📚 Year 11 CCEA Maths: Glossary Quick Memorisation Guide | CCEA 数学：词汇术语速记指南
Mastering mathematical vocabulary is half the battle in CCEA GCSE Mathematics. This guide presents essential terms grouped by topic, with clear explanations and memory hooks so you can recall them confidently under exam pressure.
攻克 CCEA GCSE 数学，掌握数学词汇就等于赢了一半。本文按主题梳理核心术语，配有简明释义与记忆窍门，让你在考试压力下也能从容回忆。
1. Numbers and Operations | 数与运算
Integer: Any whole number that can be positive, negative or zero, such as −5, 0, 42. Integers do not include fractions or decimals.
整数： 任何正整数、负整数或零，例如 −5、0、42，不含有分数或小数部分。
Factor: A whole number that divides another number exactly with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.
因数： 能够整除另一个数的整数。12 的因数是 1、2、3、4、6 和 12。
Multiple: The product of a number and any integer. The first four multiples of 7 are 7, 14, 21 and 28.
倍数： 一个数与任意整数的乘积。7 的前四个倍数是 7、14、21 和 28。
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are primes; 1 is not prime.
质数（素数）： 大于 1 且只有两个不同因数的数，即 1 和它本身。2、3、5、7、11 是质数，1 不是质数。
Highest common factor (HCF): The largest factor shared by two or more numbers. The HCF of 18 and 24 is 6.
最大公因数（HCF）： 两个或多个数的公有因数中最大的一个。18 和 24 的最大公因数是 6。
Lowest common multiple (LCM): The smallest multiple that two or more numbers have in common. The LCM of 4 and 5 is 20.
最小公倍数（LCM）： 两个或多个数公有的倍数中最小的一个。4 和 5 的最小公倍数是 20。
Order of operations: The rule telling you which calculation to do first in a multi‑step expression. Remember the sequence BIDMAS: Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right).
运算顺序： 混合运算时遵循顺序规则。牢记 BIDMAS（括号、指数、乘除从左到右、加减从左到右）。
- B – Brackets 括号 ( )
- I – Indices 指数, like squares and cubes
- DM – Division and Multiplication 除法和乘法, work left to right
- AS – Addition and Subtraction 加法和减法, work left to right
2. Algebra Basics | 代数基础
Expression: A combination of numbers, letters and operations but with no equals sign. For example, 3x + 5y − 2 is an expression.
表达式： 由数字、字母和运算符组成的式子，不含等号。如 3x + 5y − 2 是一个表达式。
Term: A single number, variable or product of numbers and variables. In 4a² − 7b + 9, the terms are 4a², −7b and 9.
项： 单一的数、变量或数与变量的乘积。在 4a² − 7b + 9 中，项是 4a²、−7b 和 9。
Coefficient: The numeric factor multiplying a variable. In 7pq, the coefficient of pq is 7.
系数： 变量前面的数字因子。在 7pq 中，pq 的系数是 7。
Constant: A term with a fixed value that does not change; it contains no variables. In 2x + 3, the constant is 3.
常数： 值固定不变的项，不含变量。在 2x + 3 中，常数是 3。
Simplify: Collecting like terms to write an expression in the shortest possible form. 5x + 3y − 2x + y simplifies to 3x + 4y.
化简： 合并同类项，将表达式写成最简形式。5x + 3y − 2x + y 化简为 3x + 4y。
Expand: Multiplying out brackets to remove them. Using the distributive law: a(b + c) = ab + ac.
展开： 通过乘法去掉括号，运用分配律：a(b + c) = ab + ac。
Factorise: Rewriting an expression as a product of its factors – the reverse of expanding. 6x + 9 factorises to 3(2x + 3).
因式分解： 将表达式写成几个因式的乘积，是展开的逆过程。6x + 9 因式分解为 3(2x + 3)。
Indices: Also called powers or exponents. aⁿ means a multiplied by itself n times. Special names: a² is ‘a squared’, a³ is ‘a cubed’.
指数： 又称幂。aⁿ 表示 a 自乘 n 次。特殊读法：a² 读作“a 的平方”，a³ 读作“a 的立方”。
3. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement showing that two expressions are equal, linked by an equals sign. Example: 2x + 1 = 9.
方程： 表示两个表达式相等的式子，用等号连接。例：2x + 1 = 9。
Solve: To find the value(s) of a variable that make the equation true. Solving 3x = 12 gives x = 4.
解方程： 求出使方程成立的未知数的值。解 3x = 12 得 x = 4。
Inverse operation: The opposite process used to isolate the variable. Addition undoes subtraction, multiplication undoes division.
