SMITH | SMART | JAMES | MAHONY | LANGSFORD WILLING AUSTRALIAN CURRICULUM v9.0 AUSTRALIAN CURRICULUM | FIFTH EDITION
JACARANDA MATHS QUEST 7
JACARANDA MATHSQUEST7
AUSTRALIANCURRICULUM|FIFTHEDITION
INSPECTIONPROOFS
INSPECTIONPROOFS
JACARANDA
AUSTRALIANCURRICULUM|FIFTHEDITION CATHERINESMITH JAMESSMART GEETHAJAMES CAITLINMAHONY BEVERLYLANGSFORDWILLING CONTRIBUTINGAUTHORS MichaelSheedy|KahniBurrows|PaulMenta INSPECTIONPROOFS
MATHSQUEST7
Fiftheditionpublished2023by
JohnWiley&SonsAustralia,Ltd
Level4,600BourkeStreet,Melbourne,Vic3000
Firsteditionpublished2011
Secondeditionpublished2014
Thirdeditionpublished2018
Fourtheditionpublished2021
Typesetin10.5/13ptTimesLTStd
©JohnWiley&SonsAustralia,Ltd2011,2014,2018,2021,2023
Themoralrightsoftheauthorshavebeenasserted.
ISBN:978-1-394-19426-1
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Illustratedbyvariousartists,diacriTechandWileyCompositionServices
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Contents Aboutthisresource vii Acknowledgements xiv PoweringupforYear7 Week1 Findingyourplace Week2 Numberingup Week3 Thinkingquickly Week4 Fishingforfractions Week5 Gettingtothepoint Week6 Giving100% NAPLANpractice SetA Calculatorallowed SetB Non-calculator SetC Calculatorallowed SetD Non-calculator SetE Calculatorallowed SetF Non-calculator 1 Positiveintegers 1 1.1 Overview 2 1.2 Placevalue 4 1.3 Strategiesforaddingandsubtracting positiveintegers 10 1.4 Algorithmsforaddingandsubtracting positiveintegers 16 1.5 Multiplyingpositiveintegers 25 1.6 Dividingpositiveintegers 34 1.7 Roundingandestimating 41 1.8 Orderofoperations 45 1.9 Review 52 Answers 61 2 Positiveandnegativeintegers67 2.1 Overview 68 2.2 Integersonthenumberline 70 2.3 Integersonthenumberplane 75 2.4 Addingintegers 80 2.5 Subtractingintegers 85 2.6 Multiplyinganddividingintegers 91 2.7 Orderofoperationswithintegers 97 2.8 Review 102 Answers 109 3 Factors,multiples,indicesand primes 115 3.1 Overview 116 3.2 Factorsandmultiples 118 3.3 Lowestcommonmultipleandhighest commonfactor 123 3.4 Indexnotation 128 3.5 Primeandcompositenumbers 133 3.6 Squaresandsquareroots 141 3.7 Divisibilitytests 147 3.8 Cubesandcuberoots 150 3.9 Review 155 Answers 162 4 Fractionsandpercentages167 4.1 Overview 168 4.2 Whatarefractions? 170 4.3 Simplifyingfractions 182 4.4 Mixednumbersandimproperfractions 186 4.5 Addingandsubtractingfractions 192 4.6 Multiplyingfractions 200 4.7 Dividingfractions 208 4.8 Workingwithmixednumbers 213 4.9 Percentagesasfractions 220 4.10 Calculatingpercentagesofanamount 225 4.11 Oneamountasapercentageofanother 230 4.12 Commonpercentagesandshortcuts 236 4.13 Review 242 Answers 251 5 Ratios,ratesandbestbuys261 5.1 Overview 262 5.2 Ratios 265 5.3 Rates 271 5.4 Theunitarymethodandbestbuys 276 5.5 Review 281 Answers 286 6 Decimals 289 6.1 Overview 290 6.2 Decimalsandplacevalue 292 6.3 Convertingdecimalstofractionsand fractionstodecimals 300 6.4 Roundingandrepeatingdecimals 305 6.5 Addingandsubtractingdecimals 311 6.6 Multiplyingdecimals 317 6.7 Dividingdecimals 323 6.8 Decimalsandpercentages 330 6.9 Review 333 Answers 340 CONTENTS v INSPECTIONPROOFS
