📚 Year 8 CCEA Maths: Vocabulary & Terminology Quick-Memorisation Guide | 词汇术语速记指南
Mastering the language of mathematics is the first step towards solving problems with confidence. In Year 8, you encounter a range of new and recurring terms across Number, Algebra, Geometry, and Data Handling. This guide groups essential vocabulary by topic, offers simple memory hooks, and pairs each English definition with its Chinese equivalent so you can build a bilingual maths brain.
掌握数学语言是自信解题的第一步。在八年级，你会在数、代数、几何与数据处理中遇到一系列新术语和重复出现的词汇。本指南按主题归类关键术语，提供简单的记忆方法，并将每个英文定义与中文对照起来，帮助你构建双语数学思维。
1. Number & Place Value | 数位与位值
Digits are the symbols 0–9 used to write numbers. The position of a digit determines its value — this is called place value. For example, in 3.14, the 1 is in the tenths place, worth 1/10.
数字（digits）是用于书写数字的符号 0–9。数字的位置决定其取值，这称为位值（place value）。例如在 3.14 中，1 在十分位，表示 1/10。
An integer is any whole number, positive or negative, including zero. Positive numbers are greater than zero, negative numbers are less than zero.
整数（integer）是任意正、负或零的整数。正数大于零，负数小于零。
Factors are numbers you multiply together to get another number. A multiple is the product of a number and any integer. Remember: 'Factors are the building blocks, multiples are the skyscrapers you build with them.'
因数（factors）是相乘得到另一个数的数字。倍数（multiple）是一个数与任意整数的乘积。记住：“因数是积木，倍数是搭成的摩天楼。”
A prime number has exactly two distinct factors, 1 and itself. A composite number has more than two factors. 1 is neither prime nor composite.
质数（prime number）恰好有两个不同的因数：1 和它本身。合数（composite number）有超过两个因数。1 既不是质数也不是合数。
Highest common factor (HCF) is the largest factor shared by two or more numbers. Lowest common multiple (LCM) is the smallest multiple they share. Use a Venn diagram of prime factors to find both easily.
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。用质因数的维恩图可以轻松求出两者。
- Integer → 整数
- Place value → 位值
- Factor / Multiple → 因数 / 倍数
- Prime / Composite → 质数 / 合数
- HCF / LCM → 最大公因数 / 最小公倍数
2. Fractions, Decimals & Percentages | 分数、小数与百分比
a part of a whole. The numerator is the top number, the denominator the bottom. Remember: 'Denominator is downstairs (Down-stairs = Denominator).'
分数（fraction）表示整体的一部分。分子（numerator）是上方的数，分母（denominator）是下方的数。记住：“分母在楼下（Denominator = Downstairs）。”
An improper fraction has a numerator larger than its denominator. A mixed number combines a whole number and a proper fraction.
假分数（improper fraction）的分子大于分母。带分数（mixed number）是整数与真分数的组合。
2/4 = 3/6. Simplify (cancel) fractions by dividing numerator and denominator by their HCF.
等值分数（equivalent fractions）表示相同的值，例如 1/2 = 2/4 = 3/6。通过将分子分母除以它们的最大公因数来化简（约分）分数。
To convert a fraction to a decimal, divide the numerator by the denominator. A terminating decimal stops, a recurring decimal repeats a digit or block endlessly.
将分数化为小数，用分子除以分母。有限小数（terminating decimal）会结束，循环小数（recurring decimal）会无限重复一位或一组数字。
A percentage is a fraction with denominator 100. The symbol % means 'out of 100'. To change a decimal to a percentage multiply by 100.
百分比（percentage）是分母为 100 的分数。符号 % 表示“百分之”。将小数转换为百分比乘以 100。
| Fraction 分数 | Decimal 小数 | Percentage 百分比 |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333... | 33.33…% |
- Numerator / Denominator → 分子 / 分母
- Improper fraction / Mixed number → 假分数 / 带分数
- Equivalent fraction → 等值分数
- Recurring decimal → 循环小数
3. Ratios & Proportions | 比与比例
A ratio compares parts of a whole using a colon, e.g. 3:2. It shows how much of one thing there is compared to another. Order matters: the ratio of red to blue is not the same as blue to red.
