IGCSE-Maths-past-paper数学考试题

Examiner’suseonlyTeamLeader’suseonlyPaperReference(s)4400/3HLondonExaminationsIGCSEMathematicsPaper3HHigherTierMonday10May2004–MorningTime:2hoursMaterialsrequiredforexaminationItemsincludedwithquestionpapersRulergraduatedincentimetresandNilmillimetres,protractor,compasses,pen,HBpencil,eraser,calculator.Tracingpapermaybeused.CentreNo.CandidateNo.PaperReference44003HSurnameInitial(s)SignatureTurnoverInstructionstoCandidatesIntheboxesabove,writeyourcentrenumberandcandidatenumber,yoursurname,initial(s)andsignature.Thepaperreferenceisshownatthetopofthispage.Checkthatyouhavethecorrectquestionpaper.AnswerALLthequestionsinthespacesprovidedinthisquestionpaper.Showallthestepsinanycalculations.InformationforCandidatesThereare20pagesinthisquestionpaper.Allblankpagesareindicated.Thetotalmarkforthispaperis100.Themarksforpartsofquestionsareshowninroundbrackets:e.g.(2).Youmayuseacalculator.AdvicetoCandidatesWriteyouranswersneatlyandingoodEnglish.Printer’sLog.No.N20710RAThispublicationmayonlybereproducedinaccordancewithLondonQualificationsLimitedcopyrightpolicy.©2004LondonQualificationsLimited.W850/R4400/575704/4/4/1/3/1/3/1/3/1000*N20710RA*PageLeaveNumbersBlank34567891011121314151617TotalN20710RA2IGCSEMATHEMATICS4400FORMULASHEET–HIGHERTIERPythagoras’Theoremadj=hyp×cosθopp=hyp×sinθopp=adj×tanθoropptanadjθ=adjcoshypθ=oppsinhypθ=Circumferenceofcircle=2πrAreaofcircle=πr2Areaofatrapezium=(a+b)h12baoppadjhypbahlengthsectioncrossa2+b2=c2Volumeofprism=areaofcrosssection×lengthVolumeofcylinder=πr2hCurvedsurfaceareaofcylinder=2πrhhrVolumeofcone=πr2hCurvedsurfaceareaofcone=πrl13rlrhVolumeofsphere=πr3Surfaceareaofsphere=4πr243rInanytriangleABCSineruleCosinerulea2=b2+c2–2bccosAAreaoftriangle=absinC12sinsinsinabcABC==CabcBATheQuadraticEquationThesolutionsofax2+bx+c=0wherea≠0,aregivenby242bbacxa−±−=cθAnswerALLTWENTYquestions.Writeyouranswersinthespacesprovided.Youmustwritedownallstagesinyourworking.1.InJuly2002,thepopulationofEgyptwas69million.ByJuly2003,thepopulationofEgypthadincreasedby2%.WorkoutthepopulationofEgyptinJuly2003...................million(Total3marks)2.(a)Expand3(2t+1)...............................(1)(b)Expandandsimplify(x+5)(x–3)...............................(2)(c)Factorise10p–15q...............................(1)(d)Factorisen2+4n...............................(1)(Total5marks)LeaveblankN20710RA3TurnoverQ2Q1LeaveblankN20710RA43.Acirclehasaradiusof4.7cm.(a)Workouttheareaofthecircle.Giveyouranswercorrectto3significantfigures........................cm2(2)Thediagramshowsashape.(b)Workouttheareaoftheshape........................cm2(4)(Total6marks)Q3DiagramNOTaccuratelydrawn7cm6cm3cm11cm2cmDiagramNOTaccuratelydrawn4.7cmLeaveblankN20710RA5TurnoverQ44.Thediagramshowsapointerwhichspinsaboutthecentreofafixeddisc.Whenthepointerisspun,itstopsononeofthenumbers1,2,3or4.Theprobabilitythatitwillstopononeofthenumbers1to3isgiveninthetable.Magdaisgoingtospinthepointeronce.(a)Workouttheprobabilitythatthepointerwillstopon4................................(2)(b)Workouttheprobabilitythatthepointerwillstopon1or3................................(2)Omarisgoingtospinthepointer75times.(c)Workoutanestimateforthenumberoftimesthepointerwillstopon2................................(2)(Total6marks)Number1234Probability0.350.160.27LeaveblankN20710RA6Q65.(a)Express200astheproductofitsprimefactors................................(2)(b)WorkouttheLowestCommonMultipleof75and200................................(2)(Total4marks)6.Twopoints,AandB,areplottedonacentimetregrid.Ahascoordinates(2,1)andBhascoordinates(8,5).(a)WorkoutthecoordinatesofthemidpointofthelinejoiningAandB.(............,............)(2)(b)UsePythagoras’TheoremtoworkoutthelengthofAB.Giveyouranswercorrectto3significantfigures..........................cm(4)(Total6marks)Q57.A={1,2,3,4}B={1,3,5}(a)Listthemembersoftheset(i)A∩B,...............................(ii)A∪B................................(2)(b)Explainclearlythemeaningof3∈A.............................................................................................................................................(1)(Total3marks)8.(i)Solvetheinequality3x+71...............................(ii)Onthenumberline,representthesolutiontopart(i).(Total4marks)LeaveblankN20710RA7TurnoverQ8Q7–4–3–2–1012349.Thegroupedfrequencytablegivesinformationaboutthedistanceeachof150peopletraveltowork.(a)Workoutwhatpercentageofthe150peopletravelmorethan20kmtowork...........................%(2)(b)Workoutanestimateforthemeandistancetravelledtoworkbythepeople.........................km(4)(c)Completethecumulativefrequencytable.(1)LeaveblankN20710RA8Distancetravelled(dkm)Frequency0d≤5345d≤104810d≤152615d≤201820d≤251625d≤308Distancetravelled(dkm)Cumulativefrequency0d≤50d≤100d≤150d≤200d≤250d≤30(d)Onthegrid,drawacumulativefrequencygraphforyourtable.(2)(e)Useyourgraphtofindanestimateforthemedianofthedistancetravelledtoworkbythepeople.Showyourmethodclearly.........................km(2)(Total11marks)LeaveblankN20710RA9Turnover160–140–120–100–80–60–40–20–Cumulativefrequency––