[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207792-en":3,"doc-seo-207792-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207792,1099525198933,"Terk","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","A-level Mathematics - Formulae Booklet - v1.2","Formulae for A-level Mathematics (7357) provide a required reference for exam preparation under the new specifications first taught from September 2017. The booklet compiles essential results across pure mathematics, mechanics, and probability and statistics, including binomial and arithmetic/geometric series, trigonometry for small angles and identities, differentiation and integration rules, numerical methods, constant-acceleration mechanics equations, and key probability expressions such as union/intersection and conditional probability, plus standard deviation and sampling distribution forms.","[www.mymathscloud.com](www.mymathscloud.com)  \nFormulae for A‑level Mathematics  \nAS Mathematics (7356)  \nA‑level Mathematics (7357)  \nv1 .2 First issued August 2017  \nFor the new specifications for first teaching from September 2017.  \nThis booklet of formulae is required for all AS and A‑level Mathematics exams.  \nThere is a larger booklet of formulae and statistical tables for all AS and A‑level Further Mathematics exams.  \nPage Bros/E7 MFB8  \n2  \n[www.mymathscloud.com](www.mymathscloud.com)  \nFurther copies of this booklet are available from: Telephone: 0844 209 6614 Fax: 01483 452819 or download [from the AQA website www.aqa.org.uk](from the AQA website www.aqa.org.uk)  \n[Copyright](Copyright) © 2017 AQA and its licensors. All rights reserved.  \nCopyright  \nAQA 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 centre.  \nSet and published by AQA.  \nAQA 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 6EX  \n3  \nContents  \nPage  \n[www.mymathscloud.com](www.mymathscloud.com)  \nPure mathematics 4  \nMechanics 6  \nProbability and statistics 6  \n4  \nPure mathematics  \nBinomial series  \n(a + b)n = an + 􀀝􀀜􀀛 n1􀀚􀀙􀀘 an−1b + 􀀝􀀜􀀛 n2􀀚􀀙􀀘 an−2b2 + … + 􀀛􀀝􀀜nr􀀚􀀙􀀘 an−rbr + … + bn (n ∈ 􀁠)  \n[www.mymathscloud.com](www.mymathscloud.com)  \nwhere 􀀝n􀀚 n 􀀛􀀜r􀀙􀀘 = Cr  \nn!  \n=  \nr!(n − r)!  \n(1 + x)n = 1 + nx +  \nn(n − 1) 1.2  \n2  \nx +   +  \nn(n − 1)   (n − r + 1)  \n1.2   r  \nxr + … ( x \u003C 1, n ∈ 􀁟)  \nArithmetic series  \nSn = 12 n(a + l) = 12 n[2a + (n − 1)d]  \nGeometric series  \na(1 − rn)  \nS = ~~ ~~  \nn 1 − r  \nS∞ = 1~~ ~~~~ ~~r for | r | \u003C 1  \nTrigonometry: small angles  \nFor small angle θ , measured in radians: sin θ ≈ θ  \ncos θ ≈ 1 − θ22  \ntan θ ≈ θ  \nTrigonometric identities  \nsin (A ± B) = sinAcosB ± cosAsin B  \ncos (A ± B) = cosA cos B  sinAsinB  \n tanA ± tan B  1  \ntan (A ± B) = (A ± B ≠ (k + ~~ ~~ )π)  \n1 􀁂 tan AtanB 2  \n5  \nDifferentiation  \nf(x) f ′(x)  \ntan x sec2 x  \n[www.mymathscloud.com](www.mymathscloud.com)  \ncosec x  \nsec x  \ncotx  \nf (x)  \ng (x)  \n−cosec x cotx  \nsec x tan x  \n−cosec2 x  \nf􀀟(x)g(x) − f(x)g􀀟(x)(g (x))2  \nDifferentiation from first principles  \nf􀀟(x) = lim f(x + h) − f(x)  \nh→0 h  \nIntegration  \n∫ u dvdx dx = uv − ∫ v dudx dx ∫ ~~ ~~ff􀀟((xx)) dx = ln |f(x) | + cf(x) ∫ f(x) dx  \ntan x ln |sec x| + c  \ncotx ln |sin x| + c  \nNumerical solution of equations  \nThe Newton‑Raphson iteration for solving f (x) = 0 : xn+1 = xn − ff~~􀀟~~((xxnn))  \nNumerical integration  \nThe trapezium rule: ∫bay dx ≈ 12 h{(y 0 + yn) + 2(y 1 + y 2 + … + yn−1)} , where h = b~~ ~~−n~~ ~~a  \n6  \nMechanics  \nConstant acceleration  \n[www.mymathscloud.com](www.mymathscloud.com)  \ns = ut + 12 at2  \ns = vt − 12 at2  \nv = u + at  \ns = 12 (u + v)t  \ns = ut + 12 at2  \ns = vt − 12 at2 v = u + at  \ns = 12 ( u + v)t  \nv2 = u2 + 2as  \nProbability and statistics Probability  \nP(A ∪ B) = P(A) + P(B) − P(A ∩ B) P(A ∩ B) = P(A) × P(B|A)  \nStandard deviation  \nDiscrete distributions  \n\n| Distribution of X | P(X = x) | Mean | Variance |\n| --- | --- | --- | --- |\n| Binomial B(n, p) | 􀀝n􀀚\u003Cbr>􀀛􀀜x􀀙􀀘px(1 − p)n−x | np | np(1 − p) |\n\nSampling distributions  \nFor a random sample of n observations from N(μ , σ 2) :  \nX~~ ~~~~ ~~μ ~ N(0, 1)  \nn  \nEnd of formulae  \n[www.mymathscloud.com](www.mymathscloud.com)  \n[www.mymathscloud.com](www.mymathscloud.com)  \n(MFB8)","cbCaifDXzg7PPTnL","https://ap.wps.com/l/cbCaifDXzg7PPTnL","pdf",798555,1,8,"English","en",105,"# Contents\n## Pure mathematics\n## Mechanics\n## Probability and statistics","[{\"question\":\"What exams require this A-level Mathematics formulae booklet?\",\"answer\":\"The booklet is required for all AS and A-level Mathematics exams.\"},{\"question\":\"What main topics are included in the formulae?\",\"answer\":\"It covers pure mathematics, mechanics, and probability and statistics, ending with numerical solution and integration essentials.\"},{\"question\":\"What is the stated version and issue information for this booklet?\",\"answer\":\"The booklet states v1.2 and notes first issued August 2017, for new specifications first teaching from September 2017.\"}]","A-level Mathematics - 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