比（ratio）用冒号比较整体的部分，例如 3:2。它表示一个量与另一个量相比有多少。顺序很重要：红与蓝的比不等同于蓝与红的比。
Proportion compares a part to the whole. If the ratio of boys to girls is 2:3, the proportion of boys is 2/5 of the whole class.
比例（proportion）将部分与整体进行比较。如果男孩与女孩的比是 2:3，男孩的比例就是全班人数的 2/5。
t the same rate. You can use a multiplier or a constant of proportionality k where y = kx.
正比例（direct proportion）意味着一个量增加，另一个量以相同的速率增加。你可以用乘数或比例常数 k，其中 y = kx。
divide a quantity in a given ratio, add the parts, then find the value of one part. Share £50 in the ratio 3:2 → total parts = 5, one part = £10, so shares are £30 and £20.
按给定比例分配数量时，先将各部分相加，再求出一份的值。将 50 英镑按 3:2 分配 → 总份数 = 5，一份 = 10 英镑，所以分配额为 30 英镑和 20 英镑。
- Ratio → 比
- Proportion → 比例
- Direct proportion → 正比例
- Constant of proportionality → 比例常数
4. Algebraic Expressions | 代数表达式
Algebra uses letters (variables) to represent unknown or changing quantities. An expression is a combination of variables, numbers, and operations without an equals sign, e.g. 3a + 2b - 5.
代数（algebra）使用字母（变量）表示未知或变化的量。表达式（expression）是由变量、数字和运算组合而成的，没有等号，例如 3a + 2b - 5。
A term is a single number, variable, or product of both, separated by + or − signs. In 4x + 7y − 3, there are three terms. A coefficient is the number multiplying a variable, e.g. 4 is the coefficient of x.
项（term）是单个数字、变量或两者的乘积，由加号或减号分隔。在 4x + 7y − 3 中有三项。系数（coefficient）是乘以变量的数字，例如 4 是 x 的系数。
lify expressions by collecting like terms: 2x + 5x = 7x, but 2x + 5y cannot be simplified.
同类项（like terms）具有完全相同的变量部分（相同的字母与指数）。通过合并同类项来简化表达式：2x + 5x = 7x，但 2x + 5y 不能化简。
An equation is a mathematical statement showing that two expressions are equal, using an equals sign. Solving an equation means finding the value of the variable that makes the statement true.
方程（equation）是用等号表示两个表达式相等的数学语句。解方程意味着求出使等式成立的变量的值。
rising is the reverse process, writing an expression as a product, e.g. 3x + 6 = 3(x + 2).
括号表示乘法；展开括号是将外部因数乘以括号内的每一项：3(x + 2) = 3x + 6。因式分解（factorise）是逆过程，将表达式写为乘积形式，如 3x + 6 = 3(x + 2)。
- Variable → 变量
- Expression / Equation → 表达式 / 方程
- Term / Coefficient → 项 / 系数
- Like terms → 同类项
- Expand / Factorise → 展开 / 因式分解
5. Sequences & Functions | 数列与函数
A sequence is an ordered set of numbers connected by a rule. Each number is a term. The term-to-term rule tells you how to move from one term to the next, e.g. 'add 3' each time.
数列（sequence）是由一个规则联系起来的有序数字集。每个数字都是一项（term）。逐项规则（term-to-term rule）告诉你如何从一项移至下一项，例如每次“加3”。
The position-to-term rule (nth term) lets you find any term's value directly from its position n. For the sequence 2, 5, 8, 11, …, the nth term is 3n − 1.
