Efofex Help

Efofex Help

© 2017 Efofex Software

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Efofex Software

PO Box 189 Claremont WA 6910 Australia

Email: [email protected]

Web: www.efofex.com

Efofex Help

User's Guide

by Efofex Software

Efofex Help

© 2017 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 registered 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.

Efofex Help

Table of Contents

Part I About Efofex Software

Part II Introducing Efofex Cloud

Part III Graphics Tools

1 Creating, Editing and Using Graphics

Using Efofex Cloud

Usernames

Private Or Public

Editing Someone Else's Graphic

Can Someone Else Mess Up My Graphic?

History

Graphics Properties

The Invisible ID

Potential Problems

Using the Deprecated OLE System

Using OLE Graphics in Word for WIndows

Adding The Graphics Programs (OLE) to Word

Using The Graphics Programs (OLE) in Microsoft Word

Using OLE Graphics In Other Products

Moving From OLE To Efofex Cloud

Should I Change?

Converting One Image

Converting All Images In a Document

Converting All Images In a Folder

Moving From Connections to Efofex Cloud

Should I Change?

2 FX Draw

Converting All Images In a Document

Basic FX Draw Concepts

Select & Draw

Drawing With A Mouse

A First Look

The Main Drawing Toolbar

Geometrically Aware Drawing (GAD)

Using GAD

Changing the GAD Level

Overriding GAD

GAD Links

What are GAD Links?

Breaking GAD Links

Figure Information

Creating Annotations

Editing Annotations

The Toolbars

Show Grid Button

Isometric Grid Button

Autopoint Button

Zoom Toolbar

Line Type Toolbar

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Fill Type Toolbar

GAD Level Toolbar

Break GAD Links Button

Lock Button

Layout Toolbar

Format Painter Toolbar

Grouping Toolbar

Reflection Toolbar

Subscription Toolbar

Control Points

Manipulating Figures

Selecting Figures

Moving Figures

Resizing Figures

Rotating Figures

Sliders

Editing Properties

Grid

Setting Defaults

Font Management

Changing The Font For All Selected Objects

Changing All Default Fonts

Grouping and Ungrouping

Changing the Drawing Order

Printing

Cut / Copy / Paste

Undo and Redo

Keyboard Shortcuts

Exporting to Graphics Files

What Formats are Offered?

Tools

Select

The Lines

Line Defined By End Points

Line Defined By Mid Point and End Point

Line Defined By Three Points (Ray)

Line Defined By Four Points (Extended Line)

Line Defined By Start Point, Rise and Run

Line Defined By Start Point, Length and Angle

Drawing Lines Using Defaults

Adding Regularly Spaced Points To Lines

Ruler

Dimensions

The Circles

Centre Radius Circle

Diameter Circle

Three Point Circle

Circle in a Square

Compass Circle

The Quadrilaterals

Rectangle

Angled Rectangle

Parallelogram

Rhombus

Kite 1 and Kite 2

Trapezium

Rounded Rectangle

Bitmap Tool

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Text/Equation Boxes

Basic Usage

Text Formatting

Introducing FX Autoquate

Manually Marking Equations

Plain Text Boxes

Equation Boxes

Equation Toolbar

Point

Smooth Lines

Smoothed Line

Bezier Curve

Triangles, Polygons and Smoothed Lines

Triangles

Isosceles Triangles 1 & 2

Equilateral Triangle

Right Triangles 1 & 2

Polygons

Regular Polygons 1

Regular Polygons 2

The Ellipses

The Arcs / Sectors / Segments

End Points & Point on Arc

Centre & Two Ends

Four Corner (Elliptical) Arcs

Parabolic Arcs

Compass Arc

Angle Tools - Marks and Protractors

One Click Angle Marking

Two Click Angle Marking

Angle Mark Size

Angle Mark Options

Marking Angles in Radians

The Protractors

180 Degree Protractor

360 Degree Protractor

Bearings

Shade Regions

Specialized Mathematical Tools

Function Graphs

Statistical Graphs

3D Objects

Normal Distribution Curve

Two Circle Venn

Three Circle Venn

Number Line

Graph Papers

Unit Circle

Tree Diagrams

Clocks

The Galleries

Selecting a Gallery Image

Drawing a Gallery Image

Saving to Galleries

Other Gallery Issues

Preferences

Grid

Other Preferences

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Draw Main Preferences

Measurement System

Default File Location

Gallery Location

Control Point Size

Increase Selection Area

Show Bounding Rectangle

Line Colours

Insert Into Word

Draw Other Preferences

Bitmap Resolutions

Transparent PNG Files

View Zoom

Graph

Axes

Background Rectangle

Sizes

Tick Style

Blank Under Scale

Add Space for Arrows

Expand Grid to Edge

Other

Shade Accept Region

Dot Density

Domain Size

Discontinuity Size

Key Zoom Ratio

Right Click on Axes

Statistics

Axes

Other

Reset All Options

Hints & Tips

How Do I Select Figures?

How Do I Change a Figure's Properties?

What Are Sliders?

What Is The Most Under-utilized FX Draw Feature?

How Do I Change a Figure's Default Properties?

Why Is There an Equation Tool?

How Do I Draw Network Diagrams Easily?

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

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

How Do I Draw Polar Graphs?

How Do I Draw Inverse Graphs?

How Do I Enter Domains?

Can FX Draw Draw Piecewise Defined Functions?

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

What is a Group?

How Do I Group Figures?

How Do I Ungroup Figures?

What Can Groups Be Used For?

What Is A Gallery?

How Do I Use the Galleries?

How Does the Direction of Drawing Affect the Gallery Images?

How Do I Save My Own Graphics To a Gallery?

Can I Edit Gallery Images?

What Is The Grid?

How Can I Remember The Greek Letter Codes?

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Does The Equation Tool Balance Brackets?

Why Are Spaces So Important?

How Do I Enter An Ordered Pair?

How Do I Stop the Equation Tool From Formatting Something?

How Do I Enter A Matrix?

How Do I Enter a Degrees Sign?

3 FX Graph

Using The Graph Tool

4 FX Stat

Using The Statistics Tool

5 FX ChemStruct

How to Enter Structures

Basic Structures

Branched Structures

Benzene Rings

Unformatted Text / Comments

Clicking on Compounds I

Clicking on Compounds II

Rotating and Reflecting

Clearing Clicks, Rotations and Reflections

Isomers

The Arrows

Spaces

R & R'

Nitronium Ion

Entering Phase Information

Overriding Charges

Ionic Compounds

Polyatomic Ions

Ring Structures

Preventing Bonding

Degrees

Display Options

Hiding ?-H Bonds

Displaying Charges

Compounds Without Bonds

Allowing for Unbonded Electron Pairs

Showing All Electrons

Examples

Resonance Structures

Carbohydrates

EDTA

Co(NO3)2 becomes CO(NO3)2!

Changing Your Structures

Font

Equation and Structure Options

My Structure is Not Formatted Correctly!

Part IV Equation Tools

1 Creating, Editing and Using Equations

Efofex Cloud and Equations

Using OLE Equations

Using OLE Equations in Word for WIndows

Adding The Equation Programs (OLE) to Word

Using The Equation Programs (OLE) in Microsoft Word

Why is My Text Red?

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Using OLE Equations In Other Products

Targeting

Setting the Target

Targets

Targeting Office Products

Native Office Equations (OMML)

Getting Equations into Word

Editing Existing Equations

Restrictions

Equations in Apple Pages

2 FX Equation

Entering Equations

Getting Started

Introducing Autoquate

The Calculator

Toolbar Equation Entry

Detect Column Vectors

Equation Tool Reference

International Considerations

Set As Default

Complex Equations

My Equation is Not Formatted Correctly!

Hints & Tips

Does FX Equation Balance Brackets?

Why Are Spaces So Important?

How Do I Enter An Ordered Pair?

How Do I Enter A Matrix?

How Do I Enter a Degrees Sign?

3 FX Chem

Using FX Chem

How to Enter the Equations

The Arrows

Unformatted Text

Nuclear Chemistry

Multiline Equations

Editing Your Equations

Co(NO3)2 becomes CO(NO3)2!

Degrees

Delta H

Neutrinos and Anti-neutrinos

Changing Your Equations

Text Formatting

Other Options

Organic Chemistry

Can FX Chem Balance Equations?

My Equation is Not Formatted Correctly!

A Neat Trick

Part V Appendices

1 A - Equation Tool Reference

Absolute Value

Arcs

Boxes

Combinations & Permutations

Complex Numbers

Composite Functions

Decimals

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Definite Integral Bounds

Degrees

Derivative At A Point

Displaying Units

Dots

Entering Equations

Equation Numbers

Equation Options

Accessing Equation Options

Fonts

Standard Equation Font

Font Modifiers

Vectors

Column Vectors

Automatic Vectors

Lowercase Vectors

Double Capitals

Styles

Multiplication Sign

Raising The Decimal Point

Integrals

Mixed Numerals

Negative Numbers

Units

Matrix

Shortcuts

Fractions

Greatest Integer

Greek Letters

Horizontal Lines

Integrals

International Considerations

Limits

Logarithms

Logic Symbols

Matrices

Means and Complements

Mixed Numerals

Multiplication Sign

Negative Numbers

No Width Spaces

nth Roots

Piecewise Defined Functions

Powers

Predictions

Preventing Formatting

Product Notation

Raising The Decimal Point

Recognized Functions

Recurring Decimals

Scientific Notation

Short Division

Shortcuts

Sigma Notation

Spaces

Square Roots

Subscripts

Symbols

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Text Formatting

Strikeout

The Default Font

Standard Fonts

Brackets

Vector Support

Column Vectors

Automatic Vectors

Lowercase Vectors

Double Capitals

2 B - Statistics Tool Reference

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

The Graph View

Graph Control Buttons

Creating A Graph

Changing Graph Type

Editing Graph Properties/Options

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

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Stacked Frequency Polygon

Histogram

Stacked Histogram

Cumulative Histogram

Stacked Cumulative Histogram

Back-to-Back Histogram

Line Graph

Pie Graph and Divided Bar Graph

Residuals Graph

Scattergraph

Link Graphs

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

Bivariate Data

Time Series Data

Dice

Customizing The Stat Tool

Setting Defaults

System Options

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)

Rand(number)

RandBernoulli(probability,number)

RandBetween(low,high,number)

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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)

3 C - Function Graph Tool Reference

Creating Graphs

Quick Entry Screen

Function Entry

Important Points About Function Entry

Masking Graphs

Graphing in 3D

Entering 3D Functions

Forcing 3D

3D Quick Entry Screen

Standard Axis Alignments

Rotating 3D Axes

Animating Axes

Types of Functions

Overview

Cartesian Functions

"Multiple Armed" Functions

Polar Functions

Inverse Cartesian

Implicitly Defined

Parametric

Point Functions (Cartesian & Polar)

Groups of Points

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Efofex Help XI

Vectors

Smoothed Curves

First Order Differentials

Complex Numbers

Greatest Integer Functions, Sgn Functions and Piecewise Defined Functions

Piecewise Defined Functions

3D Cartesian Functions

3D Polar Functions

3D Points and Vectors

3D Parametric Functions

Function Reference

Points of Interest

Right Clicking

Function Control Toolba2

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

Variables

Inequations & Feasible Regions

Entering Inequations

Inequation Shading 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

Editing Integrals

Approximations To The Integral

Volumes of Solids of Revolution

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

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Efofex Help XII

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

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

Arc / Curve Lengths

Rulers

Part VI Installation

1 System Requirements

2 Installing Efofex Products on Your Computer (Basic)

3 The Preference Interview

4 Installation Notes (Windows)

Administrator Privileges

Integrating Efofex Products into Word (Windows)

Unlocking The Software

Adobe Acrobat

5 Installation Notes (Mac)

Installing the Products

Unlocking The Software

6 Installation Notes For Network Administrators

Internet Access Required

New Registration System

Windows Installations

Silent Installs (Command Line Interface)

Registering Large Numbers of Computers

Using a License Server (Deprecated)

Restricting User Options

Integrating Into Word

Mac Installations

7 Registration Code is Accepted but is Then Immediately "Forgotten"

8 MSI Packages

Part VII Support

1 Support Questions

2 Connectivity Issues

Detecting A Connectivity Issue

Benefits of Allowing A Connection

Unblocking A Connection

Technical Details

Registering Without A Connection

Registering Multiple Windows Computers Without A Connection

Using Efofex Cloud Without A Connection

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3 Some Digital Certificates Have Expired

4 Toolbars Buttons Not Appearing

Toolbar Buttons Not Appearing (All Mac Users)

Toolbar Buttons Not Appearing (Office 2007 and later)

5 Products Not Working

Our Products Reporting That Windows Files Are Missing

6 Cannot Find Efofex ID in Graphic

Word 2011 (Mac)

Word Picture Styles

Simple Graphics In Word (Windows)

7 Do You Have PDF Manuals?

Part VIII Legal Information

1 General Conditions

2 Personal Use Subscription

3 Full Site Licence / Subscription

4 Distribution Licence / Subscription

5 Personal Use Perpetual License (Deprecated)

6 Details

7 Website Terms of Service Agreement

8 Refund Policy

9 Privacy Statement

Index

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Efofex Help About Efofex Software

1

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About Efofex Software

Efofex Software was formed in 1989 to provide software tools for mathematics and science teachers that allowed them to create the graphics that they need to create for their work. We provide tools that allow you to create just about any graphic required by a mathematics teacher as well as high productivity tools for chemistry teachers.

Our products first started as tools to produce graphics for insertion into Word documents that were later printed. As the teaching profession has started embracing technology, our focus has changed to producing graphics for use in just about any context, as well as providing a dynamic mathematical environment that can be used for student investigation and teacher demonstration.

We are a proud Australian company providing high quality software to teachers and students around the world.

Efofex Software

PO Box 189

Claremont WA 6910

Australia

Email:

Voice:

Fax: [email protected]

+61 8 9200 5044

+61 8 9200 5674

Facebook: Efofex Facebook

Instagram: Efofex Instagram

Introducing Efofex Cloud

Efofex Cloud is a new way of using and editing Efofex graphics. This video gives you a quick introduction to the changes we have made.

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© 2017 Efofex Software

Efofex Help Introducing Efofex Cloud 2

Introduc ing Efofex Cloud

In Summary:

The information used to define your graphics is no longer stored in separate files or inside your Word Document. It is stored in a database on your computer.

The contents of the database are automatically backed up to the cloud.

Graphics are automatically downloaded onto any computer you log in to your account.

All graphics are given an invisible ID that can be used to download the information used to create the graphic.

You can use your graphics in any location and edit them later - providing the graphics are not significantly modified by the location.

3 Graphics Tools

3.1

Creating, Editing and Using Graphics

The main aim of our products is to produce graphics that can be inserted into other documents and platforms. Things like word-processors, presentation tools and websites.

The problem with this is that it creates a separation between the graphic (the "picture") and the data that has been used to create the graphic, and might be needed later on to allow you to edit the graphic.

In the early days of Efofex products the main game in town was inserting graphics into

Word documents on Windows computers and our products evolved to address this need.

Luckily, Word for Windows has a technology designed specifically to allow you to include the data for the graphic inside the document itself. It is a very neat technology (officially called OLE) and is (mostly) very user friendly. Unfortunately, it does come with a number of major problems:

It is only useful on Windows.

It only works properly on Microsoft products (and not even all of them!)

© 2017 Efofex Software

Efofex Help Graphics Tools

It is "fragile" and might stop working at any time.

It requires modifications to your copy of Word to allow it to work efficiently.

The new Efofex Cloud versions of our programs allow you to keep using the old OLE system if you wish, but introduces a totally new way of using the graphics products that is much more powerful and useful.

It works on any platform (Mac and Windows, Google Docs, Moodle - in fact just about anywhere you might want graphics)

It is robust

Your data is automatically backed up to the cloud and synced with any computers you use.

No integration with Word (or any other program) is necessary.

For those of you who have been using our "Connections" system on a Mac computer - it is much the same process, with all of the kinks and inconveniences worked out.

If you are using OLE, we STRONGLY recommend that you move over to using the Efofex Cloud system.

Efofex Cloud completely replaces the Connections system that we introduced with our Mac versions

Using Efofex Cloud

Using the Deprecated OLE System

3.1.1

Using Efofex Cloud

The basic process for creating a graphic using Efofex Cloud enabled versions of our products is simple.

Start the program from the Start menu/task bar or dock (NOT from inside Word).

Create a graphic

Press the green check-mark button

Paste it into your desired location

Editing a graphic is also simple.

Copy the graphic you want to edit to the clipboard.

Switch to the drawing program (eg. FX Draw).

FX Draw will automatically find and load the data that goes with the graphic so you can edit it.

When you have finished, press the green check-mark button.

Paste the new version into your desired location.

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Take a quick look at this video which shows the basic processes in action.

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3.1.1.1

Usernames

When you first use one of the graphics programs, you may be asked for a username.

You will be asked for a username if you are using a Full Site or Distribution license. The username does NOT have to be unique and your initials will usually be a suitable choice.

You should use the same user name on every computer you use.

The username is used to divide up graphics created under the same license. If we did not have usernames, all graphics created under one license would be copied to all computers.

This might mean that your computer is storing images created by dozens or even hundreds of other users. This creates a lot of unnecessary movement of information and

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storage of data.

If you use the same username on every computer you use, all of your graphics will be automatically synced between all of the computers. This makes moving your documents and graphics between computers trivial.

3.1.1.2

Private Or Public

Every graphic you create can be public or private. You can set a graphic to be public or private using this button.

5

You can also set a graphic's public/private setting in the graphic properties screen.

By default, all graphics are public. This means that ANYONE with a copy of the graphic will be able to make a copy of the data and edit it for themselves (note that NO ONE can

EVER edit YOUR copy of a graphic, regardless of this setting). This is not as permissive as it might first seem and is actually very similar to the old OLE graphics which always had the data embedded in them. Do not be afraid of making a graphic public!

If you make a graphic private, only your license will be able to edit it. This means that you, or any colleagues using the same license, can edit it. Other license holders will be told that the graphic has been marked as private.

3.1.1.3

Editing Someone Else's Graphic

Editing someone else's graphic is almost identical to editing your own. You copy the graphic to the clipboard and switch to the Efofex program. If the graphic has an ID, the program will first search for the data in the local database. As this will be someone else's graphic, the data will not be held locally and your computer will send a request to our servers to see if the data can be found in the cloud. If the data exists, our servers will send it back.

This all takes a little time so loading the graphic will be slower. The Efofex product will make sure that you are kept up to date with progress.

Once you have edited the graphic, a new ID will be created and the new graphic becomes

"yours". The data will be stored locally and all future loading will be much faster.

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3.1.1.4

Can Someone Else Mess Up My Graphic?

No.

Never.

In fact not even you can mess up a graphic as every version of the graphic has its own ID.

This is because Editing Creates a New Graphic. This means that no one can ever mess up your data.

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3.1.1.5

History

Every Efofex product now has a history of the last three months of your graphics. Every time you create or edit a graphic, it will be recorded in the history. This makes it easy to go back to an earlier version of a graphic or find that perfect graphic that you created a few weeks ago.

You access the graphic history screen by pushing this button.

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Double click on the desired graphic to open it

3.1.1.6

Graphics Properties

All graphics have extra properties that can be accessed using the graphic properties button.

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The graphic properties screen allows you to turn off public sharing of the graphic. You can also add a topic description and a link. Topic descriptions are currently supported but have no function within the software (we do have plans for this in the future). Links are a more important addition.

If you put a valid web link into the Link box, the program will show an extra button.

Pushing this button will load the web page that the link points to.

We will be using the link to provide videos on how to draw the diagram in the graphic. You might use them to link to source data or a description of problem you are solving. The uses are endless.

3.1.1.7

The Invisible ID

We keep saying that every graphic has an "Invisible ID" but you might be asking what the

ID is and what it looks like.

The products will show you the ID sometimes. For example, when a graphic is first loaded, its ID will be shown for a short period of time.

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It is also shown in the History screen if you hover over a graphic.

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Normally you will never have to deal with these ID's but they are how Efofex keeps track of each individual graphic.

The ID's are encoded into an almost invisible set of colors that are added to edge of images. These colors are not visible on most screens and printers will not print them. They are basically invisible. In this example we have made the colors visible so you can see what is going on.

When a graphic is loaded into an Efofex product, it finds these colors and decodes them back to an ID which it then uses to find the data behind the graphic. The ID's are encoded four times, once along each edge, which makes the system extremely robust.

3.1.1.8

Potential Problems

It is possible that the invisible ID can be stripped from a graphic. This can happen in one of three ways.

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1.

2.

3.

The graphic is cropped so that the ID is removed.

The graphic is modified so that the ID's are damaged.

The image is compressed which will remove the ID.

In the vast majority of cases the graphic is returned to our products intact and these issues do not occur.

3.1.2

Using the Deprecated OLE System

Efofex has used OLE for over 25 years and it is very popular with users (despite the issues that can occur). If you decide to continue using the OLE system, any graphics you create with Efofex Cloud versions of our products will be tagged with and ID and have their data saved to the database automatically. This will greatly assist any later change to using the full Efofex Cloud system.

3.1.2.1

Using OLE Graphics in Word for WIndows

3.1.2.1.1 Adding The Graphics Programs (OLE) to Word

The most efficient way to use the OLE graphics in Word (Windows only) is to integrate the products with Word. This adds an Efofex toolbar to your Word ribbon that makes inserting new graphics easy.

To integrate with Word, start one of the graphics programs and then go to the Help menu.

Select Integrate Efofex Products into Word. Integration is automatic.

You will need to restart Word and you will then see a new Efofex tab on your ribbon bar.

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The buttons insert a new graphic into your document.

3.1.2.1.2 Using The Graphics Programs (OLE) in Microsoft Word

Creating a Graphic

· Push the appropriate toolbar button

·

· Generate your graphic.

Click the Green tick

When you insert a graphic object into your document, the selected graphics program will start and you can use it in the same way you use it 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 structure, push the appropriate button to return to

Word.

Editing

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To edit an existing graphic, double click on the graphic in your Word document.

3.1.2.2

Using OLE Graphics In Other Products

Quite a few products support OLE graphics. To insert an OLE graphic into your program, look for the "Insert Object" option and insert an FX Draw, FX Graph, FX Stat or FX

ChemStruct object.

Support for OLE is patchy and often changes between versions of software. We cannot guarantee that any particular usage you make of OLE graphics will be supported in future versions of the software you insert the graphics into.

3.1.3

Moving From OLE To Efofex Cloud

3.1.3.1

Should I Change?

Yes.

OLE is old, buggy and Microsoft might decide to cease support at any time. Moving from

OLE to Efofex Cloud is an investment in the future. There is almost no downside to Efofex

Cloud. It is different to OLE but basically achieves the same result.

Having said that, OLE will be familiar to many people and we are certain that many will choose to keep on using it. If your workload is largely restricted to using our products in

Word, on a Windows machine then this makes sense. For ANYBODY else, moving to Efofex

Cloud is the only practical choice.

Efofex Cloud products are designed to make the transition away from OLE as easy as possible, whether you choose to do it now or some time in the future. Every time you edit an OLE graphic, Efofex Cloud will tag the new image with an ID and save its data to the database. This is all invisible to the user, but will make transitioning to Efofex Cloud trivial in the future.

3.1.3.2

Converting One Image

To move one image to Efofex Cloud, just edit it by double-clicking on it and then press the green check mark. This will create a new image which has an embedded ID and the image's data will be automatically added to the database. This means that you, or anyone else, will be able to edit the image later on without using OLE.

3.1.3.3

Converting All Images In a Document

The Windows versions of our products have the capability to extract each OLE image in a document and replace the image with an image tagged with an ID. This process is automatic.

