📚 Vocabulary & Terminology Quick-Reference Guide | 词汇术语速记指南
Mastering the language of mathematics is the first step to solving problems with confidence. This guide covers the essential Year 7 CAIE maths vocabulary you will meet in topics from number and algebra to geometry and statistics. Each term is explained in simple English followed by its Chinese equivalent, with clear examples to help you remember it quickly.
掌握数学语言是自信解题的第一步。本指南涵盖了 Year 7 CAIE 数学中从数与代数到几何与统计的基本词汇。每个术语先用简单的英文解释，再附上中文对应说法，并给出明确示例，帮助你快速记忆。
1. Numbers and Place Value | 数字与位值
A digit is any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers. For example, the number 507 has three digits.
数字（digit）是指用来书写数的符号 0–9。例如，数 507 有三位数字。
The place value of a digit tells us its value according to its position in the number. In 3 482, the digit 3 stands for 3 thousands, 4 stands for 4 hundreds, 8 stands for 8 tens and 2 stands for 2 ones.
位值（place value）告诉我们一个数字在数中的位置所代表的值。在 3 482 中，数字 3 表示 3 个千，4 表示 4 个百，8 表示 8 个十，2 表示 2 个一。
An integer is any whole number, positive, negative or zero, such as −5, 0, 12.
整数（integer）包括正整数、负整数和零，如 −5、0、12。
2. Integers: Factors, Multiples and Primes | 整数：因数、倍数与质数
A factor of a number is a whole number that divides exactly into that number without leaving a remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.
因数（factor）是指能整除某个数的整数，且没有余数。12 的因数有 1、2、3、4、6 和 12。
A multiple of a number is the result of multiplying that number by any integer. The first five multiples of 7 are 7, 14, 21, 28 and 35.
倍数（multiple）是用某个数乘以任意整数得到的结果。7 的前五个倍数是 7、14、21、28 和 35。
A prime number is an integer greater than 1 that has exactly two factors: 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13.
质数（prime number）是大于 1 且只有两个因数（1 和它本身）的整数。最小的几个质数是 2、3、5、7、11、13。
A square number is the product of a number multiplied by itself. 5² = 25 is a square number. We say ‘5 squared equals 25’.
平方数（square number）是一个数与自己相乘的结果。5² = 25 就是一个平方数，我们读作“5 的平方等于 25”。
A cube number is the product of a number used three times in multiplication. 2³ = 8 is a cube number.
立方数（cube number）是一个数自己相乘三次的结果。2³ = 8 是一个立方数。
3. Fractions and Equivalent Fractions | 分数与等值分数
A fraction represents a part of a whole. It is written as a/b, where a is the numerator and b is the denominator ( b ≠ 0 ).
分数（fraction）表示整体的一部分，写为 a/b，其中 a 是分子（numerator），b 是分母（denominator）（b ≠ 0）。
Equivalent fractions are different fractions that represent the same value. ½ = ²/₄ = ⁴/₈. To find equivalent fractions, multiply or divide the numerator and denominator by the same number.
等值分数（equivalent fractions）是数值相同但形式不同的分数，如 ½ = ²/₄ = ⁴/₈。要得到等值分数，可以将分子和分母同时乘以或除以相同的数。
A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. ¾ is in simplest form.
当分子和分母除了 1 以外没有其他公因数时，这个分数就是最简形式（simplest form）。¾ 已经是最简形式。
An improper fraction has a numerator greater than or equal to the denominator, like ⁷/₄. A mixed number combines a whole number and a proper fraction, like 1¾.
假分数（improper fraction）的分子大于或等于分母，如 ⁷/₄。带分数（mixed number）由一个整数和一个真分数组成，如 1¾。
4. Decimals and Percentages | 小数与百分数
A decimal is a number written using the base‑10 place value system, with a decimal point separating whole numbers from fractional parts. In 3.75, 7 is in the tenths place and 5 is in the hundredths place.
小数（decimal）是使用十进制位值系统写出的数，小数点将整数部分和小数部分分开。在 3.75 中，7 在十分位，5 在百分位。
Percent means ‘out of 100’. The symbol % is used. 45% = ⁴⁵/₁₀₀ = 0.45.
