📚 Year 11 WJEC Maths: Quick-Memorise Glossary of Key Terms | Year 11 WJEC 数学：词汇术语速记指南
Mastering the vocabulary of mathematics is half the battle for Year 11 WJEC students. This guide packs the essential terms you must know — from number and algebra to geometry and statistics — into simple, paired definitions that speed up recall and build exam confidence.
掌握数学词汇，是 Year 11 WJEC 学生备考成功的一半。本指南将你必须掌握的核心术语——从数与代数，到几何与统计——浓缩成简洁的中英对照释义，帮助你加速记忆，提升考试信心。
1. Number and Arithmetic Terms | 数与算术术语
An integer is any whole number, positive or negative, including zero, with no fractional or decimal part.
整数是指任何不含分数或小数部分的整数，可以是正数、负数或零。
A rational number is any number that can be written as a fraction a/b, where a and b are integers and b is not zero.
有理数是可以写成分数 a/b 形式的数，其中 a 和 b 都是整数，且 b 不为零。
licative inverse of a number; for example, the reciprocal of 3 is 1/3 because 3 × 1/3 = 1.
倒数是指一个数的乘法逆元；例如 3 的倒数是 1/3，因为 3 × 1/3 = 1。
A factor is a whole number that divides exactly into another number, while a multiple is the result of multiplying that number by any integer.
因数是一个能整除另一个数的整数，而倍数则是将该数乘以任意整数得到的结果。
The product of two numbers is their multiplication result, whereas the sum is their addition result.
两个数的积是它们相乘的结果，而和是它们相加的结果。
2. Algebra Essentials | 代数基础
An algebraic expression is a combination of numbers, letters and operation symbols without an equals sign, such as 3x + 2.
代数表达式是由数字、字母和运算符号组成的式子，不带等号，例如 3x + 2。
An equation states that two expressions are equal, always containing an equals sign, and can often be solved to find the value of an unknown.
方程是表示两个表达式相等的语句，始终包含等号，通常可解出未知数的值。
The variable is the letter representing an unknown quantity, and the coefficient is the number multiplied by that variable.
变量是代表未知量的字母，系数则是乘以该变量的数字。
To expand brackets means to multiply each term inside the bracket by the term outside, while factorising is the reverse process of writing an expression as a product of its factors.
去括号是指将括号外的项与括号内的每一项相乘，而因式分解则是逆过程，将表达式写成其因式的乘积。
A like term has exactly the same variable part and power, so 5a and -2a can be combined, but 5a and 5a² cannot.
同类项具有完全相同的变量部分和幂次，因此 5a 与 -2a 可以合并，但 5a 与 5a² 不行。
3. Geometry and Measure Vocabulary | 几何与测量词汇
An acute angle measures less than 90°, a right angle is exactly 90°, an obtuse angle lies between 90° and 180°, and a reflex angle is greater than 180° but less than 360°.
锐角小于 90°，直角正好 90°，钝角在 90° 与 180° 之间，而优角大于 180° 且小于 360°。
Parallel lines are lines in a plane that never meet, and perpendicular lines intersect at a right angle.
平行线是同一平面内永不相交的直线，而垂直线是相交成直角的直线。
A polygon is a closed 2D shape with straight sides; a regular polygon has all sides and all angles equal.
多边形是由直线段围成的封闭二维图形；正多边形的所有边和所有角都相等。
The perimeter is the total distance around the outside of a 2D shape, while the area is the amount of surface enclosed within it.
周长是绕二维图形外边缘的总长度，面积则是其内部所围的平面大小。
Volume measures the amount of space a 3D object occupies, and surface area is the total area of all its faces combined.
体积衡量三维物体所占据的空间大小，表面积则是其所有面面积的总和。
4. Ratio, Proportion and Rates of Change | 比、比例与变化率
A ratio compares two or more quantities of the same kind, written as a : b and simplified by dividing by common factors.
比是比较两个或多个同类量的关系，写作 a : b，并通过除以公因数来化简。
Direct proportion means that when one quantity is multiplied by a factor, the other quantity is multiplied by the same factor; their graph is a straight line through the origin.
正比例是指当一个量乘以某个倍数时，另一个量也乘以同一倍数；其图像是一条过原点的直线。
Inverse proportion means that as one quantity increases, the other decreases at an equal rate, so their product remains constant.
反比例是指当一个量增加时，另一个量以相同的比率减少，因此它们的乘积保持不变。
The word rate usually describes how one quantity changes relative to another, such as speed (distance per time) or density (mass per volume).
率通常描述一个量相对于另一个量的变化情况，例如速度（单位时间内的距离）或密度（单位体积的质量）。
Percentage change is calculated as (change ÷ original value) × 100%, used for profit, loss and repeated compound changes.
百分比变化用 (变化量 ÷ 原值) × 100% 计算，适用于利润、亏损和多次复合变化。
5. Statistics Key Terms | 统计学关键术语
The mean of a data set is found by adding all values and dividing by the number of values; it is the arithmetic average.
数据集的均值是将所有数值相加后除以数值的个数得到，即算术平均值。
The median is the middle value when data are arranged in order, and the mode is the value that appears most frequently.
中位数是将数据排序后位于中间的值，众数是出现频率最高的值。
The range measures spread and is simply the difference between the largest and smallest values.
极差用来衡量离散程度，即最大值与最小值的差。
A cumulative frequency graph allows you to estimate medians, quartiles and percentiles by reading values off the curve.
