📚 Year 9 Cambridge Math: Vocabulary and Terminology Quick Memorization Guide | 九年级剑桥数学：词汇术语速记指南
Grasping the vocabulary of mathematics is just as important as learning the procedures. In Year 9 Cambridge Mathematics, you will encounter a wide range of technical terms that form the building blocks for IGCSE. This guide provides memorable tricks, root words, and visual hooks for key terms across the entire syllabus, helping you speak and think like a confident mathematician.
掌握数学词汇与学习运算方法同样重要。在九年级剑桥数学课程中，你会接触到大量为 IGCSE 奠定基础的专业术语。本指南为全纲核心词汇提供了难忘的记忆技巧、词根联想和图像钩子，让你像自信的数学家一样说话和思考。
1. Integers and Number Theory | 整数与数论
An integer is any whole number that can be positive, negative, or zero. Values such as -3, 0, 15 and 2048 are integers, while ½, √2 and 3.14 are not.
整数是任何可以是正数、负数或零的整数。像 -3、0、15 和 2048 这样的值是整数，而 ½、√2 和 3.14 不是。
A factor of a number divides it exactly without leaving a remainder. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
一个数的因数可以整除它，没有余数。例如，24 的因数是 1、2、3、4、6、8、12 和 24。
A multiple is the product of a number and any integer. Multiples of 7 include 7, 14, 21, 28, 35 … and they go on forever.
倍数是某个数与任意整数的乘积。7 的倍数有 7、14、21、28、35…… 并且无限延伸。
A prime number has exactly two distinct factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13. Remember that 1 is not prime because it has only one factor. Memory hook: 'Prime numbers are the atoms of arithmetic – they cannot be broken down further.'
质数恰好有两个不同的因数：1 和它自身。前几个质数是 2、3、5、7、11、13。记住 1 不是质数，因为它只有一个因数。记忆钩子：“质数是算术的原子——它们不能再分解”。
Composite numbers have more than two factors. For instance, 12 is composite because it can be divided by 1, 2, 3, 4, 6 and 12.
合数有两个以上的因数。例如，12 是合数，因为它可以被 1、2、3、4、6 和 12 整除。
The Highest Common Factor (HCF) is the largest factor shared by two or more numbers. The Lowest Common Multiple (LCM) is the smallest multiple they share. To find the HCF of 24 and 36, list factors: 24 (1,2,3,4,6,8,12,24) and 36 (1,2,3,4,6,9,12,18,36); the HCF is 12.
最大公因数 (HCF) 是两个或多个数共有的最大因数。最小公倍数 (LCM) 是它们共有的最小倍数。要找出 24 和 36 的 HCF，列出因数：24 的有 1,2,3,4,6,8,12,24，36 的有 1,2,3,4,6,9,12,18,36；HCF 是 12。
For 60, the factor tree gives 2² × 3 × 5. Use indexes (powers) to keep the notation tidy.
质因数分解把一个数写成质因数的乘积。对 60，因数树给出 2² × 3 × 5。用指数（幂）使记号整洁。
| Term | 中文 | Quick Memory Tip |
|---|---|---|
| Integer | 整数 | 'Integer' sounds like 'intact' – a whole number with no fragments. |
| Prime | 质数 | Think 'primary' – they are the primary building blocks. |
| HCF | 最大公因数 | 'Highest' common friend among numbers. |
| LCM | 最小公倍数 | 'Smallest' shared multiple – think of the first common stop in times tables. |
2. Fractions, Decimals and Percentages | 分数、小数与百分比
A fraction shows a part of a whole. It has a numerator (top number) and a denominator (bottom number). The denominator names how many equal parts the whole is split into; the numerator counts how many of those parts we have.
分数表示整体的一部分。它有分子（上面的数）和分母（下面的数）。分母表明整体被分成多少等份；分子表示我们占有几份。
A proper fraction has a numerator smaller than its denominator, like 3/8. An improper fraction has a larger numerator, e.g. 11/4, and can be converted into a mixed number (2 3/4).
真分数的分子比分母小，比如 3/8。假分数的分子更大，例如 11/4，它可以化成带分数 (2 3/4)。
To compare or add fractions, we often need a common denominator. The lowest common denominator (LCD) is the LCM of the denominators.
要比较或相加分数，我们经常需要公分母。最小公分母 (LCD) 就是分母的最小公倍数。
A terminating decimal has a finite number of digits after the decimal point, like 0.75 (which equals 3/4). A recurring decimal has a pattern that repeats forever, such as 0.333… (written as 0.3̅). Every fraction produces either a terminating or a recurring decimal.
