📚 Year 7 AQA Maths: Vocabulary & Terminology Quick Guide | Year 7 AQA 数学：词汇术语速记指南
Building a strong mathematical vocabulary early on is one of the most important steps towards becoming a confident problem solver. This guide gathers all the key terms you will meet in Year 7 AQA maths, from number work and algebra to geometry and statistics. Each term is explained clearly with paired English and Chinese definitions so you can learn, revise and check quickly – perfect for homework, tests and classroom discussions.
尽早建立扎实的数学词汇是成为自信解题者的关键一步。本指南汇集了你将在 Year 7 AQA 数学中遇到的所有核心术语，涵盖数字运算、代数、几何和统计。每个术语都配有清晰的中英文双语解释，方便你学习、复习和快速查阅——非常适合作业、测验和课堂讨论。
1. Number Types and Place Value | 数的类型与位值
An integer is any whole number that can be positive, negative or zero. Fractions and decimals are not integers.
整数是可以为正、负或零的任何完整数字，分数和小数不是整数。
Place value tells us the value of each digit in a number depending on its position. In 357, the digit 3 means 300 because it is in the hundreds column.
位值告诉我们一个数字中每个数码根据其位置所具有的值。在 357 中，数字 3 表示 300，因为它处于百位。
A natural number is a positive integer used for counting: 1, 2, 3, 4 … Some definitions include 0.
自然数是用来计数的正整数：1, 2, 3, 4…… 有些定义也包含 0。
A digit is a single symbol used to make numbers. Our system uses the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
数码是用于构成数字的单个符号。我们的系统使用 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 这十个数字。
The numeral is the written symbol for a number, while the number itself is an idea of quantity.
数字符号是数的书写形式，而数本身是表示数量的概念。
2. Factors, Multiples and Primes | 因数、倍数和质数
A factor of a number is a whole number that divides exactly into it with no remainder. For example, 1, 2, 3 and 6 are all factors of 6.
一个数的因数是能整除该数而没有余数的整数。例如，1、2、3 和 6 都是 6 的因数。
A multiple of a number is the result of multiplying it by any whole number. The multiples of 5 include 5, 10, 15, 20 …
一个数的倍数是用任何整数去乘该数得到的结果。5 的倍数包括 5、10、15、20……
A prime number has exactly two distinct factors: 1 and itself. The number 2 is the smallest prime and the only even prime.
质数恰好有两个不同的因数：1 和它本身。数字 2 是最小的质数，也是唯一的偶质数。
A composite number has more than two factors. For instance, 12 has factors 1, 2, 3, 4, 6 and 12, so it is composite.
合数有超过两个因数。例如 12 有因数 1, 2, 3, 4, 6 和 12，所以它是合数。
The highest common factor (HCF) of two numbers is the largest factor they share. The HCF of 12 and 18 is 6.
两个数的最大公因数 (HCF) 是它们共有的最大因数。12 和 18 的最大公因数是 6。
The lowest common multiple (LCM) is the smallest multiple that two numbers share. The LCM of 4 and 6 is 12.
最小公倍数 (LCM) 是两个数共有的最小倍数。4 和 6 的最小公倍数是 12。
Prime factorisation means writing a number as a product of prime factors only. 30 = 2 × 3 × 5.
质因数分解是指将一个数写成仅由质因数相乘的形式。30 = 2 × 3 × 5。
3. Powers and Roots | 幂与根
A square number is the result of multiplying a whole number by itself. The first few square numbers are 1, 4, 9, 16, 25.
平方数是将一个整数乘以自身得到的结果。前几个平方数是 1、4、9、16、25。
A cube number comes from multiplying a whole number by itself twice. 2³ = 2 × 2 × 2 = 8, so 8 is a cube number.
立方数是由一个整数乘以自身两次得到的。2³ = 2 × 2 × 2 = 8，因此 8 是立方数。
The square root of a number is the value that, when multiplied by itself, gives the original number. √25 = 5 because 5 × 5 = 25.
一个数的平方根是乘以自身后得到原数的值。√25 = 5，因为 5 × 5 = 25。
The cube root is the number that gives the original when cubed. ∛27 = 3, since 3³ = 27.
