Maths 10A Teacher Edition.pdf

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  MATHS QUEST for the AustralianCurriculum KYLIE BOUCHER DEBBIE KEMPFF LYN ELMS RUTH BAKOGIANISDOUGLAS SCOTT CORAL CONNOR TOBIAS COOPER  CONTRIBUTING AUTHORSCAROL PATTERSON |  ROBERT CAHN |  ANITA CANN |  JACINTA DEYLANBRENDAN OWEN |  IRENE KIROFF |  ROSETTA BATSAKIS |  ELENA IAMPOLSKY  10  +  10A    T   E   A   C   H   E   R   E   D   I   T   I   O   N  First published 2012 byJohn Wiley & Sons Australia, Ltd42 McDougall Street, Milton, Qld 4064Typeset in 10/12pt Times LT© John Wiley & Sons Australia, Ltd 2012The moral rights of the authors have been asserted.National Library of AustraliaCataloguing-in-Publication dataTitle: Maths quest 10+10A for the Australian curriculum/ Kylie Boucher [et al.]ISBN: 978 0 7303 4178 9 (student ed. : pbk) 978 0 7303 4179 6 (student ed. : ebook) 978 0 7303 4181 9 (teacher ed. : pbk) 978 0 7303 4182 6 (teacher ed. : ebook)Series: Maths quest series.Notes: Includes indexTarget Audience: For secondary school age.Subjects: Mathematics—Textbooks. Mathematics—Study and teaching (Secondary)Other Authors/ Contributors: Boucher, Kylie.Dewey Number: 510 Reproduction and communication for educational purposes The Australian Copyright Act 1968  (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL). Reproduction and communication for other purposes Except as permitted under the Act (for example, a fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher.Internal design images: © Shutterstock/Nikolai Bird, 2010Illustrated by Aptara and the Wiley Art StudioTypeset in India by AptaraPrinted in Singapore byCraft Print International Ltd10 9 8 7 6 5 4 3 2 1  Contents  Introduction viii About eBookPLUS x Acknowledgements xi CHAPTER 1 NUMBER AND ALGEBRAPATTERNS AND ALGEBRA Indices 1 Are you ready? 2  1A Review of index laws 3 Exercise 1A 5  1B Negative indices 7 Exercise 1B 10  1C Fractional indices 12 Exercise 1C 14  1D Combining index laws 17 Exercise 1D 20 Summary 23Chapter review 24eBookPLUS activities 26 CHAPTER 2 NUMBER AND ALGEBRAPATTERNS AND ALGEBRA Linear algebra 27 Are you ready? 28  2A Substitution 29 Exercise 2A 31  2B Adding and subtracting algebraic fractions 33 Exercise 2B 36  2C Multiplying and dividing algebraic fractions 37 Exercise 2C 39  2D Solving linear equations 40 Exercise 2D 43  2E Solving equations with algebraic fractions and multiple brackets 45 Exercise 2E 48 Summary 50Chapter review 52eBookPLUS activities 54 CHAPTER 3 NUMBER AND ALGEBRALINEAR AND NON-LINEAR RELATIONSHIPS Coordinate geometry 55 Are you ready? 56  3A Sketching linear graphs 57 Exercise 3A 62  3B Determining linear equations 64 Exercise 3B 67  3C The distance between two points on a straight line 68 Exercise 3C 70  3D The midpoint of a line segment 71 Exercise 3D 73  3E Parallel and perpendicular lines 74 Exercise 3E 79 Summary 83Chapter review 85eBookPLUS activities 88 CHAPTER 4 NUMBER AND ALGEBRALINEAR AND NON-LINEAR RELATIONSHIPS Simultaneous linear equations and inequations 89 Are you ready? 90  4A Graphical solution of simultaneous linear equations 91 Exercise 4A 94  4B Solving simultaneous linear equations using substitution 96 Exercise 4B 98  4C Solving simultaneous linear equations using elimination 99 Exercise 4C 101  4D Problem solving using simultaneous linear equations 103Exercise 4D 105  4E Solving linear inequations 106 Exercise 4E 108  4F Sketching linear inequations 110 Exercise 4F 113  4G Solving simultaneous linear inequations 116 Exercise 4G 118 Summary 123Chapter review 125eBookPLUS activities 130 CHAPTER 5 MEASUREMENT AND GEOMETRYPYTHAGORAS AND TRIGONOMETRY Trigonometry I  131 Are you ready? 132  5A Pythagoras’ theorem 133 Exercise 5A 137  iv Contents  5B Pythagoras’ theorem in three dimensions 140 Exercise 5B 143  5C Trigonometric ratios 145 Exercise 5C 149  5D Using trigonometry to calculate side lengths 151 Exercise 5D 154  5E Using trigonometry to calculate angle size 156 Exercise 5E 158  5F Angles of elevation and depression 161 Exercise 5F 163  5G Bearings and compass directions 165 Exercise 5G 169  5H Applications 172 Exercise 5H 173 Summary 177Chapter review 179eBookPLUS activities 182 CHAPTER 6 MEASUREMENT AND GEOMETRYUSING UNITS OF MEASUREMENT Surface area and volume 183 Are you ready? 184  6A Area 185 Exercise 6A 189  6B Total surface area 193 Exercise 6B 199  6C Volume 203 Exercise 6C 208 Summary 213Chapter review 214eBookPLUS activities 218 CHAPTER 7 NUMBER AND ALGEBRAPATTERNS AND ALGEBRA Quadratic expressions 219 Are you ready? 220  7A Expanding algebraic expressions 221 Exercise 7A 225  7B Factorising expressions with three terms 227 Exercise 7B 229  7C Factorising expressions with two or four terms 231 Exercise 7C 234  7D Factorising by completing the square 236 Exercise 7D 239  7E Mixed factorisation 240 Exercise 7E 240 Summary 242Chapter review 244eBookPLUS activities 246 CHAPTER 8 NUMBER AND ALGEBRALINEAR AND NON-LINEAR RELATIONSHIPS Quadratic equations 247 Are you ready? 248  8A Solving quadratic equations 249 Exercise 8A 253  8B The quadratic formula 255 Exercise 8B 257  8C Solving quadratic equations by inspecting graphs 258 Exercise 8C 261  8D Finding solutions to quadratic equations by interpolation and using the discriminant 263 Exercise 8D 267  8E Solving a quadratic equation and a linear equation simultaneously 269 Exercise 8E 272 Summary 274Chapter review 276eBookPLUS activities 278 CHAPTER 9 NUMBER AND ALGEBRALINEAR AND NON-LINEAR RELATIONSHIPS Functions 279 Are you ready? 280  9A Plotting parabolas 281 Exercise 9A 284  9B Sketching parabolas using the basic graph of  y   =    x 2  287 Exercise 9B 291  9C Sketching parabolas in turning point form 292 Exercise 9C 296  9D Sketching parabolas of the form  y   =    ax 2   +    bx   +    c  298 Exercise 9D 302  9E Exponential functions and their graphs 306 Exercise 9E 309  9F The hyperbola 312 Exercise 9F 314  9G The circle 315 Exercise 9G 317 Summary 319Chapter review 321eBookPLUS activities 324
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