Edexcel A Level Maths: Year 2 Pure Topics Explained | Edexcel 数学：A Level 第二年纯数知识点精讲

📚 Edexcel A Level Maths: Year 2 Pure Topics Explained | Edexcel 数学：A Level 第二年纯数知识点精讲

Edexcel A Level Mathematics Year 2 Pure builds on the foundations of Year 1, introducing more sophisticated algebra, trigonometry, calculus, and vectors. This article walks you through every core topic, explaining key concepts, essential formulae, and common problem-solving strategies.

Edexcel A Level 数学第二年纯数在第一年的基础上引入了更复杂的代数、三角、微积分和向量内容。本文带你逐一梳理核心主题，讲解关键概念、必备公式和常见解题策略。

1. Algebraic Methods: Partial Fractions | 代数方法：部分分式

Partial fractions allow us to express a complex rational function as a sum of simpler fractions. This makes integration, differentiation, or series expansion much easier. For distinct linear factors in the denominator, such as 1/((x+1)(x-2)), we write it as A/(x+1) + B/(x-2).

部分分式能将复杂的有理函数拆分为简单分式的和。这大大简化了积分、求导或级数展开。对于分母中的不同线性因式，如 1/((x+1)(x-2))，即可拆成 A/(x+1) + B/(x-2)。

To find the constants A and B, multiply through by the denominator and either equate coefficients or substitute convenient x-values. For repeated factors like (x+1)², the decomposition includes A/(x+1) + B/(x+1)². Quadratic factors require a linear numerator term.

求常数 A、B 时，需通乘分母，并比较系数或代入合适的 x 值。若出现重因式如 (x+1)²，拆分形式为 A/(x+1) + B/(x+1)²。二次因式则需要线性分子项。

1/((x+1)(x-2)) = A/(x+