📚 Year 7 CIE Maths: Vocabulary & Terminology Quick-Reference Guide | Year 7 CIE 数学：词汇术语速记指南
When you start Year 7 CIE Maths, many questions use specific words that you must understand instantly. This guide groups the key vocabulary by topic and gives you simple memory tricks, so you can read a problem and know exactly what to do. Use it to revise before tests, complete homework, and build confidence in class discussions.
进入 Year 7 CIE 数学后，你会发现很多题目用词非常讲究，必须一看就懂。这份指南按主题把核心词汇分类整理，还附上了简单的记忆窍门，帮助你读题即懂、立刻反应。用它来考前复习、完成作业、提升课堂讨论的自信吧。
1. Basic Operations | 基本运算
The word 'sum' always means the result of adding two or more numbers. For example, the sum of 8 and 5 is 13.
「sum（和）」这个词总是指两个或两个以上数字相加的结果。例如 8 与 5 的和是 13。
'Difference' is the answer when you subtract one number from another. Ask yourself: how many apart are they? The difference between 14 and 9 is 5.
「difference（差）」是把一个数从另一个数里减去得到的答案。问问自己：它们之间差了多少？14 和 9 的差是 5。
'Product' means the result of multiplication. It comes from 'produce' — multiplication produces a bigger amount. The product of 6 and 4 is 24.
「product（积）」是乘法的结果。它来自「produce（产出）」，乘法会「产」出一个更大的数。6 和 4 的积是 24。
'Quotient' is the result of division. Think of it as the 'quote' of how many times one number fits into another. The quotient of 20 ÷ 5 is 4.
「quotient（商）」是除法的结果。可以想像它是报告「报价」那样，一个数里能装下多少个另一个数。20 ÷ 5 的商是 4。
In word problems, 'altogether', 'total' and 'in all' point to addition. 'How many left', 'less' and 'change' suggest subtraction. 'Each', 'times' and 'double' signal multiplication. 'Share equally', 'per' and 'split' are clues for division.
在应用题中，「altogether、total、in all」暗示加法；「how many left、less、change」提示减法；「each、times、double」是乘法的信号；「share equally、per、split」则是除法的线索。
2. Types of Numbers | 数字的类型
Whole numbers like 0, 1, 2, 3, 4 … are called 'integers' when they include negative numbers too. Positive integers are greater than zero; negative integers are less than zero and always have a minus sign.
像 0, 1, 2, 3, 4 … 这样的数如果也包括负数，就称为「integer（整数）」。正整数大于零；负整数小于零，并且总是带着一个减号。
An 'even' number can be divided exactly by 2, ending in 0, 2, 4, 6 or 8. An 'odd' number leaves a remainder of 1 when divided by 2, ending in 1, 3, 5, 7 or 9.
「even（偶数）」能被 2 整除，末尾数字是 0、2、4、6、8。「odd（奇数）」除以 2 会余 1，末尾是 1、3、5、7、9。
'Square numbers' come from multiplying a number by itself: 1 × 1 = 1, 2 × 2 = 4, 3 × 3 = 9. 'Cube numbers' come from using a number three times: 2³ = 8.
「square numbers（平方数）」是把一个数目乘得到：1 × 1 = 1, 2 × 2 = 4, 3 × 3 = 9。「cube numbers（立方数）」则是把一个数用三次：2³ = 8。
'Prime numbers' have exactly two factors: 1 and themselves. 2, 3, 5, 7, 11 are primes. The number 1 is not prime. 'Composite numbers' have more than two factors, like 4, 6, 8, 9.
「prime numbers（质数）」恰好只有两个因数：1 和它本身。2、3、5、7、11 是质数。数字 1 不是质数。「composite numbers（合数）」有两个以上的因数，例如 4、6、8、9。
3. Fractions, Decimals & Percentages | 分数、小数与百分数
A fraction has a 'numerator' (top number) and a 'denominator' (bottom number). The denominator tells you how many equal parts the whole is split into; the numerator tells you how many parts you have.
