MATHS Quest 11 YEAR

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MATHS

Quest

MATHS

Quest

YEAR

11

Contributing author

Tony MacPherson

LYN ELMS NICK SIMPSON

M

ATHS

A

M

ATHS

A

FOR QUEENSLAND

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First published 2001 by John Wiley & Sons Australia, Ltd 33 Park Road, Milton, Qld 4064

Offices also in Sydney and Melbourne

Typeset in 10.5/12.5pt Times

National Library of Australia Cataloguing-in-Publication data

Elms, Lyn.

Maths quest: Year 11, Maths A for Queensland.

ISBN 0 7016 3624 6.

1. Mathematics — Problems, exercises, etc. 2. Mathematics. Simpson, Nick. II. MacPherson, Tony. III. Title.

(Series: Maths quest series).

510

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher.

Edited by Merv Littmann

Illustrated by the Wiley Art Department

Printed in Singapore by Markono Print Media Pte Ltd

10 9 8 7 6 5 4 3

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CHAPTER 1

Earning money 1

Introduction 2

Skills check 2

Calculating salary payments 2

Exercise 1A 4

Calculating wages 5

Exercise 1B 7

10 Quick Questions 1 10

Commission and royalties 10

Exercise 1C 13

Payment by piece 15

Exercise 1D 17

Working overtime 20

Exercise 1E 22

Additions to and deductions from gross pay 25

Exercise 1F 27

Summary 32 Chapter review 33

CHAPTER 2

Taxation 35

Income tax 36

Skills check 36

Allowable deductions 37

Exercise 2A 39

Taxable income 41

Exercise 2B 43

Medicare levy 47

Exercise 2C 47

Calculating tax 48

Exercise 2D 52

Calculating GST and VAT 56

Exercise 2E 58

CHAPTER 3

Spending money 63

Introduction 64

Skills check 64

Discount 65

Exercise 3A 67

Profit and loss 70

Exercise 3B 72

Budgeting 75

Exercise 3C 78

Cost of services 80

Exercise 3D 81

Credit cards 88

Exercise 3E 92

The exchange rate 94

Exercise 3F 95

CHAPTER 4

Length, area and volume 101

Introduction 102

Skills check 103

Two-dimensional objects 105

Exercise 4A 108

Exercise 4B 116

10 Quick Questions 1 119

Three-dimensional objects 123

Exercise 4C 129

Volume and capacity 134

Exercise 4D 141

Summary 151 Chapter review 153

CHAPTER 5

Right-angled triangles and

trigonometry 157

Introduction 158

History of mathematics — Pythagoras of Samos 159

Right-angled triangles 162 Pythagoras’ theorem 162

Exercise 5A 166

Similar triangles and shadow sticks 173

Exercise 5B 175

Calculating trigonometric ratios 176

Exercise 5C 182

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Finding an unknown side 182

Exercise 5D 186

Finding angles 190

Exercise 5E 192

Angles of elevation and depression 196

Exercise 5F 198

Summary 203 Chapter review 204

CHAPTER 6

Earth geometry 207

Introduction 208

Skill check 209

Position on Earth 209

Exercise 6A 215

Distances on the Earth’s surface 216

Exercise 6B 219

Time zones 221

Exercise 6C 225

CHAPTER 7

Basics of construction 231

Introduction 232

Skill check 233

Scale drawings 234

Exercise 7A 235

Building plans 237

Exercise 7B 240 Exercise 7C 245

Preparing to build 249

Pegging out the perimeter 250

Exercise 7D 252

Footings and slab 253

Exercise 7E 258

The frame 260

Exercise 7F 266

The roof 267

Exercise 7G 270 Exercise 7H 276

Bricking the walls 277

Exercise 7I 280

Summary 282 Chapter review 283

CHAPTER 8

Construction: The finishing

touches 289

Finishing touches 290

Finishing the walls 291

Exercise 8A 296

Finishing the floors 297

Exercise 8B 305

Landscaping 308

Exercise 8C 319

CHAPTER 9

Collecting and entering

data 325

Introduction 326

Types of data 327

Exercise 9A 328

Collecting data 330

Exercise 9B 339

Data preparation 340

Organising and displaying data 341

Exercise 9C 345

Methods of misrepresenting data 350

Exercise 9D 355

Other forms of graphical display 359

Exercise 9E 362 Exercise 9F 368 Exercise 9G 374

CHAPTER 10

Describing, exploring and

comparing data 381

Introduction 382

Calculating the mean 384

Exercise 10A 386

Frequency distribution tables 388

Exercise 10B 390

Grouping data and using grouped data 392

Exercise 10C 394

Median and mode 397

Exercise 10D 401

