📚 Year 11 OCR Maths: Vocabulary Quick Memorisation Guide | Year 11 OCR 数学：词汇术语速记指南
Mastering mathematical terminology is the key to unlocking exam success. In OCR GCSE Maths, a clear understanding of keywords helps you interpret questions accurately, communicate reasoning, and avoid careless mistakes. This guide breaks down essential terms by topic, pairing English definitions with their Chinese equivalents so you can learn and revise efficiently.
掌握数学术语是取得考试成功的关键。在OCR GCSE数学中，清晰理解关键词有助于准确解读题干、表述推理过程并避免粗心错误。本指南按主题分解基本术语，将英文定义与中文释义配对，方便你高效学习和复习。
1. Number and Place Value | 数与位值
Number terms form the backbone of all calculations. Being confident with these will support algebra, ratio, and more.
数词是所有计算的基础。熟练掌握这些术语将为代数、比例等内容提供支撑。
Integer: A whole number that can be positive, negative, or zero. Examples: -3, 0, 7.
整数：可以是正数、负数或零的整数。例如：-3, 0, 7。
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself. The first five primes are 2, 3, 5, 7, 11.
质数（素数）：大于1且恰好有两个不同因数（1和自身）的数。前五个质数是2, 3, 5, 7, 11。
Reciprocal: The multiplicative inverse of a number; when you multiply a number by its reciprocal, the result is 1. The reciprocal of 5 is ⅕.
倒数：一个数的乘法逆元；一个数与其倒数相乘得1。5的倒数是⅕。
Surd: An irrational root that cannot be simplified to a whole number or fraction, such as √2 or 3√5. Surds are left in root form for exact values.
根式：无法化简为整数或分数的无理根，如√2或3√5。根式保留根号形式以表示精确值。
Significant figure (s.f.): A digit that contributes to the precision of a number. In 0.004506, the first significant figure is 4. Rounding to 3 s.f. gives 0.00451.
有效数字：影响数字精度的数字。在0.004506中，首个有效数字是4。四舍五入到三位有效数字为0.00451。
Standard form: A way of writing very large or very small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. Example: 3.2 × 10⁵.
标准形式（科学记数法）：以a × 10ⁿ表示极大或极小数的方法，其中1 ≤ a < 10，n为整数。例如：3.2 × 10⁵。
2. Algebra: Expressions and Equations | 代数：表达式与方程
Algebraic vocabulary allows you to manipulate symbols and solve problems systematically.
代数词汇能让你系统地操作符号并解决问题。
Expression: A combination of symbols, numbers, and operators without an equals sign. Example: 3x² + 2x – 5.
表达式：不含等号的符号、数字和运算符组合。例如：3x² + 2x – 5。
Equation: A statement that two expressions are equal, shown by an ‘=’ sign. Solving an equation finds the unknown value(s).
方程：通过’=’号表明两个表达式相等的陈述。解方程就是求出未知数的值。
Identity: An equation that is true for all values of the variable, often written with an ‘≡’ sign. Example: (x+1)² ≡ x² + 2x + 1.
恒等式：对变量所有取值都成立的等式，常用’≡’号表示。例如：(x+1)² ≡ x² + 2x + 1。
Expand: To multiply out brackets and simplify. Expanding (x+3)(x-2) gives x² + x – 6.
展开：去括号并化简。展开(x+3)(x-2)得x² + x – 6。
Factorise: The reverse of expanding; writing an expression as a product of its factors. x² – 9 factorises to (x+3)(x-3).
因式分解：展开的逆运算；将表达式写成其因式的乘积。x² – 9因式分解为(x+3)(x-3)。
Coefficient: The numerical factor in a term. In 7x³, the coefficient of x³ is 7.
系数：单项式中的数字因子。在7x³中，x³的系数为7。
3. Sequences | 数列
Sequences are ordered lists of numbers following a rule. Recognising their language helps you find missing terms and nth-term rules.
数列是按照规则排列的有序数字列表。认识这些术语有助于找出缺失项和通项公式。
Sequence: An ordered set of numbers, called terms. Each term is formed by a specific rule.
