Maths Quest Victorian Curriculum 3e Preview

VICTORIAN CURRICULUM

SMITH | SMART | JAMES | MAHONY | LANGSFORD WILLING

JACARANDA

MATHS QUEST VICTORIAN CURRICULUM THIRD EDITION

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JACARANDA

MATHS QUEST

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VICTORIAN CURRICULUM

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JACARANDA

MATHS QUEST

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VICTORIAN CURRICULUM

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THIRD EDITION

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CATHERINE SMITH JAMES SMART GEETHA JAMES CAITLIN MAHONY

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BEVERLY LANGSFORD WILLING

CONTRIBUTING AUTHORS Michael Sheedy | Kahni Burrows | Paul Menta

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Third edition published 2023 by John Wiley & Sons Australia, Ltd Level 4, 600 Bourke Street, Melbourne, Vic 3000

The Publishers of this series acknowledge and pay their respects to Aboriginal Peoples and Torres Strait Islander Peoples as the traditional custodians of the land on which this resource was produced.

First edition published 2014 Revised edition published 2018 Second edition published 2021

This suite of resources may include references to (including names, images, footage or voices of) people of Aboriginal and/or Torres Strait Islander heritage who are deceased. These images and references have been included to help Australian students from all cultural backgrounds develop a better understanding of Aboriginal and Torres Strait Islander Peoples’ history, culture and lived experience.

Typeset in 10.5/13 pt TimesLT Std

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© John Wiley & Sons Australia, Ltd 2014, 2018, 2021, 2023

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All activities in this resource have been written with the safety of both teacher and student in mind. Some, however, involve physical activity or the use of equipment or tools. All due care should be taken when performing such activities. To the maximum extent permitted by law, the author and publisher disclaim all responsibility and liability for any injury or loss that may be sustained when completing activities described in this resource.

The Publisher acknowledges ongoing discussions related to gender-based population data. At the time of publishing, there was insufficient data available to allow for the meaningful analysis of trends and patterns to broaden our discussion of demographics beyond male and female gender identification.

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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.

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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).

It is strongly recommended that teachers examine resources on topics related to Aboriginal and/or Torres Strait Islander Cultures and Peoples to assess their suitability for their own specific class and school context. It is also recommended that teachers know and follow the guidelines laid down by the relevant educational authorities and local Elders or community advisors regarding content about all First Nations Peoples.

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ISBN: 978-1-394-23540-7

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The moral rights of the authors have been asserted.

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Trademarks Jacaranda, the JacPLUS logo, the learnON, assessON and studyON logos, Wiley and the Wiley logo, and any related trade dress are trademarks or registered trademarks of John Wiley & Sons Inc. and/or its affiliates in the United States, Australia and in other countries, and may not be used without written permission. All other trademarks are the property of their respective owners.

Front cover images: © virinaflora/Adobe Stock Photos; © Marish/Shutterstock; © Good Studio/Adobe Stock Photos; © Visual Generation/Shutterstock Illustrated by various artists, diacriTech and Wiley Composition Services

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Typeset in India by diacriTech

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Contents About this resource.......................................................................vii Acknowledgements.....................................................................xiv

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3.1 Overview ....................................................... 148 3.2 Solving linear equations and inequations ...... 150 3.3 Solving linear equations with brackets .......... 161 3.4 Solving linear equations with variables on both sides ..................................................... 165 3.5 Solving problems with linear equations ......... 169 3.6 Rearranging formulas ................................... 175 3.7 Review .......................................................... 181 Answers ................................................................. 187

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NAPLAN practice

3 Linear equations

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Set A Calculator allowed Set B Non-calculator Set C Calculator allowed Set D Non-calculator Set E Calculator allowed Set F Non-calculator

4 Congruence and similarity

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2 Algebra

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1.1 Overview ........................................................... 2 1.2 Real numbers ................................................... 4 1.3 Rounding numbers and significant figures ...... 11 1.4 Review of exponent laws ................................ 16 1.5 Raising powers ............................................... 24 1.6 Negative exponents ........................................ 28 1.7 Scientific notation ........................................... 34 1.8 Square roots and cube roots .......................... 41 1.9 Surds (extending) ............................................ 44 1.10 Review ............................................................ 56 Answers ................................................................... 64

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1 Number skills and exponent laws

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4.1 Overview ....................................................... 192 4.2 Ratio and scale ............................................. 195 4.3 Congruent figures ......................................... 204 4.4 Nets, polyhedra and Euler’s formula ............. 212 4.5 Similar figures ............................................... 217 4.6 Area and volume of similar figures ................ 229 4.7 Review .......................................................... 238 Answers ................................................................. 247

