Igcse数学历年真题.docx
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Igcse数学历年真题.docx
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Igcse数学历年真题
4400/4H
EdexcelIGCSE
Mathematics
Paper4H
HigherTier
Friday11June2010–Afternoon
Time:
2hours
MaterialsrequiredforexaminationItemsincludedwithquestionpapers
RulergraduatedincentimetresandNil
millimetres,protractor,compasses,
pen,HBpencil,eraser,calculator.
Tracingpapermaybeused.
InstructionstoCandidates
Intheboxesabove,writeyourcentrenumber,candidatenumber,yoursurname,initialsandsignature.
Checkthatyouhavethecorrectquestionpaper.
AnswerALLthequestions.Writeyouranswersinthespacesprovidedinthisquestionpaper.
YoumustNOTwriteontheformulaepage.AnythingyouwriteontheformulaepagewillgainNOcredit.
Ifyouneedmorespacetocompleteyouranswertoanyquestion,useadditionalanswersheets.
InformationforCandidates
Themarksforindividualquestionsandthepartsofquestionsareshowninroundbrackets:
e.g.
(2).
Thereare22questionsinthisquestionpaper.Thetotalmarkforthispaperis100.
Youmayuseacalculator.
AdvicetoCandidates
WriteyouranswersneatlyandingoodEnglish.
Thispublicationmaybereproducedonlyinaccordancewith
EdexcelLimitedcopyrightpolicy.
©2010EdexcelLimited.
Printer’sLog.No.N36905A
IGCSEMATHEMATICS4400
FORMULASHEET–HIGHERTIER
AnswerALLTWENTYTWOquestions.
Writeyouranswersinthespacesprovided.
Youmustwritedownallstagesinyourworking.
1.Solve6y–9=3y+7
y=................................
(Total3marks)
2.Thediagramshowstwotowns,AandB,onamap.
(a)Bymeasurement,findthebearingofBfromA.
....................................
(2)
Cisanothertown.
ThebearingofCfromAis050.
(b)FindthebearingofAfromC.
....................................
(2)
(Total4marks)
3.Aspinnercanlandonredorblueoryellow.
Thespinnerisbiased.
Theprobabilitythatitwilllandonredis0.5
Theprobabilitythatitwilllandonblueis0.2
Imadspinsthespinneronce.
(a)Workouttheprobabilitythatitwilllandonyellow.
.....................................
(2)
Janetspinsthespinner30times.
(b)Workoutanestimateforthenumberoftimesthespinnerwilllandonblue.
.....................................
(2)
(Total4marks)
4.Rosettadrives85kilometresin1hour15minutes.
(a)Workoutheraveragespeedinkilometresperhour.
.....................................km/h
(2)
Rosettadrivesatotaldistanceof136kilometres.
(b)Workout85asapercentageof136
.................................%
(2)
SometimesRosettatravelsbytraintosavemoney.
Thecostofherjourneybycaris£12
Thecostofherjourneybytrainis15%lessthanthecostofherjourneybycar.
(c)WorkoutthecostofRosetta’sjourneybytrain.
£...................................
(3)
(Total7marks)
5.
Calculatethevalueofx.
Giveyouranswercorrectto3significantfigures.
x=................................
(Total3marks)
6.A={2,3,4,5}
B={4,5,6,7}
(a)(i)ListthemembersofAB.
.....................................
(ii)HowmanymembersareinAB?
.....................................
(2)
ℰ={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)
7.Rectangulartileshavewidth(x+1)cmandheight(5x–2)cm.
Someofthesetilesareusedtoformalargerectangle.
Thelargerectangleis7tileswideand3tileshigh.
Theperimeterofthelargerectangleis68cm.
(a)Writedownanequationinx.
..............................................................................................................
(3)
(b)Solvethisequationtofindthevalueofx.
x=................................
(3)
(Total6marks)
8.Showthat1
1
=1
9.Thedepthofwaterinareservoirincreasesfrom14mto15.75m.
Workoutthepercentageincrease.
.................................%
(Total3marks)
10.QuadrilateralsABCDandPQRSaresimilar.
ABcorrespondstoPQ.
BCcorrespondstoQR.
CDcorrespondstoRS.
Findthevalueof
(a)x
x=...............................
(2)
(b)y
y=...............................
(1)
(Total3marks)
11.Simplifyfully
+
.....................................
(Total3marks)
12.
(a)FindtheequationofthelineL.
.....................................
(3)
(b)Findthethreeinequalitesthatdefinetheunshadedregionshowninthediagrambelow.
.....................................
.....................................
.....................................
(3)
(Total6marks)
13.(a)Solvex2–8x+12=0
.....................................
(3)
(b)Solvethesimultaneousequations
y=2x
4x–5y=9
x=................................
y=................................
(3)
(Total6marks)
14.
Theareaofthetriangleis6.75cm2.
Theanglex°isacute.
Findthevalueofx.
Giveyouranswercorrectto1decimalplace.
x=................................
(Total3marks)
15.Theunfinishedhistogramshowsinformationabouttheheights,hmetres,ofsometrees.
(a)Calculateanestimateforthenumberoftreeswithheightsintheinterval4.5 ..................................... (3) (b)Thereare75treeswithheightsintheinterval10 Usethisinformationtocompletethehistogram. (2) (Total5marks) 16.Abagcontains3whitediscsand1blackdisc. Johntakesatrandom2discsfromthebagwithoutreplacement. (a)Completetheprobabilitytreediagram. FirstdiscSeconddisc (3) (b)Findtheprobabilitythatbothdiscsarewhite. ..................................... (2) Allthediscsarenowreplacedinthebag. Pradeeptakesatrandom3discsfromthebagwithoutreplacement. (c)Findtheprobabilitythatthediscleftinthebagiswhite. ..................................... (3) (Total8marks) 17.Thediagramshowsasectorofacircle,radius45cm,withangle84°. Calculatetheareaofthesector. Giveyouranswercorrectto3significantfigures. .............................cm2 (Total3marks) 18. CalculatethelengthofAC. Giveyouranswercorrectto3significantfigures. ...............................cm (Total3marks) 19.Aconehasslantheight4cmandbaseradiusrcm. Thetotalsurfaceareaoftheconeis πcm2. Calculatethevalueofr. r=................................ (Total4marks) 20.f(x)=(x–1)2 (a)Findf(8) ..................................... (1) Thedomainoffisallvaluesofxwherex≥7 (a)Findtherangeoff. ..................................... (2) g(x)= (c)Solvetheequationg(x)=1.2 ..................................... (2) (d)(i)Expresstheinversefunctiong–1intheformg–1(x)=....... g–1(x)=................................... (ii)Hencewritedowngg(x)intermsofx. gg(x)=.................................... (6) (Total11marks) 21. Inthediagram =aand =c. (a)Find intermsofaandc. ..................................... (1) ThepointBissuchthat = c. (b)GivethemathematicalnameforthequadrilateralOABC. ..................................... (1) ThepointPissuchthat =a+kc,wherek≥0 (c)Statethetwoconditionsrelatingtoa+kcthatmustbetrueforOAPCtobearhombus. (2) (Total4marks) 22.(a)Workout5.2×102+2.3×104 Giveyouranswerinstandardform. ..................................... (2) a×102+b×104=c×104 (b)Expresscintermsofaandb. c=................................ (2) (Total4marks) TOTALFORPAPER=100MARKS END
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