📚 Year 11 OCR Maths Vocabulary & Terminology Quick Guide | Year 11 OCR 数学词汇术语速记指南
Mastering key mathematical terms is essential for understanding OCR GCSE questions and expressing answers clearly. This bilingual guide pairs essential Year 11 vocabulary with concise explanations, helping you memorise and recall the terms quickly.
掌握 OCR GCSE 数学中的关键术语，对于理解题目和清晰作答至关重要。这篇中英双语速记指南将 Year 11 的核心词汇配以简明解释，帮助你快速记忆和回想。
1. Number & Arithmetic Terms | 数字与算术术语
An integer is any whole number that can be positive, negative or zero, but it cannot be a fraction or a decimal.
整数是指任何正整数、负整数或零，但不能是分数或小数。
A prime number is a number greater than 1 that has exactly two distinct factors: 1 and the number itself. For example, 2, 3, 5, 7 and 11 are primes.
质数是大于 1 且恰好有两个不同因数的数：1 和它本身。例如 2、3、5、7 和 11 都是质数。
A factor of a number divides into it exactly without leaving a remainder. A multiple is the result of multiplying that number by an integer.
因数是能够整除某个数的数；倍数则是该数与整数相乘得到的结果。
The highest common factor (HCF) of two numbers is the largest factor they share. The lowest common multiple (LCM) is the smallest multiple they both divide into.
最大公因数（HCF）是两个数共有的最大因数；最小公倍数（LCM）是两个数都能整除的最小倍数。
Prime factor decomposition means writing a number as a product of its prime factors, often using a factor tree.
质因数分解是指将一个数写成其质因数的乘积，通常借助因数树完成。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
A proper fraction has a numerator smaller than its denominator, e.g. 3/4. An improper fraction has a numerator larger than or equal to the denominator, such as 7/4.
真分数的分子小于分母，如 3/4；假分数的分子大于或等于分母，如 7/4。
A mixed number combines an integer and a proper fraction, for instance 1½. The reciprocal of a number is 1 divided by that number; flipping a fraction gives its reciprocal.
带分数由整数和真分数组成，如 1½。一个数的倒数就是 1 除以该数；将分数上下颠倒即可得到其倒数。
Terminating decimals come to an end, like 0.25. Recurring decimals have a digit or block of digits that repeat forever, such as 0.333… or 0.142857142857…
有限小数会终止，如 0.25；循环小数有数字或数字块无限重复，例如 0.333… 或 0.142857142857…
Percentage change compares the actual change to the original amount and is expressed as a percentage. Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus accumulated interest.
百分比变化将实际变化量与原始量比较，并以百分比表示。单利只对本金计算利息，而复利则是对本金加上累积的利息计算利息。
3. Powers, Roots & Surds | 幂、根式与无理根式
result is 8. A negative index gives the reciprocal of the positive power, e.g. x⁻² = 1/x².
在 2³ = 8 中，底数是 2，指数是 3，结果是 8。负指数表示正指数幂的倒数，如 x⁻² = 1/x²。
Fractional indices represent roots: x½ means the square root √x, and x⅓ means the cube root ∛x.
分数指数表示根式：x½ 表示平方根 √x，x⅓ 表示立方根 ∛x。
A surd is an irrational root that cannot be simplified to remove the root, such as √2 or 3√5. Rationalising the denominator means eliminating a surd from the bottom of a fraction by multiplying numerator and denominator by a suitable value.
无理根式（surd）是无法化简去掉根号的无理数，如 √2 或 3√5。分母有理化是通过将分子分母同乘一个合适的值，从而消去分母中的根式。
is an integer. It is used to represent very large or very small numbers, e.g. 6.02 × 10²³.
标准形式将一个数写成 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。它用于表示非常大或非常小的数，如 6.02 × 10²³。
4. Algebraic Expressions & Identities | 代数表达式与恒等式
An algebraic expression combines numbers, variables and operations, such as 3x + 2y - 7. A term is a single part of an expression separated by + or - signs.
代数表达式将数字、变量和运算符号组合在一起，如 3x + 2y - 7。项是用加号或减号分隔的表达式中的单个部分。
A coefficient is the numerical factor in a term. In 5x², 5 is the coefficient of x². A constant is a term that does not contain any variable.
系数是项中的数字因子。在 5x² 中，5 是 x² 的系数。常数是不含任何变量的项。
An identity is an equation that holds true for all values of the variables. It is often written with the ≡ symbol. For example, x² - y² ≡ (x + y)(x - y).
恒等式是对变量的所有取值都成立的等式，常用 ≡ 符号表示。例如 x² - y² ≡ (x + y)(x - y)。
ce of two squares x² - a² = (x + a)(x - a), and factorising quadratic trinomials like x² + 5x + 6.
因式分解是将表达式写成其因式的乘积。常见情况包括提取公因式，识别平方差 x² - a² = (x + a)(x - a)，以及对二次三项式如 x² + 5x + 6 进行因式分解。
Completing the square rewrites a quadratic expression in the form a(x + p)² + q, revealing the turning point of its graph.
