📚 Year 7 Cambridge Maths: Vocabulary & Terminology Quick Guide | Year 7 剑桥数学：词汇术语速记指南
Welcome to your Year 7 Cambridge Maths vocabulary quick guide. Building a strong mental dictionary of mathematical terms can turn a confusing question into a clear set of instructions. This article covers key words from number, algebra, geometry, statistics and probability, giving you clear definitions, memory tricks and word origins so that you can learn faster and remember longer.
欢迎使用你的 Year 7 剑桥数学词汇速记指南。在大脑中建立一本强大的数学术语词典，可以把令人困惑的题目变成清晰的指令。本文涵盖数、代数、几何、统计和概率中的关键词汇，为你提供清晰的定义、记忆技巧和词源，帮助你学得更快、记得更牢。
1. Number Basics: Integers, Factors, Multiples & Primes | 数的基础：整数、因数、倍数与质数
The word 'integer' comes from a Latin root meaning 'whole' or 'untouched'. An integer is any whole number that can be positive, negative or zero: ... -3, -2, -1, 0, 1, 2, 3 ... Think of integers as complete steps on a number line, never fractions or decimals.
'Integer' 一词源自拉丁语，意为“完整的”或“未被触碰的”。整数是任何可以是正数、负数或零的整数：... -3, -2, -1, 0, 1, 2, 3 ... 可以把整数想象成数轴上完整的步伐，绝不是分数或小数。
A factor s of 12 are 1, 2, 3, 4, 6 and 12 because 12 ÷ 2 = 6 and so on. Memory aid: factors are the 'factory workers' that multiply together to build a product.
因数是能整除另一个数的整数，且不留余数。例如，12 的因数有 1、2、3、4、6 和 12，因为 12 ÷ 2 = 6，等等。记忆妙招：因数就像是“工厂工人”，它们相乘建造出一个乘积。
A multiple is the result of multiplying a number by any integer. For instance, the multiples of 5 are 5, 10, 15, 20, 25 ... Notice that 'multiple' shares its root with 'multiply'. To list multiples, just keep adding the original number.
倍数是将一个数乘以任何整数所得到的结果。例如，5 的倍数有 5、10、15、20、25…… 注意，“multiple” 与 “multiply” 同源。要列出倍数，只需不断加上原数即可。
A prime number is a whole number greater than 1 that has exactly two distinct factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11 and 13. The word 'prime' comes from Latin 'primus', meaning 'first'. Remember: prime numbers are the 'first building blocks' of all integers because every number can be written as a product of primes (prime factorisation).
质数是大于 1 且恰好有两个不同因数的整数：1 和它本身。前几个质数是 2、3、5、7、11 和 13。“prime” 一词来自拉丁语 “primus”，意为“第一的”。记住：质数是所有整数的“最初积木”，因为每个数都可以写成质数的乘积（质因数分解）。
The Highest Common Factor (HCF) of two numbers is the largest factor they both share. The Lowest Common Multiple (LCM) is the smallest multiple they both have. To find them, list the factors or multiples and pick the highest or lowest one that appears in both lists.
两个数的最大公因数 (HCF) 是它们共有的最大因数。最小公倍数 (LCM) 是它们共有的最小倍数。要求出它们，可以列出因数或倍数，然后选出同时出现在两个列表中的最大值或最小值。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
A fraction has a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have. Think: 'denominator' sounds like 'denomination' – the type of part, like a quarter or a third.
分数有分子（上面的数）和分母（下面的数）。分母告诉你整体被分成了多少等份；分子则告诉你拥有其中的几份。联想记忆：“denominator” 听起来像 “denomination”（面额），表示份的种类，比如四分之一或三分之一。
A proper fraction has a numerator smaller than its denominator (value less than 1). An improper fraction has a numerator greater than or equal to the denominator. A mixed number combines a whole number and a proper fraction, such as 2 ½.
真分数的分子小于分母（值小于 1）。假分数的分子大于或等于分母。带分数由一个整数和一个真分数组合而成，比如 2 ½。
A decimal uses a decimal point to show parts of a whole based on powers of ten. The word comes from Latin 'decimus', meaning tenth. A recurring decimal has a digit or group of digits that repeat forever, shown with a dot or line over the repeating part.
小数使用小数点，以十的幂为基础表示整体的一部分。该词源自拉丁语 “decimus”，意为“第十”。循环小数有一位或多位数字无限重复，通常在重复部分上方加点或横线表示。
A percentage means 'per hundred' (per cent). It is a fraction with denominator 100. To convert a fraction to a percentage, make denominator 100 or multiply by 100%. The sign % reminds you of the two zeroes in 100.