7 Algebra 347 7.1 Overview 348 7.2 Introductiontoalgebra 350 7.3 Substitutingandevaluating 358 7.4 Simplifyingexpressionsusingliketerms 362 7.5 Multiplyinganddividingterms 367 7.6 Numberlaws 371 7.7 Expandingbrackets 375 7.8 Review 379 Answers 385 Semesterreview1 390 8 Equations 393 8.1 Overview 394 8.2 Introductiontoequations 396 8.3 Buildingupexpressionsandbacktracking 402 8.4 Solvingequationsusingbacktracking 408 8.5 Solvingequationsusinginverse operations 415 8.6 Checkingsolutions 424 8.7 Review 429 Answers 435 9 Geometry 441 9.1 Overview 442 9.2 Measuringangles 445 9.3 Constructingangleswithaprotractor 453 9.4 Typesofanglesandnamingangles 459 9.5 Triangles 465 9.6 Quadrilateralsandtheirproperties 477 9.7 Parallelandperpendicularlines 487 9.8 Review 498 Answers 507 10 Measurement 517 10.1 Overview 518 10.2 Unitsofmeasurement 521 10.3 Readingscalesandmeasuringlength 528 10.4 Perimeter 536 10.5 Circlesandcircumference 544 10.6 Area 553 10.7 Areaofcompositeshapes 566 10.8 Volumeofrectangularprisms 571 10.9 Capacity 579 10.10 Drawingsolids 583 10.11 Review 594 Answers 605 11 CoordinatesandtheCartesian plane 613 11.1 Overview 614 11.2 TheCartesianplane 617 11.3 Linearnumberpatterns 625 11.4 Plottingsimplelinearrelationships 632 11.5 Interpretinggraphs 639 11.6 Review 651 Answers 659 12 Transformations 671 12.1 Overview 672 12.2 Lineandrotationalsymmetry 674 12.3 Translations 680 12.4 Reflections 686 12.5 Rotationsandcombinedtransformations 693 12.6 Review 705 Answers 711 13 Introductiontoprobability723 13.1 Overview 724 13.2 Thelanguageofchance 726 13.3 Thesamplespace 731 13.4 Simpleprobability 736 13.5 Experimentalprobability 742 13.6 Review 750 Answers 757 14 Representingandinterpreting data 763 14.1 Overview 764 14.2 Collectingandclassifyingdata 767 14.3 Displayingdataintables 774 14.4 Measuresofcentreandspread 780 14.5 Columngraphsanddotplots 791 14.6 Stem-and-leafplots 798 14.7 Piechartsanddividedbargraphs 804 14.8 Comparingdata 814 14.9 Review 820 Answers 829 Semesterreview2 842 15 Algorithmicthinking 15.1 Overview 15.2 Variables 15.3 Expressions 15.4 Sequences 15.5 Algorithms 15.6 Review Answers Glossary 844 Index 850 vi CONTENTS INSPECTIONPROOFS
About this resource NEW FOR
JACARANDA MATHS QUEST 7
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 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.
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.
AUSTRALIAN CURRICULUM V9.0ABOUT THIS RESOURCE vii
Learn online with Australia’s most
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
Everything 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
ABOUT THIS RESOURCE ix INSPECTIONPROOFS
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
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.
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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 eWorkbook
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.
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.
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.
Images
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©Katilda/Shutterstock: 489 •©Kostyazar/Shutterstock: 384 •©LightFieldStudios/Shutterstock: 518 •© Luca9257/Shutterstock: 532 •©Mak3t/Shutterstock: 675 •©MinervaStudio/Shutterstock: 310 •©Monkey
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•©AdamMiddleton/Shutterstock: 653 •©aekikuis/Shutterstock: 283 •©al7/Shutterstock: 434 •©Alberto Loyo/Shutterstock: 249 •©alessandro0770/Shutterstock: 228 •©AlexandraLande/Shutterstock: 674 •© AlinuteSilzeviciute/Shutterstock: 818