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Best summary statistics 406

Exercise 10E 408

Measures of dispersion or spread 412

Exercise 10F 416

Standard deviation 419

Exercise 10G 423

10 Quick Questions 2 427

Comparing sets of data 430

Exercise 10H 435

CHAPTER 11

Scatterplots and time

series 451

Introduction 452

Scatterplots 453

Exercise 11A 457

Fitting straight lines to bivariate data 459

Regression lines 461

Exercise 11B 470

Time series and trend lines 475

Exercise 11C 479

CHAPTER 12

Introduction to

probability 487

Introduction 488

Information description of chance 491

Exercise 12A 494

Sample space 496

Exercise 12B 498

Tree diagrams 504

Exercise 12C 507

Equally likely outcomes 508

Exercise 12D 513

Using the fundamental counting

principle 515

Exercise 12E 518

Relative frequency 522

Exercise 12F 524

Single event probability 527

Exercise 12G 530

10 Quick Questions 3 533

Writing probabilities as decimals and

percentages 535

Exercise 12H 536

Range of probabilities 538

Exercise 12I 540

Complementary events 543

Exercise 12J 545

Glossary 555

Answers 560

Index 588

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Introduction

Maths Quest Maths A Year 11 for Queensland is one of the exciting new

Maths Quest resources specifically designed for the Queensland senior Mathematics syllabuses beginning in 2002. It has been written and compiled by practising Queensland Maths A teachers. It breaks new ground in Mathematics textbook publishing.

This resource contains: • a student textbook • a student CD-ROM.

Student textbook

Full colour is used throughout to produce clearer graphs and headings, to provide bright, stimulating photos and to make navigation through the text easier.

Skills check exercises at the beginning of each chapter enable a quick diag-nostic assessment of students’ grasp of the basic mathematics needed.

Clear, concise theory sections contain worked examples, graphics calculator

tips and highlighted important text and remember boxes.

Worked examples in a Think/Write format provide clear explanation of key steps and suggest how solutions can be presented.

Exercises contain many carefully graded skills and application problems, including multiple-choice questions. Cross-references to relevant worked examples appear beside the first ‘matching’ question throughout the exercises.

Sets of 10 Quick Questions allow students to quickly review the concepts just

learnt before proceeding further in the chapter.

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

Each chapter concludes with asummary and chapter review exercise

contain-ing questions that help consolidate students’ learncontain-ing of new concepts.

A glossary of mathematical terms is provided to assist students’ understand-ing of the terminology introduced in each unit of the course. Words in bold type in the theory sections of each chapter are defined in the glossary at the back of the book.

Technology is fully integrated within the resource. As well as graphics

calcu-lators, the Maths Quest for Queensland series features computer algebra

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

the free accompanying CD-ROM.

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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 home computers, and cut and paste material for revision or assignments.

Clearly labelled icons within the electronic version of the text hyperlink to hundreds of technology files for programs such as Mathcad, Excel and Cabri Geometry 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.

WorkSHEET and Test yourself icons link to editable Word 97 documents that may be completed on screen, or printed and completed later.

SkillSHEET icons link to printable pages that contain additional examples and problems designed to help students revise required concepts.

A special feature of the CD-ROM is the incorporation of a CD-ROM developed by G.J. Gardner Homes. This CD-ROM enables students to inter-actively experience the construction of a house. G.J. Gardner icons in Chapters 7 and 8 direct students to this section of the Maths A Year 11 for Queensland CD-ROM.

