最新ALEVEL-高等数学2-further-maths

英国A-level数学教材内容汇总

A-Leve l数学(Mathe matl cs)由四亍郃分姐成.换业数学・C ore Mathe matlcs h 力学数学t M ech an les Mathemati csx 轨计數H (Stali^tl cs Mathematitsy 决第數学Decision M ath&mati c& □选择学耳数学(Mathematics)^生，際了孩心数学心时Mathemahcs：^必修的基础数学之尔学生还需^据自己将来的犬学报读若业选择茸中T磯学『力Mechanics Mathematics},统计数学:Statistics f.fathemstics}.决董数学Decision Mathematics]・50将采读工程删]字主.可追力学数学谢xhanlcs);读社会科学觀金融经桥类的.可选:比计數字(Slatistlcs)：僂计算机嗽件类的.町选: 决策数韋Decision Maltieinalics^Core Mathematicsl (AS/A2) ------ 核心数学11. Algebra and fun ctio ns --- 代数和函数2. Quadratic functions ----- 二次函数3. Equati ons and in equalities --- 等式和不等式4. Sketchi ng 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. Seque nces and series——数歹U7. Differe ntiation ------ 微分8. In tegrati on --- 积分Core Mathematics2 (AS/A2) ----- 核心数学21. Algebra and fun ctio ns --- 代数和函数2. The sine and cos ine rule ---- 正弦和余弦定理3. Expo nen tials 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 bi no mial expa nsion --- 二项展开式6. Radia n measure and its applicati on --- 弧度制及其应用7. Geometric seque nces and series ---- 等比数歹U8. Graphs of trig ono metric functions ----- 三角函数的图形9. Differe ntiation ------ 微分10. Trigonometric identities and simple equations ------ 三角恒等式和简单的三角等式11. I ntegration ---- 积分Core Mathematics3 (AS/A2) ----- 核心数学31. Algebra fractio ns ------ 分式代数2. Functions ------ 函数3. The expo nen tial and log fun ctio ns --- 指数函数和对数函数4. Numerical method ----- 数值法5. Tran sform ing graph of functions ---- 函数的图形变换6. Trigon ometry ------- 三角7. Further trig ono metric and their applicati ons ---- 高级三角恒等式及其应用8. Differe ntiation ------ 微分Core Mathematics4 (AS/A2) ----- 核心数学41. Partial fractio ns ---- 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 bi no mial expa nsion --- 二项展开式4. Differe ntiation ------ 微分5. Vectors ----- 向量6. In tegrati on --- 积分A-Level :核心数学 Core Maths ，力学数学，统计数学，决策数学 1 2 3 4 5 6 7oio14 14 1520 24 252b3S丽48b4Core Mathematics1 (AS/A2 ) ----- 核心数学 1 8. In tegrati on ------ 积分每章内容：SketclSketching < \4.1 4.2 4.3 4.44.5Quadratic functions 2A2.2 2.3 2.4 2.5 2.6 1 Algebra and futictlons1.1 1.2 L3 1用 IS L6 L7 L8 Summary of key poinisPlotting the s^phs of Solvingquadratic eqi 】“ 沪巧 Completingthe: Solving quddratiuSolving quadrate t ions by “Sketching Z> JSummary of kfy 尸為Equations 匚 M Solving sinSolving simultaneob.Using substISolving linGi 『 in 何亦It 華& Solving quadratic^^^ii^sj.jtions by elimination 屈tion* by substitutinn f equation Is linear and the other is quadraticSimplifying an expression by collecting like termsThe laws Qf indicesExpanding an expression Factorhing an expressionFactorising a quadr^k expressionThv las\s of indices for dll rational exponents The use and nianipulation of it rdsRationalising the iknonnridtor of a fraction ivhen 才二dw: XCxsE by ractor i sa ti映>；肯『 c equtijLArby comgTfctjng th 」square .' 'J u iht^m uh Quadratic formulae ； ^ncc^is liiKar rq 3.13.2 33 3J 3.5Suiiunary of 匕叮心疋试he 护ph$ of cubic functions Interpr^lW^yaphs nf cubk fuiKtioiuSketch inutile reciprocal function JK ■ttivinicr sect ion points of o[ functions to solv< equations of the triinsfbr mat ions f(x + ⑷ dnd 冃工-川舉effect of the transforiiiations fiux) and'Fftrfotming transformations on the sketches of curves詁ry of key pointsAlgebra and fun ctio ns ----- 代数和函数 Quadratic functions ----- 二次函数Equati ons and in equalities --- 等式和不等式 Sketchi ng curves --- 画图(草图)Coordinate geometry in the (x , y ) plane -------- 平面坐标系中的坐标几何 Seque nces and series ——数列Differe ntiation ------ 微分5 Coordinate geonwtry in the (x9 y) plane 6S5.1 The equation of a straight line in the form y = nix + c or ax + 如 + c = 0 655.2 The gradient of a straight line 605.3 The equation of a straight line of the form y - y严ifi(x - 心) 7&5.4 The formula for finding the equation of a straight line5.5 The conditions for two straight lines to be parallel or perpendicular ' 75Summary of key points6 Sequences and series6.1 Introduction to sequences6.2 The nth term of a sequence 0 836.3 Sequences generated by a recurrence relationship i \ // ()856.4 Arithmetic sequences 二886.5 Arithmetic series \C/^ \ °°6.6 The sum to n of an arithmetic series 936.7 Using X notation 」97Summary of key points ' 〃丿) 101 7 Differentiation (//. 