IGCSE-math-数学试卷0580-s17-qp-43

Thisdocumentconsistsof19printedpagesand1blankpage.DC(NH/JG)130218/2©UCLES2017[Turnover*0731247115*MATHEMATICS0580/43Paper4(Extended)May/June20172hours30minutesCandidatesanswerontheQuestionPaper.AdditionalMaterials:ElectroniccalculatorGeometricalinstrumentsTracingpaper(optional).READTHESEINSTRUCTIONSFIRSTWriteyourCentrenumber,candidatenumberandnameonalltheworkyouhandin.Writeindarkblueorblackpen.YoumayuseanHBpencilforanydiagramsorgraphs.Donotusestaples,paperclips,glueorcorrectionfluid.DONOTWRITEINANYBARCODES.Answerallquestions.Ifworkingisneededforanyquestionitmustbeshownbelowthatquestion.Electroniccalculatorsshouldbeused.Ifthedegreeofaccuracyisnotspecifiedinthequestion,andiftheanswerisnotexact,givetheanswertothreesignificantfigures.Giveanswersindegreestoonedecimalplace.Forπ,useeitheryourcalculatorvalueor3.142.Attheendoftheexamination,fastenallyourworksecurelytogether.Thenumberofmarksisgiveninbrackets[]attheendofeachquestionorpartquestion.Thetotalofthemarksforthispaperis130.CambridgeInternationalExaminationsCambridgeInternationalGeneralCertificateofSecondaryEducation20580/43/M/J/17©UCLES20171(a)In2016,acompanysold9600cars,correcttothenearesthundred.(i)Writedownthelowerboundforthenumberofcarssold....................................................[1](ii)Theaverageprofitoneachcarsoldwas$2430,correcttothenearest$10.Calculatethelowerboundforthetotalprofit.Writedowntheexactanswer.$...................................................[2](iii)Writeyouranswertopart(a)(ii)correctto4significantfigures.$...................................................[1](iv)Writeyouranswertopart(a)(iii)instandardform.$...................................................[1](b)InApril,thenumberofcarssoldwas546.Thiswasanincreaseof5%onthenumberofcarssoldinMarch.CalculatethenumberofcarssoldinMarch....................................................[3]30580/43/M/J/17©UCLES2017[Turnover(c)Thepriceofanewcargrowsexponentiallyby3%peryear.Anewcarhasapriceof$3000in2013.Findthepriceofanewcar4yearslater.$...................................................[2]40580/43/M/J/17©UCLES20172(a)y°x°z°DABPQSRCENOTTOSCALE24°38°PQisparalleltoRS.ABCandADEarestraightlines.Findthevaluesofx,yandz.x=..................................................y=..................................................z=..................................................[3](b)ABDCNOTTOSCALE42°ThepointsA,B,CandDlieonthecircumferenceofthecircle.AB=AD,AC=BCandangleABD=42°.FindangleCAB.AngleCAB=..................................................[3]50580/43/M/J/17©UCLES2017[Turnover(c)OQRSPNOTTOSCALE146°ThepointsP,Q,RandSlieonthecircumferenceofthecircle,centreO.AngleQOS=146°.FindangleQRS.AngleQRS=....................................................[2]60580/43/M/J/17©UCLES20173Thetableshowssomevaluesfor24yxx32=+.x–2.2–2–1.5–1–0.500.50.8y–1.940.7503.58(a)Completethetable.[4](b)Drawthegraphof24yxx32=+for2.20.8xGG-.xy–2.5–2–21234–1–1.5–1–0.50.510[4](c)Findthenumberofsolutionstotheequation243xx32+=....................................................[1]70580/43/M/J/17©UCLES2017[Turnover(d)(i)Theequation241xxx32+-=canbesolvedbydrawingastraightlineonthegrid.Writedowntheequationofthisstraightline.y=..................................................[1](ii)Useyourgraphtosolvetheequation241xxx32+-=.x=............................orx=............................orx=............................[3](e)Thetangenttothegraphof24yxx32=+hasanegativegradientwhenxk=.Completetheinequalityfork.......................1k1......................[2]80580/43/M/J/17©UCLES20174(a)ThediagramshowsasolidmetalprismwithcrosssectionABCDE.BGFKJDCAEH2cm7cm4cm8cm4cmNOTTOSCALE(i)CalculatetheareaofthecrosssectionABCDE.............................................cm2[6](ii)Theprismisoflength8cm.Calculatethevolumeoftheprism.............................................cm3[1]90580/43/M/J/17©UCLES2017[Turnover(b)Acylinderoflength13cmhasvolume280cm3.(i)Calculatetheradiusofthecylinder..............................................cm[3](ii)Thecylinderisplacedinaboxthatisacubeofside14cm.Calculatethepercentageofthevolumeoftheboxthatisoccupiedbythecylinder................................................%[3]100580/43/M/J/17©UCLES20175(a)Haroonhas200letterstopost.Thehistogramshowsinformationaboutthemasses,mgrams,oftheletters.0023145678102030Mass(grams)mFrequencydensity4050(i)Completethefrequencytableforthe200letters.Mass(mgrams)01mG10101mG20201mG25251mG30301mG50Frequency5017[3](ii)Calculateanestimateofthemeanmass.................................................g[4]110580/43/M/J/17©UCLES2017[Turnover(b)Haroonhas15parcelstopost.Thetableshowsinformationaboutthesizesoftheseparcels.SizeSmallLargeFrequency96Twoparcelsareselectedatrandom.Findtheprobabilitythat(i)bothparcelsarelarge,...................................................[2](ii)oneparcelissmallandtheotherislarge....................................................[3](c)Theprobabilitythataparcelarriveslateis803.4000parcelsareposted.Calculateanestimateofthenumberofparcelsexpectedtoarrivelate...........