📚 Support Pack 2: Contents | 支持包 2：内容指南
This article provides a comprehensive contents guide to Support Pack 2 for AQA A-Level Mathematics. It is designed to help you navigate the key topics, understand the exam requirements, and focus your revision effectively.
本文为 AQA A-Level 数学 Support Pack 2 提供了一份全面的内容指南。它旨在帮助你梳理核心主题、理解考试要求，并有效聚焦复习重点。
1. Algebraic Manipulation | 代数运算
Support Pack 2 begins with algebraic manipulation, which forms the foundation for nearly all A-Level topics. You must be confident in expanding brackets, factorising expressions, simplifying surds, and working with algebraic fractions.
Support Pack 2 从代数运算开始，这部分构成了几乎所有 A-Level 主题的基础。你必须熟练掌握展开括号、因式分解、化简根式以及处理代数分式。
Expanding products of three or more binomials
展开三个或更多二项式的乘积
Factorising quadratics, cubics, and higher-degree polynomials
因式分解二次、三次及更高次多项式
Simplifying rational expressions using common denominators
使用公分母化简有理表达式
Example: (x+2)(x−3)(x+5) = x³ + 4x² − 11x − 30
2. Functions and Graphs | 函数与图像
The concept of a function is central to A-Level mathematics. You should understand domain, range, composite functions, and inverse functions, as well as how transformations affect graphs.
函数的概念是 A-Level 数学的核心。你应该理解定义域、值域、复合函数和反函数，以及变换如何影响图像。
Notation: f(x), f⁻¹(x), fg(x)
记号：f(x)、f⁻¹(x)、fg(x)
Translations: y = f(x) + a and y = f(x − a)
平移：y = f(x) + a 与 y = f(x − a)
Reflections: y = −f(x) and y = f(−x)
反射：y = −f(x) 与 y = f(−x)
Stretches: y = af(x) and y = f(ax)
伸缩：y = af(x) 与 y = f(ax)
You should also be able to sketch the modulus function |x| and solve equations involving it.
你还应该能够绘制绝对值函数 |x| 的图像，并求解包含它的方程。
3. Coordinate Geometry | 坐标几何
This section covers straight lines and circles. You need to recall the equation of a straight line, the midpoint formula, the distance formula, and the conditions for parallel and perpendicular lines.
本节涵盖直线和圆。你需要回忆直线方程、中点公式、距离公式，以及平行与垂直的条件。
| Formula | Equation |
| Gradient | m = (y₂ − y₁)/(x₂ − x₁) |
| Midpoint | ((x₁+x₂)/2, (y₁+y₂)/2) |
| Circle equation | (x−a)² + (y−b)² = r² |
For circles, you must know how to find the centre and radius, and how to determine whether a line is a tangent, a secant, or neither, using the discriminant.
对于圆，你必须知道如何求圆心和半径，以及如何利用判别式判断一条直线是切线、割线还是既非切线也非割线。
4. Sequences and Series | 数列与级数
Arithmetic and geometric sequences often appear in both pure and applied contexts. You need to derive and use the nth term and sum formulas.
等差与等比数列经常出现在纯数学和应用数学中。你需要推导并运用通项与求和公式。
Arithmetic: uₙ = a + (n−1)d, Sₙ = (n/2)(2a + (n−1)d)
Geometric: uₙ = arⁿ⁻¹, Sₙ = a(1−rⁿ)/(1−r), S∞ = a/(1−r) for |r| < 1
You should also be familiar with Sigma notation Σ and the binomial expansion for positive integer powers.
你还应熟悉西格玛记号 Σ 以及正整数幂的二项展开。
5. Trigonometry | 三角学
Trigonometric ratios, identities, and equations are essential. You must know the exact values for common angles, the sine and cosine rules, and the area of a triangle formula.
