ALEVEL-高等数学2-further-maths

英国Alevel数学教材内容汇总大全英国Alevel数学教材内容汇总大全部门： xxx时间： xxx整理范文，仅供参考，可下载自行编辑英国A-LEVEL教材汇总Core Mathematics1<="" p="">1.Algebra and functions——代数和函数2.Quadratic functions——二次函数3.Equations and inequalities——等式和不等式4.Sketching curves——画图<草图）5.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何6.Sequences and series——数列7.Differentiation——微分8.Integration——积分Core Mathematics2<="" p="">1.Algebra and functions——代数和函数2.The sine and cosine rule——正弦和余弦定理3.Exponentials and logarithm——指数和对数4.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何5.The binomial expansion——二项展开式6.Radian measure and its application——弧度制及其应用7.Geometric sequences and series——等比数列8.Graphs of trigonometric functions——三角函数的图形9.Differentiation——微分Trigonometricidentities and simple equations——三角恒等式和简单的三角等式b5E2RGbCAP11.Integration——积分Core Mathematics3<="" p="">1.Algebra fractions——分式代数2.Functions——函数3.The exponential and log functions——指数函数和对数函数4.Numerical method——数值法5.Transforming graph of functions——函数的图形变换6.Trigonometry——三角Further trigonometric and their applications——高级三角恒等式及其应用p1EanqFDPw8.Differentiation——微分Core Mathematics4<="" p="">1.Partial fractions——部分分式2.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何3.The binomial expansion——二项展开式4.Differentiation——微分5.Vectors——向量6.Integration——积分A-Level：核心数学Core Maths，力学数学，统计数学，决策数学Core Mathematics1<="" p="">1.Algebra and functions——代数和函数2.Quadratic functions——二次函数3.Equations and inequalities——等式和不等式4.Sketching curves——画图<草图）5.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何6.Sequences and series——数列7.Differentiation——微分8.Integration——积分每章内容：Core Mathematics2<="" p="">1.Algebra and functions——代数和函数2.The sine and cosine rule——正弦和余弦定理3.Exponentials and logarithm——指数和对数4.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何5.The binomial expansion——二项展开式6.Radian measure and its application——弧度制及其应用7.Geometric sequences and series——等比数列8.Graphs of trigonometric functions——三角函数的图形9.Differentiation——微分Trigonometricidentities and simple equations——三角恒等式和简单的三角等式DXDiTa9E3d11.Integration——积分每章内容：Core Mathematics3<="" p="">1.Algebra fractions——分式代数2.Functions——函数3.The exponential and log functions——指数函数和对数函数4.Numerical method——数值法5.Transforming graph of functions——函数的图形变换6.Trigonometry——三角Further trigonometric and their applications——高级三角恒等式及其应用RTCrpUDGiT8.Differentiation——微分每章内容：Core Mathematics4<="" p="">1.Partial fractions——部分分式2.Coordinate geometry in the <x，y）plane——平面坐标系中< p="">的坐标几何3.The binomial expansion——二项展开式4.Differentiation——微分5.Vectors——向量6.Integration——积分每章内容：申明：所有资料为本人收集整理，仅限个人学习使用，勿做商业用途。

英国A-LEVEL教材汇总Core Mathematics1（AS/A2）——核心数学11.Algebra and functions——代数和函数2.Quadratic functions——二次函数3.Equations and inequalities——等式和不等式4.Sketching curves——画图（草图）5.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何6.Sequences and series——数列7.Differentiation——微分8.Integration——积分Core Mathematics2（AS/A2）——核心数学21.Algebra and functions——代数和函数2.The sine and cosine rule——正弦和余弦定理3.Exponentials and logarithm——指数和对数4.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何5.The binomial expansion——二项展开式6.Radian measure and its application——弧度制及其应用7.Geometric sequences and series——等比数列8.Graphs of trigonometric functions——三角函数的图形9.Differentiation——微分10.Trigonometric identities and simple equations——三角恒等式和简单的三角等式11.Integration——积分Core Mathematics3（AS/A2）——核心数学31.Algebra fractions——分式代数2.Functions——函数3.The exponential and log functions——指数函数和对数函数4.Numerical method——数值法5.Transforming graph of functions——函数的图形变换6.Trigonometry——三角7.Further trigonometric and their applications——高级三角恒等式及其应用8.Differentiation——微分Core Mathematics4（AS/A2）——核心数学41.Partial fractions——部分分式2.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何3.The binomial expansion——二项展开式4.Differentiation——微分5.Vectors——向量6.Integration——积分A-Level：核心数学Core Maths，力学数学，统计数学，决策数学Core Mathematics1（AS/A2）——核心数学11.Algebra and functions——代数和函数2.Quadratic functions——二次函数3.Equations and inequalities——等式和不等式4.Sketching curves——画图（草图）5.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何6.Sequences and series——数列7.Differentiation——微分8.Integration——积分每章内容：Core Mathematics2（AS/A2）——核心数学21.Algebra and functions——代数和函数2.The sine and cosine rule——正弦和余弦定理3.Exponentials and logarithm——指数和对数4.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何5.The binomial expansion——二项展开式6.Radian measure and its application——弧度制及其应用7.Geometric sequences and series——等比数列8.Graphs of trigonometric functions——三角函数的图形9.Differentiation——微分10.Trigonometric identities and simple equations——三角恒等式和简单的三角等式11.Integration——积分每章内容：1.Algebra fractions——分式代数2.Functions——函数3.The exponential and log functions——指数函数和对数函数4.Numerical method——数值法5.Transforming graph of functions——函数的图形变换6.Trigonometry——三角7.Further trigonometric and their applications——高级三角恒等式及其应用8.Differentiation——微分每章内容：1.Partial fractions——部分分式2.Coordinate geometry in the （x，y）plane——平面坐标系中的坐标几何3.The binomial expansion——二项展开式4.Differentiation——微分5.Vectors——向量6.Integration——积分每章内容：。