分数由「numerator（分子）」和「denominator（分母）」组成。分母说明把整体分成几等份；分子说明你占了几份。
'Proper fractions' have a numerator smaller than the denominator, like ¾. 'Improper fractions' have a numerator larger than or equal to the denominator, like 7/4. 'Mixed numbers' combine a whole number and a proper fraction, like 1¾.
「proper fraction（真分数）」的分子比分母小，如 ¾。「improper fraction（假分数）」的分子大于或等于分母，如 7/4。「mixed number（带分数）」由一个整数和一个真分数组成，如 1¾。
'Equivalent fractions' 8. You get them by multiplying or dividing the numerator and denominator by the same number.
「equivalent fractions（等值分数）」表示一样的量：½ = 2/4 = 4/8。通过把分子和分母同时乘或除以相同的数就能得到。
A 'decimal' uses a decimal point to separate the whole number from the part less than one. 'Percentage' means 'out of 100', so 35% change a fraction to a percentage, make the denominator 100 or divide and multiply by 100.
「decimal（小数）」用小数点把整数部分和小数部分分开。「percentage（百分数）」表示「每 100 中占多少」，所以 35% = 35/100 = 0.35。把分数化成百分数，要么让分母变成 100，要么除完再乘 100。
4. Factors, Multiples and Primes | 因数、倍数与质数
A 'factor' is a number that divides exactly into another number with no remainder. Factors of 12 are 1, 2, 3, 4, 6 and 12. A 'common factor' is shared by two or more numbers. The 'highest common factor' (HCF) is the largest one shared.
「factor（因数）」是可以整除另一个数而没余数的数。12 的因数有 1、2、3、4、6、12。「common factor（公因数）」是两个或多个数共有的因数。「highest common factor（最大公因数，HCF）」是公有中最大的那一个。
A 'multiple' is the result of multiplying a number by an integer. Multiples of 5 are 5, 10, 15, 20 … The 'lowest common multiple' (LCM) is the smallest multiple that two or more numbers share.
「multiple（倍数）」是把一个数乘整数得到的结果。5 的倍数有 5、10、15、20 …「lowest common multiple（最小公倍数，LCM）」是两个或多个数共享的最小倍数。
'Prime factorisation' means breaking a number into a product of its prime factors. For 18 it is 2 × 3 × 3 or 2 × 3². A 'factor tree' helps find all prime factors.
「prime factorisation（质因数分解）」就是把一个数拆成质因数的乘积。18 就是 2 × 3 × 3 或 2 × 3²。可以用「factor tree（因数树）」来找齐所有质因数。
The 'product of prime factors' n is often written using indices. The index tells you how many times the factor is used. E.g. 36 = 2² × 3².
「质因数乘积」常用指数来表示。指数告诉你这个因数出现了多少次。例如 36 = 2² × 3²。
5. Geometry: Shapes & Angles | 几何：形状与角
'Polygons' are flat shapes with straight sides. Triangles (3 sides), quadrilaterals (4 sides), pentagons (5), hexagons (6), heptagons (7), octagons (8). A 'regular' polygon has equal sides and equal angles.
「polygon（多边形）」是边都是直边的平面图形。三角形（3 边）、四边形（4 边）、五边形（5）、六边形（6）、七边形（7）、八边形（8）。「regular polygon（正多边形）」的每条边相等、每个角也相等。
Types of triangle: 'equilateral' (all sides equal), 'isosceles' (two equal sides) and 'scalene' (no equal sides). By angles: 'right-angled' (90°), 'acute-angled' (all angles < 90°), 'obtuse-angled' (one angle > 90°).
