Igcse-数学-历年真题-2

4400/4HEdexcelIGCSEMathematicsPaper4HHigherTierFriday11June2010–AfternoonTime:2hoursMaterialsrequiredforexaminationItemsincludedwithquestionpapersRulergraduatedincentimetresandNilmillimetres,protractor,compasses,pen,HBpencil,eraser,calculator.Tracingpapermaybeused.InstructionstoCandidatesIntheboxesabove,writeyourcentrenumber,candidatenumber,yoursurname,initialsandsignature.Checkthatyouhavethecorrectquestionpaper.AnswerALLthequestions.Writeyouranswersinthespacesprovidedinthisquestionpaper.YoumustNOTwriteontheformulaepage.AnythingyouwriteontheformulaepagewillgainNOcredit.Ifyouneedmorespacetocompleteyouranswertoanyquestion,useadditionalanswersheets.InformationforCandidatesThemarksforindividualquestionsandthepartsofquestionsareshowninroundbrackets:e.g.(2).Thereare22questionsinthisquestionpaper.Thetotalmarkforthispaperis100.Youmayuseacalculator.AdvicetoCandidatesWriteyouranswersneatlyandingoodEnglish.ThispublicationmaybereproducedonlyinaccordancewithEdexcelLimitedcopyrightpolicy.©2010EdexcelLimited.Printer’sLog.No.N36905A2IGCSEMATHEMATICS4400FORMULASHEET–HIGHERTIER3AnswerALLTWENTYTWOquestions.Writeyouranswersinthespacesprovided.Youmustwritedownallstagesinyourworking.1.Solve6y–9=3y+7y=................................(Total3marks)2.Thediagramshowstwotowns,AandB,onamap.(a)Bymeasurement,findthebearingofBfromA.....................................(2)Cisanothertown.ThebearingofCfromAis050.(b)FindthebearingofAfromC.....................................(2)(Total4marks)43.Aspinnercanlandonredorblueoryellow.Thespinnerisbiased.Theprobabilitythatitwilllandonredis0.5Theprobabilitythatitwilllandonblueis0.2Imadspinsthespinneronce.(a)Workouttheprobabilitythatitwilllandonyellow......................................(2)Janetspinsthespinner30times.(b)Workoutanestimateforthenumberoftimesthespinnerwilllandonblue......................................(2)(Total4marks)54.Rosettadrives85kilometresin1hour15minutes.(a)Workoutheraveragespeedinkilometresperhour......................................km/h(2)Rosettadrivesatotaldistanceof136kilometres.(b)Workout85asapercentageof136.................................%(2)SometimesRosettatravelsbytraintosavemoney.Thecostofherjourneybycaris£12Thecostofherjourneybytrainis15%lessthanthecostofherjourneybycar.(c)WorkoutthecostofRosetta’sjourneybytrain.£...................................(3)(Total7marks)65.Calculatethevalueofx.Giveyouranswercorrectto3significantfigures.x=................................(Total3marks)76.A={2,3,4,5}B={4,5,6,7}(a)(i)ListthemembersofAB......................................(ii)HowmanymembersareinAB?.....................................(2)ℰ={3,4,5,6,7}P={3,4,5}Twoothersets,QandR,eachcontainexactlythreemembers.PQ={3,4}PR={3,4}SetQisnotthesameassetR.(b)(i)WritedownthemembersofapossiblesetQ......................................(ii)WritedownthemembersofapossiblesetR......................................(2)(Total4marks)87.Rectangulartileshavewidth(x+1)cmandheight(5x–2)cm.Someofthesetilesareusedtoformalargerectangle.Thelargerectangleis7tileswideand3tileshigh.Theperimeterofthelargerectangleis68cm.(a)Writedownanequationinx...............................................................................................................(3)(b)Solvethisequationtofindthevalueofx.x=................................(3)(Total6marks)98.Showthat121141=1519.Thedepthofwaterinareservoirincreasesfrom14mto15.75m.Workoutthepercentageincrease..................................%(Total3marks)1010.QuadrilateralsABCDandPQRSaresimilar.ABcorrespondstoPQ.BCcorrespondstoQR.CDcorrespondstoRS.Findthevalueof(a)xx=...............................(2)(b)yy=...............................(1)(Total3marks)1111.Simplifyfully6x+43x.....................................(Total3marks)1212.(a)FindtheequationofthelineL......................................(3)13(b)Findthethreeinequalitesthatdefinetheunshadedregionshowninthediagrambelow................................................................................................................(3)(Total6marks)1413.(a)Solvex2–8x+12=0.....................................(3)(b)Solvethesimultaneousequationsy=2x4x–5y=9x=................................y=................................(3)(Total6marks)1514.Theareaofthetriangleis6.75cm2.Theanglex°isacute.Findthevalueofx.Giveyouranswercorrectto1decimalplace.x=................................(Total3marks)1615.Theunfinishedhistogramshowsinformationabouttheheights,hmetres,ofsometrees.(a)Calculateanestimateforthenumberoftreeswithheightsintheinterval4.5h≤10.....................................(3)(b)Thereare75treeswithheightsintheinterval10h≤13Usethisinformationtocompletethehistogram.(2)(Total5marks)1716.Abagcontains3whitediscsand1blackdisc.Johntakesatrandom2discsfromthebagwithoutreplacement.(a)Completetheprobabilitytreediagram.FirstdiscSeconddisc(3)(b)Findtheprobabilitythatbothdiscsarewhite......................................(2)Allthediscsarenowreplacedinthebag.Pradeeptakesatrandom3discsfromthebagwithoutreplacement.(c)Findtheprobabilitytha