1027」The derivative of f(x) as the thiCpn^kto tft^ graph y = f(x) 102105109113114115116117121122122124125126128130Core Mathematics2 (AS/A2 ) 核心数学 21. Algebra and fun ctio ns ---- 代数和函数2. The sine and cos ine rule ---- 正弦和余弦定理3. Expo nen tials 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 bi no mial expa nsion --- 二项展开式6. Radia n measure and its applicati on --- 弧度制及其应用7. Geometric seque nces and series --- 等比数歹 U8. Graphs of trig ono metric functions ---- 三角函数的图形9. Differe ntiation ------ 微分 10. Trigonometric identities and simple equations ------ 三角恒等式和简单的三角等式 11. I ntegration ---- 积分每章内容： Aigcbrj dEid luiKtions 1J1.2 13 1.4 Simplifying algebraic fractions by division Dividing apolynomial by (x i p)Factorising a polynomial using the Factor TheoremUsing the Remainder Theorem Summary of k (?y pointsThe sint ： and cosine ruleUsing the sine rule to find missing sides Using the sine nde find unF^wn angles The rule andfinding two w* Using the cosine ruEc ia Fin# Using the cosine rule tc a Using the sine tl «Calculaikng the area 2A 2.2 23 2.4 2.5 2.6 2.7 f or a nih^F Eo切 Mck ssing an^ic^ L . ■ #4RI le 3 nr< !'『庶耳竝遁 Theo re mot^Jy^ngle us)闵jExponctuiah an<r^ogaMh * 3J王2 玉33.43.5 3.6Summary of key pointsCk Coordinate in the (x, y\ plant4.1 The 4.2 The ciiibi Suniinjjy of key polrt 115 10 131718 18 21 23 24 27 30 32 36 37 37 39 4() 41 43 45 4ti 49 49 57 60 68 70 70 72 73 75 79tnsTh<bfunctk 严 Writing ns as a Calculating *丄耳 to Laws of JogarithmS Solvi ng equations 汐 a' - b Changing the mt ni ot A line M 峥曲亡two points on a line 4*3 The equatitJiiif a circle Summiiry of fr r/ points iriomTal expansion s triangle X Combinntions and factorialUsing (：) m the binomial expansion5-4 Expanding (d + bxY r using the binomial expansion Summary of key point*11o Kaaian measure ana its applications Using radians to measure angles The length ofthe arc of a circle The area of a sector of a circle The area of a segment of a circle Geometric sequences Geometric progressions and the nth term Usinggeometric sequences to solve problems The sum of a geometric seriesThe sum to infinity of a geometric series Graphs of trigonometric functionsSine, cosine andtangent(unctionsThe values of trigonomef/ functions in the Exact values and surds f Graphs of sine 0f cos J J 、 Simple transformants oDifferentiation9.1 Increasing s ・9.2 Stationarymaximun 、, minipjum and points of inflexion 9.3Using f^rninjf points to Summar 1 “ 亠 inisTrigonom^/ Jidentitie】0.161 6.2 6.3 6.4Summary of key pointsGeometric sequences and series 7.1 7.2 7.3 7.4 7.5Summary of key points8.1 8.2 8.3 8.4 &5Summary of key poE ；' le equations titles ometrical equations e formsin(nd + a), cos(n0 + a) and tan(n0 + a) = k ig?nometrical equationsSimple trigoSolving simj SolvingeqySolving qudIntegratio11.1 11.2 11.3 Are n.4 94 94 9598 100 103 109 110 110 114 117 118 121 127 141 141 146 149 151 156157 157 159 161 164 169 17710129 129 131135 1406 93 ms10.210.310.4Summary ote integrationa curvea curve that gives negative values n a straight line and a curve rapezium Rule of key points11Core Mathematics3 (AS/A2 ) 核心数学 31 2 3 4 5 6 7 8101Ki.S1 12每章内容:7.5 i'hc racloi tbrinuiai'Alxvbrdit Iriiciions1.1 1.2 1.3I'rigonomctry64 6.2AjipJying a corn^ixiatj Sketching trar^8 Differentiation8.1 B.2 8.3 K 4 8.58.68.71281301311322 E r unctioi-i^2,1 2.2 2-3 2.4 2.5Differentiating ti&ing the chain rule Differ ent tatlng using the product rult Differs nt latL ng using the quotient rukr I if fere nt iat j ng the exponential function Finding the differential of the logarithmic function. _Differentiating 5in x(C~Di fferenti ati ng cos xDifferent is tin^ t^n xDifferenliatkng further trigonometrLcaJ functions[differentiating functians formed by combining frigon 九丁贰#乎卜 cxprtncniiaL logfkritl-imLc and polynomial fLinctior^ ;Simplify algebraic fractions by LUI 1{.C IL UI ^ 口 Multiply dix jdici^frjLiujii->Adding and subtracting algvbrd k frautionsI nx alxvbriiit fr*ittic.jri^ jind tiir rcn )i»iii<lvr Ltit.