📚 Year 8 CAIE Maths: Vocabulary & Terminology Quick Memory Guide | Year 8 CAIE 数学：词汇术语速记指南
Mastering mathematical vocabulary is the first step to solving problems with confidence. In Year 8 CAIE Maths, students often face challenges not because they cannot calculate, but because they do not fully understand what the question is asking. This guide breaks down essential terms into logical groups, provides simple English explanations, and pairs each with its Chinese equivalent. Use these memory tricks, visual hints, and bilingual links to build a solid foundation for IGCSE success.
掌握数学词汇是自信解题的第一步。在 Year 8 CAIE 数学中，学生常遇到的困难并非不会计算，而是不完全理解题目在问什么。本指南将核心术语按逻辑分组，提供简洁的英文解释并配以中文对应词。利用这些记忆技巧、视觉提示和中英对照，为 IGCSE 的成功打下坚实基础。
1. Number Types & Place Value | 数类型与位值
Integers are whole numbers that can be positive, negative, or zero. Think of steps on a staircase: going up is positive, going down is negative.
整数 (Integers) 是正整数、负整数和零的总称。想象楼梯台阶：向上为正，向下为负。
Factors are numbers that divide exactly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, 12. Remember: 'Factors fit perfectly.'
因数 (Factors) 是能整除另一个数而没有余数的数。例如，12 的因数是 1、2、3、4、6、12。记住：“因数恰好装得下”。
Multiples are the results of multiplying a number by an integer. The multiples of 3 are 3, 6, 9, 12… ‘Multiples multiply.’
倍数 (Multiples) 是一个数乘整数的结果。3 的倍数有 3、6、9、12…… “倍数就是乘出来的数”。
Prime numbers have exactly two distinct factors: 1 and itself. 2 is the only even prime. Composite numbers have more than two factors.
质数 (Prime numbers) 只有两个不同的因数：1 和它本身。2 是唯一的偶质数。合数（Composite numbers）有两个以上的因数。
Place value tells us the value of a digit based on its position. In 3.76, the 7 is in the tenths place, meaning 7/10.
位值 (Place value) 根据数字的位置告诉我们它的值。在 3.76 中，7 在十分位，表示 7/10。
2. Operations & Their Keywords | 运算及其关键词
Sum means the result of addition. ‘Total’, ‘plus’, ‘increase by’ all point to adding.
和 (Sum) 是加法运算的结果。‘Total’、‘plus’、‘increase by’ 都指向加法。
Difference means the result of subtraction. ‘Minus’, ‘less than’, ‘decrease by’, ‘how many more’ indicate subtraction.
差 (Difference) 是减法运算的结果。‘Minus’、‘less than’、‘decrease by’、‘how many more’ 表示减法。
Product means the result of multiplication. ‘Times’, ‘double’, ‘triple’, ‘groups of’ signal multiplication.
积 (Product) 是乘法运算的结果。‘Times’、‘double’、‘triple’、‘groups of’ 表示乘法。
Quotient means the result of division. ‘Divide’, ‘share equally’, ‘per’, ‘ratio’ are clues.
商 (Quotient) 是除法运算的结果。‘Divide’、‘share equally’、‘per’、‘ratio’ 是除法线索。
Index (power, exponent) tells how many times to multiply a number by itself. In 5³, 3 is the index, and we read it as ‘5 cubed’ or ‘5 to the power of 3’.
指数 (Index, power, exponent) 表示一个数被自身乘的次数。5³ 中，3 是指数，读作“5 的立方”或“5 的 3 次方”。
3. Fractions, Decimals & Percentages | 分数、小数和百分数
Numerator is the top part of a fraction; denominator is the bottom part. Think: ‘Numerator up, Denominator down.’
分子 (Numerator) 是分数的上部；分母 (Denominator) 是分数的下部。记：分子在上，分母在下。
Equivalent fractions represent the same value, like ½ = ²⁄₄. Multiply or divide both numerator and denominator by the same number.
等值分数 (Equivalent fractions) 表示相同的值，如 ½ = ²⁄₄。分子分母同时乘或除同一个数就能得到。
Improper fraction has a numerator larger than the denominator, e.g., ⁷⁄₄. A mixed number combines a whole number and a proper fraction, e.g., 1¾.
