📚 Year 8 AQA Maths: Vocabulary Quick-Reference Guide | 八年级 AQA 数学：词汇速记指南
Mastering the language of mathematics is half the battle. In Year 8, you will encounter a wide range of terms that describe numbers, shapes, patterns and data. This quick-reference guide groups essential vocabulary by topic, gives a clear definition in English and Chinese, and highlights key connections you need to succeed in AQA assessments. Use it for revision, homework, and building confidence before tests.
掌握数学的语言是成功的一半。八年级你会接触到大量描述数字、图形、规律和数据的术语。这份速记指南按主题将核心词汇分组，给出清晰的中英文释义，并突出你在 AQA 测评中必须掌握的关键联系。用它来复习、做作业，并在考试前建立信心。
1. Number and Place Value | 数字与位值
Integer: A whole number that can be positive, negative or zero. Examples: −5, 0, 12.
整数：可以是正数、负数或零的完整数字。例如：−5, 0, 12。
Negative number: A number less than zero, written with a minus sign. Used for temperature, debt or height below sea level.
负数：小于零的数，用减号书写。用于温度、负债或海拔以下的高度。
Absolute value: The distance of a number from zero on the number line, always positive. |−7| = 7.
绝对值：数轴上某个数到零的距离，始终为正。|−7| = 7。
Place value: The value of a digit depending on its position. In 3.52, the 5 is in the tenths column and represents ⁵⁄₁₀.
位值：数字依据其位置而具有的值。在 3.52 中，5 在十分位，表示 ⁵⁄₁₀。
Order of operations (BIDMAS/BODMAS): The rule for evaluating expressions: Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right).
运算顺序 (BIDMAS/BODMAS)：计算表达式的规则：括号、指数、除法和乘法（从左到右）、加法和减法（从左到右）。
Factor: A whole number that divides another exactly without a remainder. Factors of 12: 1, 2, 3, 4, 6, 12.
因数（因子）：能整除另一个数的整数。12 的因数：1, 2, 3, 4, 6, 12。
Multiple: The product of a number and any integer. The first four multiples of 5 are 5, 10, 15, 20.
倍数：一个数与任意整数的乘积。5 的前四个倍数：5, 10, 15, 20。
Prime number: An integer greater than 1 with exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are primes.
质数（素数）：大于 1 且仅有两个不同因数的整数：1 和它本身。2, 3, 5, 7, 11 是质数。
Square number: The result of multiplying a whole number by itself. 1, 4, 9, 16, 25 are square numbers (1², 2², 3² …).
平方数：一个整数自乘的结果。1, 4, 9, 16, 25 是平方数（1², 2², 3² …）。
Cube number: The result of multiplying a whole number by itself twice. 8 = 2³.
立方数：一个整数自乘两次的结果。8 = 2³。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Numerator: The top number in a fraction; it shows how many parts are taken. In ³⁄₄, 3 is the numerator.
分子：分数中上面的数字；表示取了多少份。在 ³⁄₄ 中，3 是分子。
Denominator: The bottom number in a fraction; it tells into how many equal parts the whole is divided. In ³⁄₄, 4 is the denominator.
分母：分数中下面的数字；表示整体被分成了多少等份。在 ³⁄₄ 中，4 是分母。
Equivalent fractions: Fractions that represent the same value. ¹⁄₂ = ²⁄₄ = ⁴⁄₈.
等值分数：表示相同值的分数。¹⁄₂ = ²⁄₄ = ⁴⁄₈。
Simplify (reduce) a fraction: Divide numerator and denominator by their highest common factor. ⁸⁄₁₂ simplifies to ²⁄₃.
约分：用分子和分母的最大公因数相除。⁸⁄₁₂ 约分为 ²⁄₃。
Mixed number: A whole number and a proper fraction combined. 2½ means two whole ones and a half.
带分数：整数与真分数的组合。2½ 表示两个整体和一个二分之一。
Improper fraction: A fraction where the numerator is larger than the denominator, e.g. ⁷⁄₄.
假分数：分子大于分母的分数，例如 ⁷⁄₄。
Decimal: A number written using a decimal point to separate whole and fractional parts. 0.75 is a decimal.
小数：使用小数点分隔整数部分与小数部分的数字。0.75 是一个小数。
Recurring decimal or more digits repeat forever, shown with a dot above the repeating digit(s). ¹⁄₃ = 0.333…
循环小数：一个或多个数字无限重复的小数，在重复数字上加点表示。¹⁄₃ = 0.333…
Percentage: A fraction out of 100, written with the % symbol. 45% means 45 out of 100.
百分比：表示占 100 分之多少的数，用% 符号书写。45% 表示每 100 份中的 45 份。
Convert between FDP: Link ¹⁄₂ = 0.5 = 50% — memorise common equivalents to speed up problem-solving.
分数、小数、百分比的转换：联系 ¹⁄₂ = 0.5 = 50% —— 熟记常见等值关系能加快解题速度。
3. Algebra Basics | 代数基础
Variable: A symbol, usually a letter, used to represent a number we do not know yet. In 3n + 5, n is the variable.