数列：一组有序的数，称为项。每一项由特定规则生成。
Arithmetic sequence: A sequence where the difference between consecutive terms is constant. This is the common difference d.
等差数列：相邻项之差为常数的数列。这个差称为公差d。
Geometric sequence: A sequence where each term is found by multiplying the previous term by a constant common ratio r.
等比数列：每一项由前一项乘以常数公比r得到的数列。
Quadratic sequence: A sequence where the second differences are constant. Its nth term is of the form an² + bn + c.
二次数列：二阶差分为常数的数列。其第n项形式为an² + bn + c。
Fibonacci sequence: A famous sequence where each term is the sum of the two preceding terms: 1, 1, 2, 3, 5, 8, …
斐波那契数列：著名的数列，每项是前两项之和：1, 1, 2, 3, 5, 8, …
4. Graphs and Functions | 图像与函数
Graphs translate algebraic relationships into visual form, and precise vocabulary ensures you describe them correctly.
图像将代数关系转化为视觉形式，精确的术语确保你能正确描述它们。
Gradient: The measure of steepness of a line, calculated as change in y divided by change in x. A positive gradient slopes upwards.
斜率（梯度）：直线陡峭程度的度量，由y的变化量除以x的变化量计算。正斜率向上倾斜。
Intercept: The point where a graph crosses an axis. The y-intercept is where x = 0. In y = 2x + 3, the y-intercept is 3.
截距：图像与坐标轴的交点。y轴截距是x=0时的点。在y = 2x + 3中，y轴截距为3。
Linear function: A function whose graph is a straight line, generally written as y = mx + c.
线性函数：图像为直线的函数，通式为y = mx + c。
Quadratic function: A function of the form y = ax² + bx + c. Its graph is a parabola.
二次函数：形式为y = ax² + bx + c的函数。其图像是一条抛物线。
asymptote: A line that a curve approaches but never touches, common in reciprocal graphs like y = 1/x.
渐近线：曲线无限接近但永不触及的直线，常见于如y = 1/x的倒数图像中。
5. Ratio and Proportion | 比与比例
Ratio and proportion appear in real-world contexts, from recipes to scale drawings. Clear terms prevent confusion between multiplicative and additive comparisons.
比与比例出现在现实世界的许多情境中，从食谱到比例图。清晰的概念能避免混淆乘法比较和加法比较。
Ratio: A way to compare two or more quantities. A ratio of 3:2 means for every 3 parts of one, there are 2 parts of another.
比：比较两个或多个量的一种方式。3:2的比意味着每一个有3份，另一个就有2份。
Proportion: A statement that two ratios are equal. If a is proportional to b, a = kb for some constant k.
比例：两个比相等的陈述。若a与b成比例，则a = kb，k为常数。
Direct proportion: Two quantities increase or decrease at the same rate; y = kx. The graph is a straight line through the origin.
正比例：两个量以相同速率增加或减少；y = kx。图像是一条过原点的直线。
Inverse proportion: As one quantity increases, the other decreases; y = k/x. The product xy remains constant.
反比例：一个量增加时另一个减少；y = k/x。乘积xy保持不变。
Scale factor: The multiplier that enlarges or reduces a shape. An enlargement with scale factor 2 doubles all lengths.
比例因子：放大或缩小图形的乘数。比例因子为2的放大将所有长度加倍。
6. Geometry: Angles and Lines | 几何：角与线
Angle facts and line properties are tested repeatedly. Naming angles correctly avoids ambiguity in multi-step problems.
角的性质与线性特征在考试中反复出现。正确命名角度能避免多步问题中的歧义。
Acute angle: An angle between 0° and 90°.
锐角：介于0°到90°之间的角。
Obtuse angle: An angle between 90° and 180°.
钝角：介于90°到180°之间的角。
Reflex angle: An angle between 180° and 360°.
优角：介于180°到360°之间的角。
Parallel lines: Straight lines that remain the same distance apart and never meet. Identified by arrow marks.