三角形的类型：「equilateral triangle（等边三角形/正三角形）」三边都相等，「isosceles triangle（等腰三角形）」两边相等，「scalene triangle（不等边三角形）」各边都不等。按角分：「right-angled triangle（直角三角形）」有一个 90° 角，「acute-angled triangle（锐角三角形）」所有角都小于 90°，「obtuse-angled triangle（钝角三角形）」有一个角大于 90°。
'Parallel lines' never meet, like train tracks. 'Perpendicular lines' meet at a right angle (90°). An 'acute angle' is less than 90°, a 'right angle' is exactly 90°, an 'obtuse angle' is between 90° and 180°, and a 'reflex angle' is between 180° and 360°.
「parallel lines（平行线）」永不交错，像铁轨。「perpendicular lines（垂直线）」相交成直角（90°）。「acute angle（锐角）」小于 90°，「right angle（直角）」恰好 90°，「obtuse angle（钝角）」介于 90° 到 180°，「reflex angle（优角）」大于 180° 小于 360°。
'Vertically opposite angles' are equal when two lines cross. 'Adjacent angles on a straight line' sum to 180°. 'Angles around a point' sum to 360°.
「vertically opposite angles（对顶角）」在两条直线相交时相等。同一直线上的「adjacent angles（邻角）」和为 180°。围绕一个点的「angles at a point（同点角）」和为 360°。
6. Measurement: Length, Area & Volume | 测量：长度、面积与体积
'Perimeter' is the total distance around the outside of a shape. For a rectangle it is 2 × (length + width). 'Area' is the amount of space inside a shape. Rectangle area = length × width, measured in square units like cm².
「perimeter（周长）」是绕图形外围一圈的总长度。长方形的周长 = 2 ×（长 + 宽）。「area（面积）」是形状内部空间的大小。长方形面积 = 长 × 宽，单位是平方单位，如 cm²。
'Volume' ccupies. For a cuboid, volume = length × width × height, measured in cubic units like cm³. 'Capacity' is how much liquid a container can hold, often in litres or millilitres.
「volume（体积）」衡量三维物体占据的空间。长方体体积 = 长 × 宽 × 高，单位是立方单位如 cm³。「capacity（容量）」是容器可以容纳的液体量，通常用升或毫升。
1 km = 1000 m. For mass, 1 kg = 1000 g. For volume/capacity, 1 L = 1000 mL, 1 cm³ = 1 mL.
常用单位：1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m。质量上，1 kg = 1000 g。体积/容量上，1 升 = 1000 毫升，1 cm³ = 1 毫升。
'Compound shapes' for area involve splitting into simpler rectangles and adding or subtracting. Remember to label units correctly in your final answer.
计算「compound shapes（复合图形）」的面积时，先拆分成简单的长方形再加或减。记得在最终答案中正确标注单位。
7. Algebraic Expressions | 代数表达式
An 'expression' ematical phrase with numbers, variables and operation symbols, but no equals sign: 3a + 2b – 7. An 'equation' states that two expressions are equal, like 2x + 5 = 13.
「expression（代数式）」是由数字、变量和运算符号组成的数学词组，没有等号：3a + 2b – 7。「equation（方程）」则声明两边的表达式相等，如 2x + 5 = 13。
A 'variable' is a letter that stands for an unknown number. In '2n + 3', n is the variable. A 'coefficient' is the number multiplying the variable: in 4y, the coefficient is 4. A 'constant' is a number on its own, like the 3 in 2n + 3.
「variable（变量）」是用来表示未知数的字母。在「2n + 3」中，n 是变量。「coefficient（系数）」是乘在变量前面的数字：4y 的系数是 4。「constant（常数）」是单独出现的数字，如 2n + 3 中的 3。
'Simplifying expressions' means collecting 'like terms' rms have exactly the same variable part: 5x and 3x are like terms, but 2x² and 3x are not. 'Expanding brackets' uses the distributive law: 3(x + 4) = 3x + 12.
「simplifying expressions（化简代数式）」就是合并「like terms（同类项）」。同类项的变量部分完全相同：5x 和 3x 是同类项，但 2x² 和 3x 不是。「expanding brackets（展开括号）」运用分配律：3(x + 4) = 3x + 12。
In an equation, 'solving' means finding the value of the variable that makes the statement true. 'Substitution' means replacing the variable with a given number to evaluate an expression.