1.

Open the document you wish to convert in Word.

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2.

3.

Open the Efofex product (usually FX Draw).

Choose Convert OLE Graphics in Word Document

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FX Draw will automatically convert all OLE graphics in the currently active Word document.

WARNING: This process can be slow for documents with lots of graphics

The new graphics are still OLE objects but now have an ID and an entry in the database.

This means that anyone can edit the graphic, on any platform.

3.1.3.4

Converting All Images In a Folder

The Windows versions of our products have the capability to extract each OLE image in a folder of Word documents and replace the images with images tagged with an ID. This process is automatic.

1.

2.

Open the Efofex product (usually FX Draw).

Choose Convert OLE Graphics in A Folder

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FX Draw will automatically convert all OLE graphics in any Word documents in the selected folder.

WARNING: This process can be extremely slow for documents with lots of graphics or large numbers of documents. The number of documents that can be converted in one action is limited to 100.

The new graphics are still OLE objects but now have an ID and an entry in the database.

This means that anyone can edit the graphic, on any platform.

3.1.4

Moving From Connections to Efofex Cloud

3.1.4.1

Should I Change?

Yes. Connections are no longer supported. The Efofex Cloud system is SIMILAR to

Connections but is far superior to the older system.

3.1.4.2

Converting All Images In a Document

The two biggest problems with the Connections system were:

1.

You had a second data file that you needed to keep with your document. This created a management issue if the two files became separated.

2.

The system could not always match an image with its data.

These two flaws also conspire to make moving from Connections to Efofex Cloud a little more difficult.

The only way to move systems is to:

1.

Open the data file in the Efofex product. This will automatically load all of the images and save them to the database.

2.

You need to replace each image in your document with a new image generated in the Efofex product. This is to ensure that the images have an ID that Efofex Cloud can use later on.

3.2

FX Draw

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 provides a quick and easy solution to your diagramming needs.

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FX Draw lets you draw images like this (as a tiny example of its capabilities) and much more, quickly and easily.

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3.2.1

Basic FX Draw Concepts

3.2.1.1

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.

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

3.2.1.2

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 remember that you must hold down the mouse button to draw.

3.2.1.3

A First Look

FX Draw is a comprehensive mathematical drawing package so it is not surprising that the

FX Draw screen is fairly complex.

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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.

3.2.1.4

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. Tools with other tools

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hiding behind them have a little down arrow next to the tool.

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To access the extra tools, click on the down arrow

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

and I can now draw rulers on the drawing canvas.

3.2.1.5

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

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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.

For example.

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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.

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

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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 pass 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.

3.2.1.6

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.

3.2.1.7

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.

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To overcome these problems, FX Draw has four levels of GAD available.

No GAD FX Draw uses the mouse position for all actions

Grid Only

Limited GAD

(Default)

"Infinite"

GAD

FX Draw draws everything to the underlying grid with no geometric analysis.

FX Draw determines geometrically important points and relationships but as the number of figures increases, the 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.

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

The GAD level is selected using the GAD toolbar

3.2.1.8

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.

3.2.1.9

GAD Links

3.2.1.9.1 What are GAD Links?

Your first contact 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.

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The colours represent relationships that the user 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.

3.2.1.9.2 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.

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!

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

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.

figure

You can also break ALL of the links for a figure without moving it at all. Select the and press the Break GAD Links button

This will break any GAD links for all selected figures.

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3.2.1.10 Figure Information

FX Draw 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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3.2.1.11 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.

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

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adding an annotation or editing the properties.

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

3.2.1.12 Editing Annotations

Editing annotations is just like editing any other figure in FX Draw - you right click on them.

The Annotation toolbar will pop up.

The Annotation Text 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 can be seen by pushing the Parameters button.

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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.

In this area you can also control background colors for the annotation rectangle as well as the style of anchor lines and rectangle borders.

Annotation text is interpreted using our FX Autoquate technology and editing annotations is similar to our normal text boxes.

Move with Point controls whether the annotation moves when the point it is attached to moves. Usually it is turned on so the annotation follows things around the screen.

Sometimes, particularly when animating graphs, the annotation will jump around the screen as the point moves. Turning this option off allows you to lock the annotation in one place.

3.2.1.13 The Toolbars

3.2.1.13.1 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.

3.2.1.13.2 Isometric Grid Button

Pushing the Isometric Grid button has three effects:

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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.

3.2.1.13.3 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.

3.2.1.13.4 Zoom Toolbar

Autopoint O n

Autopoint O ff

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

3.2.1.13.5 Line Type Toolbar

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

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 supported units (cm, mm, pt and ")

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The final button allows you to choose the color 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.

3.2.1.13.6 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. Note that the light grey/white checkerboard pattern is used to represent No Shading or Transparent.

You can select a figure's fill colour by pushing the colour button.

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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3.2.1.13.7 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).

No GAD

Grid Only

FX Draw uses the mouse position for all actions

FX Draw draws everything to the underlying grid with no geometric analysis.

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Limited GAD

(Default)

"Infinite"

GAD

FX Draw determines geometrically important points and relationships but as the number of figures increases, the 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.

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

3.2.1.13.8 Break GAD Links Button

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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 maintain its dependencies.

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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.

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.

3.2.1.13.9 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.

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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.

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 remember 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.

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3.2.1.13.10 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.

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3.2.1.13.11 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.

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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.

3.2.1.13.12 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.

3.2.1.13.13 Reflection Toolbar

Allows you to reflect the currently selected figures.

3.2.1.13.14 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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3.2.1.14 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.

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For example, the diagram above shows a circle defined by three control points. By moving the points, the circle will be redrawn to pass 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?

3.2.1.15 Manipulating Figures

3.2.1.15.1 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.

3.2.1.15.2 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.

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Holding down Ctrl and an arrow key will move figures 1 mm.

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

3.2.1.15.3 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.

3.2.1.15.4 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

Ctrl + Pg Dn

Shift + Ctrl + Pg Up

Shift + Ctrl + Pg Dn

Rotates 15° anti-clockwise

Rotates 15° clockwise

Rotates 1° anti-clockwise

Rotates 1° clockwise

Rotating figures with the mouse

When you select figures, you will usually see a rotate point.

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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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3.2.1.16 Sliders

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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.

3.2.1.17 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.

3.2.1.18 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.

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

3.2.1.19 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.

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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

3.2.1.20 Font Management

Most objects in an FX Draw diagram contain some sort of text and every object can have its text rendered in its own font. While this provides enormous flexibility, it does mean that fonts are adjusted (and set as defaults) in many different locations. This can make managing your fonts difficult, particularly if you wish to change the fonts of a large number of objects.

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FX Draw provides you with two tools that make the process of managing your fonts much easier

Changing The Font For All Selected Objects

Changing All Default Fonts

3.2.1.20.1 Changing The Font For All Selected Objects

You can change the font for any selected objects using the Edit menu.

Select the objects you wish to change.

Choose "Change Font Of Selected Objects..." from the Edit menu.

Use the window to select a new font.

Using the tool in this mode allows you set a common font family for all items (for example,

I might want everything to be in Times New Roman) without affecting the size of the fonts. You might like to use this to keep titles large and angle marks small, but change the font.

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If you also want to change the font size for all selected objects, place a check mark in the

Modify Font Size box and select the font size you wish to use. This new font will be applied to ALL text in the selected objects, including things like titles of graphs. This is not always what you will want to do.

3.2.1.20.2 Changing All Default Fonts

You can change all of the default fonts for all available objects in one place. This will not change the font of any existing objects, only new objects created from the defaults.

Changing the default fonts allows you to easily standardise on one font for all of your diagrams.

Go to the Tools menu and choose Change All Default Fonts...

Use the window to select a new font.

Using the tool in this mode allows you set a common default font family for all items (for example, I might want everything to be in Times New Roman) without affecting the size of the fonts. You might like to use this to keep titles large and angle marks small, but change the font.

If you also want to change the font size for all default fonts, place a check mark in the

Modify Font Size box and select the font size you wish to use. This new font will be applied to ALL text in the objects, including things like titles of graphs. This is not always what you will want to do.

3.2.1.21 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.

3.2.1.22 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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3.2.1.23 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)

3.2.1.24 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.

3.2.1.25 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.

3.2.1.26 Keyboard Shortcuts

Keyboard shortcuts can make using FX Draw a quicker experience.

Overriding GAD

Shift grid.

Ctrl

Alt

Ignores Geometrically Important Points and instead jumps to the

Ignores grid and any Geometrically Important Points.

Ignores grid and jumps to any Geometrically Important Points.

Returning to Word

Ctrl + R Returns to Word and updates diagram.

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Editing

Ctrl + A

Ctrl + X

Ctrl + C

Ctrl + V

Ctrl + D

Ctrl + Z

Ctrl + Y

Selects all figures.

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 Rotates selected figures 15° anti-clockwise

Ctrl + Pg Dn Rotates selected figures 15° clockwise

Shift + Ctrl + Pg Up Rotates selected figures 1° anti-clockwise

Shift + Ctrl + Pg Dn 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

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diagrams, graphs, grids etc) can be forced to a square by holding the Shift key when creating them.

3.2.1.27 Exporting to Graphics Files

FX Draw can save its images to a variety of graphics formats.

1. Draw your diagram

2. Choose File / Save As from the menus

3. Select whether you want your graphic saved as a SVG file, JPG file, PNG file, TIF file or a BMP file (see below)

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3.2.1.27.1 What Formats are Offered?

FX Draw can create PNG, TIF, JPG, SVG and BMP format bitmaps. You should normally use the PNG or SVG format. BMP and TIF bitmaps are very large and should only be used if a third party product you need cannot handle PNG style bitmaps. JPG files are best suited to photographs and tend to not produce good results with line drawings.

3.2.2

Tools

3.2.2.1

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 remember 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.

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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.

3.2.2.2

The Lines

Why so many lines??

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.

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You have a choice of twenty-one 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/equations to the line. You can angle the text.

When set to Automatic, FX Draw will use AutoQuate technology to automatically detect equations.

This can be used to good effect when drawing networks or to indicate measurements.

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See

Entering Equations on how to enter equations into FX Draw.

All lines have these options.

Available Parameters for Lines

$start

$stop

$length

$angle

$mid

- start point

- stop point

- midpoint

3.2.2.2.1 Line Defined By End Points

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

3.2.2.2.2 Line Defined By Mid Point and End Point

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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.

3.2.2.2.3 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.

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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.

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.

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

Click again and your ray will appear.

If we select the ray you will see three selection squares.

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3.2.2.2.4 Line Defined By Four Points (Extended Line)

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The extended line allows you to draw a line where the end points of the line are independent of the points defining the direction of a line. For example, if you wish to draw the cotangent of two circles but want the cotangent to extend beyond the circles.

1.

Select the tool,

2.

Draw the line joining the two tangent points just as if you were using the simple

"line defined by end points" tool. This process will determine the direction of the line but we are not finished yet. Next we have to tell FX Draw where to stop and start the line.

3.

Move the mouse to one end of the line you want to draw and click. Then move to the other end of the line and click.

The line will be created with four control points. The two red control points (1) are fixed to the cotangent points and define the direction of the line. The two amber control points (2)

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define the ends of the line. These control points are amber because they are locked onto the line defined by the first two points.

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3.2.2.2.5 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.

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

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3.2.2.2.6 Line Defined By Start Point, Length and Angle

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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.

3.2.2.2.7 Drawing Lines Using Defaults

All FX Draw objects have default settings that you can use to make drawing standard objects easy. For example, when drawing graphs, you can set a default font size on the axes. When drawing rounded rectangles, you can set a default radius for the corners.

Defaults save you time and all objects use their defaults when you first create them.

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Lines have defaults that can be set and setting defaults for lines can be extremely useful.

For example, if you are drawing network diagrams, you can set the default line to be something like this.

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To set the default, draw a line and right click on it. Set the ends to open circles and press

Set As Default

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FX Draw also offers a number of pre-set default lines that you can use to make this process simpler and quicker. Simply select one of the pre-sets from the list and the current default line is automatically set for you.

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Now every line I draw will have open circles at each end and drawing network diagrams will be simple - at least that is how every OTHER FX Draw object works.

Lines are different.

Lines don't use their defaults unless you specifically tell them to.

The reason for this is that much of the time, you will not want to use the line defaults, you will just want to draw simple lines. Always using the defaults just gets in the way.

To work around this problem, using defaults for lines is toggled by the user. To use defaults, select Use Defaults (D) from the line tools.

Any lines drawn now will use the current defaults. You can turn this off by repeating the process. Alternatively, you can turn line defaults on and off at any time using the D key.

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3.2.2.2.8 Adding Regularly Spaced Points To Lines

You can divide any line by adding dividing points to the line.

First select the line, then right click on it and choose Add Dividing Points...

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Now enter how many parts you wish to divide the line into. You can also choose to add points to the ends of the line.

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The points are attached to the line and will move with it.

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You can also delete the line and the equally spaced points will remain on the canvas.

3.2.2.3

Ruler

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

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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.

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.

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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.

3.2.2.4

Dimensions

The Dimension tool allows you to easily add dimensions to any figure.

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Adding a dimension is a bit like drawing a line but with one extra step.

1.

2.

Select the Dimension tool

Use the tool to "draw a line" along the edge you wish to measure. You will see the dimension arrows as you draw.

3.

Once you have drawn along the edge, the dimension line will move with mouse so you can adjust how far the dimension line sits from the edge. Once you are happy, click again and the dimension will be added.

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By default, the dimension will show the actual measurement of the edge but this can be easily changed. To change a dimension, right click on it.

This screen allows you control how the dimension appears but also allows you to control what text is shown on the dimension. There are two ways of changing the text on the dimension.

1.

You can choose to enter your own text on the line. Change this setting to Show

Text and type whatever you wish to show. You can also decide whether your text is interpreted as plain text or as an equation.

2.

You can enter a global scaling factor which will affect ALL dimensions on the canvas. For example, if you change the scale to 1:250 and change the units to metres, ALL the dimensions in the diagram are scaled.

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3.2.2.5

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

3.2.2.5.1 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

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circle could extend beyond the bounds of the drawing area. If this occurs, FX Draw will draw as much of the circle as possible.

3.2.2.5.2 Diameter Circle

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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.

3.2.2.5.3 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.

3.2.2.5.4 Circle in a Square

The four corner circle will draw a circle inscribed in a square region defined by four control points.

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.

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3.2.2.5.5 Compass Circle

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When you use a compass 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 about using a compass is that with a compass you can keep the same radius to draw more circles.

That is what the Compass Circle tool does. It is a Centre/Radius circle that remembers the radius.

The first time you use the compass 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 compass circle tool remembers the radius and marks the circle.

The compass circle tool will remember the radius for as long as it is selected.

You can force the compass circle tool to reset its radius by: a) b)

Selecting another tool and then reselecting the compass circle tool.

Right clicking on a blank part of the drawing canvas.

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3.2.2.6

The Quadrilaterals

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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.

3.2.2.6.1 Rectangle

Right-clicking on one of the sides of a rectangle will allow you to add arrowheads to the middle of the edge. You can also direct the rectangle to divide itself into columns and rows.

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Available Parameters for Rectangles

$height

$width

$perimeter

$area

3.2.2.6.2 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 edge. You can also direct the rectangle to divide itself into columns and rows.

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Available Parameters for Rectangles

$height

$width

$perimeter

$area

3.2.2.6.3 Parallelogram

Graphics Tools 76

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.

3.2.2.6.4 Rhombus

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

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3.2.2.6.5 Kite 1 and Kite 2

The two kite tools provide two slightly different ways of drawing kites.

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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.

3.2.2.6.6 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.

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3.2.2.6.7 Rounded Rectangle

Graphics Tools 80

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

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$perimeter

$area

$radius

3.2.2.6.8 Bitmap Tool

Graphics Tools 81

The bitmap tool allows you to place any bitmap into an FX Draw diagram - but you have to supply the bitmap.

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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3.

Select a file and click on Open

Available Parameters for Bitmaps

$height

$width

$xpixels

$ypixels

- width of original bitmap in pixels

- height of original bitmap in pixels

3.2.2.7

Text/Equation Boxes

3.2.2.7.1 Basic Usage

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1.

2.

3.

Select the Automatic Text/Equation Box tool

Click on the drawing canvas where you want the text box to appear.

Start typing!

As soon as you have clicked, the text toolbar will appear at the bottom of the screen. This is where you enter and edit the text you want.

3.2.2.7.2 Text Formatting

The Text toolbar contains basic formatting controls that are similar to those in most word processors.

Select some text and use the controls to change text size, color and formatting.

3.2.2.7.3 Introducing FX Autoquate

You may have noticed something special about our first example - FX Draw had done something special with some of the text we typed.

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We call this new technology "FX Autoquate" - a system which looks at what you have typed and automatically finds the bits which should be formatted as equations (using our traditional FX Equation technology). YOU don't have to do anything except type! This new feature can massively improve your productivity when typing mathematics.

FX Autoquate is pretty good and will almost always find the bits that need to be automatically made into equations. Sometimes you will want to override its suggestions.

You can do this by removing the check mark from the Auto box. Once this is removed, you can manually mark which bits of your typing you want interpreted as an equation.

3.2.2.7.4 Manually Marking Equations

When you turn off FX Autoquate, you need to manually mark sections of your text as equations. You do this by marking the text and pressing the 1/x button.

You should notice that Auto is off and the 1/x button is depressed. In the text entry section, the word "equation" has been underlined which is how FX Draw shows you that it is going to interpret that section as an equation. Your should also notice that, on the canvas, the word "equation" has been rather strangely formatted (including replacing io with the Greek letter io).

Manually marking the equations allows you to produce just about anything.

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3.2.2.7.5 Plain Text Boxes

Graphics Tools 85

If you know that what you are about to type definitely should be interpreted as plain text, choose a Text box rather than an automatic text box. What you get is exactly the same, it is just that Auto is turned off and the 1/x button has not been pushed.

This can be particularly useful if you want to type an ordered pair and FX Autoquate keeps turning them into column vectors.

Plain Text boxes can also be useful if FX Autoquate is consistently misinterpreting something you are often typing. PLEASE TELL US if this occurs. We are always looking to improve the accuracy of FX Autoquate!

3.2.2.7.6 Equation Boxes

If you know that what you are about to type definitely should be interpreted as an equation, choose an Equation box rather than an automatic text box. What you get is exactly the same, it is just that Auto is turned off and the 1/x button has been pushed so anything you type will definitely be interpreted as an equation.

A full discussion on how to enter equations using the equation tool is available in

Entering Equations

.

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3.2.2.7.7 Equation Toolbar

FX Equation 4 has long had a toolbar to make entering some of the more esoteric equations a bit easier. FX Draw 5 now provides you with the same functionality.

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Each button provides you with access to FX Equation features. You never HAVE to use the buttons. All equations can be entered solely using the keyboard as discussed in

Entering

Equations

Enters a degree sign

Allows entry of most mathematical symbols.

Allows entry of lower case Greek letters.

Allow entry of upper case Greek letters.

Allows the creation of many mathematical expressions. Usually the current selection is affected.

Allow for the creation of more complicated mathematical constructs such as limits, integrals and summation.

Allows you to create numbers in circles which are useful for simultaneous equations

Matrices Vectors and Piecewise defined functions

Options

Change the equation options. The equation options are discussed in

Equation

3.2.2.8

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.

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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.

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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.

3.2.2.9

Smooth Lines

3.2.2.9.1 Smoothed Line

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

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.

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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

3.2.2.9.2 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.

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

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3.2.2.10 Triangles, Polygons and Smoothed Lines

3.2.2.10.1 Triangles

Graphics Tools 90

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

$b

$c

$sa

$sb

$sc

Altitudes

Angle sizes

Side lengths

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3.2.2.10.2 Isosceles Triangles 1 & 2

The isosceles triangles tools provide slightly different ways of drawing isosceles triangles.

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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.

3.2.2.10.3 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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3.2.2.10.4 Right Triangles 1 & 2

The right triangles tools provide slightly different ways of drawing right triangles.

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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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3.2.2.10.5 Polygons

Graphics Tools 94

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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3.2.2.10.6 Regular Polygons 1

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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

3.2.2.10.7 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

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$sides

$sidelen

$perimeter

$area

$anglesum side length

3.2.2.11 The Ellipses

Graphics Tools 98

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.

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.

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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.

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

- length of major axis

- length of minor axis

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3.2.2.12 The Arcs / Sectors / Segments

Graphics Tools 100

FX Draw provides 4 arc tools - end points and point on the arc; centre and end points, four corner (elliptical) arcs and compass 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.

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.

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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 of curvature $centre

$start

$stop

$radius

$length

$sector

$segment

$angle

- area of sector defined by arc

- area of segment defined by arc

- central angle

Available Parameters for Elliptical Arcs

- centre of curvature $centre

$start

$stop

$length

$minoraxis

$majoraxis

$angle

$eccentricity

- length of minor axis

- length of major axis

- central angle

3.2.2.12.1 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.

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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.

3.2.2.12.2 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.

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.

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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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3.2.2.12.3 Four Corner (Elliptical) Arcs

Graphics Tools 104

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.

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.

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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.

3.2.2.12.4 Parabolic Arcs

The parabolic arc tool draws a parabolic arc which is part of a parabola with a vertical axis.

The three points define the two end points and a point on the parabolic 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.

3.2.2.12.5 Compass Arc

When you use a compass to draw an arc, you place the point on the centre, set the radius and draw - just like the centre/end points arc tool.

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The thing that IS different about using a compass is that with a compass you can keep the same radius to draw more arcs.

That is what the Compass Arc tool does. It is a Centre/End Points circle that remembers the radius.

The first time you use the compass 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 compass arc tool remembers the radius and marks the circle so you can set the end points.

The compass arc tool will remember the radius for as long as it is selected.

You can force the compass arc tool to reset its radius by: a) b)

Selecting another tool and then reselecting the compass arc tool.

Right clicking on a blank part of the drawing canvas.

3.2.2.13 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 or radians, 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.

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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.

3.2.2.13.1 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.

3.2.2.13.2 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.

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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.

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.

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3.2.2.13.3 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.

3.2.2.13.4 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.

3.2.2.13.5 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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3.2.2.14 The Protractors

3.2.2.14.1 180 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.

3.2.2.14.2 360 Degree Protractor

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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 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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3.2.2.15 Bearings

Graphics Tools 115

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.

3.2.2.16 Shade Regions

Shading regions is a great new addition to FX Draw's tool set but you need to remember 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

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

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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

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.

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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.

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.

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3.2.2.17 Specialized Mathematical Tools

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3.2.2.17.1 Function Graphs

The graph tool allows you to draw graphs of Cartesian, polar, parametric, implicitly defined and inverse functions.

FX Draw shares the graphing tool with FX Graph and a full discussion on how to use it is included in

Quick Entry Screen

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

$area

- definition of integral function

- area of definite integral

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$upper - upper bound of integral

$lower - lower bound of integral

when annotating a tangent line

$slope

$equation

- gradient of tangent line

- definition of derivative function

$tangentline - equation of tangent line

$at - point at which tangent line touches function

$intercept - y intercept of tangent line

3.2.2.17.2 Statistical Graphs

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The statistics tool allows you to draw a comprehensive selection of statistical graphs as well as providing a statistical environment that you can use to perform statistical analysis.

FX Draw shares the statistics tool with FX Stat and a full discussion on how to use it is included in

The Three Views

3.2.2.17.3 3D Objects

FX Draw can draw 3D objects which can be rotated on screen. These are not flat shapes, but full 3D representations of objects.

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Select the 3D object tool and then sweep out a rectangle. FX Draw will draw the current

3D object inside the rectangle.