立方根是立方后得到原数的数。∛27 = 3，因为 3³ = 27。
The index or power tells us how many times to multiply a number by itself. In 5⁴, the index is 4 and the base is 5.
指数或幂告诉我们一个数量需要自乘多少次。在 5⁴ 中，指数是 4，底数是 5。
4. Fractions | 分数
The numerator is the top number of a fraction. It shows how many equal parts we have. In ³/₅, 3 is the numerator.
分子是分数线上方的数字，表示我们拥有多少等份。在 ³/₅ 中，3 是分子。
The denominator is the bottom number. It shows the total number of equal parts the whole is divided into. In ³/₅, 5 is the denominator.
分母是分数线下方的数字，表示整体被分成的等份总数。在 ³/₅ 中，5 是分母。
A proper fraction has a numerator smaller than its denominator, like ²/₃. Its value is less than 1.
真分数的分子小于分母，例如 ²/₃，其值小于 1。
An improper fraction has a numerator bigger than or equal to its denominator, like ⁷/₄. Its value is 1 or greater.
假分数的分子大于或等于分母，例如 ⁷/₄，其值大于或等于 1。
A mixed number combines a whole number and a proper fraction, such as 2½. It shows the value more clearly than an improper fraction.
带分数结合了一个整数和一个真分数，例如 2½。它比假分数更清晰地表示数量。
Equivalent fractions have the same value but different numerators and denominators. ¹/₂ = ²/₄ = ⁴/₈.
等价分数具有相同的值，但分子和分母不同。¹/₂ = ²/₄ = ⁴/₈。
To simplify a fraction, divide the numerator and denominator by their highest common factor. ⁸/₁₂ simplifies to ²/₃.
化简一个分数，需要用分子和分母的最大公因数去除它们。⁸/₁₂ 化简为 ²/₃。
The reciprocal of a number is 1 divided by that number. The reciprocal of ⁴/₅ is ⁵/₄.
一个数的倒数是 1 除以该数。⁴/₅ 的倒数是 ⁵/₄。
5. Decimals and Percentages | 小数和百分比
A decimal is a number that has a decimal point separating the whole part from the fractional part. 3.47 means 3 units, 4 tenths and 7 hundredths.
小数是用小数点将整数部分和小数部分分开的数。3.47 表示 3 个一、4 个十分之一和 7 个百分之一。
Tenths and hundredths are the first two decimal places. The digit immediately after the point counts tenths; the next counts hundredths.
十分位和百分位是前两个小数位。小数点后第一位是十分位，第二位是百分位。
Percentage means ‘out of 100’. The symbol % is used, so 30% means 30 out of every 100.
百分比表示“每百分之一”。使用符号 %，所以 30% 表示每 100 份中的 30 份。
To convert a fraction to a decimal, divide the numerator by the denominator. ³/₅ = 3 ÷ 5 = 0.6.
将分数转换为小数，用分子除以分母。³/₅ = 3 ÷ 5 = 0.6。
To change a decimal to a percentage, multiply by 100. 0.47 × 100 = 47%.
将小数转换为百分比，乘以 100。0.47 × 100 = 47%。
A recurring decimal has a digit or group of digits that repeats forever, shown with a dot or bar above the repeating part.
循环小数有一个或一组数字一直重复，通常在重复的数字上方标点或横线来表示。
6. Algebraic Expressions | 代数表达式
Algebra uses letters and symbols to represent numbers and relationships. A variable is a letter that stands for an unknown or changing value, such as x or y.
代数使用字母和符号来表示数字和关系。变量是代表未知或变化数值的字母，例如 x 或 y。
A term is a single number, variable or the product of numbers and variables. In the expression 4x + 7, 4x and 7 are terms.
项是单个数字、变量或数字与变量的乘积。在表达式 4x + 7 中，4x 和 7 都是项。
The coefficient is the number part that multiplies a variable. In 5y, 5 is the coefficient of y.
系数是乘以变量的数字部分。在 5y 中，5 是 y 的系数。
A constant is a term with a fixed value that does not change. In 3a + 8, 8 is a constant.