-c.i^int <ln y 4-cn U>iTi 耳$ [JCX JJ€»TLOkl t k J I fLIIlC'Floriiir^^of <> gr^jj^/ica11 y 「_ ___2 =」cth^Js^lcrlind approximate root 萤 of 陶仟彳Tran 露Fermi 订呂 graf^/of fui^ctiini^5-1 Sketch! tig graphs ot 1^hhockx!^^ 4^u net ion y 一 lf(x)l 5u2 Sketching g^r^phs y = f(lxl) (A p olvin^a mcxluliis mictions to sketch erv«?« 什fih 订花JJ CFIM H 11 台 Mlielling lhe co-ordinates ofgiven H, cosecant 仇 and cotaingEfU 丹 f ^tant 也 cosecant 优 and cotangent 甘 xpressicmsj proving iclentiti^ iind solving equations, usingMapping diingrarns and 耳of opaeiiitions ( JFunc-tions <irid functioii notatk>tiRange, mapping diagrams,, graphs and definitionsJUsing composite functions #*f 丿Finding and using inverse-The exponential and log f u net ion s°3/1 Introdticing exponent ial ・ rtions of lhe I'omCj^ . h 心 3・立 Graphs of exponential旷卞：」^ 前m 扌匸卩存占；逆"二tlxfn 琴，严U^irig 护 ^Eidinwu b©■—主亠二亠亠」一■■Numerical method? ” 4.1 Finding approx if 4.2 U^ing ilerati algebraic iiicthi l ^irs'lw^nnd approximate rt>ots The fijnr/Q?6?/I TieSimplifying £ sec 他 cowO?R and cot Hidcnlitles l 十 lan 2^ = $2H and 1 + cot-^ = cosec 2IJs.iriglmerse trigcinometricai Uinclions and their graphs7 ..Further tngimonietrk identities and theif applies HonsSt/LMrig addition trigoiionietrical lormulac二Using double an^lc trigoiiDmctrical farmulae7?T Solving equdtiom and proving Idcntltiics using doubk iirigle foniiuLie ^^7 4 Usin^ the fonii a cos b sin B lin striving trigonotnetrical piobiennAlgebra fractions ------ 分式代数 Functions ----- 函数Transforming graph of functions -------函数的图形变换 Trigonometry ----- 三角Further trigonometric and their applications ------ 高级三角恒等式及其应用 Differentiation ------ 微分The exponential and log functions Numerical method ------ 数值法指数函数和对数函数Core Mathematics3 (AS/A2 ) 核心数学4Core Mathematics3 (AS/A2 ) 核心数学 51 2 3 4 556 vector37074 11B4 2110ft6J1111126139 SI6264 fi2 «2 AIXJUL L l||\ ULHJK2A3.2 33 Exam style paperFormulae you need to know List of symbols and notation AnswersIndexof two vectors n of a straightAdding and subtracting algehraic fractionsPartial fractions with two linear factors in the denominatorPartial fractions with ttnee or mor^ linear factors in th<? denominator Partial tract ions with repeated linear factors in the denominator Improper fractions into partial fractions1 Partial fractions L:y 1 ■jitrgrating £t^ndard Junctions Integrating using the reverse chain rule Using trigonometric identities in integrationUsing partial fractions to Integrate expressionsUsing standard patterns to integrdle expre^iorr liitvgraUon by subtjtiti.ition Integration by parts Numericalintegration Integration to find ateas and volumes 1Using integration to solvedifferential equations Difkrtntiai rquatjom in context2 Cootdinate geometry in the (x, y) 2」Parametric equations used toParametric equations used to dtiine the uxirdin^tes ot a Using paranictrkequ 訓 UKndinate 驴oimtr* Converting paramet^. jitions into cartesian 世qiut 档才 Finding the itrea ^iidche airve given by pannr 严旷 ^quations3 Fhe binomial ex3,i UMII^ VtXUMl IU UtSUilW J-^JJJLS I ；In 2 or 3 dimensions 二,二二 55Cartesian toniponeidi Gf a \yytor in 2dimensionsCartesian components ol in 3 dimensio%7^； Extending 2 /悸幺？冲results io ]he seal;| The vect*[nUT^clrnjfetraighi line vector 戸理逖石kFx linesJo between two straight Using partial fracti>#w$ Kjtw tiiv ■binamiai expanjy^f \、 Different la Uon4.1 Differentki(I nti ；ons givenpararnetricaifrf/4 2 Diffenyitiating^uationwhich arc implicitO43 Diffett»y^a!ing the function a 1 4.4｛垃 tSftitiibn and rates of change4.5 唏蛙少他rtrntjai equations 5 VecS^ ?<^54,Ve?tor d^fmitipns 4nd vector ^^iiAgrams r 、§,2 Vector arithmetic and the unit vectorThe binomial expulsion a - positive integral index Using the binomidexpand + l^x)"\ j ' 6. In tegrati on ------ 积分每章内容：The bi no mial expa nsion --- 二项展开式 Differe ntiation ------微分 Vectors ----- 向量Partial fractio ns ---- 部分分式 Coordin ate geometry in the ( x , y ) pla ne 平面坐标系中的坐标几何。