配方法将二次表达式改写为 a(x + p)² + q 的形式，从而揭示其图像的最高点或最低点。
5. Equations & Inequalities | 方程与不等式
nown values. A linear equation has the variable raised to the power of 1, e.g. 2x + 3 = 7.
方程表示两个表达式相等，通常可以求解出未知数的值。线性方程中变量的指数为 1，如 2x + 3 = 7。
s solutions are called roots. The discriminant b² - 4ac tells you the nature of the roots.
二次方程的最高次数为 2，可写成 ax² + bx + c = 0。它的解称为根。判别式 b² - 4ac 可以判断根的性质。
x = (-b ± √b² - 4ac) / (2a)
x = (-b ± √b² - 4ac) / (2a)
Simultaneous equations involve two or more equations with shared variables that are solved together. Solutions can be found by elimination, substitution or graphically.
联立方程涉及两个或更多共享变量的方程，需同时求解。可通过消元法、代入法或图像法找到解。
ad of equality. Solving inequalities works similarly to equations but reverses the inequality sign when multiplying or dividing by a negative number.
不等式使用 <, >, ≤ 或 ≥ 等符号比较表达式，而不要求相等。解不等式与解方程类似，但当乘以或除以一个负数时，不等号方向要改变。
6. Sequences | 数列
A sequence is an ordered list of numbers generated by a rule. An arithmetic sequence has a constant difference between consecutive terms, called the common difference, d.
数列是按规则生成的有序数字列表。等差数列的相邻项之差为常数，称为公差 d。
The nth term of an arithmetic sequence can be written as a + (n - 1)d, where a is the first term. This is a position-to-term rule.
等差数列的第 n 项可写成 a + (n - 1)d，其中 a 为首项。这是一种用项位置求值的规则。
A geometric sequence has a constant ratio between consecutive terms, called the common ratio, r. Each term is found by multiplying the previous term by r.
等比数列中相邻项的比值为常数，称为公比 r。每一项由前一项乘以 r 得到。
Other sequences, such as Fibonacci-style sequences, define each term by adding the two previous terms. Term-to-term rules describe how to move from one term to the next.
其他数列，如斐波那契型数列，通过将前两项相加来定义每一项。项对项规则描述如何从一项得到下一项。
7. Graphs & Coordinates | 图形与坐标
Coordinates are written as (x, y) and locate points on a Cartesian grid. The x-axis is horizontal and the y-axis is vertical.
坐标写作 (x, y)，用于在直角坐标系中定位点。x 轴是水平轴，y 轴是垂直轴。
The gradient of a straight line measures its steepness and is often found as change in y divided by change in x. The y-intercept is the point where the line crosses the y-axis.
直线的斜率衡量其倾斜程度，通常由 y 的变化量除以 x 的变化量来求。y 轴截距是直线与 y 轴的交点。
a straight line is typically y = mx + c, where m is the gradient and c is the y-intercept.
直线方程通常为 y = mx + c，其中 m 是斜率，c 是 y 轴截距。
A quadratic graph forms a parabola. Its turning point can be a maximum or a minimum. The roots of the equation are the x-values where the graph crosses the x-axis.
二次函数图像是一条抛物线。它的转折点可以是最高点或最低点。方程的根是图像与 x 轴相交时的 x 值。
When you sketch a graph, you show its main features such as intercepts, turning points and general shape, but you do not need to plot it point by point.
画草图时，你需要展示图像的主要特征，如截距、转折点和大致形状，但无需逐点绘制。
8. Ratio, Proportion & Rates | 比率、比例与速率
A ratio compares the sizes of two or more quantities. It is usually written in simplest form using integers, such as 3 : 2.
比率比较两个或多个量的大小，通常用最简整数比表示，如 3 : 2。
means two quantities increase or decrease at the same rate, so y = kx for some constant k.
比例描述一个量与整体的关系。正比例意味着两个量以相同速率增加或减少，因此 y = kx，其中 k 为常数。
uantity increases, the other decreases so that their product stays constant, i.e. y = k/x.
反比例意味着一个量增加时另一个量减少，保持乘积不变，即 y = k/x。
The unitary method involves finding the value of one unit first, then scaling up or down to find the required amount. Rates like speed, density and pressure are common examples of compound measures.
单位法先求出一个单位的量，再按比例放大或缩小求得所需数量。速度、密度、压强等速率是常见的复合度量。
Speed is distance divided by time. Density is mass per unit volume. Pressure is force per unit area.
速度 = 距离 ÷ 时间。密度是单位体积的质量。压强是单位面积上的力。
9. Geometry & Measures | 几何与测量
Angles are measured in degrees (°). Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are between 90° and 180°, and reflex angles are between 180° and 360°.
角度以度（°）为单位。锐角小于 90°，直角为 90°，钝角在 90° 到 180° 之间，优角在 180° 到 360° 之间。
Parallel lines never meet and have equal corresponding angles, alternate angles and co-interior angles that sum to 180°. Perpendicular lines intersect at right angles.
平行线永不相交，其同位角相等、内错角相等、同旁内角之和为 180°。垂线相交成直角。
Circle theorems describe properties of angles within circles, such as the angle in a semicircle being a right angle, and angles at the centre being twice the angle at the circumference.
