📚 Vocabulary and Terminology Quick-Reference Guide for Year 8 CAIE Maths | Year 8 CAIE 数学：词汇术语速记指南
This quick-reference guide is designed for Year 8 students following the CAIE Mathematics curriculum. Mastering mathematical vocabulary is essential for understanding questions, communicating ideas clearly and building a solid foundation for IGCSE. Here you will find key terms grouped by topic, with simple definitions in English and Chinese, plus memory tips to help you learn faster. Read through the sections, say the words aloud and try to use them when you explain a problem. The guide covers integers, fractions, algebra, geometry, data handling and more, making revision efficient and exam-ready.
这份速记指南专为学习 CAIE 数学课程的 Year 8 学生编写。掌握数学词汇对于理解题目、清晰表达思路以及为 IGCSE 打下坚实基础至关重要。书中按主题分类列出了关键术语，提供简单易懂的中英文释义，并附有记忆小技巧帮助你更快学习。通读各个小节，大声朗读这些词，并尝试在解释问题时运用它们。本指南涵盖整数、分数、代数、几何、数据处理等内容，让复习更高效，备考更从容。
1. Integers and Place Value | 整数与数位
Integer: An integer is any whole number that can be positive, negative or zero. It does not include fractions or decimals. For example, −5, 0 and 12 are all integers.
整数：整数是任何正整数、负整数或零，不包括分数或小数。例如，−5、0 和 12 都是整数。
Place value: The value of a digit depending on its position in a number. In 4526, the digit 5 is in the hundreds place, so its value is 500. Understanding place value helps with rounding and comparing numbers.
数位：一个数字中某位数字根据其位置所代表的值。在 4526 中，数字 5 位于百位，因此其值为 500。理解数位有助于进行四舍五入和比较大小。
Ascending order: Arranging numbers from smallest to largest. For instance, −3, 0, 2, 9 is in ascending order. Remember 'A' for 'ascending' goes up like a ladder.
升序：将数字从小到大的顺序排列。例如，−3、0、2、9 是升序排列。联想“上楼梯”来记忆升序是逐渐增大。
Descending order: Arranging numbers from largest to smallest, such as 14, 7, 1, −2. Think of 'descending' as going down, like coming down a mountain.
降序：将数字从大到小的顺序排列，例如 14、7、1、−2。联想“下山”来记忆降序是逐渐减小。
2. Arithmetic Operations | 四则运算
Sum: The result of adding two or more numbers. In 8 + 5 = 13, 13 is the sum. Use the phrase 'all together' to recall that sum involves addition.
和：两个或多个数相加的结果。在 8 + 5 = 13 中，13 就是和。用“总共是多少”来记忆和与加法相关。
Difference: : The answer when one number is subtracted from another. In 20 − 7 = 13, the difference is 13. Remember that 'difference' asks 'How far apart are the numbers?'
差：一个数减去另一个数得到的结果。在 20 − 7 = 13 中，差为 13。记住“差”询问的是“两个数相距多远”。
Product: The result of multiplication. For 6 × 4 = 24, 24 is the product. Think of 'product' as something produced when numbers are multiplied.
积：乘法运算的结果。对于 6 × 4 = 24，24 就是积。联想“生产”来记忆：将数相乘就能“产生”积。
Quotient: he : The answer after dividing one number by another. In 45 ÷ 5 = 9, the quotient is 9. The word 'quote' sounds similar — when you divide, you state how many times one number fits into another.
商：一个数除以另一个数所得的结果。在 45 ÷ 5 = 9 中，商为 9。“商”和“商量分配”有关联，想象分配物品时每人分到多少。
BIDMAS/BODMAS: The order of operations: Brackets, Indices (or Orders), Division and Multiplication (left to right), Addition and Subtraction (left to right). This rule prevents calculation mistakes.
BIDMAS / BODMAS 规则：运算顺序：括号、指数（或乘方）、除法和乘法（从左到右）、加法和减法（从左到右）。牢记此规则可以避免计算错误。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
Numerator: t of a fraction, showing how many equal parts are taken. In 3/8, the numerator is 3. Think 'numerator' = 'number of parts'.