假分数 (Improper fraction) 分子大于分母，如 ⁷⁄₄。带分数 (Mixed number) 由整数和真分数组成，如 1¾。
Decimal point separates the whole part from the fractional part. Recurring decimal has a digit or block that repeats endlessly, shown with a dot above the repeating digit(s).
小数点 (Decimal point) 分隔整数部分和小数部分。循环小数 (Recurring decimal) 有一位或多位数字无限重复，在重复数字上方加点表示。
Percentage means ‘out of 100’. The symbol % is a quick way to write /100. To convert a decimal to a percentage, multiply by 100.
百分数 (Percentage) 意为“每一百份”。符号 % 是 /100 的简写。小数化百分数，乘以 100 即可。
4. Ratios, Rates & Proportions | 比、比率与比例
Ratio compares two or more quantities. The order is vital: 2:3 is not the same as 3:2. Use ‘to’ when reading, e.g., ‘2 to 3’.
比 (Ratio) 用于比较两个或多个量。顺序至关重要：2:3 与 3:2 不同。读作“2 比 3”。
Proportion says that two ratios are equal. In a recipe, if you double one ingredient, you double all others to keep the proportion the same.
比例 (Proportion) 表示两个比值相等。食谱中，如果一种原料加倍，其他所有原料也要加倍以保持比例不变。
Rate compares two quantities with different units, such as speed (km/h) or unit price (£/kg). A unit rate has a denominator of 1.
比率 (Rate) 比较两种不同单位的量，如速度（km/h）或单价（£/kg）。单位比率的分母为 1。
Direct proportion means as one quantity increases, the other increases at the same rate; the graph is a straight line through the origin.
正比例 (Direct proportion) 一个量增加，另一个量以相同速率增加；图像是一条过原点的直线。
5. Algebraic Expressions & Equations | 代数表达式与方程
Variable is a letter that stands for an unknown number, often x or y. A constant is a fixed number, like 5 or –3.
变量 (Variable) 是表示未知数的字母，常见 x 或 y。常量 (Constant) 是固定的数，如 5 或 –3。
Term is a single number, variable, or product of numbers and variables, e.g., 3x². Coefficient is the number part in front, in 3x² the coefficient is 3.
项 (Term) 是单独的一个数、变量或数与变量的积，如 3x²。系数 (Coefficient) 是字母前面的数字部分，3x² 中系数是 3。
Expression is a combination of terms without an equals sign, e.g., 2x + 5. An equation has an equals sign and shows two expressions are equal, e.g., 2x + 5 = 11.
表达式 (Expression) 由项组合而成，没有等号，如 2x + 5。方程 (Equation) 含有等号，表明两个表达式相等，如 2x + 5 = 11。
Like terms have exactly the same variable and power; only like terms can be combined by adding or subtracting their coefficients.
同类项 (Like terms) 变量和指数完全相同；只有同类项才能通过系数加减合并。
Simplify means to write an expression in its most compact form. Solve means to find the value of the variable that makes the equation true.
化简 (Simplify) 是把式子写成最紧凑的形式。解方程 (Solve) 是求出使方程成立的变量的值。
6. Sequences & Patterns | 数列与模式
A sequence is an ordered list of numbers following a rule. Each number is a term.
数列 (Sequence) 是按规则排列的一列数。每个数称为项 (Term)。
An arithmetic sequence has a constant difference between terms, e.g., 3, 7, 11, 15… (add 4). The common difference is the number added each time.
等差数列 (Arithmetic sequence) 每项之间的差是常数，如 3, 7, 11, 15…（每次加 4）。公差 (Common difference) 是每次加的数。
The nth term rule lets you find any term without listing all previous ones. For 2, 5, 8, 11… the nth term is 3n – 1.
第 n 项公式 (nth term) 使你不必列出前面各项也能求出任意一项。2, 5, 8, 11… 的第 n 项为 3n – 1。
Square numbers: 1, 4, 9, 16… form the pattern n². Triangular numbers: 1, 3, 6, 10… are sums of consecutive integers.
