📚 KS3 CCEA Further Mathematics: Vocabulary and Terminology Quick Revision Guide | KS3 CCEA 进阶数学：词汇术语速记指南
This quick revision guide covers the essential terms and vocabulary you need to master for KS3 CCEA Further Mathematics. Each entry includes the English term, a clear definition in English, and its Chinese equivalent with an explanation — all carefully paired to help bilingual learners solidify their understanding and recall under pressure.
这份速记指南涵盖了 KS3 CCEA 进阶数学必学的核心术语与词汇。每个条目都包含英文术语、清晰的英文定义以及中文对应词和解释——所有内容均以配对形式呈现，帮助双语学习者巩固理解并在考试中迅速回忆。
1. Number and Place Value | 数与位值
An integer is any whole number, positive or negative, including zero. Integers do not have fractional or decimal parts, and they are used in counting, ordering, and basic operations.
整数 是任何正整数、负整数或零，不含分数或小数部分，用于计数、排序和基本运算。
Place value tells us the value of a digit based on its position in a number. For example, in 3,852 the digit '8' has a place value of 800 because it is in the hundreds column.
位值 指数字在某个数中所处位置对应的值。例如，在 3852 中，数字 '8' 的位值是 800，因为它位于百位上。
The highest common factor (HCF) of two or more numbers is the largest number that divides exactly into all of them. The lowest common multiple (LCM) is the smallest number that is a multiple of each of the given numbers.
最大公因数 (HCF) 是两个或多个数都能整除的最大数。最小公倍数 (LCM) 是这些数各自的倍数中最小的那个。
- HCF of 12 and 18 is 6. | 12 和 18 的最大公因数是 6。
- LCM of 4 and 5 is 20. | 4 和 5 的最小公倍数是 20。
2. Fractions, Decimals, and Percentages | 分数、小数与百分数
A fraction has a numerator (top) and a denominator (bottom). An improper fraction has a numerator larger than the denominator, while a mixed number combines a whole number and a proper fraction.
分数 有分子（上）和分母（下）。假分数 的分子大于分母，而带分数 由一个整数和一个真分数合并而成。
To convert a fraction to a decimal, divide the numerator by the denominator. A terminating decimal ends after a finite number of digits, while a recurring decimal has a pattern that repeats forever, often indicated by a dot or bar.
要把分数化为小数，用分子除以分母。有限小数 在有限位数后终止，而循环小数 有一个无限重复的模式，通常用点或上划线表示。
A percentage is a fraction out of 100. To increase an amount by a percentage, multiply by (1 + (percentage ÷ 100)); to decrease, multiply by (1 − (percentage ÷ 100)).
百分数 是一种分母为 100 的分数。要将一个数量增加某个百分比，乘 (1 + (百分数 ÷ 100))；要减少，乘 (1 − (百分数 ÷ 100))。
Fraction → Decimal: ¼ = 0.25 | 分数转小数：¼ = 0.25
3. Ratios and Proportion | 比与比例
A ratio compares two or more quantities. It is written using a colon, for example 3 : 2. To simplify a ratio, divide all parts by their highest common factor.
比 是比较两个或多个量，用冒号书写，如 3 : 2。化简比时，将各部分除以它们的最大公因数。
Direct proportion means that as one quantity increases, the other increases at the same rate. The graph of a direct proportion is a straight line through the origin.
正比例 指一个量增加时，另一个量以相同的速率增加。正比例关系的图像是一条过原点的直线。
Inverse proportion means that as one quantity increases, the other decreases. Their product remains constant.
反比例 指一个量增加时另一个量减少，它们的乘积保持不变。
| Term | Meaning | 中文 |
|---|---|---|
| Ratio | Comparison of quantities | 比 |
| Proportion | Equation showing two ratios are equal | 比例 |
4. Algebraic Expressions | 代数表达式
An algebraic expression is a combination of numbers, letters (variables), and operations. For example, 3x + 2y − 7 is an expression. A term is a single part of an expression separated by '+' or '−'.
代数表达式 由数字、字母（变量）和运算符号组成，如 3x + 2y − 7。项 是表达式中用 '+' 或 '−' 分隔的单个部分。
A coefficient is the number in front of a variable. In 5x, 5 is the coefficient. A constant is a term with no variable, such as 8.
