Year 12 CIE Maths: Key Terminology Quick Reference Guide | Year 12 CIE 数学：词汇术语速记指南

📚 Year 12 CIE Maths: Key Terminology Quick Reference Guide | Year 12 CIE 数学：词汇术语速记指南

Mastering the core mathematical vocabulary is essential for success in Year 12 CIE Maths. This guide provides clear definitions of key terms across pure mathematics and statistics, paired with Chinese translations to support bilingual learners. Use it to review concepts and strengthen your exam technique.

掌握核心数学词汇对于 Year 12 CIE 数学考试的成功至关重要。本指南提供了纯数学和统计学的关键术语的清晰定义，并配有中文翻译，以支持双语学习者。用它来复习概念、强化你的考试技巧。

1. Functions & Graphs | 函数与图形

Function: A relation where each input has exactly one output; expressed as f(x).

函数：每个输入都恰好有一个输出的关系；记作 f(x)。

Domain: The set of all possible input values (x-values) for which the function is defined.

定义域：使函数有定义的所有可能输入值（x值）的集合。

Range: The set of all possible output values (y-values) the function can produce.

值域：函数可以产生的所有可能输出值（y值）的集合。

One-to-one (injective) function: A function where each output is produced by exactly one input; passes the horizontal line test.

一一映射（单射）函数：每个输出恰好由一个输入产生的函数；满足水平线检验。

Inverse function: Reverses the effect of the original function; denoted f⁻¹(x), domain of f becomes range of f⁻¹.

反函数：逆转原函数效果的函数；记为 f⁻¹(x)，f 的定义域成为 f⁻¹ 的值域。

Composite function: A function formed by applying one function to the result of another; e.g., (f∘g)(x) = f(g(x)).

复合函数：将一个函数应用到另一个函数的结果上所形成的函数；例如 (f∘g)(x) = f(g(x))。

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2. Quadratics & Inequalities | 二次函数与不等式

Quadratic expression: An expression of the form ax² + bx + c, where a ≠ 0.

二次式：形如 ax² + bx + c 的式子，其中 a ≠ 0。

Discriminant: The expression Δ = b² − 4ac that determines the nature of the roots of a quadratic equation.

判别式：表达式 Δ = b² − 4ac，用于判断二次方程根的性质。

Roots / solutions: Values of x that satisfy the equation; if Δ > 0, two distinct real roots; Δ = 0, one repeated root; Δ < 0, no real roots.

根 / 解：满足方程的 x 值；如果 Δ > 0，两个不相等实根；Δ = 0，一个重根；Δ < 0，无实根。

Completing the square: Rewriting ax² + bx + c as a(x + p)² + q, used to find vertex and solve equations.

配方法：将 ax² + bx + c 改写为 a(x + p)² + q 的形式，用于求顶点和解方程。

Critical values: Values of x that make a quadratic expression equal to zero; used to solve inequalities.

关键值：使二次式等于零的 x 值；用于解不等式。

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3. Exponentials & Logarithms | 指数与对数

Exponential function: A function of the form aˣ, where a > 0 and a ≠ 1; most commonly eˣ (the exponential function with base e).

指数函数：形如 aˣ 的函数，其中 a > 0 且 a ≠ 1；最常见的是 eˣ（以 e 为底的指数函数）。

Logarithm: The inverse of exponentiation; if y = aˣ then logₐ(y) = x.

对数：指数运算的逆运算；如果 y = aˣ，那么 logₐ(y) = x。

Natural logarithm (ln): Logarithm to base e; ln(y) = x ⇔ eˣ = y.

自然对数（ln）：以 e 为底的对数；ln(y) = x ⇔ eˣ = y。

Laws of logarithms: log(a) + log(b) = log(ab); log(a) − log(b) = log(a/b); n·log(a) = log(aⁿ).

对数运算法则：log(a) + log(b) = log(ab)；log(a) − log(b) = log(a/b)；n·log(a) = log(aⁿ)。

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4. Trigonometry | 三角函数

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