百分数（percent）表示“每一百”，用 % 符号。45% = ⁴⁵/₁₀₀ = 0.45。
To convert a fraction to a percentage, find an equivalent fraction with denominator 100, or multiply by 100%. For example, ⅕ = 20%.
将分数转换为百分数，可以找到一个分母为 100 的等值分数，或将分数乘以 100%。例如 ⅕ = 20%。
A recurring decimal is a decimal that has a repeating pattern of digits, often shown with a dot above the repeating digit(s). ⅓ = 0.3̇.
循环小数（recurring decimal）是小数部分有重复数字串的小数，通常在重复数字上加一个点表示。⅓ = 0.3̇。
5. Operations and BODMAS | 运算与BODMAS法则
Addition (+), subtraction (−), multiplication (×) and division (÷) are the four basic operations. The sum is the result of addition, the difference is the result of subtraction, the product is the result of multiplication, and the quotient is the result of division.
加法 (+)、减法 (−)、乘法 (×) 和除法 (÷) 是四种基本运算。加法的结果叫和（sum），减法的结果叫差（difference），乘法的结果叫积（product），除法的结果叫商（quotient）。
When a calculation involves more than one operation, we follow the BODMAS order: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. Division and multiplication have the same priority and are worked left to right; the same applies to addition and subtraction.
当计算包含多种运算时，我们遵循BODMAS 法则：括号（Brackets）、指数/方根（Orders）、除法和乘法（Division and Multiplication）、加法和减法（Addition and Subtraction）。除法和乘法等级相同，从左到右计算；加法和减法也一样。
For example: 3 + 6 × 2 = 3 + 12 = 15, not 18.
例如：3 + 6 × 2 = 3 + 12 = 15，而不是 18。
6. Introduction to Algebra | 代数学简介
In algebra, we use letters to stand for unknown numbers. These letters are called variables.
在代数中，我们用字母代表未知数，这些字母称为变量（variable）。
An algebraic expression is a combination of numbers, variables and operation signs, such as 3x + 2 or 4y − 7.
代数式（algebraic expression）是由数字、变量和运算符号组成的式子，如 3x + 2 或 4y − 7。
A term is a single mathematical ‘building block’ separated by + or − signs. In 5a + 2b − 3, the terms are 5a, 2b and −3.
项（term）是由 + 或 − 分隔开的单个数学“积木块”。在 5a + 2b − 3 中，各项是 5a、2b 和 −3。
A coefficient is the number part of a term that contains a variable. In 7m, 7 is the coefficient.
系数（coefficient）是含变量的项中的数字部分。在 7m 中，7 就是系数。
An equation is a statement that two expressions are equal, using the equals sign. Solving an equation means finding the value of the variable that makes the statement true. For example, x + 5 = 12 → x = 7.
方程（equation）是用等号表示两个表达式相等的语句。解方程意味着求出使等式成立的变量的值。例如 x + 5 = 12 → x = 7。
7. Geometry: Lines, Angles and Shapes | 几何：线、角与形状
A point is an exact location in space. A line is a straight set of points extending infinitely in both directions. A line segment is part of a line with two endpoints. A ray has one endpoint and extends infinitely in one direction.
点（point）是空间中的确切位置。直线（line）是向两个方向无限延伸的点集。线段（line segment）有两个端点。射线（ray）有一个端点，并向一个方向无限延伸。
Parallel lines are straight lines that never meet, no matter how far they are extended. Perpendicular lines intersect at a right angle (90°).
平行线（parallel lines）是不论怎样延伸都不会相交的直线。垂直线（perpendicular lines）相交成直角（90°）。
An angle measures the amount of turn. We classify angles by size:
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: between 90° and 180°
- Straight angle: exactly 180°
- Reflex angle: between 180° and 360°
角（angle）度量旋转的大小。我们根据大小将角分类：
- 锐角（acute angle）：小于 90°
- 直角（right angle）：等于 90°
- 钝角（obtuse angle）：介于 90° 和 180° 之间
- 平角（straight angle）：等于 180°
- 优角（reflex angle）：介于 180° 和 360° 之间
A polygon is a closed flat shape with three or more straight sides. Triangles and quadrilaterals are common polygons. A regular polygon has all sides and all angles equal.
