Cambridge Mathematics Applications Units 1&2 for Western Australia

529 Pages·2023·10.965 MB·English

by  Darshan Gendah, Jennifer Prosser, Peter Jones, Kay Lipson, David Main, Kyle Staggard, Barbara Tulloch

CambridgeSeniorMathsforWesternAustralia ISBN978-1-009-25891-3 (cid:13)c Jonesetal.2023 CambridgeUniversityPress
MathematicsApplications1&2 Photocopyingisrestrictedunderlawandthismaterialmustnotbetransferredtoanotherparty.
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Contents
Introduction viii
Overview ix
Acknowledgements xiii
1
Computationandpracticalarithmetic 1
1A Orderofoperations . . . . . . . . . . . . . . . . . . . . . 2
1B Directednumbers . . . . . . . . . . . . . . . . . . . . . . 3
1C Powersandroots . . . . . . . . . . . . . . . . . . . . . . 5
1D Approximations,decimalplacesandsignificantfigures . . . 6
1E Currencyexchangerates . . . . . . . . . . . . . . . . . . 13
1F Percentages. . . . . . . . . . . . . . . . . . . . . . . . . 18
1G Percentageincreaseanddecrease . . . . . . . . . . . . . 22
1H Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1I Expressingratiosintheirsimplestform . . . . . . . . . . . 29
1J Unitcostmethod . . . . . . . . . . . . . . . . . . . . . . 32
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Keyideasandchaptersummary . . . . . . . . . . . . . . 34
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 35
Short-answerquestions . . . . . . . . . . . . . . . . . 35
Extended-responsequestions . . . . . . . . . . . . . . . 37
2
Consumerarithmetic 40
2A Percentagesandapplications . . . . . . . . . . . . . . . . 41
2B Simpleinterest . . . . . . . . . . . . . . . . . . . . . . . 47
2C Rearrangingthesimpleinterestformula . . . . . . . . . . 58
2D Compoundinterest . . . . . . . . . . . . . . . . . . . . . 62
2E Timepaymentagreements . . . . . . . . . . . . . . . . . . 71
2F Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
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iv Contents
2G Calculatingincomeandpreparingpersonalbudgets . . . . . 80
2H Governmentallowancesandpensions . . . . . . . . . . . . 90
2I Sharesanddividends . . . . . . . . . . . . . . . . . . . . 94
2J Financialinvestigation:buyingacar . . . . . . . . . . . . . 98
2K Usingspreadsheets . . . . . . . . . . . . . . . . . . . . . 98
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Keyideasandchaptersummary . . . . . . . . . . . . . . 103
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 104
Short-answerquestions . . . . . . . . . . . . . . . . . 105
Extended-responsequestions . . . . . . . . . . . . . . . 107
3
Shapeandmeasurement 109
3A Pythagoras’theorem . . . . . . . . . . . . . . . . . . . . 110
3B Pythagoras’theoreminthreedimensions . . . . . . . . . . 114
3C Mensuration:perimeterandarea . . . . . . . . . . . . . . 121
3D Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3E Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3F Volumeofacone . . . . . . . . . . . . . . . . . . . . . . 140
3G Volumeofapyramid . . . . . . . . . . . . . . . . . . . . . 143
3H Volumeofasphere . . . . . . . . . . . . . . . . . . . . . 146
3I Surfacearea . . . . . . . . . . . . . . . . . . . . . . . . 147
3J Similarfigures . . . . . . . . . . . . . . . . . . . . . . . 153
3K Similartriangles . . . . . . . . . . . . . . . . . . . . . . 160
3L Similarsolids . . . . . . . . . . . . . . . . . . . . . . . . 164
3M Problemsolvingandmodelling . . . . . . . . . . . . . . . 167
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Keyideasandchaptersummary . . . . . . . . . . . . . . 169
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 170
Short-answerquestions . . . . . . . . . . . . . . . . . 171
Extended-responsequestions . . . . . . . . . . . . . . . 173
4
Linearandnon-linearexpressions 176
4A Substitutionofvaluesintoaformula . . . . . . . . . . . . . 177
4B Usingformulas . . . . . . . . . . . . . . . . . . . . . . . 183
4C Constructingatableofvalues . . . . . . . . . . . . . . . . 186
4D Solvinglinearequationswithoneunknown . . . . . . . . . 192
4E Developingaformula:settinguplinearequationsin
