool uses a default domain for parametric graphs. Parametric graphs

0 £ t £ 20

In most cases the default domains produce acceptable results. Sometimes you may need to override the default domains in order to create the result you are after. See Domains for more details on how to explicitly define the domain of your function. Regional Issues If you use a comma as a decimal point (eg 3,2) you must use a colon to separate the two parts of a parametric equation. x = 6cos t : y = 6sin 3t

6.17.1.4.8 Point Functions (Cartesian & Polar)

The graph tool allows you to mark points on functions and points on the plane using the Marked Point tool but sometimes you will want to mark points that include constants or as ed points. the graph tool allows you to by entering

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points as functions. Points are entered as ordered pairs - optionally separated by semicolons (see regional issues). (2,3) (1,1); (-1,-1) (-3,2)

By prefixing one of the points by a P, the graph tool will interpret all of the points as being in polar form, (r, q). When entering points in polar form, you need to enter the angle in the currently selected angle type. P(6,pi/4) (3,3pi/4)

-

angle set to Radians

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Constants Points can contain constants which are discussed later in this manual. You can enter a point of (-3a,b) for example. Regional Issues If you use a comma as a decimal point (eg 3,2) you must use a semicolon to separate the two coordinates and (optionally) a colon to separate the individual points. (2;3) (1,1;1,1) : (-1;-1) (-3;2)

6.17.1.4.9 Groups of Points

The graph tool can plot groups of points and them together. Simply place a + sign between the points. See regional issues. (3,5)+(3,6)+(4,5)+(5,5)+(5,4)+(3,4)+(2,3)+(2,0)+(1,0)+(1,3)+(-1,3)+(-1,0)+(-2,0)+(2,3)+(-3,4)+(-5,2)+(-5,3)+(-3,5)+(3,5)

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You can mix points and groups of points in the same function. Regional Issues If you use a comma as a decimal point (eg 3,2) you must use a semicolon to separate the two coordinates. (3;5)+(3;6)+(4;5)+(5;5)+(5;4)+(3;4)+(2;3)+(2;0)+(1;0)+(1;3)+(-1;3)+(-1;0)+(-2;0)+ (-2;3)+(-3;4)+(-5;2)+(-5;3)+(-3;5)+(3;5)

6.17.1.4.10 Vectors

Vectors are entered as <2,3>. They can be added, subtracted and combined with a point. See regional issues For example: (-2,-3) + <4,7> + <3,-3> - <4,0>

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Polar Vectors If you prefix one of the vectors/points with a P, the graph tool will interpret the points and vectors as polars. You must enter any angles using the current angle measurement (degrees or radians). p(1,pi) + <2,pi/3> - <6,-pi/4>

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Constants Vectors can contain constants which are discussed later in this manual. You can enter a vector of <-3a,b> for example. Regional Issues If you use a comma as a decimal point (eg 3,2) you must use a semicolon to separate the two coordinates. (-2;-3) + <4;7> + <3;-3> - <4;0>

6.17.1.4.11 First Order Differentials

To enter a first order differential, include a y ' or f '(x) in the function definition. For example, type y'=3x+2y

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Each little line shows the slope at the point. If you hover over one of the slope lines, the graph tool will calculate the slope at that point. If you select the Marked Point tool.

and add a point on top of one of the slope lines.

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the graph tool will solve the differential equation at the marked point and show you on screen. You can add multiple points if you wish.

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6.17.1.4.12 Complex Numbers

The graph tool introduces some for complex numbers. It is possible to confuse the graph tool, but in the vast majority of school situations, it will produce the desired result. To enter a complex number, just type it in as it is written. z = 4+3i

z = 3cis(pi/3)

Complex calculations will be performed prior to graphing the result z = (2 + 3i)2

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The graph tool can also solve some complex equations z5= 50+200i

Finally, the graph tool understands magnitudes and can graph most cases. | z - i | >= 4 © 1989-2011 Efofex Software

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6.17.1.4.13 Greatest Integer Functions, Sgn Functions and Piecewise Defined Functions

Greatest Integer Functions and Sgn Functions involve discontinuities that can sometimes be difficult to analyse. Simple functions such as y = gint(x) are easy to interpret and discontinuities will be correctly shown.

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Due to the graph tool's ability to graph functions of arbitrary complexity it is possible to construct functions that confuse the graph tool's analysis routines and have the discontinuities incorrectly shown. 6.17.1.4.14 Piecewise Defined Functions

The graph tool automatically detects and graphs piecewise defined functions. All you have to do is to enter functions with domains that line up.

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6.17.1.5 Function Reference

Command e pi sin cos tan asin or sin-1

Description constant e = 2.18281828… constant p = 3.141592654… sine of an angle cosine of an angle tangent of an angle arcsine or inverse sine

Example y = e^x y = pi x2 y = sin 2x y = cos3 x r = 2tan th y = asin(x) y= sin-1(x) acos or cos-1 arccosine or inverse cosine as above atan or tan-1 arctangent or inverse tangent as above sec secant of an angle y = sec2 x cosec cosecant of an angle as above cot cotangent of an angle as above cosh hyperbolic cosine y = cosh x sinh hyperbolic sine y = sinh x tanh hyperbolic tangent y = tanh x ln natural logarithm y = ln(2x) log base 10 logarithm y = log(x) log base n base n logarithms y = log2 x sr or sqrt square root y = sr(x) y= sqrt(x-2) abs absolute value y = abs x | absolute value y = |x - 2| root nth root. Any root of the argument can y = 3root x y= be found by adding the number in front 5root(x2) of the word "root" normal calculates the normal probability y = normal(x) distribution for x standard deviations from the mean gint greatest integer function y = gint(x) greatest integer function y = [| x |] sgn sign function y = sgn(x)

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6.17.1.6 Points of Interest

The graph tool finds most points of interest for you - automatically. You do not need to "do" anything - just move the mouse around the graph. Any points of interest will be marked and a short message giving the coordinates and why it is "interesting". All of the points in this diagram have been found automatically and displayed by hovering the mouse over the point.

6.17.1.7 Right Clicking

Much of the graph tool's functionality is accessed by right-clicking. · If you right click on blank space on the graph's grid, the Quick Entry screen is displayed. · If you right click on most components of a graph, a mini-menu is displayed that allows you to edit the object or add an annotation.

6.17.1.8 Select Mode

Select Mode is the basic mode of the graph tool. You can choose select mode by pressing the button on the toolbar. When in select mode, you can select most objects in a graph. If you sweep out a rectangle, you can select multiple objects at the same time.

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6.17.1.9 Moving Around The Plane Using The Keyboard

You can move around your axes using the arrow keys on your computer. If we have a set of axes such as

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pushing the right arrow a few times will result in

We have moved to the right. If we push the right arrow a few more times we will see

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The graph tool will break the scale (if you have allowed it to) and move further to the right of the plane. You can use all four arrow keys to move anywhere on the plane. The Home Key Pressing the home key at any stage will return you to the origin.

6.17.1.10 Zooming

The graph tool's Point of Interest system greatly reduces the number of times you will wish to zoom into a graph but the graph tool s zooming in a number of ways. 6.17.1.10.1 Zooming with the Keyboard

You can zoom in and out using the keyboard. Page Up Page Down Home -

Zooms the axes out Zooms the axes in Centres the axes on the origin. Starting Axes

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Zooms OUT by 33%

Zooms IN by 33%

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6.17.1.10.2 Zooming with the Mouse 6.17.1.10.2.1 Zoom Mode

Before using your mouse to zoom, you must first enter Zoom Mode. Push the button on the graph tool's toolbar. Once in Zoom mode you can use the mouse to Zoom into and out from functions.

6.17.1.10.2.2 Click Zooming

If you click the left mouse button somewhere on the plane, the graph tool will zoom in to the point you click on. This allows you to quickly and easily zoom in on points of interest. If you right click, the graph tool will zoom out. 6.17.1.10.2.3 Rectangle Zooming

If you sweep out a rectangle while holding down the left mouse button, the graph tool will zoom into the rectangle you have defined.

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6.17.1.10.2.4 Undo Zoom

Undo re zoom events so you can undo any zoom by choosing Undo from the Edit menu or by typing Ctrl+Z 6.17.1.11 Domains

Domains can be entered for most functions using one of two formats. 1. Using greater than, less than, greater than or equal to and less than or equal to signs. These are typed after a semicolon (or colon if you use a , as a decimal point) after the function when entering functions in the Quick Entry screen. For example:

2. You can also enter domains using bracket notation, (-2,3] for example. Parentheses indicate > or < and square brackets £ or ³. This style of domain © 1989-2011 Efofex Software

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is quicker to use and does not require a semicolon (or colon). For example:

Constants Domains can contain constants which are discussed later in this manual. You can have a domain of [-3a,b) for example. Regional Issues If you use a comma as a decimal point (eg 3,2) you must enter domains either as x2 : -2<=x<2 or x2 [-2;2) 6.17.1.12 Default Domains

If you have not explicitly set a domain, the graph tool will choose one for you. Cartesian and inverse graphs have a domain implied by the size of the axes and the graph tool will automatically draw a graph for this implied domain. Polar and parametric graphs have no implied domain so the graph tool uses: Polar graphs

0 £ q £ 360 (degrees mode) 0 £ q £ 2p (radian mode)

Parametric graphs

0 £ t £ 20

If your polar or parametric graph is incomplete, you may need to set your own domain.

6.17.1.13 Constants 6.17.1.13.1 Entering Constants

The graph tool understands seven constants. Fixed Constants e

~

2.718281828

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3.141592654

These constants can be used in functions, axes, domains, points and vectors. Variable Constants Variable constants (now there is an interesting concept - they probably should be called parameters) allow you to examine how changing numbers in a function affects the function's shape. The graph tool reserves a, b, c, d and m as constants that can be included in functions. They are entered in the same way as the variables x, y, r, t and th. For example, you can enter the following function y = ax2 + bx + c and examine how changing a, b and c affects the parabola.

6.17.1.13.2 Changing Constants

When the graph tool detects a constant in a function, it automatically adds a constant controller to the bottom of its screen. FX Graph adds one constant controller for each constant.

Let's look at a constant controller in more detail. The first edit box allows you to explicitly set the value of the constant. You can type in any value for the constant - including e or pi. For example, you can set the value of a to be pi/2. The slider allows you to modify the constant interactively. As you slide the slider left or right, the constant will be incremented or decremented by the amount shown as delta.

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The second edit box allows you to set the Delta for the constant - how much it changes each time you move the slider (or draw a family of curves or animate). You can type any value in for delta - including values based on e or pi.

The final two buttons allow you to draw families of curves or animate a graph. These are discussed in the next sections.

6.17.1.13.3 Families of Curves

The graph tool can graph a family of curves by changing a constant. Just push the button

For example, if you have entered the function y = ax2.

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I have set a to be 1 and the delta to be 0.25. The graph shows a family of curves, centred around a = 1 with a varying from -0.25 to 2.25. In other words we have graphed: y = -0.25x^2 y = 0x^2 y = 1.25x^2 y = 1.5x^2

y = 0.25x^2 y = 0.5x^2 y = 1.75x^2 y = 2x^2

y = 0.75x^2 y = 1x^2 and y = 2.25x^2

all on the same set of axes. This graph also shows one of the graph tool 4's new features where graphs away from the "main" value of a have reduced transparency. This can more clearly demonstrate some concepts. This, in turn, brings us to the other window in the constant controllers.

Two of controls in this window affect families of curves. The slider changes the number of curves in the family, or how many steps away from the "main" value the graph tool moves. By moving the slider all the way to the right, we greatly increase the number of curves in the family. Underneath the slider, the graph tool shows the range of values that a will take based on your current settings. In our case a is varying from -0.25 to 2.25. You can also turn off the transparency effect using the indicated button.

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6.17.1.13.4 Animations

All constants can be animated. Just push the animate button on the constant you wish to animate.

The constant will immediately start animating. a will increase and decrease in steps of delta.

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The second controller window allows you to control the animation.

The Number of Iterations slider controls how far from the "main" value the graph tool travels in the iteration. The Animation Speed slider controls the speed of the animation. The Reversing/One-Way button controls whether the animation goes

Up ... Down ... Up ... Down ... Up ... Down ... Up or

Up ... Start Again ... Up ... Start Again ... Up ... Start Again ... Up Brain Drain Animating functions in the graph tool is very computationally intensive because the graph tool has so much to calculate each time. Intercepts, maxima and minima, integrals, derivatives... everything is recalculated. This means that on slower computers, the animations may not be as fast as you would like. Stopping an Animation You can stop an animation by clicking on the animate button again.

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Animation with Multiple Constants If you have more than one constant, you can change the other constants during the animation. Try animating the c constant in y = ax2 + bx + c. While the animation is running, change a and b. 6.17.1.13.5 Constants Everywhere

You are not restricted to using constants just in function definitions. The can be used in most situations in the graph tool. · · · · ·

In domains. In the bounds of integrals. In the number of divisions for integral approximations. In the "At" point of tangent/secant lines In the Delta of tangent/secant lines.

Using constants in these locations allows you to easily create some fairly fancy animations and families of curves. 6.17.1.14 Inequations & Feasible Regions 6.17.1.14.1 Entering Inequations

Inequations are entered by replacing the = sign in your equation by either, >, <, >= or <= Inequations can be entered for all function types except parametric. x + y <= 4 r > 2 sin th xy2 >= yx2 + 4 y >= 2x-7 x>0 |z| <= 4 The graph tool will produce a shaded graph depending on your Feasible Region Options.

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6.17.1.14.2 Feasible Region Options

On many occasions, you will be entering a number of inequations and trying to identify the region that satisfies ALL the inequations - also known as the feasible region. The graph tool can show the feasible region in a number of ways - depending on your needs. The feasible region options can be changed by opening the Quick Entry screen

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The Feasible Region options are described in the next sections. 6.17.1.14.2.1 Half Planes or Feasible Region

When graphing multiple inequations, the graph tool can graph each as a half plane, or combine the inequations and shade ONLY the feasible region. For example, if we graph 2x + y <= 8 and x + 2y <= 10

Half Planes

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Shading half planes When shading half planes, the graph tool shades the region which satisfies each equation INDIVIDUALLY. In the above example, the region which satisfies both inequations has been shaded twice. the graph tool uses each function's color for its shading. But Wait! I Was Expecting The Graph Tool to Shade the Other Side! Unfortunately, which side of the inequation to shade depends on where you live. Some school systems want the side that satisfies the inequation shaded - some the side that does NOT satisfy the inequation. the graph tool can handle either. Choose Preferences from the Tools menu and then select Graph

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In the screen above, the graph tool is set to shade the region which satisfies the inequation. If I uncheck the box, the graph tool will shade the region which does not satisfy the inequation. This setting only affects Half Plane Shading.

Only Feasible Region Alternatively you can tell the graph tool to shade ONLY the feasible region. This is often clearer.

In this graph, the graph tool has calculated the region which satisfies BOTH inequations and has shaded just that region. The area is shaded using the color, style and opacity selected in the Quick Entry screen.

Don't Get Tricked!! Some s get tricked when the graph tool produces this graph even when it is

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set to shade the side that does not satisfy the equation.

In this case, the graph tool is doing exactly what it was asked to do. We have told it NOT to shade the region which satisfies the inequation but this only only affects Half Planes. We have also told it to shade ONLY the feasible region - the region which satisfies all inequations. This overrides the other setting. If we had two inequations, what the graph tool was doing would be clear. Only having one inequation active means that the graph tool seems to be ignoring us.

6.17.1.14.2.2 Solid Shading

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Solid Shading Solid shading is one block of solid color. Solid shading has the advantage of being faster to calculate and displays better on some devices. The graph tool uses solid shading when you have allowed it to and when the system of inequations is not too complicated for its systems.

Dotted shading Uses an array of dots. The graph tool tests an array of coordinates and determines whether each point satisfies all inequations. Any points which satisfy all inequations are displayed. Dotted shading is a more robust approach - the complexity of the regions does not matter - but it is computationally intensive and does not display as well on some devices. The graph tool will use dotted shading when the system of inequations is too

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complicated to solve. For example,

In this case it is the magenta implicitly defined equation that is causing the graph tool to drop down to dotted shading.

6.17.1.15 Derivative Curves

Cartesian functions can displayed with their first and second derivative curves.

To draw derivative curves for a function you have two options. © 1989-2011 Efofex Software

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Right Click If you right click on an existing function you will see this mini-menu

You can select 1st and 2nd derivative curves on this mini menu. Function Properties You can access the Function Properties by pushing the Function Properties option on the Quick Entry screen.

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You can turn the derivative curves on or off and can change the line style, weight and colour. 6.17.1.16 Integrals

The graph tool can graph integrals for any Cartesian function.

6.17.1.16.1 Using Your Mouse to Create Integrals 6.17.1.16.1.1 Integral Mode

Before using your mouse to create an integral, you must first enter Integral Mode. Push the

button on the graph tool's toolbar.

