📚 IGCSE CAIE Additional Mathematics: Past Paper Deep-Dive | IGCSE CAIE 进阶数学：历年真题深度解析
Past papers are the most reliable map to the real IGCSE CAIE Additional Mathematics examination. This deep-dive article uses years of Paper 1 and Paper 2 questions to reveal recurring question types, examiner expectations and high-leverage revision targets.
历年真题是了解 IGCSE CAIE 进阶数学考试最可靠的地图。本文通过多年 Paper 1 与 Paper 2 真题，揭示反复出现的题型、评分标准与高效率复习重点。
1. Syllabus Blueprint and Topic Weighting | 考纲蓝图与主题权重
The 0606 syllabus is examined through two equally weighted papers, each 2 hours long and worth 80 marks. Functions, trigonometry and calculus dominate, but a structured topic analysis shows that “small-topic” questions such as circular measure and vectors are often the ones that separate Grade A from A*.
0606 大纲由两份权重相同的试卷组成，每卷 2 小时、80 分。函数、三角与微积分占比最高，但对主题的结构化分析显示，弧度制、向量等“小题”往往是区分 A 与 A* 的关键。
| Topic | Typical weight | Past-paper trend |
|---|---|---|
| Functions | 10–15% | Inverse and composite functions appear almost every session. |
| Trigonometry | 15–20% | Identity-based equation solving is highly predictable. |
| Calculus | 20–25% | Stationary points, kinematics and area are recurring. |
| Circular measure / vectors | 8–12% | Short but discriminating questions. |
These percentages are indicative, not official, but they match the balance seen in recent papers.
这些百分比为指示性数据，并非官方比例，但与近年试卷的分布高度一致。
2. Functions, Domain and Inverse Functions | 函数、定义域与反函数
A function f(x) only has an inverse if it is one-to-one. Questions frequently ask for f⁻¹(x), then give a restricted domain, expecting you to state the range from the original domain and swap x and y systematically.
函数 f(x) 只有在一一对应时才有反函数。真题常要求先求 f⁻¹(x)，再给出限制定义域，要求你根据原定义域写出值域，并系统地交换 x 与 y。
The most common error is forgetting to restrict a quadratic such as f(x) = (x – 2)² + 1. On a full domain it has no inverse; after restricting to x ≥ 2, the inverse is f⁻¹(x) = 2 + √(x – 1).
最常见错误是忘记对二次函数如 f(x) = (x – 2)² + 1 限制定义域。在完整定义域上它没有反函数；限制为 x ≥ 2 后，其反函数为 f
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