Igcse数学历年真题Word格式文档下载.docx

Igcse数学历年真题Word格式文档下载.docx

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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.

（Total4marks）

3.Aspinnercanlandonredorblueoryellow.

Thespinnerisbiased.

Theprobabilitythatitwilllandonredis0.5

Theprobabilitythatitwilllandonblueis0.2

Imadspinsthespinneronce.

（a）Workouttheprobabilitythatitwilllandonyellow.

.....................................

Janetspinsthespinner30times.

（b）Workoutanestimateforthenumberoftimesthespinnerwilllandonblue.

（Total4marks）

4.Rosettadrives85kilometresin1hour15minutes.

（a）Workoutheraveragespeedinkilometresperhour.

.....................................km/h

Rosettadrivesatotaldistanceof136kilometres.

（b）Workout85asapercentageof136

.................................%

SometimesRosettatravelsbytraintosavemoney.

Thecostofherjourneybycaris£

12

Thecostofherjourneybytrainis15%lessthanthecostofherjourneybycar.

（c）WorkoutthecostofRosetta’sjourneybytrain.

£

...................................

（3）

（Total7marks）

5.

Calculatethevalueofx.

Giveyouranswercorrectto3significantfigures.

x=................................

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

B={4,5,6,7}

（a）（i）ListthemembersofAB.

（ii）HowmanymembersareinAB?

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.

7.Rectangulartileshavewidth（x+1）cmandheight（5x–2）cm.

Someofthesetilesareusedtoformalargerectangle.

Thelargerectangleis7tileswideand3tileshigh.

Theperimeterofthelargerectangleis68cm.

（a）Writedownanequationinx.

..............................................................................................................

（b）Solvethisequationtofindthevalueofx.

（Total6marks）

8.Showthat1

1

=1

9.Thedepthofwaterinareservoirincreasesfrom14mto15.75m.

Workoutthepercentageincrease.

（Total3marks）

10.QuadrilateralsABCDandPQRSaresimilar.

ABcorrespondstoPQ.

BCcorrespondstoQR.

CDcorrespondstoRS.

Findthevalueof

（a）x

x=...............................

（b）y

y=...............................

（1）

11.Simplifyfully

+

12.

（a）FindtheequationofthelineL.

（b）Findthethreeinequalitesthatdefinetheunshadedregionshowninthediagrambelow.

13.（a）Solvex2–8x+12=0

（b）Solvethesimultaneousequations

y=2x

4x–5y=9

14.

Theareaofthetriangleis6.75cm2.

Theanglex°

isacute.

Findthevalueofx.

Giveyouranswercorrectto1decimalplace.

15.Theunfinishedhistogramshowsinformationabouttheheights,hmetres,ofsometrees.

（a）Calculateanestimateforthenumberoftreeswithheightsintheinterval4.5<

h≤10

（b）Thereare75treeswithheightsintheinterval10<

h≤13

Usethisinformationtocompletethehistogram.

（Total5marks）

16.Abagcontains3whitediscsand1blackdisc.

Johntakesatrandom2discsfromthebagwithoutreplacement.

（a）Completetheprobabilitytreediagram.

FirstdiscSeconddisc

（b）Findtheprobabilitythatbothdiscsarewhite.

Allthediscsarenowreplacedinthebag.

Pradeeptakesatrandom3discsfromthebagwithoutreplacement.

（c）Findtheprobabilitythatthediscleftinthebagiswhite.

（Total8marks）

17.Thediagramshowsasectorofacircle,radius45cm,withangle84°

.

Calculatetheareaofthesector.

.............................cm2

18.

CalculatethelengthofAC.

...............................cm

19.Aconehasslantheight4cmandbaseradiusrcm.

Thetotalsurfaceareaoftheconeis

πcm2.

Calculatethevalueofr.

r=................................

20.f（x）=（x–1）2

（a）Findf（8）

Thedomainoffisallvaluesofxwherex≥7

（a）Findtherangeoff.

g（x）=

（c）Solvetheequationg（x）=1.2

（d）（i）Expresstheinversefunctiong–1intheformg–1（x）=.......

g–1（x）=...................................

（ii）Hencewritedowngg（x）intermsofx.

gg（x）=....................................

（6）

（Total11marks）

21.

Inthediagram

=aand

=c.

（a）Find

intermsofaandc.

ThepointBissuchthat

=

c.

（b）GivethemathematicalnameforthequadrilateralOABC.

ThepointPissuchthat

=a+kc,wherek≥0

（c）Statethetwoconditionsrelatingtoa+kcthatmustbetrueforOAPCtobearhombus.

22.（a）Workout5.2×

102+2.3×

104

Giveyouranswerinstandardform.

a×

102+b×

104=c×

（b）Expresscintermsofaandb.

c=................................

TOTALFORPAPER=100MARKS

END