111111VCE MAVCE MATHEMATHEMATICS UNITS 1 & 2TICS UNITS 1 & 2

MAMATTHS HS QuestQuestGeneral Mathematics

Prelims Gen Maths Page i Wednesday, December 15, 1999 10:22 PM

Prelims Gen Maths Page ii Wednesday, December 15, 1999 10:22 PM

JENNIFER NOLAN GEOFF PHILLIPS

ELENA IAMPOLSKY SONJA STAMBULIC

111111MAMATTHS HS QuestQuestGeneral Mathematics

Support materialRoss Allen • John Dowsey • Dennis Fitzgerald • Emily HuiVinod Narayan • David Phillips • Peter Swain • David Tynan

Contributing authorsMurray Anderson • Robert Cahn • Kathy Chambers • Michael Halfpenny

Carolyn Mews • David Phillips • John Short • Nick Simpson• Boris Smolyar • Jenny Watson • Barbara Woods

VCE MAVCE MATHEMATHEMATICS UNITS 1 & 2TICS UNITS 1 & 2

Prelims Gen Maths Page iii Monday, July 8, 2002 11:18 AM

First published 2000 byJohn Wiley & Sons Australia, Ltd33 Park Road, Milton, Qld 4064

Offices also in Sydney and Melbourne

Typeset in 10.5/12.5pt Times

© John Wiley & Sons Australia, Ltd

National Library of AustraliaCataloguing-in-Publication data

Maths Quest 11: General Mathematics VCE MathematicsUnits 1 and 2

ISBN 0 7016 3396 4 (student book)ISBN 0 7016 3456 1 (teacher edition)

1. Mathematics. 2. Victorian Certificate of Educationexamination — Study guides. I. Nolan, Jennifer.

510

All rights reserved. No part of this publication may bereproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical,photocopying, recording, or otherwise, without the priorpermission of the publisher.

Edited by Merv Littmann, Margaret Falk, Joy Windowand Jennifer Wright

Illustrated by the Wiley Art Department

Cover photograph: © PhotoDisc 1998

Printed in Singapore

10 9 8 7

Prelims Gen Maths Page iv Friday, May 4, 2001 3:41 PM

Contents

CHAPTER 1

�

Arithmetic 1

Mental computations 2

Exercise 1A 6

Calculator computations 7

Exercise 1B 10

Rounding-off 12

Exercise 1C 15

Estimation and approximation 17

Exercise 1D 18

Estimation errors 20

Ratios 21

Exercise 1E 23

Proportion 25

Exercise 1F 27

Gears and drive belts 28

Percentages 29

Career profile: Darren Blood 31

Exercise 1G 32

Percentage change 34

Exercise 1H 36

Summary 38Chapter review 40

CHAPTER 2

�

Applications of arithmetic 43

Discount 44

Exercise 2A 46

Profit and loss 49

Exercise 2B 51

Commission 53

Exercise 2C 55

Payroll calculations 57

Exercise 2D 60

Career profile: Noelene Clahsen 61

Income tax 62

Exercise 2E 64

Tax rates and the GST 65Career profile: Brett Comer 65

Budgeting 66

The Australian budget 68

Exercise 2F 69

Cost of services 71

Exercise 2G 71

Credit cards 79

Exercise 2H 83

Reducing-interest loans 85

Exercise 2I 89

Buying a house 90

Summary 91Chapter review 93

CHAPTER 3

�

Financial arithmetic 97

Simple interest 98

Exercise 3A 102

Compound interest 104

Exercise 3B 110

Straight-line depreciation 112

Exercise 3C 117

Reducing-balance depreciation 119

Exercise 3D 124

Unit cost depreciation 126

Exercise 3E 128

Career profile: Nadine Lyons 129

Hire-purchase, flat rate and real rate of interest 130

Exercise 3F 135

Break-even analysis 137

Exercise 3G 140

Summary 142Chapter review 144

CHAPTER 4

�

Variation 147

Direct variation 148

Exercise 4A 153

Further direct variation 156

Exercise 4B 159

Inverse variation 163

Exercise 4C 168

Further inverse variation 172

Exercise 4D 174

The effect of changing one variable on another 176

Joint variation 177

Exercise 4E 180

viPart variation 184

Exercise 4F 186Transformation of data 188

Exercise 4G 190Reaction times 191Summary 192Chapter review 193

CHAPTER 5� Sequences and series 199Describing sequences 200

Exercise 5A 203History of mathematics: Leonardo Fibonacci 204Arithmetic sequences 205

