2013年CIE剑桥国际考试IGCSE数学真题(43)

1、READTHESEINSTRUCTIONSFIRSTWriteyourCentrenumber,candidatenumberandnameonalltheworkyouhandin.Writeindarkblueorblackpen.Youmayuseapencilforanydiagramsorgraphs.Donotusestaples,paperclips,highlighters,glueorcorrectionfluid.DONOTWRITEINANYBARCODES.Answerallquestions.Ifworkingisneededforanyquestionitmustb

2、eshownbelowthatquestion.Electroniccalculatorsshouldbeused.Ifthedegreeofaccuracyisnotspecifiedinthequestion,andiftheanswerisnotexact,givetheanswertothreesignificantfigures.Giveanswersindegreestoonedecimalplace.For,useeitheryourcalculatorvalueor3.142.Attheendoftheexamination,fastenallyourworksecurelyt

3、ogether.Thenumberofmarksisgiveninbracketsattheendofeachquestionorpartquestion.Thetotalofthemarksforthispaperis130.MATHEMATICS0580/43Paper4(Extended)May/June20132hours30minutesCandidatesanswerontheQuestionPaper.AdditionalMaterials:ElectroniccalculatorGeometricalinstrumentsTracingpaper(optional)UNIVER

4、SITYOFCAMBRIDGEINTERNATIONALEXAMINATIONSInternationalGeneralCertificateofSecondaryEducationThisdocumentconsistsof19printedpagesand1blankpage.TurnoverIB1306_0580_43/5RPUCLES2013*9687546924*畅享冠军纯正特产？快来绵羊国正品代购！20580/43/M/J/13UCLES2013ForExaminersUse1(a)AliandBenreceiveasumofmoney.Theyshareitintheratio5

5、:1.Alireceives$2345.Calculatethetotalamount.Answer(a)$.2(b)Aliuses11%ofhis$2345tobuyatelevision.Calculatethecostofthetelevision.Answer(b)$.2(c)Adifferenttelevisioncosts$330.(i)Benbuysoneinasalewhenthiscostisreducedby15%.HowmuchdoesBenpay?Answer(c)(i)$.2(ii)$330is12%lessthanthecostlastyear.Calculatet

6、hecostlastyear.Answer(c)(ii)$.3畅享冠军纯正特产？快来绵羊国正品代购！30580/43/M/J/13UCLES2013TurnoverForExaminersUse(d)Aliinvests$1500ofhisshareinabankaccount.Theaccountpayscompoundinterestatarateof2.3%peryear.Calculatethetotalamountintheaccountattheendof3years.Answer(d)$.3(e)Alialsobuysacomputerfor$325.Helatersellsth

7、iscomputerfor$250.CalculateAlispercentageloss.Answer(e).%3_畅享冠军纯正特产？快来绵羊国正品代购！40580/43/M/J/13UCLES2013ForExaminersUse2(a)Inthisquestionshowallyourconstructionarcsanduseonlyarulerandcompassestodrawtheboundariesofyourregion.Thisscaledrawingshowsthepositionsoffourtowns,P,Q,RandS,onamapwhere1cmrepresent

8、s10km.PSRQNorthScale:1cmto10kmAnaturereserveliesinthequadrilateralPQRS.Theboundariesofthenaturereserveare:equidistantfromQandfromRequidistantfromPSandfromPQ60kmfromRalongQR.(i)Shadetheregionwhichrepresentsthenaturereserve.7(ii)MeasurethebearingofSfromP.Answer(a)(ii).1畅享冠军纯正特产？快来绵羊国正品代购！50580/43/M/J/

9、13UCLES2013TurnoverForExaminersUse(b)Acircularlakeinthenaturereservehasaradiusof45m.(i)Calculatetheareaofthelake.Answer(b)(i).m22(ii)NOTTOSCALEAfenceisplacedalongpartofthecircumferenceofthelake.Thisarcsubtendsanangleof210atthecentreofthecircle.Calculatethelengthofthefence.Answer(b)(ii).m2_畅享冠军纯正特产？快

10、来绵羊国正品代购！60580/43/M/J/13UCLES2013ForExaminersUse3(a)Lukwantstobuyxgoatsandysheep.(i)Hewantstobuyatleast5goats.Writedownaninequalityinxtorepresentthiscondition.Answer(a)(i).1(ii)Hewantstobuyatleast11sheep.Writedownaninequalityinytorepresentthiscondition.Answer(a)(ii).1(iii)Hewantstobuyatleast20animal

11、s.Writedownaninequalityinxandytorepresentthiscondition.Answer(a)(iii).1(b)Goatscost$4andsheepcost$8.ThemaximumLukcanspendis$160.Writedownaninequalityinxandyandshowthatitsimplifiestox+2yY40.Answer(b)1畅享冠军纯正特产？快来绵羊国正品代购！70580/43/M/J/13UCLES2013TurnoverForExaminersUse(c)(i)Onthegridbelow,drawfourlinest

12、oshowthefourinequalitiesandshadetheunwantedregions.403530252015105yx05101520253035407(ii)WorkoutthemaximumnumberofanimalsthatLukcanbuy.Answer(c)(ii).2_畅享冠军纯正特产？快来绵羊国正品代购！80580/43/M/J/13UCLES2013ForExaminersUse4IGEFJH40cm22cm7cmNOTTOSCALEEFGHIJisasolidmetalprismoflength40cm.ThecrosssectionEFGisaright

13、-angledtriangle.EF=7cmandEG=22cm.(a)Calculatethevolumeoftheprism.Answer(a).cm32(b)CalculatethelengthFJ.Answer(b)FJ=.cm4畅享冠军纯正特产？快来绵羊国正品代购！90580/43/M/J/13UCLES2013TurnoverForExaminersUse(c)CalculatetheanglebetweenFJandthebaseEGJHoftheprism.Answer(c).3(d)Theprismismeltedandmadeintospheres.Eachsphereha