Rotating The Object With the Mouse

Click inside the rectangle and move the mouse whilst holding down the left mouse button.

The 3D object will move with the mouse

Rotating The Object With the Keyboard

Your 3D object can be rotated using the keyboard.

X and Shift X rotate the object around the x Axis

Y and Shift Y rotate the object around the y Axis

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Z and Shift Z rotate the object around the z Axis

Resetting the Axes

The arrow keys will align the object with some predefined projections. The arrow keys by themselves use isometric projections. The arrow keys combined with the Shift key will use oblique projections.

Changing the Object

Right click on the image and select a new object from available objects.

Rendering the Object

FX Draw can render objects using four different styles. You can also turn off hidden lines.

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Colouring One Face

You can select one face using the mouse and change its colour individually.

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3.2.2.17.4 Normal Distribution Curve

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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.

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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.

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 - area (probability) below lower bound

$between - area (probability) between upper and lower bounds

$above - area (probability) above upper bound

$low - lower bound

$high - upper bound

3.2.2.17.5 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.

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3.2.2.17.6 Three Circle Venn

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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.

3.2.2.17.7 Number Line

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 terms 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.

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-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.

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Use Brackets allows you to use parentheses and square brackets instead of open and closed circles.

Available Parameters in Number Line

$f1

$f2

$f3

3.2.2.17.8 Graph Papers

- definition of function 1

- definition of function 2

- definition of function 3

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.

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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.

3.2.2.17.9 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 or by explicitly entering the angle in the screen above.

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Important Points

The unit circle can show positive or negative angles. To get a negative angle, or an angle greater than 360 degrees, explicitly set the angle or use the keyboard commands.

Angles set by moving the control point with the mouse will always be between 0 and

360 degrees.

Explicit angles in radians can be entered in terms of pi. For example, type 3pi/4.

Angles greater than 360 degrees will be show with an arc with multiple rotations.

Keyboard Commands

For demonstration purposes, 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

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$angle

$degrees

$radians

$sin

$cos

$tan

$cot

3.2.2.17.10 Tree Diagrams

Graphics Tools

Angle expressed as the current angle type (degrees or radians)

Angle in degrees

Angle in radians. Angle will be show as a multiple of pi if possible.

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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.

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

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breaks into four branches.

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The only limits imposed on your tree are that a level must have no more than 30 branches. Just remember 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.

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.

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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 dramatically

- especially if the text is formatted as equations.

3.2.2.17.11 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.

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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.

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 12:10 5:14.20

18,12.45

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3.2.2.18 The Galleries

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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.

3.2.2.18.1 Selecting a Gallery Image

When you push the right button to select an image, you will see something like this screen.

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.

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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.

3.2.2.18.2 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 been drawn has been indicated on each shape.

This ability to be resized makes each gallery figure extremely powerful.

Gallery images remember 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

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be forced to maintain this aspect ratio.

3.2.2.18.3 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). You will only be able to save to a user created gallery. Factory galleries are locked. You can modify factory galleries by copying them to the user gallery location.

The selected objects will be placed into the gallery you select from the list of available

User galleries. User created galleries always have a "User - " prefix.

3.2.2.18.4 Other Gallery Issues

If you select a User Created Gallery, you have some other options. These allow you to delete and move figures in the gallery. You can also edit the Gallery Title and descriptions.

These extra options are NOT available when selecting from a factory created gallery.

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3.2.3

Preferences

FX Draw preferences allow you to customise FX Draw to account for local differences in mathematics. All preferences are set from the Tools menu.

3.2.3.1

Grid

Grid preferences control the background grid - the light grid behind your diagrams. Grids can make drawing many images much simpler.

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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.

3.2.3.2

Other 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.

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3.2.3.2.1 Draw Main Preferences

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3.2.3.2.1.1 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.

3.2.3.2.1.2 Default File Location

ADVANCED

This field is mostly used in network situations. FX Draw will attempt to save diagrams into this location.

3.2.3.2.1.3 Gallery Location

ADVANCED

This field is mostly used in network situations. FX Draw will search for galleries in this directory.

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3.2.3.2.1.4 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.

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3.2.3.2.1.5 Increase Selection Area

If you are having trouble selecting objects, this option increases the size of the area you can click.

3.2.3.2.1.6 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.

3.2.3.2.1.7 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.

3.2.3.2.1.8 Insert Into Word

This setting helps control how OLE objects are inserted into Word. MOST users will want to leave it set to Wrap Text. Normally this setting should only be changed under instruction from Efofex.

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3.2.3.2.2 Draw Other Preferences

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3.2.3.2.2.1 Bitmap Resolutions

FX Draw 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.

3.2.3.2.2.2 Transparent PNG Files

Transparent PNG 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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3.2.3.2.2.3 View Zoom

This is an "underlying" zoom that is applied over the entire FX Draw system. It is independent of the zoom you see on the top toolbar. Most people find that by setting this to about 150%, they produce diagrams the "right" size when they are returned to

Word.

3.2.3.2.3 Graph

3.2.3.2.3.1 Axes

The Graph Axes screen lets you modify the axes style for function graphs. Statistics graphs can have separate settings.

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Graphs can have a shaded background rectangle. Check the Fill Background option and select your colour.

All sizes are in mm and control different aspects of the axes

This preference controls how the ticks are drawn on the axes. The various options are best shown in a diagram.

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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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 Spac e for Arrows O N Allow Spac e for Arrows O FF

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Allows you to select between two different types of grids.

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Expand Grid to Edges O FF Expand Grid to Edges O N

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3.2.3.2.3.2 Other

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When shading the feasible region for an inequality, some locations shade the region that

AGREES with or accepts the inequality.

y >= x and some schools shade the region which disagrees with or does not accept the inequality y >= x

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If you tick Shade Accept region, y >= x will produce the first graph.

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 computers but you can decrease the density on slower computers or increase it on faster computers.

Sets the size of the domain end points. The size is the radius of the circles - in millimetres.

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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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.

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.

3.2.3.2.4 Statistics

3.2.3.2.4.1 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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3.2.3.2.4.2 Other

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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.

3.2.3.2.5 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.

You can also use this screen to manually edit the configuration file. Normally this is only used by advanced users or when Efofex specifically asks you to.

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3.2.4

Hints & Tips

3.2.4.1

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.

3.2.4.2

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.

3.2.4.3

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!

3.2.4.4

What Is The Most Under-utilized FX Draw Feature?

Changing a figure's default properties. This can make using FX Draw much easier.

3.2.4.5

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.

3.2.4.6

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.

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3.2.4.7

How Do I Draw Network Diagrams Easily?

Change the arrow line's default to be a line with an open circle at each end (see

Drawing

Lines Using Defaults ). 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.

3.2.4.8

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.

3.2.4.9

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.

3.2.4.10 How Do I Draw Polar Graphs?

Polar functions must be typed in so that they are prefixed with "r =" and are in terms of t

(used as a substitute for theta). An example of a polar function is "r = 2sin(4t)".

3.2.4.11 How Do I Draw Inverse Graphs?

Inverse functions are typed in so that they are prefixed with "x=" or "f(y)=" and are in terms of y. An example of an inverse function is "x=2sin(y)".

3.2.4.12 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 terms of x or t).

For example x > 2 t <= 4 -3 < x <=7

Alternatively you can use the bracket notation for domain

For example y = x2 [-2,3) will produce

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3.2.4.13 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.

3.2.4.14 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.

3.2.4.15 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.

3.2.4.16 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.

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3.2.4.17 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.

3.2.4.18 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.

3.2.4.19 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.

3.2.4.20 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.

3.2.4.21 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.

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3.2.4.22 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.

3.2.4.23 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.

3.2.4.24 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.

3.2.4.25 How Can I Remember 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

3.2.4.26 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.

3.2.4.27 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.

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3.2.4.28 How Do I Enter An Ordered Pair?

Do 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.

3.2.4.29 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 q ere. By enclosing a section of your equation in quotes ("and" and "there") you prevent the tool from formatting that part of the equation.

Please note that this is much less of an issue when using FX Autoquate automatic equations.

3.2.4.30 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

3.2.4.31 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).

3.3

FX Graph

FX Graph is a simple to use, but incredibly powerful 2D and 3D graphing program that is useful for students and teachers. From simple Cartesian functions through to Argand diagrams, slope fields, and vector diagrams, FX Graph can provide an comprehensive and dynamic environment for investigating functions.

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3.3.1

Using The Graph Tool

FX Graph shares its graphing tool with FX Draw.

Instructions on how to use the graphing tool can be found in

Creating Graphs

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3.4

FX Stat

FX Stat shares its statistics tool with FX Draw.

Instructions on how to use the statistics tool can be found in

The Three Views

3.4.1

Using The Statistics Tool

FX Stat shares its statistics tool with FX Draw.

Instructions on how to use the statistics tool can be found in

The Three Views

3.5

FX ChemStruct

FX ChemStruct makes drawing chemical structures easy. Drawing something as simple as acetic acid is a time consuming and tedious task but with FX ChemStruct all you have to do is:

Load FX ChemStruct

Type ch3cooh

FX ChemStruct takes this information and formats it into the structure above. You never need to indicate what goes where - you simply type the structural formula. Users of FX

Chem will find FX ChemStruct very familiar - similar rules - different output.

FX ChemStruct cannot draw every chemical structure but it can draw the vast majority of chemical structures required by a secondary school chemistry teacher - quickly and easily.

FX ChemStruct can draw a wide variety of different styles of chemical structures - even drawing the structure with no bonds so the students can fill them it.

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3.5.1

How to Enter Structures

Just type the information. Do NOT capitalise the elements (i.e. enter sn NOT Sn for tin).

FX ChemStruct will do everything else. There are a few tricks to learn, but they should only take you a minute or so to grasp.

Perhaps the major "trick" to entering structures is that you must give FX ChemStruct some structural information as you are entering the structure.

For example, if you are trying to draw propane, do NOT enter c3h8. FX ChemStruct will take this information and try to build a structure out of it but will get confused as it is ambiguous.

Instead enter propane as ch3ch2ch3. This tells FX ChemStruct WHERE to place each hydrogen.

There is much more information regarding how to enter different structures later in the help information.

3.5.1.1

Basic Structures

Most simple structures are entered as you would write them. Notice that you do NOT have to capitalize elements - FX ChemStruct almost always takes care of that for you.

Alkanes

ch3ch2ch2ch3 ch3(ch2)4ch3

Alkenes

ch2ch2

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Alkynes

chch

Aldehydes

ch3ch2coh

Carboxylic Acids

ch3cooh

Ketones

ch3coch3

Ethers

ch3och3

Amides

ch3conh2

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Esters

ch3cooch3

3.5.1.2

Branched Structures

Branched structures are slightly more difficult to enter but are not too hard if you remember the basic rule

Enter a branch completely before starting the next branch.

For example, to enter 4-methyl-2-heptene enter the structure up to the green elements, then choose one of the branches to enter we have chosen the red branch. One that branch is complete, we enter the blue branch. ch3ch2ch2 ch ch3 chchch3

Quite complicated structures can be entered in this way - citric acid for example.

coohch2cohcoohch2cooh

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3.5.1.3

Benzene Rings

Benzene rings can be entered using the code bz. IF you have the option selected, you can also use ph to indicate a benzene ring.

For example: bzcooh phcooch2ch3 bzbz bzbzbz

3.5.1.4

Unformatted Text / Comments

FX ChemStruct will always try to make "chemical sense" out of what you have typed. This can lead to problems. For example, if you type catalyst into an structure, FX ChemStruct will try to interpret it as elements and will format it this way.

Calcium, Tantalum, an "l" that it cannot convert to an element, Yttrium, Sulphur and a renegade "t". Probably not what you intended!

You can force FX ChemStruct to leave this text alone by surrounding it in quotes. By typing "catalyst" with the quotes, you will get what you intended.

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3.5.1.5

Clicking on Compounds I

Chemical formulae are ambiguous so when you enter a structure, there is often more than one valid way of displaying it. How do you tell FX ChemStruct which version you are after.

In FX ChemStruct you can change a structure's "structure" by clicking on the elements.

For example, if you type ch3chch3ch2chch3ch3 you will see

If you want

You have to have some way of telling FX ChemStruct what you are after. To achieve this new version, you need to click on the CH we have coloured green. As you click on elements, FX ChemStruct will colour the element green so you can track which element you clicked on.

Clicking on an element shuffles the bonds around that element

3.5.1.6

Clicking on Compounds II

Clicking on an element shuffles the bonds from the element but as the number of bonds increases, so does the number of possible arrangements.

Most of the time, you will only want access to the main "arrangements" of atoms and FX

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ChemStruct cycles through these main ones as you click on the element.

Sometimes you will want to access some less likely arrangements. If you hold down the

Shift key when you click, FX ChemStruct will cycle through ALL possible arrangements.

For example: ch3chclchclch3

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if you click on the second CH, you will alternate between these two versions of the molecule.

if you hold down Shift and click, you can obtain the following.

3.5.1.7

Rotating and Reflecting

All structures can be rotated and reflected.

These four buttons will only affect the last compound clicked or, if no compound has been clicked yet, they affect the first compound.

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The first two buttons rotate the structure in 15 degree increments either anti-clockwise or clockwise.

The second two buttons reflect the structure over the vertical or horizontal axis.

3.5.1.8

Clearing Clicks, Rotations and Reflections

Sometimes you have clicked, reflected and rotated a diagram and you just want to start again. Push the eraser button to remove all modifications.

3.5.1.9

Isomers

An obvious use of "clicking" is to produce different isomers. For example: ch3chchch3 will produce cis-2-butene

One click later and we have trans-2-butene

The same applies to benzene compounds para, meta and ortho dinitrobenzene

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3.5.1.10 The Arrows

Reaction arrows appear in many equations and you need to remember the codes necessary to produce them. FX ChemStruct uses EXACTLY the same codes and methods as FX Chem.

=>

< > gives you a single arrow gives you a double arrow

="above">

="above","below"> well adds a message above the arrow the comma allows information below the arrow as

If you do not include the quotes, FX ChemStruct will interpret the text on the arrow as a chemical equation (NOT a chemical structure)

3.5.1.11 Spaces

Spaces can be used between compounds to help achieve the spacing you require.

A space IN a compound breaks the compound into two separate pieces from FX

ChemStruct's point of view. FX ChemStruct will NOT try to attach the second part to the first. Often this will mean that what you have typed no longer makes sense.

ch3cooh ch3c ooh

A space is often necessary with ionic compounds caso4

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ca so4

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3.5.1.12 R & R'

FX ChemStruct supports the use of R and R' in chemical structures.

For example: rcor'

3.5.1.13 Nitronium Ion

You can enter the nitronium ion (NO2+) by typing ono

PLEASE NOTE. This is an interim solution to this problem.

3.5.1.14 Entering Phase Information

FX ChemStruct can accept phase information in the same way as FX Chem.

For example: ch3cooh(aq)

3.5.1.15 Overriding Charges

FX ChemStruct automatically calculates charge on elements and ions. If you wish to override the charge with your own value, just type the charge after the ion. The main use for this is metallic ions that have different oxidation levels. This feature allows you to created charged structures that are incorrect.

For example:

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Fe

2+

Fe

3+

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so43+

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fe fe3+

Fe

2+

Fe

3+

3.5.1.16 Ionic Compounds

To create ionic compounds, it is usually necessary to add a space between the cation and anion. This prevents FX ChemStruct trying to bond the two pieces together and clearly shows the charge of each ion.

For example: fe so3 feso3

In the second example, FX ChemStruct has tried to create one molecule out of the cation and anion and become "confused". The space makes all the difference.

3.5.1.17 Polyatomic Ions

Most polyatomic ions are recognized by FX ChemStruct but you should surround the ion with spaces so that FX ChemStruct does not attempt to join the ion to another structure.

3.5.1.18 Ring Structures

There is limited support for ring structures in FX ChemStruct. FX ChemStruct can handle ring structures automatically - which provides limited functionality - or the user can explicitly indicate the rings

You can turn automatic recognition on and off using the Structure Options screen.

Automatic Recognition

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If automatic recognition is turned on, FX ChemStruct will look to see if the elements entered can be formed into a ring. If possible, FX ChemStruct will automatically "link" the ring. Automatic recognition is very limited and is best used for carbon based rings.

For example: ch2ch2ch2 ch2ch2ch2ch2ch2 ch2ch2ch2chchch2

Explicit Indication

If automatic recognition is NOT turned on, you can explicitly indicate ring structures.

Surround the elements in the ring structure with curly brackets and FX ChemStruct will attempt to form them into a ring.

For example:

{chchch2}

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{chchch}coch3

{cchnchnh}ch2chnh2cooh

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Explicitly indicating rings allows many more structures to be drawn but it is important to note that not all structures can be entered this way.

3.5.1.19 Preventing Bonding

FX ChemStruct uses a complicated algorithm to determine where the "next" element is attached to the existing structure. Sometimes this can cause problems if you want to leave a "bonding site" unbonded.

For example:

EDTA

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Imagine you are trying to enter this structure into FX ChemStruct. You might start with one of the N's and move out one of the arms nch2coo

So far so good. Now if you attempt to start another arm - by typing a C - things start to go wrong nch2cooc

FX ChemStruct has no way of knowing that you have finished the first arm and attached the C to the remaining bonding site on the O. Oops! What we need is a way of telling FX

ChemStruct to stop there. You can do this using the * key.

nch2coo*c

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The * has prevented the C from bonding to the O so FX ChemStruct bonds the C to the N instead.

To enter EDTA we can use nch2ch2nch2coo*ch2coo*ch2coo*ch2coo* or nch2ch2n(ch2coo*)4

Note: There are other possible ways of entering EDTA - but all require the use of the * key.

3.5.1.20 Degrees

You can enter a degrees sign (eg 24°) by using the ` key. This is a small backwards dash and it is normally found on the top left hand side of the keyboard, next to the 1 key and under the ~ (tilde). This character will be automatically replaced with the degrees sign.

This is the same convention we use in all Efofex products.

3.5.2

Display Options

FX ChemStruct has many display options that allow you construct structures exactly as you want them.

The display options are access through the display toolbar.

3.5.2.1

Hiding ?-H Bonds

The first two buttons on the display allow you to chose whether to show or hide ?-H bond

For example, if you type ch3chch2ch3ch2hc3

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3.5.2.2

Displaying Charges

FX ChemStruct calculates the charge on any entered structure and can display it in one of three ways - ignore the charge; display the charges on each atom or display the overall charge of the ion.

For example: so4

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Please note. If you override the charge and enter your own charge, FX ChemStruct will display the "overall" charge regardless of any other settings.

3.5.2.3

Compounds Without Bonds

You might wish to display your compounds, ions or structures without any bonds or electrons shown. This could allow you to construct questions for students.

There are two ways of displaying without bonds - allowing for unbonded electron pairs or not allowing for unbonded electron pairs.

For example: ch3cooh

(do not allow for unbonded pairs)

(allow for unbonded pairs

3.5.2.4

Allowing for Unbonded Electron Pairs

FX ChemStruct can allow for unbonded electron pairs when displaying a structure. You can choose whether or not to show the unbonded pairs.

For example

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h2o

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(do not allow for unbonded pairs)

(allow for unbonded pairs but do not show them)

(show unbonded pairs)

3.5.2.5

Showing All Electrons

FX ChemStruct can show all electrons in a structure. Just push the last button on the display toolbar

For example ch3cohnh

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3.5.3

Examples

3.5.3.1

Resonance Structures

Resonance structures need to be entered twice (or once for each possible arrangement) and then the structures need to be reflected or "clicked" to obtain the resonance structures.

Examples:

Ozone

Type o3 <> o3

Click on the central oxygen atom of the second ozone molecule.

Nitrate Ion

Type no3 <> no3 <> no3

Click on the central atom of the second ion and rotate the third ion.

3.5.3.2

Carbohydrates

Most carbohydrates require "clicking" on an atom.

Examples: glucose ch2ohchohchohchohchohcoh

Need to click on the green C in the diagram below.

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fructose ch2ohchohchohchohcoch2oh

3.5.3.3

EDTA

EDTA requires the use of the * key to

Prevent Bonding

nch2ch2nch2coo*ch2coo*ch2coo*ch2coo*

3.5.4

Co(NO3)2 becomes CO(NO3)2!

One of FX ChemStruct's most useful features is its ability to capitalise elements for you.

This can save you large amounts of time when entering equations. Some elements will cause FX ChemStruct problems. For example, if you type co, FX ChemStruct will ALWAYS interpret that as carbon/oxygen and change it to CO. This, obviously, will almost always be a correct interpretation. If you really want cobalt, Co, enter it correctly capitalised as Co

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and FX ChemStruct will leave it alone. In other words, if your compound contains ONLY lower case letters, FX ChemStruct will capitalise it for you taking its best guess. If FX

ChemStruct finds any upper case letters in your compound it will leave it as you wrote it.

That way you can always get the required result.

3.5.5

Changing Your Structures

3.5.5.1

Font

You can change the font used for structures here.

The font size determines the size of the font for the elements in your structure. All other sizes are proportional to this.

3.5.5.2

Equation and Structure Options

Press the options button.

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This screen allows you to control the way FX ChemStruct draws your structures.

The Sizes area allows you to control the sizes of different components of the structure.

Structural Bonds / Other Bonds - Most bonds apart from ?-H bonds. Shortening the length of the bonds hydrogen makes with other elements usually produces a better output. Please note that the difference in lengths has no chemical basis. It is merely a display setting.

Benzene - Determines the length of the side of a benzene ring.

Dot Size - Determines the size of the electrons.

Line Thickness sets the thickness of the lines used to draw the bonds. The size is measured in points. 1 point = 1/72 inches = 0.352777755 mm.

By default, FX ChemStruct allows the use of ph to enter Phenol (or benzene) but this makes drawing compounds involving phosphorus and hydrogen more difficult. You can turn off the ph code if you wish.

You can ask FX ChemStruct to automatically detect ring structures or you can explicitly indicate ring structures using curly brackets.

You can show arrows and/or charges on coordinate bonds

Benzene Style allows you to set whether benzene rings will be drawn with the aromatic circle or lines on double bonds.

By pushing Set As Default, the current settings will be used for all future structures.

The Equation Options button allows you to change the settings for chemical equations that are included in your structures.

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Using this screen, you can change the level and relative size of the different components of any equations. This gives you fine control over what is produced. Try moving the sliders up and down and keep an eye on the example equation at the top. It will show you the results of your changes.

The Equilibrium Arrow Type allows you to select between four different ways of drawing equilibrium arrows. You should select the one that best suits your local conventions. The example equation at the top will change to reflect the different arrow types.

Reaction arrows are automatically resized to accommodate any text you have above and below the arrow. If there is no text, the arrow will revert to a minimum size. You can set this minimum size by moving the Default Arrow Width slider.

The Italicize Phase check box determines whether FX ChemStruct italicizes phase information.

The Reset button will reset all options to the original settings as supplied.

The Set as Default button saves your current settings and will use them for all future structures.

3.5.6

My Structure is Not Formatted Correctly!

FX ChemStruct makes its best attempt to interpret what the user has typed in a logical way. 99% of the time this will be fine. In the other 1% you may have to revert to other means. Chemistry is a science of exceptions and your structure may contain one that FX

ChemStruct does not know about yet. If you inform us of the structure that FX

ChemStruct has not processed correctly, we will do what we can to get FX ChemStruct to

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recognise it.

4 Equation Tools

4.1

Creating, Editing and Using Equations

Our two equation products, FX Equation and FX Chem, are designed to produce highquality equations as fast as possible.

There are three, quite distinct ways of using the equation tools.

Word On Windows

If you are only using Microsoft Word on a Windows machine, using the equation tools as

OLE objects provides the best interface. If you choose to use the equation tools in this way, you will not be able to access the equations on a Mac machine. This usage is discussed in

Using OLE Equations

.