alevel数学章节（原创实用版）目录1.A-level 数学简介2.A-level 数学的章节划分3.A-level 数学各章节内容概述4.如何学习 A-level 数学正文【A-level 数学简介】A-level 数学是英国普通中等教育证书考试（A-level）中的一门学科，适用于年龄在 16-18 岁的学生。

A-level 数学作为英国高中教育的重要组成部分，旨在培养学生的逻辑思维、分析问题和解决问题的能力，为学生进入大学继续深造打下坚实的基础。

【A-level 数学的章节划分】A-level 数学分为两个主要部分：纯数学和统计学。

在这两个部分中，又包含了若干个章节。

【纯数学部分】1.代数2.几何3.微积分4.三角函数5.指数与对数6.概率与统计初步【统计学部分】1.数据收集与处理2.概率分布3.抽样与抽样分布4.假设检验5.回归分析与相关【A-level 数学各章节内容概述】1.代数：代数是数学的基础，涉及方程、不等式、函数、向量等概念。

学习代数有助于培养学生的计算能力和解决实际问题的能力。

2.几何：几何主要研究空间中点、线、面的性质和关系。

学习几何有助于培养学生的空间想象力和逻辑思维能力。

3.微积分：微积分包括导数、积分等内容。

学习微积分有助于培养学生的分析问题和解决问题的能力。

4.三角函数：三角函数涉及正弦、余弦、正切等函数的性质和应用。

学习三角函数有助于培养学生的计算能力和解决实际问题的能力。

5.指数与对数：指数与对数是数学中的基本概念，涉及幂运算、对数运算等。

学习指数与对数有助于培养学生的计算能力和理解数学概念的能力。

6.概率与统计初步：概率与统计初步涉及概率的基本概念、概率分布、抽样等。

学习概率与统计初步有助于培养学生的数据分析能力和解决实际问题的能力。

【如何学习 A-level 数学】学习 A-level 数学需要掌握一定的学习方法和策略。

首先，要重视基础知识的学习，加强对代数、几何等基本概念的理解。

alevel数学p2知识点（最新版）目录1.Alevel 数学 P2 的定义与意义2.Alevel 数学 P2 的主要知识点3.Alevel 数学 P2 的难点与解决方法4.Alevel 数学 P2 的学习建议正文【1】Alevel 数学 P2 的定义与意义Alevel 数学 P2 是英国普通中等教育证书考试（A-Level）中的一门课程，主要面向 16-18 岁的学生。

它是 Alevel 数学的第一个部分，通常与 P1 一起教授。

P2 主要涉及纯数学的知识，包括代数、几何、三角函数等。

学习 Alevel 数学 P2 不仅有助于提高学生的数学技能，还能为进入大学学习更高阶的数学课程奠定基础。

【2】Alevel 数学 P2 的主要知识点Alevel 数学 P2 的主要知识点如下：1）代数：二次方程、二次不等式、指数与对数、函数与导数。

2）几何：平面几何、空间几何、几何变换。

3）三角函数：正弦、余弦、正切、反三角函数、三角恒等式。

4）概率与统计：事件与概率、条件概率、离散型随机变量、连续型随机变量、统计量、参数估计、假设检验。

【3】Alevel 数学 P2 的难点与解决方法Alevel 数学 P2 的难点主要体现在以下几个方面：1）复杂的代数运算：学生需要熟练掌握代数运算法则，解决复杂的方程和不等式。