Integral mode is only available if you have entered a function that the graph tool can integrate. Once in Integral mode you can use the mouse to create integrals. 6.17.1.16.1.2 Integration with One Function Graphed

Sketching integrals is easiest when you only have one function graphed because it is obvious which function you wish to integrate!

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Draw your function Select Integral Mode Move the mouse to the lower bound you wish to integrate. Click and drag the mouse to the upper bound you wish to integrate. the graph tool will show the · Release the mouse. · · · ·

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Easy! If you move the cursor over the integral and "hover", the graph tool will display the details of the integral.

Often you will want to create an integral that starts or finishes at a special point x intercepts for example. This is almost as easy - you just need to move the mouse near the x intercept and wait for the graph tool to find the intercept before you click or release the mouse.

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6.17.1.16.1.3 Integration with Two (or More) Functions Graphed

Integration with two or more functions graphed is slightly more difficult - simply because you need to tell the graph tool which of the functions you want to integrate. This is not too hard however. Move your cursor near the function at the lower bound and wait until the graph tool finds the function. Then click, drag, release - just like before.

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6.17.1.16.1.4 Integral Between Two Curves

To create an integral between two curves using the mouse, your first click must be on an intersection between the two curves. This is normally exactly what you want. © 1989-2011 Efofex Software

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Move until the point of intersection has been found

If you start your integral now, the integral will be between the two curves.

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Notice that even though the integral had to start at an intersection, it does not have to end at one. But I Don't Want My Integral to Start at the Intersection! Then either create your integral with the mouse, starting at the intersection (or even under just one of the functions) and edit it later. See Editing Integrals for more details on how to edit integrals 6.17.1.16.1.5 Integral to y Axis

You cannot create an integral (or area) to the y axis using the mouse. To create a y axis integral, you need to create it to the x axis using the mouse and edit the integral later (see Editing Integrals) 6.17.1.16.2 Editing Integrals With a Mouse

You can edit some aspects of an integral using your mouse.

Selecting an Integral Click anywhere within the integral to select it. When selected, the integrals border with thicken.

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Deleting an Integral When an integral is selected, press Delete to delete it.

Changing Bounds When an integral is selected, click and drag either of the bounds to modify the integral.

6.17.1.16.3 Editing Integrals

You can edit any integral by right clicking on it and then selecting Edit Properties.

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This allows you to select the function for which the integral is found and the upper and lower bounds of integration. Notice that the graph tool shows you a formatted integral so you can clearly see exactly what you are finding. Bounds can be expressed in of pi or e and can contain constants. Including a constant in your bounds of integration allows you to produce some very useful animations. The Swap button will swap the bounds of integration which will reverse the sign of the result.

The second drop down box allows you to change how the integral is calculated. Here you can select an integral to the y axis or select a second function so that the graph tool finds the integral between two functions. This allows you to select any possible integral.

The bottom pane of the integral screen allows you to set the pen and shading for the selected integral.

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If this is selected, the graph tool will calculate and show the area of an integral as well as the actual integral.

6.17.1.16.4 Approximations To The Integral

The graph tool can produce seven different approximations to the integral.

Original Integral

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Minimum - uses the minimum in each division

Maximum - uses the maximum in each division

Left - uses the left hand value of each division

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Right - uses the right hand value of each division

Trapezium Rule

Simpson's Rule (2 divisions)

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the approximation was indistinguishable from the actual integral! Each of the approximations divides the integral in to the given number of divisions (in most of the example above we have used 6 divisions). You can use a constant in the divisions box. This allows you to show students how quickly the various approximations approach the integral.

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With just 4 divisions, Simpson's Rule approximates the integral to 3 decimal places.

6.17.1.17 Tangent and Secant Lines

The graph tool can attach Tangent and Secant Lines to any Cartesian function.

6.17.1.17.1 Using Your Mouse to Create Tangent Lines 6.17.1.17.1.1 Tangent / Secant Line Mode

Before using your mouse to create a tangent or secant, you must first enter Tangent / Secant Line Mode. Push the button on the graph tool's toolbar. The cursor will change to remind you that you are using Tangent / Secant Line mode. Tangent / Secant Line mode is only available if you have entered a function that the graph tool can attach a tangent line to. Once in Tangent / Secant Line mode you can use the mouse to create tangent and secant lines.

6.17.1.17.1.2 Tangent Line on a Curve

Attaching a tangent line to a function is easy. Just click on the curve you wish to attach the tangent line to. BEFORE you click, make sure that the graph tool has found the curve. You will know it has found the curve when it displays the curve's definition.

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6.17.1.17.1.3 Secant Line on a Curve

Attaching a secant line to a function is not difficult. Click on the curve you wish to attach the tangent line to and drag your mouse to the second point on the line before releasing. BEFORE you click, make sure that the graph tool has found the curve. You will know it has found the curve when it displays the curve's definition.

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The point you initially clicked on is the main, fixed point of the secant line. The release point is mobile.

6.17.1.17.1.4 Selecting Tangent/Secant Lines

You can select a tangent/secant line by clicking anywhere on it. The selected line will increase in thickness. 6.17.1.17.1.5 Moving a Tangent / Secant Line With Your Mouse

You can move a tangent or secant line on a curve by selecting it then moving it with your mouse. First, select the line. When the line is selected, it will be drawn thicker.

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You can move the line by clicking and dragging. You can also use the keyboard to move a selected tangent / secant line. See Using Your Keyboard for more details.

6.17.1.17.2 Using Your Keyboard

Tangent Lines The left and right arrows will move your tangent line left and right.

Secant Lines The left and right arrows will move the release point of the secant line. If you hold down the Shift or Ctrl key, the left and right arrows will move the main point of the secant line. 6.17.1.17.3 Editing a Tangent / Secant Line

You can edit a tangent / secant line by right-clicking on it and then choosing Edit Properties

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Here you can change the function, location, delta and line properties. 6.17.1.18 Tables of Values 6.17.1.18.1 What are Tables of Values?

Tables of Values are data generated from the functions you have entered. One of their main uses is to copy data out of the graph tool and into other products such as Word or Excel.

6.17.1.18.2 Tables Mode

Before using your mouse to create a table of values , you must first enter Tables Mode. Push the button on the graph tool's toolbar. The cursor will change to remind you that you are using Tables mode. Tables mode is available when you have entered a function. 6.17.1.18.3 Adding a Table of Values

Easy. · · · ·

Draw a function. Select Table of Values mode Hover over a function so that the graph tool finds the function. Click

A table will be inserted using your current defaults.

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You can then move and modify the table to suit your needs. 6.17.1.18.4 Moving a Table of Values

You can click on a table of values to select it. Once selected, a table can be moved using the mouse. 6.17.1.18.5 Horizontal or Vertical?

Tables of Values can be horizontal or vertical. The original table of values will be based on your current default. You can change the orientation of the table by right-clicking on it.

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6.17.1.18.6 Copying Data to The Clipboard

Data in a table of values can be copied to the clipboard. Right click on a table of values and choose Copy Data to Clipboard. Data will be placed on the clipboard in the same orientation as table of values.

x 1 y 1

-10 2 100 4

-9 3 81 9

-8 4 64 16

-7 5 49 25

-6 6 36 36

-5 7 25 49

-4 8 16 64

-3 9 9 81

-2 10 4 100

-1

0

1

0

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Table data is placed on the clipboard in formats suitable for insertion into most word processors and spreadsheets. 6.17.1.18.7 Where Do The Entries Come From?

When you first insert a table, the graph tool will fill the table with entries automatically. These entries are taken from the current axes settings. If your axes are from -10 to 10 in steps of 1, the table will use the same settings. If your axes are from -pi to pi in steps of pi/8, the table will be the same. 6.17.1.18.8 Editing Tables of Values

Right click on a table of values and choose Edit Table Properties.

1. Tables of values have four vertical and four horizontal styles. 2. Tables of values are normally coloured based on the function that they are derived on so normally this will be kept checked. If you want to specify different colours you can turn this off and set the shading and pen explicitly. 3. Entries are normally automatic but you can explicitly set a starting point, increment and count. 6.17.1.18.9 Moving Tables of Values to the Edge

Tables of values normally overlay the graph. If you move a table of value to the edge of the screen, the graph tool will resize the graph to allow the Table of Values to sit by itself. Horizontal tables can be moved to the top or bottom. Vertical tables to the left or right.

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6.17.1.19 Marked Points 6.17.1.19.1 What is a Marked Point?

A marked point is a point that has been added to your diagram by clicking on the screen, rather than entering the coordinates of the point as a "function". They are quicker and easier to use than entered points. 6.17.1.19.2 Marked Point Mode

Before using your mouse to create a marked point, you must first enter Marked Point Mode. Push the button on FX Graph's toolbar. The cursor will change to remind you that you are using Marked Point mode. Marked Point mode is always available.

6.17.1.19.3 Free Marked Points

When in marked point mode, you can click and add marked points anywhere on the plane. These points are not logically connected to any other feature on the graph.

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If you click on a free marked point it will be selected. Selected points increase in size.

Moving Free Marked Points A selected free marked point can be moved with the mouse or with the arrow keys on the keyboard. 6.17.1.19.4 Marked Points on Functions

If you have a function on screen and move your mouse so that FX Graph finds the function, any marked point will be attached to the function.

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The resulting marked point can still be selected but, when moving, it will be attached to the function.

Whether you move this point with the mouse or with the left and right arrow keys, the point will always be on the function.

6.17.1.19.5 Marked Points on Slope Fields

Marked points on slope fields are treated differently. If the marked point is attached to one of the slope points (you have to make sure that FX Graph has found the point), FX Graph will solve the differential equation through that point.

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This marked point can be selected and moved with the mouse or keyboard.

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6.17.1.19.6 Editing Marked Points

Right click on a marked point and choose Edit Properties to change the marked point's properties.

Here you can change the points style, size and colour. 6.17.2 Statistical Graphs

FX Draw provides a comprehensive statistical graphing tool. If you are familiar with FX Stat you will find this tool to be very similar. To draw a statistical graph, sweep a rectangular region with your mouse. A set of axes will fill the rectangle. Right click on the axes to start graphing.

6.17.2.1 Using The Stat Tool 6.17.2.1.1 The Three Views

The stat tool provides three views of your data. The data view, statistics view and the graph view.

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6.17.2.1.2 The Data View

The data view is the main area in the stat tool and it contains most of the less obvious features. A good look at this section will pay large dividends in the use of the stat tool. 6.17.2.1.2.1 Think in Columns!

The stat tool "thinks" in columns and you need to keep this in mind when using it.

· Graphs show the information in whole columns. · Statistics are calculated on whole columns. · Formulas operate on the whole column at once. It is perhaps the last point that is most different to a spreadsheet. For example, moving into column B and typing = Rank(A)

will place the rank of each datum in column A into column B. It works on the whole column at once. In a traditional spreadsheet you would need to copy this formula into each cell in the column. 6.17.2.1.2.2 Formulas Work Once!

Formulas in the stat tool only work once. Move into a column, type your formula and that column is updated. Your column will NOT continue to be updated automatically as new data is entered. If you want your column to automatically update, you need to use a formula column. 6.17.2.1.2.3 Column Types

the stat tool s five different types of columns:

Data Columns

Data columns are used to enter raw data and are indicated with an "x" under the title.

Frequency Columns

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Frequency columns are used in conjunction with group columns and data columns to indicate frequencies of data. In the example, column B holds frequencies that relate to the data in column A. Frequency columns are indicated with a "f" under the title.

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Group Columns

Group columns hold the bounds for grouped data. They need to be associated with a frequency column to hold data. Group columns are indicated with "10-20" under the title.

Label Columns

Label columns hold text that will be used as labels for some graph types. Label columns are indicated with "ABC" under the title.

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Formula Columns

Formula columns operate a little like a traditional spreadsheet. Formula columns are automatically updated when the source data is changed. In the example, column B is a formula column that is operating the formula "= 2A". Whenever data in column A is changed, column B is automatically updated. Formula columns are indicated with "=" under the title. 6.17.2.1.2.4 Column Type Detection

The stat tool automatically detects most column types. As you enter text or groups in a column, the stat tool will quickly detect what you are doing and will change the column type to suit your entries. Any column type that has been automatically detected will be shown in grey.

In this example, all of these columns have been automatically identified by the stat tool and the column types are shown in grey.

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Sometimes, the stat tool will not be able to automatically detect a column's type. In these cases, you will need to explicitly set a column's type. Column types that you have explicitly set are shown in black.

In the example, there is no automatic way of knowing whether column B should be treated as a frequency column, attached to column A, or as a new data column. In this case I have explicitly changed the column's type to frequency. the stat tool shows this by rendering the "f" in black. 6.17.2.1.2.5 Changing Column Types

If the stat tool has not automatically identified your column correctly, you can explicitly change a column's type in two ways.

Click on the Column Type Cell

As you click on this cell, it will cycle through all the available column types. The frequency column type is not always available.

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Right Click Anywhere in the Column Column types (auto, data, label, group, frequency and formula) can be set using the data view's right-click menu.

Frequency Columns The frequency column type will only be available if the column is to the immediate right of a data or group column (or another frequency column). Frequency columns always "belong" to a group or data column to their left. If this is not possible, the frequency column option will not appear. 6.17.2.1.2.6 Data Columns

Data columns contain most data in the stat tool. They have no special features associated with them. If a data column has a frequency column to the immediate right of it, the frequency column contains the frequencies for each data item in the data column.

Column A is a normal data column. Column D is a data column with an attached frequency column. the stat tool will graph and find statistics for column D using all 19 data points.

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6.17.2.1.2.7 Label Columns

Label columns can contain alphanumeric data that will be used as labels for bar and column graphs, pie graphs and (optionally) line graphs. Normally you would only have one label column in a data set and, once a column is set to the label type, the label column is automatically used by the graph view.

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6.17.2.1.2.8 Using Frequency Columns

Frequency columns are used to indicate frequency information for both data and group columns. They allow you to enter frequency tables and grouped data.

The stat tool correctly identifies the first set of data as having 50 elements and the second set 200. Statistics and graphs are generated utilising the frequency information. Group and data columns can have multiple frequency columns attached to them each frequency column using the same groups/data.

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You can enter your data directly into frequency tables or grouped data tables. Alternatively, frequency columns can be automatically generated from raw data when you use the FreqTable, CumFreqTable, Group, GroupW and GroupE functions in the data view. 6.17.2.1.2.9 Entering Grouped Data

Grouped data is entered into a grouped data frequency table. The Group column contains the bounds of the groups and the attached frequency column(s) contain the number of data points in each group.

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What do the Group Entries Mean? The bounds of the groups are entered as two numbers separated by a hyphen; lower bound – higher bound. For example: 20 – 30 30 – 40

for data points where for data points where

20 £ x < 30 30 £ x < 40

It is important to note that a value of 30 should go into the second group. The stat tool gives you the power to automatically group data using the Group, GroupN, GroupE and GroupW functions.

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6.17.2.1.2.10 Entering Formulas

To enter a formula for a column: Move your cursor to somewhere in the column and type =. A formula entry box will pop up and allow you to enter your formula.

The stat tool has FX Equation technology built in so you can see your formulas formatted as you type. Click on OK and your column’s data will be updated - ONCE. This once-off behaviour is significantly different to the behaviour of a spreadsheet. The Formula Column check box allows you to convert the column into a formula column that automatically updates its data when you modify its source data. 6.17.2.1.2.11 Formula Columns

Formula columns contain any valid formula. The main difference is that the contents of the column are constantly updated as data in other columns changes. They behave more like a traditional spreadsheet. It is important to note that formula columns slow down the stat tool. When you change a data point, the stat tool already has to recalculate the statistics view and construct a new graph in the graph view. Adding formula columns can seriously degrade the program’s performance, particularly on slower machines.

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6.17.2.1.2.12 Column Titles

Column titles are used in some graphs and statistics. By default, the first column title is A, the second B and so on. If you wish to enter a new title for the column, right click on the column. The right-click menu will pop up.

Select the title option and enter your new title. If you right-click ON the title cell (the A at the top of the column) you will not see this right-click menu, you will just jump straight to the column title box. Even if you have given a column a title, you must still use the column’s letter in any formulas. 6.17.2.1.2.13 Fill Down

You can automatically create a lot of data by using the stat tool’s fill down.

Hover the mouse over the small square at the bottom right of the selected cells. The cursor will change to show that fill down is available.

Click and hold the left mouse button as you move down the column. the stat tool will create new cells that logically follow from the original selection.

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The fill down feature looks at the current selection and tries to intelligently continue your pattern.

6.17.2.1.2.14 Masking Data

The stat tool can mask data in columns. When data is masked, it will not be graphed and will not be part of statistics. You can mask data in the Data View by selecting it and pushing the Mask button (or typing Ctrl+M).

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Masked data is greyed out in the data view.