Writing Physically Large Equations (usually PowerPoint or

Keynote)

If the equations you are producing are large (as they tend to be in presentation products) and do not need to be aligned with other text, you can use Efofex Cloud to create and edit your equations. This will allow them to be accessed and edited on Mac computers. Small equations do not have enough room on their edges to encode the ID so Efofex Cloud is only useful for these larger equations. This usage is discussed in

Efofex Cloud and

Equations

Targeting (just about everything else)

The equation products can be used as equation translators. This allows you to enter equations using our high-speed systems, but then output them in formats that target various uses. For example, you can target LibreOffice's equation writer, Microsoft's internal equation system, LaTex output for use in things like Secta, Moodle or a number of other products. Targeting has the advantage of being extremely versatile and allows you to use the system on just about any computer. This usage is discussed in

Targeting

.

4.1.1

Efofex Cloud and Equations

Equations have two characteristics that will often prevent you from using them with

Efofex Cloud.

1.

2.

They are often physically too small to encode an ID along the edges.

You often need to align equations with existing text.

You will find Efofex Cloud useful in some situations, particularly if you need to produce a

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larger equation or a multi-line equation. This will typically happen in presentation products such as PowerPoint or Keynote but can occur in other contexts such as websites or using products such as Secta or Moodle.

You can read more about

Using Efofex Cloud here.

4.1.2

Using OLE Equations

Efofex has used OLE for over 25 years and it is very popular with users (despite the issues that can occur). If you decide to continue using the OLE system, any graphics you create with Efofex Cloud versions of our products will be tagged with and ID and have their data saved to the database automatically. This will greatly assist any later change to using the full Efofex Cloud system.

4.1.2.1

Using OLE Equations in Word for WIndows

4.1.2.1.1 Adding The Equation Programs (OLE) to Word

The most efficient way to use the OLE graphics in Word (Windows only) is to integrate the products with Word. This adds an Efofex toolbar to your Word ribbon that makes inserting new graphics easy.

To integrate with Word, start one of the graphics programs and then go to the Help menu.

Select Integrate Efofex Products into Word. Integration is automatic.

You will need to restart Word and you will then see a new Efofex tab on your ribbon bar.

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The buttons insert a new graphic into your document.

4.1.2.1.2 Using The Equation Programs (OLE) in Microsoft Word

Creating an Equation

Push the toolbar button

FX Equation/FX Chem will open a new window

Equation Tools 194

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Type your equation in the box at the top of screen - your equation will appear, formatted, in the bottom area of the screen

When you are finished, click on the green check mark and you will be returned to Word.

The equation will appear in your document adjusted to the correct level.

Note: FX Equation and FX Chem can be accessed by using the Insert/Object command from the menus but your equations will not be adjusted to line up with other text.

Editing

To edit an existing equation, double click on the equation in your Word document.

4.1.2.1.3 Why is My Text Red?

When an equation is inserted, it is inserted as a space, then the equation, then another space.

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The equation between the two spaces is lowered to line up with where the text is.

196

Why the spaces? Because of a little quirk in Word. If you manage to get your cursor in between the equation and the space, any text you type will be lowered (quite dramatically). This looks something like this

Unfortunately, compared to the next text, the equations look as if they need to be lowered. Our macros set the text color for this new text to bright red to make sure that you realise that you are in the wrong spot. If you see red, STOP and move the cursor to the other side of the space.

The best way to understand this behavior is to have a bit of a play around with it. Try typing on either side of the space to get a feel for what is going on. We have found that customers do not have a problem with it once they understand it.

4.1.2.2

Using OLE Equations In Other Products

Quite a few products support OLE graphics. To insert an OLE equation into your program, look for the "Insert Object" option and insert an FX Equation or FX Chem object.

Support for OLE is patchy and often changes between versions of software. We cannot guarantee that any particular usage you make of OLE equations will be supported in future versions of the software you insert the graphics into.

4.1.3

Targeting

Our equation tools have the capacity to translate your equations into a number of standard equation formats that can then be pasted into other applications. We call this targeting.

For example, you can type this into FX Equation.

1/(sr(x2-4))

and have it produce the following LaTex commands.

\begin{equation}{\frac{1}{{\sqrt{{x}^{2}-4}}}}\end{equation}

that can be pasted into things like Moodle.

Targeting allows you to use the equation tools in far more contexts. The major restriction of Targeting is that it is one-way. You can use our equation tools to create targeted equations but any editing will need to be done in the target application.

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4.1.3.1

Setting the Target

You should set the target you wish to export for before creating equations.

197

Or

4.1.3.2

Targets

The equation tools can target a large number of outputs:

Office Equations - Natively paste into Word, OneNote and PowerPoint (requires

Windows Word 2007 or later, Mac Word 2011 or later)

MathML

LaTex

LibreOffice

Select the appropriate output and, whenever you push the green check mark button, that format will be placed onto the clipboard for you.

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4.1.3.3

Targeting Office Products

4.1.3.3.1 Native Office Equations (OMML)

Microsoft Office products store their own equations using a specialized "language" called

Office Mathematical Markup Language (OMML). When targeting Office products, the equation tools OMML commands to the clipboard which can then be pasted directly into the Office products on both WIndows and Mac machines (requires Windows Word

2007 or later, Mac Word 2011 or later).

Once you have pasted an equation into Office, it is just as much a Office equation as one you created using Office's own equation editor. The equation tool no longer has any responsibility for what is displayed.

4.1.3.3.2 Getting Equations into Word

Once you have targeted Word, create an equation in the equation tool.

Once you have completed your equation, press the Green Check button to place a copy of the equation on the clipboard and change to Word.

Once Word has opened, Paste and your equation will be added to your Word document.

4.1.3.3.3 Editing Existing Equations

Once the equation has been pasted into Word, it is a Word equation, just like any other.

Simple editing of the equation can be done inside Word, with no further input from the equation tool.

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4.1.3.3.4 Restrictions

Native Word equations can only be rendered in Cambria font. This is a restriction in

Word rather than the equation tool. When you set the equation tool to Target Word, you will not be able to change the font.

When the equation tool gives the equation to Word, it gives up ALL control over how the equation is rendered. What you get in Word will not be exactly the same as what you saw in the equation tool.

Word has two modes for the display of equations. They can either be "In-Line" which means that they are part of a line of text, or they can be "Display" which means that they sit in the middle of the page. You can change from one to the other by clicking on the arrow near the equation.

When Word renders an "Inline" equation, it can significantly change the sizing and display of the equation. Some customers find this disconcerting. Again, this aspect of Word equations is outside of the control of the equation tool.

4.1.4

Equations in Apple Pages

Unfortunately, support for equations in the Apple Pages application is particularly poor.

The only way to insert equations into a Pages document is to use Efofex Cloud.

4.2

FX Equation

FX Equation is an equation editor that takes the chore of formatting equations away from you. It is for people who love the output from the modern equation editors but hate using them. FX Equation automatically formats, with a minimum of input from you, just about all of the equations an average mathematics teacher uses everyday.

First a simple example:

If you want a simple equation in your document

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normally you would have to load a large and cumbersome equation editor or type the equation into your word processor and manually italicise the variables and superscript the powers. Alternatively you could load FX Equation and type

F=v2/r=om2r

and press Enter.

FX Equation understands enough about equations to correctly format this for you.

Other examples of equations FX Equation can format include:

Limits ga=lim(n=>inf)(sigma(k=1,n) 1/k- ln n)=0.5772 gives you

Integrals s(t) = s\0 + int |v(t)| dt gives you

Vectors (3,2) gives you

Fractions pi/4 gives you

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4.2.1

Entering Equations

4.2.1.1

Getting Started

FX Equation is simple in concept but far more versatile that you might first expect.

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Most of the toolbar buttons are optional. The most important thing is to start typing and watch what happens!

4.2.1.2

Introducing Autoquate

FX Autoquate is an automatic equation recognition system. You type a mixture of text and equations and the system automatically detects which is which, formatting it as it goes.

No user intervention is required.

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FX Autoquate is highly efficient, extremely easy to use and will "get it right" almost all of the time.

If FX Autoquate does not produce what you were expecting, you can turn off the automatic system and manually select the sections that are equations.

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4.2.1.3

The Calculator

FX Equation includes a calculator that you can use to simplify the entry of solutions.

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To use the calculator, select a part of your entered equation and then push the Calculator

Button

FX Equation will evaluate the selection you have made and placed the value onto the clipboard. You can paste it in on the next line.

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The calculator allows you to create solutions to questions without reaching for your trusty scientific calculator.

4.2.1.4

Toolbar Equation Entry

FX Equation is designed to be used entirely from the keyboard but that relies on users remembering the codes to produce symbols and equation components. Toolbar Equation

Entry allows you to construct equations without needing to remember all the codes.

Toolbar Equation Entry also makes creation of some output, in particular piecewise defined functions and matrices, easier than just using the keyboard.

To use the Toolbar Equation Entry System:

1.

Move to the toolbar

2.

Click the button and a list of options will appear. Move to the desired tool and click again.

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3.

Sometimes FX Equation will just type the required command automatically. Other times, FX Equation will give you the opportunity to fill in some blanks.

4.

Push OK and FX Equation will build the required equation for you. Don't forget to look at the command FX Equation used so you can type your own next time (if you wish).

5.

The degrees button has no options, it will just add the degrees sign to your equation.

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4.2.1.5

Detect Column Vectors

The FX Equation toolbar has one very important button.

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This button determines how FX Equation formats things that include commas.

When the button is on, FX Equation will format something like (4,3) as a column vector. When it is off, FX Equation will leave (4,3) as an ordered pair.

This button controls an option (Detect Column Vectors) that used to be buried in the FX

Equation options screen. We have given it its own special button because it is something that you will often need to change.

Detecting column vectors also needs to be on for:

Matrices,

Piecewise Defined Functions,

Bounds of Definite Integrals

4.2.1.6

Equation Tool Reference

A full description of how to use FX Equation's equation entry technology to enter equations can be found in the Appendices.

Equation Tool Reference

4.2.1.7

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

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is entered as (3;2)

4.2.1.8

Set As Default

FX Equation keeps a "default" set of options for equations. It uses these default options whenever it creates a new equation. Once an equation is created, you can change that equation's options to suit your needs. Changing an equation's options does NOT change the default options.

If you have a option that you ALWAYS change, it is much quicker to make your setting part of the default options. This is very easy to do.

Create a new equation - it will be formatted with the default options.

Change the desired option.

Push the Set as Default button - your desired option will become the new default.

Notes for Advanced Users

The Set as Default buttons only affect the current options screen. If you make changes on multiple screens, you must push the Set As Default button on each screen.

Defaults are stored in the user's private profile. Every user gets to set their own options and defaults.

4.2.1.9

Complex Equations

The equation tool has only one limit on the complexity of the equations you can enter.

Matrices are limited to 20 by 20.

Because of the complexity of interpreting your entry, the equation tool will gradually slow as you enter a more complex equation but this will rarely impact on your use of the equation tool.

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In all likelihood, you will run out of steam before the equation tool does! Please note that the equation above is NOT meant to make any sense. It is just there to show you how capable the equation tool is.

4.2.1.10 My Equation is Not Formatted Correctly!

The equation tool makes its best attempt to interpret what the user has typed in a logical way. We have aimed to produce an equation editor that automatically formats nearly

100% of the equations a typical secondary teacher would need to produce. If your equation happens to be too ambiguous for the equation tool to handle, you may have to use one of the other tools available. We have not tried to replace these complex and highly versatile tools. We have simply tried to automate the most common equations.

4.2.2

Hints & Tips

4.2.2.1

Does FX Equation Balance Brackets?

No. FX Equation 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.

4.2.2.2

Why Are Spaces So Important?

FX Equation attempts to automatically format most equations. Unfortunately many expressions are ambiguous, sin2x for example. We wanted FX Equation to automatically recognize sin 2 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 sin

2 x. This is much easier to use than describe. In general, if FX Equation does not format your equation the way you expect, try entering a space between things.

4.2.2.3

How Do I Enter An Ordered Pair?

Entering ordered pairs into the equation tool is not simple because the equation tool uses the comma (semicolon in some locations) to indicate column vectors. You type (2,3) and get a column vector.

1.

If you never use column vectors or matrices, you can just turn off the column vector feature.

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2.

Normal ordered pairs - things like (2,3) - are best just entered in Word. They require no special formatting so the equation tool's formatting tools are not needed.

4.2.2.4

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 can also create matrices using the Matrix wizard on the toolbar.

4.2.2.5

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).

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You can also use the degrees button on the toolbar

4.3

FX Chem

The idea is simple. If you want this equation in your document you will have to spend a large amount of time formatting what you have typed making sure that everything is in the correct place.

FX Chem makes this easy. Simply load FX Chem and type: mno4-(aq) + 8h+(aq) + 5e- < > mn2+(aq) + 4h2o(l)

No formatting is required. You do not even have to capitalise the elements correctly. FX

Chem takes this information and formats it into the equation above. You never have to touch the mouse. You never have to indicate what goes where. Simply type in the information.

4.3.1

Using FX Chem

4.3.1.1

How to Enter the Equations

Just type the information. Type everything including components that should be subscripted or superscripted. Do NOT capitalise the elements (i.e. enter sn NOT Sn for tin). FX Chem will do everything else. There are a few tricks to learn, but they should only take you a minute or so to grasp.

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4.3.1.2

The Arrows

Reaction arrows appear in many equations and you need to remember the codes necessary to produce them.

=> gives you a single arrow

< > gives you a double arrow

="above"> adds a message above the arrow

="above","below"> the comma allows information below the arrow as well

Notice that the words "above" and "below" are now surrounded by quotes. This prevents

FX Chem from formatting the words as chemical equations.

4.3.1.3

Unformatted Text

FX Chem will always try to make "chemical sense" out of what you have typed. This can lead to problems. For example, if you type catalyst into an equation, FX Chem will try to interpret it as elements and will format it this way.

CaTaIYSt

Calcium, Tantalum, an "l" that it cannot convert to an element, Yttrium, Sulphur and a renegade "t". Probably not what you intended!

You can force FX Chem to leave this text alone by surrounding it in quotes. By typing

"catalyst" with the quotes, you will get what you intended.

4.3.1.4

Nuclear Chemistry

FX Chem 2 introduces the use of curly brackets (braces) to produce nuclear chemistry equations.

For example:

{238,92} U will be formatted as

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It is important to note that FX Chem does NOT check the validity of the mass numbers and atomic numbers. That is up to you. It does, however, give you a quick and easy way to produce the equations.

Neutrons, protons and electrons can be entered as follows:

{1,0} n {1,1}p {0,-1}e

The curly brackets can be used in a

neat trick

(see 5.16)

4.3.1.5

Multiline Equations

While you are creating an equation, pushing Enter/Return allows you to start a new line.

This will create a new equation on a new line.

4.3.1.6

Editing Your Equations

If you wish to edit the equation at a later time, simply double click on the equation and you will be returned to the FX Chem window. You can make any desired changes to your equation and then click outside the equation when you are happy with the changes.

4.3.1.7

Co(NO3)2 becomes CO(NO3)2!

One of FX Chem's most useful features is its ability to capitalise elements for you. This can save you large amounts of time when entering equations. Some elements will cause

FX Chem problems. For example, if you type co, FX Chem will ALWAYS interpret that as carbon/oxygen and change it to CO. This, obviously, will almost always be a correct interpretation. If you really want cobalt, Co, enter it correctly capitalised as Co and FX

Chem will leave it alone. In other words, if your compound contains ONLY lower case letters, FX Chem will capitalise it for you taking its best guess. If FX Chem finds any upper case letters in your compound it will leave it as you wrote it. That way you can always get the required result.

This issue can also affect Si compounds.

4.3.1.8

Degrees

You can enter a degrees sign (eg 24°) by using the ` key. This is a small backwards dash and it is normally found on the top left hand side of the keyboard, next to the 1 key and under the ~ (tilde). This character will be automatically replaced with the degrees sign.

This is the same convention we use in all Efofex products.

4.3.1.9

Delta H

Type deh to enter delta H to indicate changes in enthalpy. This can also be entered as

DEH.

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4.3.1.10 Neutrinos and Anti-neutrinos

Neutrinos are indicated in chemical equations using the Greek letter nu. To use neutrinos in a chemical equation, just type nu. To enter an anti-neutrino, type nu_ (nu followed by the underscore character).

4.3.1.11 Changing Your Equations

4.3.1.11.1 Text Formatting

While creating your equation, you can modify the formatting of your text using Word

Processor style commands and buttons.

In some modes you will not be able to change the font name or size as these are determined by external factors.

Press the Set Default button to set the current font to be the default font.

4.3.1.11.2 Other Options

While you are creating an equation, press the Edit Options button.

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Using this screen, you can change the level and relative size of the different components of your equations. This gives you fine control over what is produced. Try moving the sliders up and down and keep an eye on the example equation at the top. It will show you the results of your changes.

The Equilibrium Arrow Type allows you to select between four different ways of drawing equilibrium arrows. You should select the one that best suits your local conventions. The example equation at the top will change to reflect the different arrow types.

Reaction arrows are automatically resized to accommodate any text you have above and below the arrow. If there is no text, the arrow will revert to a minimum size. You can set this minimum size by moving the Default Arrow Width slider.

The Italicize Phase checkbox determines whether FX Chem italicizes phase information.

The Reset button will reset all options to the original settings as supplied.

The Set as Default button saves your current settings and will use them for all future equations.

4.3.1.12 Organic Chemistry

FX Chem recognises the use of R to represent hydrocarbon groups.

4.3.1.13 Can FX Chem Balance Equations?

The simple answer is no. FX Chem is designed as a small tool to make a difficult job much more efficient. It is a publication tool, not a teaching tool and makes no attempts to be one. FX Chem makes no attempt at checking the "validity" of what has been typed. It

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also makes no attempt at balancing the equation. This allows you to write equations that are NOT balanced for use in tests. FX Chem is not trying to replace your knowledge of chemistry, just make your job easier.

4.3.1.14 My Equation is Not Formatted Correctly!

FX Chem makes its best attempt to interpret what the user has typed in a logical way.

99% of the time this will be fine. In the other 1% you may have to revert to other means.

Chemistry is a science of exceptions and your equation may contain one that FX Chem does not know about yet. If you inform us of the equation that FX Chem has not processed correctly, we will add your exception to FX Chem's list.

4.3.1.15 A Neat Trick

The curly brackets are normally used for nuclear chemistry but they can also be used to create some "bizarre" equations that FX Chem will refuse to format automatically.

For example, if you want to write

Na2+

FX Chem will not be happy. It obviously does not "know" Na2+ and will not produce it.

Unfortunately, that is exactly the strange sort of thing a chemistry teacher will need to write sometimes - to test a student's knowledge.

You can actually create this strange ion by typing na{2+}

FX Chem will treat the 2+ as the mass number of an element and put the 2+ where you want it. This trick allows you to force things to be superscript even if FX Chem does not agree with you.

Similarly, you can use the curly brackets to force things into subscript.

na{ ,2+}

The comma tells FX Chem that the mass number is finished and the atomic number is beginning and the 2+ will be subscripted

Na2+

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5 Appendices

5.1

A - Equation Tool Reference

5.1.1

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:

|[

]| value absolute value followed by square bracket opens an absolute value square bracket followed by an absolute value closes an absolute

The square bracket will not be displayed - it is only used to indicate the direction of the absolute value sign.

is entered as |[ (|[x]| - |[y]|)/2 ]|

5.1.2

Arcs

You can mark any equation component with an arc over the top using the arc command.

Example:

ABC

is entered as arc(ABC)

NOTE: arc is not correctly rendered in Word when using Copy/Paste integration.

5.1.3

Boxes

You can draw boxes around equation components, or create empty "fill in the blank" boxes, using the box command.

Examples:

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3 + = 9 is entered as 3 + box = 9

x

2

+ 4x + 1 is entered as box(x2) + 4x + 1

5.1.4

Combinations & Permutations

Combinations and permutations are entered in nCr form. The equation tool can format the combinations and permutations in three ways.

Examples:

10

C

2 is entered as 10C2

n

P

n – 2 is entered as nP(n-2)

Set the display option on the Styles tab.

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5.1.5

Complex Numbers

The equation tool correctly formats complex numbers without any extra input on your part and recognises cis, arg and mod.

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5.1.6

Composite Functions

Enter as written fog(x)

5.1.7

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

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is entered as (3,2).

5.1.8

Definite Integral Bounds

FX Equation supports 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

5.1.9

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).

eg

32`

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5.1.10 Derivative At A Point

Derivatives at a point can be entered using the @ symbol. The location of the derivative is entered in brackets after the @ symbol.

Example:

d dx

x

2

– 4

x = 3 is entered as d/dx x2 -4 @(x=3)

The @ command is NOT dependent on the derivative being present. It can be used independently of other commands if desired.

Example:

4x + 1

4 is entered as 4x+1 @(4)

NOTE:

The @ symbol was previously used as an alternative for entering the partial derivative symbol. This use has been deprecated. If you wish to use the partial derivative symbol, you should use the pd command. Any existing equations using the @ symbol will need to be recoded to use pd.

5.1.11 Displaying Units

The equation tool 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 the equation tool what to consider a unit.

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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 Users.

Single letter, lower case units (eg s, g, h, and m) are usually best left off this list. Putting them on the list causes the equation tool to behave counter-intuitively, although totally logically.

For example...

The h has been formatted using the units formatting but not the way the user was expecting.

5.1.12 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: is entered as r : is entered as x ::

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is entered as 0.23 :

5.1.13 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.

5.1.14 Equation Numbers

FX Equation can add equation numbers to equations. These are useful when defining systems of simultaneous equations.

Equation numbers are entered by surrounding a digit with parentheses.

Example:

3x + y = 3

12x – 3y = 4 is entered as

3x+y=3 (1)

12x-3y=4 (2)

FX Equation will only render equation numbers when the equation number has some white space around it. For example, if you type sin(3), FX Equation will NOT convert the

(3) to an equation number.

You must have the following option checked to use equation numbers.

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5.1.15 Equation Options

5.1.15.1 Accessing Equation Options

There are many options for the rendering and interpretation of equations. These are accessed with this button.

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The options are discussed later in the manual.

5.1.15.2 Fonts

This screen allows you to control the fonts used in equations.

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5.1.15.2.1 Standard Equation Font

If you choose to use the current text font, your equation will just use the font that is currently selected in the text box. This means that if you are typing in Arial 12pt, your equation will also be in Arial 12pt.

Many users want to standardize on one font for equations (often Times New Roman) regardless of the text around the equation. You can choose this by choosing Use Standard

Equation Font and selecting the font you want to use.

Some users want to standardize even further and always use a specific font size for equations - regardless of the text around the equation. You can do this by checking the

Use Standard Font Size box.

Whatever you choose can be overridden by selecting parts of the equation and manually changing the formatting.

5.1.15.2.2 Font Modifiers

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. Most users choose to italicise variables.

Automatic font modifiers you choose can be overridden by selecting parts of the equation and manually changing the formatting.

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5.1.15.3 Vectors

5.1.15.3.1 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, the equation tool 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.

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5.1.15.3.2 Automatic Vectors

The equation tool can automatically recognize some vectors if you choose to turn the feature on. The equation tool 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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5.1.15.3.2.1 Lowercase Vectors

The equation tool will only detect lowercase vectors if automatic recognition is switched on.

If you are using vectors of the form

The equation tool can automatically recognise that you are typing a vector and make the r, i and j bold. The equation tool 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 the equation tool may sometimes get the automatic recognition incorrect. By default, the equation tool will take its "best guess", you can also turn this feature off or alternatively, explicitly tell the equation tool which variables to recognise as vectors.