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•©Chekyravaa/Shutterstock: 170 •©ChrisJenner/Shutterstock: 653 •© clearviewstock/Shutterstock: 756 •©CorbisRoyaltyFree: 535 •©CorepicsVOF/Shutterstock: 23 •© corund/Shutterstock: 685 •©cpaulfell/Shutterstock: 434 •©DamianPankowiec/Shutterstock: 33 •©Daniel Jedzura/Shutterstock: 218 •©debrahughes/Shutterstock: 119 •©Denphumi/Shutterstock: 732
ChameleonsEye/Shutterstock: 24
xiv ACKNOWLEDGEMENTS
•©Desmos: 697 •©DigitalStock/CorbisCorporation: 90,462 •©DigitalVision: 643 •©dim.po: 270 •© DisobeyArt/Shutterstock: 100 •©DmitryEagleOrlov/Shutterstock: 381 •©DmytroZinkevych/Shutterstock: 411 •©dolomite-summits/Shutterstock: 159 •©DOUGRAPHAEL/Shutterstock: 220 •©Dragon ImagesShutterstock: 85 •©eAlisa/Shutterstock: 244 •©Elartico/Shutterstock: 116 •©Elena Veselova/Shutterstock: 264 •©ESBProfessional/Shutterstock: 234,777 •©ET-ARTWORKS/GettyImages: 693 •©EvaSpeshneva/Shutterstock: 362 •©f11photo/Shutterstock: 50 •©fckncg/Shutterstock: 178 •©Fedor Selivanov/Shutterstock: 53 •©Fertas/Shutterstock: 433 •©freevideophotoagency/Shutterstock: 160 •© frenchiestravel/Shutterstock: 58 •©fresher/Shutterstock: 34 •©fritz16/Shutterstock: 8 •© garagestock/Shutterstock: 278 •©GentianPolovina/Shutterstock: 284 •©GinoSantaMaria/Shutterstock: 755 • ©givaga/Shutterstock: 279 •©goodluz/Shutterstock: 132 •©GorodenkoffShutterstock: 75 •© Gringoann/Shutterstock: 284 •©grum_l/Shutterstock: 739 •©gualtieroboffi/Shutterstock: 230 •© Halfpoint/Shutterstock: 126 •©hddigital/Shutterstock: 316 •©HGPhotography/Shutterstock: 192 •© Hquality/Shutterstock: 305,754 •©HugoFelix/Shutterstock: 154 •©IakovFilimonov: 212 •©ImageAddict: 229 •©ImageDiskPhotography: 7 •©imageBROKER/AlamyStockPhoto: 245 •©Imagenet/Shutterstock: 764 •©ingehogenbijl/Shutterstock: 8 •©IngridBalabanova/Shutterstock: 336 •©IrinaStrelnikova;©Marish: 1,67,115,167,261,289,347,393,441,517,613,671,723,763 •©ITStock: 462 •©Ivan MarjanovicShutterstock: 79 •©JanHopgood/Shutterstock: 394 •©Jasni/Shutterstock: 740 •©JohnWiley& SonsAustralia: 34,464 •©JohnWiley&SonsAustralia/TakenbyKari-AnnTapp: 196 •©JohnWiley&Sons Australia/CarolynMews: 450,486 •©JohnWiley&SonsAustralia/JenniferWright: 179 •©JohnWiley& SonsAustralia/JoPatterson: 532 •©JohnWiley/JoPatterson: 532 •©jokerpro/Shutterstock: 44 •©Jorge Casais/Shutterstock: 645 •©JoshuaResnick/Shutterstock: 336 •©JPLDesigns/Shutterstock: 706 •© JR-stock/Shutterstock: 361 •©Julinzy: 269 •©Kari-AnnTapp: 742 •©Krakenimages.com/Shutterstock: 755 • ©KutlayevDmitry/Shutterstock: 264 •©lightpoet/Shutterstock: 33 •©LanceBellers/Shutterstock: 730 • ©LesyaDolyuk/Shutterstock: 191 •©LightFieldStudios/Shutterstock: 264 •©M.UnalOzmenShutterstock: 58 •©MadeleineR/Shutterstock: 279 •©MaksNarodenko/Shutterstock: 189 •©MaliutinaAnnaShutterstock: 96 •©MaraZe/Shutterstock: 45 •©Maridav/Shutterstock: 219,646 •©mashurov/Shutterstock: 39 •© matimix/Shutterstock: 734 •©Maxisport/Shutterstock: 315,430 •©MCruzUA/Shutterstock: 35 •©Mega Pixel/Shutterstock: 737 •©MichaelRosskothen/Shutterstock: 653 •©MichaelJayBerlin/Shutterstock: 138 •© michaeljung/Shutterstock: 185 •©MilaSupinskayaGlashchenko/Shutterstock: 39 •©Milagli/Shutterstock: 55 •©MindProStudio/Shutterstock: 232 •©MinervaStudio/Shutterstock: 789 •©MiniDoodle/Shutterstock: 751 •©mirtmirt/Shutterstock: 735 •©MitchHutchinson/Shutterstock: 724 •©MonkeyBusiness Images/Shutterstock: 40,122,191,223,224,245,401,407,778 •©monticello/Shutterstock: 240 •© monticello/Shutterstock.com: 741 •©mooinblack/Shutterstock: 240 •©NataliGlado/Shutterstock: 788 •© NationalCouncilofTeachersofMathematics: 745 •©NealeCousland/Shutterstock: 59,229,730 •© Neirfy/Shutterstock: 381 •©NejronPhotoShutterstock: 85 •©Nerthuz/Shutterstock: 280 •©New Africa/Shutterstock: 125,246 •©NewsLtd/Newspix: 480 •©NicholasPiccillo/Shutterstock: 414 •© NicoElNino/Shutterstock: 405 •©nobeastsofierce/Shutterstock: 133 •©oksana2010/Shutterstock: 280 •© OleksiyMark/Shutterstock: 250 •©PAImages/AlamyStockPhoto: 2,290,316 •©PANAGIOTIS
