高中数学公式手汇总.docx

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1、精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结TABLE OF CONTENTSPage4Core Mathematics C14Mensuration4 Arithmetic series5 Core Mathematics C25Cosine rule5Binomial series5Logarithms and exponentials5Geometric series5 Numerical integration6 Core Mathematics C36Logarithms and expon

2、entials6Trigonometric identities6 Differentiation7 Core Mathematics C47 Integration8 Further Pure Mathematics FP18Summations8Numerical solution of equations8Coordinate geometry8Conics8 Matrix transformations9 Further Pure Mathematics FP29Area of sector16Mechanics M216Centres of mass16Mechanics M316M

3、otion in a circle16Centres of mass16 Universal law of gravitation17 Mechanics M417There are no formulae given for M4 in addition to those candidates are expected to know.17Mechanics M517Moments of inertia17 Moments as vectors18 Statistics S118Probability18Discrete distributions18 Continuous distribu

4、tions19 Correlation and regression20 The Normal distribution function21 Percentage pointsoftheNormal distribution22 Statistics S222Discrete distributions22 Continuous distributions23 Binomialcumulativedistribution function28Poissoncumulativedistribution可编辑资料 - - - 欢迎下载精品名师归纳总结9 Maclaurin s and Taylo

5、r s Seriesfunction10 Taylor polynomials11 Further Pure Mathematics FP3可编辑资料 - - - 欢迎下载精品名师归纳总结11Vectors13 Hyperbolics14 Integration14 Arc length15 Surface area of revolution16 Mechanics M116There are no formulae given for M1 in addition to those candidates are expected to know.29Statistics S329 Expe

6、ctation algebra 29Sampling distributions29Correlationand regression29Non-parametrictests30 Percentagepointsofthe2distribution31Criticalvalues for correlation coefficients32 Random numbers33Statistics S4可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 1 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎

7、下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -33Sampling distributions34Percentage points of Student s t distribution35Percentage points of the F distributionThere are no formulae provided for Decision Mathematics units D1 and D2The formulae in this booklet have been arranged according to the uniti

8、n which they are first introduced. Thus a candidate sitting a unit may be required to use the formulae that were introduced in a preceding unit e.g. candidates sitting C3 might be expected to use formulae first introduced in C1 or C2.Itmay also be the case thatcandidatessittingMechanicsand Statistic

9、sunitsneed to use formulae introduced in appropriate Core Mathematics units, as outlined in the specificationCore Mathematics C1MensurationSurface area of sphere = 4r 2Area of curved surface of cone =rslant heightArithmetic seriesun = a + n 1d可编辑资料 - - - 欢迎下载精品名师归纳总结Sn =1 na + l =21 n2a + n1d2可编辑资料

10、- - - 欢迎下载精品名师归纳总结Core Mathematics C2Candidates sitting C2 may also require those formulae listed under Core Mathematics C1.Cosine rulea2 = b2 + c2 2bc cos A Binomial series可编辑资料 - - - 欢迎下载精品名师归纳总结ab na nnwhererna n1Cnr1bn 2n. r . na nr .2 b2nanrr b rbnn. 可编辑资料 - - - 欢迎下载精品名师归纳总结1x n1nxn n 11 x 22nn

11、1nr 12r1 xr x1, n. 可编辑资料 - - - 欢迎下载精品名师归纳总结Logarithms and exponentials可编辑资料 - - - 欢迎下载精品名师归纳总结log a xlog b x log b a可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 2 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -可编辑资料 - - - 欢迎下

12、载精品名师归纳总结Geometric seriesun = arn1Sn =Numerical integrationa1 1r n rS=a1rforr 1可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结The trapezium rule:bydxa1 h y0 + yn + 2y1 + y2 + . + yn 1, wherehba2n可编辑资料 - - - 欢迎下载精品名师归纳总结Core Mathematics C3Candidates sitting C3 may also require those formulae listed

13、under Core Mathematics C1 and C2.Logarithms and exponentialse x ln aa xTrigonometric identities可编辑资料 - - - 欢迎下载精品名师归纳总结sin ABsinA cos Bcos A sin Bcos AB cos A cos BsinA sin B可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结tan ABtan Atan B AB k1可编辑资料 - - - 欢迎下载精品名师归纳总结21tan A tan B可编辑资料 - - - 欢迎下载精品名