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 for the 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

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D- ROM

EXCE

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Mathc

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WorkS HEET Grap

hicsCa

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Cabr i Geometry

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test

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Acknowledgements

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

Special acknowledgement is made to G.J. Gardner Homes for their permission

to incorporate the CD-ROM The New Home Buyers’ Guide within the Maths

A Year 11 for Queensland CD-ROM. Copyright for The New Home Buyers’

Guide CD-ROM remains with its originator, G.J. Gardner Homes.

Illustrative material

• Alexander Krivensyhev, pp. 221, 222; • Allsport/Hamish Blair, p. 496; • Ausinfo: p. 31 (From: RO447 Retail and Wholesale Industry — Fast Food Retail Shop Distributive and Allied Employees’ Association. Red Rooster Consent Award 1996. Commonwealth of Australia); pp. 248, 249 (two), 251 (two) (From: Basic Hand Tools — Basic Training Manual: Carpentry and Joinery 14-1, AGPS. 1980. Commonwealth of Australia copyright; pp. 352

(lower), 355 (lower), 356 (From: Qld Year Book, 1989, pp. 53, 125, and 205

and the ABS. Commonwealth of Australia copyright); p. 478 (From: Census of Population and Housing B03 Age by Sex (ABS 1996). Commonwealth of Australia copyright); • Brisbane City Council, pp. 84, 85; • Bureau of Meteorology, pp. 481, 482 (www.bom.gov.au, Commonwealth of Australia copyright); • © 2001 Corbis, pp. 28, 35, 42, 65, 120, 205, 215 (upper), 343 (lower), 397; • Commonwealth Bank of Australia, pp. 88 (three images and text), 89, 90, 93; • © Creative Cohesions, p. 143; • Creedon Reid & Associates Pty Ltd, p. 286; • Department of Natural Resources and Mines QLD, p. 351; • Department of Primary Industries, Water and Environment/Marine Services Division Tasmania, p. 468 (lower); • © 2001 Digital Stock, pp. 37, 202, 215 (lower), 229, 230 (lower), 260 (right), 344, 513; • © 2001 Digital Vision, pp. 207, 226; • Energex, p. 81; • G.J. Gardner, pp. 232 (lower), 241, 253, 283, 284, 285, 286; • © imageaddict.com, pp. 227, 297 (left), 317, 468 (upper), 469; • © 2001 Image Disk Photography, pp. 36, 382 (upper); • Innovations, p. 122; • Lyn Elms, pp. 102 (two), 232 (upper), 263 (two), 273, 274, 277, 278, 330; • Merv Littmann, p. 262 (lower right), 267 (lower right), 295; • Microsoft Corporation, Excel screenshots on pages 9, 24, 29, 30, 44, 45, 54, 147, 347, 349, 358, 439, 502, 503, 511; • Mitre 10 Australia, pp. 289, 309 (two), 310 (two), 311 (two), 318 (two).; © Newspix, pp. 381, 423; • Olympic Manufac-turers, pp. 302, 303, 304; • Origin Energy Retail Limited, pp. 82, 83 (upper); • Peter Storer, p. 367; • © 2001 Photodisc, Inc, pp. 1, 2, 3, 4, 6, 7, 11, 13, 15, 20, 21, 26, 33, 34, 41, 50, 51, 56, 59 (two), 61, 63, 69 (two), 72, 73, 78, 79, 80 (four), 83, 86, 96, 98, 100, 101, 119, 127 (upper), 130, 131, 132 (two), 133, 140, 157, 158 (two), 161, 162, 176, 189, 194 (two), 195, 200, 206, 230 (upper), 231, 237 (lower), 242, 246, 247, 269, 291, 297 (right), 299, 300, 314 (lower), 320, 322, 323, 324, 325, 326, 327, 328, 341, 342, 343 (upper), 362, 364, 366, 375, 382 (lower), 384, 391, 395, 401, 402, 405, 408, 421, 422, 425, 426 (two), 427, 431, 432, 438, 448, 450, 451, 452, 458, 461, 466, 471, 472, 476, 486, 487, 500, 505, 506, 509, 515 (two), 516, 518, 525, 529, 533, 537, 541 (two), 542, 546, 548; • photolibrary.com/Science Photo Library, p. 159;

