📚 Year 7 AQA Maths: A Quick Guide to Memorising Key Vocabulary Terms | Year 7 AQA 数学：词汇术语速记指南
Mastering mathematical vocabulary is essential for success in Year 7 AQA Maths. This guide provides quick memory tricks for key terms you will encounter in number, algebra, geometry and statistics. When you understand the language of maths, you can follow instructions, explain your reasoning and solve problems more confidently. Let's turn tricky words into easy-to-remember ideas.
掌握数学词汇是 Year 7 AQA 数学成功的关键。本指南为你提供数字、代数、几何和统计中常见关键词的快速记忆技巧。当你理解数学语言后，就能跟上指令、解释自己的推理过程并更自信地解题。让我们一起把难记的词汇变成容易记住的概念。
1. Number Types | 数字类型
Integer: An integer is a whole number that can be positive, negative or zero. It does not include fractions or decimals. Think of 'integer' as 'intact' – a whole, unbroken number. For example, -3, 0, 7 and 42 are all integers.
整数 (integer): 整数是完整的数，可以是正数、负数或零。它不包括分数和小数。联想 'integer' 听起来像 'intact'（完整的）——就像完好无损的数字。例如 -3、0、7 和 42 都是整数。
Natural number: Natural numbers (or counting numbers) start from 1 and go up forever: 1, 2, 3, … They do not include zero or negative numbers. Remember 'natural' means 'naturally we start counting with 1'.
自然数 (natural number): 自然数（也叫计数数）从 1 开始，一直往上增加：1, 2, 3, … 它们不包括 0 和负数。记忆法：'natural' 就是“我们天生就从 1 开始数数”。
Rational number: Any number that can be written as a fraction a/b, where a and b are integers and b is not zero. Notice that 'rational' contains 'ratio' – and a fraction is a ratio. Examples: 1/2, -4/5, 3 (which is 3/1).
有理数 (rational number): 任何可以写成分数 a/b 的数，其中 a 和 b 是整数且 b 不为零。注意 'rational' 这个词里有 'ratio'（比率），而分数就是一种比率。例如：1/2、-4/5、3（即 3/1）。
Whole number (non-negative integer): In many contexts, a whole number means an integer that is not negative: 0, 1, 2, 3, … Keep in mind that some exam questions refer to 'whole numbers' this way.
非负整数 (whole number): 在很多语境下，whole number 表示非负整数，即 0, 1, 2, 3, … 要记住考试中 'whole number' 常常指这类数。
2. Factors and Multiples | 因数与倍数
Factor: A factor is a whole number that divides another number exactly, without leaving a remainder. Think of 'factor' like a 'factory': a factory produces products, and factors multiply to produce a number. For 12, the factors are 1, 2, 3, 4, 6 and 12.
因数 (factor): 因数是一个整数，它能整除另一个数，没有余数。把 'factor' 想象成 'factory'（工厂）：工厂制造产品，因数相乘产生一个数。12 的因数有 1, 2, 3, 4, 6 和 12。
Multiple: A multiple is the result of multiplying a number by an integer. The multiples of 5 are 5, 10, 15, 20, … You can remember that multiples are 'many copies' of a number, like filling a shelf with repeated bags of sweets.
倍数 (multiple): 倍数是一个数乘以整数得到的结果。5 的倍数有 5, 10, 15, 20, … 你可以记成：倍数就是某个数量的“多次复制”，就像架子上放了同样数量的一袋袋糖果。
Common factor / common multiple: A common factor is a factor shared by two or more numbers. The highest common factor (HCF) is the largest one. A common multiple is a multiple that appears in the times tables of two or more numbers, and the lowest common multiple (LCM) is the smallest. Think 'highest shared builder' and 'lowest shared count'.
公因数 / 公倍数 (common factor / common multiple): 公因数是两个或多个数共有的因数，其中最大的叫最大公因数 (HCF)。公倍数是两个或多个数的乘法表里都出现的倍数，最小的那个叫最小公倍数 (LCM)。联想：“最高的共同建筑师”和“最小的共同次数”。
3. Prime and Composite Numbers | 质数与合数
Prime number: A prime number has exactly two distinct factors: 1 and itself. The word 'prime' means 'first in importance', and primes are the 'atoms' of numbers. Examples: 2, 3, 5, 7, 11, 13. Note that 2 is the only even prime.
