IGCSE-math-数学试卷0580-s17-qp-21

Thisdocumentconsistsof15printedpagesand1blankpage.DC(ST/FC)130071/3©UCLES2017[TurnoverCambridgeInternationalExaminationsCambridgeInternationalGeneralCertificateofSecondaryEducation*0243113261*MATHEMATICS0580/21Paper2(Extended)May/June20171hour30minutesCandidatesanswerontheQuestionPaper.AdditionalMaterials:ElectroniccalculatorGeometricalinstrumentsTracingpaper(optional)READTHESEINSTRUCTIONSFIRSTWriteyourCentrenumber,candidatenumberandnameonalltheworkyouhandin.Writeindarkblueorblackpen.YoumayuseanHBpencilforanydiagramsorgraphs.Donotusestaples,paperclips,glueorcorrectionfluid.DONOTWRITEINANYBARCODES.Answerallquestions.Ifworkingisneededforanyquestionitmustbeshownbelowthatquestion.Electroniccalculatorsshouldbeused.Ifthedegreeofaccuracyisnotspecifiedinthequestion,andiftheanswerisnotexact,givetheanswertothreesignificantfigures.Giveanswersindegreestoonedecimalplace.Forr,useeitheryourcalculatorvalueor3.142.Attheendoftheexamination,fastenallyourworksecurelytogether.Thenumberofmarksisgiveninbrackets[]attheendofeachquestionorpartquestion.Thetotalofthemarksforthispaperis70.20580/21/M/J/17©UCLES20171Simplify.(x2)5..............................................[1]2Thethicknessofonesheetofpaperis8#10-3cm.Workoutthethicknessof250sheetsofpaper.........................................cm[1]3Write23.4571correctto(a)4significantfigures,..............................................[1](b)thenearest10...............................................[1]4Thetableshowsthetemperaturesinfiveplacesat10amonedayinJanuary.PlaceTemperature(°C)Helsinki-7Chicago-10London3Moscow-4Bangkok26(a)Whichplacewasthecoldest?..............................................[1](b)At2pmthetemperatureinHelsinkihadincreasedby4°C.WritedownthetemperatureinHelsinkiat2pm..........................................°C[1]30580/21/M/J/17©UCLES2017[Turnover5Factorisecompletely.12n2-4mn..............................................[2]6(a)2161r=Findthevalueofr.r=.......................................[1](b)33t5=Findthevalueoft.t=........................................[1]7Withoutusingacalculator,workout13275+.Writedownallthestepsofyourworkingandgiveyouranswerasamixednumberinitssimplestform...............................................[3]40580/21/M/J/17©UCLES20178Simonhastwoboxesofcards.Inonebox,eachcardhasoneshapedrawnonitthatiseitheratriangleorasquare.Intheotherbox,eachcardiscolouredeitherredorblue.Simonpicksacardfromeachboxatrandom.Theprobabilityofpickingatrianglecardist.Theprobabilityofpickingaredcardisr.CompletethetableforthecardsthatSimonpicks,writingeachprobabilityintermsofrandt.EventProbabilityTriangleandredSquareandred(1-t)rTriangleandblueSquareandblue[3]9hisdirectlyproportionaltothesquarerootofp.h=5.4whenp=1.44.Findhwhenp=2.89.h=.......................................[3]50580/21/M/J/17©UCLES2017[Turnover101–1012345yx23456Byshadingtheunwantedregionsofthegrid,findandlabeltheregionRthatsatisfiesthefollowingfourinequalities.yG2yH1yG2x-1yG5-x[3]11Thetwobarrelsinthediagramaremathematicallysimilar.hcm90cmNOTTOSCALEThesmallerbarrelhasaheightofhcmandacapacityof100litres.Thelargerbarrelhasaheightof90cmandacapacityof160litres.Workoutthevalueofh.h=.......................................[3]60580/21/M/J/17©UCLES201712Alinehasgradient5.MandNaretwopointsonthisline.Misthepoint(x,8)andNisthepoint(k,23).Findanexpressionforxintermsofk.x=.......................................[3]13AEHDBCGF13cmNOTTOSCALE5cm4cmThediagramshowsacuboidABCDEFGH.AE=5cm,EH=4cmandAG=13cm.CalculatetheanglebetweenthelineAGandthebaseEFGHofthecuboid...............................................[3]70580/21/M/J/17©UCLES2017[Turnover14Thediagramshowsaregularoctagonjoinedtoanequilateraltriangle.NOTTOSCALEx°Workoutthevalueofx.x=.......................................[3]80580/21/M/J/17©UCLES201715Thediagramshowsinformationaboutthefirst100secondsofacarjourney.1002046810121416Speed(m/s)1820304050Time(s)60708090100(a)Calculatetheaccelerationduringthefirst20secondsofthejourney.......................................m/s2[1](b)Workoutthetotaldistancetravelledbythecarinthe100seconds...........................................m[3]90580/21/M/J/17©UCLES2017[Turnover16Sixstudentsreviseforatest.Thescatterdiagramshowsthetime,inhours,eachstudentspentrevisingandtheirmarkinthetest.025303540Mark455012345Time(hours)678910(a)Thedatafortwomorestudentsisshowninthetable.Time(hours)4.56.5Mark3335Plotthesetwopointsonthescatterdiagram.[1](b)Whattypeofcorrelationisshownonthescatterdiagram?..............................................[1](c)Drawalineofbestfitonthescatterdiagram.[1](d)Anotherstudentspent5.5hoursrevising.Estimateamarkforthisstudent...............................................[1]100580/21/M/J/17©UCLES201717(a)InthisVenndiagram,shadetheregionFG,l.FG[1](b)={1,2,3,4,5,6,7,8,9}A={x:xisanoddnumber}B={x:xisasquarenumber}C={x:xisamultipleof3}(i)WritealltheelementsofintheVenndiagrambelow.ABC[2](ii)Anothernumberisincludedintheset.ThisnumberisintheregionABC++l.Writedownapossiblevalueforthisnumber...........................................