变量：通常用字母表示的符号，代表尚未知道的数字。在 3n + 5 中，n 是变量。
Term: A single part of an expression separated by + or −. In 4x + 2y − 7, there are three terms.
项：表达式中由 + 或 − 分隔的单个部分。在 4x + 2y − 7 中，有三个项。
Expression: A combination of numbers, variables and operation symbols, but without an equals sign. Example: 2a + 6.
表达式：数字、变量和运算符号的组合，没有等号。示例：2a + 6。
Equation atement that two expressions are equal, containing an equals sign. 3x = 12 is an equation.
方程：说明两个表达式相等的数学陈述，含有等号。3x = 12 是一个方程。
Formula (plural: formulae) mbols, showing a relationship between quantities. A = l × w gives the area of a rectangle.
公式：用字母和符号书写的规则，表示量之间的关系。A = l × w 给出了长方形的面积。
Substitution cing a variable with a given number to evaluate an expression. If x = 4, then 2x + 3 = 11.
代入：将变量换成给定的数字以计算表达式的值。若 x = 4，则 2x + 3 = 11。
4. Equations and Expressions | 方程与表达式进阶
Collect like terms or : Simplify an expression by adding or subtracting the coefficients of terms that have identical variable parts. 5a + 3a = 8a.
合并同类项：通过将变量部分相同的项的系数相加或相减来简化表达式。5a + 3a = 8a。
Expand brackets: Multiply each term inside a bracket by the term outside. 3(y + 2) = 3y + 6.
去括号（展开）：将括号外的项乘以括号内的每一项。3(y + 2) = 3y + 6。
Factorise Write an expression as a product of factors, the reverse of expanding. 6x + 9 = 3(2x + 3).
因式分解：将表达式写成因数的乘积，是展开的逆运算。6x + 9 = 3(2x + 3)。
Solve an equation: Find the value of the variable that makes the equation true. Solve 2p − 5 = 7 → p = 6.
解方程：找到使方程成立的变量的值。解 2p − 5 = 7 → p = 6。
Inverse operation: The operation that reverses the effect of another. Addition and subtraction are inverses; multiplication and division are inverses.
逆运算：逆转另一种运算效果的运算。加减互为逆运算，乘除互为逆运算。
Linear sequence: A number pattern where the difference between consecutive terms is constant (the term-to-term rule). 3, 7, 11, 15 … has difference +4.
线性序列：相邻项之间的差为常数的数字模式（项到项规则）。3, 7, 11, 15 … 的差为 +4。
nth term: A formula that generates any term of a sequence using its position n. For 4, 7, 10, 13 … the nth term is 3n + 1.
第 n 项（通项公式）：用位置 n 生成序列中任意一项的公式。对于 4, 7, 10, 13 …，第 n 项是 3n + 1。
5. Geometry – Angles | 几何 – 角
Angle: A measure of turn, often in degrees (°). A full turn is 360°.
角：旋转的量度，常用度（°）表示。一整圈是 360°。
Acute angle: An angle between 0° and 90°.
锐角：0° 到 90° 之间的角。
Right angle: An angle of exactly 90°, often shown with a small square.
直角：恰好为 90° 的角，常用一个小方框标记。
Obtuse angle: An angle between 90° and 180°.
钝角：90° 到 180° 之间的角。
Reflex angle: An angle between 180° and 360°.
优角（反射角）：180° 到 360° 之间的角。
Complementary angles: Two angles that add up to 90°.
互余角：两个角和为 90°。
Supplementary angles: Two angles that add up to 180°.
互补角：两个角和为 180°。
Vertically opposite angles: Angles opposite each other when two lines cross. They are equal.
对顶角：两直线相交时彼此相对的角。它们相等。
Angles on a straight line: Sum to 180°.
直线上的角：和为 180°。
Angles around a point: Sum to 360°.
一点周围的角：和为 360°。
6. Geometry – Shapes and Measures | 几何 – 形状与度量
Perimeter: The total distance around the edge of a shape. Add all side lengths together.
周长：围绕图形边界的总长度。将所有边长相加。
Area of rectangle = length × width
面积：图形表面覆盖的量度，以平方单位计。
长方形的面积 = 长 × 宽
Area of triangle = ½ × base × perpendicular height
三角形的面积 = ½ × 底 × 垂直高
Area of parallelogram = base × perpendicular height
平行四边形的面积 = 底 × 垂直高
Area of trapezium = ½ × (sum of parallel sides) × perpendicular height
梯形的面积 = ½ ×（平行边之和）× 垂直高
Volume a 3D shape occupies, measured in cubic units. Volume of cuboid = length × width × height.
体积：三维形状所占空间的大小，以立方单位计。长方体的体积 = 长 × 宽 × 高。
Surface area: The total area of all faces of a 3D solid.
表面积：三维立体所有面的面积总和。
Congruent shapes: Identical in shape and size; one can be rotated or reflected to match the other exactly.