有限小数在十进制小数点后只有有限位数字，比如 0.75（等于 3/4）。循环小数有一个重复的模式，比如 0.333…（记作 0.3̅）。每个分数都对应一个有限小数或循环小数。
A percentage means 'out of 100' To convert a fraction to a percentage, multiply by 100. For instance, 2/5 = (2 ÷ 5) × 100% = 40%.
百分比表示“每一百份中的份数”。它便于比较比例。要把分数转换为百分比，乘以 100。例如，2/5 = (2 ÷ 5) × 100% = 40%。
Percentage increase = (increase ÷ original amount) × 100%. Percentage decrease works similarly. Always identify the original value correctly.
百分比增加 = (增加量 ÷ 原始量) × 100%。百分比减少类似。务必正确找到原始值。
3. Ratios and Proportion | 比与比例
A ratio compares the sizes of two or more quantities. The ratio a : b tells us how much of one thing there is compared to another. It can be simplified by dividing both sides by their common factor, just like fractions.
比比较两个或多个量的大小。比 a : b 告诉我们一种事物相对于另一种事物有多少。它可以像分数一样通过两边除以公因数来化简。
ion a/b. When sharing in a ratio, find the total number of parts first. For example, split £60 in the ratio 3 : 2: total parts = 5, so one part = £12, giving shares £36 and £24.
比可以写成三种形式：a 比 b、a : b 或分数 a/b。按比例分配时，先求出总份数。例如，按 3 : 2 分配 £60：总份数 = 5，一份 = £12，得到份额为 £36 和 £24。
t line through the origin. You can use the unitary method or the formula y = kx to solve problems.
正比表示两个量以相同速率增加。如果你把其中一个加倍，另一个也加倍。正比的图像是一条经过原点的直线。你可以用归一法或公式 y = kx 来解题。
Inverse proportion means one quantity decreases as the other increases, keeping the product constant. For example, the time taken for a journey is inversely proportional to the speed if the distance is fixed.
反比表示一个量随另一个量的增加而减少，保持乘积不变。例如，在距离固定的情况下，旅行时间与速度成反比。
4. Algebraic Expressions and Equations | 代数表达式与方程
A variable is a letter that represents an unknown or changeable number. x and y are the most common variables. A constant is a fixed number, like 5 or -2.
变量是代表未知或可变化数字的字母。x 和 y 是最常见的变量。常数是一个固定的数，比如 5 或 -2。
A term is a single mathematical element. It can be a number, a variable, or numbers and variables multiplied together. In the expression 4x² - 3xy + 7, there are three terms: 4x², -3xy, and 7.
项是单一的数学元素。它可以是一个数字、一个变量或数字与变量的乘积。在表达式 4x² - 3xy + 7 中，有三个项：4x²、-3xy 和 7。
A coefficient is the number part of a term that multiplies the variable. In -5y, the coefficient is -5. In x, the coefficient is 1 (implied).
系数是项中乘以变量的数字部分。在 -5y 中，系数是 -5。在 x 中，系数是 1（隐含的）。
an equals sign, e.g. 3x − 7 = 14. To solve an equation means to find the value of the variable that makes the statement true.
表达式是没有等号的数学短语，比如 2a + 5b。方程则是陈述两个表达式相等，含有等号，例如 3x − 7 = 14。解方程就是找出使等式成立的变量值。
erse process is called factorisation, where we find the common factor and write it outside the bracket. For 6x + 9, the common factor is 3, giving 3(2x + 3).
去括号是指把括号外的项与括号内的每一项相乘：a(b + c) = ab + ac。逆过程叫做因式分解，我们找出公因数并把它写在括号外面。对于 6x + 9，公因数是 3，得到 3(2x + 3)。
5. Sequences and Patterns | 数列与模式
A sequence is an ordered list of numbers that follow a rule. Each number in the sequence is called a term. The position of a term is often labelled with n (e.g. nth term).
数列是按照某一规则排列的一列数字。数列中的每个数字称为项。某项的位置通常用 n 标记（例如第 n 项）。
In a linear (arithmetic) sequence, the difference between consecutive terms is constant. This common difference is the coefficient of n in the nth term formula. For the sequence 5, 8, 11, 14, … the common difference is 3, and the nth term is 3n + 2.
在线性（算术）数列中，相邻两项的差是常数。这个公差就是第 n 项公式中 n 的系数。对于数列 5, 8, 11, 14, …，公差是 3，第 n 项公式为 3n + 2。
on number into the nth term formula. For the 10th term of 3n + 2, calculate 3×10 + 2 = 32.