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• photolibrary.com/Jeffrey C. Drewitz, p. 517; • Howard Pickering, p. 239 (From: Pickering, H., ‘Senior Graphics’, John Wiley & Sons Australia, copyright Howard Pickering); • PMP Data Based Marketing, p. 348; • QLD Transport (Maritime Division), p. 237 (upper) (Not to be used for navigation); • Queensland Newspapers, p. 94 (first published 29 July 2000); p. 357 (upper) (first published 21 September 1991); • Queensland Master Builders’ Associa-tion, p. 259 (lower) (From: Smith & Adams ‘Domestic Construction Manual’ 2nd edition; • Standards Australia, pp. 238 (lower), 243, 244 (lower three); • © 2001 Stockbyte, pp. 127 (lower), 530, 531, 536; • Teco Australia Pty Ltd, p. 316; • Telstra Corporation Limited, pp. 86 (upper), 87; • Toro Australia Pty Ltd, pp. 312, 313, 314 (upper), 315; • Werner Langer, pp. 464, 554.

Software

The authors and publisher would like to thank the following software pro-viders for their assistance and for permission to use their materials. However, the use of such 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 the companies listed below.

Texas Instruments 83 and 89 Graphlink software

TI 83 and 89 Graphlink Software available from Texas Instruments

Web: http://education.ti.com

Note: A Graphlink cable can be purchased from educational booksellers or calculator suppliers.

Mathcad Explorer

Reproduced with permission of Mathsoft www.mathsoft.com

Distributed in Australia by

1. Hearne Scientific Software Pty Ltd

Level 6, 552 Lonsdale Street, Melbourne 3000

e-mail: [email protected]

Web: www.hearne.com.au

Phone: (03) 9602 5088

2. Geoff Phillips Publications

8 Wattletree Avenue, Wonga Park 3115

Phone: (03) 9722 2505

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Cabri Geometry II

Reproduced with permission of Cabri. Leibniz

Cabri-géomètre 46, avenue Félix Viallet

38031 Grenoble Cedex FRANCE Web: www.cabri.net

Distributed by AAMT (Australian Association of Mathematics Teachers) Phone: (08) 8363 0288

Fax: (08) 8362 9288

Web: www.aamt.edu.au

Microsoft® Excel

Screen Shots reproduced by permission of Microsoft Corporation.

Note: Microsoft Software was used only in Screen Dumps.

Microsoft Excel is registered trademark of the Microsoft Corporation in the United 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 to rectify any error or omission in subsequent reprints will be welcome. In such cases, please contact the Permission Section of John Wiley & Sons Australia, who will arrange for the payment of the usual fee.

MATHS Quest 11 YEAR

MATHS

Contents

Introduction vi

CHAPTER 1

Introduction 2

CHAPTER 2

Income tax 36

CHAPTER 3

Introduction 64

CHAPTER 4

Introduction 102

CHAPTER 5

History of mathematics — Pythagoras of Samos 159

Summary 203 Chapter review 204

CHAPTER 6

Introduction 208

CHAPTER 7

Introduction 232

Summary 282 Chapter review 283

CHAPTER 8

Finishing touches 290

CHAPTER 9

Introduction 326

CHAPTER 10

Introduction 382

10 Quick Questions 2 427

CHAPTER 11

Introduction 452

CHAPTER 12

Introduction 488

10 Quick Questions 3 533

Introduction

MATHS Quest MATHS Quest

L LYN ELMSYN ELMS NICK SIMPSON NICK SIMPSON

Programs included

Adobe® Acrobat® Reader 4.0

TERACTIVE

CHAPTER

Acknowledgements

Illustrative material

Software

Third party software — registered full version ordering information

Mathcad Explorer

Cabri Geometry II