Year 10 WJEC Further Maths: Formula & Theorem Quick Reference | 进阶数学公式定理速查手册

📚 Year 10 WJEC Further Maths: Formula & Theorem Quick Reference | 进阶数学公式定理速查手册

This bilingual quick reference handbook collects the essential formulae and theorems for the Year 10 WJEC Further Mathematics syllabus. It is designed to help you review key results in algebra, polynomials, coordinate geometry, trigonometry, sequences, calculus, vectors, matrices, probability, and mechanics. Each entry is presented in English first, followed by a centred, bold formula and its Chinese explanation, ensuring clarity for bilingual learners.

这本双语速查手册汇集了 Year 10 WJEC 进阶数学大纲必备的公式和定理，旨在帮助你快速复习代数、多项式、坐标几何、三角学、数列、微积分、向量、矩阵、概率和力学等关键内容。每个条目先用英文陈述，再以居中加粗的公式和中文解释呈现，确保双语学习者理解清晰。

1. Algebraic Basics | 代数基础

The product rule for indices: when multiplying powers with the same base, add the exponents.

a^m × aⁿ = a^m+n

指数乘法法则：同底数幂相乘，指数相加。

The quotient rule for indices: when dividing like bases, subtract the exponents.

a^m ÷ aⁿ = a^m-n

指数除法法则：同底数幂相除，指数相减。

The power rule: when raising a power to another power, multiply the exponents.

(a^m)ⁿ = a^m×n

幂的乘方法则：幂的乘方，指数相乘。

Expanding a single bracket: multiply each term inside by the factor outside.

a(b + c) = ab + ac

单项式乘多项式：把括号外的因式乘到括号内的每一项。

Difference of two squares: the product of a sum and a difference equals the difference of squares.

(a + b)(a – b) = a² – b²

平方差公式：两数和与差的乘积等于平方差。

Perfect square expansions: square of a binomial.

(a ± b)² = a² ± 2ab + b²

完全平方公式：二项式的平方展开。

2. Quadratic Equations | 二次方程

The quadratic formula gives the roots of ax² + bx + c = 0.

x = [-b ± √(b² – 4ac)] / (2a)

二次公式给出 ax² + bx + c = 0 的根。

The discriminant Δ = b² – 4ac

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