2.1 Overview ......................................................... 72 2.2 Using variables ............................................... 74 2.3 Algebra in worded problems ........................... 83 2.4 Simplification of algebraic expressions ........... 88 2.5 Expanding brackets ........................................ 95 2.6 Difference of two squares and perfect squares ......................................................... 104 2.7 Further expansions ....................................... 109 2.8 The highest common factor .......................... 112 2.9 The highest common binomial factor ............ 118 2.10 Solving worded problems ............................. 122 2.11 Review .......................................................... 131 Answers ................................................................. 138

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5 Pythagoras and trigonometry

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5.1 Overview ....................................................... 254 5.2 Pythagoras’ theorem .................................... 258 5.3 Applications of Pythagoras’ theorem ............ 267 5.4 Trigonometric ratios ...................................... 274 5.5 Calculating unknown side lengths ................ 282 5.6 Calculating unknown angles ......................... 291 5.7 Angles of elevation and depression .............. 299 5.8 Review .......................................................... 305 Answers ................................................................. 315

6 Linear and non-linear graphs

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6.1 Overview ....................................................... 322 6.2 Plotting linear graphs .................................... 325 6.3 Features of linear graphs .............................. 331 6.4 The equation of a straight line ....................... 339 6.5 Sketching linear graphs ................................ 348 6.6 Technology and linear graphs ....................... 356 6.7 Practical applications of linear graphs .......... 360 6.8 Midpoint of a line segment and distance between two points ...................................... 365 6.9 Non-linear relations ....................................... 371 6.10 Review .......................................................... 385 Answers ................................................................. 393

Semester review 1

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CONTENTS

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7 Proportion and rates

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12 Quadratic equations and graphs

7.1 Overview ....................................................... 414 7.2 Direct linear proportion ................................. 416 7.3 Proportionality .............................................. 421 7.4 Introduction to rates ..................................... 426 7.5 Constant and variable rates .......................... 429 7.6 Review .......................................................... 436 Answers ................................................................. 444

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8 Financial mathematics (extending)

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13 Algorithmic thinking 13.1 Overview 13.2 Programs 13.3 Arrays 13.4 Loops 13.5 Set structures 13.6 Sorting algorithms 13.7 The Monte Carlo method 13.8 Review Answers

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10 Probability

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9.1 Overview ....................................................... 488 9.2 Absolute, relative and percentage error ........ 492 9.3 Perimeter and circumference ........................ 498 9.4 Area .............................................................. 508 9.5 Area and perimeter of a sector ..................... 518 9.6 Surface area of rectangular and triangular prisms ........................................................... 525 9.7 Surface area of a cylinder ............................. 531 9.8 Volume of prisms and cylinders .................... 536 9.9 Review .......................................................... 549 Answers ................................................................. 559

Semester review 2

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8.1 Overview ....................................................... 448 8.2 Salaries and wages ....................................... 451 8.3 Penalty rates ................................................. 455 8.4 Simple interest .............................................. 461 8.5 Compound interest ....................................... 469 8.6 Review .......................................................... 478 Answers ................................................................. 483

9 Measurement

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12.1 Overview ....................................................... 716 12.2 Quadratic equations ..................................... 718 12.3 The Null Factor Law ...................................... 723 12.4 Solving quadratic equations with two terms ............................................................ 727 12.5 Factorising and solving monic quadratic equations ...................................................... 731 12.6 Graphs of quadratic functions ...................... 737 12.7 Sketching parabolas of the form y Ⴝ ax2 ....... 746 12.8 Sketching parabolas of the form y Ⴝ (x Ⴜ h)2 Ⴛ k .............................................. 752 12.9 Sketching parabolas of the form y Ⴝ (x Ⴛ a)(x Ⴛ b) ............................................ 764 12.10 Applications .................................................. 768 12.11 Review .......................................................... 774 Answers ................................................................. 783

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10.1 Overview ....................................................... 566 10.2 Theoretical probability .................................. 572 10.3 Experimental probability ............................... 579 10.4 Venn diagrams and two-way tables .............. 588 10.5 Compound events ........................................ 605 10.6 Review .......................................................... 618 Answers ................................................................. 625

11 Statistics

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11.1 Overview ....................................................... 634 11.2 Collecting data ............................................. 638 11.3 Organising data ............................................ 647 11.4 Displaying data ............................................. 657 11.5 Measures of centre ....................................... 672 11.6 Measures of spread ...................................... 688 11.7 Review .......................................................... 697 Answers ................................................................. 703

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CONTENTS

Algorithms and pseudocode (Optional) ............................ 810 Glossary ............................................................................... 833 Index ..................................................................................... 840

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About this resource

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NEW FOR

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VICTORIAN CURRICULUM V2.0

JACARANDA

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MATHS QUEST 9

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Developed by teachers for students

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Tried, tested and trusted. The third edition of the Jacaranda Maths Quest series, revised second edition, continues to focus on helping teachers achieve learning success for every student — ensuring no student is left behind, and no student is held back.

