A-Level数学公式书pdf版

GCEEdexcelGCEinMathematicsMathematicalFormulaeandStatisticalTablesBTECFirstDiploma/sLevel2SubjectTitleAugust2004XXXXxxDraft8ForuseinEdexcelAdvancedSubsidiaryGCEandAdvancedGCEexaminationsCoreMathematicsC1–C4FurtherPureMathematicsFP1–FP3MechanicsM1–M5StatisticsS1–S4ForusefromJanuary2008UA018598UA018598–EdexcelAS/AlevelMathematicsFormulaeList:C1–C4,FP1–FP3–ContentsPage–Issue1–September20071TABLEOFCONTENTSPage4CoreMathematicsC14Mensuration4Arithmeticseries5CoreMathematicsC25Cosinerule5Binomialseries5Logarithmsandexponentials5Geometricseries5Numericalintegration6CoreMathematicsC36Logarithmsandexponentials6Trigonometricidentities6Differentiation7CoreMathematicsC47Integration8FurtherPureMathematicsFP18Summations8Numericalsolutionofequations8Coordinategeometry8Conics8Matrixtransformations9FurtherPureMathematicsFP29Areaofsector9Maclaurin’sandTaylor’sSeries10Taylorpolynomials11FurtherPureMathematicsFP311Vectors13Hyperbolics14Integration14Arclength15Surfaceareaofrevolution2UA018598–EdexcelAS/AlevelMathematicsFormulaeList:M1–M5,S1–S4ContentsPage–Issue1–September200716MechanicsM116TherearenoformulaegivenforM1inadditiontothosecandidatesareexpectedtoknow.16MechanicsM216Centresofmass16MechanicsM316Motioninacircle16Centresofmass16Universallawofgravitation17MechanicsM417TherearenoformulaegivenforM4inadditiontothosecandidatesareexpectedtoknow.17MechanicsM517Momentsofinertia17Momentsasvectors18StatisticsS118Probability18Discretedistributions18Continuousdistributions19Correlationandregression20TheNormaldistributionfunction21PercentagepointsoftheNormaldistribution22StatisticsS222Discretedistributions22Continuousdistributions23Binomialcumulativedistributionfunction28Poissoncumulativedistributionfunction29StatisticsS329Expectationalgebra29Samplingdistributions29Correlationandregression29Non-parametrictests30Percentagepointsofthe2distribution31Criticalvaluesforcorrelationcoefficients32Randomnumbers33StatisticsS433Samplingdistributions34PercentagepointsofStudent’stdistribution35PercentagepointsoftheFdistributionTherearenoformulaeprovidedforDecisionMathematicsunitsD1andD2.UA018598–EdexcelAS/AlevelMathematicsFormulaeList–Issue1–September20073Theformulaeinthisbooklethavebeenarrangedaccordingtotheunitinwhichtheyarefirstintroduced.Thusacandidatesittingaunitmayberequiredtousetheformulaethatwereintroducedinaprecedingunit(e.g.candidatessittingC3mightbeexpectedtouseformulaefirstintroducedinC1orC2).ItmayalsobethecasethatcandidatessittingMechanicsandStatisticsunitsneedtouseformulaeintroducedinappropriateCoreMathematicsunits,asoutlinedinthespecification.4UA018598–EdexcelAS/AlevelMathematicsFormulaeList:CoreMathematicsC1–Issue1–September2007CoreMathematicsC1MensurationSurfaceareaofsphere=4r2Areaofcurvedsurfaceofcone=rslantheightArithmeticseriesun=a+(n–1)dSn=21n(a+l)=21n[2a+(n1)d]UA018598–EdexcelAS/AlevelMathematicsFormulaeList:CoreMathematicsC2–Issue1–September20075CoreMathematicsC2CandidatessittingC2mayalsorequirethoseformulaelistedunderCoreMathematicsC1.Cosinerulea2=b2+c2–2bccosABinomialseries21)(221nrrnnnnnbbarnbanbanaba(nℕ)where)!(!!Crnrnrnrnnxxrrnnnxnnnxxrn,1(21)1()1(21)1(1)1(2ℝ)LogarithmsandexponentialsaxxbbalogloglogGeometricseriesun=arn1Sn=rran1)1(S=ra1forr1NumericalintegrationThetrapeziumrule:baxyd21h{(y0+yn)+2(y1+y2+...+yn–1)},wherenabh6UA018598–EdexcelAS/AlevelMathematicsFormulaeList:CoreMathematicsC3–Issue1–September2007CoreMathematicsC3CandidatessittingC3mayalsorequirethoseformulaelistedunderCoreMathematicsC1andC2.LogarithmsandexponentialsxaxalneTrigonometricidentitiesBABABAsincoscossin)(sinBABABAsinsincoscos)(cos))((tantan1tantan)(tan21kBABABABA2cos2sin2sinsinBABABA2sin2cos2sinsinBABABA2cos2cos2coscosBABABA2sin2sin2coscosBABABADifferentiationf(x)f(x)tankxksec2kxsecxsecxtanxcotx–cosec2xcosecx–cosecxcotx)g()f(xx))(g()(g)f()g()(f2xxxxxUA018598–EdexcelAS/AlevelMathematicsFormulaeList:CoreMathematicsC4–Issue1–September20077CoreMathematicsC4CandidatessittingC4mayalsorequirethoseformulaelistedunderCoreMathematicsC1,C2andC3.Integration(+constant)f(x)xxd)f(sec2kxk1tankxxtanxseclnxcotxsinlnxcosec)tan(lncotcosecln21xxxxsec)tan(lntansecln4121xxxxxuvuvxxvudddddd8UA018598–EdexcelAS/AlevelMathematicsFormulaeList:FurtherPureMathematicsFP1–Issue1–September2007FurtherPureMathematicsFP1CandidatessittingFP1mayalsorequirethoseformulaelistedunderCoreMathematicsC1andC2.Summations)12)(1(6112nnnrnr224113)1(nnrnrNumericalsolutionofequationsTheNewton-Raphsoniterationforsolving0)f(x:)(f)f(1nnnnxxxxCoordinategeometryTheperpendiculardistancefrom(h,k)to0cbyaxis22bacbkahTheacuteanglebetweenlineswithgradientsm1andm2is21211arctanmmmmConicsParabolaRectangularHyperbolaStandardFormaxy42xy=c2ParametricForm(at2,2at)tcct,Foci)0,(aNotrequiredDirectricesaxNotrequiredUA018598–EdexcelAS/AlevelMathematicsFormulaeList:FurtherPureMathematicsFP1–Issue1–September20079MatrixtransformationsAnticlockwiserotatio