Exercise 5B 209Arithmetic series 211

Exercise 5C 213Geometric sequences 214

Exercise 5D 218Geometric series 220

Exercise 5E 224Crossing the road 225Applications of sequences and series 226

Exercise 5F 228Difference equations 231

Exercise 5G 235Changing shape 237Summary 238Chapter review 240

CHAPTER 6� Linear graphs and modelling 243Plotting straight line graphs 245

Exercise 6A 246Using a graphics calculator to plot linear

functions 247Exercise 6B 248

Finding the gradient of a straight line 249Exercise 6C 250

Determining the equation of a straight line 252

Exercise 6D 254

Relating equations and graphs to values of gradients and intercepts 255Sketching straight line graphs 257

Exercise 6E 259Application of linear modelling 260

Exercise 6F 262Line of best fit (by eye) 264

Exercise 6G 267Graphs of non-linear functions 268Non-linear data 270

Exercise 6H 274Summary 275Chapter review 277

CHAPTER 7� Linear programming 281Graphs of linear inequations I 283

Exercise 7A 286Graphs of linear inequations II 287

Exercise 7B 288Graphs of simultaneous linear

inequations 289Exercise 7C 293

Graphs of systems of linear inequations 294Exercise 7D 296

Using technology 297Maximising and minimising linear

functions 298Exercise 7E 303

Solving linear programming problems 304Exercise 7F 306

How many in the research team? 309Further applications of linear

programming 310Exercise 7G 313

Deck chairs 314Summary 315Chapter review 316

CHAPTER 8� Sketching and interpreting graphs 321The circle 322

Exercise 8A 324

Prelims Gen Maths Page vi Wednesday, December 15, 1999 10:22 PM

viiThe ellipse 325

Exercise 8B 328The parabola 329

Exercise 8C 332The hyperbola 333

Exercise 8D 338Polar coordinates 340

Exercise 8E 342Polar equations 343

Exercise 8F 345Polar graphs 346

Exercise 8G 350A gallery of polar graphs 351Summary 352Chapter review 354

CHAPTER 9� Linear relations and equations 357Linear equations 358

Exercise 9A 363Solving problems using linear equations 365

Exercise 9B 368How much is that car? 370Substitution and transposition in linear

relations 371Exercise 9C 376

Linear recursion relationships 379Exercise 9D 383

Simultaneous equations 385Exercise 9E 391

Comparing production costs 392Solving problems using simultaneous

equations 393Exercise 9F 395

Pumping blood 397Summary 398Chapter review 399

CHAPTER 10� Non-linear relations and equations 403Substitution and transposition into non-linear

relations 404Exercise 10A 406

Further formulas 408Exercise 10B 411

Solving non-linear equations using graphs and tables 413

Exercise 10C 417Solving non-linear equations using simple

numerical approaches 418Exercise 10D 424

To converge or not to converge? 425Quadratic equations 426

Exercise 10E 428Solving simultaneous equations using

algebra 429Exercise 10F 432

Solving simultaneous equations with a graphics calculator 433

Exercise 10G 439Summary 441Chapter review 443

CHAPTER 11� Shape and measurement 447Pythagoras’ theorem in two dimensions 448

Exercise 11A 449Triathalon 450Pythagoras’ theorem in three

dimensions 451Exercise 11B 453

Perimeter and area 455Exercise 11C 460

Total surface area (TSA) 463Exercise 11D 467

Coneheads 471Volume 472

Exercise 11E 476Cone volume 479Capacity 480

Exercise 11F 481Similar figures 482

Exercise 11G 488Making an aeroplane 491Similar triangles 492

Exercise 11H 497Career profile: Nathan Gorman 500Symmetry 500

Exercise 11I 503

Prelims Gen Maths Page vii Friday, May 4, 2001 3:42 PM

viiiSummary 507Chapter review 510

CHAPTER 12� Coordinate geometry 515Distance between two points 516

Exercise 12A 518Midpoint of a line segment 519

Exercise 12B 522Dividing a line segment internally in the ratio

a:b 523Exercise 12C 526

Finding the centroid of a triangle 526Dividing a line segment externally in the ratio