质数 (prime number): 质数恰好有两个不同的因数：1 和它本身。'prime' 有“首要”的意思，质数就是数的“原子”。例如：2, 3, 5, 7, 11, 13。注意 2 是唯一的偶质数。
Composite number: A composite number has more than two factors. The word 'composite' reminds us of 'compose' – it is made up of several parts. 4, 6, 8, 9 and 12 are all composite numbers.
合数 (composite number): 合数有超过两个因数。'composite' 这个词让人想到 'compose'（组成），它是由多个部分构成的。4, 6, 8, 9 和 12 都是合数。
Number 1: The number 1 is neither prime nor composite because it has only one factor – itself. Think of 1 as the 'lonely number' that doesn't fit either club.
数字 1: 1 既不是质数也不是合数，因为它只有一个因数——它自己。可以把 1 想象成“孤单的数字”，它不属于任何一个俱乐部。
4. Powers and Roots | 幂与平方根
Square number: e number is the result of multiplying a whole number by itself. It is written with a small '2' as an index: 5² = 25. The name 'square' comes from finding the area of a square: side × side.
平方数 (square number): 平方数是一个整数乘它自己的结果。用右上角的小 '2' 来表示：5² = 25。'square' 这个名字来自正方形的面积：边长 × 边长。
Square root: : The square root (√) is the number that, when multiplied by itself, gives the original number. √25 = 5 because 5² = 25. Imagine 'undoing' the square – the root goes back to the side length of the square.
平方根 (square root): 平方根 (√) 是这样一个数：它自己乘自己等于原来的数。√25 = 5 因为 5² = 25。想象“撤销”平方运算——平方根带你回到正方形的边长。
Cube number: ube number is found by multiplying a number by itself twice: 2³ = 2 × 2 × 2 = 8. The index '3' reminds us of three dimensions, like the volume of a cube.
立方数 (cube number): 立方数是一个数乘自己两次得到的：2³ = 2 × 2 × 2 = 8。指数 '3' 代表三维，就像立方体的体积。
Index (exponent): The small raised number that tells you how many times to multiply the base. In 3⁴, the base is 3 and the index is 4. Think 'index finger pointing how many repeats'.
指数 (index / exponent): 那个写在上方的小数字，告诉你底数要乘多少次。在 3⁴ 中，底数是 3，指数是 4。联想“食指 (index finger) 指着要重复的次数”。
5. Fractions, Decimals and Percentages | 分数、小数和百分比
Numerator and denominator: In a fraction a/b, the top number is the numerator (how many parts we have), and the bottom number is the denominator (how many equal parts the whole is divided into). Memory trick: numerator starts with 'n' for 'north' (top), denominator starts with 'd' for 'down' (bottom).
分子与分母 (numerator and denominator): 在分数 a/b 中，上面的数是分子（表示我们有多少份），下面的数是分母（表示整体被分成了多少份）。记忆窍门：'numerator' 开头是 'n'，好比 north（北方/上方）；'denominator' 开头是 'd'，好比 down（下方）。
Proper and improper fractions: A proper fraction has a numerator smaller than the denominator (e.g. 3/4), while an improper fraction has a numerator larger than or equal to the denominator (e.g. 7/4). Think 'proper' means 'well‑behaved' – the top stays smaller than the bottom.
真分数和假分数 (proper and improper fraction): 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）。可以把 'proper' 想成“守规矩的”——上面的数总是比下面小。
Equivalent fractions: Fractions that look different but have the same value, like 1/2 and 2/4. You obtain them by multiplying or dividing both numerator and denominator by the same number. 'Equivalent' sounds like 'equal value'.
等值分数 (equivalent fraction): 看起来不同但数值相同的分数，如 1/2 和 2/4。通过把分子分母同时乘或除以同一个数得到。'Equivalent' 听起来像 'equal value'（相等的值）。
Percentage: A percentage is a number out of 100. The symbol % means 'per 100'. Use the phrase 'percent = per century' (a century is 100 years) to remember the link to 100.