系数 是变量前面的数字。在 5x 中，5 是系数。常数 是没有变量的项，如 8。
Like terms have exactly the same variable raised to the same power. They can be collected (simplified) by adding or subtracting their coefficients.
同类项 具有完全相同的变量和相同的幂次，可通过加减系数进行合并（化简）。
Simplify: 2a + 3b + 5a − b = 7a + 2b | 化简：2a + 3b + 5a − b = 7a + 2b
5. Equations and Inequalities | 方程与不等式
An equation states that two expressions are equal, using the '=' sign. To solve an equation, find the value of the unknown that makes the statement true.
方程 用 '=' 表示两个表达式相等。解方程就是求出使等式成立的未知数的值。
An inequality an or equal to), ≥ (greater than or equal to). A solution is often shown on a number line.
不等式 用符号比较两个表达式：< (小于), > (大于), ≤ (小于等于), ≥ (大于等于)。解集常在数轴上表示。
The balance method is a key technique: do the same operation to both sides to keep the equation balanced. Undo operations in reverse BIDMAS order.
平衡法 是一项关键技巧：在方程两边同时进行相同的运算以保持平衡，按逆 BIDMAS 顺序撤销运算。
- Solve: 2x + 3 = 11 → x = 4 | 解方程：2x + 3 = 11 → x = 4
- Inequality: x > 5 means 'x is greater than 5'. | 不等式：x > 5 表示 'x 大于 5'。
6. Sequences and Patterns | 数列与规律
A sequence is a list of numbers or objects in a special order. Each number is called a term. The nth term of a sequence gives a rule for finding any term based on its position n.
数列 是按特定顺序排列的一列数或对象。每个数称为一个项。数列的第 n 项 给出了根据位置 n 求任意项的规则。
An arithmetic sequence has a constant difference between consecutive terms. The nth term can be written as an + b, where a is the common difference.
等差数列 相邻两项的差是常数。第 n 项可写作 an + b，其中 a 是公差。
The Fibonacci sequence starts with 1, 1 and each term after is the sum of the two preceding terms. This pattern appears frequently in nature.
斐波那契数列 以 1, 1 开始，之后的每一项都是前两项之和。这一模式在自然界中频繁出现。
Sequence: 3, 7, 11, 15, ... nth term = 4n − 1 | 数列：3, 7, 11, 15, ... 第 n 项 = 4n − 1
7. Geometry: Angles and Lines | 几何：角与线
An angle is the space between two intersecting lines, measured in degrees (°). A right angle is exactly 90°. An acute angle is less than 90°, and an obtuse angle is between 90° and 180°. A reflex angle is greater than 180°.
角 是两条相交线之间的空间，以度 (°) 为单位。一个直角 恰好 90°。锐角 小于 90°，钝角 在 90° 到 180° 之间。优角 大于 180°。
Parallel lines never meet and are marked with arrows. A transversal crossing parallel lines creates corresponding angles, alternate angles, and co-interior angles, which have special properties.
平行线 永不相交，用箭头标记。一条截线 穿过平行线会产生同位角、内错角 和同旁内角，它们具有特殊性质。
- Corresponding angles are equal. | 同位角相等。
- Alternate angles are equal. | 内错角相等。
- Co-interior angles sum to 180°. | 同旁内角之和为 180°。
8. Properties of Shapes | 图形性质
Polygons are closed 2D shapes with straight sides. A regular polygon has all sides and angles equal. Names: triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), octagon (8).
多边形 是由直线边组成的封闭二维图形。正多边形 的所有边和角都相等。命名：三角形（3 边）、四边形（4）、五边形（5）、六边形（6）、八边形（8）。
d polygon = (n − 2) × 180°. Each interior angle of a regular polygon = (n − 2) × 180° ÷ n.
n 边形的内角和 = (n − 2) × 180°。正多边形每个内角 = (n − 2) × 180° ÷ n。
Quadrilaterals include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites. Each has unique side and angle properties.
四边形 包括正方形、长方形、平行四边形、菱形、梯形和风筝形。每种都有独特的边角性质。
Symmetry: a shape has reflection symmetry if one half mirrors the other. Rotational symmetry tells us how many times a shape matches itself as it turns through 360°.
