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×tanθoro ppt 关于艾滋病ppt课件精益管理ppt下载地图下载ppt可编辑假如ppt教学课件下载triz基础知识ppt anadjθ=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+7>1...............................(ii)Onthenumberline,representthesolutiontopart(i).(Total4marks)LeaveblankN20710RA7TurnoverQ8Q7–4–3–2–1012349.Thegroupedfrequencytablegivesinformationaboutthedistanceeachof150peopletraveltowork.(a)Workoutwhatpercentageofthe150peopletravelmorethan20kmtowork...........................%(2)(b)Workoutanestimateforthemeandistancetravelledtoworkbythepeople.........................km(4)(c)Completethecumulativefrequencytable.(1)LeaveblankN20710RA8Distancetravelled(dkm)Frequency0<d≤5345<d≤104810<d≤152615<d≤201820<d≤251625<d≤308Distancetravelled(dkm)Cumulativefrequency0<d≤50<d≤100<d≤150<d≤200<d≤250<d≤30(d)Onthegrid,drawacumulativefrequencygraphforyourtable.(2)(e)Useyourgraphtofindanestimateforthemedianofthedistancetravelledtoworkbythepeople.Showyourmethodclearly.........................km(2)(Total11marks)LeaveblankN20710RA9Turnover160–140–120–100–80–60–40–20–Cumulativefrequency–––102030ODistancetravelled(dkm)Q910.Thediagramshowsashape.ABisanarcofacircle,centreO.AngleAOB=90°.OA=OB=6cm.Calculatetheperimeteroftheshape.Giveyouranswercorrectto3significantfigures..........................cm(Total4marks)11.ThedistancebetweentheEarthandtheSunis150000000km.(a)Writethenumber150000000instandardform................................(1)ThedistancebetweenNeptuneandtheSunis30timesgreaterthanthedistancebetweentheEarthandtheSun.(b)CalculatethedistancebetweenNeptuneandtheSun.Giveyouranswerinstandardform.........................km(2)(Total3marks)LeaveblankN20710RA10Q11Q106cmAOB6cmDiagramNOTaccuratelydrawn12.(a)Findthegradientofthelinewithequation3x–4y=15...............................(3)(b)Workoutthecoordinatesofthepointofintersectionofthelinewithequation3x–4y=15andthelinewithequation5x+6y=6(.……….,………..)(4)(Total7marks)13.AbodyismovinginastraightlinewhichpassesthroughafixedpointO.Thedisplacement,smetres,ofthebodyfromOattimetsecondsisgivenbys=t3+4t2–5t(a)Findanexpressionforthevelocity,vm/s,attimetseconds.v=........................(2)(b)Findtheaccelerationafter2seconds.......................m/s2(2)(Total4marks)LeaveblankN20710RA11TurnoverQ13Q1214.Theunfinishedtableandhistogramshowinformationfromasurveyofwomenaboutthenumberofcaloriesinthefoodtheyeatinoneday.(a)(i)Usetheinformationinthetabletocompletethehistogram.(ii)Usetheinformationinthehistogramtocompletethetable.(3)(b)Findanestimatefortheupperquartileofthenumberofcalories.Youmustmakeyourmethodclear................................(2)(Total5marks)LeaveblankN20710RA12Q14Numberofcalories(n)Frequency0<n≤1000901000<n≤20002000<n≤25001402500<n≤4000Frequencydensity–––1000200030000Numberofcalories(n)4000–15.Thelengthofasideofasquareis6.81cm,correctto3significantfigures.(a)Workoutthelowerboundfortheperimeterofthesquare..........................cm(2)(b)Givetheperimeterofthesquaretoanappropriatedegreeofaccuracy.Youmustshowworkingtoexplainhowyouobtainedyouranswer..........................cm(2)(Total4marks)16.Expressthealgebraicfractionassimplyaspossible................................(Total3marks)22232016xxx−−−LeaveblankN20710RA13TurnoverQ16Q1517.Anelectricianhaswiresofthesamelengthmadefromthesamematerial.Theelectricalresistance,Rohms,ofawireisinverselyproportionaltothesquareofitsradius,rmm.Whenr=2,R=0.9(a)(i)ExpressRintermsofr.R=........................(ii)Ontheaxes,sketchthegraphofRagainstr.(4)Oneoftheelectrician’swireshasaradiusof3mm.(b)Calculatetheelectricalresistanceofthiswire......................ohms(1)(Total5marks)LeaveblankN20710RA14Q17▲▲ROr18.A,B,CandDarefourpointsonthecircumferenceofacircle.ThechordsACandBDintersectatE.AE=3.6cm,CE=2.8cm,DE=2.4cmandAD=4.9cm.(a)CalculatethelengthofBE..........................cm(3)(b)CalculatethesizeofangleAED.Giveyouranswercorrectto3significantfigures.°...............................(3)(Total6marks)LeaveblankN20710RA15TurnoverQ18DiagramNOTaccuratelydrawnA2.4cm3.6cmECD4.9cmB2.8cm19.f:x62x–1g:x6,x≠0(a)Findthevalueof(i)f(3),...............................(ii)fg(6)................................(2)(b)Expresstheinversefunctionf–1intheformf–1:x6..................................(2)(c)(i)Expressthecompositefunctiongfintheformgf:x6..................................(ii)Whichvalueofxmustbeexcludedfromthedomainofgf?x=........................(2)(Total6marks)3xLeaveblankN20710RA16Q1920.Q,R,SandTarepointsonthecircumferenceofacircle.PUisatangenttothecircleatT.PQRisastraightline.AnglePQT=108°.AngleSTR=44°.WorkoutthesizeofangleSTU.Youmustgiveareasonforeachstepinyourworking.°...............................(Total5marks)TOTALFORPAPER:100MARKSENDLeaveblankN20710RA17Q20DiagramNOTaccuratelydrawnPS44°R108°QTUBLANKPAGEN20710RA18