平方数 (Square numbers): 1, 4, 9, 16… 符合 n²。三角形数 (Triangular numbers): 1, 3, 6, 10… 是连续整数之和。
7. Geometry: Angles & Lines | 几何：角与线
Acute angle: less than 90°. Right angle: exactly 90°, marked with a small square. Obtuse angle: between 90° and 180°. Reflex angle: between 180° and 360°.
锐角 (Acute angle): 小于 90°。直角 (Right angle): 正好 90°，用一个小方框标记。钝角 (Obtuse angle): 90° 到 180° 之间。优角 (Reflex angle): 180° 到 360° 之间。
Complementary angles add up to 90°. Supplementary angles add up to 180°. Think: ‘C’ for Corner (90°), ‘S’ for Straight line (180°).
互余角 (Complementary angles) 和为 90°。互补角 (Supplementary angles) 和为 180°。记法：‘C’ 代表 “角 (Corner)” 90°，‘S’ 代表 “直线 (Straight line)” 180°。
Vertically opposite angles are equal when two lines cross. Adjacent angles share a vertex and a side.
对顶角 (Vertically opposite angles) 两条直线相交时相等。邻角 (Adjacent angles) 有公共顶点和一条公共边。
When a transversal cuts parallel lines: corresponding angles are equal (F-shape), alternate angles are equal (Z-shape), and co-interior angles sum to 180° (C-shape).
当截线 (Transversal) 切割平行线：同位角 (Corresponding angles) 相等（F 形），内错角 (Alternate angles) 相等（Z 形），同旁内角 (Co-interior angles) 和为 180°（C 形）。
8. Shapes, Perimeter, Area & Volume | 图形、周长、面积与体积
Perimeter is the total distance around a 2D shape – imagine walking along the fence.
周长 (Perimeter) 是二维图形一周的总长度——想象沿着篱笆走一圈。
Area pace inside a shape, measured in square units (cm², m²). Rectangle: Area = length × width.
面积 (Area) 是图形内部的空间大小，用平方单位（cm², m²）测量。长方形：面积 = 长 × 宽。
Volume cupies, measured in cubic units (cm³, m³). For a cuboid: Volume = length × width × height.
体积 (Volume) 是三维物体所占的空间，用立方单位（cm³, m³）测量。长方体：体积 = 长 × 宽 × 高。
Surface area is the total area of all faces of a 3D solid. A net is a 2D pattern that can be folded to make the solid.
表面积 (Surface area) 是三维立体所有面的总面积。展开图 (Net) 是可以折叠成立体的二维图形。
Circle vocabulary: radius (centre to edge), diameter (edge to edge through centre), circumference (distance around). π (pi) ≈ 3.14 or 22/7.
圆 (Circle) 词汇：半径 (Radius)（圆心到边缘），直径 (Diameter)（穿过圆心的两端间距），周长/圆周 (Circumference)（围绕一圈的长度）。π ≈ 3.14 或 22/7。
9. Symmetry & Transformations | 对称与变换
Line symmetry (reflection symmetry) means a shape can be folded along a line so both halves match exactly. The fold line is the line of symmetry.
线对称 (Line symmetry)（反射对称）表示图形可沿一条线对折使两部分完全重合。这条折线叫对称轴 (Line of symmetry)。
Rotational symmetry means a shape looks the same after a part-turn. The order of rotational symmetry is how many times it matches in a full 360° turn.
旋转对称 (Rotational symmetry) 表示图形旋转一定角度后与自身重合。旋转对称阶数 (Order of rotational symmetry) 是旋转一周 360° 重合的次数。
Translation slides a shape without turning or flipping; it is described by a column vector. Reflection flips a shape over a mirror line. Rotation turns a shape about a centre by a given angle and direction.
平移 (Translation) 只滑动图形不翻转不转向；用列向量描述。反射 (Reflection) 将图形沿一条镜线翻转。旋转 (Rotation) 绕一个中心按给定角度和方向转动图形。
Enlargement changes the size of a shape by a scale factor from a centre of enlargement. Scale factor >1 makes it larger; between 0 and 1 makes it smaller.