对称：如果一个图形的一半能镜像另一半，则具有反射对称。旋转对称 指图形旋转 360° 过程中能与自身重合的次数。
9. Measures and Units | 度量与单位
Perimeter is the total distance around the outside of a shape. Area is the amount of space inside a 2D shape, measured in square units (cm², m²). Volume measures the space inside a 3D object, in cubic units (cm³, m³).
周长 是图形外边总长度。面积 是二维图形内部空间大小，以平方单位（cm², m²）计量。体积 是三维物体内部空间，以立方单位（cm³, m³）计量。
ength × width; Triangle area = ½ × base × height; Cuboid volume = length × width × height.
重要公式：矩形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高；长方体体积 = 长 × 宽 × 高。
Metric conversions: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm; 1 kg = 1000 g; 1 litre = 1000 ml.
公制换算：1 公里 = 1000 米，1 米 = 100 厘米，1 厘米 = 10 毫米；1 公斤 = 1000 克；1 升 = 1000 毫升。
Area of triangle: A = ½ × b × h | 三角形面积：A = ½ × b × h
10. Statistics and Probability | 统计与概率
The mean is the average, found by adding all values and dividing by the number of values. The median is the middle value when data is ordered. The mode is the most frequent value. The range is the difference between highest and lowest values.
平均数 是全部数值相加后除以总数。中位数 是排序后位于中间的值。众数 是出现频率最高的值。极差 是最大值与最小值之差。
A pictogram uses pictures to represent data; a bar chart uses bars; a pie chart divides a circle into sectors to show proportions.
象形图 用图片表示数据；条形图 使用长条；饼图 将圆分成扇形表示比例。
Probability measures the chance of an event, written as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain). Experimental probability comes from trials; theoretical probability comes from equally likely outcomes.
概率 衡量事件发生的可能性，用 0（不可能）到 1（必然）之间的分数、小数或百分数表示。实验概率 来自试验；理论概率 来自等可能结果。
Probability = number of favourable outcomes ÷ total number of outcomes | 概率 = 有利结果数 ÷ 总结果数
11. Coordinates and Graphs | 坐标与图像
The coordinate plane uses two perpendicular axes: x-axis (horizontal) and y-axis (vertical). A point is written as (x, y). The origin is (0, 0).
坐标平面 用两根垂直的轴：x 轴（水平）和 y 轴（垂直）。一个点写作 (x, y)。原点 为 (0, 0)。
A linear graph has an equation of the form y = mx + c, where m is the gradient and c is the y-intercept.
线性图像 画出直线，方程为 y = mx + c，其中 m 是斜率，c 是 y 轴截距。
The gradient n y ÷ change in x. A positive gradient slopes upward, a negative gradient slopes downward.
斜率 衡量倾斜程度：m = y 的变化量 ÷ x 的变化量。正斜率向上倾斜，负斜率向下倾斜。
To find the midpoint of a line segment between (x₁, y₁) and (x₂, y₂), average the x-values and y-values: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
求线段中点：对 (x₁, y₁) 和 (x₂, y₂) 的 x 值和 y 值取平均：((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)。
Gradient: m = (y₂ − y₁) / (x₂ − x₁) | 斜率：m = (y₂ − y₁) / (x₂ − x₁)
12. Transformations | 变换
Translation slides a shape without turning. It is described by a column vector, e.g. (³⁄₂), meaning move 3 right and 2 up.
平移 使图形滑动而不旋转，用列向量描述，如 (³⁄₂) 表示向右移 3、向上移 2。
Reflection over a mirror line. The mirror line can be the x-axis, y-axis, or any line such as y = x.
反射 将图形沿对称轴翻转。对称轴可以是 x 轴、y 轴或任意直线如 y = x。
Rotation turns a shape about a centre of rotation by a given angle and direction (clockwise/anticlockwise). 90° anticlockwise is equivalent to 270° clockwise.
旋转 使图形绕旋转中心按给定角度和方向（顺时针/逆时针）转动。逆时针 90° 等价于顺时针 270°。
Enlargement changes the size of a shape by a scale factor from a centre of enlargement. If the scale factor is greater than 1, the shape gets bigger; if between 0 and 1, it gets smaller.
放大 以缩放因子从放大中心改变图形大小。缩放因子大于 1 时图形变大；介于 0 和 1 之间时变小。
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