GCSE AQA Maths: Formula Summary Handbook | GCSE AQA 数学：公式汇总手册

📚 GCSE AQA Maths: Formula Summary Handbook | GCSE AQA 数学：公式汇总手册

This handbook brings together all the essential formulas you need to memorise and apply in your GCSE AQA Mathematics exams. Each section groups related formulas with clear explanations, helping you revise effectively and tackle both calculator and non‑calculator papers with confidence.

本手册汇总了GCSE AQA数学考试中需要记忆并运用的所有核心公式。每个小节将相关公式归类并附上清晰说明，帮助你高效复习，自信应对计算器与非计算器试卷。

1. Arithmetic and Percentages | 算术与百分比

Key formulas for percentage change, simple and compound interest, and reversing percentage problems – essential for financial maths questions.

本节涵盖百分比变化、单利与复利以及逆向百分比问题的关键公式，是金融数学题的重要基础。

Percentage Change = (New Value − Original Value) / Original Value × 100%

百分比变化 = (新值 − 原值) / 原值 × 100%

Simple Interest I = P × r × t (r as decimal, t in years)

单利 I = 本金 × 年利率(小数) × 年数

Compound Amount A = P (1 + r/100)ⁿ (r% per period, n periods)

复利本息和 A = 本金 × (1 + 年利率%/期)^期数

Percentage Multiplier for Increase: × (1 + r/100)

增长乘数： × (1 + 增长率%/100)

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2. Algebraic Formulas | 代数公式

Master these fundamental algebraic identities and the quadratic formula – they appear throughout equations, inequalities, and sequences.

掌握这些基本代数恒等式和二次公式——它们在方程、不等式和数列中频繁出现。

Quadratic Formula: x = (−b ± √(b² − 4ac)) / (2a)

二次公式：x = (−b ± √(b² − 4ac)) / (2a)

Difference of Two Squares: a² − b² = (a − b)(a + b)

平方差公式：a² − b² = (a − b)(a + b)

Perfect Square: (a ± b)² = a² ± 2ab + b²

完全平方公式：(a ± b)² = a² ± 2ab + b²

nth term of an Arithmetic Sequence: aₙ = a + (n − 1)d

等差数列通项：aₙ = a + (n − 1)d

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3. Angle Properties and Polygons | 角的性质与多边形

Formulas for interior and exterior angles of polygons underpin geometry problems and reasoning questions.

多边形内角与外角公式是解决几何问题与推理题的基础。

Sum of Interior Angles = (n − 2) × 180°

内角和 = (n − 2) × 180°

Sum of Exterior Angles = 360° (for any convex polygon)

外角和 = 360°（任意凸多边形）

One Interior Angle of a Regular Polygon = (n − 2) × 180° / n

正多边形一个内角 = (n − 2) × 180° / n

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4. Area of Common Shapes | 常见图形面积

These area formulas cover rectilinear shapes, triangles, and parallelograms – must‑knows for mensuration questions.

以下面积公式涵盖直线图形、三角形和平行四边形——是计量问题的必会内容。

Rectangle: A = l × w

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