📚 Year 8 CCEA Mathematics: Terminology Quick Recall Guide | Year 8 CCEA 数学：词汇术语速记指南
Mastering mathematics in Year 8 requires a strong command of the special vocabulary used in class and in exams. This bilingual guide organises key terms by topic, provides clear definitions, and offers memorable hooks to help you recall them quickly. Use it to review, self‑test, and build confidence with every unit in the CCEA curriculum.
在 Year 8 学好数学离不开对课堂和考试中专用词汇的熟练掌握。这份双语指南按章节梳理核心术语，给出清晰定义，并附上有助于速记的小窍门。你可以用它复习、自测，从而在 CCEA 课程的每个单元都建立信心。
1. Understanding Place Value | 理解位值
The term place value tells us that the position of a digit determines its worth. In the number 5,632 the digit 5 stands for five thousands, 6 for six hundreds, 3 for three tens and 2 for two units (ones). Columns to the left are ten times larger; columns to the right, after the decimal point, are tenths, hundredths and thousandths.
术语 位值 告诉我们，一个数字所处的位置决定了它的数值。在 5,632 中，5 代表五千，6 代表六百，3 代表三十，2 代表两个一（个位）。每向左移动一列，数值扩大到十倍；小数点右侧的列依次是十分位、百分位和千分位。
A quick memory trick: think of each digit (0–9 symbol) sitting in a ‘place’ like a seat in a stadium – the seat label (thousands, hundreds, etc.) is its value. Units are sometimes called ones, and the decimal point separates whole numbers from parts of a whole.
速记窍门：把每个 数字（0–9 的符号）想象成体育场里的一个座位，座位标签（千位、百位等）就是它的位值。个位 就是最靠右的整数位，小数点 把整数部分与小数部分分开。
When you write a number in expanded form, you show it as a sum: 462 = 400 + 60 + 2. In Year 8 you also work with rounding – approximating a number to a given place value, such as rounding 67 to the nearest ten (70).
用 展开式 表示一个数时，你把它写成和的形式：462 = 400 + 60 + 2。Year 8 还会涉及 四舍五入——将数值近似到指定位值，比如把 67 舍入到最接近的十位得 70。
2. Integers and Negative Numbers | 整数与负数
An integer is any whole number that is positive, negative or zero. The set of integers includes … −3, −2, −1, 0, 1, 2, 3 … . Numbers less than zero are called negative numbers and are written with a minus sign. On a number line, values increase as you move right.
整数 包括所有正整数、负整数以及零。整数集合包括 … −3, −2, −1, 0, 1, 2, 3 … 。小于零的数叫 负数，书写时带负号。在数轴上，向右移动数值变大。
When we compare integers, we use symbols like > (greater than) and < (less than). A common mistake is thinking −5 is larger than −2 because 5 > 2; in fact, −5 is further left on the number line, so −5 < −2. The absolute value of an integer, written |−4| = 4, is its distance from zero, always positive.
比较整数时，我们使用 >（大于）和 <（小于）符号。一个常见错误是认为 −5 比 −2 大，因为 5 > 2；实际上，−5 在数轴上更靠左，所以 −5 < −2。一个整数的 绝对值 记作 |−4| = 4，表示它到零的距离，总是非负的。
Adding a negative is like moving left; subtracting a negative is the same as adding. Picture a lift: floors below ground are negative, ground is 0, and going up means adding, going down means subtracting.
加上一个负数相当于向左移动；减去一个负数等同于加上正数。想象电梯：地下楼层是负数，地面是 0，上行表示加，下行表示减。
3. Fractions, Decimals and Percentages | 分数、小数和百分比
A fraction has a numerator (top) and a denominator (bottom). A proper fraction has a numerator smaller than the denominator (e.g. 3/8); an improper fraction has a larger numerator (e.g. 11/4), which can be written as a mixed number (2 ¾). Equivalent fractions have the same value, such as 1/2 = 2/4.
分数 由 分子（上）和 分母（下）构成。真分数 的分子小于分母（如 3/8）；假分数 的分子大于分母（如 11/4），可化成 带分数（2 ¾）。等值分数 表示大小相等的分数，如 1/2 = 2/4。
A decimal uses a decimal point to show tenths, hundredths, etc. Terminating decimals end (0.75), while recurring decimals repeat a pattern (0.333...). A percentage is a fraction out of 100; the symbol % means ‘ decimal means divide numerator by denominator; decimal → percentage means multiply by 100.