a:b 527Exercise 12D 530

Give way 530Parallel lines 531Investigating linear equations 531

Exercise 12E 533Perpendicular lines 534Pairs of perpendicular lines 534

Exercise 12F 536Applications 537

Exercise 12G 541A Roman aqueduct 542Summary 543Chapter review 544

CHAPTER 13� Vectors 547Introduction to vectors 548

Exercise 13A 551Operations on vectors 552

Exercise 13B 556Magnitude, direction and components of

vectors 557Exercise 13C 560

, notation 561Exercise 13D 564

Angle between 2 vectors in , notation 566Applications of vectors 567

Exercise 13E 569Summary 571Chapter review 572

CHAPTER 14� Geometry in two and three dimensions 575Review of basic geometry 576

Exercise 14A 579Geometric constructions 581

Exercise 14B 584Polygons 585Star polygons 591

Exercise 14C 592Three-dimensional geometry 593

Exercise 14D 595Polyhedra vertex patterns 596Circle geometry 597

Exercise 14E 600Tangents, chords and circles 602

Exercise 14F 606Circle constructions 608Geometry in architecture, design and

art 609Career profile: Rachel Nolan 609The Golden Ratio 612

Exercise 14G 614Summary 616Chapter review 618

CHAPTER 15� Trigonometric ratios and their applications 621Trigonometry of right-angled triangles 622

Exercise 15A 626Trigonometric identities 628Applications of right-angled triangles 629

Exercise 15B 633Fly like a bird 634Non-right-angled triangles — the sine

rule 635Exercise 15C 641

Non-right-angled triangles — the cosine rule 643

Exercise 15D 646Career profile: Richard Kennedy 647Area of triangles 648

Exercise 15E 651

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Prelims Gen Maths Page viii Wednesday, December 15, 1999 10:22 PM

ixRadian measurement 653

Exercise 15F 654Arcs, sectors and segments 655

Exercise 15G 658Summary 660Chapter review 662

CHAPTER 16� Univariate data 665Working with categorical data 667

Exercise 16A 670Working with numerical data 673

Exercise 16B 679Cumulative data 682

Exercise 16C 686Measures of central tendency 690

Exercise 16D 695Mean, median, mode 697Measures of variability 698

Exercise 16E 704Stem-and-leaf plots 708

Exercise 16F 711Boxplots 714

Exercise 16G 717

Comparing sets of data 720Exercise 16H 723

Drug test analysis 726Summary 727Chapter review 729

CHAPTER 17� Bivariate data 735Scatterplots 736

Exercise 17A 741Career profile: Roger Farrer 744The correlation coefficient 745

Exercise 17B 749Does overcrowding cause unemployment? 753Linear modelling 754

Exercise 17C 758Making predictions 761

Exercise 17D 764World population 768Summary 769Chapter review 771

Answers 777

Prelims Gen Maths Page ix Wednesday, December 15, 1999 10:22 PM

x

CHAPTER 18� Number systemsClassification of numbers

Exercise 18ASet notation

Exercise 18BRecurring decimals

Exercise 18CThe Real Number System

Exercise 18DOther number systemsSurds

Exercise 18ESimplifying surds

Exercise 18FAddition and subtraction of surds

Exercise 18GMultiplication of surds

Exercise 18HDivision of surds

Exercise 18IThe Distributive Law

Exercise 18JRationalising denominators

Exercise 18KRationalising denominators using conjugate

surdsExercise 18L

ModulusExercise 18M

SummaryChapter review

CHAPTER 19� MatricesIntroduction to matricesOperations with matrices

Exercise 19AMultiplying matrices

Exercise 19BHistory of Mathematics: Olga Taussky-Todd

Multiplicative inverse and solving matrix equations

Exercise 19CApplications of matrices

Exercise 19DMatrix multiplication using a graphics calculatorMatrices and transformations