常数是一个具有固定数值、不会改变的项。在 3a + 8 中，8 是常数。
An expression is a combination of terms using operations such as addition and multiplication, but it does not contain an equals sign.
表达式是由加法和乘法等运算连接各项形成的组合，其中不包含等号。
An equation is a statement that two expressions are equal. It always has an equals sign, like 2x + 1 = 9.
方程是表明两个表达式相等的陈述，它始终含有等号，如 2x + 1 = 9。
Substitution means replacing a variable with a given number. If x = 3, then 2x + 5 becomes 2(3) + 5 = 11.
代换的意思是用给定的数值替换变量。如果 x = 3，那么 2x + 5 就变成 2(3) + 5 = 11。
Like terms have exactly the same variable part. For example, 3y and 7y are like terms and can be simplified to 10y.
同类项具有完全相同的变量部分。例如 3y 和 7y 是同类项，可以合并为 10y。
7. Geometry: Lines and Angles | 几何：线与角
Parallel lines are straight lines that never meet, no matter how far they are extended. They stay the same distance apart.
平行线是无论如何延伸都永不相交的直线，它们之间始终保持相同的距离。
Perpendicular lines meet or cross each other at a right angle of 90 degrees.
垂直线以 90 度的直角相交或交叉。
An acute angle measures more than 0° but less than 90°.
锐角大于 0° 但小于 90°。
A right angle is exactly 90°. It is often marked with a small square corner.
直角恰好等于 90°，通常用小方框角标表示。
An obtuse angle is greater than 90° but less than 180°.
钝角大于 90° 但小于 180°。
A straight angle is exactly 180°, forming a straight line.
平角恰好等于 180°，形成一条直线。
A full turn or complete angle is 360°.
圆周角或周角为 360°。
Vertically opposite angles are formed when two lines cross. They are equal in size.
对顶角是在两直线相交时形成的角，它们的大小相等。
Adjacent angles share a common vertex and a common side but do not overlap.
邻角共享一个公共顶点和一条公共边，并且不重叠。
Complementary angles add up to 90°. For example, 30° and 60° are complementary.
互余角相加等于 90°。例如 30° 和 60° 互余。
Supplementary angles add up to 180°. 110° and 70° are supplementary.
互补角相加等于 180°。例如 110° 和 70° 互补。
8. 2D Shapes and Symmetry | 二维图形与对称
A polygon is a closed 2D shape with straight sides. Triangles, quadrilaterals and pentagons are all polygons.
多边形是由直线段围成的封闭二维图形。三角形、四边形和五边形都是多边形。
A regular polygon has all sides equal and all angles equal. A square is a regular quadrilateral.
正多边形的所有边都相等，所有角都相等。正方形是正四边形。
An isosceles triangle has two equal sides and two equal angles. An equilateral triangle has three equal sides and three 60° angles.
等腰三角形有两条相等的边和两个相等的角。等边三角形三条边都相等，三个角都是 60°。
A quadrilateral is any polygon with four sides. Examples include the square, rectangle, parallelogram, rhombus, trapezium and kite.
四边形是任何有四条边的多边形。例子有正方形、长方形、平行四边形、菱形、梯形和风筝形。
Line symmetry means a shape can be folded along a line (the line of symmetry) so that both halves match exactly.
线对称意味着图形能够沿着一条线（对称线）对折，使两部分完全重合。
Rotational symmetry is when a shape looks the same after a fraction of a full turn. A square has rotational symmetry of order 4.
旋转对称是指图形旋转若干分之一圈后看起来与原来一样。正方形具有四阶旋转对称。
A pentagon has five sides, a hexagon has six, a heptagon has seven, an octagon has eight.
五边形有五条边，六边形有六条边，七边形有七条边，八边形有八条边。
9. Measures and Units | 测量与单位
Length measures how long something is. Common metric units for length are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).
长度衡量物体有多长。常用的长度公制单位有毫米 (mm)、厘米 (cm)、米 (m) 和千米 (km)。
Mass is the amount of matter in an object. It is often measured in grams (g) and kilograms (kg).