小数 借助小数点表示十分位、百分位等。有限小数 位数有限（0.75），循环小数 则不断重复某个数字序列（0.333...）。百分比 是分母为 100 的分数，符号 % 意为“百分之”。互化法则：分数化小数用分子除以分母；小数化百分比乘以 100。
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). When you find a fraction of an amount, you multiply by the numerator then divide by the denominator.
化简分数时，用分子和分母的 最大公因数（HCF） 同时相除。求一个数量的几分之几，先用分子乘，再除以分母。
4. Factors, Multiples and Primes | 因数、倍数和质数
A factor divides exactly into a number without leaving a remainder. The factors of 12 are 1, 2, 3, 4, 6, 12. A multiple is the product of that number and any integer: the first four multiples of 7 are 7, 14, 21, 28. Factors are ‘inside’ a number; multiples are what you get when you ‘extend’ it.
因数 能整除某个数且没有余数。12 的因数有 1, 2, 3, 4, 6, 12。倍数 是该数与任意整数的乘积：7 的前四个倍数是 7, 14, 21, 28。因数是“包含在”数里面的，倍数则是把这个数“放大”后得到的。
A prime number has exactly two distinct factors, 1 and itself (2, 3, 5, 7, 11…). 1 is not prime. Numbers with more than two factors are composite. Prime factorisation breaks a number into a product of primes, e.g. 20 = 2 × 2 × 5 = 2² × 5.
质数 恰好有两个不同的因数：1 和它本身（2, 3, 5, 7, 11…）。1 不是质数。有超过两个因数的数叫 合数。质因数分解 把一个数写成质数的乘积，如 20 = 2 × 2 × 5 = 2² × 5。
The highest common factor (HCF) is the largest factor shared by two or more numbers. The lowest common multiple (LCM) is the smallest multiple shared by them. Use factor trees or lists to find them.
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。可使用因数树或列举法求出。
5. Algebraic Expressions | 代数表达式
In algebra, a variable (or unknown) is a letter that stands for a number we don’t yet know, such as x or n. A term is a single number, variable, or product of the two, like 5y or −3. An expression is a combination of terms joined by + or −, with no equals sign: 2a + 7b − 4.
在代数里，变量（或 未知数）是用字母表示暂未确定的数值，如 x 或 n。项 是一个单独的数、变量或二者的乘积，如 5y 或 −3。表达式 是由 + 或 − 连接的多个项，不含等号：2a + 7b − 4。
A coefficient is the number part of a term: in 6m the coefficient is 6. A constant is a term with no variable, like the +9 in x + 9. You substitute a value for a variable when you replace the letter with a given number and work out the calculation.
系数 是项中数字部分：在 6m 里系数是 6。常数 是不含变量的项，如 x + 9 中的 +9。代入 是指将字母替换为给定数值并进行计算。
Like terms have exactly the same variable part: 3p and −5p are like terms and can be combined. Simplifying ing like terms: 2x + 3y + 4x = 6x + 3y. You cannot combine terms with different variables.
同类项 的字母部分完全相同：3p 和 −5p 是同类项，可以合并。化简 表达式就是把同类项合并：2x + 3y + 4x = 6x + 3y。不同字母的项不能合并。
6. Equations and Inequalities | 方程与不等式
An equation states that two expressions are equal, using an equals sign. For example, 2n + 5 = 13. Solving se operations: subtract 5, then divide by 2 gives n = 4. Always keep the equation balanced – whatever you do to one side, you must do to the other.
方程 用等号表示两个表达式相等，例如 2n + 5 = 13。解方程 就是找出使等式成立的未知数值，通过逆运算：先减 5，再除以 2，得 n = 4。始终要保持方程平衡——对一边做什么，另一边也要做同样的操作。
An inequality lues, often shown on a number line with an open or closed circle. 3 < x ≤ 7 means x is greater than 3 and up to 7 (including 7).
不等式 用符号 <、>、≤（小于等于）、≥（大于等于）来比较表达式。不等式的解是一个取值范围，常用数轴上的空心或实心圆点表示。3 < x ≤ 7 表示 x 大于 3 且不超过 7（含 7）。
uare. You can rearrange a formula to make a different variable the subject, using the same balancing rules.
