Year 10 CCEA Maths: Formula & Theorem Quick Reference Guide | CCEA Year 10 数学公式定理速查手册

📚 Year 10 CCEA Maths: Formula & Theorem Quick Reference Guide | CCEA Year 10 数学公式定理速查手册

Welcome to your comprehensive quick-reference guide for Year 10 CCEA Mathematics. This handbook brings together all the essential formulas, theorems, and key facts you need to master the GCSE foundation and higher topics. Keep it handy for revision, homework, and exam preparation.

欢迎使用 Year 10 CCEA 数学全面速查手册。本手册汇集了掌握 GCSE 基础与高阶主题所需的所有基本公式、定理和关键知识点。方便复习、家庭作业和备考使用。

1. Algebraic Fundamentals | 代数基础

Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, a⁰ = 1 (a ≠ 0). When the index is negative, a⁻ⁿ = 1 / aⁿ.

指数法则： aᵐ × aⁿ = aᵐ⁺ⁿ，(aᵐ)ⁿ = aᵐⁿ，aᵐ ÷ aⁿ = aᵐ⁻ⁿ，a⁰ = 1（a ≠ 0）。指数为负时，a⁻ⁿ = 1 / aⁿ。

Expanding single brackets: a(b + c) = ab + ac. You can extend this to a(b + c + d) = ab + ac + ad.

展开单项括号： a(b + c) = ab + ac。也可推广为 a(b + c + d) = ab + ac + ad。

Expanding double brackets: (x + a)(x + b) = x² + (a + b)x + ab. For a general case (ax + b)(cx + d), use FOIL to obtain acx² + (ad + bc)x + bd.

展开二项式： (x + a)(x + b) = x² + (a + b)x + ab。一般情形 (ax + b)(cx + d) 可用 FOIL 展开得 acx² + (ad + bc)x + bd。

Factorising by common factor: ab + ac = a(b + c). Always look for the highest common factor first.

提取公因式分解： ab + ac = a(b + c)。首先寻找最大公因式。

Difference of two squares: a² − b² = (a + b)(a − b). This is one of the most useful factorisation patterns.

平方差公式： a² − b² = (a + b)(a − b)。这是最有用的因式分解模式之一。

2. Equations and Inequalities | 方程与不等式

Solving a linear equation: For ax + b = c, isolate x by subtracting b and dividing by a, giving x = (c − b)/a. Always check your solution.

解一元一次方程： ax + b = c，通过移项和除以 a 得 x = (c − b)/a。务必验算。

Quadratic formula: If ax² + bx + c = 0, then x = [−b ± √(b² − 4ac)] / (2a). The discriminant Δ = b² − 4ac determines the number of real roots.

二次公式： 若 ax² + bx + c = 0，则 x = [−b ± √(b² − 4ac)] / (2a)。判别式 Δ = b² − 4ac 决定了实根个数。

Inequalities: Solve them like equations but remember: multiplying or dividing by a negative number reverses the inequality sign. Represent solutions on a number line with open/closed circles.

不等式： 解法类似方程，但谨记：乘或除以负数时不等号要反向。在数轴上用空心或实心圆表示解集。

Compound inequalities: A statement such as 3 < 2x + 1 ≤ 7 is solved by

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