📚 Year 8 CIE Maths: A Quick Guide to Memorising Vocabulary Terms | Year 8 CIE 数学：词汇术语速记指南
Mastering mathematical vocabulary is key to success in Year 8 CIE Maths. Understanding the precise meaning of terms like 'factor', 'median', or 'perpendicular' helps you solve problems correctly and communicate your reasoning clearly. This guide breaks down essential maths words into memorable chunks, with simple explanations in both English and Chinese to speed up your learning. Each section pairs a term's definition with a quick memory trick, so you can recall it when you need it most.
掌握数学词汇是 Year 8 CIE 数学成功的关键。理解诸如 "因数"、"中位数" 或 "垂直" 这些术语的精确含义，能帮助你正确解题并清晰地表达推理过程。本指南将关键数学词汇分解成便于记忆的模块，配以中英文简明解释，加速你的学习。每个术语都配有一个快速记忆技巧，让你在需要时能够立刻回想起来。
1. Number Basics | 数字基础
An integer is a whole number that can be positive, negative, or zero. It has no fractional or decimal part. Examples: −7, 0, 12, −1.
整数是正数、负数或零的完整数字，没有分数或小数部分。例如：−7, 0, 12, −1。
A natural number is a positive integer used for counting: 1, 2, 3, … Some definitions include 0, but in Year 8 CIE, natural numbers usually start from 1.
自然数是用于计数的正整数：1, 2, 3, … 有些定义包含 0，但在 Year 8 CIE 课程中，自然数通常从 1 开始。
Whole numbers are the set of natural numbers together with zero: 0, 1, 2, 3, … Think of them as the 'complete' numbers without fractions or negatives.
整数（whole number）是自然数与零的集合：0, 1, 2, 3, … 你可以把它们看作没有分数和负数的"完整"数字。
A prime number has exactly two distinct factors: 1 and itself. 2 is the only even prime. Numbers like 3, 5, 7, 11 are prime. 1 is not prime because it only has one factor.
质数恰好有两个不同的因数：1 和它本身。2 是唯一的偶质数。像 3, 5, 7, 11 这样的数是质数。1 不是质数，因为它只有一个因数。
A composite number has more than two factors. For example, 12 has factors 1, 2, 3, 4, 6, 12. Every whole number greater than 1 is either prime or composite.
合数有两个以上的因数。例如，12 的因数是 1, 2, 3, 4, 6, 12。每一个大于 1 的整数，要么是质数，要么是合数。
A factor is a number that divides exactly into another number without leaving a remainder. The factors of 18 are 1, 2, 3, 6, 9, 18. A multiple is the result of multiplying a number by an integer. The multiples of 4 are 4, 8, 12, 16, …
因数是可以整除另一个数而没有余数的数。18 的因数是 1, 2, 3, 6, 9, 18。倍数是把一个数乘以一个整数得到的结果。4 的倍数有 4, 8, 12, 16, …
y itself: 5 x 5 = 25, so 25 is a square number. The square root is the opposite operation. √25 g three copies of the same integer: 2 x 2 x 2 = 8, so 8 is a cube number. Its cube root is ∛8 = 2.
平方数是一个整数乘以它自身的结果：5 × 5 = 25，所以 25 是平方数。平方根是相反运算。√25 = 5。立方数是用同一个整数乘三次得到：2 × 2 × 2 = 8，所以 8 是立方数，它的立方根是 ∛8 = 2。
is greater than zero. The absolute value of a number is its distance from zero, always non‑negative. |−8| = 8 and |8| = 8.
负数是任何小于零的数，正数大于零。一个数的绝对值是它到零的距离，总是非负的。|−8| = 8，|8| = 8。
2. Fractions and Decimals | 分数与小数
A fraction represents a part of a whole. The numerator is the top number, showing how many parts we have. The denominator is the bottom number, showing how many equal parts the whole is split into. For 3/4, the numerator is 3 and denominator is 4.