alevel数学章节

alevel数学章节摘要：1.A-level 数学简介2.A-level 数学的章节划分3.各章节主要内容概述4.如何学习A-level 数学正文：A-level 数学是英国普通中等教育证书考试（A-level）中的一门重要学科，其地位相当于我国高中阶段的数学课程。

A-level 数学旨在为学生提供扎实的数学基础，培养逻辑思维和解决问题的能力，为后续的大学学习和职业发展奠定基础。

A-level 数学的章节划分为：纯数学、统计学、概率学和机械学。

各个部分包含了不同的章节，具体如下：1.纯数学部分包括：- 代数- 函数- 数据与数据表示- 几何学- 三角学- 微积分- 向量学2.统计学部分包括：- 收集、整理和分析数据- 概率分布- 抽样与统计推断- 回归分析与相关3.概率学部分包括：- 随机事件与概率- 概率分布- 离散型随机变量- 连续型随机变量4.机械学部分包括：- 物理量的测量- 力学- 波动与光学- 电磁学- 核物理与粒子物理学习A-level 数学需要掌握一定的学习方法，以下是一些建议：1.建立良好的数学基础。

学习A-level 数学需要具备一定的数学基础，例如代数、几何和三角函数等。

建议提前预习，以便更好地理解和掌握课程内容。

2.系统学习。

按照教材和大纲的顺序逐步学习，理解每个章节的核心概念和方法，避免跳跃式学习。

3.多做练习题。

数学学习需要多做题，通过练习巩固所学知识，提高解题能力。

可以参考课本、习题集和网络资源，寻找适合自己的练习题。

4.及时复习。

学习新知识的同时，不要忘记复习旧知识。

定期整理学习笔记，归纳总结，形成自己的知识体系。

5.寻求帮助。

遇到问题不要害怕，可以向老师、同学请教，或者在网上寻找相关资源。

积极参加课堂讨论，与同学们共同进步。

总之，A-level 数学是一门涉及广泛、内容丰富的学科。

要想学好这门课程，需要掌握正确的学习方法，勤于练习，不断巩固和拓展知识。

《高等数学II》教学大纲

《高等数学II》课程教学大纲一、课程基本信息课程代码：课程名称：高等数学II英文名称：Higher mathematics II课程类别：公共课学时：64学分：4适用对象: 理工科专业考核方式：考试先修课程：高等数学I二、课程简介《高等数学II》是高等学校理工科专业学生的必修课。

通过本课程的学习，使学生掌握高等数学的基本概念、基本理论和基本运算技能，为学习后续课程和获得进一步的数学知识奠定必要的基础。

通过知识内容的传授，培养学生的运算能力、抽象思维能力、逻辑推理能力、空间想象能力及综合运用所学知识去分析问题和解决问题的能力。

其具体内容包括：空间解析几何与向量代数；多元函数微积分学（多元函数微分学、重积分、曲线积分和曲面积分）；无穷级数。

Higher mathematics II is a compulsory course for students majoring in science and engineering in institutions of higher learning. Through learning of this course, make the students master the basic concepts of higher mathematics and the basic theory and basic computing skills, for learning the follow-up courses and further the mathematics knowledge to lay the necessary foundation. Through the knowledge content of teaching, cultivate students' operation ability, abstract thinking ability, logical reasoning ability, space imagination ability and the integrated use of knowledge to the ability to analyze and solve problems. The specific contents include: spatial analytic geometry and vector algebra; Multifunction calculus (multifunction differential calculus, reintegration, curvilinear integral and surface integral); Infinite series.三、课程性质与教学目的目前，《高等数学II》已成为理工科类及部分经济、管理类专业的主干学科基础课程，是教育部审定的核心课程和硕士研究生入学考试“数学1”和“数学2”的必考科目，对学好其它专业课程意义重大。