Exercise 19ECommutativity of transformationsSummaryChapter review

CHAPTER 20� Algebra and logicStatements, connectives and truth tables

Exercise 20AValid and invalid arguments

Exercise 20BTechniques of proofProof by mathematical induction

Exercise 20CSets and Boolean algebra

Exercise 20DHistory of Mathematics: George BooleDigital logic

Exercise 20EA computer storage deviceBinary additionSummaryChapter review

CHAPTER 21� Undirected graphs and

networksUndirected graphs and networksVertices and edges

Exercise 21APlanar graphs

Exercise 21BSchlegel diagramsMap colouring

Additional chapters on CD-ROM only

Prelims Gen Maths Page x Wednesday, December 15, 1999 10:22 PM

xi

Eulerian paths and circuits

Exercise 21C

Hamiltonian paths and circuits

Exercise 21D

Trees

Exercise 21E

SummaryChapter review

CHAPTER 22

�

Sampling for attributesPopulations and samples

Exercise 22ADistribution of sample proportions

Exercise 22BThe 95% spread of sample proportions

Exercise 22CConfidence intervals

Exercise 22DUsing confidence intervals

Exercise 22ESummaryChapter review

CHAPTER 23� CombinatoricsThe addition and multiplication principles

Exercise 23AFactorials and permutations

Exercise 23BArrangements involving restrictions and like

objectsExercise 23C

CombinationsExercise 23D

Applications of permutations and combinations

Exercise 23EPascal’s triangle and the binomial theoremCounting paths

Exercise 23FHistory of Mathematics: Blaise PascalSummaryChapter review

CHAPTER 24� Introductory probabilityBasic probability conceptsEvents, event spaces and random events

Exercise 24ARandom numbers and simulations

Exercise 24BLong-run proportion

Exercise 24CSimple and compound events — independent

eventsExercise 24D

Compound events — mutually exclusive events

Exercise 24ECompound events — Venn diagrams

Exercise 24FCompound events — conditional probability

Exercise 24GRecording and interpreting simulations

Exercise 24HTarget practiceFooty seasonThe Ace of HeartsSummaryChapter review

Prelims Gen Maths Page xi Wednesday, December 15, 1999 10:22 PM

Introduction

Maths Quest 11 General Mathematics

is one of the exciting new

MathsQuest

resources specifically designed for the new VCE (2000–2003) Mathe-matics course. It breaks new ground in Mathematics textbook publishing.

This resource contains:• a student textbook with accompanying CD-ROM and • a teacher edition with accompanying CD-ROM.

Student textbook

Full colour

is used throughout to produce clearer graphs and headings, toprovide bright, stimulating photos and to make navigation through the texteasier.

Clear, concise

theory sections

contain

worked examples

,

graphics calculatortips

and

highlighted important text

and

remember boxes

.

Worked examples

in a Think/Write format provide clear explanation of keysteps and suggest presentation of solutions.

Exercises

contain many carefully graded skills and application problems,including multiple choice questions. Cross references to relevant workedexamples appear beside the first ‘matching’ question throughout theexercises.

Career profiles

and

History of mathematics

place mathematical concepts incontext.

Investigations

, often suggesting the use of technology, provide further dis-covery learning opportunities.

Each chapter concludes with a

summary

and

chapter review

exercise contain-ing examination style questions (multiple choice, short answer and analysis)which help consolidate students’ learning of new concepts.

Technology

is fully integrated (in line with VCE 2000 recommendations). Aswell as graphics calculators,

Maths Quest

features computer algebra systems,spreadsheets, dynamic geometry software and several graphing packages.Not only does the text promote these technologies as learning tools, but dem-onstration versions of the programs (with the exception of Microsoft Excel)are also included, as well as hundreds of supporting files on the

bonus

accom-panying CD-ROM.

Student CD-ROM

The accompanying CD-ROM contains the entire student textbook plus addi-tional exercises. Students may work from the CD on laptops, school or homecomputers, and cut and paste material for revision or assignments.

Clearly labelled icons within the electronic version of the text

hyperlink

tohundreds of technology files for programs such as

Mathcad

,

Excel

and

CabriGeometry

to allow further exploration of ‘what if’ scenarios.

TI-83 Graphics calculator programs can be downloaded to students’ calcu-lators using the Graphlink software provided.

111111MATHS QuestQuest

JENNIFER NOLAN GEOFF PHILLIPS ELENA IAMPOLSKY SONJA STAMBULICJENNIFER NOLAN GEOFF PHILLIPS ELENA IAMPOLSKY SONJA STJENNIFER NOLAN GEOFF PHILLIPS ELENA IAMPOLSKY SONJA STAMBULICAMBULIC

JAC

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MA

THSQUES

T

VCE MAVCE MATHEMATHEMATICS UNITS 1 & 2TICS UNITS 1 & 2

General MathematicsGeneral Mathematics

INTE

RACTIVE

C

D- ROM

Cabri

Geometry

EXCEL

Spreadsheet

Mathca

d

GCpro

gram

Prelims Gen Maths Page xii Tuesday, July 20, 2004 6:43 AM

xiii

WorkSHEET

and

Test yourself

icons link to editable

Word 97

documents, andmay be completed on screen or printed and completed.