百分比表示“每百中”（percent 即 per cent）。它是一个分母为 100 的分数。要将分数转换为百分比，可以把分母变成 100，或者乘以 100%。百分号 % 可以让你联想到 100 中的两个零。
3. Powers and Roots | 幂与方根
A power is a shorthand way of writing repeated multiplication. The base is the number being multiplied, and the exponent you how many times to multiply the base by itself. For example, 2³ = 2 × 2 × 2 = 8. We say '5 squared' for 5² and '5 cubed' for 5³.
幂是重复乘法的简写形式。底数是被乘的数，而指数告诉你要将底数自乘多少次。例如，2³ = 2 × 2 × 2 = 8。我们称 5² 为“5 的平方”，5³ 为“5 的立方”。
The square root of a number is a value that, when multiplied by itself, gives the original number. √25 = 5 because 5² = 25. The cube root ∛27 = 3 because 3³ = 27. Remember: a square root 'undoes' squaring, just like division undoes multiplication.
一个数的平方根是这样是一个值，它自乘后得到原数。√25 = 5，因为 5² = 25。立方根 ∛27 = 3，因为 3³ = 27。记住：平方根“撤销”平方运算，就像除法撤销乘法一样。
4. Algebraic Expressions: Terms, Coefficients & Variables | 代数表达式：项、系数与变量
An algebraic expression is a combination of numbers, letters (variables) and operation symbols that represents a value. It does not contain an equals sign. A term is a single number, a single variable, or numbers and variables multiplied together, separated by + or - signs.
代数表达式是由数字、字母（变量）和运算符号组成的组合，代表一个值。它不含等号。项可以是一个数字、一个变量，或者数字与变量相乘，项之间由 + 或 - 号隔开。
A variable is a symbol (often a letter) that stands for a number we do not yet know. The word means 'able to vary'. A constant is a fixed number that does not change. In 3x + 7, x is the variable and 7 is the constant.
变量是一个符号（通常是字母），代表我们暂时未知的数。这个词的意思是“能够变化的”。常数是一个固定不变的数。在 3x + 7 中，x 是变量，7 是常数。
A coefficient is the number multiplied by a variable in a term. In 5y, 5 is the coefficient. Think of 'co-efficient' as the number that works together with the variable. Like terms have exactly the same variable part; they can be combined by adding or subtracting their coefficients.
系数是项中与变量相乘的数。在 5y 中，5 就是系数。可以把 “co-efficient” 理解为与变量“共同起作用”的数。同类项拥有完全相同的变量部分；可以通过加减它们的系数来合并。
5. Equations and Formulae | 方程与公式
An equation statement showing that two expressions are equal, always containing an equals sign (=). To solve an equation means to find the value of the unknown that makes the statement true. 'Equation' shares its root with 'equal' – balance is the key idea.
方程是一个数学陈述，表明两个表达式相等，它总是包含等号 (=)。解方程就意味着求出使等式成立的未知数的值。“Equation” 与 “equal” 词根相同——平衡是关键思想。
A formula a links two or more variables and is used to calculate one quantity when others are known.
公式（复数：formulae）是用符号表示的规则或关系。例如，矩形面积公式为 A = l × w。公式将两个或多个变量联系起来，当知道其他量时，就可以用来计算某个量。
6. Geometry: Angles and Lines | 几何：角与线
An angle is formed when two straight lines meet at a point. It is measured in degrees (°). An acute angle is greater than 0° and less than 90°; think 'a-cute little angle' – sharp and small. A right angle is exactly 90°, often marked with a small square. An obtuse angle is greater than 90° but less than 180°; it sounds like 'obtuse', meaning blunt or dull. A straight angle is exactly 180°, forming a straight line.
当两条直线在一点相遇时，就形成了一个角，以度 (°) 为单位测量。锐角大于 0° 且小于 90°；可以联想 “a-cute little angle” —— 又尖又小。直角正好是 90°，通常用一个小的正方形标记。钝角大于 90° 但小于 180°；它听起来像 “obtuse”，意为“钝的、不锋利的”。平角正好是 180°，形成一条直线。
A reflex angle is greater than 180° but less than 360°. Perpendicular lines meet at a right angle (90°). Parallel lines are always the same distance apart and never meet; think of the two L's in 'parallel' running side by side.
优角大于 180° 但小于 360°。垂线相交成直角 (90°)。平行线总是保持相同距离，永不相交；可以联想 “parallel” 中的两个 L 像两条平行线并排延伸。
7. 2D Shapes: Polygons and Symmetry | 平面图形：多边形与对称性
A polygon is a closed 2D shape with straight sides. The word comes from Greek 'poly' (many) and 'gonia' (angle). A regular polygon has all sides and angles equal; an irregular polygon does not. Name polygons by the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).