alevel数学范围

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数学内容

alevel数学内容
A-level数学是高中阶段的一门重要学科，旨在培养学生的数学思维和解决问题的能力。

它涵盖了广泛的数学概念和技巧，包括代数、几何、微积分、统计学和概率论等内容。

在A-level数学课程中，学生将学习如何应用数学概念来解决实际问题。

代数部分涵盖了方程、函数和不等式等内容，学生需要学会解方程、求解函数的性质以及解决复杂的不等式问题。

几何部分涵盖了平面几何和立体几何，学生需要熟练掌握几何图形的性质和相应的定理。

微积分是A-level数学的核心部分，包括导数和积分的概念和应用。

学生将学习如何求导和积分，以及如何应用微积分解决实际问题。

统计学和概率论也是A-level数学课程的重要内容。

学生将学习如何收集和分析数据，以及如何应用统计学的方法进行数据推断和假设检验。

概率论部分涵盖了概率的概念和计算，学生需要学会计算概率，并应用概率理论解决一系列问题。

除了这些具体的数学概念和技巧，A-level数学还注重培养学生的数学思维和解决问题的能力。

学生将学会观察问题、提出假设、开展推理和验证，并提出合理的解决方案。

他们将学会如何运用数学的方法和技巧来解决实际生活中的各种问题，培养出分析、推理和抽象思维的能力。

总之，A-level数学是一门既实用又有挑战性的学科。

通过学习
A-level数学，学生将不仅获得扎实的数学基础，还能培养出解决问题和思考的能力，为未来的学术研究和职业发展打下坚实的基础。

爱德思alevel数学课程内容

爱德思alevel数学课程内容全文共四篇示例，供读者参考第一篇示例：爱德思A level数学课程分为两个阶段，分别是AS阶段和A2阶段。

学生可以选择修读其中一个阶段或者同时修读两个阶段以获得完整的A level数学资格。

下面将介绍一下该课程各个阶段的具体内容：第一阶段：AS阶段在AS阶段，学生将学习以下几个主要主题：1. Pure Mathematics（纯粹数学）在这个模块中，学生将学习代数、函数、三角学、微积分和向量等基础概念。