全等形：形状和大小完全相同；一个可通过旋转或反射与另一个完全重合。
Similar shapes: Same shape but different size; corresponding angles equal and sides in proportion.
相似形：形状相同但大小不同；对应角相等，对应边成比例。
Metric units: Length: mm, cm, m, km. Mass: g, kg. Capacity: ml, L. King Henry's Daughters Make Chocolate Mice = km, hm, dam, m, dm, cm, mm (alternative mnemonic).
公制单位：长度：毫米、厘米、米、千米。质量：克、千克。容积：毫升、升。
7. Statistics and Probability | 统计与概率
Mean dding all values and dividing by the number of values. Mean of 3, 5, 10 is (3+5+10)÷3 = 6.
平均数（均值）：将所有数值相加后除以数值个数所得。3, 5, 10 的均值为 (3+5+10)÷3 = 6。
Median: The middle value when data is arranged in order. For 2, 3, 7, 9, 11, the median is 7.
中位数：数据排序后位于中间的值。对于 2, 3, 7, 9, 11，中位数是 7。
Mode: The value that occurs most often. In 1, 2, 2, 4, 5, the mode is 2.
众数：出现频率最高的值。在 1, 2, 2, 4, 5 中，众数为 2。
Range: The difference between the largest and smallest values. In 12, 5, 9, range = 12 − 5 = 7.
极差（范围）：最大值与最小值之差。在 12, 5, 9 中，极差 = 12 − 5 = 7。
Outlier: A data point that is much larger or smaller than the rest of the data.
异常值：远大于或远小于其他数据的数据点。
Discrete data: Data that can only take certain specific values, often integers. Number of students is discrete.
离散数据：只能取特定值的数据，通常是整数。学生人数是离散的。
Continuous data: Data that can take any value within a range, e.g. height, time.
连续数据：在某一范围内可取任意值的数据，如身高、时间。
Probability: A measure of how likely an event is, on a scale from 0 (impossible) to 1 (certain). Expressed as a fraction, decimal or percentage.
概率：衡量事件发生可能性的尺度，从 0（不可能）到 1（必然）。可用分数、小数或百分比表示。
Expected frequency appen based on probability. If P(head) = ½ and you toss a coin 100 times, expect 50 heads.
期望频数：根据概率估计事件发生的次数。若 P(正面) = ½，投掷硬币 100 次，期望 50 次正面。
Mutually exclusive events: Two events that cannot happen at the same time. Rolling a 1 and rolling a 6 on a single die are mutually exclusive.
互斥事件：不可能同时发生的两个事件。掷一次骰子，出现 1 点和出现 6 点是互斥的。
Sample space: The set of all possible outcomes. For tossing a coin, sample space = {Head, Tail}.
样本空间：所有可能结果的集合。抛一次硬币的样本空间 = {正面，反面}。
8. Ratio, Proportion and Rates of Change | 比、比例与变化率
Ratio: A way to compare quantities. The ratio of boys to girls 2:3 means for every 2 boys there are 3 girls.
比：比较数量的一种方式。男女生人数比为 2:3 表示每 2 个男生对应 3 个女生。
Simplify a ratio: Divide all parts by their highest common factor. 10:15 simplifies to 2:3.
化简比：将所有部分除以它们的最大公因数。10:15 化简为 2:3。
Proportion: An equation showing two ratios are equal. If your recipe uses 2 eggs for 4 people, it uses 4 eggs for 8 people – the eggs and servings are in direct proportion.
比例：表示两个比相等的等式。若食谱为 4 人份用 2 个鸡蛋，则 8 人份用 4 个鸡蛋——鸡蛋数量与份数成正比例。
Direct proportion: As one quantity increases, the other increases at the same rate. Graph is a straight line through the origin.
正比例：一个量增加时，另一个量以相同速率增加。图像是一条过原点的直线。
Inverse proportion: As one quantity increases, the other decreases at a matching rate. The product of the two quantities is constant.
反比例：一个量增加时，另一个量以相应的速率减少。两个量的乘积是常数。
Unitary method: Find the value of 1 unit first, then multiply to find the required amount. If 5 pens cost £3, 1 pen costs £0.60, so 8 pens cost £4.80.
归一法：先求出一个单位的值，再相乘得到所需数量。5 支笔 £3，1 支 £0.60，8 支 £4.80。
Scale factor: The number you multiply a shape's dimensions by to enlarge or reduce it. If a rectangle 2 cm by 3 cm is enlarged with scale factor 3, new dimensions are 6 cm by 9 cm.
比例因子（放大/缩小倍数）：将图形尺寸放大或缩小的乘数。若 2 cm × 3 cm 的长方形以比例因子 3 放大，新尺寸为 6 cm × 9 cm。
Percentage change se or : The increase or decrease expressed as a percentage of the original amount. (change ÷ original) × 100%.
百分比变化：用原量的百分比表示的增减量。公式：(变化量 ÷ 原量) × 100%。
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