SkillSHEET

icons link to printable pages designed to help students reviserequired concepts, and contain additional examples and problems.

Programs included

Mathcad Explorer

: a computer algebra system and graphing program

Graphmatica

: an excellent graphing utility

Equation grapher and regression analyser

: like a graphics calculator forthe PC

GrafEq

: graphs any relation, including complicated inequalities

Poly

: for visualising 3D polyhedra and their nets

TI Graphlink 83 and 89

: calculator screen capture and program transfer

Cabri Geometry II

: dynamic geometry program

Adobe

®

Acrobat

®

Reader 4.0

Teacher edition with accompanying CD-ROM

The teacher edition textbook contains everything in the student textbook andmore. To support teachers assisting students in class,

answers

appear in rednext to most questions in the exercises. Each exercise is annotated withrelevant study design points. A readily accessible

Work program

lists allavailable resources and provides curriculum coverage information.

The accompanying teacher CD-ROM contains everything in the studentCD-ROM and more. Two tests per chapter, fully worked solutions to

WorkSHEETs

, the work program and other curriculum advice in editable

Word 97

format are provided.

Web site:

www.jaconline.com.au/maths

The

Maths Quest

Web site will provide support in the form of additionaltechnology files, worksheets, links to other sites, assessment materialsincluding practice examinations and more.

Maths Quest

is a rich collection of teaching and learning resources withinone package.

Maths Quest 11 General Mathematics

provides ample material, such asexercises, analysis questions, investigations, worksheets and technology files,from which teachers may set school assessed coursework (SAC).

WorkS

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APTERyyourselfourself

testyyourselfourself 3.2testtestCH

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TEACHERTEACHER EDITION

EDITION111111MATHS QuestQuest

JENNIFER NOLAN GEOFF PHILLIPS ELENA IAMPOLSKY SONJA STAMBULICJENNIFER NOLAN GEOFF PHILLIPS ELENA IAMPOLSKY SONJA STAMBULIC

JAC

ARANDAMA

THSQUES

T

VCE MAVCE MATHEMATHEMATICS UNITS 1 & 2TICS UNITS 1 & 2

General MathematicsGeneral Mathematics

INTE

RACTIVE

C

D- ROM

Prelims Gen Maths Page xiii Thursday, April 17, 2003 6:43 AM

Acknowledgements

The authors and publisher would like to thank the following copyright holders,organisations and individuals for their assistance and for permission toreproduce copyright material in this book.

Illustrative material

• © Australian Picture Library p. 609(upper)/Peter Solness, p. 666/Photoedit, p. 698/Zefa Netherland, p. 739/John Carnemolla; • © Austral pp. 462(upper), 477; • © Cooee Picture Library p. 28 (four), 454, 613(two); • © Corbis pp. 44, 53, 69, 230, 236, 513(upper), 547, 548; • © Digital Stock pp. 37, 129(upper), 136, 205, 309, 403, 407, 569, 611; • © Photodisc (cover), pp. 1, 11, 19, 22, 24, 33, 43, 48(two), 51, 52, 55, 56, 58, 59, 60, 66, 70, 73, 76, 78(lower), 90, 97, 98, 100, 101, 108, 110, 125, 138, 141, 144, 147, 161, 170, 171, 175, 181, 182, 183, 198, 199(lower), 200(upper), 214, 225, 228, 229, 242, 243, 251(two), 262, 263(two), 281, 282(two), 306, 313, 321, 324, 328, 332, 339 (twice), 357, 369, 370, 384, 392, 396, 397, 402, 411, 412, 447, 457, 462(lower), 463, 478, 481, 482, 499, 512, 513(lower), 515, 530, 542, 551, 559, 560, 565, 574, 634, 651, 652, 663, 664, 665, 683, 687, 688, 697(two), 712, 719, 721, 744(upper), 753, 771, 772, 773, 776;• Reproduced with permission of: Commonwealth Bank of Australia pp. 79, 84, 461; Creative cohesions pp. 199(upper), 200(lower), 516, 570, 621, 642; Malcolm Cross pp. 31, 129(lower), 191, 609(lower), 647, 744(lower); Department of Primary Industries, Water and Environment p. 767; Ford Motor Company of Australia p. 113; Glen Eira City Council p. 78(upper); Ikon Energy Pty Ltd pp. 73, 74; Melbourne Exhibition and Convention Centre pp. 575, 576; National Australia Bank p. 461; Prima Australia Pty Ltd p. 46(four); South East Water p. 75; Peter Storer pp. 465, 490; Telstra pp. 76, 77; United Energy Ltd pp. 71, 72; University of Queensland, Dianne Lilley p. 196; University of Southern Queensland pp. 199(upper), 200(lower); • © Microsoft Corporation. Screenshots reproduced by permission of Microsoft Corporation; • © Stockbyte p. 366; • The Photo Library – Sydney: p. 187/Index Stock, p. 204/Science Photo Library, p. 450/Tim Davis, p. 470/Julian Meehan, p. 690/David Allan Brandt, pp. 735, 736/J. F. Causse, p. 760/Martin Dohrn/SPL.

