Igcse 数学 历年真题 2

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4400/4H

EdexcelIGCSE

Mathematics

Paper4H

HigherTier

Friday11June2010–Afternoon

Time:2hours

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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.

WorkoutthecostofRosetta’sjourneybytrain.

£

<3>

<Total7marks>

5.

Calculatethevalueofx.

Giveyouranswercorrectto3significantfigures.

x=

<Total3marks>

6.A={2,3,4,5}

B={4,5,6,7}

<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.

<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.Showthat11=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.

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<h≤10

<3>

<b>Thereare75treeswithheightsintheinterval10<h≤13

Usethisinformationtocompletethehistogram.

<2>

<Total5marks>

16.Abagcontains3whitediscsand1blackdisc.

Johntakesatrandom2discsfromthebagwithoutreplacement.

<a>Completetheprobabilitytreediagram.

FirstdiscSeconddisc

<3>

Findtheprobabilitythatbothdiscsarewhite.

<2>

Allthediscsarenowreplacedinthebag.

Pradeeptakesatrandom3discsfromthebagwithoutreplacement.

Findtheprobabilitythatthediscleftinthebagiswhite.

<3>

<Total8marks>

17.Thediagramshowsasectorofacircle,radius45cm,withangle84°.

Calculatetheareaofthesector.

Giveyouranswercorrectto3significantfigures.

cm2

<Total3marks>

18.

CalculatethelengthofAC.

Giveyouranswercorrectto3significantfigures.

cm

<Total3marks>

19.Aconehasslantheight4cmandbaseradiusrcm.

Thetotalsurfaceareaoftheconeisπcm2.

Calculatethevalueofr.

r=

<Total4marks>

20.f<x>=<x–1>2

<a>Findf<8>

<1>

Thedomainoffisallvaluesofxwherex≥7

Findtherangeoff.

<2>

g<x>=

<c>Solvetheequationg<x>=1.2

<2>

<d><i>Expresstheinversefunctiong–1intheform