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It is important to remember that you do not need to tell the equation tool that you are working with a vector, the equation tool 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.

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5.1.15.3.2.2 Double Capitals

The equation tool will only detect Double Capital vectors if automatic recognition is switched on.

Double capital letters are used to represent line segments, rays and vectors. The equation tool 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 the equation tool can be set using the Vector Options

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Appendices 230

5.1.15.4.1 Multiplication Sign

When using the equation tool, you enter a multiplication sign using the * key. The equation tool can display your sign in one of three ways, as an ´, a raised dot ( × ) or an *.

The equation tool will display any entered multiplication sign AND the multiplication sign in scientific notation using this setting.

5.1.15.4.2 Raising The Decimal Point

Some locations prefer that the decimal point is raised.

ie.

3·2 rather than 3.2

This option will only take effect if you use a dot as a decimal point.

5.1.15.4.3 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.

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5.1.15.4.4 Mixed Numerals

Mixed Numerals are created automatically if you have selected the Format Mixed

Numerals option.

is entered as 3 1/2

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5.1.15.4.5 Negative Numbers

The equation tool offers you the option to display negative numbers differently to subtraction signs.

The three options produce these results.

5.1.15.5 Units

The equation tool 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 the equation tool what to consider a unit.

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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 Users.

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 user was expecting.

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5.1.15.6 Matrix

You can adjust vertical and horizontal spacing for your matrices as well as alignment.

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5.1.15.7 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

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the list and start typing.

Shortcuts are formatted as

The code - followed by the tab key - followed by the desired output

Example: 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.

5.1.16 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)

234

is entered as x=(-b +- sr(b2-4ac))/2a or you 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

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5.1.17 Greatest Integer

Greatest Integer signs are entered as [ | and | ]

Example: is entered as [|x2+3x-1|]

5.1.18 Greek Letters

All Greek letters are supported. 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 supported. (eg upper case alpha = A) ph ch ps om rh si ta up mu nu xi pi th io ka la de ep ze et

Code al be ga

Lower Case Greek Letter a b e z g d n x l m i k h q u f c y w s t p r alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu nu xi pi rho sigma tau upsilon phi chi psi omega

Code

GA

DE

TH

LA

XI

Upper Case Greek Letter

G

D

Q

L

X gamma delta theta lamda xi

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PI

SI

UP

PH

PS

OM

P

S

¡

F

Y

W pi sigma upsilon phi psi omega

Examples: is entered as pi/4 is entered as sin2 th

5.1.19 Horizontal Lines

You can add a horizontal line to any multiline equation using the hl command.

236

5.1.20 Integrals

Integrals can be entered using the int command.

Example: is entered as int x dx

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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 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.

5.1.21 International Considerations

,

The equation tool 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

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is entered as (3;2)

5.1.22 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)

5.1.23 Logarithms

Normally, numbers written immediately after a function are raised as a power automatically.

Example: is entered as cos2 x log is treated differently. Entering log2 x will generate.

This makes generation of logarithms automatic.

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5.1.24 Logic Symbols

The equation tool supports the creation of logic equations. All logic codes are preceded by

_

_and

_or

_not

_iff

_imp

_nor

_qed

~ or ¬ or or or •

Codes with multiple possible outputs are controlled using the Logic Symbols page on the options screen.

Select the symbols you wish to use for each code then press Set As Default.

5.1.25 Matrices

Examples: is entered as [2,3 4,6]

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is entered as [1,2,3 4,-5,6 7a,8,1/2 ]

The equation tool MUST be set to detect column vectors in order to detect matrices.

5.1.26 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_

5.1.27 Mixed Numerals

Mixed Numerals are created automatically if you have selected the Format Mixed

Numerals option.

is entered as 3 1/2

The Format Mixed Numerals option is available in the Styles page of the equation tools options.

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5.1.28 Multiplication Sign

When using the equation tool, you enter a multiplication sign using the * key. The equation tool can display your sign in one of three ways.

The equation tool will display any entered multiplication sign AND the multiplication sign in

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scientific notation.

Appendices

5.1.29 Negative Numbers

The equation tool will detect most negative numbers. For example, if you type

-9 - -3

The equation tool will detect that the first and third - signs are indicating negation whereas the middle - is indicating subtraction.

The equation tool offers you the option to display negative numbers differently.

242

The three options produce these results.

5.1.30 No Width Spaces

Sometimes you need to enter a space so that the equation tool correctly formats your input, but the extra space messes up the output.

For example if you need to enter...

you have a problem. If you enter pirh the equation tool will interpret the rh as rho and produce:

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but if you add a space between the r and h, the equation tool will produce:

243

What you need is a way of stopping the equation tool from treating the rh as one thing.

You need to separate the r and h to stop the character replacement.

To stop the replacement, type !! The !! will be used by the equation tool to format your input but will NOT effect the output.

5.1.31 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

5.1.32 Piecewise Defined Functions

The equation tool'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)

5.1.33 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.

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Examples:

is entered as x2 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)

5.1.34 Predictions

Statistical predictions ("y hat") are entered using a DOUBLE power symbol.

Example:

is entered as y^^

5.1.35 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

Please note that this is usually not an issue when using FX Autoquate automatic equation recognition.

5.1.36 Product Notation

Product notation is entered using the product command. The parameters are placed in brackets and are separated with a comma.

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Example:

is entered as product(i=1,10) x\i

5.1.37 Raising The Decimal Point

Some locations prefer that the decimal point is raised.

ie.

3·2 rather than 3.2

Appendices 245

This option will only take effect if you use a dot as a decimal point.

5.1.38 Recognized Functions

The equation tool automatically recognises functions and formats them differently, according to your preferences. The functions that the equation tool recognises are:

sin cos tan ln asin acos atan log sec cosec cot abs sinh tanh arg cosh

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normal cis mod

Appendices 246

5.1.39 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

5.1.40 Scientific Notation

The equation tool can automatically format scientific notation. The capital E followed by a number will be transformed into 10 to the power of the number.

The equation tool will correctly format numbers with negative exponents.

The equation tool will use the currently selected multiplication symbol ( or ).

Examples: is entered as 1.2E15

is entered as -3.2E-1+1.2E1

5.1.41 Short Division

You can create a short division using the div command.

Example:

x – 1 x

2

– 1 is entered as (x-1)div(x2-1)

NOTE: div is not correctly rendered in Word when using Copy/Paste integration.

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5.1.42 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 but you can edit our shortcuts or create your own to suit your workstyle.

Editing Shortcuts

5.1.43 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

5.1.44 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

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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

5.1.45 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

5.1.46 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))

5.1.47 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

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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 remembered 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

Code

< =

> =

< > or = /

= ~ or ~=

~ ~

- =

+ -

- +

*

/ (followed by a space)

` or o

- >

= > dp inf tri ang perp

$and

$or element notelement subset notsubset propersubset es prop

Symbol

*, or ·

·

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pd tf te fa nabla au

CC

ZZ

QQ

RR

NN

_and

_or

_not

_iff

_imp

_nor

_qed

Note: Some symbols have two codes.

Å

Complex Number Set Symbol

Integer Number Set Symbol

Rational Number Set Symbol

Real Number Set Symbol

Natural Number Set Symbol or •

~ or ¬ or or is entered as 0` <= x <= 360` is entered as x -> inf

5.1.48 Text Formatting

Text can be formatted using standard Word Processing tools.

250

You can change fonts, sizes, colours and styles. Most of these options will behave exactly as you expect but there are a few small but significant differences.

5.1.48.1 Strikeout

If you select some text and choose the strikeout option, the results will look a little different to what you expect, particularly in equations.

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This allows you to clearly show process in some questions.

5.1.48.2 The Default Font

If you press the Set Default Font button, the currently selected font will be set as FX

Equation's default font. This will affect and text and equations entered into a new FX

Equation box.

You can override the default font for all or part of an equation by selecting the relevant text and changing the formatting.

Note: This setting will NOT override the Standard Equation Font if you have set one.

5.1.48.3 Standard Fonts

Many teachers want to use a standard font (and sometimes font size) for all equations, regardless of any other formatting. For example, you might want to render all equations in Times New Roman 12 point.

Push the Options button and select the Fonts Page

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If this is set to Use Current Text Font, FX Equation will use whatever font you currently have selected. This font may have come from Word, or it may be FX Equation's default font or some other font you have set.

With this setting (Use Standard Equation Font but not a Standard Size), FX Equation will use whatever font size is currently selected to render the equation but the equation will

ALWAYS be rendered in Times New Roman regardless of any font settings I have selected.

With these settings, all equations will be rendered in Times New Roman 12 pt.

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5.1.49 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]

5.1.50 Vector Support

The equation tool supports 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 the equation tool to detect and display vectors automatically.

5.1.50.1 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, the equation tool 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 the equation tool to detect column vectors and matrices.

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or

Appendices 254

5.1.50.2 Automatic Vectors

The equation tool can automatically recognize some vectors if you choose to turn the feature on. The equation tool 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.

5.1.50.2.1 Lowercase Vectors

The equation tool will only detect lowercase vectors if automatic recognition is switched on.

If you are using vectors of the form

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The equation tool can automatically recognise that you are typing a vector and make the r, i and j bold. The equation tool 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 the equation tool may sometimes get the automatic recognition incorrect. By default, the equation tool will take its "best guess", you can also turn this feature off or alternatively, explicitly tell the equation tool which variables to recognise as vectors.

It is important to remember that you do not need to tell the equation tool that you are working with a vector, the equation tool 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.

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5.1.50.2.2 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. The equation tool 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 the equation tool can be set using the Vector Options

5.2

B - Statistics Tool Reference

5.2.1

Using The Stat Tool

5.2.1.1

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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5.2.1.2

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.

5.2.1.2.1 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.

5.2.1.2.2 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 .

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5.2.1.2.3 Column Types

The stat tool supports five different types of columns:

Data Columns

Appendices 258

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

Frequency Columns

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

Appendices 259

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

Appendices 260

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.

5.2.1.2.4 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.

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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.

5.2.1.2.5 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.

262

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.

5.2.1.2.6 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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5.2.1.2.7 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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5.2.1.2.8 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.

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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.

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.

5.2.1.2.9 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

30

£

£

x < 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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5.2.1.2.10 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.

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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.

5.2.1.2.11 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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5.2.1.2.12 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.

5.2.1.2.13 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.

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

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5.2.1.2.14 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).

Masked data is greyed out in the data view.

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5.2.1.2.15 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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5.2.1.2.16 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.

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

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5.2.1.2.17 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

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able to be graphed. Label and Group columns cannot be graphed.

5.2.1.2.18 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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5.2.1.2.19 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.

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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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5.2.1.2.20 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.

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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.

5.2.1.2.21 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

( )

RandHyperGeometric

( )

RandNegBinomial ( )

RandExponential ( )

RandStudent

( )

RandBernoulli ( )

RandGeometric ( )

RandNormal ( )

RandPoisson ( )

RandBetween ( )

RandLogNormal ( )

RandChiSquared ( )

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Regression and Time Series Data

MPA

( )

PredictX ( )

ResidualX ( )

Predict ( )

Residual ( )

Seasonalise

( )

Sorting

Sort

( )

SortCol

( )

Ranking

Rank ( )

SortA

( )

SortColA ( )

RankD

( )

Frequency Tables

FreqTable ( )

Grouping Data

Group ( )

GroupW

( )

CumFreqTable ( )

GroupN

( )

Deciles / Stanines and Percentiles

Decile ( )

Stanine ( )

Miscellaneous Functions

Inc

( )

Deviation ( )

PredictY ( )

ResidualY ( )

SortD ( )

SortColD ( )

RankA ( )

GroupE ( )

Percentile

( )

Round

( )

5.2.1.3

The Statistics View

5.2.1.3.1 Automatic Statistics

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

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5.2.1.3.2 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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5.2.1.3.3 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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5.2.1.3.4 Copying Statistics to Clipboard

Statistics can be copied to the clipboard by:

1. Selecting the desired statistics in the statistics view.

Appendices 279

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.

Median

Minimum

Maximum

Range

Standard Deviation

A

50.635

25.39

77.11

51.72

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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5.2.1.4

The Graph View

5.2.1.4.1 Graph Control Buttons

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

280

The graph type button allows you to change the graph type the tats 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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5.2.1.4.2 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

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will be added to the first available position in the data boxes. This is usually the quickest way to create graphs.

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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5.2.1.4.3 Changing Graph Type

Press the Graph Type button.

and select from the available graph types.

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5.2.1.4.4 Editing Graph Properties/Options

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

283

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.

5.2.1.4.4.1 Axes Properties

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

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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 users will set their desired option as the default.

None

Arrows

Circ le x Axis y Axis

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

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5.2.1.4.4.2 Scale Properties

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.

Appendices 287

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

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Scales

Appendices 288

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.

290

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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5.2.1.4.4.3 Grid Properties

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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5.2.1.4.4.4 Titles

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

Appendices 295

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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5.2.1.4.4.5 Specific Graph Type Properties

Appendices 296

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.

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.

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Column graphs are very similar to

Bar Graphs

.

Column 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.

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.

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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

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

Median –

IQR

n

and Median +

IQR

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 P erc entage

The only difference between the graphs is how the y axis is displayed.

Relative

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.

300

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.

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.

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Group width = 5 Group width = 1 0

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:

Absolute P erc entage

The only difference between the graphs is how the y axis is displayed.

Relative

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

Join 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 Join 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 Stac ked

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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.

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.

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Group width = 5 Group width = 1 0

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 P erc entage

The only difference between the graphs is how the y axis is displayed.

Relative

Percentage frequencies and relative frequencies are most useful when comparing data sets which have different numbers of scores.

Frequency Densities

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

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Stacked frequency polygons share all of normal

Histogram's properties.

The Join 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 Stac ked

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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.

Appendices 309

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.

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.

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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 join up the data.

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

Appendices 312

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.

Moving P oint Average Seasonalized

Line

Regression

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/Divided Bar Graph at a time so the number of data boxes is reduced to one when drawing a pie graph.

Display Type

Pie and divided bar 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 user has no control over the colors used (after picking the data box color).

Multiple Colors pie graphs give the user 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 and divided bar 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.

Labels and P erc entages No Labels - Just Use P erc entages

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You can also turn off angled text

Appendices 316

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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.

Sc attergraph 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.

Show Line and Show Residuals O N Show Line and Show Residuals O FF

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Join Dots

If you turn this option on, the stat tool will join 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.

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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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Link graphs have 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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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. 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.

2. 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.

Appendices 323

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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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5.2.1.4.4.6 Data Box Properties

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 O pac ity Medium O pac ity High O pac ity

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

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

20 40 60 80

x

328

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5.2.1.4.5 Selecting Data On Graph

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

Clic k Highlighted Selec ted

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

Sweep Highlighted Selec ted

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5.2.1.4.6 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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5.2.1.4.7 Combining Graph Types

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

331

Frequenc y P olygon and Histogram Histogram and Box P lot and Cumulative Histogram

Frequenc y P olygon

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 remember 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 O ut - 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.

333

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!

Appendices 334

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5.2.1.5

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.

335

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

5.2.1.5.1 Discrete

5.2.1.5.1.1 Equi-Likely Integers

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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.

5.2.1.5.1.2 Bernoulli

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 generate results with a given probability of success.

5.2.1.5.1.3 Binomial

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.

5.2.1.5.1.4 HyperGeometric

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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?

5.2.1.5.1.5 Geometric

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?

5.2.1.5.1.6 Negative Binomial

The negative binomial data generator allows you to simulate trials where you count how many attempts are required before the n th

success. An example question might be: How many rolls of the die does it take before you have rolled 5 sixes?

5.2.1.5.1.7 Poisson

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.

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5.2.1.5.2 Continuous

5.2.1.5.2.1 Uniform

Appendices 338

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.

5.2.1.5.2.2 Normal

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

5.2.1.5.2.3 Exponential

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

Where is the rate parameter of the function.

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5.2.1.5.2.4 Log Normal

Appendices 339

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

5.2.1.5.2.5 Chi Squared

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

5.2.1.5.3 Bivariate Data

The bivariate data generator allows you to quickly and easily generate bivariate data that satisfies a set of given parameters.

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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

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 account 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.

5.2.1.5.4 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

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5.2.1.5.5 Dice

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.

341

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 six-sided dice and add them.

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5.2.1.6

Customizing The Stat Tool

5.2.1.6.1 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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5.2.1.6.2 System Options

Appendices 343

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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5.2.2

The Statistics Functions

5.2.2.1

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 cf

10 2

11

12

13

5

12

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)

5.2.2.2

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)

5.2.2.3

Deviation(column)

Calculates the deviation from the mean for each score in column, using the calculated mean of the column.

Example: Deviation(A)

5.2.2.4

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

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5.2.2.5

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 f

10 2

11

12

13 8

3

7

This 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: FreqTable(A)

5.2.2.6

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

32

1

1

This is the result of Group(A,7)

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

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5.2.2.7

GroupE(column)

Appendices 347

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)

5.2.2.8

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

5

1

71

35

1

3

26

58

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

5.2.2.9

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

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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

5.2.2.10 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)

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

5.2.2.11 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)

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5.2.2.12 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)

5.2.2.13 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)

5.2.2.14 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.

5.2.2.15 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)

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regtype is the regression model

2

3

4

5

1 linear regression quadratic regression power regression exponential regression logarithmic regression

6

7 median line reciprocal regression

Please note that it is not necessary to remember 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.

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

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5.2.2.16 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.

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

5.2.2.17 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.

5.2.2.18 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

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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

352

5.2.2.19 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

5.2.2.20 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?

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

5.2.2.21 RandChiSquared(degrees, number)

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

5.2.2.22 RandExponential(rate, number)

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

Where is the rate parameter of the function.

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5.2.2.23 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

353

5.2.2.24 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) 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

5.2.2.25 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,

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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

354

5.2.2.26 RandLognormal(mean, sd, number)

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

5.2.2.27 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:

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

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5.2.2.28 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.

5.2.2.29 RandStudentt(degrees,number)

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

5.2.2.30 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.

5.2.2.31 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).

5.2.2.32 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

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6

7

4

5

1

2

3 linear regression quadratic regression power regression exponential regression logarithmic regression median line reciprocal regression

Please note that it is not necessary to remember 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( )

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

5.2.2.33 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.

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Note: If you type decimals using a comma (eg 3,2) you should enter this formula as

R esidualX(A; B; 1) - using the ; as a separator

5.2.2.34 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)

54.05133

21

93.58500

93

79.51597

64

78.21893

97

52.41859

18

49.49797

05

57.37784

96

11.90832

24

54.05

93.59

79.52

78.22

52.42

49.5

57.38

11.91

94 80 78 52 49 57 12 Round(A

,0)

54

Round(A

,-1)

50 90 80 80 50 50 60 10

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

5.2.2.35 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.

5.2.2.36 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

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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

358

5.2.2.37 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)

5.2.2.38 SortD(column)

Sort the entire data set using column as the sort key. Sorts into descending order. All columns are affected.

Example: SortD(A)

5.2.2.39 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)

5.2.2.40 SortColD(column)

Sorts only the data in column into descending order. No other column is affected.

Example: SortColD(A)

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5.2.2.41 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).

5.2.2.42 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

5.2.2.43 Triangular(number)

Generates number triangular numbers.

Example: Triangular(10)

5.2.2.44 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

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5.2.2.45 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)

5.2.3

Other Functions

5.2.3.1

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.

5.2.3.2

Inverse Trigonometric Functions

asin(x), acos(x), atan(x) calculate the inverse trigonometric functions.

5.2.3.3

Hyperbolic Functions

cosh(x), sinh(x), tanh(x) calculates the appropriate hyperbolic functions.

5.2.3.4

Abs(x)

Calculates the absolute value of the parameter x.

5.2.3.5

Exp(x)

Calculates e x

5.2.3.6

Ln(x)

Calculates the natural logarithm of x

5.2.3.7

Log(x)

Calculates the base 10 logarithm of x

5.2.3.8

Sqrt(x) / SR(x)

Calculates the square root of x

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5.3

C - Function Graph Tool Reference

5.3.1

Creating Graphs

The graphing tool makes it simple to create graphs of complicated situations. The core of the graphing tool is the Quick Entry Screen.

You can access the quick entry screen by right-clicking on the plane or pushing the y= button.

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5.3.2

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.

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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 remember your current settings and use them for all future graphs.

5.3.3

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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5.3.4

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.

Theta

Greater than or equal to

Less than or equal to

Plus Minus

Normal

Symbol

´

Multiplication

Exponentiation

(Powers)

Division

Pi

none (eg 2x) ^ (eg 2^x) Only needed when the graph tool fails to automatically recognise the power.

¸ p

/ (followed by a space) pi

The / character is more often used (without the space) to enter fractions.

Can be used in both functions q th and axes.

Used in polar functions

³

£

±

Graph

Tool

*

>=

<=

+-

Notes

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

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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.

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.

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5.3.5

Masking Graphs

You can mask any graph you draw. Draw your graph and then push the mask button.

Any graphs you have drawn are removed from the axes and the axes are overlaid by a

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faint "mask"

The mask will not appear on any generated graphics.

You will only see it on the screen as you are drawing. It is there so that you know that the graph has been masked.

Why?

You might use the mask to hide the answers to a question. You can draw up the answer but then mask it so that it is not displayed for students. Later, when creating solutions to the question, you can quickly unmask all of your work.

5.3.6

Graphing in 3D

5.3.6.1

Entering 3D Functions

There are two ways of getting FX Graph to graph in 3D. The first is to type in a function that is clearly 3D z = x2-y2 r = sin th + cos ph x = sin t; y = cos t; z = 3cos 2t + sin 3t

(1,2,3)+<1,4,-2>

All of these entries are clearly 3D in nature and FX Graph will automatically go into 3D mode. You do not need to do anything else.

5.3.6.2

Forcing 3D

The 3D button forces FX Graph into 3D mode even if there is no function entered or the entered function is not inherently 3D. You can enter something like y=x2-4 and press the 3D button.

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The function will be displayed on the xy plane of the 3D axes.

Appendices 370

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5.3.6.3

3D Quick Entry Screen

Appendices 371

The 3D Quick Entry screen is similar to the 2D screen with two major differences:

1.

2.

You can control the z axis annotation and maximum.

You can change how FX Graph renders surfaces.

Shaded - Low Opacity

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Shaded - High Opacity

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Contour Lines - Normal Divisions

Appendices 373

Contour Lines - High Divisions

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5.3.6.4

Standard Axis Alignments

There are three standard 3D axes alignments that you can quickly select.

374

These allow you to reorientate the axes to suit various functions, or to reset the axes to a known orientation after you have rotated them.

5.3.6.5

Rotating 3D Axes

You can rotate 3D axes using the x, y and z keys. Pressing the key rotates the space around the axis by 10 degrees. If you hold down the Shift key when pressing x, y or z, the space will rotate by -10 degrees.

5.3.6.6

Animating Axes

When FX Graph is in 3D mode, these buttons allow you to animate the axes. Pressing any of the buttons will rotate the space around the indicated axis.

5.3.7

Types of Functions

5.3.7.1

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.

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

5.3.7.2

Cartesian Functions

Normal Cartesian functions (y = ...) can be entered into the graph tool with or without the y=.

y = 3x - 7

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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.

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.

5.3.7.3

"Multiple Armed" Functions

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

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5.3.7.4

Polar Functions

Polar functions are entered in terms of r and Because there is no key on a computer keyboard, the graph tool uses th to represent .

You can enter a normal polar equation such as r = 5 sin 3 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 terms 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

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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 £

2 p

(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.

5.3.7.5

Inverse Cartesian

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

3y2+3y-4

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the x = is optional

Appendices 379

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.