6.17.2.1.2.15 Highlighting Data

The stat tool can highlight data in columns. You can highlight data in the Data View by selecting it and pushing the Highlight button (or typing Ctrl+B).

Highlighted data is green in the data view.

In most (but not all) cases, the highlighted data will also be highlighted on the graph. Each graph type has its own way of showing highlighted data.

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6.17.2.1.2.16 Re Run Formulas

The re-run button allows you to re-run the last formula in the currently selected column. As the data generators are based on formulas, the re-run button can also re-run data generators.

There are two ways of using the button. · Re-run the formula in a new column. This allows you to quickly construct a number of data sets.

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Re-run the formula in the same column. This allows you to rapidly simulate a large number of trials.

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6.17.2.1.2.17 Quick Graph

If you right-click on a column, you can quickly add the column to your graph view.

Quick graph adds the column to the first available graph slot.

The Quick Graph option will only appear in the right-click menu if the column you click in is able to be graphed. Label and Group columns cannot be graphed. 6.17.2.1.2.18 Quick Group

If you right-click on a data column, you can quickly group the data using the stat tool's default settings.

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the stat tool will place the grouped data in the first available columns.

Quick group is only available for data columns.

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6.17.2.1.2.19 Quick Sort

Right-clicking on a data column allows you to quickly sort ALL of the columns (with the exception of grouped data) in the table using your source column as a key.

Notice that column A has been sorted into ascending order and the data in column B has been sorted with column A to maintain any horizontal relationships.

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6.17.2.1.2.20 Quick Statistics

Columns are automatically added to the statistics view when they are graphed. This relationship is shown by color coding and allows you to quickly relate data, statistics and graphs.

Sometimes you will want to obtain statistics for data that is not being graphed. You can do this by using Quick Statistics. Right-clicking on Quick Statistics will add the selected column to the statistics view without it being graphed. The statistics information will be color-coded in grey to indicate that the data has not been graphed.

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Right click on the column a second time to remove the column from the statistics view.

6.17.2.1.2.21 Statistics Specific Functions

The stat tool contains many statistics specific functions that can be used in your data analysis and creation tasks. Full details on the meaning, use and syntax of these commands are available in the function reference section.

Normal Distribution Normal( ) NormPDF( )

NormP( ) ZScore( )

NormQ( ) Standardise( )

Random Number Generation Rand( ) RandBinomial( ) RandNegBinomial( )

RandBernoulli( ) RandGeometric( ) RandNormal( )

RandBetween( ) RandHyperGeometric( ) RandLogNormal( ) © 1989-2011 Efofex Software

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RandChiSquared( )

Regression and Time Series Data MPA( ) PredictX( ) ResidualX( )

Predict( ) Residual( ) Seasonalise( )

PredictY( ) ResidualY( )

SortA( ) SortColA( )

SortD( ) SortColD( )

RankD( )

RankA( )

Sorting Sort( ) SortCol( )

Ranking Rank( )

Frequency Tables FreqTable( )

CumFreqTable( )

Grouping Data Group( ) GroupW( )

GroupN( )

GroupE( )

Deciles / Stanines and Percentiles Decile( )

Stanine( )

Percentile( )

Miscellaneous Functions Inc( )

Deviation( )

Round( )

6.17.2.1.3 The Statistics View 6.17.2.1.3.1 Automatic Statistics

The stat tool automatically generates summary statistics for any data column that you have graphed. If you are graphing a two variable graph type, the stat tool will automatically generate two variable statistics. Colour coding is used to relate the three views together.

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6.17.2.1.3.2 Expanding Subsections

Each statistics column contains a large number of statistics. One variable statistics are broken into five sections. · Main - Mean, Median, Minimum, Maximum, Range, Standard Deviation, Sample standard deviation and Inter-quartile range · Other - Mode, Geometric Mean, Variance, Upper Quartile, Lower Quartile, Mean Absolute Deviation, Sum and Sum of squares · Deciles · Stanines · Percentiles Two variable statistics are also broken into sections. · Regression Information (which is dependent on the current regression model selected). · Summary Statistics for First Column · Summary Statistics for Second Column. You can expand or contract each section by clicking on the section header.

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6.17.2.1.3.3 Extra Columns

You can add extra columns to the statistics view, of data that is not currently being graphed by right-clicking on the column and selecting Quick Statistics. See the Quick Statistics page for more information. Once a column has been added, you can remove it by right-clicking on the statistics column and selecting Remove From Statistics.

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6.17.2.1.3.4 Copying Statistics to Clipboard

Statistics can be copied to the clipboard by: 1. Selecting the desired statistics in the statistics view.

2. Right-clicking and choosing Copy Selected Statistics

3. The statistics will be placed on the clipboard in a format suitable for insertion into Word Processors or Spreadsheets. A Median 50.635 Minimum 25.39 Maximum 77.11 Range 51.72 Standard Deviation 10.17727885 Sample standard deviation 10.07499204 Inter-quartile range 10.82 Choosing Copy All Statistics will copy all displayed statistics to the clipboard.

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6.17.2.1.4 The Graph View 6.17.2.1.4.1 Graph Control Buttons

The Graph Control Buttons allow you to control most aspects of the graph view.

The graph type button allows you to change the graph type the stat tool will draw. The Data Boxes allow you to graph up to six different sets of data on your graph. Each box represents a data set. As you add columns to your graph, they will fill the data boxes. The data boxes are colour coded to be the same as the data they represent.

In this example, the first data box is graphing column A and is shown in red on the graph. The second data box is graphing column B and is shown in green. If you have selected a bivariate (or trivariate) graph type, you will need to add more than one column to each data box to create a graph. In the example below, we have added two columns (A and B) to the first data box in order to create a scatter graph.

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6.17.2.1.4.2 Creating A Graph

To create a graph, we need to add columns to the data boxes. There are a number of ways of doing this.

Quick Graph Right click on the column we want to add and choose Quick Graph. The selected column will be added to the first available position in the data boxes. This is usually the quickest way to create graphs.

Right click on column

Column A added to first data box

Drag and Drop

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If you drag the title of the column and drop it in a data box, the column will be added to the data box.

Click and Drag

Drop Here

Column B Added

Data Box Button If you push a data box button, you can change the properties of the data box including which column is being graphed.

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6.17.2.1.4.3 Changing Graph Type

Press the Graph Type button.

and select from the available graph types.

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6.17.2.1.4.4 Editing Graph Properties

The Graph Properties screen (shown below) can be accessed in many ways.

The screen's left hand pane shows a list of pages of options. When you access the Graph Properties screen, you will start on one of the pages (depending on how you get to the screen) but the other pages are always available. At the moment we are looking at the options for Axes.

Set As Default This permits you to save your preferences for future use. If, for example, you prefer that the origin is never marked, change the Origin Mark option to None and press Set As Default.

Apply Applies the new settings to the graph without closing the Graph Properties screen. This lets you make quick "try it and see" modifications to your graph without committing to the change by pressing OK

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Axes properties allow you to control the lines used to construct the axes you see on screen.

x Axis / y Axis The x Axis and y Axis sections allow you to control the line type, color and thickness of the lines used.

They also allow you to turn the scale, ticks and axis off.

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If you turn off the scale and the axis, you will be left with just the ticks.

Origin Mark Provides the different options for marking the origin. Most s will set their desired option as the default.

None

Circle

x Axis

y Axis

Arrows Set the type of arrow head used and whether they are shown on the positive and negative ends of axes.

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The scale is the numbers on the axes. Scale properties lets you control the numbers and the domain and range of your axes. Most of the time, you can just leave this all up to the stat tool.

x Axis / y Axis The stat tool can automatically scale itself to suit the data you are graphing and you will not normally need to explicitly set scales. If you wish to override the stat tool's automatic scaling you need to: · Uncheck the entry you wish to change. · Enter your minimum, maximum, major or minor setting manually.

Minor and Major set the location of the tick marks on the axis. Minor ticks are smaller and have no numbers attached. Major ticks are larger and have a scale number.

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You can use multiples of pi and fractions when entering data.

You can also set both the x any y axis to be logarithmic.

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Scales

Free scales have no relationship between the x and y axes. 1 on the x axis might be much smaller than 1 on the y axis. Most statistical graphs have free scales.

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Equal Aspect scales force the x and y axes to use the same sizing. For example, 3 on the x axis and 3 on the y axis should be identical size. This is not often needed in statistical graphs but can be useful.

Fixed scales allow you to set exactly how many millimetres should be used per unit on the graph. This permits you to create a scale that is exactly sized as you need it. This option is not commonly used.

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Broken Scales The stat tool will automatically use broken scales if allowed, and the data suits.

You can also FORCE the stat tool to break scales, even if the data really does not suit. Just set the x minimum (or y minimum) to the minimum value before the break.

Even though this example does not really "deserve" a broken scale, the stat tool will break the scale for you at 20.

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If you do not allow broken scales, the stat tool will not break the scale regardless of the data or your other settings. the stat tool has a selection of five different ways of breaking the scale that can be selected from this page.

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Show Grid Allows you to turn the grid on and off.

Lines The stat tool can show a grid using lines of different styles, weights and colours. Selecting a style of None, prevents that line from showing. This allows you to create some fairly strange grids if you wish!

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Points The points option allows you to place a point at the intersection of grid lines, rather than drawing the lines. You can control the point type, size and colour.

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Polar Grids The stat tool can also display polar grids using both lines and points.

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Each graph has five main "titles" that you can change.

These titles and their fonts and colours can be changed on the Titles page.

Note that each title has an Eqn (equation) option. If you select this, whatever you type as a title will be interpreted using FX Equation technology and render as an equation

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Bar graphs only have one option - the width of the bar.

Moving this slider will change the bars from very narrow, with a large gap, up to bars which touch each other.

Plotting multiple data boxes on one set of axes will result in multiple bars per category. Bars within a category will not have a gap.

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Bar graphs will automatically use any label column you have created.

Stacked Bar Graphs are similar to Bar Graphs and share the same properties. The only difference is that when multiple data boxes are plotted, the data is stacked rather than displayed side by side.

Column graphs are very similar to Bar Graphs. Column graphs only have one option - the width of the bar.

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Moving this slider will change the bars from very narrow, with a large gap, up to bars which touch each other. Plotting multiple data boxes on one set of axes will result in multiple bars per category. Bars within a category will not have a gap. Column graphs will automatically use any label column you have created.

Stacked Column Graphs are similar to Column Graphs (and Bar Graphs) and share the same properties. The only difference is that when multiple data boxes are plotted, the data is stacked rather than displayed side by side.

The two box plot types only differ in their orientation. All other options are equivalent.

You can choose whether to show outliers on the box plot. You can also choose whether or not to differentiate between extreme outliers and mild outliers. the stat tool uses the following definitions for outliers. Outlier Extreme Outlier

>1.5 Interquartile Ranges from the Median > 3 Interquartile Ranges from the Median

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You can also add an "informal" confidence interval bar to a box plot. This is a recent addition to the New Zealand curriculum. The confidence interval bar is drawn between IQR Median –

n

IQR and

Median +

n

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Cumulative frequency graphs have two main options - how the frequencies are shown and whether to show the dots.

Show Frequencies As The cumulative frequency graph can show frequencies as absolute, relative or as percentages. For example, if we have 20 data points ranging from 5 to 15, the graph could look like:

Absolute

Percentage

Relative

The only difference between the graphs is how the y axis is displayed. Percentage frequencies and relative frequencies are most useful when comparing data sets which have different numbers of scores.

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Show Dots You can choose to show a dot for each data point or to just show the line. Show dots is usually only useful for small number of data points. If you use transparent shading for your data points, the colour of the shading of the dots indicates how many data points had that value.

In the example, the point on the left was shaded twice (for two data points) and the point on the right has only been shaded once.

The Dot Plot graph type has no specific properties. The main property that you might want to change, the dot type, is controlled by the Data Box property page.

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Frequency polygons do a similar job to histograms and share many of the same options.

Standard frequency polygons (as opposed to stacked frequency polygons) show multiple data sets as overlayed polygons. Using the stat tool's transparency feature allows you to compare data sets.

Default Group Width This option only has an effect when you are graphing ungrouped data. If your data is already grouped, the stat tool will honour the groups you have set up. If the Default Group Width is set to Auto, the stat tool will automatically decide how wide the groups should be when grouping your raw data. the stat tool will usually get it "right" but you can override the group width to produce the results you are after. If you click on the Default Group Width, the stat tool will offer you a selection of standard group widths.

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You are NOT limited to just these group widths. If you want to have a group width of 16.2, just type the value into the Default Group Width box and the stat tool will use your width to group the raw data.

Group width = 5

Group width = 10

These two graphs show the same data graphed with two different group widths.

Show Frequencies As The frequency polygon graph type can show frequencies as absolute, relative, percentages or as frequency densities. For example, if we have 20 data points ranging from 5 to 15, the graph could look like:

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Relative

The only difference between the graphs is how the y axis is displayed. Percentage frequencies and relative frequencies are most useful when comparing data sets which have different numbers of scores.

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Frequency Densities Frequency densities adjust the height of points on the polygon to allow for different widths in the groups. For example, if group A is twice as wide as group B but has the same number of data points, then the height of group A should be half that of group B. When using frequency densities, the stat tool will calculate the height of the data point as height =

frequency width

Polygon to Axis Most frequency polygons are "attached" to the x axis by drawing a line from the first data point down to the x axis. Some schools of thought believe that this is inappropriate and only actual data should be drawn - which disconnects the polygon from the x axis.

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Stacked frequency polygons share almost all of normal Frequency Polygon's properties.

The Polygon to x-Axis option is not present because it does not make sense for Stacked Frequency Polygons. Stacked frequency polygons only differ from normal frequency polygons in how they handle multiple data sets. Normal frequency polygons overlay the polygons. Stacked frequency polygons stack the individual data sets on top of each other. Exactly the same data is present.

Normal

Stacked

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Histograms do a similar job to frequency polygons and share many of the same options.

Standard histograms (as opposed to stacked histograms) show multiple data sets as overlays. Using the stat tool's transparency feature allows you to compare data sets.

Default Group Width This option only has an effect when you are graphing ungrouped data. If your data is already grouped, the stat tool will honour the groups you have set up. If the Default Group Width is set to Auto, the stat tool will automatically decide how wide the groups should be when grouping your raw data. the stat tool will usually get it "right" but you can override the group width to produce the results you are after. If you click on the Default Group Width, the stat tool will offer you a selection of standard group widths.

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You are NOT limited to just these group widths. If you want to have a group width of 16.2, just type the value into the Default Group Width box and the stat tool will use your width to group the raw data.

Group width = 5

Group width = 10

These two graphs show the same data graphed with two different group widths.

Show Frequencies As The histogram graph type can show frequencies as absolute, relative, percentages or as frequency densities. For example, if we have 20 data points ranging from 5 to 15, the graph could look like:

Absolute

Percentage

Relative

The only difference between the graphs is how the y axis is displayed. Percentage frequencies and relative frequencies are most useful when comparing data sets which have different numbers of scores.

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Frequency densities adjust the height of points on the histogram to allow for different widths in the groups. For example, if group A is twice as wide as group B but has the same number of data points, then the height of group A should be half that of group B. When using frequency densities, the stat tool will calculate the height of the data point as height =

frequency width

Stacked frequency polygons share all of normal Histogram's properties.

The Polygon to x-Axis option is not present because it does not make sense for Stacked Frequency Polygons. Stacked frequency polygons only differ from normal frequency polygons in how they handle multiple data sets. Normal frequency polygons overlay the polygons. Stacked frequency polygons stack the individual data sets on top of each other. Exactly the same data is present.

Normal

Stacked

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Cumulative histograms are identical to normal histograms, they just graph cumulative frequencies rather than frequencies. All options are identical to those of histograms.

Stacked cumulative histograms are identical to stacked histograms, they just graph cumulative frequencies rather than frequencies. All options are identical to those of stacked histograms.

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The Back-to-Back Histogram can only graph two data sets.

The Back-to-Back Histogram shares all of its options with Histograms.

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The stat tool's line graphs are very powerful and, therefore, have lots of properties available.

Normal Line Graphing When graphing lines, the stat tool graphs the row number on the x axis and the data on the y axis.

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Notice that in the example, there is no data point for x = 1. This behaviour is intuitive but it is necessary to understand it in order to make sense of some of the other options that the stat tool provides.

Fill Gaps in Data If you give the stat tool the following data to graph, the stat tool needs to know what to do with the gap in the data.

Basically, the stat tool has two options, either it can break the data into two separate bits or it can up the data.

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The Fill Gaps in Data option controls this behaviour. If you allow it to fill gaps in the data, the stat tool will also fill gaps in the smoothed version of the data. In this case, this allows the smoothed version to be drawn.

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Show Lines

This option allows you to turn off the lines if you wish, making the line graph more like a scattergraph.

Show Data Points The stat tool normally marks each data point with a dot. This option allows you to just draw the lines.

