📚 Year 10 OCR Maths: Vocabulary Terminology Quick Memorisation Guide | Year 10 OCR 数学：词汇术语速记指南
Mastering mathematics requires a solid grasp of key vocabulary. This guide covers essential terms from the Year 10 OCR syllabus, pairing concise English definitions with clear Chinese explanations. Use the memorisation tips to build your confidence for class work and assessments.
学好数学离不开对核心术语的扎实理解。本指南涵盖了 Year 10 OCR 课程中的关键词汇，每个术语都配有简洁的英文定义和清晰的中文解释。运用记忆技巧，帮助你更自信地应对课堂学习和考试。
1. Number and Arithmetic Terms | 数字与算术术语
Factor: A whole number that divides exactly into another number with no remainder. For example, 1, 2, 3, 4, 6, and 12 are factors of 12.
因数：能整除给定整数的整数，且没有余数。例如，1、2、3、4、6 和 12 都是 12 的因数。
Multiple: The result of multiplying a number by an integer. The multiples of 5 are 5, 10, 15, 20, and so on.
倍数：一个数乘以整数得到的结果。5 的倍数有 5、10、15、20 等。
Prime number: A whole number greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are prime.
质数（素数）：大于 1 的整数，且恰好只有两个不同的因数：1 和它本身。例如 2、3、5、7、11 都是质数。
Reciprocal: The multiplicative inverse of a number. The reciprocal of 5 is 1/5, and the reciprocal of 2/3 is 3/2. Multiplying a number by its reciprocal gives 1.
倒数：一个数的乘法逆元。5 的倒数是 1/5，2/3 的倒数是 3/2。一个数与其倒数相乘得 1。
Memory tip: 'Prime' comes from 'first', meaning they cannot be broken down further by multiplication. The reciprocal just 'flips' a fraction.
记忆技巧：'Prime' 源自古拉丁语 'primus'，意为「第一」，表示无法再被其他数（除 1 和自己外）整除。倒数就是把分数「翻转」。
2. Algebraic Expressions | 代数表达式
Expression: A combination of numbers, variables, and operation symbols, without an equals sign. Examples: 3x + 2, a² - 5b.
表达式：由数字、变量和运算符号组成的式子，没有等号。例如：3x + 2、a² - 5b。
Term: A single number, variable, or product of numbers and variables in an expression. In 4x + 7y - 3, the terms are 4x, 7y, and -3.
项：表达式中单个的数字、变量或数字与变量的乘积。在 4x + 7y - 3 中，项分别为 4x、7y 和 -3。
Coefficient: The numerical factor multiplying a variable in a term. In 5xy, the coefficient of xy is 5. In -a, the coefficient is -1.
系数：项中与变量相乘的数字因数。在 5xy 中，xy 的系数是 5。在 -a 中，系数为 -1。
Like terms: Terms that contain exactly the same variable parts raised to the same powers. 3x² and -7x² are like terms; 2x and 2y are not.
同类项：含有完全相同的变量部分且相同幂次的项。3x² 和 -7x² 是同类项；2x 和 2y 不是同类项。
Memory tip: Co- means 'together with' – coefficient works together with the variable. Like terms can be combined as you would group apples with apples.
记忆技巧：'Co-' 表示「共同」—— 系数与变量「共同」构成项。同类项可以合并，就像把苹果和苹果放在一起。
3. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement that two expressions are equal, shown by the symbol '='. Solving an equation means finding the value(s) of the variable that make it true.
方程：用等号「=」表示两个表达式相等的数学陈述。解方程就是求出使等式成立的变量值。
Inequality: ess than, or not equal to another, using symbols <, >, ≤, ≥. Example: 2x + 1 > 5.
不等式：用符号 <、>、≤、≥ 表示一个表达式大于、小于或不等于另一个表达式的陈述。例如：2x + 1 > 5。
Root (or solution): A value that satisfies an equation. For x² = 4, the roots are x = 2 and x = -2.
根（或解）：使方程成立的数值。对于 x² = 4，根为 x = 2 和 x = -2。
Identity: An equation that is true for all values of the variable, often written with '≡'. Example: (x + 1)² ≡ x² + 2x + 1.