位置-项规则（第 n 项）让你直接从位置 n 求出任意一项的值。对于数列 2, 5, 8, 11, …，第 n 项是 3n − 1。
A function is a rule that relates an input to an output, often shown as a function machine or mapping diagram. The set of inputs is the domain, outputs the range.
函数（function）是一个将输入与输出关联起来的规则，常用函数机器或映射图表示。输入集称为定义域（domain），输出集称为值域（range）。
Common sequences: square numbers (1, 4, 9, 16, …), cube numbers (1, 8, 27, …), triangular numbers (1, 3, 6, 10, …), Fibonacci sequence (next term is sum of previous two).
常见数列：平方数（1, 4, 9, 16, …）、立方数（1, 8, 27, …）、三角形数（1, 3, 6, 10, …）、斐波那契数列（下一项为前两项之和）。
- Sequence / Term → 数列 / 项
- nth term → 第 n 项
- Function → 函数
- Fibonacci → 斐波那契
6. Angles & Lines | 角与直线
An angle is formed where two lines meet, measured in degrees (°). Use a protractor to measure angles. Types by size: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (180°), reflex (between 180° and 360°).
角（angle）由两条线交汇而成，用度数（°）测量。用量角器测量角度。按大小分类：锐角（小于 90°）、直角（等于 90°）、钝角（90° 到 180° 之间）、平角（180°）、优角（180° 到 360° 之间）。
Perpendicular lines meet at right angles. Parallel lines never meet and remain the same distance apart. A transversal is a line that crosses parallel lines, creating related angles.
垂直线（perpendicular lines）相交成直角。平行线（parallel lines）永不相交，且间距始终相等。截线（transversal）是穿过平行线的直线，产生一系列相关的角。
Angles on a straight line sum to 180°. Angles around a point sum to 360°. Vertically opposite angles (X-shape) are equal.
直线上的邻角之和为 180°。围绕一个点的周角之和为 360°。对顶角（X 形）相等。
When a transversal cuts parallel lines: corresponding angles (F-shape) are equal, alternate angles (Z-shape) are equal, co-interior/allied angles (C-shape) sum to 180°.
当截线切割平行线时：同位角（F 形）相等，内错角（Z 形）相等，同旁内角（C 形）之和为 180°。
- Acute / Obtuse / Reflex → 锐角 / 钝角 / 优角
- Perpendicular / Parallel → 垂直 / 平行
- Corresponding / Alternate → 同位角 / 内错角
- Vertically opposite → 对顶角
7. 2D & 3D Shapes | 二维与三维图形
Polygons are closed 2D shapes with straight sides. Regular polygons have equal sides and equal angles. Name them by side number: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).
多边形（polygon）是由直线边围成的封闭二维图形。正多边形边等长、角等大。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）。
A quadrilateral is a four-sided polygon. Types: square, rectangle, parallelogram, rhombus, trapezium (one pair of parallel sides), kite (two pairs of adjacent equal sides).
四边形（quadrilateral）是四边多边形。类型：正方形、矩形、平行四边形、菱形、梯形（一对平行边）、风筝形（两对相邻等边）。
Perimeter is the distance around a shape. Area is the space inside a 2D shape, measured in square units (cm², m²). Volume is the space occupied by a 3D object, measured in cubic units (cm³, m³).
周长（perimeter）是图形边缘的总长度。面积（area）是二维图形内部的空间，以平方单位（cm², m²）计量。体积（volume）是三维物体占据的空间，以立方单位（cm³, m³）计量。
3D shapes include cubes, cuboids, prisms (constant cross-section), pyramids, cylinders, cones, and spheres. A net is a 2D pattern that folds to make a 3D shape.
三维形状包括立方体、长方体、棱柱（横截面一致）、棱锥、圆柱、圆锥和球体。展开图（net）是折叠后形成三维图形的二维图案。
Symmetry: line symmetry (reflection) where one half mirrors the other; rotational symmetry is the number of times a shape fits onto itself in a full turn (order of rotational symmetry).