分子：分数中位于上方的部分，表示取了多少等份。在 3/8 中，分子是 3。记住“分子”就是“分割后拥有的份数”。
Denominator: The bottom part of a fraction, indicating the total number of equal parts the whole is divided into. In 3/8, the denominator is 8. 'Denominator' sounds like 'denomination' — the type of parts the whole is split into.
分母：分数中位于下方的部分，表示整体被分成的总等份数。在 3/8 中，分母是 8。“分母”就像是整体的“名称”，表示每一份的大小。
Proper fraction: A fraction where the numerator is smaller than the denominator, so its value is less than 1. Example: 2/5.
真分数：分子小于分母的分数，其值小于 1。例子：2/5。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, such as 9/4. It can be changed into a mixed number.
假分数：分子大于或等于分母的分数，例如 9/4。它可以转化为带分数。
Mixed number: A number made up of a whole number and a proper fraction, like 2 1/3. It represents a value greater than 1.
带分数：由整数和真分数组成的数，如 2 1/3。它的值大于 1。
Equivalent fractions: or dividing both numerator and denominator by the same number gives equivalent fractions.
等值分数：形式不同但表示相同数量的分数。例如，1/2 = 2/4 = 4/8。将分子和分母同时乘以或除以同一个数即可得到等值分数。
4. Algebraic Expressions | 代数式
Variable: A symbol, usually a letter, that represents an unknown or changing number. In 3x + 5, x is the variable. Think of a 'variable' as something that can vary.
变量：一个符号，通常是字母，表示未知或可变的数。在 3x + 5 中，x 是变量。联想“变化”一词来记忆，变量的值可以改变。
Coefficient: The number multiplied by a variable. In 4y, 4 is the coefficient. It tells you how many times the variable is taken.
系数：与变量相乘的数。在 4y 中，4 是系数。它表示变量被取了多少次。
Like terms: Terms that contain exactly the same variables raised to the same powers. For example, 2a and 5a are like terms, but 2a and 3a² are not. Only like terms can be combined by addition or subtraction.
同类项：含有完全相同的变量且变量的指数也相同的项。例如，2a 和 5a 是同类项，但 2a 和 3a² 不是。只有同类项才能通过加减合并。
Simplify: To write an expression in its shortest, neatest form by collecting like terms. 3x + 2y + x simplifies to 4x + 2y.
化简：通过合并同类项将代数式写成最简形式。3x + 2y + x 化简为 4x + 2y。
Expand: Multiplying out brackets to remove them. 3(a + 2) expands to 3a + 6. Always multiply each term inside the bracket.
展开：通过乘法去掉括号。3(a + 2) 展开后得到 3a + 6。务必用括号外的数乘以括号内的每一项。
5. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement showing that two expressions are equal, using the '=' sign. 2x + 3 = 11 is an equation. Solve it to find the value of the unknown.
方程：表明两个表达式相等的数学陈述，使用“=”号。2x + 3 = 11 就是一个方程。解方程就是求出未知数的值。
Inequality: greater than), ≤ (less than or equal to), ≥ (greater than or equal to). Example: x > 5.
不等式：比较两个不相等的值的陈述，使用符号：<（小于）、>（大于）、≤（小于等于）、≥（大于等于）。例子：x > 5。
Solve: he : To find the value of the variable that makes an equation true. For x + 7 = 10, solving gives x = 3.
解（方程）：求出使方程成立的变量的值。对于 x + 7 = 10，解得 x = 3。
Balance method: A way of solving equations by doing the same operation to both sides, keeping the equation balanced like a scale. If you add 2 to one side, add 2 to the other.
平衡法：解方程的一种方法，对方程两边进行相同的运算，就像保持天平平衡一样。如果一边加 2，另一边也要加 2。
Unknown: The number in an equation we do not yet know, often represented by a letter. The goal is to find the value of the unknown.
未知数：方程中我们还不知道的数，通常用字母表示。目标就是求出未知数的值。
6. Sequences and Patterns | 数列与规律
Sequence: A list of numbers or objects in a special order, often following a rule. 2, 4, 6, 8, ... is a sequence of even numbers.
数列：按特定顺序排列的一串数或物体，通常遵循某种规律。2, 4, 6, 8, ... 是一个偶数数列。
Term: Each number or figure in a sequence. The first term of the sequence 5, 10, 15, ... is 5. The 3rd term is 15. A term is like a 'member' of the sequence.