解方程「solving」就是找出使等式成立的变量值。「substitution（代入）」则是用给定的数字替换变量求值。
8. Data & Statistics | 数据与统计
'Data' is a collection of facts or numbers. 'Primary data' is collected by you, like a survey. 'Secondary data' is taken from existing sources, like the internet or books.
「data（数据）」是收集到的事实或数字。「primary data（一手数据）」是你自己收集的，如问卷调查。「secondary data（二手数据）」来自已有来源，如图书或网络。
The 'mean' is the average: add all values and divide by how many there are. The 'median' is the middle value when the data is ordered. The 'mode' is the value that appears most often. The 'range' is the difference between the largest and smallest values.
「mean（平均数）」是加总所有数值再除以数据个数。「median（中位数）」是把数据排序后正中间的值。「mode（众数）」是出现次数最多的值。「range（极差/范围）」是最大值与最小值的差。
Display data using 'bar charts' (bars separated), 'pictograms' (using symbols), 'line graphs' (trends over time) or 'pie charts' (sectors showing proportions of a whole). A 'tally chart' helps you count frequencies quickly with groups of five.
展示数据可以用「bar chart（条形图）」（柱条分离）、「pictogram（象形图）」（使用符号）、「line graph（折线图）」（显示随时间变化的趋势）或「pie chart（饼图）」（以扇形显示整体占比）。「tally chart（频数计数表）」用画正字的方式帮你快速统计频数。
Always read the title and axis labels first. Watch out for misleading scales that don’t start at zero.
读图时一定先看标题和坐标轴标签。要小心那些不从零开始的刻度，它们可能产生误导。
9. Coordinates & Graphs | 坐标系与图表
'Coordinates' are pairs of numbers (x, y) that fix a point's position on a grid. The x-coordinate (horizontal) comes first, then the y-coordinate (vertical). Remember 'along the corridor, up the stairs'.
「coordinates（坐标）」是用一对数字 (x, y) 确定网格上点的位置。x 坐标（水平方向）在前，y 坐标（竖直方向）在后。记住口诀：「先过走廊，再上楼梯」。
The 'origin' is the point (0,0) where the x-axis and y-axis cross. The 'x-axis' is horizontal; the 'y-axis' is vertical. The four 'quadrants' are labelled I, II, III, IV anticlockwise starting top-right.
「origin（原点）」是 (0,0)，x 轴和 y 轴的交点。x 轴是横轴，y 轴是纵轴。四个「quadrant（象限）」从右上角逆时针标为 I, II, III, IV。
Plotting a 'straight-line graph' oints and join them. The line shows all points that satisfy the equation, like y = 2x + 1.
要画出「straight-line graph（直线图）」，可以先做一个数值表，标出点，然后把它们连起来。这条直线显示了所有满足方程的点，例如 y = 2x + 1。
A 'conversion graph' is a straight line through the origin that converts one unit to another, such as miles to kilometres. Read from one axis, trace to the line, then read the other axis.
「conversion graph（换算图）」是一条过原点的直线，用来换算不同单位，如英里换公里。从一条轴读数，追踪到直线上，再读出另一条轴的数字就行。
10. Ratio and Proportion | 比与比例
'Ratio' compares two or more quantities in the same order. A ratio of oranges to apples as 2 : 3 means for every 2 oranges there are 3 apples. Ratios can be simplified like fractions by dividing each part by a common factor.
「ratio（比）」用来按相同顺序比较两个或多个数量。橙子和苹果的比是 2 : 3，表示每 2 个橙子就有 3 个苹果。比可以像分数一样，通过同除以公因数来化简。
'Proportion' describes a part compared to the whole. If 3 out of 5 sweets are red, the proportion of red sweets is 3/5. Direct proportion means two quantities increase at the same rate.