分数表示整体的一部分。分子是上面的数字，表示我们有多少份。分母是下面的数字，表示整体被分成了多少等份。对于 3/4，分子是 3，分母是 4。
A proper fraction has a numerator smaller than its denominator (e.g., 2/5). An improper fraction has a numerator larger than or equal to its denominator (e.g., 9/4). A mixed number combines a whole number and a proper fraction, like 2 1/3.
真分数的分子比分母小（例如 2/5）。假分数的分子大于或等于分母（例如 9/4）。带分数将整数和真分数结合在一起，比如 2 1/3。
ent the same value. Multiplying or dividing both numerator and denominator by the same non‑zero number gives an equivalent fraction. 1/2 = 2/4 = 4/8.
等值分数看起来不同，但表示相同的值。将分子和分母同时乘或除以同一个非零数，就会得到等值分数。1/2 = 2/4 = 4/8。
To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). 6/8 simplifies to 3/4 after dividing by 2.
化简分数时，用分子和分母的最大公因数（GCF）去除。6/8 除以 2 后化简为 3/4。
A decimal is another way to write a fraction whose denominator is a power of ten. The decimal point separates the whole part from the fractional part. In 3.75, the digit after the point shows tenths, hundredths, thousandths.
小数是分母为 10 的幂的另一种写法。小数点把整数部分与小数部分分开。在 3.75 中，小数点后的数字依次表示十分位、百分位、千分位。
A terminating decimal stops after a finite number of digits, like 0.25. A recurring decimal has a digit or block of digits that repeats forever, such as 0.333… or 0.142857142857… Recurring is often shown with a dot above the repeating digit(s).
有限小数在小数点后有限位数终止，例如 0.25。无限循环小数有一个数字或数字块无限重复，比如 0.333… 或 0.142857142857… 循环常用数字上方加点表示。
Place value tells us the value of each digit in a number. In 2.345, 3 is in the tenths place (3/10), 4 is hundredths, and 5 is thousandths.
位值告诉我们一个数中每个数字的值。在 2.345 中，3 在十分位（3/10），4 在百分位，5 在千分位。
3. Percentages | 百分数
A percentage is a fraction whose denominator is always 100. The symbol % means 'out of 100'. 45% means 45 out of 100, or 45/100 = 0.45.
百分数是一种分母始终为 100 的分数。符号 % 表示"百分之"。45% 表示 100 中的 45，即 45/100 = 0.45。
nd a percentage of an amount, turn the percent into a fraction or decimal and multiply. 20% of 60 is 0.20 × 60 = 12. You can also use the fraction 20/100 = 1/5.
求一个数的百分比，先把百分数化成分数或小数，然后相乘。60 的 20% 是 0.20 × 60 = 12。也可以直接用分数 20/100 = 1/5。
Percentage increase means adding a percentage of the original amount. A 10% increase on £50 gives £55. Percentage decrease subtracts that portion. A 10% decrease on £50 leaves £45.
百分比增加指在原数上增加一定的百分比。£50 增加 10% 得到 £55。百分比减少则减去相应的部分。£50 减少 10% 后剩下 £45。
A discount is a reduction in price, often expressed as a percentage. A 25% discount on a £80 item saves £20, so you pay £60. Interest is money earned (by saving) or charged (by borrowing), usually as a percentage of the original sum per year.
折扣是价格的降低，常用百分比表示。£80 的商品打 25% 折扣可省 £20，实付 £60。利息是因为储蓄而赚取或因借款而支付的金钱，通常按年利率计算。
4. Algebra Terms | 代数术语
A variable is a symbol, usually a letter, that stands for an unknown or changing number. In 3x + 2, x is the variable. A constant is a fixed number that does not change, like the 2 or 3 in the same expression.
变量是一个符号，通常是字母，代表未知或可变的数。在 3x + 2 中，x 是变量。常数是一个固定的数，不会改变，比如同一个式子中的 2 或 3。
s a statement that two expressions are equal, containing an equals sign: 3x + 5 = 14. An inequality compares two expressions using signs like <, >, ≤, or ≥.
