📚 Year 7 CIE Maths: Key Vocabulary Quick Reference Guide | Year 7 CIE 数学：核心词汇速记指南
Mastering mathematics in Year 7 starts with a solid grasp of the essential vocabulary. This quick-reference guide covers the key terms you will encounter in the CIE curriculum, grouped by topic, with simple definitions and examples to help you learn actively and retain the words that matter most. Whether you are tackling number operations, algebra, geometry, or handling data, understanding the language of maths will boost your confidence and problem-solving skills.
在 Year 7 学好数学，首先要牢固掌握核心词汇。这份速记指南按照主题分组，梳理了 CIE 课程中会遇到的各类关键术语，并配有简明释义和实例，帮助你主动学习、牢牢记住最重要的词语。不论你正在学习数的运算、代数、几何还是数据处理，理解数学语言本身都会大大增强你的自信，提高解题能力。
1. Number and Place Value | 数与位值
An integer is any whole number, positive or negative, including zero. For example, –3, 0, and 7 are all integers.
整数是指任何正、负或零的整数。例如 –3、0 和 7 都是整数。
Place value tells you the value of a digit based on its position in a number. In 3582, the digit 5 is in the hundreds place, so its value is 500.
位值表示一个数字在某个数中所处位置对应的数值。在 3582 中，数字 5 位于百位，因此它的值是 500。
A factor is a number that divides exactly into another number. The factors of 12 are 1, 2, 3, 4, 6, and 12.
因数是能整除另一个数的数。12 的因数有 1、2、3、4、6 和 12。
A multiple is the result of multiplying a number by an integer. The first five multiples of 4 are 4, 8, 12, 16, and 20.
倍数是一个数乘以整数得到的结果。4 的前五个倍数是 4、8、12、16 和 20。
2. Operations and Relationships | 运算与关系
The sum is the result of adding numbers together. The sum of 9 and 14 is 23.
和是将数字相加得到的结果。9 和 14 的和是 23。
The difference is the result of subtracting one number from another. The difference between 20 and 8 is 12.
差是一个数减去另一个数得到的结果。20 和 8 的差是 12。
The product is the result of multiplying numbers. The product of 6 and 7 is 42.
积是数字相乘得到的结果。6 和 7 的积是 42。
The quotient is the result of dividing one number by another. The quotient of 45 ÷ 9 is 5.
商是一个数除以另一个数得到的结果。45 ÷ 9 的商是 5。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
A numerator is the top part of a fraction, showing how many parts we have. In ⅗, 3 is the numerator.
分子是分数中位于上方的部分，表示我们占有多少份。在 ⅗ 中，3 是分子。
A denominator is the bottom part of a fraction, showing the total number of equal parts. In ⅗, 5 is the denominator.
分母是分数中位于下方的部分，表示整体被等分成多少份。在 ⅗ 中，5 是分母。
An equivalent fraction represents the same value using different numerators and denominators, such as ½ = ²/₄ = ⁴/₈.
等值分数是指分子和分母虽然不同，但表示的数值相同，例如 ½ = ²/₄ = ⁴/₈。
A percentage is a fraction out of 100. The symbol % means ‘per hundred’. 35% means 35 out of 100.
百分数是一个分母为 100 的分数。符号 % 的含义是“每一百”。35% 表示每一百中有 35 份。
A decimal uses a decimal point to separate whole numbers from fractional parts. 0.75 means 75 hundredths.
小数是用小数点分隔整数部分与小数部分。0.75 表示百分之七十五。
4. Primes, Squares and Roots | 质数、平方与平方根
A prime number has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11, and 13 are primes. Note that 1 is not a prime.
质数恰好有两个不同的因数：1 和它自身。2、3、5、7、11 和 13 都是质数。注意 1 不是质数。
A square number is the product of an integer multiplied by itself. 9 is a square number because 3 × 3 = 9.
平方数是某个整数与自身相乘得到的积。9 是平方数，因为 3 × 3 = 9。
A square root of a number is a value that, when multiplied by itself, gives the original number. √25 = 5 because 5² = 25.