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Use Labels for x Axis If this option is turned on, the stat tool will automatically use any labels you have entered in your data.

Smoothing Type All of the example graphs above have had a dotted line added. This line is a smoothed version of the data. You can control what type of smoothing is used here. the stat tool can automatically add moving point average lines, (de) seasonalized data or a regression line. Alternatively you can turn the smoothed line off.

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Seasonalized Regression Line

The moving point average line cycle length is entered in this section and the moving point averages are automatically centred for even length cycles. The seasonalised data is dependent on settings in other sections of the stat tool. The regression line can be one of seven as discussed below.

Regression Model The stat tool can calculate and use seven different regression models to fit data. The model used for the line graph is controlled here. the stat tool shows you a formatted version of the model's equation as you change the model.

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The stat tool can only draw one Pie Graph at a time so the number of data boxes is reduced to one when drawing a pie graph.

Display Type Pie graphs can be drawn with multiple colors or using a gradient based on the data box color.

Multiple Colors

Color Gradient

These examples show how Pie Graphs show highlighted data by exploding the sector out of the pie. Color Gradient colors are automatically generated from the current data box color and the has no control over the colors used (after picking the data box color). Multiple Colors pie graphs give the total control over the colors used in each segment. Right-clicking on a segment opens a segment color screen.

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Labels Pie graphs automatically use any labels you have entered into your data.

The labels options allow you to add the raw data or the percentages to these labels. If there are no labels, the stat tool will just list the data or percentage.

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No Labels - Just Use Percentages

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You can also turn off angled text

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A residual graph removes the regression component from two variable data and just shows the deviation from the regression line. In the example below, you can see the original scattergraph and its corresponding residuals graph.

Scattergraph

Residuals Graph

The only option for Residuals Graphs allows you to choose which of the seven regression models it uses to calculate the residuals.

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The scattergraph allows you to display and analyse bivariate data.

Show Line Allows you to turn off the regression line - shown as a solid line.

Show Residuals Allows you to turn off the residuals lines - shown as dotted lines.

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Show Line and Show Residuals OFF

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Dots If you turn this option on, the stat tool will the dots in the same order as they are listed in the table. This usually just produces a "bird's nest" - especially if the data is unsorted.

Unsorted Data

Sorted by x Values

You can use this feature, providing you enter the points in a logical order, to construct just about any diagram you wish.

Regression Model The regression model allows you to select which of the seven regression models the stat tool uses to calculate the regression line and residuals.

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The Stem & Leaf plotting tool can graph up to two data boxes. There are some differences in the way the Stem & Leaf tool plots when compared to the other tools: 1.

2.

The tool does NOT resize the plot to suit the display rectangle. All other tools automatically fit the graph into the rectangle. Because the Stem & Leaf plot’s size is determined by the font used, this is not possible. The Stem & Leaf tool can only plot information whose range is less than (about) 300. This means that some data sets will not be plotted in any reasonable form. This is an inherent limitation of Stem & Leaf plots rather than our tool.

Sort Data on Branches This option sorts the data on the branches in ascending order (lowest closest to stem). The left and right branches can be sorted independently.

Sorted Data

Unsorted Data

Sorting on double sided stem & leaf plots always places the lowest values closest to the stem.

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Round Data The stem & leaf plot tool automatically allocates continuous data to the correct branches. For example, 52.345 would have automatically be allocated as a 2 in the 5 branch in both of the stem and leaf plots below.

Data not Rounded

Data Rounded

The round data option determines what the tool does with a data value like 70.68. If round data is turned off, this will be truncated to 70 and be entered as a 0 on the 7 branch. If round data is turned on, this is rounded to 71 and will be entered as a 1 on the 7 branch.

Max Number of Stems This determines the maximum number of stems that the tool uses to create the stem & leaf plot. 15 is a good default.

Allow Split Stems Graphing data with a small range on a stem & leaf plot can create a plot with a small number of long branches.

In these cases, it is often a good idea to split the stems into a high and low branches. This increases the number of stems and can give a better impression of the shape of the data.

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Reverse Stem Order Simply reverses the order of the stems.

Add Spaces Adds extra space to the leaves to spread out the data.

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Triangular graphs show the proportional relationship between three numbers.

This means that Triangular graphs are the only graph type that require three columns to be selected as data columns.

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Grid Lines Allow you to control the size, type and color of the grid lines used in the triangular graph.

Axes Descriptions Allows you to enter your own descriptions for the three axes.

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The data box properties allow you to control the basic properties of most graph types - how to draw the lines and points; which columns the data box holds; how to fill and how to highlight. It also permits you to combine graph types on one set of axes.

Data Columns Data columns allow you to select which columns this data box is graphing. You can select columns from the drop down list or use the other approaches listed in Creating A Graph.

Line Allows you to select the style, thickness and color of any lines used to graph this data set.

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Brush Allows you to select the style, color and opacity of any brushes used to graph this data set. Setting the brush to auto lets the stat tool automatically choose the color of your brush but you can still choose the brushes style and opacity. Opacity controls how "solid" the color is and how much of the background color is permitted to be seen through the shading. Setting the opacity to zero makes the brush completely transparent. In the example we have drawn the green frequency polygon with three different opacities ranging from almost zero to completely opaque.

Low Opacity

Medium Opacity

High Opacity

Point The point controls allow you to control how any points are shown in the graphs. You can select the point type and size.

Highlight The stat tool will highlight any cell that is selected or has been manually highlighted. This section allows you to control how any highlighting is shown. You can select the line color used, the brush color used (or allow the stat tool to automatically choose the brush color) and the size of any highlighted points. Not all graph types use color to highlight data. The Pie graph highlights data by exploding the sector of the pie graph from the other sectors.

Hide Graph

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Hide Graph allows you to hide an otherwise fully formatted graph. It can be used to quickly hide and expose graphs for demonstration purposes.

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Graph Type Button The graph type button is used to combine graph types on one set of axes. This is discussed in more detail in Combining Graph Types. y

10 8 6 4 2 x 20

40

60

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6.17.2.1.4.5 Selecting Data On Graph

Most graph types allow you to select data on the graph and have the data selected in the data grid.

Click

Highlighted

Selected

You can select a number of data points by sweeping out a rectangle with your mouse.

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Selected

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6.17.2.1.4.6 Modifying Data On Graph

If you can select data on your graph, you can most probably modify it as well. If you move the mouse while data is selected, the data point will be modified on the graph and in the data grid.

The graph and statistics will interactively update themselves to accommodate the new data. In this example, you should be able to see that the regression line has bee recalculated. Different graph types allow different ranges of movement. For example, in horizontal box and whisker plots you will only be able to move the data point in the horizontal axis.

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6.17.2.1.4.7 Combining Graph Types

Many s will want to combine graph types on the same set of axes.

Frequency Polygon and Histogram

Histogram and Box Plot and Cumulative Histogram

Frequency Polygon

In all three examples, we have shown the same data in two different ways. Before we look at how to achieve this, it is important to that not all graph types can be combined. More about this later.

Add Your Data Column to Two Data Boxes Firstly, we add the data column to two data boxes using the standard commands. Your graph might look like this.

We have graphed column A in two boxes and the graph is two overlayed histograms. Not too useful yet!

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Push the Second Data Box Button Push the second data box button (the green one in this case) and the following screen will appear.

The graph type button is active which means that we can change the graph type for just this data box. For some types, this button will be greyed out which prevents you from overlaying another graph type.

Greyed Out - No Combining Available

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Push the Graph Type Button Push the graph type button and a list of available graph types will appear. Not all graph types will be available because not all graph types can be combined.

Change the Graph Type Change the graph type to your desired graph type. In this example, we will choose the frequency polygon. You may also want to decrease the opacity of the brush at this point.

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Finished!

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6.17.2.1.5 Data Generators

The stat tool provides a large number of data generators that can quickly generate data for use in your graphics. The Data Generators are accessed using the data generator toolbar.

All of these buttons load the same data generator dialog box - just starting at different pages.

6.17.2.1.5.1 Discrete

Allows you to generate random numbers between two values. If there are n integers between the highest and lowest values, the probability of each integer occurring will be 1/n.

Bernoulli trials have the possible results of 0 or 1 which is equivalent to true or false, boy or girl, head or tail. The Bernoulli data generator allows you to © 1989-2011 Efofex Software

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generate results with a given probability of success.

The binomial data generator allows you to simulate binomial trials. A example problem that this distribution might simulate is: Roll a standard die ten times and count the number of sixes. The distribution of this random number is a binomial distribution with n = 10 and p = 1/6.

The hypergeometric data generator simulates trials where items are drawn without replacement. An example problem might be: A bag contains 25 red marbles and 55 green marbles. If you draw eight marbles from the bag, how many will be red?

The geometric data generator allows you to simulate trials where you count how many attempts are required before the first success. An example question might be: How many rolls of the die does it take before you roll a 6?

The negative binomial data generator allows you to simulate trials where you count how many attempts are required before the nth success. An example question might be: How many rolls of the die does it take before you have rolled 5 sixes?

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The Poisson data generator allows you to simulate trials where you know the expected number of successes in the experiment and you wish to know the actual number of successes.

6.17.2.1.5.2 Continuous

The uniform data generator generates random numbers between 0 and 1 that are uniformly distributed. A simple transformation can be applied to the output of this generator that will produce continuous random numbers between any two values.

The Normal data generator allows you to generate data that has a given mean and standard deviation.

The exponential data generator generates data that fits this probability density function.

Where l is the rate parameter of the function.

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The log normal data generator generates log normally distributed numbers with a given mean and standard deviation.

The chi squared data generator generates chi squared distributed numbers with a given degree of freedom.

The student t data generator generates student t distributed numbers with a given degree of freedom. 6.17.2.1.5.3 Bivariate Data

The bivariate data generator allows you to quickly and easily generate bivariate data that satisfies a set of given parameters. To generate your data: · Enter the number of data points to generate. This determines the number of “dots” on the scatter graph. · Enter the low and high values for x. the stat tool will generate random x values between these two values. · Choose the regression equation © 1989-2011 Efofex Software

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· Enter the parameters for the equation (a, b and c). The c parameter is only used for quadratic regression equations. · Enter the absolute value of the target correlation coefficient. the stat tool cannot calculation correlation coefficients for quadratic regression equations but it will still take the target correlation coefficient into while generating data. If you want to generate linear regression data with a negative correlation coefficient, make b negative. · Enter the columns that the x and y data will be put into. Please note: · The generator will not produce data to exactly match your parameters but the match will be close. If the match is not good enough, you can always try again. · The “a” parameter is the least likely to be matched in all regression models. 6.17.2.1.5.4 Time Series Data

The Time Series Data Generator allows you to quickly and easily generate time series data for use in questions and examples. The time series data generator opens the above dialog box. To generate your data: · · · · ·

· ·

Enter the number of data points to generate. Choose the regression equation Enter the parameters for the equation (a, b and c). The c parameter is only used for quadratic regression equations. Enter the cycle length required. Set the noise (random) component slider. If the slider is fully to the left, there will be no random component to the data. Fully to the right and the pattern may not be recognisable. Set the volatility (cyclic) component slider. This determines how “dramatic” the cycle is. Enter the column that the data will be put into.

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6.17.2.1.5.5 Dice

The dice data generator will simulate the rolling of up to six dice. Select how many sides each dice has and push OK. The above example will roll two sixsided dice and add them.

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6.17.2.1.6 Customizing FX Stat 6.17.2.1.6.1 Setting Defaults

the stat tool comes pre-configured with a large number of default settings - but almost certainly you will want it to some things differently. Most options screens have a "Set As Default" button. Pushing this button forces the stat tool to save the current settings and use them as a default for future graphs. To set a default. 1. 2.

Create a graph that has been changed to suit your preferences. Push the Set As Default button.

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6.17.2.1.6.2 System Options

Statistics, particularly secondary school statistics, is particularly localised. The “right” way of doing something in one location is often very different to the “right” way of doing it in another location. The system options allow you to customise you version of the stat tool to suit you local conditions. System options can be accessed through the Edit menu. With all the system options it is vital that you TRY each setting and pick the one that suits your situation. Unfortunately there are no standard names for different methods of calculation.

Calculating Quartiles Efofex has found three common methods of calculating quartiles. 1, 3, 3, 4, 5, 6, 6, 8, 9, 10, 10, 11, 13, 14, 16, 18, 20 In the above example, 9 is the median. The lower quartile is the median of the bottom half of the scores BUT does the lower half include the 9 or exclude it? Depending on your answer, the lower quartile would be 4.5 or 5. This gives us two of the three options for calculating quartiles. The third is to use the 75th and 25th percentiles. The results of this option depends on how you calculate percentiles.

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Seasonalised Data Method One is to calculate the average residual between a point in the cycle and the moving point average at that point. This average residual is then removed from the data to obtain the seasonalised figure. Method Two is to calculate the average deviation between a point in the cycle and the mean of the data set. This average deviation is then removed from the data to obtain the seasonalised figure.

Calculating Percentiles The interpolated method of calculating percentiles is the same as the method in Excel . If the data point 13 indicates the 20th percentile and data point 14 is the 30th percentile, the 21st percentile is 13.1, the 22nd is 13.2, the 23rd 13.3 and so on. The interpolated method interpolates values for the percentiles that are not in the original data. The discrete method of calculating percentiles would produce 13 as the value of the percentile for the 20th up to the 29th percentile. Each percentile is guaranteed to be a number in the data set.

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6.17.3 Normal Distribution Curve

The Normal Distribution Curve tool allows you to draw shaded or unshaded normal distribution curves. If you select the Normal Distribution Curve tool and draw the curve, this will be displayed.

This is a normal distribution curve that has been shaded between z = -1 and z = 1. When selected, the normal distribution curve will have two sliders. The top slider controls the lower bound of the shading and the bottom slider controls the upper bound.

If you wish to produce a diagram where one tail is shaded, merely decrease the lower bound (or increase the upper bound) as far as possible. This will produce the desired result. You will also notice that the shading has changed. This can be achieved using the fill palette. To achieve other shading effects or to set the upper and lower bounds exactly, you will need to right click to edit the properties.

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Here you can set the mean, standard deviation and population for the distribution. Note that a population of 1 will produce standard z scores. You can also change the shading style (which allows two tailed shading) and change the pen and shading used. Finally you can explicitly set the high and low bounds for shading. In FX Draw 3, the high and low bounds were standard deviations. In FX Draw 4, they are absolute values. This is to allow shading where the mean is not zero and the population is not 1. Notice that the left hand side of the screen allows you change the axes, scales and grid used to graph the normal distribution curve. You can also show two other normal distributions - but you need to ensure that you check Show Curve.

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The normal distribution curve tool is not the only way of drawing a normal distribution curve. You can also graph a normal distribution curve by entering y = normal(x) into the function grapher. This allows you to produce much more complicated diagrams. Available Parameters for Normal Distribution Curves $below $between $above $low $high

- area (probability) below lower bound - area (probability) between upper and lower bounds - area (probability) above upper bound - lower bound - upper bound

6.17.4 Two Circle Venn

The Two Circle Venn Diagram tool allows you to draw shaded and annotated two circle Venn diagrams. After you have drawn the initial diagram, the properties of a two circle Venn diagram may be accessed by right clicking.

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In this dialog box, you can choose to add totals to different areas on the Venn diagram. Any total left blank will not be shown (see 3 circle Venn diagrams). You can also shade any of the four regions in a 2 circle Venn diagram. Finally you have access to the font used to annotate the diagram. The diagram below is the result of using the properties shown.

The shading is controlled using the fill palette. 6.17.5 Three Circle Venn

The Three Circle Venn Diagram tool allows you to draw shaded and annotated three circle Venn diagrams. The operation of the three circle Venn diagrams is exactly the same as two circle diagrams. The only difference is that there are more properties to edit.

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Notice that only those totals entered as properties are included in the diagram. 6.17.6 Number Line

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To draw a number line, you sweep out a rectangle. If the rectangle is wider than it is tall, FX Draw will create a horizontal number line. If it is taller than it is wide, FX Draw will create a vertical number line. When you have created the rectangle, FX Draw will create a blank number line. To add a graph, right click on the number line.

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This dialog box allows you to set up the axis in exactly the same way as the function graphing tool. You enter the graphs in of x and you can enter the following combinations (using –3 as the number – you obviously can use any number). x > -3 x >= -3 x < -3 x <= -3 x = -3 x <> -3

x greater than negative three x greater than or equal to negative three x less than negative three x less than or equal to negative three x equals negative three x is not equal to negative three.

You can also place x in a range. -3 < x <= 2

x is greater than negative three and less than or equal to two.

The Offset Lines option allows you to produce output such as this.

Available Parameters in Number Line $f1 $f2

- definition of function 1 - definition of function 2

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- definition of function 3

6.17.7 Grids / Dots

The grids & dots tool gives you access to nine different types of grids & dots. Start by sweeping out a rectangular area. FX Draw will fill the area with the current default grid type. Right click to access this tools options.

