IGCSE Cambridge Additional Mathematics: High-Frequency Topics and Common Mistakes Analysis | IGCSE Cambridge 进阶数学：高频考点与易错题分析

📚 IGCSE Cambridge Additional Mathematics: High-Frequency Topics and Common Mistakes Analysis | IGCSE Cambridge 进阶数学：高频考点与易错题分析

Cambridge IGCSE Additional Mathematics (0606) is a demanding course that bridges IGCSE Mathematics and A Level Mathematics. It introduces calculus, logarithmic and exponential functions, advanced trigonometry, and vectors. Examiners repeatedly test a core set of skills, and many marks are lost through avoidable mistakes in these areas. This guide identifies the high-frequency topics and the most common pitfalls, with targeted advice for revision.

剑桥 IGCSE 进阶数学（0606）是一门要求较高的课程，在 IGCSE 数学与 A Level 数学之间起衔接作用。它引入微积分、对数与指数函数、高等三角学和向量等内容。考官反复考查一组核心技能，而许多失分来自这些领域中本可避免的错误。本指南帮助你识别高频考点和最常见误区，并提供有针对性的复习建议。

1. Functions and Inverse Functions | 函数与反函数

Functions are the foundation of the syllabus. Candidates must be confident with domain, range, one-to-one and inverse functions, composite functions, and transformations. A very common error is to find f⁻¹(x) algebraically but ignore the domain of the inverse.

函数是本课程的基础。考生必须熟练掌握定义域、值域、一一函数、反函数、复合函数和图像变换。一个常见错误是只通过代数方法求出 f⁻¹(x)，却忽略反函数的定义域。

To find an inverse, write y = f(x), swap x and y, then solve for y. The domain of f⁻¹ is equal to the range of f. For example, if f(x) = x² for x ≥ 0, then f⁻¹(x) = √x, not x² again.

求反函数时，先写 y = f(x)，交换 x 与 y，再解出 y。f⁻¹ 的定义域等于 f 的值域。例如，若 f(x) = x² 且 x ≥ 0，则 f⁻¹(x) = √x，而不是再次得到 x²。

In composite functions, always apply the inner function first and check the order carefully. Also state all domains in interval notation where required.

在复合函数中，

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