公式 是表示变量之间关系的特殊方程，如正方形的周长公式 P = 4s。你可以按照平衡法则，把公式里的某个变量变成公式的主语。
7. Angles and Lines | 角与线
An angle measures the turn between two lines meeting at a vertex. Angles are measured in degrees (°). A right angle is exactly 90°; an acute angle is less than 90°; an obtuse angle is between 90° and 180°; a reflex angle is between 180° and 360°. A straight line is 180°.
角 度量的是两条线在顶点交汇处的旋转量。角的单位是 度（°）。直角 正好 90°；锐角 小于 90°；钝角 介于 90° 和 180° 之间；优角 介于 180° 和 360° 之间。一条直线形成 180°。
Complementary angles add up to 90°, supplementary angles add up to 180°. Vertically opposite angles are equal when two lines cross. Adjacent angles share a common arm and vertex. Parallel lines never meet; when a transversal cuts them, alternate angles are equal and corresponding angles are equal.
余角 相加得 90°，补角 相加得 180°。两条直线相交时，对顶角 相等。邻角 有一条公共边和公共顶点。平行线 永不相交；当一条截线穿过它们时，内错角 相等，同位角 相等。
To estimate an angle, compare it with 90° and 180° landmarks. Use a protractor to measure carefully: align the centre with the vertex and the baseline with one arm, then read the correct scale.
估测角度时，可将其与 90° 和 180° 的参照角比较。用量角器测量时要仔细：中心对准顶点，底线对齐一条边，然后读取正确的刻度。
8. 2D Shapes and Symmetry | 二维图形与对称
A polygon is a closed 2D shape with straight sides. A regular polygon has all sides and angles equal; an irregular polygon does not. Triangles are classified by sides: equilateral (3 equal sides), isosceles (2 equal sides), scalene (no equal sides). By angles: acute, right, or obtuse.
多边形 是由线段围成的封闭二维图形。正多边形 的所有边和角都相等；不规则多边形 则不是。三角形可按边分类：等边三角形（三边相等）、等腰三角形（两边相等）、不等边三角形（三边都不等）。按角分类：锐角、直角或钝角三角形。
Quadrilaterals include square (4 equal sides, 4 right angles), rectangle (opposite sides equal, 4 right angles), parallelogram (opposite sides parallel and equal), rhombus (4 equal sides, opposite angles equal), trapezium (at least one pair of parallel sides) and kite (adjacent sides equal).
四边形包括：正方形（四边相等、四个直角）、长方形（对边相等、四个直角）、平行四边形（对边平行且相等）、菱形（四边相等、对角相等）、梯形（至少一对边平行）和 风筝形（邻边相等）。
Line symmetry means a shape can be folded along a line into two identical halves. The number of such lines is the order of line symmetry. Rotational symmetry describes how many times a shape looks the same during a full 360° turn; the number of matches is the order of rotational symmetry.
线对称 表示一个图形沿某条直线对折后两边完全重合。这种线的数量就是线对称的阶数。旋转对称 描述图形在旋转一周（360°）的过程中有多少次与自身重合；重合的次数就是旋转对称的阶数。
9. Perimeter, Area and Volume | 周长、面积和体积
Perimeter is the total distance around the outside of a shape. For a rectangle, P = 2(l + w). Area triangle is (base × height) ÷ 2. For a parallelogram, area = base × perpendicular height.
周长 是围绕图形外边缘的总长度。长方形的周长 P = 2（长 + 宽）。面积 衡量二维图形内部的空间，单位为平方单位：cm²、m²。长方形的面积 = 长 × 宽。三角形的面积 =（底 × 高）÷ 2。平行四边形的面积 = 底 × 垂直高度。
Volume is the amount of space a 3D solid occupies, measured in cubic units: cm³, m³. The volume of a cuboid (rectangular prism) is length × width × height. Capacity iner can hold; 1 litre = 1000 cm³. Remember to use the correct units for each measurement.
体积 是三维物体所占空间的大小，单位为立方单位：cm³、m³。长方体 的体积 = 长 × 宽 × 高。容量 是容器能容纳液体的体积；1 升 = 1000 cm³。务必为每种度量选用正确的单位。
When calculating compound area, split the shape into simpler rectangles or triangles, find each area, then add or subtract. The same approach works with perimeter – just be careful to include all outer edges.