逆运算： 用来分离变量的相反运算。加法与减法互逆，乘法与除法互逆。
Inequality: A relationship comparing two expressions using symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式： 用符号比较两个表达式的关系：< 小于, > 大于, ≤ 小于等于, ≥ 大于等于。
Solution set: All values that satisfy an equation or inequality. For x > 3, the solution set is any number greater than 3.
解集： 满足方程或不等式的所有值。对于 x > 3，解集为所有大于 3 的数。
Quadratic equation: An equation where the highest power of the variable is 2, written as ax² + bx + c = 0 (a ≠ 0).
二次方程： 未知数最高次数为 2 的方程，一般形式 ax² + bx + c = 0（a ≠ 0）。
Roots: The solutions of a quadratic equation; also the x‑intercepts of its graph. The roots of x² − 5x + 6 = 0 are x = 2 and x = 3.
根： 二次方程的解，也指其图像与 x 轴的交点。x² − 5x + 6 = 0 的根为 x = 2 和 x = 3。
4. Sequences | 数列
Sequence: An ordered list of numbers following a rule. Each number is called a term. Example: 2, 5, 8, 11, …
数列： 按某种规则排列的一列数。其中的每一个数称为项。例：2, 5, 8, 11, …
Arithmetic sequence: A sequence where the difference between consecutive terms is constant (common difference, d). In 4, 7, 10, 13, d = 3.
等差数列： 相邻两项的差为常数的数列，该常数称为公差 d。在 4, 7, 10, 13 中，d = 3。
nth term: A formula that gives any term of a sequence based on its position n. For 3, 6, 9, 12, the nth term is 3n.
第 n 项（通项公式）： 根据项的位置 n 计算该项值的公式。对数列 3, 6, 9, 12，通项公式为 3n。
Position-to-term rule: Another name for the nth term formula. To find the 10th term of 5n − 2, substitute n = 10 to get 48.
项位公式： 第 n 项公式的另一名称。求 5n − 2 的第 10 项，代入 n = 10 得 48。
Fibonacci sequence: A sequence where each term is the sum of the two preceding terms: 1, 1, 2, 3, 5, 8, 13, …
斐波那契数列： 从第三项起每一项都等于前两项之和的数列：1, 1, 2, 3, 5, 8, 13, …
5. Geometry and Measures | 几何与测量
Angle: The measure of turn between two lines meeting at a point, measured in degrees (°). Acute < 90°, right = 90°, obtuse between 90° and 180°, reflex > 180°.
角： 两条相交直线之间转动的量，以度 (°) 计量。锐角 < 90°，直角 = 90°，钝角介于 90° 到 180°，优角 > 180°。
Triangle: A polygon with three sides and three angles. Sum of interior angles is always 180°.
三角形： 三条边和三个角组成的多边形。内角和恒为 180°。
Parallel lines: Straight lines that remain the same distance apart and never meet. Alternate angles are equal, corresponding angles are equal, co‑interior angles sum to 180°.
平行线： 永不相交且距离保持不变的直线。内错角相等，同位角相等，同旁内角互补（和为 180°）。
Perimeter: The total distance around the outside of a 2D shape. For a rectangle of length l and width w, perimeter = 2l + 2w.
周长： 二维图形外边界的总长度。长为 l、宽为 w 的矩形，周长 = 2l + 2w。
Area: The amount of space inside a 2D shape. Rectangle: A = l × w. Triangle: A = ½ × base × height.
面积： 二维图形内部空间的大小。矩形面积 A = l × w，三角形面积 A = ½ × 底 × 高。
Volume: The space occupied by a 3D solid. Cuboid: V = length × width × height. Prism: V = area of cross‑section × length.
体积： 三维实体所占的空间。长方体体积 V = 长 × 宽 × 高，棱柱体积 V = 底面积 × 长。
Surface area: The total area of all faces of a 3D shape. Think of it as the area of the net.
表面积： 三维图形所有面的总面积，可以理解为展开图的面积。
Circle vocabulary: The circumference is the perimeter of a circle; radius (r) is from centre to edge; diameter (d) = 2r. C = 2πr or πd; A = πr².
圆的术语： 圆周（circumference）即圆的周长；半径（r）从圆心到圆周；直径（d）= 2r。C = 2πr 或 πd；A = πr²。
6. Pythagoras and Trigonometry | 勾股定理与三角
Pythagoras’ theorem: In a right‑angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. a² + b² = c² where c is the hypotenuse.