平行线：始终保持相同距离且永不相交的直线。用箭头标记识别。
Alternate angles: Angles inside parallel lines on opposite sides of a transversal; they are equal.
内错角：平行线内部、截线两侧的角；它们相等。
Corresponding angles: Angles in matching corners when a transversal crosses parallel lines; they are equal.
同位角：截线与平行线相交时位置相同的角；它们相等。
Regular polygon: A polygon with all sides equal and all interior angles equal. A regular pentagon has five equal angles.
正多边形：所有边相等且所有内角相等的多边形。正五边形有五个相等的角。
7. Transformations | 变换
Transformations move or resize shapes on a grid. Using precise terms ensures your method matches the description of the transformation.
变换在网格上移动或调整图形大小。使用精确术语能让你的方法与变换描述一致。
Translation: Sliding a shape without rotation or reflection; described by a column vector. A translation of (3, -2) moves a shape 3 right and 2 down.
平移：在不旋转不翻折的情况下滑动图形；用列向量描述。平移(3, -2)表示向右移动3、向下移动2。
Reflection: Flipping a shape over a mirror line. Every point is the same perpendicular distance from the mirror line.
反射：将图形沿对称线翻转。每个点到对称线的垂直距离相等。
Rotation: Turning a shape about a centre of rotation through a specified angle and direction. A rotation of 90° clockwise about a point moves the shape.
旋转：绕旋转中心按指定角度和方向转动图形。绕某点顺时针旋转90°即可移动图形。
Enlargement: Resizing a shape from a centre of enlargement by a scale factor. Negative scale factors produce an inverted image.
放大（相似变换）：从放大中心按比例因子调整图形大小。负比例因子产生倒置图像。
Invariant point: A point that does not move under a transformation. The centre of rotation is an invariant point.
不变点：在变换下不移动的点。旋转中心就是一个不变点。
8. Pythagoras and Trigonometry | 勾股定理与三角学
Right-angled triangle problems rely on a few key terms. Memorising these alongside the SOH CAH TOA ratios is essential.
直角三角形问题依赖几个关键术语。记住这些以及SOH CAH TOA比率至关重要。
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，与直角相对。
Pythagoras’ theorem:
a² + b² = c²
where c is the hypotenuse and a and b are the other two sides.
勾股定理：
a² + b² = c²
其中c为斜边，a和b为其余两边。
Sine (sin): In a right triangle, sin θ = opposite / hypotenuse. sin 30° = 0.5.
正弦（sin）：直角三角形中，sin θ = 对边 / 斜边。sin 30° = 0.5。
Cosine (cos): cos θ = adjacent / hypotenuse.
余弦（cos）：cos θ = 邻边 / 斜边。
Tangent (tan): tan θ = opposite / adjacent.
正切（tan）：tan θ = 对边 / 邻边。
Angle of elevation: The angle measured upwards from the horizontal. A person looks up at the top of a tree, forming an angle of elevation.
仰角：从水平面向上测量的角。一个人抬头看树顶，形成仰角。
9. Area and Volume | 面积与体积
Formula-based topics demand that you know not only the calculations but also the names of shapes and measures.
基于公式的题目不仅要求你会计算，还要知道形状和度量的名称。
Perimeter: The total distance around the edge of a 2D shape. The perimeter of a rectangle is 2(l + w).
周长：二维图形边缘的总距离。矩形的周长为2(长 + 宽)。
Circumference: The perimeter of a circle, given by 2πr or πd.
圆周长：圆的周长，由公式2πr或πd给出。
Arc: A part of the circumference of a circle. Arc length is proportional to the angle at the centre.
弧：圆周长的一部分。弧长与圆心角成比例。
Sector: The region enclosed by two radii and an arc, like a ‘pizza slice’. Area of a sector = (θ/360) × πr².
扇形：由两条半径和一条弧所围成的区域，像一块’披萨片’。扇形面积 = (θ/360) × πr²。
Prism: A 3D solid with a uniform cross-section. A cylinder is a circular prism. Volume of any prism = area of cross-section × length.