平方根是这样一个数，它与自身相乘后等于原数。√25 = 5，因为 5² = 25。
A cube number is the product of an integer used three times in multiplication. 8 is a cube number because 2 × 2 × 2 = 8.
立方数是某个整数在乘法中使用三次得到的积。8 是立方数，因为 2 × 2 × 2 = 8。
5. Integers and Directed Numbers | 整数与有向数
An integer includes all whole numbers and their negatives, along with zero. The set { … –2, –1, 0, 1, 2 … } forms the integers.
整数包括所有自然数、它们的负数以及零。集合 { … –2, –1, 0, 1, 2 … } 构成整数。
A positive number is greater than zero. +4 means four units in the positive direction. The + sign is often omitted.
正数大于零。+4 表示正方向的四个单位。正号通常可以省略。
A negative number is less than zero. –7 means seven units in the negative direction.
负数小于零。–7 表示负方向的七个单位。
The absolute value is the distance of a number from zero, always non‑negative. |–8| = 8 and |5| = 5.
绝对值表示一个数到零的距离，永远非负。|–8| = 8，|5| = 5。
6. Algebra: Expressions and Equations | 代数：表达式与方程
A variable is a symbol, often a letter, that represents an unknown or changing value. In 3x + 5, x is the variable.
变量是一个符号，通常是字母，用来表示未知或变化的数值。在 3x + 5 中，x 是变量。
A coefficient is the number multiplying a variable. In 7y, the coefficient of y is 7.
系数是乘在变量前面的数字。在 7y 中，y 的系数是 7。
A term is a single number, variable, or numbers and variables multiplied together. 4a, –2, and xy are all terms.
项可以是单独的数字、单独的变量，或者是数字与变量相乘形成的一个部分。4a、–2 和 xy 都是项。
An expression is a combination of terms without an equals sign, such as 2p + 5 – q.
表达式是由项组合而成，但不包含等号，例如 2p + 5 – q。
An equation is a mathematical statement that two expressions are equal, containing an equals sign. Example: 3n = 12.
方程是说明两个表达式相等、并且包含等号的数学语句。例如 3n = 12。
7. Geometry: Lines, Angles and Shapes | 几何：线、角与图形
A point has no dimensions and is represented by a dot. We label it with a capital letter, e.g. point A.
点没有维度，用一个圆点表示。我们通常用大写字母标记，例如点 A。
A line extends infinitely in both directions, while a line segment has two endpoints.
直线向两个方向无限延伸，而线段有两个端点。
A ray has one endpoint and extends infinitely in one direction.
射线有一个端点，并向一个方向无限延伸。
An angle is formed when two rays meet at a common endpoint (the vertex). We measure angles in degrees (°).
角是由两条射线在公共端点（顶点）处相交形成的图形。我们用度（°）来度量角。
An acute angle measures less than 90°, a right angle exactly 90°, an obtuse angle between 90° and 180°, and a reflex angle between 180° and 360°.
锐角小于 90°，直角恰好等于 90°，钝角介于 90° 和 180° 之间，优角介于 180° 和 360° 之间。
8. Symmetry and Transformations | 对称与变换
Line symmetry means a shape can be folded along a line so that both halves match exactly. This line is called the line of symmetry.
线对称是指一个图形能够沿着某条直线对折，并使两部分完全重合。这条直线叫做对称轴。
Rotational symmetry means a shape looks the same after being rotated by less than 360° about its centre. The number of times it matches itself in one full turn is the order of rotational symmetry.
旋转对称是指一个图形绕其中心旋转小于 360° 后，仍能与自身重合。在完整旋转一周中与自身重合的次数，就是旋转对称的阶数。
Reflection flips a shape over a mirror line to produce a mirror image. Every point and its image are the same distance from the mirror line.
反射将图形沿一条镜线翻转，得到镜像。图形上的每一点与它的像到镜线的距离都相等。
Rotation turns a shape around a fixed centre through a given angle and direction (clockwise or anticlockwise).
旋转将一个图形绕固定的中心沿给定角度和方向（顺时针或逆时针）转动。
Translation slides a shape to a new position without turning or flipping it. We describe translation by a column vector showing horizontal and vertical movement.
