📚 Essential Maths Vocabulary for Year 9 OCR: A Quick Memorisation Guide | Year 9 OCR 数学核心词汇速记指南
Building a strong mathematical vocabulary is essential for success in Year 9 OCR Mathematics. Understanding key terms allows you to follow lessons, interpret exam questions accurately, and communicate your solutions clearly. This guide covers the most important terms you will encounter, grouped by topic. Each entry gives the English term with a clear definition, followed by its Chinese equivalent and explanation. Study these regularly to boost your confidence and fluency in maths.
建立扎实的数学词汇基础对于在 Year 9 OCR 数学中取得成功至关重要。理解关键术语能让你跟上课堂内容、准确解读考题并清晰地呈现解题过程。本指南按主题分类，覆盖你将遇到的最重要术语。每条条目先给出英文术语及清晰定义，随后是中文对应词与解释。定期学习这些词汇，能极大提升你学习数学的信心与流畅度。
1. Algebraic Expressions | 代数表达式
A variable is a symbol, usually a letter, that represents an unknown number. For example, in 3x + 5, x is the variable.
变量 是用符号（通常是字母）表示未知数。例如在 3x + 5 中，x 就是变量。
A coefficient is the number multiplied by a variable. In 7y, 7 is the coefficient.
系数 是与变量相乘的数字。在 7y 中，7 是系数。
A term is a single number, variable, or product of numbers and variables. In 4a − 2b + 9, there are three terms: 4a, −2b, and 9.
项 指单个数字、变量，或数字与变量的乘积。在 4a − 2b + 9 中，有三项：4a、−2b 和 9。
An expression is a combination of terms using operations like addition and subtraction, but without an equals sign. For instance, 2x² − 3x + 7 is an expression.
表达式 是使用加减等运算连接起来的项的组合，不含等号。例如 2x² − 3x + 7 是一个表达式。
To simplify an expression means to combine like terms. 5x + 3x simplifies to 8x.
化简 表达式指合并同类项。5x + 3x 化简后为 8x。
To expand means to remove brackets by multiplying. Expanding 3(x + 2) gives 3x + 6.
展开 指通过乘法去掉括号。展开 3(x + 2) 得到 3x + 6。
To factorise is to write an expression as a product of its factors, the reverse of expanding. 6x + 9 factorises to 3(2x + 3).
因式分解 是把表达式写成因式的乘积，是展开的逆运算。6x + 9 因式分解为 3(2x + 3)。
2. Linear Equations | 线性方程
An equation states that two things are equal, using an equals sign. 2x + 1 = 9 is an equation.
方程 用等号表示两个式子相等。2x + 1 = 9 就是一个方程。
A linear equation is one where the variable has an exponent of 1. The graph of a linear equation is a straight line.
线性 方程是指变量的指数为 1 的方程。线性方程的图像是一条直线。
To solve an equation means to find the value of the variable that makes it true. Solving 2x + 1 = 9 gives x = 4.
解 方程指求出使等式成立的变量值。解 2x + 1 = 9 得到 x = 4。
The root or solution of an equation is the value that satisfies it. 4 is the root of 2x + 1 = 9.
方程的 根 或者解是满足该等式的值。4 是方程 2x + 1 = 9 的根。
An unknown is another name for the variable in an equation. We solve for the unknown.
未知数 是方程中变量的另一名称。我们求解未知数。
The balance method means doing the same operation to both sides to keep the equation balanced. Adding 3 to both sides of x − 3 = 7 gives x = 10.
天秤法 指对等式两边同时进行相同运算，以保持平衡。在 x − 3 = 7 两边加 3 得 x = 10。
3. Graphs and Coordinates | 图像与坐标
A coordinate is a pair of numbers (x, y) that describe the position of a point on a grid. (3, 5) means 3 along the x-axis and 5 up the y-axis.
坐标 是一对数 (x, y)，用来描述网格上某一点的位置。(3, 5) 表示沿 x 轴走 3，沿 y 轴向上走 5。
The axes are the two perpendicular number lines on a graph. The horizontal line is the x-axis, and the vertical line is the y-axis.
坐标轴 是图表上两条互相垂直的数轴。水平线为 x 轴，垂直线为 y 轴。
The origin is the point where the axes meet, with coordinates (0, 0).
原点 是两轴的交点，坐标为 (0, 0)。
The gradient or slope of a line measures how steep it is. It is calculated as change in y ÷ change in x.