三角比、恒等式和方程是必考内容。你必须知道常见角度的精确值、正弦定理和余弦定理，以及三角形面积公式。
Exact values: sin30° = 1/2, cos60° = 1/2, tan45° = 1
精确值：sin30° = 1/2，cos60° = 1/2，tan45° = 1
Identities: sin²θ + cos²θ = 1; tanθ = sinθ/cosθ
恒等式：sin²θ + cos²θ = 1；tanθ = sinθ/cosθ
Radians and degrees conversion
弧度与角度换算
Solving trigonometric equations may require using inverse functions and considering the domain in radians.
解三角方程可能需要使用反函数，并以弧度为单位考虑定义域。
6. Exponentials and Logarithms | 指数与对数
Exponential growth and decay models rely on the function eˣ and the natural logarithm ln x. You need to understand the laws of logarithms and how to solve exponential equations.
指数增长与衰减模型依赖于函数 eˣ 和自然对数 ln x。你需要理解对数运算法则，并会解指数方程。
Laws: logₐ(xy) = logₐx + logₐy; logₐ(x/y) = logₐx − logₐy; logₐxⁿ = n logₐx
You should also be able to differentiate and integrate eˣ and ln x, and use them in solving problems about rates of change.
你还应该能够对 eˣ 和 ln x 进行微分和积分，并利用它们解决与变化率相关的问题。
7. Differentiation | 微分
Differentiation is a major topic in A-Level mathematics. You must know how to differentiate polynomials, products, quotients, and composite functions using the chain rule.
微分是 A-Level 数学中的重点主题。你必须知道如何利用链式法则对多项式、积、商和复合函数求导。
If y = xⁿ, then dy/dx = nxⁿ⁻¹
若 y = xⁿ，则 dy/dx = nxⁿ⁻¹
Product rule: d(uv)/dx = u dv/dx + v du/dx
乘积法则：d(uv)/dx = u dv/dx + v du/dx
Quotient rule: d(u/v)/dx = (v du/dx − u dv/dx)/v²
商法则：d(u/v)/dx = (v du/dx − u dv/dx)/v²
Applications include finding tangents, normals, stationary points, and solving optimisation problems.
应用包括求切线、法线、驻点以及解决最优化问题。
8. Integration | 积分
Integration is the reverse of differentiation. You need to integrate polynomial functions, trigonometric functions, and exponentials, and evaluate definite integrals.
积分是微分的逆运算。你需要积分多项式函数、三角函数和指数函数，并计算定积分。
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
You should also understand the area between a curve and the x-axis, and between two curves, using definite integrals.
你还应该理解通过定积分求曲线与 x 轴之间、以及两条曲线之间的面积。
Further, use integration by parts and substitution if covered in Support Pack 2 – usually these appear later in the course.
此外，如果 Support Pack 2 涉及分部积分和换元积分，这些通常在课程后期出现。
9. Statistical Sampling and Data | 统计抽样与数据
In the statistics section, you study measures of location and spread, plus the basics of probability distributions.
在统计部分，你学习位置与离散程度的度量，以及概率分布的基础。
Mean, median, mode, variance, standard deviation
均值、中位数、众数、方差、标准差
Box plots and histograms
箱线图和直方图
Correlation and regression basics
相关与回归基础
Support Pack 2 typically includes the normal distribution and hypothesis testing as extension topics.
Support Pack 2 通常包含正态分布和假设检验作为扩展主题。
10. Kinematics and Forces | 运动学与力
The mechanics section introduces motion in a straight line, constant acceleration formulas, and Newton's laws.
力学部分介绍直线运动、匀加速公式和牛顿定律。
v = u + at; s = ut + ½at²; v² = u² + 2as
These equations are known as the SUVAT equations. You must also draw force diagrams and resolve forces into components.
这些方程称为 SUVAT 方程。你还必须绘制受力图，并将力分解为分量。
Newton's second law F = ma is used to relate resultant force to acceleration.
牛顿第二定律 F = ma 用于将合力与加速度联系起来。
Final Words | 结语
Support Pack 2 provides a solid revision framework for the core AQA A-Level mathematics topics. Use this contents guide to plan your study sessions, practise past questions, and identify weaker areas.
Support Pack 2 为 AQA A-Level 数学核心主题提供了扎实的复习框架。使用本内容指南来规划学习时间、练习历年真题，并找出薄弱环节。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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