Select the options you are after and push OK. The grid you produce is "Geometrically Active". FX Draw will preferentially jump to points on the grids/dots you have defined. This makes drawing most grid based diagrams easy. 6.17.8 Unit Circle

The unit circle tool lets you draw unit circles showing the sine, cosine, tangent and cotangent ratios.

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Drawing a unit circle is identical to drawing a centre/radius circle. Unit circle properties allow you to turn each ratio on or off - as well as defining how each ratio line is shown.

You can change the angle by moving the control points at each end of the angle.

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Keyboard Commands For demonstration purpose, the unit circle's angle can be controlled using the keyboard. Home Up Arrow Down Arrow Page Up Page Down

Resets the angle to 0°. Increases angle by 1°. Decreases angle by 1°. Increase angle by 5°. Decreases angle by 5°.

Available Parameters for Unit Circles $degrees $radians $sin $cos $tan $cot

6.17.9 Tree Diagrams

The tree diagram tool constructs a tree diagram out of line segments that you can ungroup and modify. Sketch out a rectangle for the tree diagram to go into. FX Draw will then show this dialog box.

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You define your tree by typing in a string of numbers, eg 3,2,4. This would produce a tree diagram with three branches, each of which breaks into two branches, each of which breaks into four branches.

The only limits imposed on your tree are that a level must have no more than 30 branches. Just that the number of branches increases quickly and it is very easy to create an extremely complex tree. The Space slider controls how much blank space there is between the levels. This space is not blank - it is actually a white line. If we draw a tree over a grey rectangle you can see this clearly.

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After a tree diagram is drawn, it should be ungrouped so that the lines can be accessed individually. If you right click on a tree, FX Draw will offer to ungroup for you.

Now that your tree diagram is ungrouped, you can right click on each line and modify it. One of the main reasons why you would do this is to add text to a line. You can also "prune" your tree by deleting some of the lines.

The tree diagram tool can also add probabilities to each branch and cumulative probabilities to each vertex. It does this by adding text to the middle of the lines it creates. Adding text to a large tree can slow down the rendering of that tree © 1989-2011 Efofex Software

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dramatically - especially if the text is formatted as equations. 6.17.10 Clocks

The clock tool allows you to draw a wide variety of customizable clocks and clock faces. Drawing with the clock tool is like drawing circles.

Right click on the clock to change the clock properties or change the time.

Most settings are self explanatory. Note that you can turn off Show Hands which will produce a clock face that can be used to get students to show a time. The sliders circled in red set the start and stop position of marks on the clock face. Using these you (as well as turning of some marks and moving the numbers location, allows you to produce just about any clock face you need.

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Entering Times You can enter your own time into the tool. FX Draw is fairly flexible when it comes to interpreting times. All of these times will display correctly. 545

6.18

12:10

5:14.20

18,12.45

The Galleries

The gallery tool gives you access to the hundreds of pre-drawn images available in FX Draw. The left button lets you select an image, the right button lets you draw the currently selected gallery image. When you first start FX Draw the right hand button will be greyed out because no image is currently selected. In order to use the gallery tool you must first select the image you wish it to draw. To do this you need to push the left gallery button.

6.18.1 Selecting a Gallery Image

When you push the right button to select an image, you will see something like this screen.

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All you do is select the image you wish to draw and the gallery tool will draw that image every time you select it. The galleries you have on your computer will depend on which galleries you have installed and any others you have created. Efofex will create a library of galleries on our web site that you can use to expand your collection. We will be asking for contributors to the library. The gallery maintenance buttons allow you to create new galleries and maintain existing ones. You can change the title of a gallery, move figures up and down in the gallery (changing the order) and delete figures. This allows you to construct your own galleries. The gallery and image descriptions provide you with more information about the gallery images. The top pane shows a general description of the whole gallery of images. The bottom pane displays a description of the currently selected image. You can edit the descriptions by pushing the Edit buttons under each pane. While the author of the gallery will have added any descriptions that they feel would assist you, you can add your own notes to any image or gallery.

6.18.2 Drawing a Gallery Image

Once you have selected an image, the right button allows you to draw it. The right button will draw your selected image UNTIL you select a new image or restart FX Draw. When drawing using a gallery figure, the drawing is stretched to fit the rectangle you have drawn. This allows you to obtain differently proportioned shapes. The gallery figures also depend on the direction you drawn them in. All the diagrams below have been drawn with the one gallery figure. The direction that they have © 1989-2011 Efofex Software

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been drawn has been indicated on each shape.

This ability to be resized makes each gallery figure extremely powerful. Gallery images the aspect ratio (ratio of height to width) that they were originally drawn in. In many situations you will need the image to stay fixed to that aspect ratio ESPECIALLY if the image contains circles. By holding down the SHIFT key while initially creating the image, the image will be forced to maintain this aspect ratio. 6.18.3 Saving to Galleries If you have created an image that you believe should be part of a gallery, select the image and choose Save To Gallery from the File menu (or push Ctrl + T).

The selected objects will be placed into the gallery you select from the list of available galleries.

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6.18.4 Other Gallery Issues FX Draw always searches for galleries in a Galleries subdirectory of its own directory and this is where gallery images are placed by default when you first install FX Draw. If you wish to have your galleries stored in a different location, you need to tell FX Draw the new location. Go to the Tools / Preferences / General menu option and enter the new location.

7

Tools and Preferences FX Draw preferences allow you to customise FX Draw to for local differences in mathematics. All preferences are set from the Tools menu.

7.1

Grid

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Grid preferences control the background grid - the light grid behind your diagrams. Grids can make drawing many images much simpler. The grid size can be set using any measurement. You can type 1cm, 0.25" or 50pt. Ticking isometric creates an isometric grid that makes drawing isometric diagrams much simpler. Show grid turns the background dots on and off. If you are having trouble seeing the background grid (on an interactive whiteboard for instance) increase the opacity so that it becomes more obvious.

7.2

Preferences The preferences screen lets you change FX Draw to suit your needs. Select the page on the left hand side and modify the options on the right.

7.2.1

Graph Enter topic text here.

7.2.1.1

Axes

The Graph Axes screen lets you modify the axes style for function graphs. Statistics graphs can have separate settings.

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7.2.1.1.1 Background Rectangle

Graphs can have a shaded background rectangle. Check the Fill Background option and select your colour. 7.2.1.1.2 Sizes

All sizes are in mm and control different aspects of the axes

7.2.1.1.3 Tick Style

This preference controls how the ticks are drawn on the axes. The various options are best shown in a diagram.

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7.2.1.1.4 Blank Under Scale

When you add a grid to a set of axes, the lines of the grid can interfere with the scale. FX Graph will blank out an area of the grid before it writes the numbers of the scale and this prevents the grid making the scale hard to read. The blank under scale setting lets you turn off this feature. The two graphs below show you the result. The first graph has Blank Under Scale off, the second graph has it on.

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7.2.1.1.5 Add Space for Arrows

You can turn arrow heads on and off on FX Graph axes but, either way, space will be allocated for them. If you want the scale to go all the way to the edge, turn off this option.

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Allow Space for Arrows OFF

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7.2.1.1.6 Expand Grid to Edge

Allows you to select between two different types of grids.

Expand Grid to Edges OFF

7.2.1.2

Expand Grid to Edges ON

Preferences

7.2.1.2.1 Shade Accept Region

When shading the feasible region for an inequality, some locations shade the region that AGREES with or accepts the inequality. y >= x

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and some schools shade the region which disagrees with or does not accept the inequality y >= x

If you tick Shade Accept region, y >= x will produce the first graph. 7.2.1.2.2 Dot Density

The graph will often shade feasible regions with an array of dots. The greater the number of dots, the more solid the shading - but the slower the calculations. A dot density of 200 (the default) will produce acceptable results on most © 1989-2011 Efofex Software

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computers but you can decrease the density on slower computers or increase it on faster computers. 7.2.1.2.3 Domain Size

Sets the size of the domain end points. The size is the radius of the circles - in millimetres.

7.2.1.2.4 Discontinuity Size

Some functions have point discontinuities (see example below). The graph tool automatically finds these point discontinuities for rational functions and displays them with a small circle. This preference controls the radius of the circle (in millimetres).

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7.2.1.2.5 Key Zoom Ratio

Pushing the Page Up and Page Down buttons will zoom the axes in the graph tool. This number determines the ratio that the scale is increased or decreased by. For example, the default Key Zoom Ratio is 1.33333. If you axes have maxima of 10 and minima of -10, pushing the Page Up button will change the maxima to 13.33333 and the minima to -13.33333.

7.2.1.2.6 Right Click on Axes

Usually, right-clicking in the the graph tool screen will start the Quick Entry screen but if you right click on an axis, the graph tool will start the Axes properties screen. Some people dislike this behaviour and find it distracting. You can turn it off here. 7.2.2

Statistics

7.2.2.1

Axes

The statistics tool axes properties are identical to the graph tool axes properties. This screen lets you set separate axes options for statistics graphs.

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Preferences

Statistics, particularly secondary school statistics, is particularly localised. The “right” way of doing something in one location is often very different to the “right” way of doing it in another location. The system options allow you to customise you version of FX Stat to suit you local conditions. System options can be accessed through the Edit menu. With all the system options it is vital that you TRY each setting and pick the one that suits your situation. Unfortunately there are no standard names for different methods of calculation.

Calculating Quartiles Efofex has found three common methods of calculating quartiles. 1, 3, 3, 4, 5, 6, 6, 8, 9, 10, 10, 11, 13, 14, 16, 18, 20 In the above example, 9 is the median. The lower quartile is the median of the bottom half of the scores BUT does the lower half include the 9 or exclude it? Depending on your answer, the lower quartile would be 4.5 or 5. This gives us two of the three options for calculating quartiles. The third is to use the 75th and 25th percentiles. The results of this option depends on how you calculate percentiles.

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Seasonalised Data Method One is to calculate the average residual between a point in the cycle and the moving point average at that point. This average residual is then removed from the data to obtain the seasonalised figure. Method Two is to calculate the average deviation between a point in the cycle and the mean of the data set. This average deviation is then removed from the data to obtain the seasonalised figure.

Calculating Percentiles The interpolated method of calculating percentiles is the same as the method in Excel . If the data point 13 indicates the 20th percentile and data point 14 is the 30th percentile, the 21st percentile is 13.1, the 22nd is 13.2, the 23rd 13.3 and so on. The interpolated method interpolates values for the percentiles that are not in the original data. The discrete method of calculating percentiles would produce 13 as the value of the percentile for the 20th up to the 29th percentile. Each percentile is guaranteed to be a number in the data set. 7.2.3

Equation

7.2.3.1

Fonts

This screen allows you to control the fonts used in equations.

7.2.3.1.1 Use Text Font

If you choose to use the text font, the equation system will use whatever font you format the equation in the text box.

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In this example, the font is set to Times New Roman 14 point and when we return, the equation will be rendered in that font. Note that the equation's variable is still italicised as per our default - it is only the font and size that are copied over from the text.

If you want to ensure that all equations have the same formatting, turn the Use Text Font option OFF and set your font and size on the font screen. All equations will be rendered using these settings regardless of how the text box is formatted. 7.2.3.1.2 Use One Font

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By default, the equation system will format all of the equation using the same font and colour (Use One Font). It will still italicise variables (for example) according to the other settings on the fonts screen. If you wish to use different fonts for functions, quoted text, units or lower case vectors, you need to turn this option OFF. This will allow you to change the other font settings.

7.2.3.1.3 Fonts and Colours

Each component of an equation can be formatted differently. You can format functions in bold, italicise variables and lots of other options - all automatically. Just set the options for each of the different parts of your equation.

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Vectors

7.2.3.2.1 Column Vectors

If you wish to enter vectors in the vertical format, they are simply entered as (3,2) using a comma as a separator. Three-dimensional vectors are entered in the same way. If you normally use a comma as a decimal point, FX Equation technology will automatically detect this and you must use a semicolon to separate components of a vertical vector. Examples:

is entered as (3,2x) or (3;2x)

is entered as (3,2,5) or (3;2;5)

is entered as r=(2,7)+la(1,-4) or r=(2;7)+la(1;-4) You must have selected the Detect Column Vectors option to allow FX Equation to detect column vectors and matrices.

7.2.3.2.2 Automatic Vectors

FX Equation technology can automatically recognize some vectors if you choose to turn the feature on. FX Equation technology can recognize some lowercase vectors and double capital vectors. This feature is activated by default and can be controlled by on the Equation / Vectors option screen.

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7.2.3.2.2.1 Lowercase Vectors

FX Equation technology will only detect lowercase vectors if automatic recognition is switched on. If you are using vectors of the form FX Equation technology can automatically recognise that you are typing a vector and make the r, i and j bold. FX Equation technology can also be set to indicate vectors using lines, tildes or arrows, depending on your preference. This automatic recognition of vectors can save you hours of time, but FX Equation may sometimes get the automatic recognition incorrect. By default, FX Equation will take its "best guess", you can also turn this feature off or alternatively, explicitly tell FX Equation which variables to recognise as vectors.

It is important to that you do not need to tell FX Equation that you are working with a vector, FX Equation will automatically identify this.

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Example: is entered as r=(3i+2j+k)+la(i-j+3k) Lowercase vectors can be display bold, with an arrow over the top or with a line or tilde underneath the vector.

7.2.3.2.2.2 Double Capitals

FX Equation technology will only detect Double Capital vectors if automatic recognition is switched on. Double capital letters are used to represent line segments, rays and vectors. FX Equation technology can automatically place an annotation over double capitals. You would use this feature if you were, for example, entering a lot of position vectors in an exam. Examples: is entered as AB = OB - OA is entered as |OA|=sr(9+16)

is entered as cos th = (AB.BC)/(|AB | |BC|) The annotation used by FX Equation can be set using the Vector Options

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318

Styles

7.2.3.3.1 Vertical Spacing

Vertical spacing is the spacing between successive lines in a multiline equation.

7.2.3.3.2 Tabs

Tabs are set to 10mm by default in FX Equation but you can change them at any time using the Style tab on the options screen.

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7.2.3.3.3 Multiplication Sign

When using FX Equation, you enter a multiplication sign using the * key. FX Equation can display your sign in one of three ways, as an ´, a raised dot ( × ) or an *.

FX Equation will display any entered multiplication sign AND the multiplication sign in scientific notation using this setting.

7.2.3.3.4 Raising The Decimal Point

Some locations prefer that the decimal point is raised. ie.

3·2

rather than

3.2

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This option will only take effect if you use a dot as a decimal point.

7.2.3.3.5 Integrals

Integrals can be drawn in two different ways - with the bounds to the right of the integral sign or with the bounds above and below.

7.2.3.3.6 Mixed Numerals

Mixed Numerals are created automatically if you have selected the Shrink Non-Algebraic Fractions option.

is entered as 3 1/2

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7.2.3.3.7 Negative Numbers

FX Equation offers you the option to display negative numbers differently to subtraction signs.

The three options produce these results.

7.2.3.3.8 Lines

FX Equation draws lines for fractions and root signs . You can set the width of the line using the General Pen setting.

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All lines will be drawn using the main font colour.

7.2.3.4

Units

FX Equation can detect units and display them using different settings. This allows you to clearly delineate things such as

All you need to do to use this feature is to tell FX Equation what to consider a unit.

These units are our suggestions. You can set the units to whatever you require and change them on an equation by equation basis. Note for Advanced s.

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Single letter, lower case units (eg s, g, h, and m) are usually best left off this list. Putting them on the list causes FX Equation to behave counter-intuitively, although totally logically. For example...

The h has been formatted using the units formatting but not the way the was expecting. 7.2.3.5

Matrix

You can adjust vertical and horizontal spacing for your matrices as well as alignment.

7.2.3.6

Shortcuts

Each shortcut is on a separate line. To edit a shortcut, just move the cursor into the shortcut and start typing. To create a new shortcut, move the cursor to the bottom of the list and start typing. Shortcuts are formatted as The code - followed by the tab key - followed by the desired output © 1989-2011 Efofex Software

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eg qf»x=(-b+-sr(b2-4ac))/2a The qf is the code The » is produced by pushing the tab key The x=(-b+-sr(b2-4ac))/2a is the desired output.

7.2.4

General Enter topic text here.

7.2.4.1

Measurement System

FX Draw can understand four different measurement systems

The default measurement system is used for any measurements entered into FX Draw. You can always enter a measurement using a system apart from the default by using the appropriate units. The default measurement system is also use for all figure reports. 7.2.4.2

Default File Location

ADVANCED This field is mostly used in network situations. FX Draw will attempt to save diagrams into this location.

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Gallery Location

ADVANCED This field is mostly used in network situations. FX Draw will search for galleries in this directory.

7.2.4.4

Control Point Size

Control points are the small green, amber, red and grey squares that let you control figures. This setting lets you change the size of the control points.

