📚 Key Maths Vocabulary for Year 9 AQA: Quick Memorisation Guide | Year 9 AQA 数学：词汇术语速记指南
Understanding mathematical language is just as important as solving equations. This guide breaks down the essential vocabulary for Year 9 AQA Maths, with clear definitions and memory aids to help you learn faster and apply terms correctly in your exams.
理解数学语言与解方程同样重要。本指南拆解 Year 9 AQA 数学的关键词汇，提供清晰的定义和记忆辅助，帮助您更快学习并在考试中正确运用术语。
1. Number Types and Place Value | 数字类型与位值
Integer: An integer is any whole number, positive, negative, or zero. Examples: -3, 0, 7, 42.
整数： 整数是任意正整数、负整数或零。例子：-3, 0, 7, 42。
Prime Number: A prime number is an integer greater than 1 that has exactly two distinct positive factors: 1 and itself. Think of primes as the 'atoms' of multiplication – they cannot be split further.
质数： 质数是大于1且只有两个不同正因数的整数：1和它本身。可以把质数想象成乘法的“原子”——它们不能再分解。
Composite Number: t least one factor other than 1 and itself. For example, 8 is composite because 2 × 4 = 8.
合数： 合数是至少有除了1和它本身以外因数的正整数。例如8是合数，因为2 × 4 = 8。
Factor: nother number exactly without leaving a remainder. 3 is a factor of 12 because 12 ÷ 3 = 4.
因数： 因数是能整除另一个数而不留余数的数。3是12的因数，因为12 ÷ 3 = 4。
Multiple: A multiple is the product of a number and any integer. The multiples of 5 are 5, 10, 15, 20, …
倍数： 倍数是一个数与任意整数的乘积。5的倍数有5, 10, 15, 20, …
Square Root & Cube Root: gives the original. The cube root ³√ finds a number that when cubed returns the original. √25 = 5, ³√8 = 2.
平方根与立方根： 平方根√是求一个数，它乘以自己得到原数。立方根³√是求一个数，它的立方等于原数。√25 = 5，³√8 = 2。
Standard Form: ers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. 4 500 = 4.5 × 10³, 0.002 = 2 × 10⁻³.
标准形式： 标准形式用 a × 10ⁿ 表示很大或很小的数，其中 1 ≤ a < 10，n 为整数。4500 = 4.5 × 10³，0.002 = 2 × 10⁻³。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Numerator and Denominator: In a fraction, the numerator is the top number, showing how many parts we have. The denominator is the bottom number, showing how many equal parts the whole is divided into. Think: 'Denominator' names the type of part (like the denomination of a coin).
分子与分母： 分数中，分子是上线数字，表示我们拥有多少部分。分母是下线数字，表示整体被等分成多少份。记忆：分母给出份数的“名称”。
Equivalent Fractions: They are obtained by multiplying or dividing numerator and denominator by the same number.
等值分数： 等值分数代表相同的值，例如 ½ = ²⁄₄。通过将分子和分母同乘或同除一个数得到。
Recurring Decimal: imal has digits that repeat forever, shown with a dot over the repeating digit(s). ⅓ = 0.3̇ means 0.333…
循环小数： 循环小数有无限重复的数字，用点在重复的数字上标示。⅓ = 0.3̇ 即 0.333…
Percentage Increase: n : To increase an amount by a percentage, use a multiplier: new value = original × (1 + p/100). Increasing £50 by 10% gives 50 × 1.1 = £55.
百分比增加： 要按百分比增加一个量，使用乘数：新值 = 原值 × (1 + p/100)。£50 增加10%得 50 × 1.1 = £55。
Multiplier Method: A decimal multiplier converts a percentage change directly. For a 15% increase, multiplier = 1.15; for a 20% decrease, multiplier = 0.8.