表达式是由数字、变量和运算符号组成的数学短语，没有等号。例如：4y − 7, a² + b。等式是表明两个表达式相等的陈述，包含等号：3x + 5 = 14。不等式用 <, >, ≤, ≥ 等符号来比较两个表达式。
A term is a single number, variable, or product of numbers and variables. In 5x² + 3x − 2, there are three terms: 5x², 3x, and −2. A coefficient is the number part in front of a variable. The coefficient in 7a is 7.
项是单个数字、变量或数字与变量的乘积。在 5x² + 3x − 2 中，有三个项：5x²、3x 和 −2。系数是变量前面的数字部分。7a 的系数是 7。
Like terms have exactly the same variable part with the same power. 4p and −p are like terms; 3m² and m are not. To expand an expression, multiply each term inside brackets by the factor outside. 2(a + 3) expands to 2a + 6.
同类项指变量部分及其指数完全相同的项。4p 和 −p 是同类项；3m² 和 m 不是。展开表达式时，用括号外的因数去乘括号内的每一项。2(a + 3) 展开得到 2a + 6。
To factorise means to rewrite an expression as a product of factors by taking out common factors. 3x + 12 factorises to 3(x + 4). To simplify an expression, collect like terms and/or perform operations until it is written in the shortest form. 2y + 5y − 3 simplifies to 7y − 3.
因式分解是把表达式写成因式的乘积，通过提取公因数来实现。3x + 12 因式分解为 3(x + 4)。化简表达式就是合并同类项或进行运算，直到写出最短的形式。2y + 5y − 3 化简为 7y − 3。
given numbers for variables and work out the value. If x = 2, then 3x + 1 evaluates to 7.
求表达式的值时，用给定的数替换变量，然后计算出结果。如果 x = 2，那么 3x + 1 求值得到 7。
5. Geometry: Lines and Angles | 几何：线与角
A point is an exact location, often labelled with a capital letter. A line extends forever in both directions, while a line segment has two endpoints, and a ray has one endpoint and extends endlessly in one direction.
点是一个精确的位置，常用大写字母标记。直线向两端无限延伸，线段有两个端点，射线有一个端点并朝一个方向无限延伸。
Parallel lines run in the same direction and never meet, like railway tracks. Perpendicular lines meet at a right angle (90°). Think of the corner of a square.
平行线沿相同方向延伸，永不相交，就像铁轨。垂直线相交成直角 (90°)，想象一下正方形的角。
Angles are measured in degrees (°). An acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, a straight angle is exactly 180°, and a reflex angle is between 180° and 360°.
角度用度 (°) 来测量。锐角小于 90°，直角等于 90°，钝角在 90° 与 180° 之间，平角正好是 180°，优角在 180° 与 360° 之间。
Complementary angles add up to 90°. If one is 30°, the other is 60°. Supplementary angles add up to 180°. If one is 110°, the other is 70°. Vertically opposite angles are formed when two lines intersect; they are opposite each other and are equal.
互余角之和为 90°。如果一个角是 30°，另一个就是 60°。互补角之和为 180°。如果一个角是 110°，另一个就是 70°。对顶角是两条直线相交时形成的，它们位置相对且大小相等。
6. Shapes and Area | 图形与面积
A polygon is a closed 2D shape with straight sides. Triangles have 3 sides; quadrilaterals have 4; pentagons have 5; hexagons have 6. Naming follows the number of sides.
多边形是由直边组成的封闭二维图形。三角形有 3 条边；四边形有 4 条边；五边形有 5 条边；六边形有 6 条边。边的条数决定了名称。
Triangles are classified by sides and angles. An equilateral triangle has all sides equal and all angles 60°. An isosceles triangle has two equal sides and two equal base angles. A scalene triangle has all sides and all angles different.
