📚 AS AQA Maths Unit 2 January 2019: Pure Core 2 Question Paper Guide | AS AQA 数学 Unit 2 2019年1月：纯数核心2试卷解析指南
The January 2019 Unit 2 paper belongs to the legacy AQA AS Mathematics specification, where Unit 2 is Pure Core 2 (MPC2). This guide summarises the paper structure, typical question styles, key formulas, and model examples to help you revise efficiently.
2019年1月 Unit 2 试卷属于旧版 AQA AS 数学大纲，其中 Unit 2 是纯数核心2（MPC2）。本指南总结了试卷结构、典型题型、关键公式和示例题，帮助你高效复习。
1. Paper Structure and Timing | 试卷结构与时间分配
The January 2019 Unit 2 paper is worth 75 marks and lasts 1 hour 30 minutes. It contains approximately 8 to 10 compulsory questions arranged roughly in increasing difficulty, mixing straightforward knowledge with multi-step problem solving.
2019年1月 Unit 2 试卷满分75分，考试时间1小时30分钟。试卷约含8至10道必答题，难度大致递增，既有直接考查知识的题目，也有多步综合题。
The table below shows the approximate mark allocation for each topic area in a typical Pure Core 2 paper. The balance can shift slightly from session to session.
下表展示了典型纯数核心2试卷中各主题的大致分值分布。不同考次的占比可能会有小幅波动。
| Topic Area | 知识模块 | Typical Marks | 典型分值 |
|---|---|
| Algebra and functions | 代数与函数 | 15–20 |
| Sequences and series | 数列与级数 | 12–16 |
| Trigonometry | 三角学 | 14–18 |
| Exponentials and logarithms | 指数与对数 | 10–14 |
| Differentiation | 微分 | 12–16 |
| Integration | 积分 | 14–18 |
| Numerical methods | 数值方法 | 6–8 |
2. Algebra and Functions | 代数与函数
In Pure Core 2, algebra questions often involve the factor theorem, polynomial division, and curve sketching. You may be asked to show that (x − a) is a factor of a cubic, then find the remaining quadratic factor and identify the roots.
纯数核心2中，代数题常涉及因式定理、多项式除法和曲线作图。你可能需要证明 (x − a) 是三次多项式的因式，然后求出剩余的二次因式并确定根。
Example: f(x) = 2x³ − 3x² − 11x + 6. Show that (x + 2) is a factor and express f(x) as three linear factors.
示例：f(x) = 2x³ − 3x²
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