勾股定理： 直角三角形中，斜边的平方等于两直角边的平方和。a² + b² = c²，其中 c 为斜边。
Hypotenuse: The longest side of a right‑angled triangle, always opposite the right angle.
斜边： 直角三角形中最长的边，总是直角的对边。
Trigonometric ratios: For an angle θ in a right‑angled triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Remember SOH CAH TOA.
三角函数比： 直角三角形中，对于角 θ： sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边。记住口诀 SOH CAH TOA。
Angle of elevation: The angle measured upwards from the horizontal line of sight. Used in right‑triangle problems.
仰角： 从水平视线向上测量的角，用于直角三角形问题。
Angle of depression: The angle measured downwards from the horizontal line of sight. Equal to the angle of elevation from the other object (alternate angles).
俯角： 从水平视线向下测量的角。等于从另一物体看的仰角（内错角相等）。
7. Graphs | 图形
Coordinates: A pair of values (x, y) showing a point’s position on a grid. The origin is (0, 0).
坐标： 一对数值 (x, y)，表示点在网格中的位置。原点是 (0, 0)。
Linear graph: A straight‑line graph whose equation can be written as y = mx + c, where m is the gradient and c is the y‑intercept.
线性图： 方程可写成 y = mx + c 的直线图，m 是斜率（梯度），c 是 y 轴截距。
Gradient: A measure of steepness, calculated as rise over run: m = change in y ÷ change in x. A positive gradient slopes upwards, negative slopes downwards.
梯度（斜率）： 陡峭程度的度量，计算为垂向变化与水平变化的比值：m = Δy/Δx。正梯度向上倾斜，负梯度向下倾斜。
Intercept: The point where a graph crosses an axis. The y‑intercept is where x = 0; the x‑intercept is where y = 0.
截距： 图形与坐标轴相交的点。y 轴截距是 x = 0 时的点；x 轴截距是 y = 0 时的点。
Parallel lines: Lines that never meet; they have the same gradient. y = 2x + 1 and y = 2x − 4 are parallel.
平行线： 永不相交的直线，它们的梯度相等。y = 2x + 1 和 y = 2x − 4 是平行的。
Perpendicular lines: Lines that intersect at right angles. Their gradients multiply to −1 (e.g., 2 and −½).
垂直线： 以直角相交的直线，它们梯度的乘积为 −1（例如 2 和 −½）。
Quadratic graph: A U‑shaped curve called a parabola, equation y = ax² + bx + c. The turning point is the minimum or maximum.
二次函数图： 呈 U 形的曲线称为抛物线，方程为 y = ax² + bx + c。顶点是最高点或最低点。
8. Ratio, Proportion and Rates | 比、比例和率
Ratio: A way to compare quantities of the same kind. Written as a : b. The ratio 3 : 2 means for every 3 of one, there are 2 of the other.
比： 比较同类数量的一种方式，写作 a : b。比 3 : 2 表示每 3 份对应 2 份。
Simplify a ratio: Divide all parts by their HCF to get the simplest whole‑number form. 8 : 12 simplifies to 2 : 3.
化简比： 将所有部分除以最大公因数，得到最简整数比。8 : 12 化简为 2 : 3。
Proportion: An equation stating two ratios are equal. Direct proportion: as one quantity doubles, the other doubles. Inverse proportion: as one doubles, the other halves.
比例： 表示两个比相等的等式。正比：一个量翻倍，另一个量也翻倍。反比：一个量翻倍，另一个量减半。
Unitary method: Finding the value of one unit first, then scaling to the required quantity. For 3 pens cost £2.10, 1 pen costs £0.70, so 7 pens cost £4.90.
归一法： 先求出一个单位的量，再按需求缩放。若 3 支笔 2.10 英镑，1 支笔 0.70 英镑，则 7 支笔 4.90 英镑。
Percentage: A fraction out of 100. To find a % of an amount, multiply by the % and divide by 100. 20% of 60 = (20/100)×60 = 12.
百分数： 分母为 100 的分数。求一个数的百分之几，乘以百分数再除以 100。60 的 20% = (20/100)×60 = 12。
Compound interest: Interest recalculated each period on the new total. Formula: A = P(1 + r/100)ⁿ, where A is the final amount, P the principal, r the rate, n the number of periods.
复利： 每个计息周期按新总额重新计算利息。公式：A = P(1 + r/100)ⁿ，A 为最终金额，P 为本金，r 为利率，n 为周期数。
Rate: A special ratio comparing two quantities of different units. Examples: speed (km/h), density (g/cm³), unit price (pence per gram).
