GCSE Maths: Essential Formulae Handbook | GCSE 数学：必背公式手册

📚 GCSE Maths: Essential Formulae Handbook | GCSE 数学：必背公式手册

This handbook pulls together every key formula you need for GCSE Mathematics, from number work and algebra to geometry, trigonometry and statistics. Each entry is clearly explained in English and Chinese, making it a perfect bilingual revision tool. Keep it handy while you practise past papers or as a last‑minute memory check before the exam.

本手册汇总了GCSE数学中所有核心公式，涵盖数的运算、代数、几何、三角学和统计。每条公式均配有清晰的中英文解释，是绝佳的双语复习工具。在练习往年真题或考前快速回顾时，这本手册都能助你一臂之力。

1. Number Basics and Percentages | 数的基本运算与百分数

Adding and subtracting fractions: use a common denominator bd. a/b + c/d = (ad + bc)/bd. Subtraction works in the same way.

分数加减法：先通分为分母 bd。a/b + c/d = (ad + bc)/bd，减法同理。

Percentage increase: multiply the original amount by (1 + r/100), where r is the percentage. For a decrease, use (1 − r/100).

百分数增加：原数乘以 (1 + r/100)，r 为百分数。减少则乘以 (1 − r/100)。

Reverse percentages: to recover the original value before a percentage change, divide the new amount by the multiplier. After an r% increase, original = new ÷ (1 + r/100).

逆向百分数：求变化前的原值，用新值除以乘数。对于增加 r%，原值 = 新值 ÷ (1 + r/100)。

Compound interest for n years (compounded annually): A = P × (1 + r/100)ⁿ, where P is the principal, r% annual rate and n is the number of years.

复利公式（按年计息，n年）：A = P × (1 + r/100)ⁿ，P为本金，r%为年利率，n为年数。

2. Indices and Surds | 指数与根式

Multiplying powers with the same base: aᵐ × aⁿ = aᵐ⁺ⁿ.

同底数幂相乘：aᵐ × aⁿ = aᵐ⁺ⁿ。

Dividing powers: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

同底数幂相除：aᵐ ÷ aⁿ = aᵐ⁻ⁿ。

Power of a power: (aᵐ)ⁿ = aᵐⁿ.

幂的乘方：(aᵐ)ⁿ = aᵐⁿ。

Zero exponent: a⁰ = 1 (a ≠ 0). Negative exponent: a⁻ⁿ = 1 / aⁿ.

零指数：a⁰ = 1（a ≠ 0）。负指数：a⁻ⁿ = 1 / aⁿ。

Multiplying surds: √a × √b = √(ab). Dividing surds: √a / √b = √(a/b).

根式乘法：√a × √b = √(ab)。

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