「proportion（比例）」描述部分与整体的关系。如果 5 块糖中有 3 块是红色的，红色糖的比例就是 3/5。正比例表示两个量以同样的比率增加。
The 'unitary method' finds the value of one unit first, then scales up. If 4 pens cost £3, then 1 pen costs £0.75, so 10 pens cost £7.50.
「unitary method（单位法）」是先把一个单位的值算出来，然后再按倍数放缩。如果 4 支笔 3 磅，那么 1 支笔 0.75 磅，10 支笔就是 7.50 磅。
'Scale' on a map is a ratio: 1 : 50 000 means 1 cm on the map represents 50 000 cm (500 m) on the ground. Always check the units when working with scales.
地图上的「scale（比例尺）」也是一个比：1 : 50 000 表示地图上 1 cm 代表实际 50 000 cm（500 m）。使用比例尺时总是要核对单位。
11. Sequences and Patterns | 数列与模式
A 'sequence' is a set of numbers in a specific order. Each number is called a 'term'. In the sequence 3, 7, 11, 15, … the first term is 3, the second is 7, and so on.
「sequence（数列）」是一组按特定顺序排列的数字。每个数字叫一个「term（项）」。在数列 3, 7, 11, 15, … 中，第一项是 3，第二项是 7，依此类推。
The 'term-to-term rule' tells you how to go from one term to the next. In the sequence above, the rule is 'add 4'. The 'position-to-term rule' (nth term) gives you any term directly: nth term = 4n – 1.
「term-to-term rule（逐项规则）」告诉你如何从一项得到下一项。上面数列的规则是「加 4」。「position-to-term rule（第 n 项规则）」则直接给出任意一项：第 n 项 = 4n – 1。
An 'arithmetic sequence' has a common difference between terms. 'Linear sequences' grow by a constant amount, giving a straight line when plotted. Look for a constant first difference.
「arithmetic sequence（等差数列）」的相邻各项间有共同的差。「linear sequence（线性数列）」以固定数量增长，画成图形是一条直线。寻找一次差是否恒定就好。
check the first few terms by substituting n = 1, 2, 3 into the nth term formula if given.
生成数列的项就是反复运用逐项规则：从第一项出发，不断推下去。如果给出了第 n 项公式，记得把 n = 1, 2, 3 代入验证前几项。
12. Money and Time Vocabulary | 钱币与时间词汇
In money problems, 'total cost' means sum of all items. 'Change' is the amount you get back after paying. 'Discount' is a reduction in price, often a percentage off.
在钱币问题中，「total cost（总花费）」是所有商品价格之和。「change（找零）」是付钱后退回的金额。「discount（折扣）」指价格降低，常常是减一个百分数。
'Profit' is the money left after selling price minus cost price. 'Loss' happens when selling price is lower than cost price. Express profit or loss as a percentage of the cost price.
「profit（利润）」是售价减去成本剩下的钱。「loss（亏损）」发生在售价低于成本时。利润或亏损常常表述为成本的百分数。
With time, 'analogue clock' uses hands, 'digital clock' shows numbers. 'a.m.' is before midday; 'p.m.' is after midday. '12-hour' and '24-hour' times are used: 3:00 p.m. is 15:00.
时间方面，「analogue clock（指针钟）」用表针指示，「digital clock（数字钟）」直接显示数字。a.m. 指上午，p.m. 指下午。同时使用 12 小时制和 24 小时制：下午 3:00 就是 15:00。
Calculating time intervals: find the difference between two times. For a journey, 'duration' = arrival time – departure time. Be careful when hours cross midday or midnight.
计算「time interval（时间间隔）」就是找两个时间点之间的差。对于旅行，「duration（时长）」= 到达时间 - 出发时间。跨过中午或午夜时要特别留意。
and seconds: 1 hour = 60 min, 1 day = 24 h. Always underline key time words in a question.
读时间表和日历需要在天、时、分、秒之间换算：1 小时 = 60 分钟，1 天 = 24 小时。解题时一定要在题目中把关键的时间词划出来。
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