恒等式：对所有变量取值都成立的方程，常用「≡」表示。例如：(x + 1)² ≡ x² + 2x + 1。
Memory tip: Equation has 'equal', inequality has 'not equal'. An identity is 'identical' for every input.
记忆技巧：'Equation' 含 'equal'（相等）；'Inequality' 含 'not equal'（不相等）。恒等式对所有输入都「恒等」成立。
4. Graphs and Coordinates | 图形与坐标
Coordinates: An ordered pair (x, y) that specifies a point's location on a grid. The origin is (0, 0).
坐标：一个有序数对 (x, y)，用于确定点在网格上的位置。原点为 (0, 0)。
Gradient (slope): ted as change in y divided by change in x. A line with equation y = 2x + 1 has gradient 2.
斜率（梯度）：衡量直线倾斜程度的量，计算为 y 的变化量除以 x 的变化量。直线 y = 2x + 1 的斜率为 2。
Intercept: The point where a line crosses an axis. The y-intercept of y = 2x + 3 is (0, 3).
截距：直线与坐标轴的交点。y = 2x + 3 的 y 轴截距为 (0, 3)。
Linear: n can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
线性：描述直线图形，其方程可写成 y = mx + c 的形式，其中 m 为斜率，c 为 y 轴截距。
Memory tip: 'Gradient' reminds of 'grade' (steepness of a hill). The intercept is where the line 'intercepts' the axis.
记忆技巧：'Gradient' 联想到 'grade'（坡度）。截距就是直线「截断」坐标轴的地方。
5. Geometry of Shapes | 几何形状
Congruent: Two shapes are congruent if they have exactly the same size and shape. One can be mapped onto the other by translation, rotation, or reflection.
全等：两个图形大小和形状完全相同，则它们全等。其中一个图形可以通过平移、旋转或反射变换与另一个完全重合。
Similar: Two shapes are similar if their corresponding angles are equal and side lengths are in proportion. Similar shapes have the same shape but may differ in size.
相似：如果两个图形的对应角相等且对应边成比例，则它们相似。相似形状的形状相同，但大小可以不同。
Perpendicular: Two lines that intersect at a right angle (90°). The gradients of perpendicular lines multiply to -1 (unless one is vertical).
垂直：两条相交成直角（90°）的直线。两条垂直线的斜率乘积为 -1（除非其中一条为竖直线）。
Parallel: Two lines that never meet, always the same distance apart. Parallel lines have equal gradients.
平行：两条永不相交、始终等距的直线。平行线具有相等的斜率。
Memory tip: 'Congruent' = 'copy' – think of identical copies. 'Similar' has the same shape but is scaled up or down like a photo.
记忆技巧：'Congruent' 可联想到 'copy'（复制）—— 完全相同的副本。'Similar' 就像放大或缩小的照片，形状相同。
6. Measures and Units | 度量与单位
Perimeter: : The total length around the boundary of a 2D shape. For a rectangle, perimeter = 2(length + width).
周长：二维图形边界线的总长度。对于矩形，周长 = 2 × (长 + 宽)。
Area: de a 2D shape, measured in square units (cm², m²). Area of a triangle = ½ × base × height.
面积：二维图形内部的空间大小，以平方单位（cm²、m²）衡量。三角形面积 = ½ × 底 × 高。
Volume: D object, measured in cubic units (cm³, m³). Volume of a cuboid = length × width × height.
体积：三维物体所占的空间大小，以立方单位（cm³、m³）衡量。长方体的体积 = 长 × 宽 × 高。
Surface area: The total area of all faces of a 3D shape. A cube of side length a has surface area 6a².
表面积：三维物体所有面的总面积。边长为 a 的立方体表面积为 6a²。
Memory tip: 'Perimeter' = 'around measure'. 'Volume' turns up the 'vol' in 'voluminous'.
记忆技巧：'Perimeter' 含 'peri'（周围）—— 测量周围长度。'Volume' 想到 'voluminous'（体积大的）。
7. Transformations and Symmetry | 变换与对称
Translation: A transformation that slides a shape without turning or flipping. Describe by a column vector (x y) indicating horizontal and vertical shift.