Because both what and how students learn matter

Learning is effortful

Learning is rewarding

Whether students need a challenge or a helping hand, you’ll find what you need to create engaging lessons.

Learning happens when students push themselves.

With learnON, Australia’s most powerful online learning platform, students can challenge themselves, build confidence and ultimately achieve success.

Through real-time results data, students can track and monitor their own progress and easily identify areas of strength and weakness.

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Learning is personal

Whether in class or at home, students can get unstuck and progress! Scaffolded lessons, with detailed worked examples, are all supported by teacher-led video eLessons. Automatically marked, differentiated question sets are all supported by detailed worked solutions.

And Brand-new Quick Quizzes support in-depth skill acquisition.

And for teachers, Learning Analytics provide valuable insights to support student growth and drive informed intervention strategies.

ABOUT THIS RESOURCE

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Learn online with Australia’s most

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• Trusted, curriculum-aligned content • Engaging, rich multimedia • All the teacher support resources you need • Deep insights into progress • Immediate feedback for students • Create custom assignments in just a few clicks.

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Everything you need for each of your lessons in one simple view

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Practical teaching advice and ideas for each lesson provided in teachON

Teaching videos for all lessons

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Reading content and rich media including embedded videos and interactivities

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powerful learning tool, learnON

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New! Quick Quiz questions for skill acquisition

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Differentiated question sets

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Teacher and student views

Fully worked solutions eWorkbook

Digital documents Video eLessons Interactivities

Extra teaching support resources

Interactive questions with immediate feedback

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Textbook questions

ABOUT THIS RESOURCE

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Get the most from your online resources Trusted Jacaranda theory, plus tools to support teaching and make learning more engaging, personalised and visible.

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Online, these new editions are the complete package

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Embedded interactivities and videos enable students to explore concepts and learn deeply by ‘doing’.

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New teaching videos for every lesson are designed to help students learn concepts by having a ‘teacher at home’, and are flexible enough to be used for pre- and post-learning, flipped classrooms, class discussions, remediation and more.

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Brand new! Quick Quiz questions for skill acquisition in every lesson.

Instant reports give students visibility into progress and performance.

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Three differentiated question sets, with immediate feedback in every lesson, enable students to challenge themselves at their own level.

Every question has immediate, corrective feedback to help students overcome misconceptions as they occur and get unstuck as they study independently — in class and at home.

ABOUT THIS RESOURCE

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Maths Quest 7 includes Powering up for Year 7

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A six-week ‘Powering up for Year 7’ online program is designed to plug any gaps from earlier years.

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Go online to complete practice NAPLAN tests. There are 6 NAPLAN-style question sets available to help you prepare for this important event.

They are also useful for practising your Mathematics skills in general.

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NAPLAN Online Practice

Also available online is a video that provides strategies and tips to help with your preparation.

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eWorkbook

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The eWorkbook enables teachers and students to download additional activities to support deeper learning.

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A wealth of teacher resources

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Enhanced teacher support resources for every lesson, including: • work programs and curriculum grids • practical teaching advice • three levels of differentiated teaching programs • quarantined topic tests (with solutions)

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Customise and assign

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An inbuilt testmaker enables you to create custom assignments and tests from the complete bank of thousands of questions for immediate, spaced and mixed practice.

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Reports and results

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Data analytics and instant reports provide data-driven insights into progress and performance within each lesson and across the entire course.

Show students (and their parents or carers) their own assessment data in fine detail. You can filter their results to identify areas of strength and weakness.

ABOUT THIS RESOURCE

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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.

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The Victorian Curriculum F–10 content elements are © VCAA, reproduced by permission. The VCAA does not endorse or make any warranties regarding this resource. The Victorian Curriculum F-10 and related content can be accessed directly at the VCAA website.

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This may be a modified extract from the Victorian Curriculum F-10 and may include the work of other authors.

VCAA does not endorse nor verify the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. You can find the most up to date version of the Victorian Curriculum at http://victoriancurriculum.vcaa.vic.edu.au/.

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ACKNOWLEDGEMENTS

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Every effort has been made to trace the ownership of copyright material. Information that will enable the publisher to rectify any error or omission in subsequent reprints will be welcome. In such cases, please contact the Permissions Section of John Wiley & Sons Australia, Ltd.

ACKNOWLEDGEMENTS

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NAPLAN practice

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Also available online is a video that provides strategies and tips to help with your preparation.

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Go online to complete practice NAPLAN tests. There are 6 NAPLAN-style question sets available to help you prepare for this important event. They are also useful for practising your Mathematics skills in general.

SET B Non-calculator

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SET A Calculator allowed

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SET C Calculator allowed

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SET E Calculator allowed

NAPLAN PRACTICE

SET D Non-calculator

SET F Non-calculator