对称：线对称（镜面反射，一半是另一半的镜像）；旋转对称（rotational symmetry）是图形旋转一周中与自身重合的次数（旋转对称的阶数）。
- Polygon → 多边形
- Quadrilateral → 四边形
- Perimeter / Area / Volume → 周长 / 面积 / 体积
- Prism / Net → 棱柱 / 展开图
- Rotational symmetry → 旋转对称
8. Averages & Spread | 平均数与离散程度
The mean is the sum of values divided by the number of values. The median is the middle value when data are in order. The mode is the most frequent value. The range is the difference between the largest and smallest values.
平均数（mean）是数值之和除以数值个数。中位数（median）是数据排序后的中间值。众数（mode）是出现最频繁的值。极差（range）是最大值与最小值的差。
For an even number of data, the median is the mean of the two middle numbers. The range measures spread; a small range means data are clustered, a large range shows they are spread out.
数据个数为偶数时，中位数是中间两个数的平均值。极差衡量分散程度；极差小表示数据集中，极差大表示数据分散。
Compare data sets using averages and range. Mean gives an overall balance point but is affected by outliers (extreme values). Median is more robust against outliers.
使用平均数和极差比较数据集。平均数给出整体平衡点，但受异常值（极端值）影响。中位数对异常值更具鲁棒性。
- Mean / Median / Mode → 平均数 / 中位数 / 众数
- Range → 极差 / 范围
- Outlier → 异常值
9. Probability & Data Representation | 概率与数据展示
rcentage. Probability = (number of favourable outcomes) / (total number of equally likely outcomes).
概率（probability）是事件发生的可能性，用 0（不可能）到 1（必定）的尺度衡量。可写作分数、小数或百分比。概率 =（有利结果数）/（所有等可能结果总数）。
A sample space lists all possible outcomes. For two events, use a sample space diagram or a possibility space table. Random means each outcome is equally likely.
样本空间（sample space）列出所有可能的结果。对于两个事件，使用样本空间图或可能性空间表。随机（random）表示每个结果等可能发生。
Charts for data: bar charts (frequency for categories), pie charts (sectors showing proportions), line graphs (trend over time), scatter graphs (relationship between two variables; correlation describes direction and strength).
数据图表：条形图（分类的频数）、饼图（以扇形显示比例）、折线图（随时间变化的趋势）、散点图（两个变量之间的关系；相关性描述方向和强度）。
Stem-and-leaf diagrams keep raw data while showing shape. Key: '3 | 5 means 35' is essential. Two-way tables show frequencies for two categorical variables.
茎叶图（stem-and-leaf）既保留原始数据又显示分布形态。图例“3 | 5 表示 35”必不可少。双向表（two-way table）显示两个分类变量的频数。
- Probability → 概率
- Sample space → 样本空间
- Scatter graph / Correlation → 散点图 / 相关性
- Stem-and-leaf → 茎叶图
10. Key Prefixes & Symbols Quick Reference | 关键前缀与符号速查
thousand (×1000), centi- means hundredth (÷100), milli- means thousandth (÷1000). Memorise 'King Henry Died by Drinking Chocolate Milk' for kilo, hecto, deca, base, deci, centi, milli.
数学用一致的前缀来缩放单位：kilo- 表示千（×1000），centi- 表示百分之一（÷100），milli- 表示千分之一（÷1000）。记忆口诀：“King Henry Died by Drinking Chocolate Milk”对应千、百、十、基本单位、十分之一、百分之一、千分之一。
≤ less than or equal to, ≥ greater than or equal to, √ square root, Δ change or triangle.
常见符号：≈ 约等于，≠ 不等于，< 小于，> 大于，≤ 小于或等于，≥ 大于或等于，√ 平方根，Δ 变化量或三角形。
- kilo- / centi- / milli- → 千 / 百分之一 / 千分之一
- √ → 平方根
- ≈ → 约等于
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