要找到某一项，把位置数字代入第 n 项公式。对于 3n + 2 的第 10 项，计算 3×10 + 2 = 32。
Sequences can also be generated by a term-to-term rule, like 'add 4 to the previous term'. The first term must be given. You can recognise square number sequences (1, 4, 9, 16, …), cube numbers, and Fibonacci-style sequences where you add the two previous terms.
数列也可以由递推规则生成，比如“前一项加 4”。必须给出第一项。你还会识别平方数列 (1, 4, 9, 16, …)、立方数列以及斐波那契形式的数列（前两项相加）。
6. Linear Graphs and Coordinates | 线性图像与坐标
The Cartesian coordinate plane has a horizontal x-axis and a vertical y-axis. They meet at the origin (0,0). Any point is described by an ordered pair (x, y), where x comes first.
笛卡尔坐标平面有一条横轴 x 轴和一条纵轴 y 轴。它们在原点 (0,0) 相交。任意一点用有序数对 (x, y) 描述，x 在前。
y) / (change in x). A positive gradient slopes upwards from left to right; a negative gradient slopes downwards.
斜率测量直线的陡峭程度。它是纵移除以横移：斜率 = (y 的变化量) / (x 的变化量)。正斜率从左向右上升；负斜率从左向右下降。
r the gradient and c is the y-intercept. To quickly sketch a graph, plot the y-intercept first, then use the gradient to find other points.
y 轴截距是直线与 y 轴相交的点。在斜截式 y = mx + c 中，m 代表斜率，c 是 y 轴截距。要快速绘制图像，先标出 y 轴截距，然后用斜率找其他点。
Parallel lines have the same gradient but different y-intercepts. Perpendicular lines have gradients that are negative reciprocals of each other (e.g. 2 and -1/2), but you will explore this more in IGCSE.
平行线具有相同的斜率但不同的 y 轴截距。垂直线的斜率互为负倒数（例如 2 和 -1/2），不过这部分在 IGCSE 会进一步探索。
7. Angles and Polygons | 角与多边形
Angles are measured in degrees (°). Key types: acute angle (0°–90°), right angle (exactly 90°), obtuse angle (90°–180°), straight angle (180°), and reflex angle (180°–360°).
角以度 (°) 为单位。关键类型：锐角 (0°–90°)，直角（恰好 90°），钝角 (90°–180°)，平角 (180°) 和优角 (180°–360°)。
Complementary angles add to 90°; supplementary angles add to 180°. Vertically opposite angles (formed by two intersecting lines) are equal.
余角相加为 90°；补角相加为 180°。对顶角（由两相交直线形成）相等。
A polygon is a closed 2D shape with straight sides. A regular polygon has all sides and all angles equal. Naming by number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).
多边形是由直线段组成的封闭二维图形。正多边形所有边相等且所有角相等。按边数命名：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)。
ide is extended) always sum to 360°. In a regular polygon, each exterior angle = 360° / n.
n 边多边形的内角和为 (n − 2) × 180°。外角（延长一条边，每个顶点一个）之和恒为 360°。对于正多边形，每个外角 = 360° / n。
Sum of interior angles: (n − 2) × 180°
内角和公式: (n − 2) × 180°
8. Perimeter, Area and Volume | 周长、面积与体积
perimeter is called the circumference: C = 2πr or πd, where r is radius and d is diameter.
周长是二维图形外沿的总长度。对于长 l、宽 w 的长方形，P = 2(l + w)。对于圆，周长叫做圆周：C = 2πr 或 πd，其中 r 是半径，d 是直径。
Area measures the surface inside a shape. Key formulae:
- Rectangle: A = l × w
- Triangle: A = ½ × base × height
- Parallelogram: A = base × perpendicular height
- Trapezium: A = ½ × (a + b) × h, where a and b are the parallel sides.
- Circle: A = πr²
面积测量图形内部的表面大小。关键公式：长方形 A = 长 × 宽；三角形 A = ½ × 底 × 高；平行四边形 A = 底 × 垂直高；梯形 A = ½ × (上底 + 下底) × 高；圆 A = πr²。
Area of a circle: A = πr²
圆面积：A = πr²
h. For a cuboid, V = l × w × h. Capacity is often measured in litres (1 litre = 1000 cm³).
棱柱的体积等于横截面积乘以长度。对于长方体，V = 长 × 宽 × 高。容量常用升来衡量 (1 升 = 1000 立方厘米)。
Compound shapes can be split into simple shapes to find the total area or perimeter. Always check if you need to leave answers in terms of π or as a rounded decimal.
组合图形可以拆分成简单图形来求总面积或周长。务必注意答案是否需保留 π 或化为四舍五入后的小数。
9. Statistics and Probability | 统计与概率
The mean is the average: sum of all values divided by the
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