📚 Year 10 AQA Maths: Formula & Theorem Quick Reference | 十年级AQA数学公式定理速查手册
This quick reference handbook brings together all the essential formulas, theorems and rules needed for Year 10 AQA Mathematics. Covering number work, algebra, ratio, geometry, trigonometry, probability, statistics and graphs, it is designed for rapid revision, classroom support and last‑minute exam preparation. Each entry is given in a clear, concise statement followed by a worked‑example note where helpful.
本速查手册汇集了十年级 AQA 数学所需的全部核心公式、定理与法则，涵盖数与指数、代数、比例、几何、三角学、概率、统计和函数图像。每一条都用简洁的语言给出英文陈述，并配以对应的中文解释，便于快速查阅、课堂辅助和考前冲刺。
1. Number and Indices | 数与指数
Index laws for integer exponents: For any non‑ a and integers m, n: aᵐ × aⁿ = aᵐ⁺ⁿ ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ ; (aᵐ)ⁿ = aᵐⁿ ; a⁰ = 1 ; a⁻ⁿ = 1/aⁿ.
整数指数幂的运算律（a ≠ 0，m、n 为整数）：aᵐ × aⁿ = aᵐ⁺ⁿ；aᵐ ÷ aⁿ = aᵐ⁻ⁿ；(aᵐ)ⁿ = aᵐⁿ；a⁰ = 1；a⁻ⁿ = 1/aⁿ。
Fractional indices: a1/n = ⁿ√a (the nth root of a); am/n = ⁿ√aᵐ = (ⁿ√a)ᵐ. For example, 81/3 = ³√8 = 2.
分数指数：a1/n = ⁿ√a（a 的 n 次方根）；am/n = ⁿ√aᵐ = (ⁿ√a)ᵐ。如 81/3 = ³√8 = 2。
Fraction operations: a/b + c/d = (ad + bc) / bd ; a
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