7.2.4.5

Increase Selection Area

If you are having trouble selecting objects, this option increases the size of the area you can click. 7.2.4.6

Show Bounding Rectangle

FX Draw diagrams fit onto a 300mm by 300mm canvas but most drawings only use a small part of this area. FX Draw trims down the canvas to include just the figures you have drawn and returns this smaller area to Word. Showing the bounding rectangle lets you see exactly what FX Draw will return to Word.

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Line Colours

If your screen does not display some of our standard colours clearly, or you simply cannot see some colours, you can change the colours FX Draw uses to ones that suit you better.

7.2.4.8

Bitmap Resolutions

FX Graph renders all its images as bitmaps but you have the option of chosing the resolution of the bitmap you create in three different contexts. Obviously higher resolutions produce better quality - at the cost of increased size. In most cases 300 dpi is suitable for printed materials and 72 dpi is suitable for anything viewed on screen. 7.2.4.9

Transparent PNG/GIF Files

Transparent PNG or GIF files are special bitmap files where one colour (almost always white) is nominated as transparent. This permits you to place the file over the top of another image while allowing the first image to show through. You can only produce transparent files in FX Draw using the File/Save As option.

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7.2.4.10 Screen Adjust

ADVANCED FX Draw's internal coordinate system is accurate to 1/100th of a millimetre but when Windows draws our lines on your screen, the lengths are likely to be quite inaccurate. This is because Windows does not really "know" how big your screen is - the same image displayed on a 17" and a 21" inch screen will be quite different in size. FX Draw has implemented a system which allows us to adjust our lines to suit YOUR screen. When you choose Screen Adjust, FX Draw will draw a line on your screen. Measure the line as accurately as possible and enter the length in millimetres.

Once you have completed the screen adjustment, lines that FX Draw reports as 100mm long will actually be 100mm long on your screen.

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Reset All Options This resets all options back to factory defaults. You can use this if you have managed to get FX Draw seriously out of sorts. We may also direct you to reset all options if FX Draw gets into an internally inconsistent state.

8

Hints & Tips

8.1

How Do I Select Figures? You can select figures in one of two ways. If you want to select an individual figure, click on it. You need to be reasonably accurate to ensure that you select the desired figure. If you wish to select a few figures at one time, sweep out a rectangular area while holding down the left mouse button. Any figure totally contained within the rectangle will be selected. You can then move, copy or delete the selected figures.

8.2

How Do I Change a Figure's Properties? Right click on it. For example, if you have drawn a line and want to add a new end point, right click on the line. A large dialog box will appear allowing you to change many of the line's properties. Most figures have properties that can be changed.

8.3

What Are Sliders? Some figures have sliders. These little grey circles on the top or side of a figure allow you to adjust a property of the figure by sliding the circle up and down or left and right. For example, the rounded rectangle's slider adjusts the radius of the rounded corner. All properties that can be visually adjusted using sliders can be explicitly adjusted using the figures property dialog box that is accessed by right clicking on the figure. If you see a slider, move it and see what happens!

8.4

What Is The Most Under-utilized FX Draw Feature? Changing a figure's default properties. This can make using FX Draw much easier.

8.5

How Do I Change a Figure's Default Properties? Most figures have a Set To Default button on their properties dialog box. Simply set up a figure so that it is exactly what you are after and press the button. Every figure you create from then on will fit this default.

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Why Is There an Equation Tool? The text tool and equation tool are basically the same so why have an equation tool? The equation tool is simply there to make getting an equation easy. We did not want to hide FX Draw's equation capability so we made a separate button for it.

8.7

How Do I Draw Network Diagrams Easily? Change the arrow line's default to be a line with an open circle at each end. If you want to draw a directed network, select an arrowhead for the centre of the line. The arrow line tool will now allow you to easily draw a network diagram. If you right click on each arc of the network diagram, you can enter any text you require and it will be angled to suit the line.

8.8

Why Do I End Up With a Small Mess When I Use The Graph Tool? You are not moving the mouse enough when creating the graph. Your graph will fill the rectangle you sweep out with the mouse while holding down the mouse button. If you do not sweep out a large enough area, all components of the graph are drawn in a tiny area.

8.9

How Do I Draw More Than One Function On A Graph? The main function graphing tool properties dialog box has a large area for entering functions. Each function takes one line in the box. If you want more than one function, enter more than one line. Alternatively you can press the function button in the graph dialog box. This allows you finer control over the first function and allows you to enter up to nine more functions.

8.10

How Do I Draw Polar Graphs? Polar functions must be typed in so that they are prefixed with "r =" and are in of t (used as a substitute for theta). An example of a polar function is "r = 2sin(4t)".

8.11

How Do I Draw Inverse Graphs? Inverse functions are typed in so that they are prefixed with "x=" or "f(y)=" and are in of y. An example of an inverse function is "x=2sin(y)".

8.12

How Do I Enter Domains? Each function can have its own domain. These are entered by pressing the f(x) button (the first function's domain can be entered on the graph screen). Domains are entered the way you would normally write them (in of x or t).

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For example x>2 t <= 4

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-3 < x <=7

Alternatively you can use the bracket notation for domain For example y = x2 [-2,3) will produce

8.13

Can FX Draw Draw Piecewise Defined Functions? Yes. You can draw up to ten functions on one graph and give each of the functions their own domain. FX Draw will graph these correctly and can automatically add the dotted vertical lines often used for piecewise defined functions if required.

8.14

What is the Difference Between Out Of Range Arrows and High/Low End? When you graph a function you graph it with either an explicit domain, that you have typed in, or an implied domain determined by the x-axis you have selected. How the graph is represented at the high and low end of this domain is determined by the settings of the Show High End and Show Low End Options for that function. FX Draw will determine if an open circle, closed circle or arrowhead should be shown and you choose if it will be shown. Many functions will have values that lie outside the range of the axes within the domain selected, tan for example. At these values, FX Draw will add arrowheads to show that the graph continues beyond the range of the axes. These arrowheads are called out of range arrows.

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What is a Group? A group is a collection of figures that have been grouped together and are treated as one figure by FX Draw. This new grouped figure can be cut, copied, pasted and resized as easily as a simple figure such as a circle.

8.16

How Do I Group Figures? Select all the figures that you wish to include in your group and either choose group from the edit menu or type Ctrl+G.

8.17

How Do I Ungroup Figures? If you need to ungroup some figures in order to modify them individually, select the group and choose ungroup from the edit menu or type Ctrl+H.

8.18

What Can Groups Be Used For? If you have created an image that you wish to repeat on the same drawing, it is advisable to group the image together so that you do not lose any component as you copy and move the image. Gallery images are stored as groups for this very reason.

8.19

What Is A Gallery? A gallery is a collection of pre-drawn mathematical diagrams that you can use in your documents. Most gallery images are extremely versatile as they appear differently depending on the aspect ratio they are drawn into and the direction in which they were drawn.

8.20

How Do I Use the Galleries?

Push the Gallery Select button. The first gallery will appear and you can choose any of the galleries you have loaded. Once you have selected the gallery image you require, push OK. The gallery tool will now draw that image whenever the tool is selected. It is important to realize that you must move the mouse while holding down the left button to draw a gallery image. If you simply click the mouse without moving it, you will get no image.

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How Does the Direction of Drawing Affect the Gallery Images? Most gallery images will draw differently depending on which direction you draw them in. Try selecting the gallery image of a cuboid. Draw the image by holding down the mouse button while you move the mouse: · · · ·

Top left to bottom right Top right to bottom left Bottom left to top right Bottom right to top left

The combination of drawing direction and aspect ratio makes each gallery image worth much more than just clip art.

8.22

How Do I Save My Own Graphics To a Gallery? Draw the image in FX Draw and select the figures you want saved. From the File menu, choose Save To Gallery. Pick the gallery you want to save to and press OK.

8.23

Can I Edit Gallery Images? Yes. Gallery images are saved as grouped figures. When you have drawn a gallery image, you can: · Select it · Ungroup it · Modify the individual figures.

8.24

What Is The Grid? The grid is the array of points you see on the screen when you start FX Draw. Any figure will be drawn so that it fits the grid UNLESS GAD is on and another point is more attractive.

8.25

How Can I The Greek Letter Codes? All the Greek Letter codes are made from the first two letters of the Greek letter's name: Lower case pairs produce lower case Greek letters. Upper case pairs produce upper case Greek letters. For example

si SI

s S

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Does The Equation Tool Balance Brackets? No. The tool makes no attempt to examine the logical consistency of your brackets. It even treats the three types of brackets, ( { [ as being equivalent. It is up to you to ensure that what you type is logical.

8.27

Why Are Spaces So Important? The tool attempts to automatically format most equations. Unfortunately many expressions are ambiguous, sin2x for example. We wanted to automatically recognize sin2 x while still allowing you to get sin 2x if you wish. The solution was where you put a space. If you leave a space between sin and 2x, you will get sin 2x. Without the space you get sin2x. This is much easier to use than describe. In general, if the tool does not format your equation the way you expect, try entering a space between things.

8.28

How Do I Enter An Ordered Pair? It is amazing how often we are asked this question. People quickly realize that typing an ordered pair into the equation tool produces a vector and they want to know what to do if they REALLY want an ordered pair. The answer is obviously to not use the equation tool and just type your ordered pair into a text box OR use quotes to prevent the equation tool from formatting your equation.

8.29

How Do I Stop the Equation Tool From Formatting Something? This question most often occurs when someone is trying to type a word such as "and" or "there" and the tool insists on formatting it into an intersection symbol or qere. By enclosing a section of your equation in quotes ("and" and "there") you prevent the tool from formatting that part of the equation.

8.30

How Do I Enter A Matrix? Matrices are entered column by column. It is advisable to add a few spaces between the columns.

[1,2,3 4,5,6 7,8,9 :,:,: a,b,c] You are limited to three rows per column

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How Do I Enter a Degrees Sign? Degrees signs are entered with the ` key. This is normally the key NEXT to the 1 key and it normally produces a ~ when pressed whilst holding down the Shift key. The ` key is a backwards single quote. It is not the normal ' key (next to semicolon).

9

Appendices

9.1

A - The Equation Tool

9.1.1

Entering Equations Equations are entered into the equation tool by typing what you see WITHOUT formatting. On most occasions the equation tool will automatically format your equation for you. For example. If you want the equation

simply load the equation tool and enter 3x3+2x2-7. The equation tool automatically formats the powers and italicizes the variables. Simple fractions are also entered as you see them. In other words if you want

you enter it as 3x3/2x4 and The equation tool will automatically build the appropriate fraction. Most simple equations can be entered this way, with NO formatting on your part. More complicated equations will require some extra input on your part. 9.1.2

Symbols Mathematicians use a large number of specialised symbols and FX Equation attempts to make accessing these symbols as easy as possible. Any symbol that is not on the keyboard is entered using one of two methods. Either A key is designated to be automatically replaced. The two symbols that use this approach are ° uses the ` key (usually next to the 1 on the keyboard) ´ uses the * key. The * symbol is often used to represent multiplication on computers.

or A code is used and this code is automatically replaced with the appropriate symbol. The code chosen has been chosen to be easily ed and is usually a logical combination of characters. For example £ is built from < and = so the code is <= » is built from two wavy lines so the code is ~ ~ Some codes are built from the word describing the symbol. ¥ (infinity) the code is inf © 1989-2011 Efofex Software

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Symbol

<= >= <> =/ =~ ~= -= ~~ +* / (followed by a space) ` -> => inf tri ang perp and or element prop subset tf

£ ³ ¹ ¹ @ @ º » ± ´ or · ¸ ° ® Þ ¥ D Ð ^ Ç È Î µ Ì \

Note: Some symbols have two codes.

is entered as 0` <= x <= 360` is entered as x -> inf 9.1.3

Absolute Value Absolute values are entered with the | key. On most keyboards it is above the Enter key and shares the key with \. To enter | you hold Shift when entering. On some keyboards, especially languages other than English, this key is show as two vertical dashes - one above the other. eg. | | Absolute value signs are difficult for FX Equation because they have no "direction". Unlike other brackets, you can not easily tell if | is opening a new absolute value or closing an existing one. IF FX Equation interprets your absolute value incorrectly, you can use this code: |[ absolute value ]| absolute value

absolute value followed by square bracket

opens an

square bracket followed by an absolute value closes an

The square bracket will not be displayed - it is only used to indicate the direction

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of the absolute value sign.

is entered as 9.1.4

|[ (|[x]| - |[y]|)/2 ]|

Degrees Degrees signs are entered with the ` key. This is normally the key NEXT to the 1 key and it normally produces a ~ when pressed whilst holding down the Shift key. The ` key is a backwards single quote. It is not the normal ' key (next to semicolon). Alternatively, you can enter degrees using the lowercase o. eg 32` 32o

9.1.5

Greek Letters All Greek letters are ed. They are all entered using a two character code. The two character code is always the first two letters of the letter's name. Upper case Greek letters that use the same character as normal text are not explicitly ed. (eg upper case alpha = A)

Code al be ga de th la mu pi rh si ph ch om

Code DE OM

Lower Case Greek Letter a b g d q l m p r s f c w

alpha beta gamma delta theta lambda mu pi rho sigma phi chi omega

Upper Case Greek Letter D W

delta omega

Examples:

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is entered as pi/4 is entered as sin2 th 9.1.6

Square Roots sqrt or sr may be used to indicate square roots. Complicated square roots will need to be surrounded with brackets. Square roots may be included as part of more complicated equations. Examples: is entered as sr 4 or sqrt 4 is entered as sr(x2+y2) or sqrt(x2+y2)

is entered as sr3/2

9.1.7

nth Roots Any root of a function can be shown using the root keyword. Examples: is entered as 3root x is entered as xroot 2x2

9.1.8

Fractions We have already seen how to enter some simple fractions. Fractions with complicated numerators or denominators must have the numerator and/or denominator surrounded by brackets. These brackets will not be displayed, they are used as logical brackets so that you clearly indicate the elements that comprise the numerator and denominator. Examples: is entered as (3x+2)/4

is entered as ((x+1)2(x+2))/(x+1)

is entered as x=(-b +- sr(b2-4ac))/2a or you © 1989-2011 Efofex Software

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can use the qf standard shortcut.

is entered as 1/(1+4x^(3x/2)+1/(2x2+1/2)) The equation technology can be set to shrink non-algebraic fractions (like the 1/2 in the equation above). This usually produces superior results and is necessary for the display of mixed numerals

9.1.9

Using Brackets We have already seen the use of brackets to logically identify the numerator and denominator in complicated fractions. This is a very important use of brackets. Brackets are also used to logically identify powers and subscripts. All three bracket types {, [ and ( may be used interchangeably in the equation tool and the equation tool makes no distinction between them. The equation tool does not even check to see if brackets are paired. You are responsible for this. If there is a fraction inside a bracket, the bracket is automatically resized. Example:

is entered as 3[(x-2)2+1/2]

9.1.10 Powers Most powers will be automatically recognised by the equation tool. The equation tool will not automatically recognise powers if · · · ·

you require a variable as a power you require a function as a power you require a power of a number you require a complicated power.

In these cases you need to explicitly indicate the power using the ^ symbol. As with fractions, complicated powers need to be surrounded with brackets. These brackets will not be displayed. Examples:

is entered as x2

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is entered as a^m is entered as e^(sinth) is entered as 3^2 is entered as x^(2y+3) is entered as e^x2 is entered as x^(1/2)

9.1.11 Subscripts The \ (backslash) symbol is used to indicate the next character or group of characters is a subscript. Complicated subscripts must be surrounded with brackets which will not be displayed. Please Note: On some keyboards (eg Swedish) the \ key is not accessible in Word. The § key can be used instead. Examples:

is entered as T\n

(or T§n)

is entered as T\(n+1)

(or T§(n+1))

9.1.12 Integrals Integrals can be entered using the int command. Example:

is entered as int x dx For definite integrals, the upper and lower bounds are placed in brackets and separated by a comma (see Decimals).

is entered as int(-1,1)x2+1 dx

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is entered as int(pi/4,pi/2)e^(sinx) cos x dx Integrals can be drawn in two different ways - with the bounds to the right of the integral sign or with the bounds above and below. This option is set in the Styles section of the preferences.