计算 组合图形面积 时，可将其分割为简单矩形或三角形，分别求面积后相加或相减。周长的处理思路类似，注意要包含所有外围边长。
10. Statistics and Data Handling | 统计与数据处理
Data is a collection of facts or numbers. Discrete data can only take specific values (e.g. shoe sizes); continuous data can take any value within a range (e.g. height). A tally chart helps you count frequencies – every fifth mark is drawn diagonally across the previous four.
数据 是事实或数字的集合。离散数据 只能取特定值（如鞋码）；连续数据 可取某一范围内的任意值（如身高）。计分表 可帮助你清点频数——每第五画记作穿过前四画的斜杠。
A bar chart uses bars of equal width; the height shows the frequency. A pictogram uses pictures or symbols. A pie chart shows proportions of a whole – each slice angle = (category amount ÷ total) × 360°. Line graphs plot data points connected by lines, often used to show changes over time.
条形图 用等宽的竖条表示，高度代表 频数。象形图 用图标或符号表示数量。饼图 展示整体中各部分的比例——每个扇形的角度 =（该类数量 ÷ 总数）× 360°。折线图 用连线表示数据点的变化趋势，常用来展示随时间变化的数据。
The mean (average) is found by adding all values and dividing by how many there are. The median is the middle value when data are in order; the mode is the value that appears most often; the range is the difference between the highest and lowest values, giving a measure of spread.
平均数 由所有数值之和除以数据个数得到。中位数 是数据按顺序排列后位于中间的数值；众数 是出现次数最多的数值；极差 是最大值与最小值的差，用来衡量数据的离散程度。
11. Coordinates and Graphs | 坐标与图像
Coordinates are pairs of numbers written as (x, y) that fix a point on a grid. The first number is the distance along the horizontal x‑axis; the second is along the vertical y‑axis. The origin is (0, 0). The axes divide the grid into four quadrants: quadrant I is (+, +), II is (−, +), III is (−, −) and IV is (+, −).
坐标 是用 (x, y) 表示的一对数字，用来在网格上定位一个点。第一个数表示沿水平 x 轴的距离，第二个数表示沿垂直 y 轴的距离。原点是 (0, 0)。坐标轴将网格分为四个 象限：第一象限 (+,+)，第二象限 (−,+)，第三象限 (−,−)，第四象限 (+,−)。
values, mark the points and join them. If they lie in a straight line, the relationship is linear. The point where the line crosses the y‑axis is the y‑intercept; the steepness is called the gradient (or slope).
绘制 y = 2x + 1 这类方程的图形时，先填值表，标出各点，再连线。如果点落在一条直线上，这就是 线性关系。直线与 y 轴的交点叫 y 轴截距；倾斜程度称为 坡度（或 斜率）。
A conversion graph helps you change between units, such as miles and kilometres. You read across from one axis to the line, then down (or up) to the other axis. Being able to recognise the midpoint of a line segment — found by averaging the x‑ and y‑coordinates — is another useful skill.
换算图 可帮助在单位之间切换，如英里与公里。从一条轴出发触线，再垂直对应到另一条轴即可读数。识别一条线段的中点——通过平均两个端点的 x 坐标和 y 坐标得到——也是一项实用技能。
12. Probability and Likelihood | 概率与可能性
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). It can be written as a fraction, decimal or percentage. The theoretical probability f an event A is: P(A) = number of favourable outcomes / total number of possible outcomes.
概率 用来衡量事件发生的可能性，数值介于 0（不可能）和 1（必然发生）之间。它可以用分数、小数或百分比表示。事件 A 的 理论概率 为：P(A) = 有利结果数 / 所有可能结果的总数。
Words such as likely, unlikely, even chance, impossible and certain anding heads: P(heads) = ½. The sum of probabilities of all possible outcomes is always 1.
很可能、不太可能、等可能、不可能 和 必然 等词语能定性描述概率。一枚均匀硬币正面朝上的可能性是相等的：P(正面) = ½。所有可能结果的概率之和总是 1。
An experiment with equally likely outcomes is called fair. A sample space lists all possible outcomes; for two dice, it can be shown in a grid. The complement of an event is ‘the event not happening’; its probability is 1 − P(event). Understanding these terms makes it much easier to answer CCEA probability questions accurately.
具有等可能结果的试验称为 公平 试验。样本空间 列出所有可能的结果；掷两枚骰子可用网格显示。一个事件的 补事件 指“该事件不发生”；其概率为 1 − P(事件)。准确理解这些术语能让你更轻松地应对 CCEA 的概率考题。
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