2）几何证明：空间几何中的证明问题需要学生具备严密的逻辑思维和空间想象能力。

3）三角函数的运算与应用：学生需要熟练掌握各种三角函数的性质，解决实际问题。

解决这些难点的方法有：多做练习题，总结规律，加强对数学概念的理解；及时向老师请教，解决自己不能解决的问题；培养良好的学习习惯，提高学习效率。

【4】Alevel 数学 P2 的学习建议学习 Alevel 数学 P2，建议如下：1）打牢基础知识：重视基础知识的学习，加强对数学概念的理解。

2）多做练习：通过大量的练习题来提高自己的解题能力，总结解题规律。

3）及时复习：学习新知识的同时，不要忘记复习旧知识，确保自己的学习效果。

ib further math考纲IB Further Maths考纲涵盖了广泛的数学领域，包括线性代数、微积分、概率与统计、离散数学和复数。

以下是对每个领域的相关参考内容的简要介绍。

1. 线性代数:线性代数是IB Further Maths课程的重要组成部分。

考生需要了解矩阵理论、向量空间和线性变换等概念。

推荐参考书目包括《线性代数与其应用》(Linear Algebra and its Applications)by David Lay和S. André & G. M. Rucker编著的《线性代数导论》(An Introduction to Linear Algebra)。

2. 微积分:微积分是应用于解析几何、物理学和工程等领域的重要数学工具。

复习微积分的基本概念和技巧是考生取得好成绩的关键。

推荐参考书目包括James Stewart编著的《单变量微积分》(Calculus: Early Transcendentals)和Thomas' Calculus由George B. Thomas等编著的《Thomas微积分》(Thomas' Calculus)。

3. 概率与统计:概率与统计是应用于实际问题的重要数学工具。

考生需要了解概率、分布、参数估计等概念，并能应用这些知识解决实际问题。

推荐参考书目包括A. M. Studenmund编著的《应用计量经济学导论》(Using Econometrics: A Practical Guide)和吴筠等编著的《概率统计》(Probability and Statistical Theory)。

4. 离散数学:离散数学涉及离散对象和结构的研究，如集合论、图论和逻辑等。

考生需要了解这些概念并能够应用它们解决问题。

推荐参考书目包括Kenneth H. Rosen编著的《离散数学和应用》(Discrete Mathematics and Its Applications)和Richard Johnsonbaugh和Marcus Schaefer编著的《离散数学》(Discrete Mathematics).5. 复数:复数是数学中的一个重要概念，对于进一步理解和解决问题都具有重要意义。