平移将图形滑动到一个新的位置，而不旋转或翻转。我们通常用一个列向量来描述平移，表示水平和垂直方向的移动距离。
9. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the total distance around the outside of a shape. For a rectangle with length l and width w, P = 2l + 2w.
周长是图形外部边界一周的总长度。对于长为 l、宽为 w 的长方形，周长 P = 2l + 2w。
Area is the amount of space inside a flat shape, measured in square units such as cm², m². The area of a rectangle is length × width.
面积是平面图形内部的空间大小，用平方单位测量，如 cm²、m²。长方形的面积 = 长 × 宽。
Volume is the amount of space a solid object occupies, measured in cubic units such as cm³. For a cuboid, volume = length × width × height.
体积是立体物体占据空间的大小，用立方单位测量，如 cm³。对于长方体，体积 = 长 × 宽 × 高。
The net of a solid is a 2D pattern that can be folded to make the 3D shape.
展开图是立体的二维图样，可以折叠成对应的三维形状。
10. Statistics and Handling Data | 统计与数据处理
The mean (average) is calculated by adding all values and dividing by the number of values. For 3, 7, 8, the mean is (3+7+8) ÷ 3 = 6.
平均数是通过将所有数值相加再除以数值的个数计算得出。对于 3、7、8，平均数为 (3+7+8) ÷ 3 = 6。
The median is the middle value when data are arranged in order. For 2, 5, 7, 9, the median is (5+7)÷2 = 6 if there is an even number of values.
中位数是将数据按大小顺序排列后处于中间位置的值。对于 2、5、7、9，当数据个数为偶数时，中位数是 (5+7)÷2 = 6。
The mode is the value that appears most often. In 4, 5, 5, 6, 7, the mode is 5.
众数是出现次数最多的数值。在 4、5、5、6、7 中，众数是 5。
The range is the difference between the largest and smallest values. For 9, 1, 6, the range is 9 – 1 = 8.
极差是最大值和最小值之间的差。对于 9、1、6，极差为 9 – 1 = 8。
11. Probability Vocabulary | 概率词汇
Probability measures how likely an event is to happen. It is written as a fraction, decimal, or percentage between 0 and 1, where 0 means impossible and 1 means certain.
概率用来度量一个事件发生的可能性大小。可以用分数、小数或百分数表示，范围从 0 到 1，0 表示不可能，1 表示必然发生。
An outcome is a possible result of an experiment. When tossing a coin, the outcomes are heads or tails.
结果是试验可能出现的情况。抛一枚硬币时，结果可以是正面或反面。
An event is a set of one or more outcomes. Rolling an even number on a fair dice is an event that includes outcomes 2, 4, and 6.
事件是由一个或多个结果组成的集合。在掷一枚均匀骰子时，“掷出偶数”是一个事件，包括结果 2、4 和 6。
Equally likely outcomes have the same chance of occurring. On a fair six‑sided dice, each number 1 to 6 is equally likely.
等可能的结果是指每个结果出现的机会相同。在公平的六面骰子上，1 到 6 每个数字出现的可能性相等。
12. Units, Measures and Conversions | 单位、测量与换算
Metric units for length include millimetre (mm), centimetre (cm), metre (m), and kilometre (km). 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
公制长度单位包括毫米 (mm)、厘米 (cm)、米 (m) 和千米 (km)。1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m。
Mass is measured in grams (g) and kilograms (kg). 1 kg = 1000 g.
质量用克 (g) 和千克 (kg) 测量。1 kg = 1000 g。
Capacity is measured in millilitres (ml) and litres (L). 1 L = 1000 ml.
容量用毫升 (ml) 和升 (L) 测量。1 L = 1000 ml。
Time units: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day.
时间单位：60 秒 = 1 分钟，60 分钟 = 1 小时，24 小时 = 1 天。
Temperature is usually measured in degrees Celsius (°C). Water freezes at 0°C and boils at 100°C.
温度通常以摄氏度 (°C) 为单位测量。水在 0°C 结冰，在 100°C 沸腾。
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