他们将掌握解方程、表示函数、求导和积分等基本技能，并学习如何将这些技能应用到不同的数学问题中。

2. Mechanics（力学）这个模块将引导学生学习受力平衡、运动学和动力学等力学概念。

学生将学会如何分析物体在力的作用下的运动规律，并解决与运动和力有关的各种问题。

3. Statistics（统计学）在统计学模块中，学生将学习数据的收集、整理、分析和解释等统计技术。

他们将学会如何利用统计方法对数据进行推断和预测，并了解统计学在现实生活中的应用。

这个模块将扩展学生在AS阶段所学的纯粹数学知识，包括复数、微积分、微分方程和向量空间等高级数学概念。

学生将学会如何运用这些概念解决更加复杂的数学问题。

在决策数学模块中，学生将学习图论、线性规划、网络分析和算法设计等数学技术。

他们将了解如何运用这些技术解决实际生活中的优化和决策问题。

爱德思A level数学课程内容非常丰富多样，涵盖了各个数学领域的基础和高级知识，旨在培养学生的数学思维能力和解决问题的能力。

通过修读该课程，学生将获得坚实的数学基础和高水平的数学技能，为他们未来的学业和职业发展打下坚实的基础。

【字数超过了要求，但尽可能全面地描述了爱德思A level数学课程的内容】。

第二篇示例：爱德思（Edexcel）A Level数学课程是英国最著名的高中数学教育课程之一，为所有对数学感兴趣的学生提供了一个全面的学习平台。

该课程不仅涵盖了基本概念和技能，还提供了深度和广度的数学知识，旨在培养学生的数学思维能力和解决问题的能力。

英国Alevel数学教材内容汇总

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 高数

*2037772342*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certiﬁcate of Education Advanced LevelFURTHER MATHEMATICS9231/21 Paper2May/June20133hours Additional Materials:Answer Booklet/PaperGraph PaperList of Formulae(MF10)READ THESE INSTRUCTIONS FIRSTIf you have been given an Answer Booklet,follow the instructions on the front cover of the Booklet.Write your Centre number,candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a soft pencil for any diagrams or graphs.Do not use staples,paper clips,highlighters,glue or correctionﬂuid.Answer all the questions.Give non-exact numerical answers correct to3signiﬁcantﬁgures,or1decimal place in the case of angles in degrees,unless a different level of accuracy is speciﬁed in the question.Where a numerical value is necessary,take the acceleration due to gravity to be10m s−2.The use of a calculator is expected,where appropriate.Results obtained solely from a graphic calculator,without supporting working or reasoning,will not receive credit.You are reminded of the need for clear presentation in your answers.At the end of the examination,fasten all your work securely together.The number of marks is given in brackets[]at the end of each question or part question.This document consists of5printed pages and3blankpages.JC1306_9231_21/RP©UCLES2013[Turn over1A uniform rod AB,of mass m and length4a,rests with the end A on rough horizontal ground.Thepoint C on AB is such that AC=3a.A light inextensible string has one end attached to the point P which is at a distance5a vertically above A,and the other end attached to C.The rod and the string are in the same vertical plane and the system is in equilibrium with angle ACP equal to90 (see diagram).The coefﬁcient of friction between the rod and the ground is .Show that the least possible value of is2443.[8]2Three uniform small smooth spheres,A,B and C,have equal radii.Their masses are4m,2m and m respectively.They lie in a straight line on a smooth horizontal surface with B between A and C.Initially A is moving towards B with speed u,B is at rest and C is moving in the same direction as Awith speed12u.The coefﬁcient of restitution between any two of the spheres is e.Theﬁrst collisionis between A and B.In this collision sphere A loses three-quarters of its kinetic energy.Show that e=12.[6]Find the speed of B after its collision with C and deduce that there are no further collisions between the spheres.[5]3A particle P of mass m is attached to one end of a light inextensible string of length a.The other end of the string is attached to aﬁxed point O.When P is hanging vertically below O,it is given a horizontal speed u.In the subsequent motion,P moves in a complete circle.When OP makes an angle with the downward vertical,the tension in the string is T.Show thatT=mu2a+mg 3cos −2 . 5Given that the ratio of the maximum value of T to the minimum value of T is3:1,ﬁnd u in terms of a and g.[4] Assuming this value of u,ﬁnd the value of cos when the tension is half of its maximum value.[3]on asameis aﬁxed horizontal axis through C perpendicular to the plane of the ring,is 30+55 ma2.[6]Given that the system performs small oscillations of period2 5agabout this axis,ﬁnd the valueof .[6]5For a random sample of12observations of pairs of values x,y ,the product moment correlation coefﬁcient is−0.456.Test,at the5%signiﬁcance level,whether there is evidence of negative correlation between the variables.[4]6The random variable X has distribution function F given byF x =1−e−0.6x x≥0,0otherwise.Identify the distribution of X and state its mean.[2] Find(i)P X>4 ,[2] (ii)the median of X.[3]7A random sample of80observations of the continuous random variable X was taken and the values are summarised in the following table.Interval2≤x<33≤x<44≤x<55≤x<6Observed frequency362996 It is required to test the goodness ofﬁt of the distribution having probability density function f givenbyf x =3x2≤x<6, 0otherwise.Show that the expected frequency for the interval2≤x<3is40and calculate the remaining expected frequencies.[4] Carry out a goodness ofﬁt test,at the10%signiﬁcance level.[5]8The continuous random variable X has probability density function f given byf x =16x2≤x≤4, 0otherwise.The random variable Y is deﬁned by Y=X3.Show that Y has probability density function g given byg y =118y−138≤y≤64,0otherwise.[6]Find E Y .[3] 9A gardener P claims that a new type of fruit tree produces a higher annual mass of fruit than the type that he has previously grown.The old type of tree produced5.2kg of fruit per tree,on average.A random sample of10trees of the new type is chosen.The masses,x kg,of fruit produced aresummarised as follows.Σx=61.0Σx2=384.0Test,at the5%signiﬁcance level,whether gardener P’s claim is justiﬁed,assuming a normal distribution.[6] Another gardener Q has his own type of fruit tree.The masses,y kg,of fruit produced by a random sample of10trees grown by gardener Q are summarised as follows.Σy=70.0Σy2=500.6Test,at the5%signiﬁcance level,whether the mean mass of fruit produced by gardener Q’s trees is greater than the mean mass of fruit produced by gardener P’s trees.You may assume that both distributions are normal and you should state any additional assumption.[8]10Answer only one of the following two alternatives.EITHERA light elastic string has modulus of elasticity32mg and natural length a.A particle of mass m isattached to one end of the string.The other end of the string is attached to aﬁxed point A.The particle is released from rest at A.Show that when the particle has fallen a distance ka from A,where k>1,its kinetic energy is14mga 10k−3−3k2 . 3Show that the particleﬁrst comes to instantaneous rest at the point B which is at a distance3a vertically below A.[3]Show that the time taken by the particle to travel from A to B is2a+232a3. 8ORThe regression line of y on x,obtained from a random sample ofﬁve pairs of values of x and y,has equationy=x+k,where k is a constant.The following table shows the data.x2334py45842Find the two possible values of p.[8] For the smaller of these two values of p,ﬁnd(i)the product moment correlation coefﬁcient,[3] (ii)the equation of the regression line of x on y.[3]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible.Every reasonable effort has been made by the publisher(UCLES)to trace copyright holders,but if any items requiring clearance have unwittingly been included,the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the Cambridge Assessment Group.Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate(UCLES),which is itself a department of the University of Cambridge.。

alevel数学考试内容

alevel数学考试内容A-level学是一个非常重要的考试，对于想要获得一个扎实的数学基础来准备未来大学学习，或者想要从事数学相关工作的人来说，考取A-level学是非常重要的。

A-level学考试内容丰富多样，它分为数学课程和内容两个部分，考试的主要内容包括以下几点：一、函数（Functions）：学生需要学会如何使用函数，以及对函数进行求导、定义域、单调性和极值等的考察。

二、极限（Limits）：学生需要学会函数的零点、收敛性和极限的计算，以及其他涉及极限的知识。

三、微积分（Calculus）：学生需要学会基本的微积分知识，如求导、定积分、曲线积分和微分方程等。

四、线性代数（Linear Algebra）：学生需要学会矩阵计算、向量空间、行列式、线性变换、线性方程组解法等知识。

五、概率（Probability）：学生需要学会概率理论和概率统计的基本概念，以及条件概率、联合概率和随机变量的基本概念。

六、统计（Statistics）：学生需要学会概率分布、抽样方法、统计非参数检验和统计参数检验等基础知识。

A-level学考试不仅涉及数学理论，还涉及一些实践性的知识，比如，学生需要学会应用矩阵运算、解出参数方程，甚至包括编程的一些知识，如熟悉C、Java、C++等编程语言，来解决一些计算机界面的问题。

