📚 A-Level Edexcel Maths: Last-Minute Revision Notes | A-Level Edexcel 数学：考前冲刺笔记
This set of last-minute revision notes covers the most essential formulas, key techniques, and common pitfalls across the Edexcel A-Level Mathematics specification. Use them to refresh your memory and boost confidence before the exam.
这份考前冲刺笔记涵盖了Edexcel A-Level数学大纲中最关键的公式、重要技巧和常见错误。在考试前用它来快速回顾，增强信心。
1. Algebraic Manipulation | 代数运算
adratic expressions, use the discriminant Δ = b² - 4ac to determine the nature of roots: if Δ > 0, two distinct real roots; Δ = 0, one repeated real root; Δ < 0, no real roots. Be cautious when cancelling terms – only factors can be cancelled, not terms.
熟练掌握代数运算是基础。务必进行彻底因式分解，并记住平方差公式: a² - b² = (a - b)(a + b)。对于二次表达式，使用判别式 Δ = b² - 4ac 判断根的性质：Δ > 0 时有两个不等实根；Δ = 0 时有一个重根；Δ < 0 时无实根。约分时要小心——只有因子可以约去，而不能约去项。
a² - b² = (a - b)(a + b)
Δ = b² - 4ac
Surds and indices: √ab = √a × √b, and am/n = ⁿ√am. Rationalise denominators when necessary.
根式与指数：√ab = √a × √b，且 am/n = ⁿ√am。必要时进行分母有理化。
2. Functions and Graphs | 函数与图像
g(x)), apply the inner function first. The inverse function f⁻¹(x) exists only if f is one‑to‑ a horizontal shift left by a; f(x) + a is a vertical shift up by a; -f(x) reflects in the x-axis; f(-x) reflects in the y-axis.
理解定义域和值域。复合函数 fg(x) = f(g(x)) 先应用内层函数。反函数 f⁻¹(x) 仅在 f 为一一映射时存在。其图像关于直线 y = x 对称。图像变换：f(x + a) 向左平移 a 个单位；f(x) + a 向上平移 a 个单位；-f(x) 关于 x 轴对称；f(-x) 关于 y 轴对称。
f⁻¹(x): swap x and y, then solve for y
Modulus function |x|: treat as x for x ≥ 0 and -x for x < 0. When solving |f(x)| = a, consider f(x) = a or f(x) = -a.
绝对值函数 |x|: x ≥ 0 时为 x，x < 0 时为 -x。解 |f(x)| = a 时，考虑 f(x) = a 或 f(x) = -a。
3. Trigonometry | 三角学
nt. The sine rule: a/sin A = b/sin B = c/sin C. The cosine rule: a² = b² + c² - 2bc cos A. Area of triangle: ½ ab sin C. Trigonometric identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ =
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