平移：一种使图形只发生滑动而不旋转或翻转的变换。用一个列向量 (x y) 来描述，表示水平和垂直移动量。
Rotation: A transformation that turns a shape about a fixed centre point through a given angle, e.g. 90° clockwise.
旋转：图形绕着一个固定的中心点转动给定角度的变换，例如顺时针旋转 90°。
Reflection: A transformation that flips a shape over a mirror line. The image is the same perpendicular distance from the mirror line as the object.
反射：将图形沿一条镜像线翻转的变换。像和原图形到镜像线的垂直距离相等。
Enlargement: A transformation that changes the size of a shape by a scale factor from a centre of enlargement. Negative scale factors also reverse direction.
放大（伸展）：以放大中心为基点，用比例因子改变图形大小的变换。负比例因子还会产生反向的像。
Memory tip: 'Translation' = transfer location. 'Enlargement' involves a scale factor that acts like a zoom.
记忆技巧：'Translation' 可联想 'transfer'（转移）位置。'放大' 中的比例因子就像缩放镜头。
8. Trigonometry and Pythagoras | 三角学与毕达哥拉斯
Hypotenuse: The longest side of a right‑angled triangle, opposite the right angle.
斜边：直角三角形中最长的边，直角的对边。
Pythagoras' theorem: In a right‑ uare of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
毕达哥拉斯定理：在直角三角形中，斜边的平方等于另外两边的平方和：a² + b² = c²。
Sine (sin), Cosine (cos), Tangent (tan): Trigonometric ratios for an acute angle in a right‑ ngle. sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
正弦 (sin)、余弦 (cos)、正切 (tan)：直角三角形中锐角的三角函数比。sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边。
Angle of elevation/depression: Elevation is the angle measured up from the horizontal; depression is measured down from the horizontal.
仰角与俯角：仰角是从水平线向上测量的角；俯角是从水平线向下测量的角。
Memory tip: SOH CAH TOA – the classic mnemonic. Pythagoras fits any right triangle like a key.
记忆技巧：SOH CAH TOA 是最经典的口诀。毕达哥拉斯定理适用于所有直角三角形，像一把解锁的钥匙。
9. Statistics | 统计学
Mean: The average calculated by summing all data values and dividing by the number of values.
平均数（均值）：将所有数据值相加后除以数据的个数得到的平均值。
Median: The middle value when data are arranged in order. If there is an even number of values, take the mean of the two middle numbers.
中位数：将数据按大小顺序排列后位于中间的数值。如果数据个数为偶数，则取中间两个数的均值。
Mode: The value that occurs most frequently in a data set. A set can have more than one mode or no mode at all.
众数：数据集中出现频率最高的值。一组数据可以有多个众数，也可能没有众数。
Range: A measure of spread, calculated as largest value minus smallest value.
极差（范围）：衡量数据分散程度的量，计算为最大值减去最小值。
Memory tip: Think of 'median' as the medium (middle) of the road. 'Mode' sounds like 'most'.
记忆技巧：'Median' 含有 'medi'（中间），像道路的中央。'Mode' 发音似 'most'（最多）。
10. Probability | 概率
Probability: /percentage. P(event) = number of favourable outcomes / total number of possible outcomes.
概率：衡量事件发生可能性的量，用 0 到 1 之间的数、分数或百分数表示。P(事件) = 有利结果数 / 所有可能结果总数。
Sample space: The set of all possible outcomes of an experiment. For tossing two coins, the sample space is {HH, HT, TH, TT}.
样本空间：一个试验所有可能结果的集合。抛掷两枚硬币的样本空间为 {正正, 正反, 反正, 反反}。
Mutually exclusive: Events that cannot happen at the same time. For example, getting a head and a tail on a single coin toss are mutually exclusive.
互斥（互不相容）：不可能同时发生的事件。例如，一枚硬币抛掷一次得到正面和反面是互斥事件。
Independent events: Events where the outcome of one does not affect the probability of the other. Rolling a die twice gives independent results.
独立事件：一个事件的结果不影响另一个事件概率的事件。两次掷骰子的结果是独立的。
Memory tip: 'Mutually exclusive' means they exclude each other. 'Independent' events are free from influence – think of them as independently making decisions.
记忆技巧：'互斥' 表示互相排斥，不能共存。'独立事件' 互不影响，像是各自做决定。
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