oneunknown . . . . . . . . . . . . . . . . . . . . . . . . 196
4F Developingaformula:settinguplinearequationsin
twounknowns . . . . . . . . . . . . . . . . . . . . . . . . 200
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Contents v
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Keyideasandchaptersummary . . . . . . . . . . . . . . 203
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 203
Short-answerquestions . . . . . . . . . . . . . . . . . 203
Extended-responsequestions . . . . . . . . . . . . . . . 205
5
Matrices 207
5A Thebasicsofamatrix . . . . . . . . . . . . . . . . . . . . 208
5B Usingmatricestomodel(represent)practicalsituations . . . 215
5C Addingandsubtractingmatrices . . . . . . . . . . . . . . 217
5D Scalarmultiplication . . . . . . . . . . . . . . . . . . . . 220
5E Matrixmultiplication . . . . . . . . . . . . . . . . . . . . 225
5F Applicationsofmatrices . . . . . . . . . . . . . . . . . . . 232
5G Communicationsandconnections . . . . . . . . . . . . . . 236
5H Identitymatrices . . . . . . . . . . . . . . . . . . . . . . 240
5I Extendedapplicationandproblem-solvingtasks . . . . . . . 244
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Keyideasandchaptersummary . . . . . . . . . . . . . . 245
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 246
Short-answerquestions . . . . . . . . . . . . . . . . . 246
Extended-responsequestions . . . . . . . . . . . . . . . 248
6
Investigatingandcomparingdatadistributions 250
6A Typesofdata . . . . . . . . . . . . . . . . . . . . . . . . 251
6B Displayinganddescribingcategoricaldatadistributions . . . 254
6C Interpretinganddescribingfrequencytables
andbarcharts . . . . . . . . . . . . . . . . . . . . . . . 258
6D Displayinganddescribingnumericaldata . . . . . . . . . . 262
6E Characteristicsofdistributionsofnumericaldata:
shape,locationandspread . . . . . . . . . . . . . . . . . 273
6F Dotplotsandstem-and-leafplots . . . . . . . . . . . . . . 275
6G Summarisingdata . . . . . . . . . . . . . . . . . . . . . . 280
6H Boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
6I Comparingthedistributionofanumericalvariableacrosstwo
ormoregroups . . . . . . . . . . . . . . . . . . . . . . . 300
6J Statisticalinvestigation . . . . . . . . . . . . . . . . . . . 306
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Keyideasandchaptersummary . . . . . . . . . . . . . . 307
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 308
Short-answerquestions . . . . . . . . . . . . . . . . . 309
Extended-responsequestions . . . . . . . . . . . . . . . 313
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vi Contents
7
Thenormaldistribution 315
7A Thenormaldistributionandthe68–95–99.7%rule . . . . . . 316
7B DeterminationofotherpercentagesusingaCAS . . . . . . 320
7C Quantiles . . . . . . . . . . . . . . . . . . . . . . . . . . 326
7D Standardscores . . . . . . . . . . . . . . . . . . . . . . 332
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Keyideasandchaptersummary . . . . . . . . . . . . . . 337
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 337
Short-answerquestions . . . . . . . . . . . . . . . . . 337
Extended-responsequestions . . . . . . . . . . . . . . . 339
8
Right-angledtrigonometry 340
8A Trigonometrybasics . . . . . . . . . . . . . . . . . . . . . 341
8B Findinganunknownsideinaright-angledtriangle . . . . . . 345
8C Findinganangleinaright-angledtriangle . . . . . . . . . . 348
8D Applicationsofright-angledtriangles . . . . . . . . . . . . 353
8E Anglesofelevationanddepression . . . . . . . . . . . . . 356
8F Bearingsandnavigation . . . . . . . . . . . . . . . . . . . 361
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Keyideasandchaptersummary . . . . . . . . . . . . . . 366
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 367
Short-answerquestions . . . . . . . . . . . . . . . . . 367
Extended-responsequestions . . . . . . . . . . . . . . . 371
9
Non-right-angledtrigonometry 372
9A Theareaofatriangle . . . . . . . . . . . . . . . . . . . . 373
9B Thesinerule . . . . . . . . . . . . . . . . . . . . . . . . 379
9C Thecosinerule . . . . . . . . . . . . . . . . . . . . . . . 389