总的来说，A-level学考试的内容包括了所有的基础数学知识，以及一些实践性的知识，要想考取优异的成绩，学生不仅要做功课，更要有充足的考前准备，以便能够准确、熟练地回答考官提出的各种问题。

因此，对于参加A-level学考试的学生来说，要想在这次考试中取得优异成绩，必须强烈的坚持学习，好好把握考试的时间，准备考试的内容，努力复习，这样才能够在最后的考试中取得优异的成绩。

alevelm2知识点总结

alevelm2知识点总结1. KinematicsKinematics is the study of motion and its causes, including the displacement, velocity, and acceleration of objects. In A-Level Mathematics M2, students will learn about concepts such as scalar and vector quantities, displacement, velocity-time graphs, and acceleration-time graphs.Scalar and vector quantities: Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include speed and temperature, while examples of vector quantities include displacement and velocity.Displacement: Displacement is the distance and direction of an object’s change in position from its starting point to its ending point. It can be determined using vector notation, which specifies both magnitude and direction.Velocity-time graphs: Velocity-time graphs depict an object’s velocity over a period of time. The gradient of a velocity-time graph represents the acceleration of the object, while the area under the graph shows the total displacement of the object.Acceleration-time graphs: Acceleration-time graphs depict an object’s acceleration over a period of time. The gradient of an acceleration-time graph represents the rate of change of acceleration, while the area under the graph shows the total change in velocity.2. ForcesForces are interactions that cause an object to change its velocity. In A-Level Mathematics M2, students will learn about equilibrium of forces, resolution of forces, and friction. Equilibrium of forces: When the vector sum of all the forces acting on an object is zero, the object is said to be in equilibrium. This means that it is not accelerating and that the forces are balanced.Resolution of forces: Forces can be resolved into components that are perpendicular to each other. By breaking forces down into their horizontal and vertical components, students can analyze their effects more effectively.Friction: Friction is the force that opposes the motion of one surface as it moves over another surface. It can be divided into two types: static friction, which prevents two surfaces from sliding past each other, and kinetic friction, which opposes the relative motion of two surfaces that are sliding past each other.3. MomentsMoments are turning effects produced by forces. In A-Level Mathematics M2, students will learn about the principle of moments, torque, and center of mass.Principle of moments: The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that same point.Torque: Torque is the measure of a force’s tendency to produce rotational motion. It is calculated as the product of the force and the perpendicular distance from the pivot point to the line of action of the force.Center of mass: The center of mass is the point at which the mass of a body may be considered to be concentrated. It is the point at which a single force would act to cause the same motion as the actual forces acting on the body.In conclusion, A-Level Mathematics M2 covers important topics such as kinematics, forces, and moments. Students will gain a deep understanding of these concepts and their applications, allowing them to solve complex problems and analyze real-world scenarios. Mastering these knowledge points is essential for success in A-Level Mathematics and building a strong foundation for further studies in mathematics, physics, and engineering.。

高等数学二的内容介绍

高等数学二的内容介绍High Mathematics II is a critical course in the study of mathematics, building upon the foundational concepts learned in High Mathematics I. It is an essential subject for students majoring in mathematics, physics, engineering, and other related fields. This course delves deeper into topics such as differential equations, multiple integrals, vector calculus, and complex numbers, providing students with a more advanced understanding of mathematical concepts.高等数学二是数学学习中的重要课程，建立在高等数学一所学到的基本概念之上。

对于主修数学、物理、工程等相关专业的学生来说，这是一门必不可少的课程。

这门课程深入探讨了微分方程、多重积分、矢量微积分和复数等主题，为学生提供了对数学概念更加深入的理解。

One of the key topics covered in High Mathematics II is differential equations, which play a significant role in modeling real-world phenomena in various fields such as physics, engineering, and economics. By studying differential equations, students learn how to formulate and solve problems involving rates of change and howsystems evolve over time. This knowledge is crucial for understanding dynamic systems and predicting their future behavior.高等数学二涵盖的一个关键主题是微分方程，微分方程在物理、工程、经济等各个领域中对模拟真实世界现象起着重要作用。

