AUSTRALIAN CURRICULUM v9.0 AUSTRALIAN CURRICULUM | FIFTH EDITION JACARANDA MATHS
10 SMITH | LANGSFORD WILLING | BARNES | UTBER
QUEST
JACARANDA MATHSQUEST 10
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AUSTRALIANCURRICULUM|FIFTHEDITION
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JACARANDA MATHS QUEST 10
AUSTRALIAN CURRICULUM | FIFTH EDITION
CATHERINE SMITH
BEVERLY LANGSFORD WILLING
MARK BARNES
CHRISTINE UTBER
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
Typesetin10.5/13ptTimesLTStd
©JohnWiley&SonsAustralia,Ltd2011,2014,2018,2021,2023
Themoralrightsoftheauthorshavebeenasserted.
ISBN:978-1-394-19399-8
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Contents Aboutthisresource vii Acknowledgements xiv 1 Indices,surdsandlogarithms000 1.1 Overview 000 1.2 Numberclassificationreview 000 1.3 Surds 000 1.4 Operationswithsurds 000 1.5 Reviewofindexlaws 000 1.6 Negativeindices 000 1.7 Fractionalindices 000 1.8 Combiningindexlaws 000 1.9 Logarithms 000 1.10 Logarithmlaws 000 1.11 Solvingequations 000 1.12 Review 000 Answers 000 2 Algebraandequations 000 2.1 Overview 000 2.2 Substitution 000 2.3 Addingandsubtractingalgebraic fractions 000 2.4 Multiplyinganddividingalgebraic fractions 000 2.5 Solvingsimpleequations 000 2.6 Solvingmulti-stepequations 000 2.7 Literalequations 000 2.8 Review 000 Answers 000 3 Networks 000 3.1 Whatisanetwork? 000 3.2 Basicpropertiesofnetworks 000 3.3 Applicationsofnetworkstoproblem solving 000 3.4 Pathsandcircuits 000 3.5 DeterminingEulercircuitforanetwork 000 3.6 Treesandnetworks 000 3.7 Review 000 Answers 000 4 Linearrelationships 000 4.1 Overview 000 4.2 Sketchinglineargraphs 000 4.3 Determininglinearequations 000 4.4 Graphicalsolutionofsimultaneouslinear equations 000 4.5 Solvingsimultaneouslinearequations usingsubstitution 000 4.6 Solvingsimultaneouslinearequations usingelimination 000 4.7 Applicationsofsimultaneouslinear equations 000 4.8 Solvingsimultaneouslinearand non-linearequations 000 4.9 Solvinglinearinequalities 000 4.10 InequalitiesontheCartesianplane 000 4.11 Solvingsimultaneouslinearinequalities 000 4.12 Review 000 Answers 000 5 TrigonometryI 000 5.1 Overview 000 5.2 Pythagoras’theorem 000 5.3 Pythagoras’theoreminthreedimensions 000 5.4 Trigonometricratios 000 5.5 Usingtrigonometrytocalculateside lengths 000 5.6 Usingtrigonometrytocalculateanglesize 000 5.7 Anglesofelevationanddepression 000 5.8 Bearings 000 5.9 Applications 000 5.10 Review 000 Answers 000 6 Surfaceareaandvolume000 6.1 Overview 000 6.2 Area 000 6.3 Totalsurfacearea 000 6.4 Volume 000 6.5 Review 000 Answers 000 7 Quadraticexpressions 000 7.1 Overview 000 7.2 Expandingalgebraicexpressions 000 7.3 Factorisingexpressionswiththreeterms 000 7.4 Factorisingexpressionswithtwoorfour terms 000 7.5 Factorisingbycompletingthesquare 000 7.6 Mixedfactorisation 000 7.7 Review 000 Answers 000 8 Quadraticequationsand graphs 000 8.1 Overview 000 8.2 Solvingquadraticequationsalgebraically 000 8.3 Thequadraticformula 000 CONTENTS v UNCORRECTEDPAGE PROOFS
8.4 Solvingquadraticequationsgraphically 000 8.5 Thediscriminant 000 8.6 Plottingparabolasfromatableofvalues 000 8.7 Sketchingparabolasusing transformations 000 8.8 Sketchingparabolasusingturning pointform 000 8.9 Sketchingparabolasinexpandedform 000 8.10 Review 000 Answers 000 Semesterreview1 000 9 Functions,relationsand modelling 000 9.1 Overview 000 9.2 Functionsandrelations 000 9.3 Exponentialfunctions 000 9.4 Exponentialgraphs 000 9.5 Applicationofindices:Compoundinterest 000 9.6 Cubicfunctions 000 9.7 Quarticfunctions 000 9.8 Sketchingthecircle 000 9.9 Transformations 000 9.10 Mathematicalmodelling 000 9.11 Review 000 Answers 000 10 Deductivegeometry 000 10.1 Overview 000 10.2 Angles,trianglesandcongruence 000 10.3 Similartriangles 000 10.4 Quadrilaterals 000 10.5 Polygons 000 10.6 Review 000 Answers 000 11 Probability 000 11.1 Overview 000 11.2 Reviewofprobability 000 11.3 Treediagrams 000 11.4 Independentanddependentevents 000 11.5 Conditionalprobability 000 11.6 Combinatorics 000 11.7 Review 000 Answers 000 12 Univariatedata 000 12.1 Overview 000 12.2 Measuresofcentraltendency 000 12.3 Measuresofspread 000 12.4 Boxplots 000 12.5 Thestandarddeviation 000 12.6 Comparingdatasets 000 12.7 Populationsandsamples 000 12.8 Evaluatinginquirymethodsandstatistical reports 000 12.9 Review 000 Answers 000 13 Bivariatedata 000 13.1 Overview 000 13.2 Bivariatedata 000 13.3 Linesofbestfitbyeye 000 13.4 Linearregressionusingtechnology 000 13.5 Timeseries 000 13.6 Review 000 Answers 000 14 Circlegeometry 000 14.1 Overview 000 14.2 Anglesinacircle 000 14.3 Intersectingchords,secantsandtangents 000 14.4 Cyclicquadrilaterals 000 14.5 Tangents,secantsandchords 000 14.6 Review 000 Answers 000 15 TrigonometryII 000 15.1 Overview 000 15.2 Thesinerule 000 15.3 Thecosinerule 000 15.4 Areaoftriangles 000 15.5 Theunitcircle 000 15.6 Trigonometricfunctions 000 15.7 Solvingtrigonometricequations 000 15.8 Review 000 Answers 000 Semesterreview2 000 16 Algorithmicthinking 16.1 Overview 16.2 Programs 16.3 Datastructures 16.4 Algorithms 16.5 Matrices 16.6 Graphics 16.7 Simulations 16.8 Review Answers Glossary 000 Index 000 vi CONTENTS UNCORRECTEDPAGE PROOFS
About this resource NEW FOR
JACARANDA MATHS QUEST 10
AUSTRALIAN CURRICULUM V9.0
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.
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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.
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
Practical teaching advice and ideas for each lesson provided in teachON
All the teacher support resources you need
Deep insights into progress
Immediate feedback for students
Create custom assignments in just a few clicks.
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
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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
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