9.1.13 Limits Limits are entered using the lim command. The value the limit approaches is placed in brackets. Limits are the main use of the -> code which produces an arrow. Examples:

is entered as lim(x->3) 3x/4

is entered as lim(h->0) (f(x+h)-f(x))/h

is entered as lim(x->1+) h(x)

is entered as lim(x->inf)(5x2-4x+2)/(3x2+3x-2) © 1989-2011 Efofex Software

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9.1.14 Sigma Notation Sigma notation is entered using the sigma command. The parameters are placed in brackets and are separated with a comma. Example:

is entered as sigma(i=1,10) x\i

9.1.15 Product Notation Product notation is entered using the product command. The parameters are placed in brackets and are separated with a comma. Example:

is entered as product(i=1,10) x\i

9.1.16 Scientific Notation FX Equation technology can automatically format scientific notation. The capital E followed by a number will be transformed into ´10 to the power of the number. FX Equation technology will correctly format numbers with negative exponents. FX Equation technology will use the currently selected multiplication symbol (´ or ×). Examples:

is entered as 1.2E15

is entered as -3.2E-1+1.2E1 9.1.17 Vector FX Equation technology s many different ways of defining and displaying vectors. You can either indicate exactly what you want to show as a vector and how you want it shown or you can allow FX Equation technology to detect and display vectors automatically. How the technology interprets what you type can © 1989-2011 Efofex Software

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be controlled on the Tools/Preferences screen 9.1.17.1 Column Vectors (COPY)

If you wish to enter vectors in the vertical format, they are simply entered as (3,2) using a comma as a separator. Three-dimensional vectors are entered in the same way. If you normally use a comma as a decimal point, FX Equation technology will automatically detect this and you must use a semicolon to separate components of a vertical vector. Examples:

is entered as (3,2x) or (3;2x)

is entered as (3,2,5) or (3;2;5)

is entered as r=(2,7)+la(1,-4) or r=(2;7)+la(1;-4) You must have selected the Detect Column Vectors option to allow FX Equation to detect column vectors and matrices.

9.1.17.2 Automatic Vectors (COPY)

FX Equation technology can automatically recognize some vectors if you choose to turn the feature on. FX Equation technology can recognize some lowercase vectors and double capital vectors. This feature is activated by default and can be controlled by on the Equation / Vectors option screen. © 1989-2011 Efofex Software

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9.1.17.2.1 Lowercase Vectors (COPY)

FX Equation technology will only detect lowercase vectors if automatic recognition is switched on. If you are using vectors of the form FX Equation technology can automatically recognise that you are typing a vector and make the r, i and j bold. FX Equation technology can also be set to indicate vectors using lines, tildes or arrows, depending on your preference. This automatic recognition of vectors can save you hours of time, but FX Equation may sometimes get the automatic recognition incorrect. By default, FX Equation will take its "best guess", you can also turn this feature off or alternatively, explicitly tell FX Equation which variables to recognise as vectors.

It is important to that you do not need to tell FX Equation that you are

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working with a vector, FX Equation will automatically identify this. Example: is entered as r=(3i+2j+k)+la(i-j+3k) Lowercase vectors can be display bold, with an arrow over the top or with a line or tilde underneath the vector.

9.1.17.2.2 Double Capitals (COPY)

FX Equation technology will only detect Double Capital vectors if automatic recognition is switched on. Double capital letters are used to represent line segments, rays and vectors. FX Equation technology can automatically place an annotation over double capitals. You would use this feature if you were, for example, entering a lot of position vectors in an exam. Examples: is entered as AB = OB - OA is entered as |OA|=sr(9+16)

is entered as cos th = (AB.BC)/(|AB | |BC|) The annotation used by FX Equation can be set using the Vector Options

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9.1.18 Matrices Examples:

is entered as [2,3 4,6]

is entered as [1,2,3 4,-5,6 7a,8,1/2 ]

FX Equation MUST be set to detect column vectors in order to detect matrices.

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9.1.19 Complex Numbers The equation tool correctly formats complex numbers without any extra input on your part and recognises cis, arg and mod.

9.1.20 Means and Complements A character can have a line added above it by typing an underscore _ directly after the character. Only one character can be modified in this way. This can be used to show means and complements. Example: is entered as x_

9.1.21 Predictions Statistical predictions ("y hat") are entered using a DOUBLE power symbol. Example: is entered as y^^ 9.1.22 Dots A character can have a dot or two dots added above it by typing a colon or two colons directly after the character. Only one character can be modified in this way. Example: © 1989-2011 Efofex Software

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is entered as r : is entered as x :: is entered as 0.23 :

9.1.23 Preventing Formatting On occasions you will want to prevent the equation tool from formatting a section of an equation. Usually this will be if you want some text in an equation. Surrounding the text in quotes will prevent it being formatted. Example: is entered as x = 3 “and” y = 4

9.1.24 Spaces Spaces change the way a particular equation is interpreted and therefore formatted. This can best be illustrated using these examples. is entered as sin2 th is entered as sin 2th The only difference between the two equations is the location of a space. Spaces can be used to add space between characters but they can also be used to indicate a change of mode

9.1.25 Decimals The equation tool asks Windows what symbol you are using for decimal points (usually a full stop or a comma). It then uses the OTHER symbol for its vector separator. For example, Australia uses a dot as a decimal point so the equation tool uses a comma for the entering of vectors and matrices so

is entered as (3,2).

9.1.26 Recognized Functions FX Equation technology automatically recognises functions and formats them differently, according to your preferences. The functions that FX Equation recognises are: sin

asin

sec

sinh © 1989-2011 Efofex Software

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cos tan

acos atan

cosec cot

cosh tanh

ln normal

log

abs

arg

cis

348

mod

9.1.27 Mixed Numerals Mixed Numerals are created automatically if you have selected the Shrink Non-Algebraic Fractions option.

is entered as 3 1/2 The Shrink Non-Algebraic Fractions option is available in the Styles page of FX Equation's options.

9.1.28 Negative Numbers FX Equation will detect most negative numbers. For example, if you type -9 - -3 FX Equation will detect that the first and third - signs are indicating negation whereas the middle - is indicating subtraction. FX Equation offers you the option to display negative numbers differently.

The three options produce these results.

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9.1.29 Recurring Decimals Entered using the : key and the _ key. is entered as 2.4: is entered as 2.4_ is entered as 2.1_234 9.1.30 Greatest Integer Greatest Integer signs are entered as [ | and | ] Example:

is entered as [|x2+3x-1|] 9.1.31 Definite Integral Bounds FX Equation s a special notation to show the bounds of a definite integral. For example. If you wish to calculate this definite integral

You might need to enter this intermediate line in your calculations.

You can enter these bounds as [x3/3]1,2

9.1.32 Logarithms Normally, numbers written immediately after a function are raised as a power automatically. Example:

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is entered as cos2 x log is treated differently. Entering log2 x will generate.

This makes generation of logarithms automatic.

9.1.33 Piecewise Defined Functions FX Equation's matrix feature can be used to enter piecewise defined functions.

is entered as y={x2,3x,0,(5x2+1) :, :, :, : (x<-2),(-2<=x<4),(x=4),(x>4) 9.1.34 Shortcuts Shortcuts allow you to quickly add common equations to your documents. The quadratic function for example.

To enter the quadratic function in FX Equation, you would normally type x=(-b+-sr(b2-4ac))/2a to generate this equation. Shortcuts allow you to enter it by typing qf We have entered some shortcuts for you to get started.

qf pv7 pv20

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but you can edit our shortcuts or create your own to suit your workstyle. Editing Shortcuts

9.1.35 Multi-Line Equations Up to twenty lines of equations can be entered at one time. Simply push the down arrow or Enter Key to access the next line when using the main input screen.

9.1.36 International Considerations FX Equation automatically detects the symbol you use as a decimal point - either . or , If you use . as a decimal point (eg 3.2), you will use , as a separator for entering vectors or matrices.

is entered as (3,2)

If you use , as a decimal point (eg 3,2), you will use ; as a separator for entering vectors or matrices

is entered as (3;2)

9.2

B - Statistics Function Reference

9.2.1

The Statistics Functions

9.2.1.1

CumFreqTable(column)

Calculates a cumulative frequency table for column and puts it into the two columns indicated by the location of the cursor or mouse when the formula is entered. A cumulative frequency table shows the number of scores that are equal or less than each value in the table. Score 10 11 12

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20

This cumulative frequency table would be generated from this data: 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13 Example: CumFreqTable(A)

9.2.1.2

Decile(column)

Calculates the decile rank of each score in column. The decile rank is calculated using the percentile figures so any changes in the system options that affect the calculation of percentile scores will affect the calculation of the decile scores. Example: Decile(A)

9.2.1.3

Deviation(column)

Calculates the deviation from the mean for each score in column, using the calculated mean of the column. Example: Deviation(A)

9.2.1.4

Fibonacci(first, second number)

Generates number scores in a Fibonacci sequence starting with first and second numbers. Example: Fibonacci(1,1,50) Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Fibonacci(1;1;50) - using the ; as a separator

9.2.1.5

FreqTable(column)

Calculates a frequency table for column and puts it into the two columns indicated by the location of the cursor or mouse when the formula is entered. A frequency table shows the number of each score in the data set. They are used to efficiently display large numbers of scores that fall into a small number of possible values. Score 10 11 12 13

f 2 3 7 8

This frequency table would be generated from this data:

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10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13 Example: FreqTable(A)

9.2.1.6

Group(column, number) / GroupN(column, number)

These two functions are equivalent. The Group function groups data in column into number groups. The statistics tool will select appropriate group widths and in some situations it will not be able to divide the data into exactly number groups. 0-20 20-40 40-60 60-80 80-100 100-120 120-140

4 20 78 63

This is the result of Group(A,7) 32

1 1

The number parameter is optional. If it is omitted, the statistics tool will attempt to divide the data into 10 groups. The group function is used to generate data for histograms. Examples:

Group(A,10)

Group(B)

GroupN(c,4)

Note: If you type decimals using a comma (eg 3,2) you should enter these formulae as Group(A;10) - using the ; as a separator 9.2.1.7

GroupE(column)

The GroupE function allocates data in column into existing groups. To use this command you first need to decide your own groups and place them into the target column. Secondly you need to set the target column to be a group column and the next column to be a frequency column. Any data that cannot be allocated to an existing group will be allocated to an "other" group appended to your existing groups. As shown in the example, the groups do not necessarily need to be a constant width and gaps are allowable. Example: GroupE(A)

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GroupW(column,width)

Allocates data in column into groups width wide. This function is useful where you wish to force the statistics tool to group data into predetermined divisions. 0 - 14.5 14.5 - 29 29 - 43.5 43.5 - 58 58 - 72.5 72.5 - 87 87 - 101.5 101.5 - 116

1 3 26 58 71 35 5 1

Generated by GroupW(A,14.5)

Note: If you type decimals using a comma (eg 3,2) you should enter this formula as GroupW(A; 14,5) - using the ; as a separator

9.2.1.9

Inc(start,increment,number)

Inc is a data generation function. Inc generates number data points that begin with start and go up in increment. 2 2.2 2.4 2.6 2.8 3 3.2 3.4

Generated by Inc(2, 0.2, 8)

Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Inc(2; 0,2; 8) - using the ; as a separator

9.2.1.10 MPA(column,cyclelen)

Calculates the moving point average, or centred moving point average, for the data in column with a cycle length of cyclelen. The MPA function automatically centres the moving point average if cyclelen is even. The data in column B of the example has been generated using MPA(A,4)

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Note: If you type decimals using a comma (eg 3,2) you should enter this formula as MPA(A ; 4) - using the ; as a separator

9.2.1.11 Normal(column) / NormP(column)

These two functions are equivalent. The data in column is interpreted as z-scores (standard deviations) and the Normal function calculates the probability that a score will be less than or equal to the z-score in column. This function is equivalent to the P function on many scientific calculators or the normal distribution data in a tables book. The data in column B of the example has been generated using Normal(A)

9.2.1.12 NormPDF(column)

Calculates the value of the probability density function for each of the data points in column (interpreted as z-scores). Example: NormPDF(A)

9.2.1.13 NormQ(column)

The data in column is interpreted as z-scores (standard deviations) and the NormQ function calculates the probability that a score will be greater than the z-score in column. This function is equivalent to the Q function on many scientific calculators and for any input value = 1-NormP. Example: NormQ(A)

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9.2.1.14 Percentile(column)

Calculates the percentile (or percent rank) of each data point in column. The percentile represents the percentage of scores in the data set that are less than or equal to the data point. Column B in the example contains the percent ranks of scores in column A.

9.2.1.15 Predict(column1, column2, regtype) / PredictY()

These two functions are equivalent. column1 contains the independent variable's data (usually x values) column2 contains the dependent variable's data (usually y values) regtype is the regression model 1 linear regression 2 quadratic regression 3 power regression 4 exponential regression 5 logarithmic regression 6 median line 7 reciprocal regression Please note that it is not necessary to or use these codes. Predict calculates the predicted value of y for the x in column1 using the regtype regression model. All three parameters are optional. If they are not included, the current column one, column two and regression type as shown in the Statistics View are used. On most occasions you would simply type Predict( ) In the first example, column C has been generated using Predict( ). We did not use any parameters because the Statistics View was showing Linear Regression Calculations for A and B. We could have typed Predict(A,B,1) and got the same result regardless of the Statistics View. Column C fits the equation y = 23.39 – 1.29x.

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Predict can be used to predict y values for x values that are not in the data set. Simply add extra x values with no corresponding y values. Predict will correctly calculate a predicted y value. If you include a y value that corresponds with an x value, the pair will automatically be included in the data set. The second example shows predicted y scores for the x values of 7, 8 and 9.

Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Predict(A; B; 1) - using the ; as a separator

9.2.1.16 PredictX(column1, column2, regtype)

column1 contains the independent variable's data (usually x values) column2 contains the dependent variable's data (usually y values) regtype is the regression model PredictX calculates the predicted value of x for the y in column2 using the regtype regression model. PredictX operates in exactly the same manner as Predict and all three parameters are optional. In the example, column C has been generated using PredictX using the same data as shown for PredictY. PredictX can predict x values for y values not in the data set in the same way that Predict can predict y values for x values not in the data set.

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Note: If you type decimals using a comma (eg 3,2) you should enter this formula as PredictX(A; B; 1) - using the ; as a separator

9.2.1.17 Rand(number)

Calculates number uniformly distributed random numbers between 0 and 1. Use Rand(100), for example, to create 100 random numbers. The Rand function can be used to simulate other random variables.

9.2.1.18 RandBernoulli(probability,number)

Simulates number Bernoulli trials where the probability of success in each trial is probability. Probabilities are expressed as decimal values between 0 and 1. Bernoulli trials can result in either success or failure, represented by 1 and 0 respectively. The RandBernoulli function simulates Bernoulli trials. RandBernoulli(0.3,30) might generate 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandBernoulli(0,3; 30) - using the ; as a separator

9.2.1.19 RandBetween(low,high,number)

Generates number random integers between high and low inclusive. The random integers are uniformly distributed. RandBetween(5,10,30) might generate 9, 7, 7, 9, 9, 7, 10, 10, 8, 9, 8, 5, 7, 5, 8, 10, 7, 6, 9, 9, 8, 8, 5, 6, 7, 5, 6, 7, 5, 8 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandBetween(5; 10; 30) - using the ; as a separator

9.2.1.20 RandBinomial(attempts,probability,number)

Generates number random binomial trials. RandBinomial returns the number of successful attempts in attempts attempts where the probability of success on each attempt is probability. For example, when rolling a die, the probability of rolling a six is one sixth. If you roll a die 10 times, how many sixes will you roll?

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You can simulate this problem thirty times using RandBinomial(10,1/6,30) and you might generate the following data. 2, 2, 1, 1, 1, 0, 1, 3, 0, 1, 2, 1, 4, 5, 2, 1, 1, 1, 0, 3, 1, 1, 1, 1, 2, 2, 2, 1, 4, 1 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandBinomial(10; 1/6; 30) - using the ; as a separator

9.2.1.21 RandChiSquared(degrees, number)

The chi squared data generator generates chi squared distributed numbers with a given degree of freedom. 9.2.1.22 RandExponential(rate, number)

The exponential data generator generates data that fits this probability density function.