KARAPANAGIOTIS/AlamyStockPhoto: 54
•©PanyaStudio/Shutterstock: 358 •©Pepgooner/Shutterstock: 90 •©PetrenkoAndriy/Shutterstock.com: 181 •©Phatthanit/Shutterstock: 230 •©PhilsMommy/Shutterstock: 428 •©Photoagriculture/Shutterstock: 421 •©Photodisc: 198,207,463,479,486,529,772,774,801 •© PhotoDisc:Inc, 525
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•©Pressmaster/Shutterstock: 219,357 •©ProStockStudio/Shutterstock: 396 •© QilinspranceFilmmakerShutterstock: 101 •©RaduBercan/Shutterstock: 276 •©ratselmeister/Shutterstock: 263 •©Rawpixel.com/Shutterstock: 249 •©Renovacio/Shutterstock: 741 •©RichardSemik/Shutterstock: 421
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•©RobynMackenzie/Shutterstock: 339 •©RomaKoshel/Shutterstock: 748 •© RomanSamborskyiShutterstock: 32 •©ROMSVETNIK/Shutterstock: 726 •©RonaldSumners/Shutterstock: 50 •©RostislavKrál/Shutterstock: 217 •©RuthBlack/Shutterstock: 50 •©safakcakir/Shutterstock: 217 •© Sandarina/Shutterstock: 40 •©SeanDonohuePhoto/Shutterstock: 315 •©Serg64/Shutterstock: 332 •©Sergey Nivens/Shutterstock: 72
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ACKNOWLEDGEMENTS xv
•©Sonulkaster/Shutterstock: 104 •©stockcreations/Shutterstock: 90 •©StockPhotoAstur/Shutterstock: 686 •
©Sudowoodo: 363 •©SundrawPhotography/Shutterstock: 645 •©SwapanPhotography/Shutterstock: 748 •©
SydaProductions/Shutterstock: 100,181 •©technotr/GettyImages: 22 •©TetyanaKokhanets/Shutterstock: 727 •©THPStock/Shutterstock: 735 •©TKKurikawa/Shutterstock: 332 •©TORWAISTUDIO/Shutterstock: 650 •©tr3gin/Shutterstock: 218 •©trigga/GettyImages: 74 •©TylerOlson/Shutterstock: 282 •©Tyler
Olson/Shutterstock.com: 310 •©UnknownLatitudeImages/Shutterstock: 7 •©upthebanner/Shutterstock: 217 • ©v74/Shutterstock: 728 •©Velychko/Shutterstock: 199 •©VereshchaginDmitry/Shutterstock: 772 •© ViewfinderAustraliaPhotoLibrary: 535 •©ViktorFedorenko/Shutterstock: 732,738 •©
VisualArtStudioShutterstock: 22 •©vkilikovShutterstock: 17 •©VladisChern/Shutterstock: 70 •©Volodymyr
TVERDOKHLIB: 122 •©VoltCollection/Shutterstock: 296 •©VovanIvanovich/Shutterstock: 68 •©VP
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©YetiStudio/Shutterstock: 739 •©Yevgenij_D/Shutterstock: 614 •©YouTouchPixofEuToch/Shutterstock: 229 •©ZbigniewGuzowski/Shutterstock: 740 •©zbindere/GettyImages: 7 •©zentilia/Shutterstock: 734 •
©DragonImages/Shutterstock: 133 •©MichaelDBrown/Shutterstock: 753 •©Nataliya
Peregudova/Shutterstock: 225 •©AndreyArkusha/Shutterstock: 521 •©BennyMarty/Shutterstock: 521 •© BrunoHerdt/GettyImages: 449 •©Corbis: 524 •©CurrywurstmitPommes/Shutterstock: 521 •©DigitalStock: 449 •©DigitalVision: 484 •©Dimedrol68/Shutterstock: 452 •©Dimedrol68/Shutterstock: 452 •© diskoVisnja/Shutterstock: 497 •©EugeneBuchko/Shutterstock: 483 •©Haali/Shutterstock: 156,751 •© HaaliShutterstock: 53 •©JohnWiley&SonsAustralia: 532 •©JohnWiley&SonsAustralia/Photoby Kari-AnnTapp: 483 •©JohnWiley&SonsAustralia/PhotobyTheresaPagon: 484 •©
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xvi ACKNOWLEDGEMENTS