圆定理描述圆内角的性质，例如半圆上的圆周角是直角，圆心角是同一弧上圆周角的两倍。
Congruent shapes are identical in both shape and size. Similar shapes are the same shape but may differ in size, with corresponding angles equal and sides in proportion. The scale factor is the ratio of corresponding lengths.
全等形形状和大小完全相同。相似形形状相同但大小可以不同，对应角相等，对应边成比例。比例因子是对应边的长度比。
Transformations include translation (sliding), reflection (flipping), rotation (turning) and enlargement (resizing). Enlargement by a negative scale factor also involves a rotation of 180°.
变换包括平移（滑动）、反射（翻转）、旋转（转动）和放大（改变大小）。负比例因子的放大还包括 180° 的旋转。
10. Trigonometry & Vectors | 三角学与向量
Trigonometry studies the relationships between sides and angles in triangles. The three main ratios are sine (sin), cosine (cos) and tangent (tan).
三角学研究三角形中边与角的关系。三个主要的比值是正弦（sin）、余弦（cos）和正切（tan）。
The mnemonic 'SOH CAH TOA' call: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.
口诀 'SOH CAH TOA' 帮助你记忆：正弦 = 对边 / 斜边，余弦 = 邻边 / 斜边，正切 = 对边 / 邻边。
The sine rule and cosine rule are used for non-right-angled triangles. The area of any triangle can be found using ½ab sin C.
正弦定理和余弦定理用于非直角三角形。任意三角形的面积可用 ½ab sin C 求得。
t trigonometric values for 30°, 45° and 60° must be memorised, e.g. sin 30° = ½, cos 45° = √2/2, tan 60° = √3.
必须记住 30°、45° 和 60° 的精确三角值，例如 sin 30° = ½、cos 45° = √2/2、tan 60° = √3。
column vector is written like (x over y) or in bold notation. The magnitude of vector v = √x² + y².
向量既有大小又有方向。列向量可写成 (x) 的形式，上方为 x 轴向分量，下方为 y 轴向分量。向量 v 的大小为 √x² + y²。
Vectors can be added, subtracted and multiplied by a scalar. Two vectors are parallel if one is a scalar multiple of the other.
向量可以相加、相减及与标量相乘。如果两个向量成标量倍数关系，则它们平行。
11. Probability | 概率
Probability measures the likelihood of an event, expressed as a number between 0 and 1, or as a fraction, decimal or percentage. An outcome is a possible result of an experiment.
概率衡量事件发生的可能性，用一个 0 到 1 之间的数或分数、小数、百分比表示。结果是一次试验可能出现的结局。
A sample space lists all possible outcomes. For a fair coin, the sample space is {Head, Tail}. Events are sets of outcomes.
样本空间列出了所有可能的结果。对于一枚公平的硬币，样本空间为 {正面，反面}。事件是某种结果的集合。
Mutually exclusive events cannot happen at the same time. The probability of either occurring is P(A) + P(B).
互斥事件不可能同时发生。其中任意一个发生的概率为 P(A) + P(B)。
B) = P(A) × P(B). Tree diagrams are useful for showing combinations of independent events.
独立事件互不影响。对于独立事件 A 和 B，P(A 且 B) = P(A) × P(B)。树状图有助于展示独立事件的组合。
Conditional probability is the probability of an event given that another event has already occurred, written P(A|B). It can be calculated using P(A and B) / P(B).
条件概率是在另一事件已经发生的条件下，某事件发生的概率，记作 P(A|B)。可以用 P(A 且 B) / P(B) 来计算。
12. Statistics | 统计
Data can be qualitative (descriptive) or quantitative (numerical). Quantitative data is either discrete (can only take certain values) or continuous (can take any value within a range).
数据可以是定性（描述性）或定量（数值型）。定量数据又分为离散型（只能取特定值）和连续型（可在某一范围内取任意值）。
The mean is the average found by summing all values and dividing by the number of values. The median is the middle value when data are ordered. The mode is the most frequent value.
平均数是将所有数值相加再除以数值的个数。中位数是将数据排序后位于中间的数值。众数是出现次数最多的数值。
The range is the difference between the largest and smallest values. The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1), measuring the spread of the middle 50%.
极差是最大值与最小值之差。四分位距（IQR）是上四分位数（Q3）与下四分位数（Q1）之差，衡量中间 50% 数据的离散程度。
A box plot displays the minimum, Q1, median, Q3 and maximum visually. Cumulative frequency graphs show running totals and are used to find medians and quartiles.
箱线图直观展示最小值、Q1、中位数、Q3 和最大值。累积频数图展示逐步累加的总数，用于求中位数和四分位数。
ncy density = frequency ÷ class width, so bar height is proportional to frequency density.
在直方图中，每个条形的面积表示频数。频数密度 = 频数 ÷ 组距，因此条形高度与频数密度成比例。
A scatter graph shows the relationship between two sets of data. Correlation describes the direction and strength of the relationship; a line of best fit can be drawn to make predictions.
散点图展示两组数据之间的关系。相关性描述关系的方向和强度；可以绘制最佳拟合线进行预测。
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