Igcse数学历年真题2.docx

Igcse数学历年真题2.docx

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Igcse数学历年真题2

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.

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

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