AUSTRALIAN CURRICULUM v9.0 AUSTRALIAN CURRICULUM | FIFTH EDITION JACARANDA MATHS
SMITH | LANGSFORD WILLING | BARNES | UTBER
QUEST 9
JACARANDA MATHSQUEST9
AUSTRALIANCURRICULUM|FIFTHEDITION
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9 JACARANDA MATHS QUEST
AUSTRALIAN CURRICULUM | FIFTH EDITION
CATHERINE SMITH
BEVERLY LANGSFORD WILLING
MARK BARNES
CHRISTINE UTBER
CONTRIBUTING
AUTHOR:
James Smart | Geetha James | Caitlin Mahony | Rebbecca Charlesworth
Michael Sheedy | Kahni Burrows | Paul Menta
Fiftheditionpublished2023by
JohnWiley&SonsAustralia,Ltd
Level4,600BourkeStreet,Melbourne,Vic3000
Firsteditionpublished2011
Secondeditionpublished2014
Thirdeditionpublished2018
Fourtheditionpublished2021
Typesetin10.5/13ptTimesLTStd
©JohnWiley&SonsAustralia,Ltd2011,2014,2018,2021,2023
Themoralrightsoftheauthorshavebeenasserted.
ISBN:978-1-394-19408-7
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Contents Aboutthisresource vii Acknowledgements xiv NAPLANpractice SetA Calculatorallowed SetB Non-calculator SetC Calculatorallowed SetD Non-calculator SetE Calculatorallowed SetF Non-calculator 1 Numberskillsandindexlaws 1 1.1 Overview 2 1.2 Realnumbers 4 1.3 Roundingnumbersandsignificantfigures 11 1.4 Reviewofindexlaws 16 1.5 Raisingpowers 24 1.6 Negativeindices 28 1.7 Scientificnotation 34 1.8 Squarerootsandcuberoots 41 1.9 Surds(extending) 44 1.10 Review 56 Answers 64 2 Algebra 67 2.1 Overview 68 2.2 Usingpronumerals 70 2.3 Algebrainwordedproblems 79 2.4 Simplificationofalgebraicexpressions 84 2.5 Expandingbrackets 91 2.6 Differenceoftwosquaresandperfect squares 100 2.7 Furtherexpansions 105 2.8 Thehighestcommonfactor 108 2.9 Thehighestcommonbinomialfactor 114 2.10 Solvingwordedproblems 118 2.11 Review 127 Answers 134 3 Linearequations 143 3.1 Overview 144 3.2 Solvinglinearequationsandinequations 146 3.3 Solvinglinearequationswithbrackets 157 3.4 Solvinglinearequationswithpronumerals onbothsides 161 3.5 Solvingproblemswithlinearequations 165 3.6 Rearrangingformulas 171 3.7 Review 176 Answers 182 4 Congruenceandsimilarity 185 4.1 Overview 186 4.2 Ratioandscale 189 4.3 Congruentfigures 198 4.4 Nets,polyhedraandEuler’sformula 206 4.5 Similarfigures 212 4.6 Areaandvolumeofsimilarfigures 223 4.7 Review 232 Answers 241 5 Pythagorasandtrigonometry 000 5.1 Overview 000 5.2 Pythagoras’theorem 000 5.3 ApplicationsofPythagoras’theorem 000 5.4 Trigonometricratios 000 5.5 Calculatingunknownsidelengths 000 5.6 Calculatingunknownangles 000 5.7 Anglesofelevationanddepression 000 5.8 Review 000 Answers 000 6 Linearandnon-lineargraphs 000 6.1 Overview 000 6.2 Plottinglineargraphs 000 6.3 Featuresoflineargraphs 000 6.4 Theequationofastraightline 000 6.5 Sketchinglineargraphs 000 6.6 Technologyandlineargraphs 000 6.7 Practicalapplicationsoflineargraphs 000 6.8 Midpointofalinesegmentanddistance betweentwopoints 000 6.9 Non-linearrelations 000 6.10 Review 000 Answers 000 Semesterreview1 000 CONTENTS v UNCORRECTEDPAGEPROOFS
7 Proportionandrates 000 7.1 Overview 000 7.2 Directlinearproportion 000 7.3 Proportionality 000 7.4 Introductiontorates 000 7.5 Constantandvariablerates 000 7.6 Review 000 Answers 000 8 Financialmathematics (extending) 000 8.1 Overview 000 8.2 Salariesandwages 000 8.3 Penaltyrates 000 8.4 Simpleinterest 000 8.5 Compoundinterest 000 8.6 Review 000 Answers 000 9 Measurement 000 9.1 Overview 000 9.2 Measurement 000 9.3 Area 000 9.4 Areaandperimeterofasector 000 9.5 Surfaceareaofrectangularandtriangular prisms 000 9.6 Surfaceareaofacylinder 000 9.7 Volumeofprismsandcylinders 000 9.8 Review 000 Answers 000 10 Probability 000 10.1 Overview 00 10.2 Theoreticalprobability 000 10.3 Experimentalprobability 000 10.4 Venndiagramsandtwo-waytables 000 10.5 Compoundevents 000 10.6 Review 000 Answers 000 11 Statistics 000 11.1 Overview 000 11.2 Collectingdata 000 11.3 Organisingdata 000 11.4 Displayingdata 000 11.5 Measuresofcentre 000 11.6 Measuresofspread 000 11.7 Review 000 Answers 000 12 Quadraticequationsand graphs 000 12.1 Overview 000 12.2 Quadraticequations(extending) 000 12.3 TheNullFactorLaw(extending) 000 12.4 Solvingquadraticequationswithtwo terms(extending) 000 12.5 Factorisingandsolvingmonicquadratic equations(extending) 000 12.6 Graphsofquadraticfunctions 000 12.7 Sketchingparabolasoftheform y ax 2 000 12.8 Sketchingparabolasoftheform y (x h)2 k 000 12.9 Sketchingparabolasoftheform y (x a)(x b) (extending) 000 12.10 Applications 000 12.11 Review 000 Answers 000 Semesterreview2 000 13 Algorithmicthinking 13.1 Overview 13.2 Programs 13.3 Arrays 13.4 Loops 13.5 Setstructures 13.6 Sortingalgorithms 13.7 TheMonteCarlomethod 13.8 Review Answers Glossary 000 Index 000 vi CONTENTS UNCORRECTEDPAGEPROOFS
