AUSTRALIAN CURRICULUM v9.0 AUSTRALIAN CURRICULUM | FIFTH EDITION JACARANDA MATHS QUEST 8 SMITH | LANGSFORD WILLING | BARNES
JACARANDA MATHSQUEST8
AUSTRALIANCURRICULUM|FIFTHEDITION
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8 JACARANDA MATHS QUEST
AUSTRALIAN CURRICULUM | FIFTH EDITION
CATHERINE SMITH
BEVERLY LANGSFORD WILLING
MARK BARNES
CONTRIBUTING AUTHORS
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
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©JohnWiley&SonsAustralia,Ltd2011,2014,2018,2021,2023
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ISBN:978-1-394-19417-9
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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 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 173 5.1 Overview 174 5.2 Introductiontoratios 176 5.3 Simplifyingratios 183 5.4 Proportion 191 5.5 Comparingratios 197 5.6 Dividinginagivenratio 201 5.7 Rates 207 5.8 Interpretinggraphs 212 5.9 Review 221 Answers 227 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 303 7 Algebra 305 7.1 Overview 306 7.2 Usingpronumerals 308 7.3 Substitution 313 7.4 Substitutingpositiveandnegative numbers 318 7.5 Numberlaws 321 7.6 Addingandsubtractingterms 327 7.7 Multiplyinganddividingterms 331 7.8 Expandingbrackets 338 7.9 Factorising 343 7.10 Review 347 Answers 353 8 Measurement 359 8.1 Overview 360 8.2 Lengthandperimeter 363 8.3 Circumference 371 8.4 Areasofrectangles,triangles, parallelograms,rhombusesandkites 380 8.5 Areasofcircles 393 CONTENTS v UNCORRECTEDPAGE PROOFS
8.6 Areasoftrapeziums 399 8.7 Volumesofprismsandothersolids 404 8.8 Time 411 8.9 24-hourclocksandtimezones 417 8.10 Review 426 Answers 435 9 Linearequations 439 9.1 Overview 440 9.2 Backtrackingandinverseoperations 442 9.3 Keepingequationsbalanced 447 9.4 Solvinglinearequationsandinequations 451 9.5 Equationswiththeunknownonboth sides 461 9.6 Review 467 Answers 473 10 Representingandinterpreting data 477 10.1 Overview 478 10.2 Datacollectionmethods 481 10.3 Primaryandsecondarydata 492 10.4 Organisinganddisplayingdata 501 10.5 Measuresofcentreandspread 511 10.6 Analysingdata 526 10.7 Review 534 Answers 540 11 Probability 547 11.1 Overview 548 11.2 Experimentalprobability 551 11.3 Probabilityscale 559 11.4 Samplespacesandtheoreticalprobability 563 11.5 Complementaryevents 571 11.6 Venndiagramsandtwo-waytables 576 11.7 Treediagrams(extending) 589 11.8 Review 598 Answers 604 12 Coordinatesandlineargraphs611 12.1 Overview 612 12.2 TheCartesianplane 615 12.3 Linearpatterns 622 12.4 Plottinglineargraphs 629 12.5 Determiningtheruleforalinear relationship 635 12.6 Sketchinglineargraphs(extending) 650 12.7 Solvingequationsgraphically 655 12.8 Non-lineargraphs 664 12.9 Review 671 Answers 678 13 Pythagoras’theorem 697 13.1 Overview 698 13.2 Pythagoras’theorem 701 13.3 Calculatingshortersidelengths 708 13.4 ApplyingPythagoras’theorem 712 13.5 Pythagoreantriads 718 13.6 Review 722 Answers 727 Semesterreview2 729 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 732 Index 737 vi CONTENTS UNCORRECTEDPAGE PROOFS
About this resource
JACARANDA MATHS QUEST 8
AUSTRALIAN CURRICULUM FIFTH EDITION
Developed by teachers for students
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 personalLearning is effortfulLearning is rewarding
Whether students need a challenge or a helping hand, you’ll find what you need to create engaging lessons.
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.
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And for teachers, Learning Analytics provide valuable insights to support student growth and drive informed intervention strategies.
ABOUT 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
and tips to help with your preparation.
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 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.
Data analytics and instant reports provide data-driven insights into progress and performance within each lesson and across the entire course.
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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
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NAPLANpractice
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.
Also available online is a video that provides strategies and tips to help with your 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 xvi
NAPLAN PRACTICE