14、师归纳总结sin Asin B2 sinABABcos22sin Asin B2 cosABABsin22可编辑资料 - - - 欢迎下载精品名师归纳总结cos Acos B2 cosABABcos22cos Acos B2 sinABABsin22可编辑资料 - - - 欢迎下载精品名师归纳总结Differentiation可编辑资料 - - - 欢迎下载精品名师归纳总结fxf xtan kxk sec2 kxsecxsec x tan xcot xcosec2 x cosecxcosecx cot xf xfx g xf x g x可编辑资料 - - - 欢迎下载精品名师归纳总结g xCo

15、re Mathematics C42g x 可编辑资料 - - - 欢迎下载精品名师归纳总结Candidates sitting C4 may also require those formulae listed under Core Mathematics C1, C2 and C3.可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 3 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -Integration

16、+ constantf xf x dx可编辑资料 - - - 欢迎下载精品名师归纳总结sec2 kx1tan kx k可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结2tan x cot xln secx ln sin x可编辑资料 - - - 欢迎下载精品名师归纳总结cosec xln cosecxcot xln tan 1 x可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结sec xln secxtan xln tan1 x1可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - -

17、 欢迎下载精品名师归纳总结24dvudxuv dxduvdxdx可编辑资料 - - - 欢迎下载精品名师归纳总结Further Pure Mathematics FP1Candidates sitting FP1 may also require those formulae listed under Core Mathematics C1 and C2.Summations可编辑资料 - - - 欢迎下载精品名师归纳总结n6r 21 nnr 1n1 2n1可编辑资料 - - - 欢迎下载精品名师归纳总结r431 n 2 nr 11 2可编辑资料 - - - 欢迎下载精品名师归纳总结Numer

18、ical solution of equations可编辑资料 - - - 欢迎下载精品名师归纳总结The Newton-Raphson iteration for solvingf x0 :xn 1xnf xn 可编辑资料 - - - 欢迎下载精品名师归纳总结f xn 可编辑资料 - - - 欢迎下载精品名师归纳总结Coordinate geometryThe perpendicular distance from h , k toaxbyc0 isahbkc可编辑资料 - - - 欢迎下载精品名师归纳总结a 2b 2可编辑资料 - - - 欢迎下载精品名师归纳总结The acute ang

19、le between lines with gradientsm1and m2isarctanm1m21 m m可编辑资料 - - - 欢迎下载精品名师归纳总结12可编辑资料 - - - 欢迎下载精品名师归纳总结ConicsParabolaRectangular Hyperbola可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 4 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - -

20、 - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结Standard Formy 24axxy = c2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结Parametric Format2, 2atct ,c t可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结Foci a, 0Not required可编辑资料 - - - 欢迎下载精品名师归纳总结DirectricesxaNot required可编辑资料 - - - 欢迎下载精品名师归纳总结Matrix transformatio

21、nsAnticlockwise rotation throughabout O:cos sinsin cos可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结Reflection in the lineytan x:cos2 sin 2sin 2cos 2可编辑资料 - - - 欢迎下载精品名师归纳总结Further Pure Mathematics FP2Candidates sitting FP2 may also require those formulae listed under Further Pure Mathematics FP1

22、and Core Mathematics C1C4.Area of a sector可编辑资料 - - - 欢迎下载精品名师归纳总结A =12r 2dpolar coordinates可编辑资料 - - - 欢迎下载精品名师归纳总结Complex numbers可编辑资料 - - - 欢迎下载精品名师归纳总结eicosi sin可编辑资料 - - - 欢迎下载精品名师归纳总结 r cosni sinnrcos ni sin n2 k i可编辑资料 - - - 欢迎下载精品名师归纳总结The roots ofz n1are given byze n, fork0, 1, 2, n1可编辑资料 -

23、 - - 欢迎下载精品名师归纳总结Maclaurin s and Taylor s Series可编辑资料 - - - 欢迎下载精品名师归纳总结f x f 0x f 0xf 0 2.2 xa 2xf r 0 r .rxa r可编辑资料 - - - 欢迎下载精品名师归纳总结f xf a xa f a2.x 2f ax rf r ar .可编辑资料 - - - 欢迎下载精品名师归纳总结f axf a x f ax 2f a 2.xrf r ar.可编辑资料 - - - 欢迎下载精品名师归纳总结e xexp x1x2.x 2x 3forr.xrall x可编辑资料 - - - 欢迎下载精品名师归纳总

24、结ln 1xx231 r 1r1x1可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 5 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结35sin xxxx3.5.x 2x41 rx2 r2r x 2r11.for all x可编辑资料 - - - 欢迎下载精品名师归纳总结cos x1arctan x2.4.x3