项：数列中的每一个数或图形。数列 5, 10, 15, ... 的第一项是 5，第三项是 15。项就像是数列中的“成员”。
Arithmetic sequence: A sequence where the difference between consecutive terms is constant. 3, 7, 11, 15, ... has a common difference of 4. This difference is added or subtracted each time.
等差数列：相邻两项的差为常数的数列。3, 7, 11, 15, ... 的公差是 4。每次加或减同一个数得到下一项。
nth term rule: s. For 4, 7, 10, 13, ... the nth term is 3n + 1. Substitute n = 5 to get the 5th term: 16.
第 n 项公式：一个让你无需列出所有前面的项就能求出数列中任意项的公式。对于 4, 7, 10, 13, ...，第 n 项公式是 3n + 1。代入 n = 5 即可得到第 5 项：16。
Triangular numbers: Numbers that can form an equilateral triangle when arranged as dots. The sequence is 1, 3, 6, 10, 15, ... Each term is the sum of the first n natural numbers.
三角形数：能够排列成等边三角形的点阵所对应的数。数列为 1, 3, 6, 10, 15, ... 每一项是前 n 个自然数的和。
7. Geometry: Angles and Shapes | 几何：角与图形
Acute angle: An angle measuring less than 90°. A sharp corner of a piece of paper folded diagonally often creates an acute angle. Think of 'a cute little angle' — small and sharp.
锐角：小于 90° 的角。将一张纸对角折叠产生的尖角通常是锐角。用“锐”联想尖锐、细小的角。
Right angle: An angle of exactly 90°, marked with a small square. The corners of a square are right angles. It is a quarter turn.
直角：恰好为 90° 的角，用小方格标记。正方形的四个角都是直角。它代表四分之一周角。
Obtuse angle: An angle greater than 90° but less than 180°. It is larger than a right angle but not a straight line. An obtuse angle looks 'wide' and 'blunt'.
钝角：大于 90° 但小于 180° 的角。它比直角大，但还不是平角。钝角看起来比较“宽厚”。
Polygon: A closed 2D shape with straight sides. Triangles, quadrilaterals, pentagons and hexagons are all polygons. The name comes from Greek: 'poly' means many, 'gon' means angle.
多边形：由直线段围成的封闭二维图形。三角形、四边形、五边形和六边形都是多边形。词源来自希腊语，'poly' 意为许多，'gon' 意为角。
Parallel lines: Lines that are always the same distance apart and never meet. Railway tracks are a good real-life example. They are marked with arrows in diagrams.
平行线：始终保持相同距离且永不相交的直线。铁轨是一个很好的现实例子。在图中用箭头标记。
Perpendicular lines: Lines that meet or cross at a right angle (90°). The edges of a book cover are perpendicular. Think of 'perpendicular' as 'perfectly upright'.
垂直线：相交成直角（90°）的直线。书本封面的边缘相互垂直。联想“垂直”表示“笔直向上”。
8. Measures and Units | 度量与单位
Perimeter: The total distance around the outside of a shape. For a rectangle, add the lengths of all four sides. Imagine walking along the fence of a field — the distance you cover is the perimeter.
周长：一个图形外边线的总长度。对于矩形，将四条边的长度相加。想象沿着田地围栏走一圈，所经过的距离就是周长。
Area: rectangle, area = length × width. Think of how many unit squares can fit inside the shape.
面积：一个图形所占平面的大小，用平方单位（cm², m²）计量。对于矩形，面积 = 长 × 宽。想象图形里可以铺满多少个单位正方形。
Volume: ). For a cuboid, volume = length × width × height. Volume tells you the capacity of a box.
体积：三维物体所占空间的大小，用立方单位（cm³, m³）计量。对于长方体，体积 = 长 × 宽 × 高。体积告诉你一个盒子的容量。
Circumference: × diameter. Whenever you see a circular track, the length of one lap is the circumference.
圆周（周长）：圆的周长。可用公式 π × 直径来计算。看到圆形跑道时，一圈的长度就是圆周。
Here is a quick conversion table for common metric units:
以下是一个常用公制单位换算表：
| Length | 1 cm = 10 mm | 1 m = 100 cm | 1 km = 1000 m |
| Mass | 1 kg = 1000 g | 1 tonne = 1000 kg | |
| Capacity | 1 L = 1000 ml | 1 L = 1000 cm³ |
Memorise the relationships by recognising the prefixes: 'milli' means 1/1000, 'centi' means 1/100, 'kilo' means 1000. This pattern helps you convert between units quickly.