5.3.7.6

Implicitly Defined

Implicitly defined functions are treated in two stages.

1.

The graph tool tries to rearrange the function to be in terms 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 basically 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.

5.3.7.7

Parametric

Parametric curves are entered as two equations in terms 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.

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

5.3.7.8

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 joined points. the graph tool allows you to by entering points as functions. Points are entered as ordered pairs - optionally separated by semicolons (see regional issues).

(2,3) (1,1); (-1,-1) (-3,2)

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By prefixing one of the points by a P, the graph tool will interpret all of the points as being in polar form, (r, ). 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

Constants

Points can contain constants which are discussed later in this manual. You can enter a point of (-3a,b) for example.

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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)

5.3.7.9

Groups of Points

The graph tool can plot groups of points and join 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)

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)

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5.3.7.10 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>

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>

5.3.7.11 Smoothed Curves

If you join points with a tilde (~), the graph tool will draw a smoothed line joining the points.

For example, if you enter (-10,-4)~(-5,3)~(1,-1)~(6,8)~(10,-4) as your function, the graph tool will draw this graph.

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You can mix ~ and + in the same function.

(-10,-4)~(-5,3) + (1,-1)~(6,8)~(10,-4)

The smoothed curves do not have to be left to right. In other words, they do not need to represent a function.

(-10,-4)~(-5,3)~(1,-1)~(6,8)~(10,-4)~(6,-10)~(-5,5)

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5.3.7.12 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

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.

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

Appendices 388

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.

5.3.7.13 Complex Numbers

The graph tool introduces some support 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.

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To enter a complex number, just type it in as it is written.

z = 4+3i z = 3cis(pi/3)

Appendices 389

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

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

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Finally, the graph tool understands magnitudes and can graph most cases.

| z - i | >= 4

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5.3.7.14 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.

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.

5.3.7.15 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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5.3.7.16 3D Cartesian Functions

3D Cartesian functions should be entered in terms of x, y and z. z = x2/10 - y2/10

You do not have to enter the function in z= form, providing the function you enter can be transformed (internally by FX Graph) into z= or z2= format.

x2+y2+z2=64

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5.3.7.17 3D Polar Functions

3D Polar functions are entered in terms of r, th and ph (r, θ and Φ) r=2+4sin 2th + 3cos ph

5.3.7.18 3D Points and Vectors

3D points and vectors are entered in the same way as 2D points and vectors, just with three dimensions.

(4,5,-7)

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<7,-5,3>

Putting a + sign between points will join them

(1,2,3)+(4,5,2)+(-1,-6,-9)

Appendices 394

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You can add and subtract vectors.

5.3.7.19 3D Parametric Functions

Enter 3D parametric functions in terms of t. For example: x = 5 cos t; y = 5 sin t; z = 5 cos 3t

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5.3.8

Function Reference

Command

e pi sin cos tan asin or sin-1 acos or cos-1 atan or tan-1 sec cosec cot cosh sinh tanh ln log log base n sr or sqrt abs

| root

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 arccosine or inverse cosine arctangent or inverse tangent secant of an angle cosecant of an angle cotangent of an angle hyperbolic cosine hyperbolic sine hyperbolic tangent natural logarithm base 10 logarithm base n logarithms square root absolute value absolute value nth root. Any root of the argument can be found by adding the number in front of the word "root"

Example

y = e^x y = pi x2 y = sin 2x y = cos3 x r = 2tan th y = asin(x) y

= sin-1(x) as above as above y = sec2 x as above as above y = cosh x y = sinh x y = tanh x y = ln(2x) y = log(x) y = log2 x y = sr(x) y

= sqrt(x-2) y = abs x y = |x - 2| y = 3root x y

= 5root(x2)

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normal gint sgn calculates the normal probability distribution for x standard deviations from the mean greatest integer function greatest integer function sign function asec or arcsec inverse secant inverse cosecant inverse cotangent y = normal(x) y = gint(x) y = [| x |] y = sgn(x) y = asec(x) y = acosec(x) y = acot(x) acosec or arccosec acot or arccot

5.3.9

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.

5.3.10 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.

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5.3.11 Function Control Toolba2

Whenever you select a function graph in FX Draw, the function control toolbar will appear.

The function control toolbar allows you to select between the various modes available for the function graph tool. If your function contains a constant or constants, you will able to control the constants using the constant controllers that appear in this area of the screen.

5.3.12 Select Mode

Select Mode is the basic mode of the graph tool. You can choose select mode by pressing the graph.

button on the toolbar. When in select mode, you can select most objects in a

If you sweep out a rectangle, you can select multiple objects at the same time.

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5.3.13 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.

5.3.14 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 supports zooming in a number of ways.

5.3.14.1 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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Page Up Zooms OUT by 33%

Page Down Zooms IN by 33%

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5.3.14.2 Zooming with the Mouse

5.3.14.2.1 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.

5.3.14.2.2 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.

5.3.14.2.3 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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5.3.14.2.4 Undo Zoom

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

5.3.15 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 is quicker to use and does not require a semicolon (or colon).

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For example:

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When using bracket notation you can use braces ( { and } ) to control the domain but mark the end points with ARROWS. For example, entering x2-4 {-3,3} will produce this graph.

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)

5.3.16 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

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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 £

2 p

(radian mode)

Parametric graphs

0

£ t £

20

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

5.3.17 Constants

5.3.17.1 Entering Constants

The graph tool understands seven constants.

Fixed Constants e pi

~

~

2.718281828

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.

5.3.17.2 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.

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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.

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.

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5.3.17.3 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.

I have set a to be 1 and the delta to be 0.25. The graph shows a family of curves, centered 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 = 0.25x^2 y = 0.5x^2 y = 0.75x^2 y = 1x^2 y = 1.25x^2 y = 1.5x^2 y = 1.75x^2 y = 2x^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.

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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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5.3.17.4 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.

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

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You can stop an animation by clicking on the animate button again.

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.

5.3.17.5 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.

5.3.18 Variables

The graphing tool provides a variable controller for any variable in your entered function.

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If you change the display type to show a variable dot, the slider allows you to control the location of the dot and, optionally, only display part of the function.

5.3.19 Inequations & Feasible Regions

5.3.19.1 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

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The graph tool will produce a shaded graph depending on your Feasible Region Options.

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5.3.19.2 Inequation Shading 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.

5.3.19.2.1 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

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and has shaded just that region. The area is shaded using the color, style and opacity selected in the Quick Entry screen.

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Shading for One Inequation

If you only enter one inequation, FX Draw will use Half Plane shading (honoring your setting for which side to shade) regardless of the Half Plane/Feasible Region setting.

5.3.19.2.2 Solid Shading

Solid Shading

Solid shading is one block of solid color. Solid shading has the advantage of being faster to

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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 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.

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5.3.20 Derivative Curves

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

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To draw derivative curves for a function you have two options.

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.

5.3.21 Integrals

The graph tool can graph integrals for any Cartesian function.

5.3.21.1 Using Your Mouse to Create Integrals

5.3.21.1.1 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.

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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.

5.3.21.1.2 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!

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.

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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5.3.21.1.3 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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5.3.21.1.4 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.

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

5.3.21.1.5 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)

5.3.21.2 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.

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5.3.21.3 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 terms 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.

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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.

Show Area if Different

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

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5.3.21.4 Approximations To The Integral

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

429

O riginal Integral

Minimum - uses the minimum in eac h division

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Maximum - uses the maximum in eac h division

Appendices 430

Left - uses the left hand value of eac h division

Right - uses the right hand value of eac h division

Trapezium Rule

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Simpson's Rule (2 divisions)

Note that we had to reduce the number of divisions for Simpson's Rule otherwise 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 dec imal plac es.

5.3.22 Volumes of Solids of Revolution

You can create volumes of solids of revolution by:

1.

Drawing a 2D Cartesian function.

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2.

Select the Integral tool and sweep out an integral

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3.

Right click on the integral and select a rotation.

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4.

You can use the Volume slider to demonstrate or animate the rotation.

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5.3.23 Tangent and Secant Lines

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

5.3.23.1 Using Your Mouse to Create Tangent Lines

5.3.23.1.1 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.

5.3.23.1.2 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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5.3.23.1.3 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.

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5.3.23.1.4 Selecting Tangent/Secant Lines

You can select a tangent/secant line by clicking anywhere on it. The selected line will increase in thickness.

5.3.23.1.5 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.

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.

5.3.23.2 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.

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5.3.23.3 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.

5.3.24 Tables of Values

5.3.24.1 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.

5.3.24.2 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.

5.3.24.3 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.

5.3.24.4 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.

5.3.24.5 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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5.3.24.6 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 -9

2 3

100 81

4 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

1

0

0

Table data is placed on the clipboard in formats suitable for insertion into most word processors and spreadsheets.

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5.3.24.7 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.

5.3.24.8 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.

5.3.25 Marked Points

5.3.25.1 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.

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5.3.25.2 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.

5.3.25.3 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.

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.

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5.3.25.4 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.

5.3.25.5 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.

5.3.25.6 Editing Marked Points

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

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

Showing construction lines allows you to show dotted lines from the point to the x and y axes.

5.3.26 Arc / Curve Lengths

FX Draw can calculate arc/curve lengths for 2D Cartesian functions.

1.

Create a 2D Cartesian function.

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2.

Select the Curve Length Mode

3.

integral.

Use the mouse sweep out the curve length. The process is identical to creating an

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4.

Right click on the arc to change its properties.

5.3.27 Rulers

The ruler tool can be used to add a measurement to any 2D axes. Simply select the tool and add a ruler.

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Note that the ruler will show a measurement relevant to the plane. If your plane does not have a 1:1 aspect ratio, horizontal and vertical distances will not be the same length onscreen, as shown above.

6 Installation

6.1

System Requirements

Windows

Efofex products are fully tested and compatible with Windows 7, 8, 8.1 and 10. Using

Efofex products with earlier versions of Windows (2000, XP and Vista) is technically possible but may require you to install specific updates. Efofex does not provide support for running our products on Windows 2000, XP and Vista.

Efofex products work best with Microsoft Word 2007 and later.

Mac

Efofex products will run on OSX 10.7 or later.

Efofex equation tools require Microsoft Word 2011 or later in order to insert targeted equations into documents. Earlier versions do not implement Microsoft's Office Math

Markup Language that is used for this process.

March 14, 2017 : Note that we have recently been informed that Word 2011 compresses graphics even when requested not to. This is preventing the Efofex

Cloud system from identifying the embedded IDs in graphics. You can find more information

here

.

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6.2

Installing Efofex Products on Your Computer (Basic)

Windows

To install Efofex products onto your system:

Download the installation file onto your computer - noting where the file has been saved.

Double click on the installation file.

The install program will ask you which directory you would like the Efofex products to be placed in and will then make all necessary adjustments to your system.

Mac

To install Efofex products onto your system:

Download the installation file onto your computer

Open Finder and go to Downloads

Double click on the downloaded DMG file.

Drag any desired applications into your computer's Application folder

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 subscription for our products, you can enter it during installation or later, by choosing Manage Account from the Help menu of any product.

6.3

The Preference Interview

When you first start most Efofex products, they will give you an opportunity to set a series of options that allow you to set up the software to create things exactly the way you need them to.

For example, the graph tools ask which side of an inequation should be shaded (this differs around the world).

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Make you selections for each option and in a few minutes, FX Draw will be producing exactly what you want.

All options can be changed later or you can re-run the interview from the Tools menu.

6.4

Installation Notes (Windows)

6.4.1

Administrator Privileges

Efofex products require Administrator privileges in order to install and save their registration information. We recommend that if you have purchased a registration code, you enter it during installation to combine these two 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 administrator privileges to run Efofex products normally.

6.4.2

Integrating Efofex Products into Word (Windows)

Note that with the release of Efofex Cloud, integration with Word is far less crucial. You only need to complete this step if your users are using Efofex products as OLE objects.

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Some users will want to integrate our products into Word. From December 2015, we are no longer able to perform this integration for All Users of a computer due to security changes implemented by Microsoft. For this reason, we have removed the integration from the installer and integration is now performed by the user as needed.

Users can choose integrate from the Help menu at any time.

Both of these options place a copy of the Efofex dotm files (stored in the Efofex program subdirectory) into the Word startup location in the User’s Roaming profile

(usually C:\Users\%USERNAME%\AppData\Roaming\Microsoft\Word\Startup)

This process does not require administrator permissions. The template files will be loaded the next time Word starts.

From a support point of view, the only involvement you are likely to have is to remind users to use the Integration option from the Help menu if they choose No on the initial screen.

6.4.3

Unlocking The Software

Your subscriptions for Efofex products are provided as a Registered Name and Passcode

If you are evaluating the software and wish to purchase:

Choose the license you require. For a full description of the licenses available, read the license information on our website.

Contact 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 passcode from Efofex or your local distributor and use the instructions below to register your copy.

To unlock your copy during installation:

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When offered the opportunity during installation, type in your Registered Name and

Passcode as supplied by Efofex.

455

To unlock your copy after installation:

From the Help menu choose Manage Account...

Press the Enter Code button. The Enter Code window will appear.

Type in your Registered Name and Unlock Code as provided by Efofex. If you have a full site or distribution subscription, you will also be offered a place to create a user name.

Your initials make a good username.

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Once you have successfully validated your code, any products which you have a valid subscription for will operate after the 30 day evaluation period.

6.4.4

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 download from www.adobe.com.

Before downloading 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.

6.5

Installation Notes (Mac)

6.5.1

Installing the Products

Installing on a Mac is easy. Double click on the downloaded dmg file and then drag the desired apps into the applications folder. Nothing else is required.

6.5.2

Unlocking The Software

Your licenses for Efofex products are provided as a Registered

Name and Passcode

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.

Contact 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 register your copy.

To unlock your copy after installation:

From the Help menu choose Manage Account. Then choose Enter A Code

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Type in your Registered Name and Passcode as provided by Efofex. Then press Validate

Code which will check your code with our servers. You also have the option of creating a Username at this point.

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The program will now operate correctly past the thirty day evaluation period.

6.6

Installation Notes For Network Administrators

6.6.1

Internet Access Required

Efofex Cloud requires our products be given access to the Internet. They use this access for two crucial purposes:

Synchronizing the local database to our servers. This allows your teachers to use their graphics on any Mac or Windows computer seamlessly. Most graphics use about 1 kilobyte of data to synchronize so this will not create a large load on your link.

Interrogating our registration server to determine the current status of your subscription. This occurs once per invocation of the program moves about 1 kilobytes of data.

The software CAN operate without Internet access and will synchronize data and check its registration at the earliest opportunity.

6.6.2

New Registration System

The introduction of Efofex Cloud also sees the introduction of a new accounts-based registration system.

The new system pairs your registered name with a "passcode". This allows our products to interrogate our registration server and determine your current license status.

The main advantage of this system is that you only need to enter the passcode once. Our previous registration code system required you to distribute a new code to all computers whenever a subscription was extended. The new system requires no further action on your part. If you extend a subscription, we update our registration server and all computers logged in to your account will automatically download the new subscription details the next time the programs are started.

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6.6.3

Windows Installations

We have a number of tools available that allow you to install the software on Windows networks

6.6.3.1

Silent Installs (Command Line Interface)

Efofex provides installers for our products that can be installed and licensed using a command line interface. This allows network administrators to automate the installation of our products.

Command Line Interface

Efofex product installers can use the following command line parameters:

/Licences

Use a central licence server location

/Name

Create a local licence file with a given name (used with /

Passcode)

/Code, /Passcode

Create a local licence file with a given passcode (used with /

Name)

/Tasks

/Components

Can be used to disable desktop icons

Control which products are installed.

/Dir Control the installation directory for the software

/SuppressMsgBoxes

Not normally needed. Can be used to suppress the “Word is

Open” dialog box.

/NoCancel

/Manual

Not normally needed

Used to manually register computer when no connectivity is available. Only use this option after consultation with Efofex.

/noVC Prevent Installer from installing Visual C++ support files.

/Licences

Usage: /Licences="x:/dirname"

Allows the product to use a licence server. You will find more details on using licence servers later in this document.

Enter the location you wish to centrally store your licence files. This can be on a mapped drive (/Licences="D:/Licences/Efofex") or on a drive accessed with a UNC name (/Licences="//licenceserver/efofex"). You can use forward slashes

(as shown) on Windows machines. If you choose to use back slashes, you need to enter them doubled as they are interpreted as escaped characters (/Licences="D:\

\Licences\\Efofex" or /Licences="\\\\licenceserver\\efofex")

/Name

Usage: /Name="Yourtown Secondary College"

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Used in conjunction with /Passcode

You will use the /Name /Passcode parameter pair to install your licenses onto the local machines. You will find more details on using local license installations later in this document.

/Code, /Passcode

Usage: /Passcode="109B4"

Used in conjunction with /Name

/Silent ,/VerySilent

Instructs Setup to be silent or very silent. When Setup is silent the wizard and the background window are not displayed but the installation progress window is. When a setup is very silent this installation progress window is not displayed. You will usually use /

VerySilent

/Tasks

The main use for this command is to disable the creation of desktop icons.

Usage: /Tasks="!Desk"

You can also use it to add quick access buttons to the taskbar

Usage: /Tasks="Quick"

/Components

Usage (FX MathPack): /Components="Draw,Equation,Graph,Stat"

Usage (FX SciencePack): /Components="Chem,Equation,ChemStruct”

If this parameter is missing, the installer will install all components. If, for example, you wished to install only FX Draw and FX Equation from FX MathPack, you would use /

Components="Draw,Equation"

/Dir

Usage: /Dir="x:\dirname"

Overrides the default directory name displayed on the Select Destination Location wizard page. A fully qualified pathname must be specified. Note that back slashes should NOT be doubled for this parameter. If this parameter is missing, the installer will install into the machine’s program files directory. This will normally be C:\Program Files (x86)\Efofex

/SuppressMsgBoxes

Not normally required but can be used to suppress the “Word is Open” dialog box.

Instructs Setup to suppress message boxes. Only has an effect when combined with '/

SILENT' or '/VERYSILENT'. The default response in situations where there's a choice is:

-Yes in a 'Keep newer file?' situation.

-No in a 'File exists, confirm overwrite.' situation.

-Abort in Abort/Retry situations.

-Cancel in Retry/Cancel situations.

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-Yes (=continue) in DiskSpaceWarning, DirExists, DirDoesntExist, NoUninstallWarning,

ExitSetupMessage, ConfirmUninstall situations.

3 message boxes are not suppressible:

-The About Setup message box.

-The Exit Setup? message box.

-Any (error) message box displayed before Setup (or Uninstall) could read the command line parameters.

/NoCancel

Not normally required

Prevents the user from cancelling during the installation process, by disabling the Cancel button and ignoring clicks on the close button. Useful along with '/SILENT' or '/

VERYSILENT'.

/Manual

This option allows you to manually license computers in situations where connectivity is not available. To use it you must have received a manual registration block from Efofex.

We STRONGLY recommend that you instead work to fix the connectivity issue rather than use this option.

To use the option, remove the [registration] and [\registration] tags from the registration block provided by Efofex. Usage is then in the format

/manual="

0sQ1`P17eL8YG#qG6}-I;zn(f!IWdgp6x}=o(G0L)^vvM'U{(i2;V8vPmx]

HO:5;[email protected]>N>`ZT];fh,vNRZ60lilYU5P[nXH4!]p0^_ jL?Y^4sSTHK,2su}

HS`&En#Vf.Ye0toP=l8YlxZ#]Ys5Vmc`-H_KuHc&7IJk{?5W{bP'[email protected]{NAdMWg} a8b6{M<*zKFx<:mY2iyn^Y*Qm{XZ:a^$?8U9%1<;hf!G,w?i;HFVNK=|-ELg]hAW;H<W-

YeQzP=6a--t6(oe[lk5vcSaKY1m{M2ebXbFXiFK)_Kc31<m)Q3[Bb95G?2uoK19hiVH|

I~5:uZ^m_h_IGy9sxiSVBfa`Q~?K*7CjaKKJ|a&xv!*Pv4& 9zP9HNci k5$g~`kyW|| l=_=|iT6w)bEbOZ$8V4?/TJL#N(|f<b8`^8s}8Ern~XPwG<5)(`kbnG6X`=UW$R[7p

S=vmw:&z1Y,JuB[Bs9eq#3!X%9Mc/%&[email protected]{ema$#5u]PXKuEI})4Yz_UG)mHuFuMY/*C;kuf|

=:`[V?kKkLN&vqc5Sl,&f:#I14 7^?$yHP]t~s!M`aiiPPSGo:tQgB>X<N&m =,s=?

r_L$5&E:X{YY!wDUmjm9H=~nTJt6&qE|L^By4Q]11[~O.rt~?#^GQ5G1kl4<n)

[email protected]!uT~C .e3t5Bjky.R{DWn#EWb5Hho{z?w<:}UkHB,0b7iF|Er7TK#FYT|

*FlbV!xFr^Wiln2Xo(L}hDf4ca/FwGtwQ3d^JAc3~{FT/w~h?2CiMi~sotq|Uu[H?KcoEba

g-FBNrRm&c`),yLA BnQzy/:#[email protected]>l-X_v)pkuKb?Q/

{y71B^Dmm6XL^]/>.5GjzLxoo32rL^BEMYW_Z%o(4Ve70k3qk%[I|"

/noVC

Including this flag prevents the installer from checking if the appropriate Visual C++ redistributable is installed on your system. This can prevent some issues that occur when your are using mandatory profiles. Please note that this does NOT remove the requirement for these files to be present. If you choose use this flag, you are taking on responsibility for ensuring that the appropriate files are pre-installed. Normally, this flag should ONLY be used after consultation with Efofex.

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Examples

Installing FX Draw and FX Equation from FX MathPack using a central licence server and default installation directory

FXMathPackCloud.exe /verysilent /Licences="//licenceserver/efofex" /Tasks="WordInt,AllUsers" /Components="Draw,Equation"

Installing FX SciencePack with a local licence file, in a custom installation directory

FXSciencePackCloud.exe /verysilent /Name="Yourtown Secondary College" /Passcode="112B3" /Dir="D:\Applications"

Installing FX MathPack using a manual registration block.

FXMathPackCloud.exe /verysilent /Name="Yourtown Secondary College" /Passcode="112B3" /manual="0sQ1`P17eL8YG#qG6}

-I;zn(f!IWdgp6x}=o(G0L)^vvM'U{(i2;V8vPmx]HO:5;[email protected]>N>`ZT];fh,vNRZ60lilYU5P[nXH4!]p0^_ jL?Y^4sSTHK,2su}HS`&En#V f.Ye0toP=l8YlxZ#]Ys5Vmc`-H_KuHc&7IJk{?5W{bP'[email protected]{NAdMWg}a8b6{M<*zKFx<:mY2iyn^Y*Qm{XZ:a^$?8U9%1<;hf!G,w?i;HFVNK=|-ELg

]hAW;H<W-YeQzP=6a--t6(oe[lk5vcSaKY1m{M2ebXbFXiFK)_Kc31<m)Q3[Bb95G?2uoK19hiVH|I~5:uZ^m_h_IGy9sxiSVBfa`Q~?K*7CjaKKJ|a

&xv!*Pv4& 9zP9HNci k5$g~`kyW||l=_=|iT6w)bEbOZ$8V4?/TJL#N(|f<b8`^8s}8Ern~XPwG<5)(`kbnG6X`=UW$R[7p S=vmw:&z1Y,JuB[Bs9 eq#3!X%9Mc/%&[email protected]{ema$#5u]PXKuEI})4Yz_UG)mHuFuMY/*C;kuf|=:`[V?kKkLN&vqc5Sl,&f:#I14 7^?$yHP]t~s!M`aiiPPSGo:tQgB>X<N&m

=,s=?r_L$5&E:X{YY!wDUmjm9H=~nTJt6&qE|L^By4Q]11[~O.rt~?#^GQ5G1kl4<n)[email protected]!uT~C .e3t5Bjky.R{DWn#EWb5Hho{z?w<:}

UkHB,0b7iF|Er7TK#FYT|*FlbV!xFr^Wiln2Xo(L}hDf4ca/FwGtwQ3d^JAc3~{FT/w~h?2CiMi~sotq|Uu[H?KcoEba g-FBNrRm&c`),yLA BnQzy

/:#[email protected]>l-X_v)pkuKb?Q/{y71B^Dmm6XL^]/>.5GjzLxoo32rL^BEMYW_Z%o(4Ve70k3qk%[I|"

6.6.3.2

Registering Large Numbers of Computers

Option 1

The easiest way to register a large number of computers is to use the /Name and /

Passcode parameters on a silent, command line install.