Software

The authors and publisher would like to thank the following software providersfor their assistance and for permission to use their materials. However, the use ofsuch material does not imply that the providers endorse this product in any way.

Third party software — registered full version ordering information

Full versions of third party software may be obtained by contacting thecompanies listed below.

Texas Instruments 83 and 89 Graphlink software

Material reproduced with permission of the publisher. © Texas InstrumentsIncorporated.

TI 83 and 89 Graphlink Software available from Texas Instruments

Web: http://education.ti.com/us/global/software.html#connectivity

Note

: A Graphlink cable can be purchased from educational booksellers orcalculator suppliers.

Prelims Gen Maths Page xiv Monday, July 26, 2004 1:35 PM

xv

Mathcad

®

Explorer

Reproduced with permission of MathSoft Engineering & Education, Inc.

www.mathsoft.com

Distributed in Australia by Hearne Scientific Software Pty Ltd

Level 6, 552 Lonsdale Street, Melbourne 3000

e-mail: info@hearne.com.au

Web: http://www.hearne.com.au/

Phone: (03) 9602 5088

Graphmatica

Reproduced with permission of kSoft, Inc.

345 Montecillo Dr., Walnut Creek, CA 94595-2654.

e-mail: ksoft@graphmatica.com

Web: http://www.graphmatica.com

Software included is for evaluation purposes only. The user is expected toregister shareware if use exceeds 30 days. Order forms are available athttp://www.graphmatica.com/register.txt

Cabri Geometry™ II

Reproduced with permission of Cabrilog.

Cabrilog

7 av, Félix Viallet

38000 Grenoble

FRANCE

Web: http://www.cabri.com

DERIVE™

Screen shots reprinted by permission of Soft Warehouse, Inc.

DERIVE™

is atrademark of Soft Warehouse, Inc worldwide and is a registered trademark ofSoft Warehouse, Inc in the United States of America and various other countries.

Soft Warehouse, Inc.

3660 Waialae Avenue, Suite 304

Honolulu, Hawaii 96816 USA

e-mail: info@derive.com

Web: http://www.derive.com

Selected list of

DERIVE™

dealers in Australia:

EdSoft Pty Ltd http://www.edsoft.com.au

Hearne Scientific Software Pty Ltd http://www.hearne.com.au

MathStat Software http://www.mathstat.com.au

Texas Instruments http://www.education.ti.com

Prelims Gen Maths Page xv Tuesday, July 20, 2004 6:44 AM

xvi

GrafEq and Poly

Evaluation copies of GrafEq™ and Poly™ have been included with per-mission from Pedogoguery Software, Inc.

e-mail: peda@peda.com

Web: http://www.peda.com

Equation Grapher and Regression Analyser

Copyright © 1998, MF Soft International. Reproduced with permission.

e-mail: info@mfsoft.com

Web: http://www.mfsoft.com

Microsoft® Excel

Microsoft Excel is registered trademark of the Microsoft Corporation in theUnited States and/or other countries.

Every effort has been made to trace the ownership of copyright material.Information that will enable the publisher to trace the copyright holders or torectify any error or omission in subsequent reprints will be welcome. In suchcases, please contact the Permission Section of John Wiley & Sons Australia,who will arrange for the payment of the usual fee.

Prelims Gen Maths Page xvi Tuesday, July 20, 2004 6:44 AM