三角形按边和角来分类。等边三角形三条边相等，每个角都是 60°。等腰三角形有两条边相等，两个底角相等。不等边三角形所有的边和角都不相同。
Quadrilaterals include a square (all sides equal, all angles 90°), rectangle (opposite sides equal, all angles 90°), rhombus (all sides equal, opposite angles equal), parallelogram (opposite sides parallel and equal), trapezium (at least one pair of parallel sides), and kite (two pairs of adjacent equal sides).
四边形包括正方形（所有边相等，所有角 90°）、长方形（对边相等，所有角 90°）、菱形（所有边相等，对角相等）、平行四边形（对边平行且相等）、梯形（至少一对平行边）和筝形（两对邻边相等）。
e a 2D shape. For a rectangle, A = l × w. Units for area are square units, like cm² or m².
周长是图形外边界的总长度。对于长 l 宽 w 的长方形，周长 P = 2(l + w)。面积测量二维图形内部的区域大小。长方形面积 A = l × w。面积单位是平方单位，如 cm² 或 m²。
lume = length × width × height. Surface area is the total area of all faces of a 3D shape.
体积是三维物体所占空间的大小，用立方单位 (cm³, m³) 来测量。长方体的体积 = 长 × 宽 × 高。表面积是立体图形所有面的总面积。
A circle' the circle through the centre. Circumference = π × diameter or 2πr, where π is about 3.14.
圆的周长是它的边界长度。半径是圆心到圆周的距离，直径是穿过圆心的线段，是半径的两倍。周长 = π × 直径或 2πr，π 大约为 3.14。
7. Statistics and Probability | 统计与概率
The mean is the arithmetic average: add up all values and divide by how many values there are. The median is the middle value when data is ordered; if there are two middle numbers, take their mean. The mode is the value that appears most often. The range is the difference between the largest and smallest values.
平均数（均值）是算术平均：把所有数值相加，再除以数值的个数。中位数是把数据排序后位于中间的值；如果有两个中间数，就取它们的平均值。众数是出现次数最多的值。范围是最大值与最小值的差。
Frequency tells you how many times a data value occurs. A frequency table organises data values and their frequencies. A bar chart uses bars of equal width to show frequencies for categories. Bar heights represent frequency.
频数告诉你一个数据值出现了多少次。频数表将数据值及其频数整理在一起。条形统计图用等宽的条形来表示不同类别的频数，条形的高度代表频数。
A pie chart displays data as slices of a circle, where each slice's angle is proportional to its frequency. The whole circle represents the total. A line graph uses points connected by lines to show how something changes over time or another continuous scale. A scatter graph plots pairs of values to see if there is a relationship.
饼图将数据表示为圆中的扇形，每个扇形的角度与其频数成正比。整个圆代表总量。折线图用点连接成线，显示数据如何随时间或其他连续变量而变化。散点图绘制成对数据，以观察它们之间是否存在关系。
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). An outcome is one possible result. An event is a set of outcomes. If a fair coin is tossed, the probability of getting 'heads' is 1/2, sometimes called an even chance.
概率衡量事件发生的可能性，范围从 0（不可能）到 1（必然）。结果是一个可能出现的结果。事件是一组结果的集合。抛一枚公平硬币时，得到 "正面" 的概率是 1/2，有时称为均等机会。
8. Graphs and Coordinates | 图表与坐标
A coordinate is a pair of numbers (x, y) that gives a point's location on a grid. The x‑axis is horizontal, the y‑axis is vertical. The origin is the point (0, 0) where the axes meet. An ordered pair tells you to go along the x‑axis first, then up or down the y‑axis.
坐标是一对数 (x, y)，标出网格上点的位置。x 轴是水平轴，y 轴是垂直轴。原点是坐标轴相交的点 (0, 0)。有序数对表示先沿 x 轴移动，再沿 y 轴上下移动。
The gradient (or slope) of a line measures how steep it is; rise over run. A straight line's equation often looks like y = mx + c, where m is the gradient and c is the y‑intercept (where the line crosses the y‑axis).
