IGCSE CAIE Further Pure Maths: Vocabulary & Terminology Quick Memory Guide | IGCSE CAIE 进阶数学：词汇术语速记指南

📚 IGCSE CAIE Further Pure Maths: Vocabulary & Terminology Quick Memory Guide | IGCSE CAIE 进阶数学：词汇术语速记指南

Mastering the precise mathematical vocabulary is essential for success in IGCSE CAIE Further Pure Mathematics (Additional Mathematics 0606). This guide presents key terms with bilingual explanations and memory tricks to help you recall definitions quickly and apply them accurately in exams.

掌握精确的数学词汇对于 IGCSE CAIE 进阶数学（附加数学 0606）的成功至关重要。本指南通过双语解释和记忆技巧呈现关键术语，帮助您快速回忆定义并在考试中准确应用。

1. Functions and Graphs | 函数与图像

A function is a rule that assigns each input (x) exactly one output (y). Think of a ‘function machine’ – one input produces only one output. The domain is all possible input values, and the range is all possible outputs. A one-to-one function passes the horizontal line test, ensuring it has an inverse function f⁻¹(x). A composite function fg(x) means applying g first, then f.

函数是将每个输入 (x) 映射到唯一输出 (y) 的规则。可想象成“函数机器”——一个输入仅产生一个输出。定义域是所有可能的输入值，值域则是所有可能的输出。一一函数能通过水平线检验，保证其存在反函数 f⁻¹(x)。复合函数 fg(x) 表示先应用 g，再应用 f。

Memory aid: ‘Domain before Range’ alphabetically, d comes before r, just like x comes before y. For inverse, ‘reflect in y = x’ – swap x and y.

记忆法：“定义域”和“值域”的英文首字母 d 在 r 前，如同 x 在 y 前。关于反函数，“关于 y=x 对称”——交换 x 和 y。

2. Quadratic Functions | 二次函数

A quadratic function has the general form f(x) = ax² + bx + c (a ≠ 0). Its graph is a parabola. The vertex is the turning point, found by completing the square: write as a(x – h)² + k, giving vertex (h, k). The discriminant Δ = b² – 4ac determines the nature of roots: Δ > 0 two real distinct roots, Δ = 0 one repeated real root, Δ < 0 no real roots.

二次函数的一般形式为 f(x) = ax² + bx + c (a ≠ 0)。其图像是一条抛物线。顶点是转折点，通过配方法求得：写成 a(x – h)² + k，顶点为 (h, k)。判别式 Δ = b² – 4ac 决定根的性质：Δ > 0 两个不等实根，Δ = 0 一个重根，Δ < 0 无实根。

Δ = b² – 4ac

Mnemonic: ‘Discriminant discriminates’ – it tells roots apart. ‘Vertex form’ remember (h,k) as ‘horizontal and kink’.

记忆窍门：“判别式”会“判别”根的情况。“顶点式”记住 (h,k)，h 是水平移动，k 是弯曲点。

3. Equations, Inequalities and Absolute Values | 方程、不等式与绝对值

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