新加坡A-LEVEL数学纲要(英语原文)

MATHEMATICSHIGHER2(Syllabus9740)CONTENTSPageAIMS1ASSESSMENTOBJECTIVES(AO)2USEOFGRAPHICCALCULATOR(GC)2LISTOFFORMULAE2INTEGRATIONANDAPPLICATION2SCHEMEOFEXAMINATIONPAPERS3CONTENTOUTLINE4ASSUMEDKNOWLEDGE12MATHEMATICALNOTATION149740H2MATHEMATICS(2009)1AIMSThesyllabuspreparesstudentsadequatelyforuniversitycoursesincludingmathematics,physicsandengineering,wheremoremathematicscontentisrequired.Thesyllabusaimstodevelopmathematicalthinkingandproblemsolvingskillsinstudents.TopicscoveredincludeFunctionsandGraphs,SequencesandSeries,Vectors,ComplexNumbers,Calculus,PermutationsandCombinations,Probability,ProbabilityDistributions,Sampling,HypothesisTesting,andCorrelationandRegression.Studentswilllearntoanalyse,formulateandsolvedifferenttypesofproblems.Theywillalsolearntoworkwithdataandperformstatisticalanalyses.Thegeneralaimsofthesyllabusaretoenablestudentsto:1acquirethenecessarymathematicalconceptsandskillsforeverydaylife,andforcontinuouslearninginmathematicsandrelateddisciplines;2developthenecessaryprocessskillsfortheacquisitionandapplicationofmathematicalconceptsandskills;3developthemathematicalthinkingandproblemsolvingskillsandapplytheseskillstoformulateandsolveproblems;4recogniseanduseconnectionsamongmathematicalideas,andbetweenmathematicsandotherdisciplines;5developpositiveattitudestowardsmathematics;6makeeffectiveuseofavarietyofmathematicaltools(includinginformationandcommunicationtechnologytools)inthelearningandapplicationofmathematics;7produceimaginativeandcreativeworkarisingfrommathematicalideas;8developtheabilitiestoreasonlogically,tocommunicatemathematically,andtolearncooperativelyandindependently.9740H2MATHEMATICS(2009)2ASSESSMENTOBJECTIVES(AO)Therearethreelevelsofassessmentobjectivesfortheexamination.Theassessmentwilltestcandidates'abilitiesto:AO1understandandapplymathematicalconceptsandskillsinavarietyofcontexts,includingthemanipulationofmathematicalexpressionsanduseofgraphiccalculators;AO2reasonandcommunicatemathematicallythroughwritingmathematicalexplanation,argumentsandproofs,andinferences;AO3solveunfamiliarproblems;translatecommonrealisticcontextsintomathematics;interpretandevaluatemathematicalresults,andusetheresultstomakepredictions,orcommentonthecontext.USEOFGRAPHICCALCULATOR(GC)TheuseofGCwithoutcomputeralgebrasystemwillbeexpected.TheexaminationpaperswillbesetwiththeassumptionthatcandidateswillhaveaccesstoGC.Asageneralrule,unsupportedanswersobtainedfromGCareallowedunlessthequestionstatesotherwise.WhereunsupportedanswersfromGCarenotallowed,candidatesarerequiredtopresentthemathematicalstepsusingmathematicalnotationsandnotcalculatorcommands.Forquestionswheregraphsareusedtofindasolution,candidatesshouldsketchthesegraphsaspartoftheiranswers.Incorrectanswerswithoutworkingwillreceivenomarks.However,ifthereiswrittenevidenceofusingGCcorrectly,methodmarksmaybeawarded.StudentsshouldbeawarethattherearelimitationsinherentinGC.Forexample,answersobtainedbytracingalongagraphtofindrootsofanequationmaynotproducetherequiredaccuracy.LISTOFFORMULAECandidateswillbeprovidedintheexaminationwithalistofformulae.INTEGRATIONANDAPPLICATIONNotwithstandingthepresentationofthetopicsinthesyllabusdocument,itisenvisagedthatsomeexaminationquestionsmayintegrateideasfrommorethanonetopic,andthattopicsmaybetestedinthecontextsofproblemsolvingandapplicationofmathematics.9740H2MATHEMATICS(2009)3SCHEMEOFEXAMINATIONPAPERSFortheexaminationinH2Mathematics,therewillbetwo3-hourpapers,eachcarrying50%ofthetotalmark,andeachmarkedoutof100,asfollows:PAPER1(3hours)Apaperconsistingofabout10to12questionsofdifferentlengthsandmarksbasedonthePureMathematicssectionofthesyllabus.Candidateswillbeexpectedtoanswerallquestions.PAPER2(3hours)Apaperconsistingof2sections,SectionsAandB.SectionA(PureMathematics–40marks)willconsistofabout3–4questionsofdifferentlengthsandmarksbasedonthePureMathematicssectionofthesyllabus.SectionB(Statistics–60marks)willconsistofabout6–8questionsofdifferentlengthsandmarksbasedontheStatisticssectionofthesyllabus.Candidateswillbeexpectedtoanswerallquestions.9740H2MATHEMATICS(2009)4CONTENTOUTLINEKnowledgeofthecontentoftheOLevelMathematicssyllabusandofsomeofthecontentoftheOLevelAdditionalMathematicssyllabusesareassumedinthesyllabusbelowandwillnotbetesteddirectly,butitmayberequiredindirectlyinresponsetoquestionsonothertopics.TheassumedknowledgeforOLevelAdditionalMathematicsisappendedafterthissection.Topic/Sub-topicsContentPUREMATHEMATICS1Functionsandgraphs1.1Functions,inversefunctionsandcompositefunctionsInclude:conceptoffunction,domainandrangeuseofnotationssuchas5)f(2+=xx,5:f2+xxa,)(f1x−,)(fgxand)(f2xfindinginversefunctionsandcompositefunctionsconditionsfortheexistenceofinversefunctionsandcompositefunctionsdomainrestrictiontoobtainaninversefunctionrelationshipbetweenafunctionanditsinverseasreflectioninthelinexy=Excludetheuseoftherelation111fg(fg)−−−=1.2GraphingtechniquesInclude:useofagraphiccalculatortographagivenfunctionrelatingthefollowingequationswiththeirgraphs12222=±byaxdcxbaxy++=edxcbxaxy+++=2characteristicsofgraphssuchassymmetry