Jacaranda Maths Quest 8 VC 3e Prelims

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VICTORIANCURRICULUM|THIRDEDITION
JACARANDA MATHSQUEST8

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“FMPrelims_PrintPDF”—2023/8/31—6:23—pageiii—#3 JACARANDA
MARKBARNES
MATHSQUEST8 VICTORIANCURRICULUM|THIRDEDITION CATHERINESMITH BEVERLYLANGSFORDWILLING
CONTRIBUTINGAUTHORS JamesSmart|GeethaJames|CaitlinMahony|RebbeccaCharlesworth MichaelSheedy|KahniBurrows|PaulMenta VICTORIAN CURRICULUM v2.0

Thirdeditionpublished2023by

JohnWiley&SonsAustralia,Ltd

Level4,600BourkeStreet,Melbourne,Vic3000

Firsteditionpublished2014

Revisededitionpublished2018

Secondeditionpublished2021

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“FMPrelims_PrintPDF”—2023/8/31—6:23—pagev—#5 Contents Aboutthisresource vii Acknowledgements xiv NAPLANpractice SetA Calculatorallowed SetB Non-calculator SetC Calculatorallowed SetD Non-calculator SetE Calculatorallowed SetF Non-calculator 1 Integers 1 1.1 Overview 2 1.2 Addingandsubtractingintegers 4 1.3 Multiplyingintegers 11 1.4 Dividingintegers 15 1.5 Orderofoperationswithintegers 19 1.6 Review 23 Answers 29 2 Indexlaws 33 2.1 Overview 34 2.2 Reviewofindexform 36 2.3 Multiplyingpowers 41 2.4 Dividingpowers 45 2.5 Thezeroindex 50 2.6 Raisingpowers 54 2.7 Review 60 Answers 67 3 Realnumbers 71 3.1 Overview 72 3.2 Therealnumbersystem 74 3.3 Addingandsubtractingfractions 80 3.4 Multiplyinganddividingfractions 88 3.5 Terminatingandrecurringdecimals 93 3.6 Addingandsubtractingdecimals 97 3.7 Multiplyinganddividingdecimals 102 3.8 Estimation 107 3.9 Review 114 Answers 121 4 Applicationsofpercentages127 4.1 Overview 128 4.2 Percentages 130 4.3 Findingpercentagesofanamount 136 4.4 Discount 142 4.5 Profitandloss 148 4.6 GoodsandServicesTax(GST)and IncomeTax 155 4.7 Review 162 Answers 168 5 Ratiosandrates 171 5.1 Overview 172 5.2 Introductiontoratios 174 5.3 Simplifyingratios 181 5.4 Proportion 189 5.5 Comparingratios 195 5.6 Dividinginagivenratio 199 5.7 Rates 205 5.8 Interpretinggraphs 210 5.9 Review 219 Answers 225 6 Congruence 231 6.1 Overview 232 6.2 Transformationsandtessellations 236 6.3 Congruentfigures 254 6.4 Triangleconstructionsandobjectsin3D 262 6.5 Congruenttrianglesandsimilarshapes 270 6.6 Quadrilaterals 287 6.7 Review 295 Answers 302 Semesterreview1 312 7 Algebra 315 7.1 Overview 316 7.2 Usingpronumerals 318 7.3 Substitution 323 7.4 Substitutingpositiveandnegative numbers 328 7.5 Numberlaws 331 7.6 Addingandsubtractingterms 337 7.7 Multiplyinganddividingterms 341 7.8 Expandingbrackets 348 7.9 Factorising 353 7.10 Review 357 Answers 363 8 Measurement 369 8.1 Overview 370 8.2 Lengthandperimeter 373 8.3 Circumference 381 8.4 Areasofrectangles,triangles, parallelograms,rhombusesandkites 390 8.5 Areasofcircles 403 CONTENTS v
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“FMPrelims_PrintPDF”—2023/8/31—6:23—pagevi—#6 8.6 Areasoftrapeziums 409 8.7 Volumesofprismsandothersolids 414 8.8 Time 421 8.9 24-hourclocksandtimezones 427 8.10 Review 436 Answers 445 9 Linearequations 451 9.1 Overview 452 9.2 Backtrackingandinverseoperations 454 9.3 Keepingequationsbalanced 459 9.4 Solvinglinearequationsandinequations 463 9.5 Equationswiththeunknownonboth sides 473 9.6 Review 479 Answers 485 10 Representingandinterpreting data 489 10.1 Overview 490 10.2 Datacollectionmethods 493 10.3 Primaryandsecondarydata 504 10.4 Organisinganddisplayingdata 513 10.5 Measuresofcentreandspread 523 10.6 Analysingdata 538 10.7 Review 546 Answers 552 11 Probability 561 11.1 Overview 562 11.2 Experimentalprobability 565 11.3 Probabilityscale 573 11.4 Samplespacesandtheoreticalprobability 577 11.5 Complementaryevents 585 11.6 Venndiagramsandtwo-waytables 590 11.7 Treediagrams 603 11.8 Review 612 Answers 618 12 Coordinatesandlineargraphs627 12.1 Overview 628 12.2 TheCartesianplane 631 12.3 Linearpatterns 638 12.4 Plottinglineargraphs 645 12.5 Determiningtheruleforalinear relationship 651 12.6 Sketchinglineargraphs(extending) 666 12.7 Solvingequationsgraphically 671 12.8 Non-lineargraphs 680 12.9 Review 687 Answers 694 13 Pythagoras’theorem 715 13.1 Overview 716 13.2 Pythagoras’theorem 719 13.3 Calculatingshortersidelengths 726 13.4 ApplyingPythagoras’theorem 730 13.5 Pythagoreantriads 736 13.6 Review 740 Answers 745 Semesterreview2 748 14 Algorithmicthinking 14.1 Overview 14.2 Expressions 14.3 Decisions 14.4 Functions 14.5 Testing 14.6 Debugging 14.7 Review Answers Glossary 750 Index 755 vi CONTENTS UNCORRECTEDPAGEPROOFS