通过识别前缀来记忆关系：'milli' 表示 1/1000，'centi' 表示 1/100，'kilo' 表示 1000。这一规律有助于快速进行单位换算。
9. Coordinates and Graphs | 坐标与图像
Coordinates: A pair of numbers (x, y) that locate a point on a grid. The first number is the horizontal position (x-coordinate), the second is the vertical position (y-coordinate). 'Along the corridor, up the stairs' reminds you to go across first, then up.
坐标：一对数字 (x, y)，用于在网格上定位一个点。第一个数是水平位置（x 坐标），第二个数是垂直位置（y 坐标）。用“先沿走廊走，再上楼梯”来记忆先横后纵。
Origin: The point (0, 0) where the x-axis and y-axis intersect. All coordinates are measured from here. Visualise the origin as the starting point of a journey.
原点：x 轴和 y 轴相交的点 (0, 0)。所有坐标都从这里开始测量。把原点想象成旅途的起点。
Quadrant: The coordinate plane is divided into four quadrants by the axes. Quadrant I is where both x and y are positive; Quadrant II has negative x and positive y; Quadrant III both negative; Quadrant IV positive x and negative y.
象限：坐标平面被坐标轴分成四个象限。第一象限中 x 和 y 都为正；第二象限 x 为负、y 为正；第三象限两者均为负；第四象限 x 为正、y 为负。
Linear graph: ne, usually from an equation like y = 2x + 1. It shows a constant rate of change. The word 'linear' comes from 'line'.
线性图像：形成一条直线的图像，通常来自 y = 2x + 1 这样的方程。它表示变化率不变。'linear' 一词源于 'line'（线）。
Gradient: A measure of how steep a line is, calculated as rise over run (vertical change ÷ horizontal change). A steeper line has a larger gradient. A downhill line has a negative gradient.
斜率（坡度）：衡量直线陡峭程度的量，用升高量除以水平距离（纵向变化 ÷ 横向变化）计算。线越陡，斜率越大。下坡的线斜率为负。
10. Statistics and Probability | 统计与概率
Mean: by the number of values. For 2, 3, 7, the mean is (2+3+7) ÷ 3 = 4. It gives a idea of the 'centre' of the data.
平均数（均值）：通常称为平均值。将所有数据值相加，再除以数据的个数。对于 2, 3, 7，平均数为 (2+3+7) ÷ 3 = 4。它反映数据的“中心”位置。
Median: The middle value when data is ordered from smallest to largest. If there are two middle numbers, the median is their mean. The median is not affected by very large or very small outliers.
中位数：将数据从小到大排列后中间的那个值。若有两个中间数，则中位数为这两个数的平均值。中位数不易受极端值的影响。
Mode: The value that appears most frequently in a data set. A set may have one mode, more than one mode (bimodal), or no mode at all. 'Mode' sounds like 'most' — the most common value.
众数：数据集中出现次数最多的值。一组数据可能有一个众数、多个众数（双众数）或没有众数。'Mode' 发音类似 'most'，代表最常见的值。
Range: e. For 4, 11, 6, the range is 11 − 4 = 7. A small range means the data are closely packed.
极差（范围）：衡量数据分散程度的量，用最大值减最小值计算。对于 4, 11, 6，极差为 11 − 4 = 7。极差小说明数据比较集中。
Probability: The chance of an event happening, measured on a scale from 0 (impossible) to 1 (certain). It is often written as a fraction, decimal or percentage. Flipping a fair coin gives a probability of 1/2 for heads.
概率：某个事件发生的可能性，用 0（不可能）到 1（必然）的尺度衡量。通常写成分数、小数或百分数。抛一枚公平的硬币，正面朝上的概率是 1/2。
Outcome: A possible result of a probability experiment. When rolling a die, the outcomes are 1, 2, 3, 4, 5, 6. All equally likely outcomes form the sample space.
结果：概率实验中可能出现的一种情形。掷一枚骰子时，可能的结果有 1, 2, 3, 4, 5, 6。所有等可能结果构成样本空间。
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