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. 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).
2 Our registered address is AQA, Devas Street, Manchester M15 6EX3 Contents PagePure Mathematics 4 Mechanics 6 Probability and statistics 64 Pure mathematicsBinomial series()abanabnabnrabnnnnnrr+=+ + +..+ +..+ 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) dxtan x ln | sec x | + ccot x ln | sin x | + cNumerical solution of equationsThe Newton Raphson iteration for solving f (x) = 0.
3 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)
