📚 IGCSE CAIE Additional Mathematics: High-Frequency Exam Points and Common Mistake Analysis | IGCSE CAIE 进阶数学：高频考点与易错题分析
The CAIE Additional Mathematics syllabus is compact but demanding. Many candidates fail not because they do not know the method, but because they make small algebraic slips, misuse signs, or forget the domain of a function. This article breaks down the most frequently tested topics and the most common mistakes, with paired explanations in English and Chinese.
CAIE 进阶数学的大纲虽短，要求却很高。很多考生并不是不会方法，而是因为小的代数失误、符号错误或忘记函数定义域而丢分。本文按高频考点拆分，并逐一配对中英双语讲解最常见的错误。
1. Indices and Surds | 指数与根式
Indices and surds appear in almost every paper, often as the first question. You must be comfortable with the rules aᵐ × aⁿ = aᵐ⁺ⁿ and (aᵐ)ⁿ = aᵐⁿ. Equations such as 2³ˣ⁻¹ = 32 are solved by writing both sides as powers of 2.
指数与根式几乎每次考试都会出现，而且常作为第一题。你需要熟悉 aᵐ × aⁿ = aᵐ⁺ⁿ 和 (aᵐ)ⁿ = aᵐⁿ 的法则。像 2³ˣ⁻¹ = 32 这样的方程，可以两边都写成以 2 为底的幂来求解。
Common mistake 1: forgetting that a⁰ = 1 for any non-zero a,
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