9D Extendedapplicationandproblem-solvingtask . . . . . . . 396
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
Keyideasandchaptersummary . . . . . . . . . . . . . . 398
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 399
Short-answerquestions . . . . . . . . . . . . . . . . . 399
Extended-responsequestions . . . . . . . . . . . . . . . 402
10
Lineargraphsandmodels 404
10A Drawingstraight-linegraphs . . . . . . . . . . . . . . . . 405
10B Determiningtheslopeofastraightline . . . . . . . . . . . 410
10C Theintercept–slopeformoftheequationofastraightline . 415
10D Findingtheequationofastraight-linegraphfromitsintercept
andslope . . . . . . . . . . . . . . . . . . . . . . . . . . 418
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Contents vii
10E Findingtheequationofastraight-linegraphusingtwopoints
onthegraph . . . . . . . . . . . . . . . . . . . . . . . . 420
10F Findingtheequationofastraight-linegraphfromtwopoints
usingaCAScalculator . . . . . . . . . . . . . . . . . . . 421
10G Linearmodelling . . . . . . . . . . . . . . . . . . . . . . 425
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
Keyideasandchaptersummary . . . . . . . . . . . . . . 436
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 437
Short-answerquestions . . . . . . . . . . . . . . . . . 437
Extended-responsequestions . . . . . . . . . . . . . . . 441
11
Simultaneouslinearequations 443
11A Findingthepointofintersectionoftwolineargraphs . . . . 444
11B Solvingsimultaneouslinearequationsalgebraically . . . . . 448
11C SolvingsimultaneouslinearequationsusingCAS . . . . . . 453
11D Practicalapplicationsofsimultaneousequations . . . . . . 455
11E Problemsolvingandmodelling . . . . . . . . . . . . . . . 460
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
Keyideasandchaptersummary . . . . . . . . . . . . . . 462
Skillscheck . . . . . . . . . . . . . . . . . . . . . . . . 462
Short-answerquestions . . . . . . . . . . . . . . . . . 462
Extended-responsequestions . . . . . . . . . . . . . . . 464
Glossary 466
Answers 473
OnlineappendicesaccessedthroughtheInteractiveTextbookorPDFTextbook
AppendixA GuidetoTI-NspireCASCXwithOS4.0(digitalonly)
AppendixB GuidetoCasioClassPadII(digitalonly)
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Introduction
CambridgeMathematicsApplicationsforWesternAustraliaUnits1&2isaneweditionaligned
specificallytotheWesternAustralianMathematicsApplicationsYear11syllabus. Coveringboth
Units1and2inoneresource,ithasbeenwrittenwithpracticalcontextsandwordedquestionsas
itspriorityalongsideamplepracticeofferedthroughworkedexamplesandexercises. Thiscourse
followsonfromtheK–10AustralianCurriculumandexpandsuponthefundamentalskillsand
knowledgedevelopedinearlierlevels.
ComparedtothepreviousAustralianCurriculumedition,thisWAeditionhasundergoneanumber
ofrevisions. Carefuladjustmentstonotationandlanguagehavebeenmadethroughouttomatch
thatusedintheWAsyllabus,andinWAclassroomsmoregenerally. Multiple-choicequestions
thatwereformerlylocatedinthechapterreviewsandrevisionchaptershavebeenremovedforthis
edition.
Thiseditionbeginsbyintroducingcomputationandpracticalarithmeticandthenconsumer
arithmetic,buildinguponthenon-calculatorskillsnecessaryfortheYear11and12Applications
course,beforeleadingtoshapeandmeasurement,linearandnon-linearexpressions,andmatrices.
Thestudyofthenormaldistributionandinvestigatingandcomparingdatadistributionscoversthe
statisticalstrandofthesyllabus. Right-angledtrigonometryandnon-right-angledtrigonometry
arenowcoveredinseparatechapterstobetterfacilitateteachingandlearning. Chaptersonlinear
graphsandmodelsandsimultaneouslinearequationsfocuslargelyonnewapplicationsofprevious
knowledgeandskills,andgettingconfidentwithusingaCAScalculatorinappropriatecontexts.
WorkedexamplesutilisingCAScalculatorsareprovidedthroughout,withscreenshotsanddetailed
userinstructionsforbothClassPadandTI-NspireincludedforeachCASexample. TheCAS
‘ribbons’usedwithineachexercisedirectstudentstoquestionswhichshouldbecompleted
withtheaidoftechnology,andareintendedtohelppreparestudentsforexaminationsandother
assessments.
