Igcse數(shù)學(xué)歷年真題

4400/4HEdexcelIGCSEMathematicsPaper4HHigherTierFriday11June2010–AfternoonTime:2hoursMaterialsrequiredforexaminationRulergraduatedincentimetresandmillimetres,protractor,compasses,pen,HBpencil,eraser,calculator.Tracingpapermaybeused.

ItemsincludedwithquestionpapersNilInstructionstoCandidatesIntheboxesabove,writeyourcentrenumber,candidatenumber,yoursurname,initialsandsignature.Checkthatyouhavethecorrectquestionpaper.AnswerALLthequestions.Writeyouranswersinthespacesprovidedinthisquestionpaper.YoumustNOTwriteontheformulaepage.AnythingyouwriteontheformulaepagewillgainNOcredit.Ifyouneedmorespacetocompleteyouranswertoanyquestion,useadditionalanswersheets.InformationforCandidatesThemarksforindividualquestionsandthepartsofquestionsareshowninroundbrackets:e.(2)g..Thereare22questionsinthisquestionpaper.Thetotalmarkforthispaperis100.Youmayuseacalculator.AdvicetoCandidatesWriteyouranswersneatlyandingoodEnglish.ThispublicationmaybereproducedonlyinaccordancewithEdexcelLimitedcopyrightpolicy.?2010EdexcelLimited.Printer’sLog.NoN36905A.IGCSEMATHEMATICS4400FORMULASHEET–HIGHERTIER.AnswerALLTWENTYTWOquestions.Writeyouranswersinthespacesprovided.Youmustwritedownallstagesinyourworking.1.Solve6y–9=3y+7y=(Total3marks)Thediagramshowstwotowns,AandB,onamap.(a)Bymeasurement,findthebearingofBfromA(2)Cisanothertown.ThebearingofCfromAis050.(b)FindthebearingofAfromC(2)(Total4marks).Aspinnercanlandonredorblueoryellow.Thespinnerisbiased.Imadspinsthespinneronce.Workouttheprobabilitythatitwilllandonyellow(2)Janetspinsthespinner30times.(b)Workoutanestimateforthenumberoftimesthespinnerwilllandonblue(2)(Total4marks).Rosettadrives85kilometresin1hour15minutes.Workoutheraveragespeedinkilometresperhourkm/h(2)Rosettadrivesatotaldistanceof136kilometres.(b)Workout85asapercentageof136%(2)SometimesRosettatravelsbytraintosavemoney.Thecostofherjourneybycaris12￡Thecostofherjourneybytrainis15%lessthanthecostofherjourneybycar.(c)WorkoutthecostofRosetta’sjourneybytrain.￡(3)(Total7marks).5.Calculatethevalueofx.Giveyouranswercorrectto3significantfigures.x=(Total3marks).A={2,3,4,5}B={4,5,6,7}(a)(i)ListthemembersofAB(ii)HowmanymembersareinAB?(2)={3,4,5,6,7}P={3,4,5}Twoothersets,QandR,eachcontainexactlythreemembers.PQ={3,4}PR={3,4}SetQisnotthesameassetR.(b)(i)WritedownthemembersofapossiblesetQ(ii)WritedownthemembersofapossiblesetR(2)(Total4marks).Rectangulartileshavewidth(x+1)cmandheight(5x–2)cm.Someofthesetilesareusedtoformalargerectangle.Thelargerectangleis7tileswideand3tileshigh.Theperimeterofthelargerectangleis68cm.(a)Writedownanequationinx(3)(b)Solvethisequationtofindthevalueofx.x=(3)(Total6marks).8.Showthat11111=1245Thedepthofwaterinareservoirincreasesfrom14mto15.75m.Workoutthepercentageincrease%(Total3marks).QuadrilateralsABCDandPQRSaresimilar.ABcorrespondstoPQ.BCcorrespondstoQR.CDcorrespondstoRS.Findthevalueof(a)x(b)y

x=(2)y=(1)(Total3marks).x3x11.Simplifyfully+64(Total3marks).12.(a)FindtheequationofthelineL(3).(b)Findthethreeinequalitesthatdefinetheunshadedregionshowninthediagrambelow(3)(Total6marks).13.(a)Solvex2–8x+12=0(3)(b)Solvethesimultaneousequationsy=2x4x–5y=9x=y=(3)(Total6marks).14.2Theareaofthetriangleis6.75cm.Theanglex°isacute.Findthevalueofx.Giveyouranswercorrectto1decimalplace.x=(Total3marks).Theunfinishedhistogramshowsinformationabouttheheights,hmetres,ofsometrees.(a)Calculateanestimateforthenumberoftreeswithheightsintheinterval4.5<h≤10(3)Thereare75treeswithheightsintheinterval10<h≤13Usethisinformationtocompletethehistogram.(2)(Total5marks).Abagcontains3whitediscsand1blackdisc.Johntakesatrandom2discsfromthebagwithoutreplacement.Completetheprobabilitytreediagram.FirstdiscSeconddisc(b)Findtheprobabilitythatbothdiscsarewhite.Allthediscsarenowreplacedinthebag.Pradeeptakesatrandom3discsfromthebagwithoutreplacement.(c)Findtheprobabilitythatthediscleftinthebagiswhite.

(3)(2)(3)(Total8marks).Thediagramshowsasectorofacircle,radius45cm,withangle84.Calculatetheareaofthesector.Giveyouranswercorrectto3significantfigures.18.CalculatethelengthofAC.Giveyouranswercorrectto3significantfigures.

°2cm(Total3marks)cm(Total3marks).Aconehasslantheight4cmandbaseradiuscm.Thetotalsurfaceareaoftheconeis33πcm2.4Calculatethevalueofr.

r=(Total4marks).f(x)=(x–1)2Findf(8)(1)Thedomainoffisallvaluesofxwherex≥7(a)Findtherangeoff.g(x)=

(2)x1Solvetheequationg(x)=1.2(2)(d)(i)Expresstheinversefunctiong–1intheformg–1(x)=g–1(x)=(ii)Hencewritedowngg(x)intermsofx.gg(x)=(6)(Total11marks).21.InthediagramOA=aandOC=c.(a)FindCAintermsofaandc(1)ThepointBissuchthatAB=12c.(b)GivethemathematicalnameforthequadrilateralOABC(1)ThepointPissuchthatOP=a+kc,wher