Bill Pender
David Sadler, Derek Ward
Brian Dorofaeff, William McArthur SECOND
ShaftesburyRoad,CambridgeCB28EA,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467
CambridgeUniversityPress&AssessmentisadepartmentoftheUniversityofCambridge. WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org
© BillPender,DavidSadler,DerekWard,BrianDorofaeff andJuliaShea2019
© BillPender,DavidSadler,DerekWard,BrianDorofaeff andWilliamMcArthur2025
Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress&Assessment.
Firstpublished2019
SecondEdition2025 2019181716151413121110987654321
CoverdesignedbySardineDesign
TextdesignedbydiacriTech
TypesetbydiacriTech
PrintedinChinabyC&COffsetPrintingCo.Ltd.
AcataloguerecordforthisbookisavailablefromtheNationalLibraryofAustraliaat www.nla.gov.au
ISBN978-1-009-65480-7
Additionalresourcesforthispublicationatwww.cambridge.edu.au/GO
ReproductionandCommunicationforeducationalpurposes
TheAustralian CopyrightAct1968 (theAct)allowsamaximumofonechapteror10%ofthepagesofthis publication,whicheveristhegreater,tobereproducedand/orcommunicatedbyanyeducationalinstitution foritseducationalpurposesprovidedthattheeducationalinstitution(orthebodythatadministersit)hasgiven aremunerationnoticetoCopyrightAgencyLimited(CAL)undertheAct. FordetailsoftheCALlicenceforeducationalinstitutionscontact:
CopyrightAgencyLimited Level12,66GoulburnStreet
SydneyNSW2000
Telephone:(02)93947600
Facsimile:(02)93947601
Email:memberservices@copyright.com.au
ReproductionandCommunicationforotherpurposes
ExceptaspermittedundertheAct(forexampleafairdealingforthepurposesofstudy,research,criticism orreview)nopartofthispublicationmaybereproduced,storedinaretrievalsystem,communicatedor transmittedinanyformorbyanymeanswithoutpriorwrittenpermission.Allinquiriesshouldbemadeto thepublisherattheaddressabove.
CambridgeUniversityPress&AssessmenthasnoresponsibilityforthepersistenceoraccuracyofURLsfor externalorthird-partyinternetwebsitesreferredtointhispublicationanddoesnotguaranteethatanycontenton suchwebsitesis,orwillremain,accurateorappropriate.Informationregardingprices,traveltimetablesandother factualinformationgiveninthisworkiscorrectatthetimeoffirstprintingbutCambridgeUniversityPress& Assessmentdoesnotguaranteetheaccuracyofsuchinformationthereafter.
CambridgeUniversityPress & AssessmentacknowledgestheAboriginalandTorresStraitIslanderpeoplesofthis nation.Weacknowledgethetraditionalcustodiansofthelandsonwhichourcompanyislocatedandwherewe conductourbusiness.WepayourrespectstoancestorsandElders,pastandpresent.CambridgeUniversityPress & AssessmentiscommittedtohonouringAboriginalandTorresStraitIslanderpeoples’uniqueculturaland spiritualrelationshipstotheland,watersandseasandtheirrichcontributiontosociety.
Introductionandoverview vii
Acknowledgements ix
Abouttheauthors x
1 Algebrareview
1A Expandingbrackets ...............................
1B Factoring
1C Algebraicfractions ...............................
1D Solvingquadraticequations ..........................
1E Solvingsimultaneousequations
ReviewofChapter1 ...............................
2 Numbersandsurds
2A Realnumbersandintervals
2B Surdsandtheirarithmetic ...........................
2C Furthersimplificationofsurds
2D Rationalisingthedenominator
ReviewofChapter2 ...............................
3 Functionsandgraphs
3A Functionsandfunctionnotation ........................
3B Functions,relations,andgraphs ........................
3C Reviewoflineargraphs
3D Quadraticfunctions—factoringandthegraph ................
3E Completingthesquareandthegraph
3F Thequadraticformulaeandthegraph
3G Powers,cubics,andcircles ...........................
3H Twographsthathaveasymptotes
3I Directandinversevariation ..........................
4 Equationsandinequations
4A Linearequationsandinequations
4B Quadraticequationsandinequations
4C Thediscriminant ................................
4D Quadraticidentities
ReviewofChapter4 ...............................
5 Transformationsandsymmetry
5A Translationsofknowngraphs
5B Reflectioninthe y-axisand x-axis .......................
5C Evenandoddsymmetry
5D Horizontalandverticaldilations
5E Theabsolutevaluefunction ..........................
5F Compositefunctions
5G Combiningtransformations ..........................