About this resource NEW FOR
JACARANDA MATHS QUEST 9
AUSTRALIAN CURRICULUM FIFTH EDITION
Developed by teachers for students
Tried, tested and trusted. The fifth edition of the Jacaranda Maths Quest series, revised fourth 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 personal 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.
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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.
Personalise student learning pathways, ensuring that confidence builds and that students push themselves to achieve … all in learnON, Australia’s most innovative learning platform.
Through real-time results data, students can track and monitor their own progress and easily identify areas of strength and weakness.
And for teachers, Learning Analytics provide valuable insights to support student growth and drive informed intervention strategies.
AUSTRALIAN CURRICULUM V9.0ABOUT THIS RESOURCE vii
Learn online with Australia’s most
Everything you need for each of your lessons in one simple view
• 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.
Practical teaching advice and ideas for each lesson provided in teachON
Teaching videos for all lessons
Reading content and rich media including embedded videos and interactivities
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viii ABOUT THIS RESOURCE
powerful learning tool, learnON
New! Quick Quiz questions for skill acquisition
Differentiated question sets
Teacher and student views
Textbook questions
Fully worked solutions
eWorkbook
Digital documents
Video eLessons
Interactivities
Extra teaching support resources
Interactive questions with immediate feedback
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ABOUT THIS RESOURCE ix
Get
the most from your online resources
Online, these new editions are the complete package
Embedded interactivities and videos enable students to explore concepts and learn deeply by ‘doing’.
Trusted Jacaranda theory, plus tools to support teaching and make learning more engaging, personalised and visible.
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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x ABOUT
THIS RESOURCE
Brand new! Quick Quiz questions for skill acquisition in every lesson.
Three differentiated question sets, with immediate feedback in every lesson, enable students to challenge themselves at their own level
Instant reports give students visibility into progress and performance
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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 xi
Powering up for Year 7
A six-week ‘Powering up for Year 7’ online program is designed to plug any gaps from earlier years.
NAPLAN Online Practice
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.
eWorkbook
Also available online is a video that provides strategies and tips to help with your preparation.
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The eWorkbook enables teachers and students to download additional activities to support deeper learning
xii ABOUT THIS
RESOURCE
A wealth of teacher resources
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)
Customise and assign Reports and results
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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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 xiii
Acknowledgements
Theauthorsandpublisherwouldliketothankthefollowingcopyrightholders,organisationsandindividualsfor theirassistanceandforpermissiontoreproducecopyrightmaterialinthisbook.
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xiv ACKNOWLEDGEMENTS
NAPLAN practice
Go onlinetocompletepracticeNAPLANtests.Thereare6NAPLAN-stylequestionsets availabletohelpyouprepareforthisimportantevent.Theyarealsousefulforpractising yourMathematicsskillsingeneral. Alsoavailableonlineisavideothatprovidesstrategiesandtipstohelpwithyour preparation.
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SET B Non-calculator SET A Calculator allowed SET C Calculator allowed SET D Non-calculator SET E Calculator allowed SET F Non-calculator NAPLAN PRACTICE
xv