GCEEdexcel GCE in MathematicsMathematical Formulae and Statistical TablesFor use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations Core Mathematics C1 – C4Further Pure Mathematics FP1 – FP3Mechanics M1 – M5Statistics S1 – S4For use from January 2008UA018598TABLE OF CONTENTSPage4 Core Mathematics C14 Mensuration4 Arithmetic series5 Core Mathematics C25 Cosine rule5 Binomial series5 Logarithms and exponentials5 Geometric series5 Numerical integration6 Core Mathematics C36 Logarithms and exponentials6 Trigonometric identities6 Differentiation7 Core Mathematics C47 Integration8 Further Pure Mathematics FP1 8 Summations8 Numerical solution of equations 8 Coordinate geometry8 Conics8 Matrix transformations9 Further Pure Mathematics FP2 9 Area of sector9 Maclaurin’s and Taylor’s Seri es10 Taylor polynomials11 Further Pure Mathematics FP3 11 Vectors13 Hyperbolics14 Integration14 Arc length15 Surface area of revolution16 Mechanics M116 There are no formulae given for M1 in addition to those candidates are expected to know.16 Mechanics M216 Centres of mass16 Mechanics M316 Motion in a circle16 Centres of mass16 Universal law of gravitation17 Mechanics M417 There are no formulae given for M4 in addition to those candidates are expected to know.17 Mechanics M517 Moments of inertia17 Moments as vectors18 Statistics S118 Probability18 Discrete distributions18 Continuous distributions19 Correlation and regression20 The Normal distribution function21 Percentage points of the Normal distribution22 Statistics S222 Discrete distributions22 Continuous distributions23 Binomial cumulative distribution function28 Poisson cumulative distribution function29 Statistics S329 Expectation algebra29 Sampling distributions29 Correlation and regression29 Non-parametric tests30 Percentage points of the 2 distribution31 Critical values for correlation coefficients32 Random numbers33 Statistics S433 Sampling distributions34 Percentage points of Student’s t distribution35 Percentage points of the F distributionThere are no formulae provided for Decision Mathematics units D1 and D2.The formulae in this booklet have been arranged according to the unit in 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).It may also be the case that candidates sitting Mechanics and Statistics units need to use formulae introduced in appropriate Core Mathematics units, as outlined in the specification.MensurationSurface area of sphere = 4π r 2Area of curved surface of cone = π r ⨯ slant heightArithmetic series u n = a + (n – 1)dS n = 21n (a + l ) = 21n [2a + (n - 1)d ]Candidates sitting C2 may also require those formulae listed under Core Mathematics C1. Cosine rulea 2 =b 2 +c 2 – 2bc cos ABinomial series2 1)(221nr r n n n n n b b a r n b a n b a n a b a ++⎪⎪⎭⎫ ⎝⎛++⎪⎪⎭⎫ ⎝⎛+⎪⎪⎭⎫ ⎝⎛+=+--- (n ∈ ℕ) where )!(!!C r n r n r n r n -==⎪⎪⎭⎫ ⎝⎛ ∈<+⨯⨯⨯+--++⨯-++=+n x x r r n n n x n n nx x rn ,1( 21)1()1( 21)1(1)1(2 ℝ)Logarithms and exponentialsax x b b a log log log =Geometric series u n = ar n - 1S n = rr a n --1)1(S ∞ = ra-1 for ∣r ∣ < 1Numerical integrationThe trapezium rule: ⎜⎠⎛bax y d ≈ 21h {(y 0 + y n ) + 2(y 1 + y 2 + ... + y n – 1)}, where n a b h -=Candidates sitting C3 may also require those formulae listed under Core Mathematics C1 and C2.Logarithms and exponentialsx a x a =ln eTrigonometric identitiesB A B A B A sin cos cos sin )(sin ±=±B A B A B A sin sin cos cos )(cos =±))(( tan tan 1tan tan )(tan 21π+≠±±=±k B A BA BA B A 2cos2sin 2sin sin BA B A B A -+=+ 2sin2cos 2sin sin BA B A B A -+=- 2cos2cos 2cos cos BA B A B A -+=+ 2sin2sin 2cos cos BA B A B A -+-=-Differentiationf(x ) f'(x )tan kx k sec 2 kxsec x sec x tan x cot x –cosec 2 x cosec x–cosec x cot x)g()f(x x))(g()(g )f( )g()(f 2x x x x x '-'Candidates sitting C4 may also require those formulae listed under Core Mathematics C1, C2 and C3.Integration (+ constant )f(x ) ⎜⎠⎛x x d )f(sec 2 kxk1tan kxx tan x sec lnx cotx sin lnx cosec )tan(ln cot cosec ln 21x x x =+- x sec)tan(ln tan sec ln 4121π+=+x x x ⎜⎠⎛⎜⎠⎛-=x x u v uv x xv u d d d d d dFurther Pure Mathematics FP1Candidates sitting FP1 may also require those formulae listed under Core Mathematics C1 and C2.Summations)12)(1(6112++=∑=n n n rnr 224113)1(+=∑=n n rnrNumerical solution of equationsThe Newton-Raphson iteration for solving 0)f(=x : )(f )f(1n n n n x x x x '-=+Coordinate geometryThe perpendicular distance from (h , k ) to 0=++c by ax is22ba c bk ah +++The acute angle between lines with gradients m 1 and m 2 is 21211arctan m m m m +-ConicsUA018598 – Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP1 – Issue 1 – September 20079Matrix transformationsAnticlockwise rotation through θ about O : ⎪⎪⎭⎫⎝⎛-θθθθcos sin sin cosReflection in the line x y )(tan θ=: ⎪⎪⎭⎫ ⎝⎛-θθθθ2cos 2sin 2sin 2cos10UA018598 – Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP2 – Issue 1 – September 2007Candidates sitting FP2 may also require those formulae listed under Further Pure Mathematics FP1 and Core Mathematics C1–C4.Area of a sectorA = ⎜⎠⎛θd 212r (polar coordinates)Complex numbersθθθsin i cos e i +=)sin i (cos )}sin i (cos {θθθθn n r r n n +=+The roots of 1=nz are given by nk z i 2e π=, for 1 , ,2 ,1 ,0-=n kMaclaurin’s and Taylor’s Series)0(f !)0(f !2)0(f )0f()f()(2+++''+'+=r r r x x x x)(f !)( )(f !2)()(f )()f()f()(2+-++''-+'-+=a r a x a a x a a x a x r r)(f ! )(f !2)(f )f()f()(2+++''+'+=+a r x a x a x a x a r rx r x x x x rxall for !!21)ex p(e 2 +++++==)11( )1( 32)1(ln 132≤<-+-+-+-=++x rx x x x x rr x r x x x x x r rall for )!12()1( !5!3sin 1253 ++-+-+-=+x r x x x x r r all for )!2()1( !4!21cos 242 +-+-+-= )11( 12)1( 53arctan 1253≤≤-++-+-+-=+x r x x x x x r r Taylor polynomialserror )(f !2)(f )f()f(2+''+'+=+a h a h a h a)0( )(f !2)(f )f()f(2h a h a h a h a <<+''+'+=+ξξerror )(f !2)()(f )()f()f(2+''-+'-+=a a x a a x a x)( )(f !2)()(f )()f()f(2x a a x a a x a x <<''-+'-+=ξξUA018598 – Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 – Issue 1 – September 200711Candidates sitting FP3 may also require those formulae listed under Further Pure Mathematics FP1, and Core Mathematics C1–C4. VectorsThe resolved part of a in the direction of b is ba.bThe point dividing AB in the ratio μλ: is μλλμ++baVector product: ⎪⎪⎪⎭⎫ ⎝⎛---===⨯122131132332321321ˆ sin b a b a b a b a b a b a b b b a a a k j inb a b a θ)()()(321321321b a c.ac b.c b a.⨯=⨯==⨯c c c b b b a a ac a.b b a.c c b a )()()(-=⨯⨯If A is the point with position vector k j i a 321a a a ++= and the direction vector b is given by k j i b 321b b b ++=, then the straight line through A with direction vector b has cartesian equation)( 332211λ=-=-=-b a z b a y b a xThe plane through A with normal vector k j i n 321n n n ++= has cartesian equationa.n -==+++d d z n y n x n where 0321The plane through non-collinear points A , B and C has vector equationc b a a c a b a r μλμλμλ++--=-+-+=)1()()(The plane through the point with position vector a and parallel to b and c has equationc b a r t s ++=The perpendicular distance of ) , ,(γβα from 0321=+++d z n y n x n is232221321nn n dn n n +++++γβα.12 UA018598 – Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 – Issue 1 – September 2007Hyperbolic functions1sinh cosh 22=-x x x x x cosh sinh 22sinh = x x x 22sinh cosh 2cosh +=)1( 1ln arcosh }{2≥-+=x x x x}{1ln arsinh 2++=x x x)1( 11ln artanh 21<⎪⎭⎫ ⎝⎛-+=x x x x ConicsUA018598 – Edexcel AS/A level Mathematics Formulae List – Issue 1 – September 200713Differentiationf(x )f'(x )x arcsin211x - x arccos211x--x arctan 211x + x sinh x cosh x coshx sinhx tanhx 2sech x arsinh 211x+ x arcosh112-xartanh x211x - Integration (+ constant ; 0>a where relevant )f(x )⎜⎠⎛x x d )f( x sinh x cosh x cosh x sinh x tanhx cosh ln221xa -)( arcsin a x a x <⎪⎭⎫⎝⎛221x a + ⎪⎭⎫ ⎝⎛a x a arctan 1 221a x - )( ln arcosh }{22a x a x x a x >-+=⎪⎭⎫⎝⎛221x a +}{22ln arsinh a x x a x ++=⎪⎭⎫⎝⎛221x a - )( artanh 1ln 21a x a x a x a x a a <⎪⎭⎫⎝⎛=-+ 221a x -ax a x a +-ln 2114 UA018598 – Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 – Issue 1 – September 2007Arc lengthx x y s d d d 12⎜⎠⎛⎪⎭⎫⎝⎛+= (cartesian coordinates)t t y t x s d d d d d 22⎜⎠⎛⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛= (parametric form)Surface area of revolution2d 2x S y s t ππ⎛⎜⎜⎜⎠==⎰BLANK PAGETURN OVER FOR MECHANICS & STATISTICS FORMULAEUA018598 – Edexcel AS/A level Mathematics Formulae List – Issue 1 – September 2007 1516 UA018598 – Edexcel AS/A level Mathematics Formulae List: Mechanics M1–M3 – Issue 1 – September 2007There are no formulae given for M1 in addition to those candidates are expected to know.Candidates sitting M1 may also require those formulae listed under Core Mathematics C1.Mechanics M2Candidates sitting M2 may also require those formulae listed under Core Mathematics C1, C2 and C3.Centres of mass For uniform bodies:Triangular lamina: 32 along median from vertex Circular arc, radius r , angle at centre 2α :ααsin r from centreSector of circle, radius r , angle at centre 2α : αα3sin 2r from centreMechanics M3Candidates sitting M3 may also require those formulae listed under