FXMathPackCloud.exe /verysilent /Name="Yourtown Secondary College" /Passcode="112B3"

This will install the software in the default location and save a registration file for all users on the computer. Our new, accounts-based registration code system means that you will not need to repeat this process.

Option 2

The passcode and name are stored in FXRegistration.ini which is stored in the program installation directory (C:\Program Files (x86)\Efofex by default). You can register a new computer by copying this file to the program installation directory on the new computer.

This file has the following format

[Registration]

Name=Yourtown Secondary College

PassCode=112B3

You can manually create this file or copy it from a previously registered computer.

Option 3

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You can ask individual users to register themselves. Any user-entered registration (which will be done without Administrator rights) will be saved in the User's Roaming Profile and will not be available to any other users on the same computer.

Option 4 (With No Connectivity)

The easiest way to register a large number of computers is to use the /Name, /Passcode and /Manual parameters on a silent, command line install.

FXMathPackCloud.exe /verysilent /Name="Yourtown Secondary College" /Passcode="112B3" /Manual="0sQ1`P17eL8YG#qG6}

-I;zn(f!IWdgp6x}=o(G0L)^vvM'U{(i2;V8vPmx]HO:5;[email protected]>N>`ZT];fh,vNRZ60lilYU5P[nXH4!]p0^_ jL?Y^4sSTHK,2su}HS`&En#V f.Ye0toP=l8YlxZ#]Ys5Vmc`-H_KuHc&7IJk{?5W{bP'[email protected]{NAdMWg}a8b6{M<*zKFx<:mY2iyn^Y*Qm{XZ:a^$?8U9%1<;hf!G,w?i;HFVNK=|-ELg

]hAW;H<W-YeQzP=6a--t6(oe[lk5vcSaKY1m{M2ebXbFXiFK)_Kc31<m)Q3[Bb95G?2uoK19hiVH|I~5:uZ^m_h_IGy9sxiSVBfa`Q~?K*7CjaKKJ|a

&xv!*Pv4& 9zP9HNci k5$g~`kyW||l=_=|iT6w)bEbOZ$8V4?/TJL#N(|f<b8`^8s}8Ern~XPwG<5)(`kbnG6X`=UW$R[7p S=vmw:&z1Y,JuB[Bs9 eq#3!X%9Mc/%&[email protected]{ema$#5u]PXKuEI})4Yz_UG)mHuFuMY/*C;kuf|=:`[V?kKkLN&vqc5Sl,&f:#I14 7^?$yHP]t~s!M`aiiPPSGo:tQgB>X<N&m

=,s=?r_L$5&E:X{YY!wDUmjm9H=~nTJt6&qE|L^By4Q]11[~O.rt~?#^GQ5G1kl4<n)[email protected]!uT~C .e3t5Bjky.R{DWn#EWb5Hho{z?w<:}

UkHB,0b7iF|Er7TK#FYT|*FlbV!xFr^Wiln2Xo(L}hDf4ca/FwGtwQ3d^JAc3~{FT/w~h?2CiMi~sotq|Uu[H?KcoEba g-FBNrRm&c`),yLA BnQzy

/:#[email protected]>l-X_v)pkuKb?Q/{y71B^Dmm6XL^]/>.5GjzLxoo32rL^BEMYW_Z%o(4Ve70k3qk%[I| "

Note that the manual registration block will be provided to you by Efofex

This will install the software in the default location and save a registration file for all users on the computer. The lack of connectivity will mean that this process will need to be repeated for any new license

6.6.3.3

Using a License Server (Deprecated)

While it is still possible to use a License Server, our new accounts-based registration system makes this effectively useless. Accordingly, we are deprecating this feature.

Efofex supports the use of a centralised licensing server which stores the licensing files and provides them to network computers on demand.

To use centralised licensing, networked computers need to be told where to find their licensing information. This information is stored in a simple, editable INI file.

FXLicenceLocation.INI

A proforma copy of this file is automatically installed into C:\Program Files (x86)\Efofex during installation. The proforma INI file contains detailed instructions on how to manually enter the desired network location of the licence files.

Note: FXLicenceLocation.INI can be created automatically during installation using the /Licences command line parameter and this is the recommended method. See the section on using the command line interface for more details.

The final step is to create the required license files and place them in the network location

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pointed to by FXLicenceLocation.INI

The easiest way to create the required license files is to install the product on a computer and enter the license information during installation.

What if the License Server is Not Available?

Whenever Efofex products access license files, they take a copy of the license file and store it in the user’s profile. If the license server is not available, the products will use the cached copy of the license file to unlock itself. This is particularly useful for computers which go off-site, such as teacher notebooks.

Please note that the caching system will not operate if you wipe user profiles as part of your security policies.

6.6.3.4

Restricting User Options

In the school environment, network administrators often want to prevent users from checking for updates or changing registration information. This can be achieved by adding the line

AllowRegistration=0 to the licensing INI file. This will prevent the user from making changes to the registration or being informed of updates.

6.6.3.5

Integrating Into Word

Note that with the release of Efofex Cloud, integration with Word is far less crucial. You only need to complete this step if your users are using Efofex products as OLE objects.

Some users will want to integrate our products into Word. From December 2015, we are no longer able to perform this integration for All Users of a computer due to security changes implemented by Microsoft. For this reason, we have removed the integration from the installer and integration is now performed by the user as needed.

Users can choose integrate from the Help menu at any time.

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Both of these options place a copy of the Efofex dotm files (stored in the Efofex program subdirectory) into the Word startup location in the User’s Roaming profile

(usually C:\Users\%USERNAME%\AppData\Roaming\Microsoft\Word\Startup)

This process does not require administrator permissions. The template files will be loaded the next time Word starts.

From a support point of view, the only involvement you are likely to have is to remind users to use the Integration option from the Help menu if they choose No on the initial screen.

6.6.4

Mac Installations

Installing an Efofex produce on multiple Mac computers does not need to create a large workload for system administrators. The applications are self-contained can be copied across computers without impediment. There are no specific installation requirements.

Copying registration information across computers takes a little more work.

Installing a License on Multiple Mac Computers

The easiest way to license multiple computers is to provide your users with the registered name and passcode. Users can enter the information themselves (the information only needs to be entered once) and then all future licensing will be carried out automatically.

Alternatively, you can automatically register multiple computers using the following procedure.

1.

2.

Register the software on one computer.

This will create a registration file in:

%currentuser%/Library/Application Support/Efofex/fxregistration.ini

3.

It is best to strip the Username from this file so that new users are not registered to the same username. Remove the line

User=**** (the asterisks represent whatever username the user may have created)

4.

Consider changing the AllowRegistration line to AllowRegistration=false. This will prevent normal users from changing the settings.

5.

Copy your modified file to

Users/Shared/Efofex Registration Data/fxregistration.ini

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on any computer you wish to automatically register. The software will automatically register itself when first loaded.

6.7

Registration Code is Accepted but is Then Immediately

"Forgotten"

If our product is accepting your registration code and works normally - but the next time you start the program it reports that it has expired and you need to re-enter the registration code. The registration code does not seem to "stick".

This issue is usually caused by some process that is wiping the FXRegistration.ini file in the

User's Roaming profile. Some school networks reset a user's profile regularly.

The easiest way to fix this issue is to either include FXRegistration.ini in the standard operating environment OR enter the license information during installation when the information is written, under administrator privileges, to the installation directory.

6.8

MSI Packages

Efofex does not produce MSI packages for our products. We have not been able to produce MSI packages that can be installed by a majority of our customers and would need to produce customised MSI Transform for most networks. We recommend that you use one of the commercially available MSI repackagers if you require MSI functionality.

7 Support

7.1

Support Questions

Many support questions are addressed in the next topics. All other support questions should be sent to [email protected]

7.2

Connectivity Issues

The main type of connectivity issue that will impact users is school-level blocking of

Internet traffic for applications. This usually involves all traffic being blocked apart from specific "white-listed" applications such as browsers. This means that our products will be reporting a connectivity issue even when your computer obviously has access to the Internet.

Detecting A Connectivity Issue

Benefits of Allowing A Connection

Unblocking A Connection

Technical Details

Registering Without A Connection

Registering Multiple Windows Computers Without A

Connection

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Using Efofex Cloud Without A Connection

7.2.1

Detecting A Connectivity Issue

There are two ways you can detect a connectivity issue.

If you start one of our products and let it sit, it will regularly try to sync its local graphics with the cloud. If it cannot connect with our server, it will display this message in the status bar...

The loss of connection may be temporary (if there are external problems with your link) but, if the message is appearing regularly, it is more likely to be an indication that Efofex products are being blocked by your school's firewall.

If you go to the Help menu and choose Manage Account, then choose Enter Code, you will see a screen something like this.

The enter code screen will inform you that there is no connection and will provide some assistance that allows you to make progress with the registration.

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7.2.2

Benefits of Allowing A Connection

Efofex products use your Internet connection for two purposes.

All of your graphics are synced to the cloud. This allows you to share them easily as well as to edit your graphics on any computer that you have licensed. It allows Efofex graphics to be used anywhere.

We have centralised our registration system so that you have one passcode that never changes and computers regularly poll our registration server to see the current state of your registration. This permits you to renew a license without ever touching user computers. All of the new registration details are automatically propagated.

If connections are not allowed, we cannot provide these benefits. It is possible to use our products without a connection but the use is more limited.

7.2.3

Unblocking A Connection

Unblocking a connection will usually require the intervention of technical support. They will need to add Efofex products to the white-list of products that are permitted to access the internet. They will likely need access to the information in the next topic,

Technical

Details

.

7.2.4

Technical Details

Port and Protocol

Efofex products communicate with our servers by use of simple http post requests through port 80. This is exactly the same process that browsers use to load web pages so it is extremely unlikely to be blocked on a system wide level. No special ports or protocols are required. All interaction is through two php files.

http://efofex.com/registrationServer.php

http://efofex.com/graphicsDatabase.php

You can visit these pages through your web-browser to test if the servers are active. You can use this to determine if the connectivity issue is a site based issue or an application white-list issue.

Domain White-Listing

Domain white-listing is unlikely to be the cause of connectivity issues. All interaction occurs through our main domain, efofex.com. If your web browser can visit efofex.com

but one of our products cannot, it is likely that our product has not been placed on an application white-list.

Data Requirements

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When downloading registration information from our registration server, data packets are about 0.3kB in size.

When syncing graphics, the average graphic size is about 1kB. Most graphics are only synced once.

Data requirements for the use of Efofex cloud are trivial and should have minimal impact on your Internet link even if large numbers of users are using the software.

Proxies

Efofex products will use any system wide proxies that are in place. They do not have the capability of using a dedicated proxy and a dedicated proxy should not be needed for normal use.

7.2.5

Registering Without A Connection

If you are unable to organise an Internet connection, you can manually register your computer. This is far less convenient but will allow you to continue to use the software.

Registering without a connection is a two-step process.

First, request a manual registration email from Efofex. You can do this at Request Manual

Registration or you can send an email to [email protected]

We will send you an email that will contain a registration block (as well as other information) that will look something like this...

[registration]0sQ1`P17e1UL8YG#qG6}-I;zn(f!IWdgp6x}=o(G0L)

^vvM'U{(i2;V8vPmx]HO:5;[email protected]>N>`ZT];fh,vNRZ60lilYU5P[nXH4!]p0^_ jL?

Y^4sSTHK,2su}HS`&En#Vf.Ye0toP=l8YlxZ#]Ys5Vmc`-H_KuHc&7IJk{?

5W{bP'[email protected]{NAdMWg}a8b6{M<*zKFx<:mY2iyn^Y*Qm{XZ:a^$?8U9%1<;hf!G,w?

i;HFVNK=|-ELg]hAW;H<W-YeQzP=6a--t6(oe[lk5vcSaKY1m{M2ebXbFXiFK)_Kc31<m)

Q3[Bb95G?2uoK19hiVH|I~5:uZ^m_h_IGy9sxiSVBfa`Q~?K*7CjaKKJ|a&xv!*Pv4&

9zP9HNci k5$g~`kyW||l=_=|iT6w)bEbOZ$8V4?/TJL#N(|f<b8`^8s}8Ern~XPwG<5)

(`kbnG6X`=UW$R[7p S=vmw:&z1Y,JuB[Bs9eq#3!X%9Mc/%&[email protected]{ema$#5u]PXKuEI})

4Yz_UG)mHuFuMY/*C;kuf|=:`[V?kKkLN&vqc5Sl,&f:#I14 7^?$yHP] t~s!M`aiiPPSGo:tQgB>X<N&m =,s=?r_L$5&E:X{YY!wDUmjm9H=~nTJt6&qE|L^By4Q]

11[~O.rt~?#^GQ5G1kl4<n)[email protected]!uT~C .e3t5Bjky.R{DWn#EWb5Hho{z?w<:}

UkHB,0b7iF|Er7TK#FYT|*FlbV!xFr^Wiln2Xo(L}hDf4ca/FwGtwQ3d^JAc3~{FT/w~h?

2CiMi~sotq|Uu[H?KcoEba g-FBNrRm&c`),yLA BnQzy/:#[email protected]>l-

X_v)pkuKb?Q/{y71B^Dmm6XL^]/>.5GjzLxoo32rL^BEMYW_Z%o(4Ve70k3qk%[I|[/ registration]

Second, open any of our products and choose Manage Account from the Help menu.

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Now press Enter A Code

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You will almost certainly be told that the product cannot contact the server (1) but you can push the Paste Manual Registration button (2)

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Copy and paste the registration block (or the whole email that we send) into the box and press OK. The registration block will register your computer.

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7.2.6

Registering Multiple Windows Computers Without A Connection

If you are unable to organise an Internet connection, you can manually register your computers. This is far less convenient but will allow you to continue to use the software.

Registering without a connection is a two-step process.

First, request a manual registration email from Efofex. You can do this at Request Manual

Registration or you can send an email to [email protected]

We will send you an email that will contain a registration block (as well as other information) that will look something like this...

[registration]0sQ1`P17e1UL8YG#qG6}-I;zn(f!IWdgp6x}=o(G0L)

^vvM'U{(i2;V8vPmx]HO:5;[email protected]>N>`ZT];fh,vNRZ60lilYU5P[nXH4!]p0^_ jL?

Y^4sSTHK,2su}HS`&En#Vf.Ye0toP=l8YlxZ#]Ys5Vmc`-H_KuHc&7IJk{?

5W{bP'[email protected]{NAdMWg}a8b6{M<*zKFx<:mY2iyn^Y*Qm{XZ:a^$?8U9%1<;hf!G,w?

i;HFVNK=|-ELg]hAW;H<W-YeQzP=6a--t6(oe[lk5vcSaKY1m{M2ebXbFXiFK)_Kc31<m)

Q3[Bb95G?2uoK19hiVH|I~5:uZ^m_h_IGy9sxiSVBfa`Q~?K*7CjaKKJ|a&xv!*Pv4&

9zP9HNci k5$g~`kyW||l=_=|iT6w)bEbOZ$8V4?/TJL#N(|f<b8`^8s}8Ern~XPwG<5)

(`kbnG6X`=UW$R[7p S=vmw:&z1Y,JuB[Bs9eq#3!X%9Mc/%&[email protected]{ema$#5u]PXKuEI})

4Yz_UG)mHuFuMY/*C;kuf|=:`[V?kKkLN&vqc5Sl,&f:#I14 7^?$yHP] t~s!M`aiiPPSGo:tQgB>X<N&m =,s=?r_L$5&E:X{YY!wDUmjm9H=~nTJt6&qE|L^By4Q]

11[~O.rt~?#^GQ5G1kl4<n)[email protected]!uT~C .e3t5Bjky.R{DWn#EWb5Hho{z?w<:}

UkHB,0b7iF|Er7TK#FYT|*FlbV!xFr^Wiln2Xo(L}hDf4ca/FwGtwQ3d^JAc3~{FT/w~h?

2CiMi~sotq|Uu[H?KcoEba g-FBNrRm&c`),yLA BnQzy/:#[email protected]>l-

X_v)pkuKb?Q/{y71B^Dmm6XL^]/>.5GjzLxoo32rL^BEMYW_Z%o(4Ve70k3qk%[I|[/ registration]

The easiest way to propagate this manual registration information out to computers is to include it as part of a silent, command line driven install. This process is discussed in

Silent

Installs

7.2.7

Using Efofex Cloud Without A Connection

Our products can be used without a connection to the Internet but you will lose access to some of the new features. In particular:

1.

Your graphics will not be automatically synchronised between your devices. You will need to manually synchronise your graphics.

2.

Your graphics will not be automatically backed up to our servers. You can work around this by regularly backing up an exported database of grahics.

2.

You will not be able to edit graphics created by another user.

Manually synchronising graphics is simple.

1.

2.

Export your graphics file on one machine.

Merge that graphics file on the second machine.

Exporting Your Graphics Database

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Choose Export Graphics Database from the File menu of any product.

473

This will export ALL graphics from your machine, regardless of the product they were created in.

You will be asked which folder to save the exported file into. The file will be given a name based on the date of export - eg efofexDatabase-170304.db This file can be used to backup your graphics if you wish.

Merging A Graphics Database

Choose Merge a Graphics Database from the File menu of any product.

Find the database file you wish to merge and press OK. Your graphics FROM ALL

PRODUCTS will be merged into one database.

7.3

Some Digital Certificates Have Expired

Description

Users sometimes notice that one or more of the files they are installing on their systems have been signed with an expired digital certificate and contact us asking for new copies.

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No Action Required

This is not a fault. The expired certificate will have no impact on your use of the products.

If there is a fault then something else is causing it.

Discussion

All of our files are signed with our current certificate at the time they are produced. The files are time-stamped as part of the signing process and there is absolutely nothing wrong with having a file that has been signed with a now expired certificate, providing that the certificate was current at the moment the file was signed. This is as it should be, otherwise you would need to download new copies of everything, just because a developer's certificate expired - which they all do eventually.

Most of our files are updated fairly regularly, so the vast majority of them will have been signed with our current, up-to-date certificate. Some of the files will not have been updated for a while so were last signed with the old certificate. This will have no impact on your use of the software.

Windows will have no trouble with the expired certificate from a practical point of view

7.4

Toolbars Buttons Not Appearing

7.4.1

Toolbar Buttons Not Appearing (All Mac Users)

Description

You have installed one of our products on a Mac computer but no toolbars have been added to Word

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Answer

Our products operate quite differently on a Mac computer and we do NOT add toolbars to

Word. This is by design. Mac users should read the discussion on

Using Efofex Cloud to see

how our products should be used on a Mac computer.

Details

Our products were originally developed to integrate with Microsoft Word on Windows computers. The utilise a technology called OLE and the easiest way to access them using

OLE was to add toolbar buttons to your copy of Word. OLE is the technology that allows you to double-click on an inserted graphic in order to edit it. This system has been used by some customers for over 25 years so feels very familiar.

There are two problems with OLE:

1.

It is simply not available on Mac computers and never will be. This is a decision that Microsoft has made and is totally outside of our control.

2.

OLE is inherently flawed and causes us lots of problems. We are constantly working around issues it creates.

Our new Efofex Cloud products allow you to seamlessly work around these two issues and

we recommend that you read the discussion on Using Efofex Cloud to understand more

about the new system.

7.4.2

Toolbar Buttons Not Appearing (Office 2007 and later)

Cause

Loading the required toolbar definition file has been turned off in Word. This is quite common and Word can sometimes decide to turn the toolbar off ALL BY ITSELF - often for no apparent reason.

Action

Open Word and go to the File menu - then choose Options

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Push the Add-Ins tab then select Templates from the Manage list and press Go

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Place check (tick) marks next to all Efofex templates.

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7.5

Products Not Working

7.5.1

Our Products Reporting That Windows Files Are Missing

Question:

FX Draw is not running after installation. It is saying that api-ms-win-crt-runtime-1-1-0.d11

(or similar) is missing. What's happening?

Answer:

We have recently started compiling our products for Windows 10, but this creates dependencies on new files. These files SHOULD have been automatically updated on your older version of Windows but some computers have not been updated correctly (or in the case of some school computers, at all) and the files are missing. They are not our files, they are Microsoft's.

We are currently deciding whether we should add the required files to our installer but we would like to avoid this as they add significantly to the size and are not necessary for most users.

For the moment, if you have installed one of our products and see a failure like this,

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download and run the required packages from Microsoft using this link.

https://www.microsoft.com/en-au/download/details.aspx?id=53587

7.6

Cannot Find Efofex ID in Graphic

Whenever you return to one of our products, they look at any graphic on the clipboard and try and find an embedded Efofex ID. They use this ID to find the graphic's data, either locally or online. So what does it mean if you KNOW that the graphic on the clipboard was generated with one of our products, but the product reports that it cannot find an ID?

If you see this message on a known graphic, it means that the embedded ID has been stripped or modified in some way.

The embedded ID is coded into subtly coloured semicircles on the edge of your graphic.

Here is a graphic with the changes GREATLY amplified. Normally the embedded code is so subtle it is effectively invisible.

Graphics have the ID embedded on each of its four sides (for redundancy).

If the embedded ID has been stripped, it is almost always for one of two reasons.

1.

2.

The edge of the graphic has been modified or cropped.

The graphic has been compressed by your target program.

Specific situations are discussed in later topics.

7.6.1

Word 2011 (Mac)

Recent versions of Word 2011 for Mac seem to have had changes implemented which cause Word to compress ALL embedded graphics, even when told not to. This compression strips the embedded ID and prevents our products from accessing the graphic.

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There is currently nothing we can do to prevent Word from compressing the graphics. The problem lies with Word 2011.

We are keeping a close eye on this issue and have reported the compression issue to

Microsoft.

In the short term, old graphics can be accessed with the

History

button.

7.6.2

Word Picture Styles

If you add picture styles to a graphic in Word, Word includes these modified edges when you copy the graphic to the clip. This prevents the ID system from finding the embedded

ID.

Standard Graphic

Graphic With Shadow Effec t

If you are using picture styles in Word, you will need to remove the style before copying to clipboard if you want to edit the graphic.

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7.6.3

Simple Graphics In Word (Windows)

If you are using Word for Windows and generate VERY simple graphics that are comprised of large rectangular blocks of colour, Word will compress the images regardless of any other settings.

Compression Triggered Compression NO T Triggered

By adding ANY complexity to the diagram, you avoid the compression from being triggered.

This issue does not cause any issues in regular usage as few people will use FX Draw to draw a simple rectangle. It does sometimes occur when users are testing our products.

7.7

Do You Have PDF Manuals?

With the release of the Efofex Cloud products, we no longer produce PDF versions of our manuals. All the information is now provided online through this website.

We stopped producing PDF manuals for three reasons:

The added significantly to the size of the downloads for the products and many of our users have constrained Internet links.

Users tended to archive the manuals which led to them using out-of-date information.

