📚 KS3 CIE Further Mathematics: Vocabulary & Terminology Quick Memorisation Guide | KS3 CIE 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is the foundation for understanding and communicating ideas in Further Mathematics. This guide gives clear bilingual explanations of essential terms, helping you memorise them quickly and link concepts across topics.
掌握数学词汇是理解并交流进阶数学思想的基础。本指南通过清晰的双语解释核心术语，帮助你快速记忆并串联各主题概念。
1. Numbers and Number Sets | 数与数集
Natural numbers (ℕ): The counting numbers starting from 1: {1, 2, 3, ...}. They exclude zero, fractions, or negatives.
自然数（ℕ）：从 1 开始的计数数字：{1, 2, 3, ...}。不包括零、分数或负数。
Integers (ℤ): Whole numbers that include zero and negative whole numbers: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
整数（ℤ）：包括零和负整数的完整数字：{..., -3, -2, -1, 0, 1, 2, 3, ...}。
Rational numbers (ℚ): Numbers that can be expressed as a fraction a/b, where a and b are integers and b ≠ 0. They include terminating and repeating decimals.
有理数（ℚ）：可以表示为分数 a/b 的数，其中 a 和 b 为整数且 b ≠ 0。包括有限小数和循环小数。
Irrational numbers: Real numbers that cannot be written as a simple fraction. Their decimal expansions go on forever without repeating. Examples: √2, π.
无理数：不可以写成简单分数的实数。它们的小数展开是无限不循环的。例如：√2，π。
Real numbers (ℝ): All rational and irrational numbers together. They form a continuous number line.
实数（ℝ）：所有有理数和无理数的集合。它们构成一条连续的数轴。
Prime number: A number greater than 1 that has exactly two distinct positive factors: 1 and itself. Composite number: has more than two factors.
质数：大于 1 且恰好有两个不同正因数的数：1 和它自身。合数：拥有超过两个因数。
Prime factorisation: Expressing a composite number as a product of prime numbers. Example: 60 = 2 × 2 × 3 × 5.
质因数分解：将一个合数表示为质数的乘积。例如：60 = 2 × 2 × 3 × 5。
2. Algebraic Expressions & Manipulation | 代数表达式与运算
Term: A single number, variable, or product of numbers and variables. e.g., 3x, -2y², 7.
项：一个单独的数字、变量或数字与变量的乘积。例如：3x, -2y², 7。
Coefficient: The number factor in a term. In 4xy, 4 is the coefficient; in x², the coefficient is 1.
系数：项中的数字因子。在 4xy 中，系数是 4；在 x² 中，系数是 1。
Variable: A symbol, usually a letter, that represents an unknown or changeable value.
变量：通常为一个字母，表示未知或可以变化的值。
Constant: A term with a fixed value, such as 5, -3, or π.
常量：具有固定值的项，如 5、-3 或 π。
Like terms: Terms that have exactly the same variables raised to the same powers. Only like terms can be added or subtracted. e.g., 2x and -5x are like; 3x² and 3x are not.
同类项：具有完全相同变量和指数的项。只有同类项才能相加或相减。例如：2x 和 -5x 是同类项；3x² 和 3x 不是。
Expand: e : To remove brackets by multiplying each term inside by the factor outside. e.g., 2(x + 3) = 2x + 6.
展开：通过分配律去掉括号，将括号外的因数乘以括号内的每一项。例如：2(x + 3) = 2x + 6。
Factorise: f : The reverse of expanding; rewriting an expression as a product of its factors. e.g., 2x + 6 = 2(x + 3).
因式分解：展开的逆过程；将表达式改写为因式的乘积。例如：2x + 6 = 2(x + 3)。
Simplify: To collect like terms and perform operations to write an expression in its shortest form.
化简：合并同类项并执行运算，以最简短的形式写出表达式。
3. Equations and Inequalities | 方程与不等式
Equation: matical statement that shows two expressions are equal, using the = sign. e.g., x + 3 = 7.
方程：使用等号 = 表示两个表达式相等的数学陈述。例如：x + 3 = 7。
Solution / Root: The value of the variable that makes an equation true. Solving means finding all solutions.
解 / 根：使方程成立的变量的值。求解即找出所有解。
Identity: An equation that is true for all values of the variable, often using the ≡ sign. e.g., (a+b)² ≡ a² + 2ab + b².
恒等式：对所有变量值都成立的等式，常用 ≡ 表示。例如：(a+b)² ≡ a² + 2ab + b²。
2x + 3 = 11 → x = 4
Inequality: ressions using symbols >, <, ≥, ≤ or ≠. Solution sets can be shown on a number line.
不等式：用 >、<、≥、≤ 或 ≠ 比较两个表达式的陈述。解集可在数轴上表示。
Solving inequalities: Follow similar rules as equations, but reverse the inequality sign when multiplying or dividing by a negative number.
解不等式：遵循与方程类似的规则，但当乘或除以一个负数时，要反转不等号方向。
-2x < 6 → x > -3
4. Graphs and Functions | 图表与函数
Coordinate plane: Formed by the x‑axis (horizontal) and y‑axis (vertical). Their intersection is the origin (0,0). Points are written as (x, y).
坐标平面：由 x 轴（水平）和 y 轴（垂直）构成。
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