Mechanics M2, and also those formulae listed under Core Mathematics C1–C4.Motion in a circleTransverse velocity: θr v = Transverse acceleration: θ r v= Radial acceleration: rvr 22-=-θCentres of mass For uniform bodies:Solid hemisphere, radius r : r 83from centre Hemispherical shell, radius r : r 21 from centre Solid cone or pyramid of height h : h 41 above the base on the line from centre of base to vertex Conical shell of height h : h 31 above the base on the line from centre of base to vertex Universal law of gravitation221Force d m Gm =UA018598 – Edexcel AS/A level Mathematics Formulae List: Mechanics M4–M5 – Issue 1 – September 200717There are no formulae given for M4 in addition to those candidates are expected to know.Candidates sitting M4 may also require those formulae listed under Mechanics M2 and M3, and also those formulae listed under Core Mathematics C1–C4 and Further Pure Mathematics FP1.Mechanics M5Candidates sitting M5 may also require those formulae listed under Mechanics M2 and M3, and also those formulae listed under Core Mathematics C1–C4 and Further Pure Mathematics FP1.Moments of inertiaFor uniform bodies of mass m :Thin rod, length 2l , about perpendicular axis through centre: 231ml Rectangular lamina about axis in plane bisecting edges of length 2l : 231ml Thin rod, length 2l , about perpendicular axis through end: 234ml Rectangular lamina about edge perpendicular to edges of length 2l : 234ml Rectangular lamina, sides 2a and 2b , about perpendicular axis through centre: )(2231b a m + Hoop or cylindrical shell of radius r about axis through centre: 2mrHoop of radius r about a diameter: 221mr Disc or solid cylinder of radius r about axis through centre: 221mr Disc of radius r about a diameter: 241mr Solid sphere, radius r , about diameter: 252mr Spherical shell of radius r about a diameter: 232mrParallel axes theorem: 2)(AG m I I G A +=Perpendicular axes theorem: y x z I I I += (for a lamina in the x -y plane) Moments as vectorsThe moment about O of F acting at r is F r ⨯18 UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S1 – Issue 1 – September 2007Statistics S1Probability)P()P()P()P(B A B A B A ⋂-+=⋃ )|P()P()P(A B A B A =⋂ )P()|P()P()|P()P()|P()|P(A A B A A B A A B B A ''+=Discrete distributionsFor a discrete random variable X taking values i x with probabilities P(X = x i )Expectation (mean): E(X ) = μ = ∑x i P(X = x i )Variance: Var(X ) = σ 2 = ∑(x i – μ )2 P(X = x i ) = ∑2i x P(X = x i ) – μ 2 For a function )g(X : E(g(X )) = ∑g(x i ) P(X = x i )Continuous distributionsStandard continuous distribution:Correlation and regressionFor a set of n pairs of values ) ,(i i y xn x x x x S i i i xx 222)()(∑-∑=-∑= ny y y y S i ii yy 222)()(∑-∑=-∑=ny x y x y y x x S i i i i i i xy ))(())((∑∑-∑=--∑=The product moment correlation coefficient is⎪⎪⎭⎫⎝⎛∑-∑⎪⎪⎭⎫ ⎝⎛∑-∑∑∑-∑=-∑-∑--∑==n y y n x x n y x y x y y x x y y x x S S S r i i i i i i i i i i i i yyxx xy 222222)( )())(()()())((}}{{The regression coefficient of y on x is 2)())((x x y y x x S S b i i i xxxy -∑--∑==Least squares regression line of y on x is bx a y += where x b y a -=THE NORMAL DISTRIBUTION FUNCTIONThe function tabulated below is Φ(z ), defined as Φ(z ) = t e zt d 21221⎜⎠⎛∞--π.PERCENTAGE POINTS OF THE NORMAL DISTRIBUTIONThe values z in the table are those which a random variable Z ~N(0, 1) exceeds with probability p; that is, P(Z > z) = 1 -Φ(z) = p.Statistics S2Candidates sitting S2 may also require those formulae listed under Statistics S1, and also those listed under Core Mathematics C1 and C2.Discrete distributionsStandard discrete distributions:Continuous distributionsFor a continuous random variable X having probability density function fExpectation (mean): ⎰==x x x X d )f()E(μVariance: ⎰⎰-=-==2222d )f(d )f()()Var(μμσx x x x x x X For a function )g(X : ⎰=x x x X d )f()g())E(g(Cumulative distribution function: ⎜⎠⎛=≤=∞-000d )(f )P()F(xt t x X xStandard continuous distribution:BINOMIAL CUMULATIVE DISTRIBUTION FUNCTIONThe tabulated value is P(X x), where X has a binomial distribution with index n and parameter p.POISSON CUMULATIVE DISTRIBUTION FUNCTION The tabulated value is P(X ≤x), where X has a Poisson distribution with parameter λ.UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S3 – Issue 1 – September 200729Statistics S3Candidates sitting S3 may also require those formulae listed under Statistics S1 and S2.Expectation algebraFor independent random variables X and Y)E()E()E(Y X XY =, )V ar()V ar()V ar(22Y b X a bY aX +=±Sampling distributionsFor a random sample n X X X , , ,21 of n independent observations from a distribution having mean μ and variance 2σX is an unbiased estimator of μ , with nX 2)V ar(σ=2S is an unbiased estimator of 2σ, where 1)(22--∑=n X X S iFor a random sample of n observations from ) ,N(2σμ)1 ,0N(~/n X σμ-For a random sample of x n observations from ) ,N(2x x σμ and, independently, a random sample of y n observations from ) ,N(2y y σμ)1 ,0N(~)()(22yyxxy x n n Y X σσμμ+---Correlation and regressionSpearman’s rank correlation coefficient is )1(6122-∑-=n n d r sNon-parametric testsGoodness-of-fit test and contingency tables:22~)(νχ∑-ii i E E OPERCENTAGE POINTS OF THE χ2 DISTRIBUTIONThe values in the table are those which a random variable with the χ2 distribution on νdegrees of freedom exceeds with the probability shown.30 UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S3 – Issue 1 – September 2007CRITICAL VALUES FOR CORRELATION COEFFICIENTSThese tables concern tests of the hypothesis that a population correlation coefficient is 0. The values in the tables are the minimum values which need to be reached by a sample correlation coefficient in order to be significant at the level shown, on a one-tailed test.UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S3 – Issue 1 – September 2007 31RANDOM NUMBERS86 13 84 10 07 30 39 05 97 96 88 07 37 26 04 89 13 48 19 2060 78 48 12 99 47 09 46 91 33 17 21 03 94 79 00 08 50 40 1678 48 06 37 82 26 01 06 64 65 94 41 17 26 74 66 61 93 24 9780 56 90 79 66 94 18 40 97 79 93 20 41 51 25 04 20 71 76 0499 09 39 25 66 31 70 56 30 15 52 17 87 55 31 11 10 68 98 2356 32 32 72 91 65 97 36 56 61 12 79 95 17 57 16 53 58 96 3666 02 49 93 97 44 99 15 56 86 80 57 11 78 40 23 58 40 86 1431 77 53 94 05 93 56 14 71 23 60 46 05 33 23 72 93 10 81 2398 79 72 43 14 76 54 77 66 29 84 09 88 56 75 86 41 67 04 4250 97 92 15 10 01 57 01 87 33 73 17 70 18 40 21 24 20 66 6290 51 94 50 12 48 88 95 09 34 09 30 22 27 25 56 40 76 01 5931 99 52 24 13 43 27 88 11 39 41 65 00 84 13 06 31 79 74 9722 96 23 34 46 12 67 11 48 06 99 24 14 83 78 37 65 73 39 4706 84 55 41 27 06 74 59 14 29 20 14 45 75 31 16 05 41 22 9608 64 89 30 25 25 71 35 33 31 04 56 12 67 03 74 07 16 49 3286 87 62 43 15 11 76 49 79 13 78 80 93 89 09 57 07 14 40 7494 44 97 13 77 04 35 02 12 76 60 91 93 40 81 06 85 85 72 8463 25 55 14 66 47 99 90 02 90 83 43 16 01 19 69 11 78 87 1611 22 83 98 15 21 18 57 53 42 91 91 26 52 89 13 86 00 47 6101 70 10 83 94 71 13 67 11 12 36 54 53 32 90 43 79 01 95 15 32 UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S3 – Issue 1 – September 2007UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S4 – Issue 1 – September 200733Statistics S4Candidates sitting S4 may also require those formulae listed under Statistics S1, S2 and S3.Sampling distributionsFor a random sample of n observations from ) ,N(2σμ2122~)1(--n S n χσ 1~/--n t nS X μ(also valid in matched-pairs situations)For a random sample of x n observations from ) ,N(2x x σμ and, independently, a random sample of y n observations from ) ,N(2y y σμ1,12222~//--y n x nyy xx F S S σσIf 222σσσ==y x (unknown) then22~11)()(-+⎪⎪⎭⎫ ⎝⎛+---yn x ny x py x t n n S Y X μμ where 2)1()1(222-+-+-=y x yy x x p n n S n S n SPERC ENTAGE POINTS OF STUDENT’S t DISTRIBUTIONThe values in the table are those which a random variable with Student’s t distribution on ν degrees of freedom exceeds with the probability shown.34 UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S4 – Issue 1 – September 2007PERCENTAGE POINTS OF THE F DISTRIBUTIONThe values in the table are those which a random variable with the F distribution on ν1and ν2 degrees of freedom exceeds with probability 0.05 or 0.01.If an upper percentage point of the F distribution on ν1 and ν2 degrees of freedom is f , then the corresponding lower percentage point of the F distribution on ν2 and ν1 degrees of freedom is 1/ f . UA018598 – Edexcel AS/A level Mathematics Formulae List: Statistics S4 – Issue 1 – September 2007 35BLANK PAGEFurther copies of this publication are available fromEdexcel Publications, Adamsway, Mansfield, Notts, NG18 4FNTelephone 01623 467467Fax 01623 450481E-mail:*****************************Publication Code UA018598For more information on Edexcel qualifications please contactCustomer Response Centre on 0870 240 9800or or visit our website: London Qualifications Limited, trading as Edexcel. Registered in England and Wales No. 4496750 Registered Office: 190 High Holborn, London WC1V 7BH。