A-level数学教材内容汇总

对于广大Alevel课程的学生来说，数学教学材料是必不可少的。

小编今天在网上搜罗了相关资料进行汇总，希望能帮助到大家。

Core Mathematics1(AS/A2)——核心数学11. Algebra and functions——代数和函数2. 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. Exponential 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. Rad 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. 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. 2. The sine and cosine rule——正弦和余弦定理3. 3. Exponential 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. Rad 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：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——微分每章内容：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——积分上面就是所有Alevel的教学材料汇总，如果想了解更多可以联系相关培训机构进行了解。

alevel高数内容 -回复

alevel高数内容-回复高中数学是一门基础课程，其中包括了高等数学的内容。

在高中阶段，学生们将学习一系列的具体和抽象的数学概念，以及解决各种数学问题的技巧和方法。

其中，A-Level的高等数学内容更加深入和广泛，为学生打下进一步学习数学的基础。

本文将以"高等数学内容"为主题，一步一步回答。

高等数学的内容非常广泛，主要包括微积分、线性代数和微分方程。

这些部分相互关联，构成了数学的核心。

首先，我们将探讨微积分。

微积分是数学的一个重要分支，主要研究函数的极限、连续性、导数和积分等概念。

在微积分中，学生将学习如何计算函数的导数和积分，以及它们的应用。

在学习微积分时，首先要理解函数的极限。

极限是函数在某一点或无穷远处的行为趋势。

学生需要掌握求极限的各种方法和技巧，例如代数运算、利用夹逼准则和洛必达法则等。

接下来，学生将学习函数的连续性。

连续性是指函数在整个定义域内没有突变或断裂。

学生需要了解连续性的定义和性质，并学会通过检查函数的定义域、导数、极限等方式来判断函数的连续性。

而函数的导数是另一个重要的概念。

导数描述了函数在每一点的瞬时变化率。

学生需要学会计算函数的导数，掌握求导的各种法则，例如常见函数的导数公式、链式法则和隐函数求导法等。

此外，学生还需要理解导数的几何意义，如切线和曲率等。

最后，学生将学习函数的积分。

积分是导数的反运算，描述了函数下面的面积或累积效果。

学生需要学会计算函数的不定积分和定积分，理解积分的定义和性质，以及积分的应用，如求面积、体积、弧长和物理问题等。

除了微积分，线性代数也是高等数学的重要部分。

线性代数研究线性方程组、矩阵以及线性变换等内容。

在线性代数中，学生将学习矩阵的运算，如加法、乘法和转置等。

他们还将学习线性方程组的求解方法，如高斯消元法和矩阵代数法等。

此外，学生还将了解向量空间、特征值与特征向量、正交和内积等概念。

最后，微分方程是高等数学的最后一部分。

爱德思高数选课

爱德思高数选课
爱德思A-level数学分为AS和A2两个等级，每个等级又包含基础数学和进阶数学。

其中AS阶段基础数学必考单元为P1和P2，进阶数学必考单元为F1，从M1、S1、D1中任选一个单元进行学习；A2阶段基础数学必考单元为P1、P2、P3、P4，进阶数学有两种组合模式，第一种为F1+F2/F3（二选一）+（M1、M2、M3、S1、S2、S3、D1）（7选4，基础数学已选的单元不能重复选择），第二种为F1+F2+F3+（M1、M2、M3、S1、S2、S3、D1）（7选3，基础数学已选的单元不能重复选择），考够6个单元即可。

爱德思A-level数学的选课方法比较灵活，你可以结合自己的兴趣和擅长的领域进行选择。

如需了解更多A-level数学选课内容，你可以继续向我提问。

alevel的高数知识概要 -回复

alevel的高数知识概要-回复[A-level高数知识概要]高等数学是一门重要的数学课程，它是大学数学的基础。

在A-level数学中，高等数学起到了承上启下的作用，既是高中数学的延伸，也是大学数学的预备。

本文将从基本概念、函数与极限、导数与微分、积分以及微分方程等方面，详细介绍A-level高等数学的知识要点。

第一部分：基本概念在学习高等数学之前，我们首先需要了解基本概念。

数学的基本概念有实数、复数、集合、数列等。

实数包括有理数和无理数两部分，有理数是可以表示成两个整数之比的数，无理数是不能表示成两个整数之比的数，例如根号2。

复数是由实部和虚部构成的数，通常用a+bi的形式表示，其中a是实部，b是虚部。

集合是具有特定性质的事物的总体，数学中有很多集合，例如自然数集、整数集、实数集等。

数列是数的按照一定顺序排列的一个序列，例如等差数列和等比数列。

第二部分：函数与极限函数是数学中的一种重要关系，它将一个集合中的每个元素映射到另一个集合中的唯一元素。

数学中常见的函数有多项式函数、指数函数、对数函数、三角函数等。

极限是函数在某一点或无穷远处的特征值，用来描述函数的趋势和性质。

研究函数极限时，我们需要学习邻域、数列极限以及无穷小量等概念。

邻域是指函数在某一点附近的取值范围，数列极限是指数列中的值随着自变量的变化趋于某个常数，无穷小量是指当变量趋于无穷大或无穷小时，函数值无限趋近于0。

第三部分：导数与微分导数是函数在某一点的变化速率，是描述函数局部行为的重要工具。

学习导数时，我们需要掌握导数的定义、求导法则以及常见函数的导数。

导数的定义是极限的概念，表示函数在某一点的切线斜率。

求导法则是用来求解不同函数导数的公式，包括常数倍、和差、乘积、商数法则以及复合函数法则等。

常见函数的导数是指常见函数的导数表达式，如幂函数、指数函数、对数函数以及三角函数的导数等。

微分是函数局部变化的线性近似。

学习微分时，我们需要了解微分的定义、微分的性质以及微分的应用。