📚 A-Level CCEA Mathematics: End-of-Term Revision Checklist | A-Level CCEA 数学：期末复习提纲
This comprehensive revision guide covers the essential topics for the CCEA A-Level Mathematics examinations, including both AS and A2 units. Key areas from Pure Mathematics, Mechanics, and Statistics are summarised to help you focus your end-of-term revision efficiently.
这份全面的复习指南涵盖了 CCEA A-Level 数学考试的核心主题，包括 AS 和 A2 单元。我们总结了纯数学、力学和统计学的关键领域，帮助你高效聚焦期末复习。
1. Algebraic Techniques | 代数技巧
Master the manipulation of indices and surds, including simplifying expressions like √8 ÷ √2 and rationalising denominators. Quadratic equations should be solved via factorisation, completing the square, or the quadratic formula; always check the discriminant (b² − 4ac) to determine the nature of roots.
掌握指数和根式的运算，包括化简如 √8 ÷ √2 以及分母有理化。二次方程应通过因式分解、配方法或求根公式求解；务必检查判别式 (b² − 4ac) 以确定根的性质。
Simultaneous equations, both linear and one linear with one quadratic, must be tackled analytically. Algebraic fractions and polynomial division (up to cubics) are tested regularly; remember the Factor Theorem: if f(a)=0, then (x−a) is a factor.
联立方程组（包括两个线性或一个线性一个二次）需要解析求解。代数分式和多项式除法（最高三次）经常出现；记住因式定理：若 f(a)=0，则 (x−a) 为一个因式。
Inequalities should be solved graphically or algebraically, watching for sign changes when multiplying by a negative. Express solutions using set notation or interval notation.
不等式需通过图像或代数方法求解，注意乘以负数时不等号的方向变化。用集合符号或区间符号表示解集。
2. Functions and Graphs | 函数与图像
Understand the definitions of domain, range, and one-one/many-one mappings. For composite functions fg(x), apply the inner function first. Ensure you can find inverse functions f⁻¹(x) by swapping x and y and rearranging, and know that the graph of f⁻¹ is a reflection in y=x.
理解定义域、值域以及单射/多射映射的定义。对于复合函数 fg(x)，先应用内层函数。确保能通过交换 x 和 y 再重排找到反函数 f⁻¹(x)，并知道反函数的图像是关于 y=x 的反射。
Transformations of graphs: translations (y = f(x) + a, y = f(x + a)), stretches (y = a f(x), y = f(ax)), and reflections (y = −f(x), y = f(−x)). You should be able to sketch modulus functions y = |f(x)| and y = f(|x|).
图像变换：平移（y = f(x) + a, y = f(x + a)）、伸缩（y = a f(x), y = f(ax)）和反射（y = −f(x), y = f(−x)）。你应该能够绘制模函数 y = |f(x)| 和 y = f(|x|) 的图像。
Recognise standard functions: quadratic, cubic, reciprocal, exponential, logarithmic and trigonometric graphs, including their asymptotes and key features.
识别标准函数：二次、三次、倒数、指数、对数和三角函数图像，包括它们的渐近线和关键特征。
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