描点从原点开始。对于 (3, −2)，先沿 x 轴向右走 3 格，再向下走 2 格。直线斜率 (gradient) 衡量它的倾斜程度，用"铅垂变化除以水平变化"来计算。直线的方程通常写作 y = mx + c，其中 m 是斜率，c 是 y 轴截距（直线与 y 轴的交点）。
A linear graph is a straight‑line graph. Linear relationships have a constant rate of change. Plotting points from a table of values and joining them reveals the line.
线性图是直线图形。线性关系有恒定的变化率。从数值表描点并连接起来就得到这条直线。
9. Ratio and Proportion | 比与比例
A ratio compares two or more quantities, showing their relative sizes. The ratio 3 : 2 means for every 3 of the first quantity, there are 2 of the second. Ratios can be simplified like fractions by dividing each part by the same factor.
比用来比较两个或多个数量，显示它们的相对大小。比 3 : 2 表示第一个量每有 3 份，第二个量就有 2 份。比可以像分数一样化简，将各项除以同一个因数。
Proportion describes how one quantity changes with another. Two quantities are in direct proportion when the ratio between them stays constant. If you double one, the other doubles. For example, number of apples and total cost are directly proportional when each apple has the same price.
比例描述一个量如何随另一个量变化。当两个量的比值保持恒定时，它们成正比。如果其中一个翻倍，另一个也翻倍。例如，苹果的数量和总成本成正比，当每个苹果价格相同时。
A scale factor is the number by which we multiply to enlarge or reduce a shape. A map scale shows the ratio of a distance on the map to the actual distance. 1 : 25 000 means 1 cm on the map represents 25 000 cm (or 250 m) on the ground.
比例因子是用来放大或缩小图形的乘数。地图比例尺显示地图上的距离与实际距离的比。1 : 25 000 表示地图上 1 cm 代表地面上 25 000 cm（或 250 m）。
ram. To find the unit price, divide the total price by the number of units. If 5 pens cost £2, the unit rate is £2 ÷ 5 = £0.40 per pen.
单位比率表示每单位其他量的数量，比如每小时英里数或每千克价格。求单价时，用总价除以数量。如果 5 支笔 £2，单位比率是 £2 ÷ 5 = £0.40 每支。
10. Measurement Units | 测量单位
cm, 1 km = 1000 m. When converting to a smaller unit, multiply; to a larger unit, divide.
公制长度单位包括毫米 (mm)、厘米 (cm)、米 (m) 和千米 (km)。1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m。换算成较小单位用乘法，换算成较大单位用除法。
res how much liquid a container holds, using millilitre (mL) and litre (L). 1 L = 1000 mL.
质量（重量）单位是毫克 (mg)、克 (g)、千克 (kg) 和吨 (t)。1 g = 1000 mg, 1 kg = 1000 g, 1 t = 1000 kg。容量测量容器能装多少液体，常用毫升 (mL) 和升 (L)。1 L = 1000 mL。
rs (h). 1 min = 60 s, 1 h = 60 min. When adding times, remember to regroup at 60, not 100.
时间间隔使用秒 (s)、分钟 (min) 和小时 (h)。1 min = 60 s, 1 h = 60 min。做时间加法时，注意满 60 进 1，而不是 100。
Perimeter and area units must match the shape' ea is in cm². For area conversions, remember 1 m² is not 100 cm², but 100 cm × 100 cm = 10 000 cm². Volume conversions work similarly: 1 m³ = 1 000 000 cm³.
周长和面积的单位必须与图形的尺寸单位一致。如果边长用 cm 测量，面积就是 cm²。进行面积换算时，记住 1 m² 不是 100 cm²，而是 100 cm × 100 cm = 10 000 cm²。体积换算类似：1 m³ = 1 000 000 cm³。
Always write the correct unit after your answer. A measurement without a unit loses its meaning. Double‑check whether the question asks for mm, cm, kg, etc., and if you need to convert before calculating.
一定要在答案后面写上正确的单位。没有单位的测量结果毫无意义。再次检查题目要求的是 mm, cm, kg 等单位，以及计算前是否需要先进行单位换算。
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