📚 IGCSE Cambridge Additional Mathematics: Glossary & Terminology Quick Memory Guide | IGCSE 剑桥进阶数学：词汇术语速记指南
Mastering terminology is a fast route to higher marks in Cambridge IGCSE Additional Mathematics. Many exam errors come from misreading a word such as 'domain', 'discriminant' or 'differentiate'. This bilingual glossary organises the most frequently tested terms by topic, with short memory hooks to help you recall them under time pressure.
掌握术语是在剑桥 IGCSE 进阶数学中快速提分的途径。许多考试失分源于误读 domain、discriminant 或 differentiate 等关键词。本双语词汇表按主题整理最高频考查的术语，并配简短记忆提示，帮助你在时间压力下快速回忆。
1. Functions and Relations | 函数与关系
Function | 函数 – maps every input to exactly one output, written f(x) = ... . Think: one input, one output.
函数：将每个输入对应到唯一输出的规则，记作 f(x) = ...。记忆：一个输入只产生一个输出。
Domain | 定义域 – The set of all allowed input values for a function.
定义域：函数所有允许输入值的集合。
Range | 值域 – The set of all output values actually produced from the domain.
值域：由定义域实际产生的所有输出值的集合。
One-one function | 一一函数 – A function where each output is produced by only one input; it passes the horizontal line test and has an inverse.
一一函数：每个输出只由一个输入产生的函数；它通过水平线检验，并且存在反函数。
Composite function | 复合函数 – Combining two functions by applying one after another: gf(x) = g(f(x)).
复合函数：将一个函数代入另一个函数，如 gf(x) = g(f(x))。
2. Quadratic Functions | 二次函数
Quadratic function | 二次函数 – A function of the form ax² + bx + c, where a ≠ 0. Its graph is a parabola.
二次函数：形如 ax² + bx + c 的函数，其中 a ≠ 0。图像为抛物线。
Vertex | 顶点 – The maximum or minimum point of a parabola.
顶点：抛物线的最高点或最低点。
Axis of symmetry | 对称轴 – The vertical line through the vertex; for y = ax² + bx + c, it is x = −b/(2a).
对称轴：经过顶点的竖直线；对 y = ax² + bx + c，对称轴为 x = −b/(2a)。
Discriminant | 判别式 – The value Δ = b² − 4ac, which tells how many real roots a quadratic has.
判别式：Δ = b² − 4ac，用于判断二次方程实数根的个数。
Discriminant: Δ = b² − 4ac
Roots | 根 – The x-values where f(x) = 0; also called solutions or x-intercepts.
根：使 f(x) = 0 的 x 值，也叫解或 x 轴截距。
3. Indices and Surds | 指数与根式
Index / exponent | 指数 – The power to which a base is raised; in aⁿ, n is the index.
指数：底数被乘方的次数；在 aⁿ 中，n 是指数。
Base | 底数 – The number being multiplied repeatedly; in aⁿ, a is the base.
底数：被反复相乘的数；在 aⁿ 中，a 是底数。
Surd | 根式 – An irrational root such as √2 or √3 that cannot be simplified to a rational number.
根式：无法化简为有理数的无理根，如 √2 或 √3。
Rationalising the denominator | 分母有理化 – Removing a surd from the bottom of a fraction by multiplying top and bottom by a suitable root.
分母有理化：通过分子分母同乘适当根式，消去分母中的根号。
Index laws | 指数法则 – Rules such as aᵐ × aⁿ = aᵐ⁺ⁿ and (a
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