TheTI-NspirecalculatorexamplesandinstructionshavebeencompletedbyRussellBrownand
thosefortheCasioClassPadhavebeencompletedbyMariaSchaffner.
Theintegrationofthefeaturesofthetextbookandthenewdigitalcomponentsofthepackage,
poweredbyCambridgeHOTmaths,areillustratedonpagesixtoxii.
About Cambridge HOTmaths
CambridgeHOTmathsisacomprehensive,award-winningmathematicslearningsystem–an
interactiveonlinemathslearning,teachingandassessmentresourceforstudentsandteachers,
forindividualsorwholeclasses,forschoolandathome. Itsdigitalengineorplatformisusedto
hostandpowertheInteractiveTextbookandtheOnlineTeachingSuite,andselectedtopicsfrom
HOTmaths’ownYears9and10coursesareaareavailableforrevisionofpriorknowledge. Allthis
isincludedinthepriceofthetextbook.
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MathematicsApplications1&2 Photocopyingisrestrictedunderlawandthismaterialmustnotbetransferredtoanotherparty.
Overview
Overview of the print book
1 Gradedstep-by-stepworkedexampleswithpreciseexplanations(andvideoversions)
encourageindependentlearning,andarelinkedtoexercisequestions.
2 AdditionallinkedresourcesintheInteractiveTextbookareindicatedbyicons,suchas
skillsheetsandvideoversionsofexamples.
3 QuestionsthatsuittheuseofaCAScalculatortosolvethemareidentifiedwithin
exercises.
4 Chapterreviewscontainachaptersummaryandshort-answerandextended-response
questions.
5 Theglossaryincludespagenumbersofthemainexplanationofeachterm.
Numbersrefertodescriptionsabove.
2
3 4 5
1
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x Overview
Overview of the
downloadable PDF
textbook
6 Theconvenienceofadownloadable
PDFtextbookhasbeenretainedfor
timeswhenuserscannotgoonline.
7 PDFannotationandsearchfeaturesare
enabled.
7 7
Overview of the Interactive Textbook
TheInteractiveTextbook(ITB)isanonlineHTMLversionoftheprinttextbookpowered
bytheHOTmathsplatform,includedwiththeprintbookoravailableasaseparatepurchase.
8 Thematerialisformattedforonscreenusewithaconvenientandeasy-to-usenavigation
systemandlinkstoallresources.
9 Workspacesforallquestions,whichcanbeenabledordisabledbytheteacher,allow
studentstoenterworkingandanswersonlineandtosavethem. Inputisbytyping,
withthehelpofasymbolpalette,handwritinganddrawingontablets,orbyuploading
imagesofwritingordrawingdoneonpaper.
10 Self-assessmenttoolsenablestudentstocheckanswers,marktheirownwork,andrate
theirconfidencelevelintheirwork. Thishelpsdevelopresponsibilityforlearningand
communicatesprogressandperformancetotheteacher. Studentaccountscanbelinked
tothelearningmanagementsystemusedbytheteacherintheOnlineTeachingSuite,so
thatteacherscanreviewstudentself-assessmentandprovidefeedbackoradjustmarks.
11 Allworkedexampleshavevideoversionstoencourageindependentlearning.
12 WorkedsolutionsareincludedandcanbeenabledordisabledinthestudentITB
accountsbytheteacher.
13 Anexpandedandrevisedsetof Desmosinteractivesandactivitiesbasedonembedded
graphicscalculatorandgeometrytoolwindowsdemonstratekeyconceptsandenable
studentstovisualisethemathematics.
14 TheDesmosgraphicscalculator,scientificcalculator,andgeometrytoolarealso
embeddedforstudentstousefortheirowncalculationsandexploration.
15 RevisionofpriorknowledgeisprovidedwithlinkstodiagnostictestsandYear10
HOTmathslessons.
16 Quickquizzescontainingautomarkedmultiple-choicequestionshavebeenthoroughly
expandedandrevised,enablingstudentstochecktheirunderstanding.
17 Definitionspopupforkeytermsinthetext,andarealsoprovidedinadictionary.
18 Messagesfromtheteacherassigntasksandtests.
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