百分比 (percentage): 百分比是一个以 100 为分母的比率。符号 % 代表“每一百份”。用“percent = per century (每个世纪 100 年)”来记住与 100 的联系。
6. Algebra Basics | 代数基础
Variable: A variable is a symbol, often a letter, that represents a number we don't know yet or that can change. Think of it as a 'varying' ticket – its value can vary.
变量 (variable): 变量是一个符号，通常是字母，用来代表未知或可以变化的数。把它想象成一张“会变 (vary) 的票”——它的数值可以改变。
Expression: (like +, −, ×, ÷) without an equals sign. For instance, 3x + 2 is an expression. Remember 'expression' is like a 'phrase' in language – it doesn't tell a full story yet.
表达式 (expression): 表达式是由数字、变量和运算符号（如 +, −, ×, ÷）组成的式子，没有等号。例如 3x + 2 就是一个表达式。记住 'expression' 就像语言里的“短语”——它还没说完一个完整的句子。
Equation: : An equation shows that two expressions are equal, with an equals sign. 2x + 3 = 7 is an equation. Think of an equation as a balanced seesaw – both sides must have the same value.
方程 (equation): 方程用等号表示两个表达式相等。2x + 3 = 7 就是一个方程。把方程想象成平衡的跷跷板——两边必须数值相等。
Term, coefficient, like terms: A term is a single number or variable, or numbers and variables multiplied together. In 5y + 3, 5y and 3 are terms. The coefficient is the number part (5). 'Like terms' have exactly the same variable raised to the same power, e.g. 2a and 7a. Link: 'coefficient' co‑operates with the variable.
项、系数与同类项 (term, coefficient, like terms): 项是单个数字、变量或数字与变量的乘积。在 5y + 3 中，5y 和 3 是项。系数是数字部分 (5)。同类项是指变量和它的指数完全相同的项，如 2a 和 7a。联想：'coefficient' 里的 'co' 表示与变量“合作”。
7. Geometry: Angles and Shapes | 几何：角与形状
Angle types: An acute angle is less than 90°. Think 'a cute little angle'. A right angle is exactly 90°, marked with a small square. An obtuse angle is between 90° and 180° – imagine 'obtuse' sounds like 'obvious', so it's obviously bigger. A reflex angle is between 180° and 360°, like a 'reflex' bending backward.
角的类型 (angle types): 锐角小于 90°，联想 'a cute'（一个可爱的小角）。直角恰好等于 90°，用小方格标记。钝角介于 90° 到 180° 之间——'obtuse' 发音像 'obvious'（明显的），所以它明显比较大。优角（反射角）在 180° 到 360° 之间，像身体向后“反射”弯曲。
Polygon: A polygon is a 2D closed shape with straight sides. The name comes from Greek 'poly' (many) + 'gon' (angle). Triangles, quadrilaterals, pentagons and hexagons are all polygons. Count the sides to name them.
多边形 (polygon): 多边形是由直线段围成的封闭二维图形。名字来自希腊语 'poly'（多）+ 'gon'（角）。三角形、四边形、五边形和六边形都是多边形。通过数边数来命名它们。
Vertices, edges, faces: For 3D shapes, a vertex (plural: vertices) is a corner where edges meet. An edge is a line segment where two faces meet. A face is a flat surface. Memory aid: 'vertex' sounds like 'vortex' – the pointy corner of a whirlpool; 'edge' is the border; 'face' you can see.
顶点、棱和面 (vertices, edges, faces): 对于三维图形，顶点是棱相交的角点。棱是两个面相交的线段。面是平的表面。记忆法：'vertex' 像 'vortex'（漩涡的尖角）；'edge' 就是边缘；'face' 是你能看见的那个面。
Line symmetry and rotational symmetry: A shape has line symmetry if you can fold it along a line so both halves match exactly. Rotational symmetry tells you how many times a shape looks the same when rotated (less than a full turn). Imagine a reflection in a mirror for line symmetry, and a spinning fan for rotational symmetry.
线对称与旋转对称 (line symmetry and rotational symmetry): 如果一个图形能沿一条直线对折后完全重合，它就具有线对称。旋转对称是指图形旋转不到一圈时，有多少次与自身重合。线对称想象成镜面反射，旋转对称想象成电扇转动时看起来一样的次数。
8. Measures: Perimeter, Area, Volume | 测量：周长、面积、体积
Perimeter: The perimeter is the total distance around the outside of a 2D shape. The word 'perimeter' contains 'rim' – the rim of a cup or the border of a field. For a rectangle, perimeter = 2(length + width).