5H Continuityandpiecewise-definedfunctions ..................
ReviewofChapter5
6 FurthergraphsEXTENSION
6A Solvingtwoparticularinequations
6B Thesignofafunction
6C Sketchingreciprocalfunctions .........................
6D Sketchingsumsanddifferences
6E Modifyingafunctionusingabsolutevalue ...................
6F Inverserelationsandfunctions ........................
6G Inversefunctionnotation
6H Definingfunctionsandrelationsparametrically ...............
ReviewofChapter7
7 Trigonometry
7A Trigonometrywithright-angledtriangles
7B Problemsinvolvingright-angledtriangles ...................
7C Trigonometricfunctionsofageneralangle ..................
7D Quadrant,sign,andrelatedacuteangle
7E Givenonetrigonometricfunction,findanother ................
7F Trigonometricidentities
7G Trigonometricequations
7H Thesineruleandtheareaformula ......................
7I Thecosinerule
7J Problemsinvolvinggeneraltriangles .....................
ReviewofChapter7 ...............................
8
Linesinthecoordinateplane
8A Lengthsandmidpointsoflinesegments ....................
8B Gradientsoflinesegmentsandlines
8C Equationsoflines
8D Furtherequationsoflines ...........................
8E Usingpronumeralsinplaceofnumbers
ReviewofChapter8 ...............................
9 Exponentialandlogarithmicfunctions
9A Indices
9B Fractionalindices ................................
9C Logarithms
9D Thelawsforlogarithms
9E Equationsinvolvinglogarithmsandindices ..................
9F Exponentialandlogarithmicgraphs
9G Applicationsofthesefunctions .........................
ReviewofChapter9 ...............................
10 Differentiation
10A Tangentsandthederivative
10B Thederivativeasalimit
10C Arulefordifferentiatingpowersof x .....................
10D Thenotation dy/dx forthederivative
10E Thechainrule ..................................
10F Differentiatingpowerswithnegativeindices .................
10G Differentiatingpowerswithfractionalindices
10H Theproductrule ................................
10I Thequotientrule
10J Ratesofchange
10K Averagevelocityandaveragespeed ......................
10L Instantaneousvelocityandspeed
ReviewofChapter10 ..............................
11 PolynomialsEXTENSION
11A Thelanguageofpolynomials
11B Graphsofpolynomialfunctions ........................
11C Divisionofpolynomials
11D Theremainderandfactortheorems
11E Consequencesofthefactortheorem .....................
11F Sumsandproductsofzeroes
11G Geometryusingpolynomialtechniques ....................
ReviewofChapter11 ..............................
12 Euler’snumber
12A Theexponentialfunctionbase e ........................
12B Transformationsofexponentialfunctions
12C Thelogarithmicfunctionbase e
ReviewofChapter12 ..............................
13 Radianmeasureofangles
13A Radianmeasureofanglesize
13B Solvingtrigonometricequations
13C Arcsandsectorsofcircles ...........................
13D Trigonometricgraphsinradians
ReviewofChapter13 ..............................
14 Probability
14A SetsandVenndiagrams
14B Probabilityandsamplespaces .........................
14C Samplespacegraphsandtreediagrams
14D Venndiagramsandtheadditiontheorem
14E Multi-stageexperimentsandtheproductrule ................
14F Probabilitytreediagrams
14G Conditionalprobability .............................
ReviewofChapter14 ..............................
15 Dataandprobability
15A Randomvariablesandfrequencytables ....................
15B Cumulativefrequency
15C Groupeddata
ReviewofChapter15 ..............................
16 FurthertrigonometryEXTENSION
16A Three-dimensionaltrigonometry
16B Trigonometricfunctionsofcompoundangles .................
16C Thedouble-angleformulae
16D TrigonometricEquations ............................
16E Thesumofsineandcosinefunctions
ReviewofChapter16
17 CombinatoricsEXTENSION
17A Factorialnotation
17B Orderedselectionswithandwithoutrepetition
17C Orderedselections—threemoreprinciples .................
17D Orderedselectionswithidenticalelements
17E Countingunorderedselections ........................
17F Usingcountinginprobability ..........................
17G Arrangementsinacircle
ReviewofChapter17 ..............................
18 ThebinomialtheoremEXTENSION
18A BinomialexpansionsandPascal’striangle
18B Binomialexpansionswithseveralvariables ..................
18C Thebinomialtheorem
18D Usingthegeneralterm .............................
18E IdentitiesinPascal’striangle ..........................
18F FurtheridentitiesinPascal’striangle
ReviewofChapter18 ..............................
Answers