质量是物体所含物质的多少，通常以克 (g) 和千克 (kg) 来度量。
Capacity measures the amount of liquid a container can hold. Units include millilitres (ml) and litres (l).
容量度量容器能容纳的液体量，单位有毫升 (ml) 和升 (l)。
Perimeter is the total distance around the outside of a 2D shape. To find the perimeter, add the lengths of all sides.
周长是围绕二维图形外部的总距离。计算周长，需要将所有边的长度相加。
Area measures the amount of space inside a 2D shape. It is recorded in square units, such as cm² or m².
面积度量二维图形内部的空间大小，以平方单位记录，如 cm² 或 m²。
Volume measures the space inside a 3D object. It is recorded in cubic units, such as cm³ or m³.
体积度量三维物体内部的空间，以立方单位记录，如 cm³ 或 m³。
When converting between units, remember: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 litre = 1000 ml.
进行单位换算时记住：1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 litre = 1000 ml。
10. Averages and Range | 平均值与范围
The mean is calculated by adding up all the values and dividing by how many values there are. It is often called the average.
平均数的计算方法是将所有数值相加，再除以数值的个数，通常称为均值。
The median is the middle value when the data set is arranged in order. For an even number of data, the median is the mean of the two middle numbers.
中位数是将数据按大小顺序排列后处于中间位置的数值。如果数据个数为偶数，则中位数是中间两个数的平均数。
The mode is the value that appears most often. A set of data can have one mode, more than one mode or no mode.
众数是出现次数最多的数值。一组数据可以有一个众数、多个众数或没有众数。
The range shows how spread out the data is. It is the difference between the largest and the smallest value.
极差显示数据的分散程度，等于最大值与最小值之差。
11. Data and Charts | 数据与图表
Frequency is the number of times a particular piece of data occurs. A frequency table helps organise raw data.
频率是某一个数据出现的次数。频率表有助于整理原始数据。
A bar chart uses rectangular bars to show frequencies. The height or length of each bar represents the frequency.
条形图使用长方形条来表示频率，每条的高度或长度代表频率的大小。
A pictogram uses symbols or pictures to represent data. A key tells you how many items each symbol stands for.
象形图用符号或图画来表示数据，图例会说明每个符号代表多少个项目。
Discrete data can only take certain values, often whole numbers. For example, the number of students in a class is discrete.
离散数据只能取特定的数值，通常是整数。例如一个班级的学生人数就是离散数据。
Continuous data can take any value within a range. Height, weight and time are examples of continuous data.
连续数据可以在一个范围内取任意数值。身高、体重和时间是连续数据的例子。
12. Probability | 概率
Probability is a measure of how likely an event is to happen. It is written as a number between 0 and 1, or as a fraction, decimal or percentage.
概率是衡量一个事件发生可能性的指标，用 0 到 1 之间的数字表示，也可以用分数、小数或百分数。
An outcome is a possible result of an experiment or event. When you flip a coin, the possible outcomes are heads and tails.
结果是试验或事件可能发生的情况。掷一枚硬币时，可能的结果是正面和反面。
An event is a set of outcomes that you are interested in. Rolling an even number on a dice is an event that includes the outcomes {2, 4, 6}.
事件是你感兴趣的一组结果。在骰子上掷出偶数是一个事件，它包含的结果是 {2, 4, 6}。
Something impossible has a probability of 0. Something certain has a probability of 1. Most real events are somewhere in between.
不可能发生的事件概率为 0。必然发生的事件概率为 1。大多数现实事件的概率介于两者之间。
Outcomes are equally likely when each has the same chance of happening. A fair dice gives equally likely outcomes.
当每个结果发生的机会相同时，它们是等可能的。一枚公平的骰子给出的结果是等可能的。
The probability of an event = (number of favourable outcomes) / (total number of possible outcomes). For a fair six-sided dice, P(rolling a 4) = ⅙.
事件的概率 = （有利结果的数量） / （所有可能结果的总数）。对于公平的六面骰子，掷出 4 的概率为 ⅙。
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