斜率 衡量一条直线的倾斜程度。计算公式为 y 的变化量 ÷ x 的变化量。
The intercept is where a line crosses an axis. The y-intercept is the point where the line crosses the y-axis.
截距 是直线与坐标轴的交点。y 轴截距是直线与 y 轴相交的点。
To plot a point means to mark it on a graph using its coordinates. Plot the point (2, −1) by moving right 2 and down 1.
描点 指根据坐标在图上标注一个点。描点 (2, −1) 的方法是向右移 2、向下移 1。
4. Sequences | 数列
A sequence is an ordered list of numbers following a rule. For example, 2, 5, 8, 11, … is an arithmetic sequence.
数列 是按照某种规则排列的一组有序的数。例如 2, 5, 8, 11, … 就是一个等差数列。
Each number in a sequence is called a term. The first term is often called u₁ or a.
数列中的每一个数叫做 项。首项常记为 u₁ 或 a。
The nth term is a rule that lets you find any term in a sequence. For the sequence 5, 8, 11, 14, …, the nth term is 3n + 2.
第 n 项 是能求出数列中任意项的规则。数列 5, 8, 11, 14, … 的第 n 项为 3n + 2。
An arithmetic sequence is one where the difference between successive terms is constant. This difference is called the common difference, often denoted by d.
等差 数列是相邻两项差值为常数的数列。这个差值叫做 公差，常用 d 表示。
To generate a sequence means to write out its terms using the nth term rule. For 2n − 1, the first three terms are 1, 3, 5.
生成 数列指利用第 n 项规则写出各项。对于 2n − 1，前三项为 1, 3, 5。
5. Geometry Basics | 几何基础
An angle is formed where two lines meet. It is measured in degrees (°).
角 由两条线相交而成，以度 (°) 为单位测量。
Parallel lines are lines in the same plane that never meet. The symbol for parallel is //.
平行 线是在同一平面内永不相交的直线。平行用符号 // 表示。
Perpendicular lines meet at a right angle (90°).
垂直 线相交成直角 (90°)。
A polygon is a closed flat shape with straight sides. Triangles, quadrilaterals, and pentagons are polygons.
多边形 是由直边围成的封闭平面图形。三角形、四边形和五边形都是多边形。
The interior angle of a polygon is the angle inside the shape between two sides. Exterior angles are formed by extending one side outward.
多边形的 内角 是图形内部两条边所夹的角。外角由一边向外延长而形成。
The sum of the exterior angles of any polygon is always 360°. For a regular polygon, each exterior angle = 360° ÷ n, where n is the number of sides.
任意多边形的外角和总是 360°。对于正多边形，每个外角 = 360° ÷ n，n 为边数。
6. Pythagoras’ Theorem | 勾股定理
Pythagoras’ theorem applies to right-angled triangles. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².
勾股定理 适用于直角三角形。它指出斜边的平方等于另外两条边的平方和：a² + b² = c²。
The hypotenuse is the longest side of a right-angled triangle, always opposite the right angle.
斜边 是直角三角形中最长的一条边，始终对着直角。
A right-angled triangle has one angle equal to 90°. The other two angles are acute and add up to 90°.
直角三角形 有一个角等于 90°。另外两个角为锐角，且和为 90°。
To find the hypotenuse, if the other sides are 3 cm and 4 cm: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5 cm.
如果另外两条边是 3 cm 和 4 cm，求斜边：c² = 3² + 4² = 9 + 16 = 25，所以 c = √25 = 5 cm。
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², such as 3, 4, 5 or 5, 12, 13.
勾股数 是指能满足 a² + b² = c² 的三个整数，如 3, 4, 5 或 5, 12, 13。
The square root (√) undoes squaring. √49 = 7 because 7² = 49.
平方根 (√) 是平方的逆运算。√49 = 7，因为 7² = 49。
7. Ratio and Proportion | 比与比例
A ratio compares two or more quantities. The ratio of boys to girls in a class might be 14 : 12, which simplifies to 7 : 6.
比 用来比较两个或多个数量。一个班级男女生比例可能是 14 : 12，化简后为 7 : 6。
To simplify a ratio, divide all parts by their highest common factor. 18 : 24 simplified is 3 : 4.
化简 比时，所有部分都除以它们的最大公因数。18 : 24 化简后为 3 : 4。
Proportion describes how one quantity changes with another. If y = 3x, we say y is proportional to x.
比例 描述一个量如何随另一个量变化。如果 y = 3x，我们说 y 与 x 成比例。
Direct proportion means as one quantity doubles, the other doubles. The graph is a straight line through the origin.