Where l is the rate parameter of the function. 9.2.1.23 RandGeometric(probability,number)

Generates number random geometric trials. RandGeometric returns the number of attempts before a success where the probability of success on each attempt is probability. For example, how many rolls of a die does it take to roll a 6? You can simulate this problem thirty times using RandGeometric(1/6,30) and you might generate the following data. 16, 3, 6, 9, 7, 10, 10, 3, 5, 11, 1, 9, 2, 6, 5, 7, 20, 21, 4, 2, 5, 5, 2, 10, 6, 2, 13, 1, 1, 10 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandGeometric(1/6; 30) - using the ; as a separator

9.2.1.24 RandHyperGeometric(select,total,success,number)

Generates number random hypergeometric trials. RandHyperGeometric returns the number of successes when select selections are made, without replacement, from a total where success successes are present. For example, five marbles are drawn, without replacement, from a bag of 10 marbles, six red and four green. How many red marbles will be drawn? You can simulate this problem thirty times using RandHyperGeometric(5,10,6,30)

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and you might generate the following data. 3, 2, 3, 4, 1, 4, 2, 3, 3, 3, 3, 3, 3, 5, 4, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 2, 3, 3 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandHyperGeometric(5; 10; 6; 30) - using the ; as a separator

9.2.1.25 RandNegBinomial(successes, probability, number)

Generates number random negative binomial trials. RandNegBinomial returns the number of attempts before a successes successes where the probability of success on each attempt is probability. For example, how many rolls of a die does it take to roll a total of four 6's? You can simulate this problem thirty times using RandNegBinomial(4,1/6,30) and you might generate the following data. 19, 18, 23, 18, 14, 25, 52, 69, 17, 24, 21, 29, 12, 36, 52, 36, 17, 22, 8, 30, 8, 26, 11, 41, 18, 13, 41, 18, 30, 25 Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandNegBinomial(4; 1/6; 30) - using the ; as a separator

9.2.1.26 RandLognormal(mean, sd, number)

The log normal data generator generates log normally distributed numbers with a given mean and standard deviation. 9.2.1.27 RandNormal(mean, sd, number)

Generates number normally distributed scores with a mean of mean and a sample deviation of sd. The RandNormal function can quickly produce normally distributed data sets and can produce data sets with almost exactly the given mean and standard deviation. For example, RandNormal(60,15,30) might return 71.14, 64.14, 53.42, 60.18, 85.18, 33.88, 77.8, 64.43, 54.79, 40.79, 42.7, 72.37, 69.64, 27.99, 61.92, 49.87, 64.42, 61.74, 71.67, 83.69, 70.52, 54.36, 63, 24.77, 57.12, 77.01, 57.06, 72.68, 66.49, 45.23 This set of thirty numbers has a mean of exactly 60, a standard deviation of 14.9995591 and has a distribution that looks like this:

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Note: If you type decimals using a comma (eg 3,2) you should enter this formula as RandNormal(60; 15; 30) - using the ; as a separator

9.2.1.28 RandPoisson(successes, number))

The Poisson data generator allows you to simulate trials where you know the expected number of successes in the experiment and you wish to know the actual number of successes. 9.2.1.29 RandStudentt(degrees,number)

The student t data generator generates student t distributed numbers with a given degree of freedom. 9.2.1.30 Rank(column) / RankD(column)

Generates the rank of each data point in column. Higher values ranked first. The example shows column B containing the rank of column A. This column was generated using Rank(A). Because there are two 18's in the data set, they are both given a rank of 3 and 17.2, the next value, is given a rank of 5.

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9.2.1.31 RankA(column)

Generates the rank of each data point in column. Lower values ranked first. The example shows column B containing the rank of column A. This column was generated using RankA(A).

9.2.1.32 Residual(column1, column2, regtype) / ResidualY( )

These two functions are equivalent. column1 contains the independent variable's data (usually x values) column2 contains the dependent variable's data (usually y values) regtype is the regression model 1 2 3 4 5 6 7

linear regression quadratic regression power regression exponential regression logarithmic regression median line reciprocal regression

Please note that it is not necessary to or use these codes. Calculates the residual value of y for the x in column1 using the regtype regression model. The residual value is the difference between the actual value and the predicted value. All three parameters are optional. If they are not included, the current column one, column two and regression type as shown in the Statistics View are used. On most occasions you would simply type Residual( )

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In the example, column C has been generated using Residual( ). We did not use any parameters because the Statistics View was showing Linear Regression Calculations for A and B. We could have typed Residual(A,B,1) and got the same result regardless of the Statistics View. Column C fits the equation y = 23.39 – 1.29x. Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Residual(A; B; 1) - using the ; as a separator

9.2.1.33 ResidualX(column1, column2, regtype)

column1 contains the independent variable's data (usually x values) column2 contains the dependent variable's data (usually y values) regtype is the regression model ResidualX calculates the residual value of x for the y in column2 using the regtype regression model. ResidualX operates in exactly the same manner as Residual and all three parameters are optional. In the example, column C has been generated using ResidualX using the same data as shown for Residual.

Note: If you type decimals using a comma (eg 3,2) you should enter this formula as ResidualX(A; B; 1) - using the ; as a separator

9.2.1.34 Round(column, decimalplaces)

Rounds data points in column to decimalplaces number of decimal places. If decimalplaces is negative, the data points are rounded to the nearest 10, 100, 1000 and so on. Data Round( A,2) Round( A,0) Round( A,-1)

54.0513321 93.5850093 79.5159764 78.2189397 52.4185918 49.4979705 57.3778496 11.9083224

54.05

93.59

79.52

78.22

52.42

49.5

57.38

11.91

54

94

80

78

52

49

57

12

50

90

80

80

50

50

60

10

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Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Round(A; 1) - using the ; as a separator

9.2.1.35 Row / @

The word Row or the @ symbol can be used in any formula and it will be replaced by the row number when performing the calculation.

9.2.1.36 Seasonalise(column, cyclelen)

Generates de-seasonalised data from column assuming a cycle length of cyclelen. Seasonal data often shows cyclic variations. This function removes cyclic variations and allows you to see the underlying trends. Seasonalise analyses cyclic deviations and removes them. Please note that the output of the seasonalise function is dependent on the System Options settings. De-seasonalising data involves particularly localised procedures. The parameters in the Seasonalise function are optional. If they are omitted, the Seasonalise function will seasonalise whatever column is currently selected in the Statistics View and will assume a cycle length of 4. Example: Seasonalise(A, 4) Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Seasonalise(A; 4) - using the ; as a separator

9.2.1.37 Sort(column) / SortA(column)

These functions are equivalent. Sort the entire data set using column as the sort key. Sorts into ascending order. All columns are affected. Example: Sort(A)

9.2.1.38 SortD(column)

Sort the entire data set using column as the sort key. Sorts into descending order. All columns are affected. Example: SortD(A)

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9.2.1.39 SortCol(column) / SortColA(column)

These functions are equivalent. Sorts only the data in column into ascending order. No other column is affected. Example: SortCol(A)

9.2.1.40 SortColD(column)

Sorts only the data in column into descending order. No other column is affected. Example: SortColD(A)

9.2.1.41 Stanine(column)

Calculates the stanine score for each data point in column. Stanines allocate a score from 1 to 9 to each score in a data set. The width of each stanine group is approximately equal, in other words if stanine 1 is allocated to scores from 10-20, stanine 2 will be allocated to scores from approximately 20-30. Because stanines are usually allocated to normally distributed data, even though they have approximately equal widths, 54% of all scores are allocated stanines of 4, 5 and 6. The example shows stanines in column B. They were calculated using Stanine(A).

9.2.1.42 Standardise(column, mean, sd)

Standardises the data in column so that it has a new mean of mean and a new standard deviation of sd. Each data point maintains its zscore (each score stays the same number of standard deviations from the mean). Example: Standardise(A,60,15) Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Standardise(A; 60; 15) - using the ; as a separator

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9.2.1.43 Triangular(number)

Generates number triangular numbers. Example: Triangular(10)

9.2.1.44 Tribonacci(first, second, third, number)

Generates number scores in a Tribonacci sequence starting with first, second and third. Example: Tribonacci(1,1,1,20) Note: If you type decimals using a comma (eg 3,2) you should enter this formula as Tribonacci(1; 1; 1; 20) - using the ; as a separator

9.2.1.45 ZScore(column)

Calculates the zscore for each data point in column. The zscore is the number of standard deviations from the mean. Alternatively, Zscore effectively standardises the data to have a mean of 0 and a standard deviation of 1. Example: Zscore(A)

9.2.2

Other Functions

9.2.2.1

Trigonometric Functions

Sin(x), Cos(x), Tan(x), Sec(x), Cosec(x), Cot(x) calculate the appropriate trigonometric ratios. x can be in degrees, radians or grads as chosen in System Options.

9.2.2.2

Inverse Trigonometric Functions

asin(x), acos(x), atan(x) calculate the inverse trigonometric functions.

9.2.2.3

Hyperbolic Functions

cosh(x), sinh(x), tanh(x) calculates the appropriate hyperbolic functions.

9.2.2.4

Abs(x)

Calculates the absolute value of the parameter x.

9.2.2.5

Exp(x)

Calculates ex

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Ln(x)

Calculates the natural logarithm of x 9.2.2.7

Log(x)

Calculates the base 10 logarithm of x 9.2.2.8

Sqrt(x) / SR(x)

Calculates the square root of x

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368

Index

-B-

-++-

115

-11st Derivative

154

-22000 5 2nd Derivative

154

-995 98

5 5

-Aa 141 abs 133 Absolute Frequency 235, 239, 240, 242, 243, 244 absolute value 366 acos 133 Acrobat 6 add and subtract figures 35 5, 7 Adobe 6 Advanced 7 Angle 93 Animation 145 anti-clockwise 37 Arcs 87 arrow line 40, 47 Arrows 217 asin 133 Asymptotes 134 atan 133 Autoscale 109 Axes 85, 109, 217, 228, 310 Axis 85

b 141 Bar Graph 229, 230 Basic Concept 1 Bernoulli 358 Bernoulli Trial 276 Binomial Distribution 277, 358 bisect 11 Bivariate Data 279 Blank 304 Box Plots 231 Brackets 112, 338 Broken Scale 219 Brush 264

-Cc 141 Cartesian 108, 114, 292 CD 5 centre 55, 70 Changing Column Types 187 Chi Squared Distribution 279 circle 55 circumference 11 Clipboard 209 clockwise 37 Column 183, 186 Column Graph 230, 231 Column Titles 194 Columns 183 Combine Graph Types 272 Complements 346 Complex Numbers 346 Conditions 2 Constant Controller 142 Constants 141 Continuous - Chi Squared 279 Continuous - Exponential 278 Continuous - Log Normal 279 Continuous - Normal 278 Continuous - Student t 279 Continuous - Uniform 278 control points 35 Copy 42, 46, 47 Copy Statistics 209 Copyright 4 © 1989-2011 Efofex Software

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Cos 133, 366 Cosec 133, 366 cosh 133, 366 Cot 133, 366 Create 111 Create Graph 212 cross 24 Ctrl 15, 35, 39, 42, 47 Cumulative Frequency 233, 243, 351 cumulative frequency table 351 Cumulative Histogram 243 curvature 87 Cut 42

-Dd 141 Data 46 Data Box 264 Data Boxes 210 Data Columns 183, 188 Data Generator 194, 276, 279, 280, 281 Data View 182, 183 Decile 352 Decimals 347 default 109, 328 Definite Integral 156 Degrees 109, 334, 336 Derivative 154 Deseasonalise 364 Deviation 352 Diameter 55 Dice 281 direction 332 Discontinuity 309 Discrete - Bernoulli 276 Discrete - Binomial 277 Discrete - Equi-Likely 276 Discrete - Geometric 277 Discrete - HyperGeometric 277 Discrete - Negative Binomial 277 Discrete - Poisson 278 Discrete - Uniform 276 Distribution 3 domain 140, 141, 309, 329 Dot Plot 234 Dot to Dot 123 dots 292 double-clicking 45

369

5 Drawing Order

32, 41, 42

-Ee 133, 366 edit 45 Ellipse 85 elliptical arcs 87 end points 11 Equation 70, 329, 333 Equations 334 Equi-Likely Distribution 276 Evaluation 6 Excel 47 Exclusion 4 Exponential Distribution 278

-FFamilies of Curves 143 Family 143 Feasible Region 109 Feasible Regions 307 Fibonacci 352 Fill Down 194 Fill Type 27 foci 85 Formula Columns 183, 193 Formulas 183, 193 Fractions 337 Frequency 351, 352 Frequency Columns 183, 190 Frequency Density 240, 242, 243, 244 Frequency Polygon 235, 239 Frequency Table 351, 352 Frequency Tables 190 Full Site 3 Functions 108, 109, 111, 204, 347 FX Graph 108 FX Stat 182

-GGAD 11, 15, 28, 39, 42, 93 Galleries 298 Gallery 40, 42, 331, 332 Geometric 359 Geometric Distribution 277 © 1989-2011 Efofex Software

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Geometrically Aware Drawing geometry 11 Grads 109 Graph 212 Graph Type 210, 214 Graph Types 264, 272 Graph View 182 Greek 332, 336 green tick 8, 44 grid 39, 109, 225, 332 Grid - Polar 225 grids 292 group 34, 35, 40, 42, 331 Group Columns 183, 191 Group data 353, 354 Grouped Data 191, 200 Groups 331 Groups of Points 123

9, 11

-H-

-LLabel Columns 183, 189 Labels 189, 245 Layout 32, 41 Liability 4 Licence 2 Limitation 4 Limits 340 Line 47, 264 Line Graph 245 Line Type 25 ln 133 Local Maxima/Minima 134 log 133 Log Normal Distribution 279 Log Scale 219 logarithm 367 Logarithmic 292

-MHeadings 228 Hexagonal 292 Hide Graph 264 Highlight Data 196, 264 Histogram 240, 242, 243, 244 hyperbolic 366 Hypergeometric 359 HyperGeometric Distribution 277

-IImplicit 119 Implicitly Defined 119 Important 2 Increment 354 insert 8 Install 5 Integral 156 Integrals 320, 339 Intercepts 134 Intersection 93, 134 Inverse 108, 118, 329 Isometric 292

m 141 Macros 7 major 87 Major / Minor Angles 93 Mask Data 195 Matrices 333, 345 Maximum 219 Me 5 Mean Deviation 352 Means 346 measurements 47 Mess 329 mid point 11 Minimum 219 minor 87 Modify 270 mouse 9 Moving Point Average 245, 354 Multi-Line 351 Multiple Graph Types 264, 272

-N-

-KKeyboard shortcut

42

natural logarithm 367 Negative Binomial 360 Negative Binomial Distribution

277

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network 7, 329 networks 47 New Features 1 Normal 360 Normal Distribution 278, 285, 355 NT 5 nth Root 337 Nudge 36, 42 number line 289 nverse trigonometric 366

-O-

371

Product Notation 341 Profile 7 properties 38, 328

-Qquarter point 11 Quartiles 283 Quick Graph 200 Quick Group 200 Quick Sort 202 Quick Statistics 203

-Robject 8 OLE 7 Ordered Pair 333 Origin 217 Outliers 231 overlapping 32 Ownership 4

-Pparallels 11 Parametric 108, 120 Paste 42 Percentage Frequency 235, 239, 240, 242, 243, 244 Percentile 356 Percentiles 283 Perpendiculars 11, 93 Personal Use 2 pi 133 Pie Graph 251 Piecewise Defined Function 330 Plane 135 Point 70, 264 Points 121 Points of Inflection 134 Points of intersection 11 Poisson Distribution 278 Polar 108, 116, 121, 123, 124, 292, 329 Polar Grid 225 Powers 112, 338 Prediction 356, 357 Predictions 346 Prices 6 print 42 Privileges 5, 7

Radians 109 Radius 55 rainbow 25, 27 Random 276, 277, 278, 279, 280, 281 Random Numbers 358, 359, 360 Rank 361, 362 rectangle 58 red cross 8, 44 Redo 42 reflect 34 Reflection 34 Registration 6 Registry 7 Regression 245, 255, 256, 356, 357, 362, 363 Relative Frequency 235, 239, 240, 242, 243, 244 Requirement 5 Rerun formulas 198 Residual 362, 363 Residuals 255, 256 Residuals Graph 255 Restrictions 112 right clicking 38 root 133 Roots 112 Rotating 37, 42 Round 363 Rounding 363 Row 364

-SSave To Gallery 300 Scale 219 Scale - Broken 219 © 1989-2011 Efofex Software

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Scale - Equal Aspect 219 Scale - Fractions 219 Scale - Free 219 Scale - Log 219 Scale - Pi 219 Scattergraph 256 Seasonalize 245, 283 Seasonlise 364 Sec 133, 366 Sectors 87 Segments 87 select 35, 47, 268, 328 Select Mode 134 Set To Default 40, 328 Setting Defaults 40, 282 Shift 15, 39, 42, 87 Sigma Notation 341 Sin 133, 366 sinh 133, 366 sizing 45 sliders 38, 328 Sort 364, 365 Sort Data 202 Spaces 112, 333 sqrt 133 square root 133, 337, 367 Staff Use 3 Standalone 8 Standardise 365 stanine 365 Statistics 203, 205, 208 Statistics Functions 204 Statistics View 182 Stem & Leaf Plot 259 Student t Distribution 279 Student Use 3 Subscripts 339 Symbols 112, 334 System 5, 7

-TTan 133, 366 Tangent 11 Tangent Lines 169 tangential 11 tanh 133, 366 Termination 4 text 67

372

third points 11 tick 24 Ticks 217, 303 Time Series 280 Time Series Data 354 Titles 194, 228 Transparency 264 Triangle Graph 262 triangular numbers 366 Tribonacci 366 Turning Points 134 Two Arms 115

-UUndo 42 ungroup 34, 40, 331 Uniform Distribution 278, 358 Uninstall 7 Upgrade 2, 4

-VVectors 124 Venn 287, 288 Viewing Statistics

207

-WWarranty 4 Windows 5 Word 6, 44

-XXP

5

-Yy=

114

-ZZ Score 365, 366 Zoom 137, 139, 310

© 1989-2011 Efofex Software