We make constant changes to our products as we respond to users' needs and the

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ever-changing landscape of operating system upgrades.

PDF manuals are harder to search than this website. The full PDF manuals are over 500 pages in length and are so unwieldy that users were simply not looking at them.

8 Legal Information

8.1

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 terms and conditions. By loading or using the Software, you agree to the terms 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.

8.2

Personal Use Subscription

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. Schools are permitted to purchase a personal use subscription for their teachers but the license will be issued in the teacher's name.

8.3

Full Site Licence / Subscription

A full site 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

Subscription to be fair use PROVIDING such use is solely restricted to producing materials for use within the institution. This means that a school can use its full site subscription to provide copies for their teachers regardless of where they do their work.

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8.4

Distribution Licence / Subscription

A distribution 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, administration staff, gardeners ...) at no extra charge to the institution.

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.

8.5

Personal Use Perpetual License (Deprecated)

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.

8.6

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 support 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 terms 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

I f 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)

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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 terms. 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.

8.7

Website Terms of Service Agreement

Welcome to the Efofex Software website. We maintain this web site as a service to our visitors and customers. By using our site, you are agreeing to comply with and be bound by the following terms of use. Please review the following terms carefully. If you do not agree to these terms, you should not review information or obtain goods or products from this site.

1. Acceptance of Agreement.

You agree to the terms and conditions outlined in this Terms of Service Agreement

("Agreement") with respect to our site (the "Site"). This Agreement constitutes the entire and only agreement between us and you, and supersedes all prior or contemporaneous

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agreements, representations, warranties and understandings with respect to the Site, the content, products or services provided by or through the Site, and the subject matter of this Agreement. This Agreement may be amended at any time by us from time to time without specific notice to you. The latest Agreement will be posted on the Site, and you should review this Agreement prior to using the Site.

2. Intellectual Property; Limited License to Users

The Materials and Services on this Site, as well as their selection and arrangement, are protected by copyright, trademark, patent, and/or other intellectual property laws, and any unauthorized use of the Materials or Services at this Site may violate such laws and the Terms of Use. Except as expressly provided herein, Efofex Software and its suppliers do not grant any express or implied rights to use the Materials and Services. You agree not to copy, republish, frame, download, transmit, modify, rent, lease, loan, sell, assign, distribute, license, sublicense, reverse engineer, or create derivative works based on the

Site, its Materials, or its Services or their selection and arrangement, except as expressly authorized herein. In addition, you agree not to use any data mining, robots, or similar data gathering and extraction methods in connection with the Site.

3. Copyright.

The content, organization, graphics, design, audio, animation, video, compilation, magnetic translation, digital conversion and other matters related to the Site are protected under applicable copyrights, trademarks and other proprietary (including but not limited to intellectual property) rights. The copying, redistribution, use or publication by you of any such matters or any part of the Site, except as allowed by Section 4, is strictly prohibited.

You do not acquire ownership rights to any content, document or other materials viewed through the Site. The posting of information or materials on the Site does not constitute a waiver of any right in such information and materials.

4. Trademarks.

The trademarks, logos, and service marks ("Marks") displayed on this Site are the property of Efofex Software or other third parties. You are not permitted to use the Marks without the prior written consent of Efofex Software or such third party that may own the Marks.

All other trademarks and registered trademarks are the property of their respective owners.

5. Use of Software

The software and accompanying documentation that is made available to download from this Site is the copyrighted and/or patented work of Efofex Software and/or its suppliers.

Use of the software is governed by the terms of the license agreement that accompanies or is included with such software. Such terms are available for review and are incorporated herein by this reference. You will not be able to download or install any software that is accompanied by or includes a license agreement unless you agree to the terms of such license agreement. If you do not agree to such terms, you will not be able to use the software. Absent a license agreement that accompanies the software, use of

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the software will be governed by the Terms of Use. You agree that you will not decompile, reverse engineer, or otherwise attempt to discover the source code of the software available on the Site.

6. Limited Right to Use

The viewing, printing or downloading of any content, graphic, form or document from the

Site grants you only a limited, nonexclusive license for use solely by you for your own personal use and not for republication, distribution, assignment, sublicense, sale, preparation of derivative works or other use. No part of any content, form or document may be reproduced in any form or incorporated into any information retrieval system, electronic or mechanical, other than for your personal use (but not for resale or redistribution). Efofex Software reserves the right to revoke the authorization to view, download, and print the Efofex Software Content and User Content available on this Site at any time, and any such use shall be discontinued immediately upon notice from Efofex

Software. The rights granted to you constitute a license and not a transfer of title.

7. Editing, Deleting and Modification.

We reserve the right in our sole discretion to edit or delete any documents, information or other content appearing on the Site.

8. Indemnification.

You agree to indemnify, defend and hold us and our partners, attorneys, staff and affiliates

(collectively, "Affiliated Parties") harmless from any liability, loss, claim and expense, including reasonable attorney's fees, related to your violation of this Agreement or use of the Site.

9. Nontransferable.

Your right to use the Site is not transferable. Any password or right given to you to obtain information or documents is not transferable.

10. Disclaimer and Limits.

THE INFORMATION FROM OR THROUGH THE SITE ARE PROVIDED "AS-IS," "AS

AVAILABLE," AND ALL WARRANTIES, EXPRESS OR IMPLIED, ARE DISCLAIMED (INCLUDING

BUT NOT LIMITED TO THE DISCLAIMER OF ANY IMPLIED WARRANTIES OF

MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE). THE INFORMATION AND

SERVICES MAY CONTAIN BUGS, ERRORS, PROBLEMS OR OTHER LIMITATIONS. WE AND

OUR AFFILIATED PARTIES HAVE NO LIABILITY WHATSOEVER FOR YOUR USE OF ANY

INFORMATION OR SERVICE. IN PARTICULAR, BUT NOT AS A LIMITATION THEREOF, WE

AND OUR AFFILIATED PARTIES ARE NOT LIABLE FOR ANY INDIRECT, SPECIAL, INCIDENTAL

OR CONSEQUENTIAL DAMAGES (INCLUDING DAMAGES FOR LOSS OF BUSINESS, LOSS OF

PROFITS, LITIGATION, OR THE LIKE), WHETHER BASED ON BREACH OF CONTRACT,

BREACH OF WARRANTY, TORT (INCLUDING NEGLIGENCE), PRODUCT LIABILITY OR

OTHERWISE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. THE NEGATION

OF DAMAGES SET FORTH ABOVE ARE FUNDAMENTAL ELEMENTS OF THE BASIS OF THE

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BARGAIN BETWEEN US AND YOU. THIS SITE AND THE INFORMATION WOULD NOT BE

PROVIDED WITHOUT SUCH LIMITATIONS. NO ADVICE OR INFORMATION, WHETHER ORAL

OR WRITTEN, OBTAINED BY YOU FROM US THROUGH THE SITE SHALL CREATE ANY

WARRANTY, REPRESENTATION OR GUARANTEE NOT EXPRESSLY STATED IN THIS

AGREEMENT.

ALL RESPONSIBILITY OR LIABILITY FOR ANY DAMAGES CAUSED BY VIRUSES CONTAINED

WITHIN THE ELECTRONIC FILE CONTAINING THE FORM OR DOCUMENT IS DISCLAIMED.

WE WILL NOT BE LIABLE TO YOU FOR ANY INCIDENTAL, SPECIAL OR CONSEQUENTIAL

DAMAGES OF ANY KIND THAT MAY RESULT FROM USE OF OR INABILITY TO USE OUR

SITE. OUR MAXIMUM LIABILITY TO YOU UNDER ALL CIRCUMSTANCES WILL BE EQUAL TO

THE PURCHASE PRICE YOU PAY FOR ANY GOODS, SERVICES OR INFORMATION.

11. Use of Information.

We reserve the right, and you authorize us, to the use and assignment of all information regarding Site uses by you and all information provided by you in any manner consistent with our Privacy Policy.

12. Third-Party Services.

We may allow access to or advertise third-party merchant sites ("Merchants") from which you may purchase certain goods or services. You understand that we do not operate or control the products or services offered by Merchants. Merchants are responsible for all aspects of order processing, fulfillment, billing and customer service. We are not a party to the transactions entered into between you and Merchants. You agree that use of such

Merchants is AT YOUR SOLE RISK AND IS WITHOUT WARRANTIES OF ANY KIND BY US,

EXPRESSED, IMPLIED OR OTHERWISE INCLUDING WARRANTIES OF TITLE, FITNESS FOR

PURPOSE, MERCHANTABILITY OR NON-INFRINGEMENT. UNDER NO CIRCUMSTANCES

ARE WE LIABLE FOR ANY DAMAGES ARISING FROM THE TRANSACTIONS BETWEEN YOU

AND MERCHANTS OR FOR ANY INFORMATION APPEARING ON MERCHANT SITES OR ANY

OTHER SITE LINKED TO OUR SITE.

13. Third-Party Merchant Policies.

All rules, policies (including privacy policies) and operating procedures of Merchants will apply to you while on such sites. We are not responsible for information provided by you to Merchants. We and the Merchants are independent contractors and neither party has authority to make any representations or commitments on behalf of the other.

14. Privacy Policy.

Our Privacy Policy, as it may change from time to time, is a part of this Agreement.

15. Payments.

You represent and warrant that if you are purchasing something from us or from

Merchants that (i) any credit information you supply is true and complete, (ii) charges incurred by you will be honored by your credit card company, and (iii) you will pay the charges incurred by you at the posted prices, including any applicable taxes.

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16. Links to other Web Sites.

The Site may contain links to other Web sites. We are not responsible for the content, accuracy or opinions express in such Web sites, and such Web sites are not investigated, monitored or checked for accuracy or completeness by us. Inclusion of any linked Web site on our Site does not imply approval or endorsement of the linked Web site by us. If you decide to leave our Site and access these third-party sites, you do so at your own risk.

17. Information and Press Releases.

The Site contains information and press releases about us. While this information was believed to be accurate as of the date prepared, we disclaim any duty or obligation to update this information or any press releases. Information about companies other than ours contained in the press release or otherwise, should not be relied upon as being provided or endorsed by us.

18. Miscellaneous.

This Agreement shall be treated as though it were executed and performed in Perth,

Western Australia, and shall be governed by and construed in accordance with the laws of the State of Western Australia (without regard to conflict of law principles). Any cause of action by you with respect to the Site (and/or any information, products or services related thereto) must be instituted within one (1) year after the cause of action arose or be forever waived and barred. All actions shall be subject to the limitations set forth in

Section 7 and Section 9. The language in this Agreement shall be interpreted as to its fair meaning and not strictly for or against either party. All legal proceedings arising out of or in connection with this Agreement shall be brought solely in Perth, Western Australia. You expressly submit to the exclusive jurisdiction of said courts and consents to extraterritorial service of process. Should any part of this Agreement be held invalid or unenforceable, that portion shall be construed consistent with applicable law and the remaining portions shall remain in full force and effect. To the extent that anything in or associated with the Site is in conflict or inconsistent with this Agreement, this Agreement shall take precedence. Our failure to enforce any provision of this Agreement shall not be deemed a waiver of such provision nor of the right to enforce such provision.

Contacting the Web Site

If you have any questions about this privacy statement, the practices of this site, or your dealings with this Web site, you can contact webmaster

Efofex Software

PO Box 189

Claremont WA 6910

Australia [email protected]

© 2017 Efofex Software

Efofex Help Legal Information 489

8.8

Refund Policy

Since our company is offering non-tangible irrevocable goods we do not normally issue refunds after the product is shipped, which you are responsible for understanding upon purchasing. Please make sure that you have carefully read all relevant documentation and tried out the fully functional evaluation version. We only make exceptions with this rule when the product appears to be not-as-described on a case by case basis in agreement of the parties concerned. The deadline for any refund claim is one week after the delivery date.

If you find a bug in our software, you can report it to [email protected] and we will fix it in the next version. We understand that it is impossible for us to test our software on every platform and every configuration it may encounter on other computer. Therefore if you are unable to get our software up and running on your computer then please contact us and we will do everything within our knowledge and experience to get our software to work on your computer.

8.9

Privacy Statement

Efofex Software has created this privacy statement in order to demonstrate our firm commitment to privacy. The following discloses our information gathering and dissemination practices for this website: www.efofex.com

.

We use your IP address to help diagnose problems with our server, and to administer our

Web site. We do not log IP addresses for any other purpose

Our site's registration form requires users to give us their email address. We use customer contact information from the registration form to send the user information about our company. We do not disseminate your email address to any other parties.

Users may opt-out of receiving future mailings; see the choice/opt-out section below.

This site contains links to other sites. Efofex is not responsible for the privacy practices or the content of such Web sites.

Our site uses an order form for customers to request information, products, and services.

We collect visitor's contact information (like their email address) and financial information

(like their account or credit card numbers). Contact information from the order form is used to send orders to our customers. The customer's contact information is used to get in touch with the visitor when necessary. Users may opt-out of receiving future mailings; see the choice/opt-out section below. Financial information that is collected is used to bill the user for products and services. No financial information is retained by Efofex after processing of payments.

Security

This site has security measures in place to protect the loss, misuse and alteration of the information under our control.

Choice/Opt-Out

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Our site provides users the opportunity to opt-out of receiving communications from us at the point where we request information about the visitor.

This site gives users the following options for removing their information from our database to not receive future communications or to no longer receive our service.

You can send email to [email protected]

You can send mail to the following postal address:

PO Box 189, Claremont WA 6910, Australia

Correct/Update

This site gives users the following options for changing and modifying information previously provided.

You can send email to [email protected]

You can send mail to the following postal address:

PO Box 189, Claremont WA 6910, Australia

Contacting the Web Site

If you have any questions about this privacy statement, the practices of this site, or your dealings with this Web site, you can contact webmaster

Efofex Software

PO Box 189

Claremont WA 6910

Australia [email protected]

© 2017 Efofex Software

Efofex Help 491

Index

- B -

- + -

+- 375

- 1 -

1st Derivative 419

- 2 -

2000 451

2nd Derivative 419

- 9 -

b 406

Balance 215

Bar Graph 296

Basic 170

Benzene 173

Bernoulli 351

Bernoulli Trial 336

Binomial Distribution 336, 352 bisect 19

Bivariate Data 339

Blank 151

Bonds 183, 185

Box Plots 297

Braces 212

Brackets 209, 253, 366

Branched 172

Broken Scale 286

Brush 326

- C -

95 451

98 451

- A -

a 406 abs 396

Absolute Frequency 301, 304, 305, 307, 308, 309 absolute value 360 acos 396

Acrobat 456 add and subtract figures 40

Administrator 453

Adobe 456

Angle 106

Animation 410 anti-clockwise 42

Arcs 100

Arrow 177 arrow line 44, 52

Arrows 212, 283 asin 396

Asymptotes 397 atan 396

Atomic Number 212

Autoscale 362

Axes 98, 157, 283, 295, 362

Axis 98 c 406

Capitalise 170, 211

Carbohydrates 187

Cartesian 121, 134, 374

CD 452 centre 69, 86

Change 191, 216

Changing Column Types 261

Charge 184

Charges 178

Chi Squared Distribution 339 circle 69 circumference 19 cis 176

Clicking 174, 176

Clipboard 279 clockwise 42

Cobalt 188, 213

Codes 212

Column 258, 260

Column Graph 297

Column Titles 267

Columns 257

Combine Graph Types 331

Comments 173

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Complements 240

Complex 172

Complex Numbers 218

Conditions 482

Constant Controller 406

Constants 406

Continuous - Chi Squared 339

Continuous - Exponential 338

Continuous - Log Normal 339

Continuous - Normal 338

Continuous - Uniform 338 control points 40

Copy 49

Copy Statistics 279

Copyright 483 cos 360, 396 cosec 360, 396 cosh 360, 396 cot 360, 396

Create 365

Create Graph 281

Ctrl 23, 40, 44, 49, 51

Cumulative Frequency 299, 308, 345 cumulative frequency table 345

Cumulative Histogram 308

Curly Brackets 212 curvature 100

Cut 49

- D -

d 406

Data Box 326

Data Boxes 280

Data Columns 258, 262

Data Generator 267, 335, 339, 340, 341

Data View 256, 257

Decile 345

Decimals 219

Default 160, 189, 214, 362

Definite Integral 420

Degrees 165, 210, 219, 362

Derivative 419

Deseasonalise 357

Deviation 345

Diameter 69

Dice 341 direction 163

Discontinuity 156

492

Discrete - Bernoulli 336

Discrete - Binomial 336

Discrete - Equi-Likely 335

Discrete - Geometric 337

Discrete - HyperGeometric 336

Discrete - Negative Binomial 337

Discrete - Poisson 337

Discrete - Uniform 335

Distribution 483

Domain 156, 161, 404, 405

Dot Plot 300

Dot to Dot 383 dots 134

Double click 213

Download 452

Drawing Order 38, 48, 49

- E -

e 360, 396

Edit 213

Electron Pairs 185

Electrons 186

Ellipse 98 elliptical arcs 100 end points 19

Equation 160, 164, 165

Equation Level 195

Equations 222

Equilibrium 177

Equilibrium Arrow 212

Equi-Likely Distribution 335

Error 191, 216

Evaluation 454, 456

Exclusion 483

Exponential Distribution 338

- F -

Families of Curves 408

Family 408

Feasible Region 362

Feasible Regions 155

Fibonacci 345

Fill Down 267

Fill Type 33 foci 98

Font 189, 214

Formula Columns 258, 266

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Formulas 257, 266

Fractions 234

Frequency 345, 346

Frequency Columns 258, 264

Frequency Density 305, 307, 308, 309

Frequency Polygon 301, 304

Frequency Table 345, 346

Frequency Tables 264

Full Site 482

Functions 121, 245, 275, 362, 365

FX Graph 121

FX Stat 122

- G -

GAD 19, 22, 23, 34, 44, 49, 106

Galleries 142

Gallery 47, 49, 163, 164

Geometric 353

Geometric Distribution 337

Geometrically Aware Drawing 17, 19 geometry 19

Grads 362

Graph 281

Graph Type 280, 282

Graph Types 326, 331

Graph View 256

Greek 164, 235

Grid 44, 164, 292, 362

Grid - Polar 292 grids 134 group 39, 40, 47, 49, 162

Group Columns 258, 264

Group data 346, 347

Grouped Data 264, 272

Groups 163

Groups of Points 383

- H -

Headings 295

Hexagonal 134

Hide Graph 326

Highlight Data 269, 326

Histogram 305, 307, 308, 309 hyperbolic 360

Hypergeometric 353

HyperGeometric Distribution 336

493

- I -

Implicit 379

Implicitly Defined 379

Important 482

Increment 347

Insert Object 11, 194

Install 452

Integral 420

Integrals 230, 236

Intercepts 397

Intersection 106, 397

Inverse 121, 161, 378

Ionic 179

Ions 179

Isomer 176

Isometric 134

Italic 189, 214

- K -

Keyboard shortcut 49

- L -

Label Columns 258, 263

Labels 263, 310

Layout 38, 48

Levels 189, 214

Liability 483

Licence 482

Limitation 483

Limits 238

Line 52, 326

Line Graph 310

Line Type 32 ln 396

Local Maxima/Minima 397 log 396

Log Normal Distribution 339

Log Scale 286 logarithm 360

Logarithmic 134

- M -

m 406 major 100

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Major / Minor Angles 106

Mask Data 268

Mass Number 212

Matrices 165, 210, 239

Maximum 286

Me 451

Mean Deviation 345

Means 240 measurements 52

Mess 161 meta 176 mid point 19

Minimum 286 minor 100

Modify 330 mouse 17

Moving Point Average 310, 348

Multiple Graph Types 326, 331

- N -

natural logarithm 360

Negative Binomial 353

Negative Binomial Distribution 337 network 161 networks 52

Normal 354

Normal Distribution 127, 338, 348, 349

NT 451 nth Root 243

Nuclear Chemistry 212

Nudge 41, 49 number line 132 nverse trigonometric 360

- O -

Options 189, 214

Ordered Pair 165, 209

Organic Chemistry 215

Origin 283 ortho 176

Outliers 297 overlapping 38

Ownership 483

- P -

para 176

494

parallels 19

Parametric 121, 380

Paste 49

Percentage Frequency 301, 304, 305, 307, 308,

309

Percentile 349

Percentiles 343

Perpendiculars 19, 106

Personal Use 483

Phase 178

Phenol 173 pi 396

Pie Graph 314

Piecewise Defined Function 162

Plane 399

Point 86, 326

Points 381

Points of Inflection 397

Points of intersection 19

Poisson Distribution 337

Polar 121, 134, 161, 376, 381, 383, 384

Polar Grid 292

Polyatomic Ions 179

Powers 243, 366

Prediction 349, 351

Predictions 244

Prices 454, 456 print 49

Privileges 453

Product Notation 244 properties 43, 160

- Q -

quarter point 19

Quartiles 343

Quick Graph 271

Quick Group 272

Quick Sort 273

Quick Statistics 274

Quotes 212

- R -

R 178, 215

Radians 362

Radius 69 rainbow 32, 33

Random 335, 336, 337, 338, 339, 340, 341

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Efofex Help 495

Random Numbers 351, 352, 353, 354

Rank 355

Reaction 177

Reaction Arrow 212 rectangle 73

Redo 49

Reflect 39, 175, 176

Reflection 39

Registration 454, 456

Regression 310, 317, 318, 349, 351, 355, 356

Relative Frequency 301, 304, 305, 307, 308, 309

Requirement 451

Rerun formulas 270

Reset to default 189, 214

Residual 355, 356

Residuals 317, 318

Residuals Graph 317

Resonance 187

Restrictions 366 right clicking 43

Ring Structures 179 root 396

Roots 366

Rotate 175, 176

Rotating 42, 49

Round 357

Rounding 357

Row 357

- S -

Shift 23, 44, 49, 100

Sigma Notation 247

Silicon 188, 213 sin 360, 396 sinh 360, 396

Size 189, 214 sliders 43, 160

Sort 358

Sort Data 273

Spaces 164, 209, 366

Spacing 177 sqrt 396 square root 248, 360, 396

Staff Use 482, 483

Standardise 359 stanine 359

State 178

Statistics 274, 276, 278

Statistics Functions 275

Statistics View 256

Stem & Leaf Plot 321

Structures 170

Student Use 483

Subscript 170, 211

Subscripts 248

Superscript 170, 211

Symbols 248, 366

System 451

- T -

Save To Gallery 144

Scale 286

Scale - Broken 286

Scale - Equal Aspect 286

Scale - Fractions 286

Scale - Free 286

Scale - Log 286

Scale - Pi 286

Scattergraph 318

Seasonalize 310, 343

Seasonlise 357 sec 360, 396

Sectors 100

Segments 100

Select 40, 51, 160, 329

Select Mode 398

Set To Default 44, 160

Setting Defaults 44, 342 tan 360, 396

Tangent 19

Tangent Lines 437 tangential 19 tanh 360, 396

Termination 483

Text Style 189, 214 third points 19

Ticks 151, 283

Time Series 340

Time Series Data 348

Titles 267, 295

Toolbar 10, 11, 193, 194 trans 176

Transform 174, 176

Transparency 326

Triangle Graph 324 triangular numbers 359

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Efofex Help

Tribonacci 359

Turning Points 397

Two Arms 375

- U -

Undo 49

Unformatted 173

Unformatted Text 212 ungroup 39, 47, 163

Uniform Distribution 338, 351

Upgrade 483

- V -

Vectors 384

Vectors - (a b) 209

Venn 129, 131

Viewing Statistics 277

- W -

Warranty 483

Windows 451

- X -

XP 451

- Y -

y = 374

- Z -

Z Score 359, 360

Zoom 157, 401, 403

496

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