Transcription of Formulae for A‑level Mathematics
1 Formulae for A level Mathematics AS Mathematics (7356)A level Mathematics (7357) First issued August 2017 For the new specifications for first teaching from September booklet of Formulae is required for all AS and A level Mathematics is a larger booklet of Formulae and statistical tables for all AS and A level Further Mathematics Bros/E7 MFB82 Further copies of this booklet are available from:Telephone: 0844 209 6614 Fax: 01483 452819 or download from the AQA website Copyright 2017 AQA and its licensors. All rights retains the copyright on all its publications.
2 However, registered centres of AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the and published by Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX3 Contents PagePure Mathematics 4 Mechanics 6 Probability and statistics 64 Pure mathematicsBinomial series()abanabnabnrabnnnnnrr+=+ + +.
3 + +..+ 12122bbnn() where nrnrnrnr == C!!!()()()()()() +=++ +..+ .. +..+..< xnxnnxnnnrrxxnnr, Arithmetic seriesSn = 12n (a + l) = 12n [2a + (n 1)d]Geometric seriesSn = arrn()11 S = ar1 for | r | < 1 Trigonometry: small anglesFor small angle , measured in radians:sin cos 1 22tan Trigonometric identitiessin (A B) = sin A cos B cos A sin Bcos (A B) = cos A cos B sin A sin Btan (A B) = tantan1tan tanABAB (A B (k + 12) )5 Differentiationf(x) f (x)tan x sec2 xcosec x cosec x cot xsec x sec x tan xcot x cosec2 xfg()()xx f()g()f()g(g())()xxxxx 2 Differentiation from first principlesf()f()f()0limhxhxxh + = Integration uddvxdx = uv vdduxdx f()df()f()xxxcx=+ln ||f(x) f(x)
4 Dxtan x ln | sec x | + ccot x ln | sin x | + cNumerical solution of equationsThe Newton Raphson iteration for solving f (x) = 0: xn+1 = xn f()f()nnxx Numerical integrationThe trapezium rule: ab y dx 12h{(y0 + yn) + 2(y1 + y2 + .. + yn 1)}, where h = ban 6 MechanicsConstant accelerations = ut + 12at2 s = ut + 12at2s = vt 12at2 s = vt 12at2v = u + at v = u + ats = 12(u + v)t s = 12(u + v)tv2 = u2 + 2asProbability and statisticsProbabilityP(A B) = P(A) + P(B) P(A B)P(A B) = P(A) P(B | A)Standard deviation () xxxxnn = 222 Discrete distributionsDistribution of XP(X = x)MeanVarianceBinomial B(n, p)nx p x(1 p)n xnpnp(1 p)Sampling distributionsFor a random sample of n observations from N( , 2):X n ~ N(0, 1)End of Formulae (MFB8)