乘数法： 小数乘数直接转换百分比变化。增加15%，乘数为1.15；减少20%，乘数为0.8。
3. Algebraic Expressions | 代数表达式
Term: A term is a single number, variable, or product of numbers and variables separated by + or −. In 3x² + 2y − 5, the terms are 3x², 2y, and −5.
项： 项是由加号或减号隔开的单个数字、变量或数字与变量的乘积。在 3x² + 2y − 5 中，项是 3x²、2y 和 −5。
Coefficient: The coefficient is the numerical factor multiplying a variable. In 7a, 7 is the coefficient of a.
系数： 系数是乘以变量的数字因数。在 7a 中，7 是 a 的系数。
Variable and Constant: A variable is a symbol, usually a letter, that represents an unknown or changing value. A constant is a fixed number. In 4x + 9, x is the variable, 9 is the constant.
变量与常量： 变量是表示未知或变化值的符号，通常是字母。常量是固定数字。在 4x + 9 中，x 是变量，9 是常量。
Simplify: Simplifying an expression means collecting like terms (terms with the same variable and power) by adding or subtracting their coefficients. 2x + 5x – x simplifies to 6x.
简化： 简化表达式意味着合并同类项（变量及指数均相同的项），将其系数相加或相减。2x + 5x – x 简化得 6x。
Expand: Expanding removes brackets by multiplying each term inside the bracket by the term outside. 3(x + 4) expands to 3x + 12. Double brackets: (x + 2)(x + 3) expands to x² + 5x + 6.
展开： 展开是将括号外的项乘以括号内的每一项以去除括号。3(x + 4) 展开得 3x + 12。双括号：(x + 2)(x + 3) 展开得 x² + 5x + 6。
Factorise: Factorising is the reverse of expanding – it puts brackets back by taking out common factors. 2x + 6 factorises to 2(x + 3).
因式分解： 因式分解是展开的逆运算——提取公因数后放回括号。2x + 6 因式分解为 2(x + 3)。
Identity: An identity is an equation that is true for all values of the variable, often written with the ≡ symbol. (x + 1)² ≡ x² + 2x + 1.
恒等式： 恒等式是对变量的所有值都成立的等式，常用 ≡ 符号表示。(x + 1)² ≡ x² + 2x + 1。
4. Equations and Inequalities | 方程与不等式
Equation: n by the equals sign =. To solve an equation means to find the value(s) that make it true.
方程： 方程是表明两个表达式相等的数学语句，用等号 = 表示。解方程意味着找出使其成立的值。
Balance Method: We solve linear equations by using inverse operations to keep the equation balanced – what you do to one side, you must do to the other.
天平法： 使用逆运算解一次方程，保持等式平衡——对一边做什么，另一边也必须做同样的操作。
Inequality: an), ≤ (less than or equal), ≥ (greater than or equal). The solution is a range of values.
不等式： 不等式使用 <（小于）、>（大于）、≤（小于或等于）、≥（大于或等于）比较两个表达式。解是一个数值范围。
Linear Expression: A linear expression contains variables only to the power 1 (no x², x³, etc.). Its graph is a straight line. 2x + 5 is linear; x² + 3 is not.
一次表达式： 一次表达式仅包含指数为1的变量（无 x²、x³ 等）。其图像是一条直线。2x + 5 是一次；x² + 3 不是。
5. Sequences | 数列
Sequence: A sequence is an ordered list of numbers following a rule. Each number is called a term. Example: 2, 4, 6, 8, … is an arithmetic sequence.
数列： 数列是按规则排列的一列有序数字。每个数称为项。例如：2, 4, 6, 8, … 是一个等差数列。
nth Term: The nth term is a formula that generates any term in a sequence based on its position n. For 3, 5, 7, 9,…, the nth term is 2n + 1. 'n' is the position number.
第 n 项： 第 n 项是一个公式，根据位置 n 生成数列中的任一项。对于 3, 5, 7, 9,…，第 n 项是 2n + 1。“n”代表位置编号。
Arithmetic
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