周长 (perimeter): 周长是围绕二维图形外边界的总长度。'perimeter' 这个词里有 'rim'（边缘）——想象杯口或田地的边界。长方形的周长 = 2 × (长 + 宽)。
Area: is measured in square units, like cm² or m². Picture spreading square tiles across a floor – area. For a rectangle, area = length × width. For a triangle, area = 1/2 × base × height.
面积 (area): 面积衡量二维图形内部空间的大小，以平方单位计量，如 cm² 或 m²。想象在地板上铺正方形瓷砖——那就是面积。长方形的面积 = 长 × 宽。三角形的面积 = 1/2 × 底 × 高。
Volume: cm³. Think of filling a box with cubes. The volume of a cuboid is length × width × height. 'Volume' also means 'how loud', but here it's how much 'bulk'.
体积 (volume): 体积衡量三维物体内部空间的大小，以立方单位计量，如 cm³。想象用一个个小立方体填满一个盒子。长方体的体积 = 长 × 宽 × 高。'volume' 除了“体积”，还有“音量”的意思，但这里它代表能容纳多少“货”。
9. Statistics: Averages and Range | 统计：平均数与范围
Mean: The mean is the sum of the data values divided by the number of values. It is often called 'the average'. Remember that mean takes the most work – you must add everything and then divide, so it's the 'meanest' calculation of the three.
平均数 (mean): 平均数是所有数据值之和除以数据个数的结果，常直接叫“平均值”。记住 mean 的计算最费力——你得先全部加起来再除以个数，所以是三个集中量数里最“mean (麻烦)”的。
Median: The median is the middle value when the data is ordered from smallest to largest. If there are two middle numbers, take their mean. Think of a road's median strip – it sits in the middle of the road.
中位数 (median): 将数据从小到大排列后，正中间的那个值就是中位数；如果中间有两个数，就取它们的平均数。联想马路中间的隔离带 (median strip) ——它就在正中间。
Mode: The mode is the value that appears most often. There can be no mode, one mode or several modes. 'Mode' sounds like 'mode' in fashion – the most popular style. So the mode is the most popular data value.
众数 (mode): 众数是出现次数最多的那个值，可能没有众数，有一个或多个众数。'mode' 在时尚里有“流行款式”的意思——最受欢迎的样式。因此众数就是数据里最“流行”的值。
Range: The range is the difference between the largest and smallest values: range = maximum – minimum. It tells you how spread out the data is. Think of a mountain range – it covers a wide spread of peaks.
范围 (range): 范围是最大值与最小值的差：范围 = 最大值 – 最小值。它告诉你数据散布得有多开。想象一条山脉 (mountain range) ——它横跨很宽的区域。
10. Coordinates and Graphs | 坐标与图形
Axes and origin: The x-axis is the horizontal number line, and the y-axis is the vertical number line. They meet at the origin, (0,0). Remember 'x is a cross' (the x‑axis crosses the page horizontally) and 'y points to the sky' (y-axis goes up). The origin is where the journey begins.
坐标轴与原点 (axes and origin): x 轴是水平的数轴，y 轴是竖直的数轴。它们相交于原点 (0,0)。记忆法：'x' 像一个十字，所以 x 轴横跨页面；'y' 指向天空，所以 y 轴向上。原点是旅途的起点。
Coordinates (ordered pair): A point is written as (x, y) – the first number tells you how far across the x‑axis, the second how far up or down the y‑axis. Say 'along the corridor, up the stairs': first go along the x, then up the y.
坐标 (coordinates / ordered pair): 一个点写作 (x, y) ——第一个数字告诉你沿 x 轴走多远，第二个数字告诉你沿 y 轴走多高。口诀：先沿走廊走 (x)，再爬楼梯 (y)。
Plotting and line graphs: Plotting means marking points on a grid using their coordinates. A line graph is formed by joining plotted points with straight lines. Think of plotting as 'planting a flag' at an exact location, and then connecting the flags to see the path.
描点与折线图 (plotting and line graphs):
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