25、x5x351 r2r .x2r 11 r2r1for all x1x1可编辑资料 - - - 欢迎下载精品名师归纳总结Taylor polynomials可编辑资料 - - - 欢迎下载精品名师归纳总结f ahf ahf a f a h f ah f ahf a 2.22hfa 2.error0h可编辑资料 - - - 欢迎下载精品名师归纳总结f xf a xa fa x xa 2a 2f2.aerror可编辑资料 - - - 欢迎下载精品名师归纳总结f xf a xa fa f ax2.可编辑资料 - - - 欢迎下载精品名师归纳总结Further Pure Mathematics FP3C

26、andidates sitting FP3 may also require those formulae listed under Further Pure Mathematics FP1, and Core Mathematics C1C4.Vectors可编辑资料 - - - 欢迎下载精品名师归纳总结The resolved part ofa in the direction of b isa.b b可编辑资料 - - - 欢迎下载精品名师归纳总结The point dividing AB in the ratio:isab可编辑资料 - - - 欢迎下载精品名师归纳总结Vector p

27、roduct:aba b sinn.ijka1a2a 3b1b2b3a2 b3 a3 b1 a1b2a 3b 2 a1b3 a 2b1可编辑资料 - - - 欢迎下载精品名师归纳总结a1a 2a 3a.bcb1b 2b3b.cac.ab c1c2c3可编辑资料 - - - 欢迎下载精品名师归纳总结a bca.cba.bc可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结If A is the point with position vectoraa1 ia2 ja3 kand the direction vectorb is given by可编辑

28、资料 - - - 欢迎下载精品名师归纳总结b b1ib2 jb3 k, then the straight line throughA with direction vector b has cartesian可编辑资料 - - - 欢迎下载精品名师归纳总结equation可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 6 页，共 9 页 - - - - - - - - - -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -可编辑资料 - - - 欢迎下载精品

29、名师归纳总结xa1 b1y a 2b 2z a 3 b3可编辑资料 - - - 欢迎下载精品名师归纳总结The plane throughA with normal vectornn1in2 jn3 khas cartesian equation可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结n1 xn 2 yn3 zd0 where da.n可编辑资料 - - - 欢迎下载精品名师归纳总结The plane through non-collinear pointsA, B and C has vector equation可编辑资料 - - -

30、 欢迎下载精品名师归纳总结rabaca1abc可编辑资料 - - - 欢迎下载精品名师归纳总结The plane through the point with position vectora and parallel tob and c has equationrasbtc可编辑资料 - - - 欢迎下载精品名师归纳总结The perpendicular distance of ,fromn1 xn 2 yn 3 zd0is可编辑资料 - - - 欢迎下载精品名师归纳总结n1n 2n3d.nnn222123Hyperbolic functions可编辑资料 - - - 欢迎下载精品名师归纳总

31、结cosh 2 xsinh 2 x1sinh 2x2 sinh x cosh xcosh 2xcosh 2 xsinh 2 x可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结arcosh xln xx21 x1arsinh xln xx 21可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结artanh x1 ln1x21x x1可编辑资料 - - - 欢迎下载精品名师归纳总结ConicsEllipseParabolaHyperbolaRectangularHyperbola可编辑资料 - - - 欢

32、迎下载精品名师归纳总结Standard Formx2y 21a 2b 2y 24 axx2y 21a 2b 2xyc 2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结Parametric a cos, b sin at 2 , 2at a sec, b tanct ,c可编辑资料 - - - 欢迎下载精品名师归纳总结Forma cosh, b sinhte1e1可编辑资料 - - - 欢迎下载精品名师归纳总结Eccentricityb2a 2 1e2 e1b 2a 2 e 21e =2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料

33、- - - 欢迎下载精品名师归纳总结Fociae, 0 a, 0ae, 02c,2c可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结aDirectricesxxa eaxx + y =2ce可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结Asymptotesnonenonexyxab0, y0可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结学习资料 名师精选 - - - - - - - - - -第 7 页，共 9 页 - - - - - - - -

34、- -可编辑资料 - - - 欢迎下载精品名师归纳总结资料word 精心总结归纳 - - - - - - - - - - - -Differentiationfxf x可编辑资料 - - - 欢迎下载精品名师归纳总结arcsin xarccos x11x 211x 2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结arctan x11x2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结sinh x cosh xcoshx sinh x可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结tanh xsech2 x可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结arsinhx11x2可编辑资料 - - - 欢迎下载精品名师归纳总结可编辑资料 - - - 欢迎下载精品名师归纳总结arcosh x