率： 比较两个不同单位量的特殊比。如速度（km/h）、密度（g/cm³）、单价（便士/克）。
9. Statistics | 统计
Mean: The arithmetic average, found by summing all values and dividing by the number of values. Mean of 4, 6, 8 is (4+6+8)/3 = 6.
平均数（均值）： 所有数值之和除以数据的个数。4, 6, 8 的平均数为 (4+6+8)/3 = 6。
Median: The middle value when data is ordered. For an even count, median is the mean of the two middle numbers.
中位数： 将数据排序后位于中间的数。偶数个数据时，中位数为中间两个数的均值。
Mode: The value that occurs most frequently. A data set can have no mode, one mode (unimodal) or more than one (multimodal).
众数： 出现次数最多的数值。数据可以没有众数、一个众数（单峰）或多个众数（多峰）。
Range: A measure of spread: Range = highest value − lowest value.
极差（范围）： 衡量离散程度的量：极差 = 最大值 − 最小值。
Outlier: An extreme value that lies significantly apart from the rest of the data, often identified as more than 1.5 × interquartile range beyond a quartile.
异常值： 与其他数据点明显不同的极端值，常被识别为超出四分位数 1.5 倍四分位距的值。
Frequency table: A table listing data values or groups alongside how often each occurs.
频数表： 列出数据值或组别及其出现次数的表格。
Cumulative frequency: The running total of frequencies. Used to find medians and quartiles on a cumulative frequency graph.
累积频数： 频数的累加总和，用于在累积频数图上求中位数和四分位数。
Scatter graph: A plot of two variables to show relationship (correlation). Positive correlation: as x increases, y tends to increase. Negative correlation: as x increases, y tends to decrease.
散点图： 描绘两个变量关系的图表。正相关：x 增大，y 趋向增大。负相关：x 增大，y 趋向减小。
Line of best fit: A straight line drawn through a scatter graph to show the trend, passing as close to as many points as possible. Used for estimating values (interpolation/extrapolation).
最佳拟合线： 在散点图上绘制的反映趋势的直线，尽量贴近多数点。用于估计数值（内插/外推）。
10. Probability | 概率
Probability: A measure of how likely an event is, on a scale from 0 (impossible) to 1 (certain). P(event) = number of favourable outcomes ÷ total number of possible outcomes.
概率： 事件发生可能性的度量，范围从 0（不可能）到 1（必然）。P(事件) = 有利结果数 ÷ 所有可能结果总数。
Sample space: The set of all possible outcomes. The sample space for rolling a die is {1, 2, 3, 4, 5, 6}.
样本空间： 所有可能结果的集合。掷一枚骰子的样本空间是 {1, 2, 3, 4, 5, 6}。
Mutually exclusive events: Events that cannot happen at the same time. Getting a head and a tail on a single coin toss are mutually exclusive.
互斥事件： 不能同时发生的事件。掷一次硬币得到正面与得到反面是互斥的。
Exhaustive events: A set of events that covers all possible outcomes. The probabilities of all exhaustive mutually exclusive events sum to 1.
完备事件组： 涵盖所有可能结果的一系列事件。一组完备且互斥的事件的概率之和为 1。
Independent events: Events where the outcome of one does not affect the outcome of the other. For independent events A and B, P(A and B) = P(A) × P(B).
独立事件： 一个事件的发生不影响另一事件发生的概率。对于独立事件 A 和 B，P(A 与 B) = P(A) × P(B)。
Dependent events: Events where the outcome changes the probability of another event; often represented with tree diagrams where probabilities change on the second branch.
相依事件： 一个事件的结果会改变另一事件概率的情况，常用概率树表示，分支上的概率随之变化。
Venn diagram: A diagram using circles to show relationships between sets, useful for visualising unions, intersections and complements.
韦恩图： 用圆圈表示集合关系的图表，便于直观展示并集、交集和补集。
Union (∪): The set of outcomes that belong to either event A or event B or both. A ∪ B.
并集 (∪)： 属于事件 A 或事件 B 或两者兼有的结果集合，记作 A ∪ B。
Intersection (∩): The set of outcomes belonging to both A and B. A ∩ B.
交集 (∩)： 同时属于 A 和 B 的结果集合，记作 A ∩ B。
Probability tree diagram: A branching diagram showing all possible outcomes of successive events. Multiply along branches for combined probabilities; add probabilities for different ways an outcome can occur.
概率树图： 展示连续事件所有可能结果的分支图。沿分支相乘得组合概率；不同路径概率相加得到同一结果的总概率。
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