正比例 指一个量翻倍，另一个量也翻倍。图像为通过原点的直线。
A scale factor is the ratio of corresponding lengths in similar figures. Enlarging a shape by scale factor 2 doubles all side lengths.
比例因子 是相似图形中对应边的比值。以比例因子 2 放大图形，所有边长加倍。
The unitary method finds the value of one unit first, then scales up. If 5 pens cost £2, one pen costs 40p, so 8 pens cost £3.20.
归一法 先求出一个单位的值，再放大。若 5 支笔 2 英镑，一支笔 40 便士，8 支笔就是 3.20 英镑。
8. Statistics and Data | 统计与数据
The mean is the average, found by adding all data values and dividing by the number of values. For {3, 7, 8}, mean = (3+7+8)/3 = 6.
平均数（均值）是将所有数据相加再除以数据个数。对 {3, 7, 8}，均值 = (3+7+8)/3 = 6。
The median is the middle value when data is ordered. In {2, 4, 7, 9, 11}, the median is 7.
中位数 是排序后位于中间的数据。在 {2, 4, 7, 9, 11} 中，中位数是 7。
The mode is the value that occurs most often. In {1, 3, 3, 5, 7}, the mode is 3.
众数 是出现最频繁的值。在 {1, 3, 3, 5, 7} 中，众数是 3。
The range measures spread: it is the difference between the highest and lowest value. Range = maximum − minimum.
极差 衡量离散程度：最大值与最小值的差。极差 = 最大值 − 最小值。
Frequency is the number of times a value occurs. In a survey of pets, ‘dog’ might have a frequency of 15.
频数 指某个值出现的次数。在宠物调查中，“狗”的频数可能为 15。
An outlier is a value far removed from the rest of the data, which can affect the mean significantly.
异常值 是远离其余数据的值，可能显著影响平均值。
9. Probability | 概率
Probability is a measure of how likely an event is to happen, ranging from 0 (impossible) to 1 (certain). The probability of rolling a 3 on a fair die is 1/6.
概率 衡量事件发生的可能性，取值范围从 0（不可能）到 1（必然）。掷一个均匀骰子得到 3 的概率是 1/6。
An event is an outcome or set of outcomes. Drawing a red card from a deck is an event.
事件 是一个或一组结果。从一副牌中抽到红牌就是一个事件。
An outcome is a possible result of an experiment. When you flip a coin, the possible outcomes are heads and tails.
结果 是试验的一个可能结果。抛一枚硬币时，可能的结果是正面和反面。
The sample space is the set of all possible outcomes. For a die, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间 是所有可能结果的集合。对于一枚骰子，样本空间是 {1, 2, 3, 4, 5, 6}。
Relative frequency is an estimate of probability based on doing an experiment: number of times event occurs ÷ total number of trials.
相对频率 是基于实验的概率估计值：事件发生次数 ÷ 总试验次数。
Independent events are those where the outcome of one does not affect the other. Flipping a coin twice involves independent events.
独立 事件是指一个事件的结果不影响另一个事件。连续抛两次硬币就是独立事件。
10. Measures and Units | 测量与单位
Perimeter is the total distance around the outside of a shape. For a rectangle, perimeter = 2(length + width).
周长 是围绕图形外边界的总长度。对于矩形，周长 = 2 × (长 + 宽)。
Area measures the space inside a shape. Area of a rectangle = length × width.
面积 衡量图形内部的空间大小。矩形面积 = 长 × 宽。
Volume is the amount of space a 3D object occupies. Volume of a cuboid = length × width × height.
体积 是三维物体所占的空间量。长方体体积 = 长 × 宽 × 高。
Capacity is the amount a container can hold, often measured in litres (L) or millilitres (ml). 1 L = 1000 ml.
容量 指容器能容纳的量，通常以升 (L) 或毫升 (ml) 为单位。1 L = 1000 ml。
Unit conversion requires multiplying or dividing by powers of 10. To convert 2.5 km to metres, multiply by 1000 to get 2500 m.
单位换算 需要乘以或除以 10 的幂。将 2.5 km 换算为米，乘以 1000 得 2500 m。
A compound unit combines two units, like speed in metres per second (m/s) or density in grams per cm³. Speed = distance ÷ time.
复合单位 由两个单位组成，如速度单位米每秒 (m/s) 或密度单位克每立方厘米。速度 = 距离 ÷ 时间。
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