A-Level Maths: Formula Summary Handbook | A-Level 数学：公式汇总手册

📚 A-Level Maths: Formula Summary Handbook | A-Level 数学：公式汇总手册

This handbook compiles essential formulae across all major topics in A-Level Mathematics, serving as a quick reference for revision and problem-solving. Mastering these formulas is crucial for success in the examinations.

本手册汇集了A-Level数学各主要专题的核心公式，可作为复习与解题的快速参考。熟练掌握这些公式是考试成功的关键。

1. Algebraic Formulae & Quadratic Equations | 代数公式与二次方程

a² – b² = (a – b)(a + b)

The difference of two squares factorises into the product of the sum and difference of the terms.

平方差可分解为两项和与差的乘积。

(a ± b)² = a² ± 2ab + b²

A perfect square expands to the square of the first term, plus or minus twice the product, plus the square of the second term.

完全平方展开为第一项的平方，加减两倍乘积，再加第二项的平方。

x = (-b ± √(b² – 4ac)) / (2a)

The quadratic formula solves ax² + bx + c = 0. The discriminant Δ = b² – 4ac determines the nature of the roots.

二次公式用于求解 ax² + bx + c = 0。判别式 Δ = b² – 4ac 决定根的性质。

Δ = b² – 4ac

If Δ > 0, two distinct real roots; Δ = 0, one repeated real root; Δ < 0, no real roots.

若 Δ > 0，有两个不等实根；Δ = 0，有两个相等实根；Δ < 0，无实根。

α + β = -b/a, αβ = c/a

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