多边形是一个由直边围成的封闭二维图形。这个词来自希腊语 “poly”（多）和 “gonia”（角）。正多边形的所有边和角都相等；不规则多边形则不全等。根据边数命名多边形：三角形 (3)、四边形 (4)、五边形 (5)、六边形 (6)、七边形 (7)、八边形 (8)、九边形 (9)、十边形 (10)。
Line symmetry means a shape can be folded along a line so that both halves match exactly. The fold line is called a line of symmetry. Rotational symmetry means a shape looks the same more than once when rotated through a full turn. The order of rotational symmetry is the number of times it matches itself in one complete rotation.
线对称是指一个图形可以沿某条线折叠，使两半完全重合。这条折叠线叫作对称轴。旋转对称是指一个图形在绕中心旋转一周的过程中，有不止一次与原来图形重合。旋转对称的阶数就是它在完整旋转一周中与自身重合的次数。
8. Perimeter, Area, and Volume | 周长、面积与体积
Perimeter is the total distance around the outside of a 2D shape. It comes from Greek 'peri' (around) and 'metron' + width). Always add the lengths of all sides. Think of walking the fence around a garden.
周长是二维图形外边界的总距离。它来自希腊语 “peri”（周围）和 “metron”（测量）。对于矩形，周长 = 2 ×（长 + 宽）。总是把所有边长加在一起。想象沿着花园篱笆走一圈。
Area ce a shape covers, measured in square units (e.g. cm², m²). The word area originally meant 'open space' = length × width. To estimate areas of irregular shapes, we often count squares on a grid.
面积是一个图形所覆盖的表面量，用平方单位（如 cm²、m²）测量。“area” 一词最初意为“空地”。对于矩形，面积 = 长 × 宽。估算不规则图形的面积时，我们常在方格纸上数格子。
Volume me as how much water can fill the shape. The formula shows how many unit cubes fit inside.
体积是一个三维物体占据的空间量，用立方单位（cm³、m³）测量。对于长方体，体积 = 长 × 宽 × 高。把体积想象成能装满该形状的水量。公式表示能放入多少个单位立方体。
9. Statistics: Mean, Median, Mode & Range | 统计：平均数、中位数、众数与范围
The mean is the average you find by adding all the values and dividing by how many values there are. It shares out the total equally. The word is short for 'arithmetic mean'. It can be affected by very high or very low outliers.
平均数是将所有数值相加，再除以数值的个数得到的平均值。它把总和平均分配。这个词是“算术平均数”的简称。平均数容易受极高或极低异常值的影响。
The median is the middle value when the data is arranged in order. If there are two middle numbers, average them. 'Median' sounds like 'medium' – think of the middle strip of a road. The median is not influenced by outliers.
中位数是将数据按顺序排列后位于中间的值。如果有两个中间数，就取它们的平均值。“Median” 听起来像 “medium”（中间），可以联想为马路中间的隔离带。中位数不受异常值的影响。
The mode is the value that appears most often. It's the 'most' popular item. A data set can have one mode, more than one mode, or no mode at all if all values occur equally often.
众数是出现次数最多的值。它就是“最”流行的项目。一个数据集可以有一个众数、多个众数，或者如果所有值出现次数相同，则没有众数。
The range measures how spread out the data is. It is the difference between the largest and smallest values: range = max – min. A small range means the data are tightly grouped; a large range shows wide variation.
范围衡量数据的分散程度。它是最大值与最小值的差：范围 = 最大值 – 最小值。范围小说明数据集中在一起；范围大说明数据变动幅度大。
10. Probability Vocabulary | 概率术语
Probability describes how likely an event is to happen. It is measured on a scale from 0 to 1, or as a percentage from 0% to 100%. A probability of 0 means an event is impossible; a probability of 1 means it is certain.
概率描述事件发生的可能性大小。它用 0 到 1 的尺度衡量，或者用从 0% 到 100% 的百分比表示。概率为 0 意味着事件不可能发生；概率为 1 意味着事件必然发生。
An even chance has a probability of ½ or 50%, meaning it is just as likely to happen as not to happen. Words like 'likely', 'unlikely', 'good chance' and 'poor chance' are used to describe probability qualitatively. The probability scale helps you place these terms along a number line.
对等机会的概率为 ½ 或 50%，意味着发生与不发生的可能性相同。像“很可能”、“不太可能”、“很有机会”和“机会渺茫”这样的词语用于定性描述概率。概率尺度帮助你在数轴上定位这些术语。
An outcome is one possible result of an event. An event is a set of one or more outcomes. When all outcomes are equally likely, the theoretical probability is: number of favourable outcomes ÷ total number of possible outcomes. A fair coin or die means each outcome has the same chance. A random event happens without a predictable pattern.
结果是事件的一种可能结果。事件由一个或多个结果构成。当所有结果等可能时，理论概率为：有利结果的数量 ÷ 所有可能结果的总数。公平的硬币或骰子意味着每个结果的机会均等。随机事件的发生没有可预测的模式。
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