多边形（polygon）是由三条或更多直线段围成的封闭平面图形。三角形和四边形是常见的多边形。正多边形（regular polygon）的各条边和各个角都相等。
Triangles can be classified by sides: equilateral (three equal sides), isosceles (two equal sides) and scalene (no equal sides).
三角形可按边分类：等边三角形（equilateral，三条边相等）、等腰三角形（isosceles，两条边相等）和不等边三角形（scalene，没有边相等）。
8. Symmetry and Transformations | 对称与变换
A shape has line symmetry (reflective symmetry) if you can fold it along a line so that the two halves match exactly. The fold line is called a line of symmetry.
如果一个图形可以沿着一条线对折，两边完全重合，那么这个图形就有线对称（line symmetry），这条折线叫做对称轴（line of symmetry）。
Rotational symmetry occurs when a shape can be rotated about a central point and still look the same in less than a full turn. The order of rotational symmetry is the number of times it matches itself in one full turn.
旋转对称（rotational symmetry）是指图形绕中心点旋转不到一圈时能与自身重合。它在一整圈中与自身重合的次数称为旋转对称的阶（order of rotational symmetry）。
A transformation moves or changes a shape. The four main transformations are:
- Translation (slide): moving a shape without rotating, resizing or flipping it.
- Reflection (flip): making a mirror image over a line.
- Rotation (turn): turning a shape about a fixed point.
- Enlargement: changing the size of a shape by a scale factor.
变换（transformation）是指移动或改变图形。主要有四种变换：
- 平移（translation）：只移动图形，不旋转、不改变大小、不翻转。
- 反射（reflection）：沿一条线做出镜像。
- 旋转（rotation）：绕一固定点转动图形。
- 放大（enlargement）：按比例因子改变图形大小。
9. Measures: Perimeter, Area and Volume | 测量：周长、面积与体积
The perimeter of a shape is the total distance around its outside edge. For a rectangle of length l and width w, perimeter = 2(l + w).
图形的周长（perimeter）是它外边缘的总长度。对于长为 l、宽为 w 的长方形，周长 = 2(l + w)。
Area is the amount of surface a shape covers. It is measured in square units, such as cm² or m². The area of a rectangle is length × width.
面积（area）是图形所占表面的大小，用平方单位（如 cm²、m²）来度量。长方形的面积为 长 × 宽。
Volume is the amount of space a solid object takes up. It is measured in cubic units, like cm³ or m³. The volume of a cuboid is length × width × height.
体积（volume）是立体物体所占空间的大小，用立方单位（如 cm³、m³）来度量。长方体的体积为 长 × 宽 × 高。
A square centimetre (cm²) is the area of a square with sides 1 cm long. A cubic centimetre (cm³) is the volume of a cube with side length 1 cm.
平方厘米（cm²）是边长为 1 cm 的正方形的面积。立方厘米（cm³）是边长为 1 cm 的正方体的体积。
Converting between units of length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. For area, remember: 1 m² = 10 000 cm², because 1 m = 100 cm, and 100 × 100 = 10 000.
长度单位的换算：1 km = 1000 m，1 m = 100 cm，1 cm = 10 mm。面积换算时要注意：1 m² = 10 000 cm²，因为 1 m = 100 cm，而 100 × 100 = 10 000。
10. Data Handling and Statistics | 数据处理与统计
Data is a collection of facts, numbers or measurements. It can be collected using surveys, experiments or observations.
数据（data）是关于事实、数字或测量结果的集合，可通过调查、实验或观察来收集。
We often display data using bar charts, pictograms, line graphs and pie charts. A bar chart compares categories, a line graph shows change over time, and a pie chart shows how a whole is divided into parts.