棱柱：具有均匀横截面的三维立体。圆柱是一种圆形棱柱。任何棱柱的体积 = 横截面积 × 长度。
Frustum: The solid left when the top of a cone or pyramid is cut off parallel to the base.
平截头体：圆锥或棱锥顶部被平行于底面的平面截去后剩余的部分。
10. Probability | 概率
Probability terms help quantify chance. Using the correct words avoids errors when combining events.
概率术语有助于量化机会。使用恰当的词汇能避免组合事件时出错。
Sample space: The set of all possible outcomes. When rolling a fair die, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间：所有可能结果的集合。掷一个均匀骰子时，样本空间为{1, 2, 3, 4, 5, 6}。
Mutually exclusive events: Events that cannot happen at the same time. Rolling a 2 and an odd number on a single die are mutually exclusive.
互斥事件：不能同时发生的事件。掷单个骰子时，掷出2和掷出奇数是互斥的。
Independent events: Events where the outcome of one does not affect the outcome of the other. Flipping a coin twice are independent events.
独立事件：一个事件的结果不影响另一个事件结果的事件。抛硬币两次是独立事件。
Relative frequency: An estimate of probability from an experiment: number of successful trials divided by total number of trials.
相对频率：从实验中得到的概率估计：成功试次除以总试次。
Tree diagram: A branching diagram showing all possible outcomes of two or more events, with probabilities labelled on branches.
树状图：显示两个或多个事件所有可能结果的分支图，分支上标注概率。
11. Statistics: Averages and Spread | 统计：平均值与离散程度
Interpreting data is a key skill. Statistical terms must be used accurately to summarise and compare datasets.
解读数据是一项关键技能。统计术语必须准确使用，以总结和比较数据集。
Mean: The sum of all values divided by the number of values. It is affected by extreme outliers.
平均数（均值）：所有数值之和除以数值个数。易受极端异常值影响。
Median: The middle value when data are arranged in order. For an even number of values, it is the average of the two middle numbers.
中位数：将数据排序后处于中间位置的数值。若数据个数为偶数，则为中间两个数的平均值。
Mode: The value that appears most frequently. A dataset can have no mode or more than one mode.
众数：出现频率最高的数值。一组数据可能没有众数或有多个众数。
Range: The difference between the largest and smallest values. It measures spread but is sensitive to outliers.
极差（范围）：最大值与最小值的差。衡量离散度，但对异常值敏感。
Interquartile range (IQR): The difference between the upper quartile (Q3) and lower quartile (Q1). IQR shows the spread of the middle 50% of data.
四分位距（IQR）：上四分位数(Q3)与下四分位数(Q1)的差。IQR显示中间50%数据的分布范围。
Cumulative frequency: The running total of frequencies up to a certain value. A cumulative frequency graph can be used to find quartiles.
累积频率：截至某一数值的频率逐次累计。累积频率图可用于找出四分位数。
Frequency density: Used in histograms when class widths are unequal: frequency density = frequency ÷ class width.
频率密度：当组距不等时用于直方图：频率密度 = 频率 ÷ 组距。
12. Vectors | 向量
Vectors combine direction and magnitude. The vocabulary here bridges geometry and algebra.
向量同时包含方向与大小。此处的术语连通几何与代数。
Vector: A quantity with both magnitude and direction, often represented by a column vector or a bold letter. Displacement is a vector.
向量：既有大小又有方向的量，常用列向量或粗体字母表示。位移是一个向量。
Scalar: A quantity with magnitude only, such as speed or distance. Scalars are real numbers multiplying vectors.
标量：仅有大小的量，如速率或距离。标量是乘以向量的实数。
Magnitude: The length (size) of a vector. The magnitude of vector v is written |v|.
模（大小）：向量的长度。向量v的模记作|v|。
Resultant vector: The single vector that has the same effect as two or more vectors added together. It is the sum of the vectors.
合向量：等同于两个或多个向量相加效果的一个单独向量。它是各向量的和。
Parallel vectors: Vectors that are scalar multiples of each other. If a = 2b, then a and b are parallel.
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