alevel数学范围【1】A Level数学简介A Level数学是英国高中教育体系中的一部分，针对16-18岁的学生开设。

该课程旨在培养学生的数学思维能力、问题解决能力和批判性思维，为学生日后的学术和职业生涯奠定基础。

【2】A Level数学范围概述A Level数学分为两个部分：AS数学和A2数学。

AS数学主要包括五个模块，分别是：核心数学、概率与统计、进阶数学、决策数学和应用数学。

A2数学则在AS基础上进一步拓展，包括六个模块：核心数学2、概率与统计2、进阶数学2、决策数学2、应用数学2和选修模块。

【3】各个模块的详细内容1.核心数学：包括代数、几何、三角函数、微积分等基本数学知识。

2.概率与统计：涉及概率分布、统计量、假设检验、线性回归等统计方法。

3.进阶数学：涵盖微积分、线性代数、微分方程、数值计算等高级数学内容。

4.决策数学：包括线性规划、图论、网络流等应用数学方法。

5.应用数学：涉及物理、工程、经济等领域的实际问题，如动力学、电磁学、经济学模型等。

6.选修模块：包括计算机科学、数据结构与算法、数学建模等方向。

【4】考试评估与评分标准A Level数学考试分为paper 1和paper 2，分别测试学生的核心数学和进阶数学能力。

考试形式为选择题和解答题，答对得分，答错或不答不得分。

评分标准根据题目的难度和学生的表现而定，满分分别为90分和150分。

【5】学习建议与策略1.扎实掌握基础知识，为进阶学习打下基础。

2.勤于练习，尤其是解答题，提高解题能力和速度。

3.学会总结归纳，整理笔记，形成自己的知识体系。

4.关注历年真题，熟悉考试题型和难度。

5.寻求专业指导，及时解决学习中遇到的问题。

alevel数学知识点
A Level数学是高中学生在英国的一门高级数学课程，涵盖了广泛的数学知识点。

以下是一些重要的A Level数学知识点：
1.代数：
-多项式和有理函数
-指数和对数函数
-三角函数和三角恒等式
-向量和矩阵运算
-数列和等差数列
2.几何：
-平面和空间几何
-直线和圆的性质
-三角形、四边形和多边形的性质
-三维几何和立体几何
-平移、旋转和放缩
3.概率与统计：
-概率计算和概率分布
-结合概率的问题
-统计数据的收集和整理
-统计指标的计算和应用
-正态分布和假设检验4.微积分：
-函数的导数和求导法则
-函数的积分和积分法则
-微分方程的解法
-曲线绘制和区域计算
-极限和无穷级数
5.数字与分析：
-算法和数值计算方法
-复数和复数函数
-多元函数和偏导数
-特殊函数和级数
-微分方程的数值解法6.三角学：
-扇形和弧的性质
-三角函数之间的关系
-三角方程和三角恒等式
-三角函数的图像和变换
-微分和积分的三角学应用
这些知识点构成了A Level数学课程的核心内容。

学生需要熟练掌握
这些知识，并能够应用于实际问题的解决过程中。

在A Level数学考试中，学生将面对多种题型，包括选择题、填空题、解答题和证明题。

考试注重学生对于数学知识和解题技巧的理解和运用能力。

A Level数学的学习不仅仅是为了考试，更是为了培养学生的逻辑思
维和问题解决能力。

这些数学知识点将对学生今后的学业和职业发展产生
积极的影响。