累积频率图可以通过从曲线上读取数值来估计中位数、四分位数和百分位数。
The interquartile range (IQR) is the difference between the upper quartile and lower quartile, describing the spread of the middle 50% of data.
四分位距 (IQR) 是上四分位数与下四分位数之差，描述了中间 50% 数据的离散程度。
6. Probability Language | 概率语言
An outcome is a single possible result of an experiment, while an event is a set of one or more outcomes that we are interested in.
结果是一次实验中可能出现的单个情形，而事件是我们关注的一个或多个结果的集合。
The probability of an event is a number between 0 and 1, where 0 means impossible and 1 means certain.
事件的概率是 0 到 1 之间的一个数，0 表示不可能发生，1 表示必然发生。
Mutually exclusive events cannot happen at the same time, so P(A or B) = P(A) + P(B).
互斥事件不可能同时发生，因此 P(A 或 B) = P(A) + P(B)。
Independent events refer to situations where the outcome of one event does not affect the outcome of another, and we multiply their probabilities to find the combined probability.
独立事件指一个事件的结果不影响另一个事件结果的情况，我们通过概率相乘来求联合概率。
A sample space diagram lists all possible outcomes systematically to help us calculate probabilities precisely.
样本空间图系统地列出所有可能的结果，帮助我们精确计算概率。
7. Graphs and Functions | 图像与函数
Coordinates are written as (x, y), where x is the horizontal position and y is the vertical position from the origin.
坐标写作 (x, y)，其中 x 是从原点出发的水平位置，y 是垂直位置。
The gradient of a straight line measures its steepness and is calculated as rise over run, or change in y divided by change in x.
直线的斜率衡量其倾斜程度，通过垂直变化量除以水平变化量（y 的变化量除以 x 的变化量）来计算。
The y-intercept is the point where the line crosses the y-axis, and the x-intercept is where it crosses the x-axis.
y 轴截距是直线与 y 轴的交点，x 轴截距是直线与 x 轴的交点。
pped to exactly one output value; common examples are linear functions such as y = 2x + 5.
在函数中，每个输入值唯一对应一个输出值；常见的例子有线性函数，如 y = 2x + 5。
Distance–time graphs show how distance changes over time, where the gradient represents speed.
距离 – 时间图展示距离如何随时间变化，其斜率代表速度。
8. Sequences and Patterns | 数列与规律
A sequence is an ordered list of numbers following a rule; each number in the sequence is called a term.
数列是按一定规则排列的一列数；数列中的每一个数称为项。
The term-to-term rule describes how to get from one term to the next, such as 'add 4' or 'multiply by 2'.
项间规则描述如何从一项得到下一项，例如“加 4”或“乘以 2”。
The nth term is an algebraic expression that generates the value of any term directly from its position n.
第 n 项是一个代数式，能直接从位置 n 给出该项的值。
An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio.
等差数列相邻两项的差为常数，而等比数列相邻两项的比为常数。
Square numbers, cubic numbers and triangular numbers are special sequences that appear frequently in WJEC number pattern questions.
平方数、立方数和三角形数是 WJEC 数字规律题中频繁出现的特殊数列。
9. Trigonometry Basics | 三角学基础
In a right-angled triangle, the side opposite the right angle is the longest side and is called the hypotenuse.
在直角三角形中，直角所对的边最长，称为斜边。
The sine of an acute angle (shortened to sin θ) is the ratio of the length of the opposite side to the hypotenuse.
锐角的正弦（简写为 sin θ）是对边长度与斜边长度的比值。
The cosine of an acute angle (cos θ) is the ratio of the length of the adjacent side to the hypotenuse.
锐角的余弦（cos θ）是邻边长度与斜边长度的比值。
The tangent of an acute angle (tan θ) is the ratio of the length of the opposite side to the adjacent side.
锐角的正切（tan θ）是对边长度与邻边长度的比值。
site over Hypotenuse, Cosine = Adjacent over Hypotenuse, Tangent = Opposite over Adjacent.
助记口诀 SOH CAH TOA 帮助学生快速回忆这三种比值：正弦 = 对边/斜边，余弦 = 邻边/斜边，正切 = 对边/邻边。
10. Exam-Friendly Symbols and Notation | 考试常用符号与标记
The symbol ≈ means 'is approximately equal to', and ⩵ (with a double tilde) is sometimes used for 'is proportional to', though the standard propto symbol ∝ is common.
符号 ≈ 表示“约等于”，而 ∝ 通常表示“成正比”；有时也用 \u2A75 表示比例，但 WJEC 常用 ∝。
Rounding notation: 5.34 to 1 decimal place is written as 5.3; significant figure rounding follows similar rules but focuses on the most important digits from the left.
近似值写法：5.34 保留一位小数写作 5.3；有效数字四舍五入遵循类似规则，但关注左侧最重要的数位。
ndard form writes large or small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
标准形式将很大或很小的数写作 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。
The Union symbol ∪ means 'or' in probability (A ∪ B), while the Intersection symbol ∩ means 'and' (A ∩ B).
并集符号 ∪ 在概率中表示“或”（A ∪ B），交集符号 ∩ 表示“且”（A ∩ B）。
Set notation { } is used to list elements of a set, and the symbol ∈ means 'is an element of', while ∉ means 'is not an element of'.
集合符号 { } 用于列出一个集合的元素，∈ 表示“属于”，∉ 表示“不属于”。
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