About this resource NEW FOR

JACARANDA MATHS QUEST 8

VICTORIAN CURRICULUM

THIRD EDITION

Developed by teachers for students

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 personal Learning is effortfulLearning 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.

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.

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

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ABOUT THIS RESOURCE vii

Learn online with Australia’s most

Everything

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
you need for each of your lessons in one simple view

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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THIS RESOURCE ix
ABOUT

Get the most from your online resources

Trusted Jacaranda theory, plus tools to support teaching and make learning more engaging, personalised and visible.

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

and

New teaching videos for every lesson are designed to help students learn concepts by having a ‘teacher at home’, and e 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

Three differentiated question sets, with immediate feedback in every lesson, enablestudents to challenge themselves at theirown 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

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

Maths Quest 8 includes 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

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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

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.

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.

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ABOUT THIS RESOURCE xiii

Acknowledgements

Theauthorsandpublisherwouldliketothankthefollowingcopyrightholders,organisationsandindividualsfor theirassistanceandforpermissiontoreproducecopyrightmaterialinthisbook.

TheVictorianCurriculumF–10contentelementsare©VCAA,reproducedbypermission.TheVCAAdoesnot endorseormakeanywarrantiesregardingthisresource.TheVictorianCurriculumF-10andrelatedcontentcan beaccesseddirectlyattheVCAAwebsite.

ThismaybeamodifiedextractfromtheVictorianCurriculumF-10andmayincludetheworkofotherauthors. VCAAdoesnotendorsenorverifytheaccuracyoftheinformationprovidedandacceptsnoresponsibilityfor incompleteorinaccurateinformation.YoucanfindthemostuptodateversionoftheVictorianCurriculumat http://victoriancurriculum.vcaa.vic.edu.au/.

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