14、saradius1.5cm.Workoutthegreatestnumberofspheresthatcanbemade.Thevolume,V,ofaspherewithradiusrisV=34r3.Answer(d).3(e)(i)Aright-angledtriangleisthecrosssectionofanotherprism.Thistrianglehasheight4.5cmandbase11.0cm.Bothmeasurementsarecorrectto1decimalplace.Calculatetheupperboundfortheareaofthistriangle

15、.Answer(e)(i).cm22(ii)Writeyouranswertopart(e)(i)correctto4significantfigures.Answer(e)(ii).cm21_畅享冠军纯正特产？快来绵羊国正品代购！100580/43/M/J/13UCLES2013ForExaminersUse5(a)Completethistableofvaluesforthefunctionf(x)=x1x2,x0.x3210.50.20.20.5123f(x)9.334.522.254.963.58.673(b)Drawthegraphoff(x)=x1x2for3YxY0.2and0.

16、2YxY3.yx543211234567891001123235畅享冠军纯正特产？快来绵羊国正品代购！110580/43/M/J/13UCLES2013TurnoverForExaminersUse(c)Useyourgraphtosolvef(x)=3.Answer(c)x=.orx=.orx=.3(d)Bydrawingasuitablelineonyourgraph,solvetheequationf(x)=2x2.Answer(d)x=.orx=.orx=.3(e)Bydrawingasuitabletangent,workoutanestimateofthegradientofthe

17、curveatthepointwherex=2.Youmustshowyourworking.Answer(e).3_畅享冠军纯正特产？快来绵羊国正品代购！120580/43/M/J/13UCLES2013ForExaminersUse6Inaboxthereare7redcardsand3bluecards.Acardisdrawnatrandomfromtheboxandisnotreplaced.Asecondcardisthendrawnatrandomfromthebox.(a)Completethistreediagram.RedBlueRedBlueBlueRed.Firstca

18、rdSecondcard7103(b)Workouttheprobabilitythatthetwocardsareofdifferentcolours.Giveyouranswerasafraction.Answer(b).3_畅享冠军纯正特产？快来绵羊国正品代购！130580/43/M/J/13UCLES2013TurnoverForExaminersUse7ABxy10987654321012345678(a)(i)DrawtheimageofshapeAafterastretch,factor3,x-axisinvariant.2(ii)Writedownthematrixrepres

19、entingastretch,factor3,x-axisinvariant.Answer(a)(ii)eo2(b)(i)DescribefullythesingletransformationwhichmapsshapeAontoshapeB.Answer(b)(i).3(ii)WritedownthematrixrepresentingthetransformationwhichmapsshapeAontoshapeB.Answer(b)(ii)eo2_畅享冠军纯正特产？快来绵羊国正品代购！140580/43/M/J/13UCLES2013ForExaminersUse8(a)27BCOA

20、EDNOTTOSCALEA,B,C,DandEarepointsonthecirclecentreO.AngleABD=27.Find(i)angleACD,Answer(a)(i)AngleACD=.1(ii)angleAOD,Answer(a)(ii)AngleAOD=.1(iii)angleAED.Answer(a)(iii)AngleAED=.1(b)LKNM6710045cm32cmNOTTOSCALEThediagramshowsquadrilateralKLMN.KL=45cm,LN=32cm,angleKLN=100andangleNLM=67.畅享冠军纯正特产？快来绵羊国正品

21、代购！150580/43/M/J/13UCLES2013TurnoverForExaminersUse(i)CalculatethelengthKN.Answer(b)(i)KN=.cm4(ii)TheareaoftriangleLMNis324cm2.CalculatethelengthLM.Answer(b)(ii)LM=.cm3(iii)AnothertriangleXYZismathematicallysimilartotriangleLMN.LNMXZYNOTTOSCALEXZ=16cmandtheareaoftriangleLMNis324cm2.Calculatetheareao

22、ftriangleXYZ.Answer(b)(iii).cm22_畅享冠军纯正特产？快来绵羊国正品代购！160580/43/M/J/13UCLES2013ForExaminersUse9Samasked80peoplehowmanyminutestheirjourneytoworktookononeday.Thecumulativefrequencydiagramshowsthetimestaken(mminutes).8070605040302010m01020304050CumulativefrequencyTime(minutes)(a)Find(i)themedian,Answer(a

23、)(i).min1(ii)thelowerquartile,Answer(a)(ii).min1(iii)theinter-quartilerange.Answer(a)(iii).min1畅享冠军纯正特产？快来绵羊国正品代购！170580/43/M/J/13UCLES2013TurnoverForExaminersUse(b)Oneofthe80peopleischosenatrandom.Findtheprobabilitythattheirjourneytoworktookmorethan35minutes.Giveyouranswerasafraction.Answer(b).2(c)

24、Usethecumulativefrequencydiagramtocompletethisfrequencytable.Time(mminutes)0mY1010mY1515mY3030mY4040mY50Frequency3012182(d)Usingmid-intervalvalues,calculateanestimateofthemeanjourneytimeforthe80people.Answer(d).min3(e)Usethetableinpart(c)tocompletethehistogramtoshowthetimestakenbythe80people.Onecolumnhasalreadybeencompletedforyou.FrequencydensityTime(minutes)432101020304050m5_畅享冠军纯正特产？快来绵羊国正品代购！180580/43/M/J/13UCLES2013ForExaminersUse10(a)(i)Solve2(3x7)=13.Answer(a)(i)x=.3(ii)Solvebyfactorisingx27x+6=0.Answer(a)(ii)x=.orx=.3(iii)Solve5x