放大/缩小 (Enlargement) 通过比例因子 (Scale factor) 从一个中心点改变图形大小。比例因子 >1 放大；0 到 1 之间缩小。
10. Statistics: Averages & Charts | 统计：平均数与图表
Mean: sum of all values divided by the number of values. Median: the middle value when data is ordered. Mode: the value that appears most often. Range: difference between highest and lowest values.
平均数/均值 (Mean): 所有数值之和除以个数。中位数 (Median): 数据排序后居中的值。众数 (Mode): 出现次数最多的值。极差 (Range): 最大值与最小值的差。
A bar chart uses bars to represent categorical data; the height shows frequency. A pictogram uses symbols to represent data – always check the key.
条形图 (Bar chart) 用条形表示分类数据；高度表示频数。象形图 (Pictogram) 用符号表示数据——一定要看清图例。
A pie chart uses sectors of a circle to show proportions; the total angle is 360°. Line graph is used for data changing over time.
饼图 (Pie chart) 用圆的扇形表示比例；总角度为 360°。折线图 (Line graph) 用于显示随时间变化的数据。
Discrete data can only take specific values (e.g., shoe sizes). Continuous data can take any value within a range (e.g., height).
离散数据 (Discrete data) 只能取特定值（如鞋码）。连续数据 (Continuous data) 可取范围内的任意值（如身高）。
11. Probability & Chance | 概率与可能性
Probability measures how likely an event is to happen, written as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain).
概率 (Probability) 衡量事件发生的可能性，用 0（不可能）到 1（必然）之间的分数、小数或百分数表示。
Outcome is a possible result. An event obability of an event = number of favourable outcomes / total number of possible outcomes.
结果 (Outcome) 是可能的结果。事件 (Event) 是一组结果的集合。事件概率 = 有利结果数 / 所有可能结果总数。
If all outcomes are equally likely, we say they are fair. A sample space is a list or diagram of all possible outcomes.
若所有结果可能性相等，称为等可能 (Fair)。样本空间 (Sample space) 是所有可能结果的列表或图表。
The probability scale: 0 = impossible, ½ = even chance, 1 = certain. Words like ‘likely’, ‘unlikely’, ‘even chance’ help describe probability without numbers.
概率标度 (Probability scale): 0 = 不可能，½ = 等可能性，1 = 必然。‘Likely’、‘unlikely’、‘even chance’ 等词用来不靠数字描述概率。
12. Quick Memory Tricks & Common Confusions | 速记贴士与常见混淆
BIDMAS / BODMAS (Brackets, Indices/Orders, Division/Multiplication, Addition/Subtraction) tells the order of operations. Multiplication and division are equal priority – work left to right.
运算顺序 BIDMAS / BODMAS（括号、指数、除法/乘法、加法/减法）。乘法和除法优先级相同——从左到右计算。
Difference between expression and equation uals sign (2x+3); equation has one (2x+3=7). You simplify expressions but solve equations.
表达式与方程的区别：表达式无等号（2x+3）；方程有等号（2x+3=7）。你化简表达式，解方程。
Factor vs. Multiple: Factors are what you multiply to get a number; multiples are what you get when you multiply a number by integers. Mnemonic: ‘Factors are Fewer, Multiples are More’.
因数 vs. 倍数：因数是乘起来得到原数的数；倍数是原数乘整数得到的结果。助记：“因少倍多”。
HCF (Highest Common Factor) – the biggest factor shared by two or more numbers. LCM (Lowest Common Multiple) – the smallest multiple shared.
最大公因数 (HCF)——两个或多个数共有的最大因数。最小公倍数 (LCM)——共有的最小倍数。
Metric conversions: King Henry Died By Drinking Chocolate Milk – Kilo, Hecto, Deca, Base (m, g, L), Deci, Centi, Milli. Move decimal point accordingly.
公制单位转换：千 (Kilo)、百 (Hecto)、十 (Deca)、基本单位 (Base: m, g, L)、分 (Deci)、厘 (Centi)、毫 (Milli)。相应地移动小数点。
Published by TutorHao | CAIE Year 8 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图