我们常用条形图（bar chart）、象形图（pictogram）、折线图（line graph）和饼图（pie chart）来展示数据。条形图比较类别，折线图展示随时间的变化，饼图展示整体如何分成各部分。
The mean (average) is found by adding all values and dividing by the number of values. The median is the middle value when the data is put in order. The mode is the value that appears most often. The range is the difference between the largest and the smallest values.
平均数（mean）是将所有数值相加后除以数值的个数。中位数（median）是将数据排序后位于中间的值。众数（mode）是出现次数最多的值。极差（range）是最大值与最小值的差。
For the data set 3, 5, 5, 7, 9: mean = (3+5+5+7+9) ÷ 5 = 5.8; median = 5; mode = 5; range = 9 − 3 = 6.
对于数据集 3, 5, 5, 7, 9：平均数 = (3+5+5+7+9) ÷ 5 = 5.8；中位数 = 5；众数 = 5；极差 = 9 − 3 = 6。
Probability words are also introduced in Year 7. Certain means an event will definitely happen (probability = 1), impossible means it cannot happen (probability = 0), and even chance means it is equally likely to happen or not happen (probability = ½).
Year 7 中也会引入概率词汇。必然（certain）表示事件一定会发生（概率 = 1），不可能（impossible）表示事件不会发生（概率 = 0），等可能性（even chance）表示发生与不发生的可能性相等（概率 = ½）。
11. Sequences and Patterns | 数列与规律
A sequence is a list of numbers or shapes arranged in a particular order. Each number in a sequence is called a term. For example, the sequence 2, 5, 8, 11, … has a term‑to‑term rule of ‘add 3’.
数列（sequence）是按特定顺序排列的一列数或图形，数列中的每个数称为项（term）。例如，数列 2, 5, 8, 11, … 的邻项规则（term‑to‑term rule）是“加 3”。
A linear sequence is one where the difference between consecutive terms is constant. This difference is called the common difference. The sequence 4, 7, 10, 13 has a common difference of 3.
线性数列（linear sequence）是相邻两项的差保持不变的数列，这个差称为公差（common difference）。数列 4, 7, 10, 13 的公差为 3。
We can describe a sequence using an nth term rule. For the sequence 5, 10, 15, 20, … the nth term is 5n. The 10th term would be 5 × 10 = 50.
我们可以用第 n 项公式（nth term rule）来描述数列。对于数列 5, 10, 15, 20, …，第 n 项为 5n。第 10 项就是 5 × 10 = 50。
Square number sequences: 1, 4, 9, 16, 25, … (nth term is n²). Cube number sequences: 1, 8, 27, 64, … (nth term is n³).
平方数数列：1, 4, 9, 16, 25, …（第 n 项为 n²）。立方数数列：1, 8, 27, 64, …（第 n 项为 n³）。
12. Ratios and Proportions | 比与比例
A ratio compares two or more quantities. It can be written with a colon, such as 2 : 3, or as a fraction. The order of the numbers matters: 2 : 3 is not the same as 3 : 2.
比（ratio）用于比较两个或更多的数量，可以用冒号（如 2 : 3）或分数表示。数字的顺序很重要：2 : 3 与 3 : 2 不同。
Ratios can be simplified by dividing all parts by a common factor, just like simplifying fractions. 6 : 9 simplifies to 2 : 3.
比可以通过将所有部分除以公因数来化简，和化简分数一样。6 : 9 可化简为 2 : 3。
When two quantities are in direct proportion, they increase or decrease at the same rate. For example, if 3 pens cost £1.50, then 6 pens cost £3.00. We can use a multiplier or the unitary method to find unknown amounts.
如果两个量成正比例（direct proportion），它们以相同的速率增加或减少。例如 3 支笔价格 £1.50，那么 6 支笔的价格就是 £3.00。我们可以用乘法因子或单位法来求未知量。
A scale factor is the number you multiply or divide by when enlarging or reducing shapes in proportion. If a rectangle of length 4 cm is enlarged by a scale factor of 3, the new length is 12 cm.
比例因子（scale factor）是在按比例放大或缩小图形时所乘或除以的数。如果一个长 4 cm 的长方形以比例因子 3 放大，新的长为 12 cm。
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