📚 Year 8 CIE Maths: Vocabulary & Terminology Quick Guide | Year 8 CIE 数学：词汇术语速记指南
Mathematical vocabulary is half the battle in Year 8. CIE examiners expect you to understand the exact meaning of every instruction word, and a single misunderstood term can cost you easy marks. This quick guide breaks down the essential Year 8 CIE Maths terms section by section, adds memory tricks, and shows how each word appears in real questions.
掌握数学词汇是 Year 8 学习成功的一半。CIE 考官要求你准确理解每个指令词的含义，一个术语理解错就可能白白丢分。本速记指南按板块系统梳理 Year 8 CIE 数学核心术语，配以记忆窍门，并说明每个词在真实题目中的用法。
1. Number Types & Place Value | 数的类型与位值
Integer: a whole number that can be positive, negative or zero. Link 'integer' to 'entire' - a complete number with no fractional part. So 7 and −12 are integers, but 7.5 is not.
整数：可以是正数、负数或零的完整数字。把 "integer" 联想成 "entire"（完整的），没有分数部分。所以 7 和 −12 是整数，而 7.5 不是。
Place value: the value a digit carries because of the column it sits in. In 4 712 the digit '7' means 700 because it stands in the hundreds column.
位值：数字因其所在数位而具有的值。在 4 712 中，数字 "7" 位于百位，所以表示 700。
Digit: any one of the symbols 0 to 9 used to write numbers. Remember that 'digit' also means finger - we first learned to count on our fingers.
数字：用来书写数字的 0 到 9 中的任意一个符号。记住 "digit" 也有"手指"的意思——我们最初就是掰着手指学数数的。
Negative number: a number less than zero, usually written with a minus sign. Picture a thermometer dropping below freezing: −5 °C is five degrees below zero.
负数：小于零的数，通常带负号书写。想象温度计降到冰点以下：−5 °C 就是零下五度。
Positive number: a number greater than zero, normally written without a sign. Every ordinary counting number you use in daily life is positive.
正数：大于零的数，通常不带符号书写。日常生活中你数数用到的都是正数。
Rounding: approximating a number to a given place value. The classic chant is '5 or more, raise the score; 4 or less, let it rest.'
四舍五入：把数字近似到指定的位值。经典口诀是："5 或以上，向上进位；4 或以下，保持不变。"
| Digit in 4 712 | Column | 数位 | Value | 数值 |
| 4 | thousands 千位 | 4 000 |
| 7 | hundreds 百位 | 700 |
| 1 | tens 十位 | 10 |
| 2 | ones 个位 | 2 |
2. Fractions, Decimals & Percentages | 分数、小数与百分比
Numerator: the top number of a fraction; it counts how many equal parts we have. 'Numerator' begins like 'number', so it is the counting part.
分子：分数线上方的数，表示有多少个等份。分子 "numerator" 开头像 "number"（数数），所以它是负责计数的部分。
Denominator: the bottom number of a fraction; it names the size of each equal part. 'Denominator' contains 'nom', the same root as 'name'.
分母：分数线下方的数，标明每个等份的大小。分母 "denominator" 含有 "nom"，与 "name"（命名）同源。
You make them by multiplying or dividing the numerator and denominator by the same number.
等值分数：表示相同数值的不同分数，例如 ½ = 2/4 = 50/100。做法是分子与分母同时乘以或除以同一个数。
Simplify (lowest terms): dividing the numerator and denominator by their highest common factor until no common factor remains.
约分（最简形式）：用分子和分母的最大公因数去除，直到没有公因数为止。
Mixed number and improper fraction: a mixed number has a whole part and a fraction part, like 2½; an improper fraction has a numerator larger than its denominator, like 5/2.
带分数与假分数：带分数由整数部分和分数部分组成，如 2½；假分数的分子大于分母，如 5/2。
ng decimal repeats a pattern forever and is written with a dot notation, for example 0.333… = 0.3̇. A terminating decimal stops, such as 0.25.
循环小数会无限重复某个模式，用点号表示，例如 0.333… = 0.3̇；有限小数会终止，如 0.25。
Percentage means 'per hundred', so 35% is simply 35/100 = 0.35. To convert between the three forms, remember the key links below.
百分比的意思是"每一百"，所以 35% 就是 35/100 = 0.35。三种形式之间的转换，记住下面的关键关系。
Fraction → Decimal: divide the numerator by the denominator | 分数 → 小数：分子 ÷ 分母
Decimal → Percentage: × 100 | 小数 → 百分比：× 100
Percentage → Decimal: ÷ 100 | 百分比 → 小数：÷ 100
3. Operations, Order of Operations & Factors | 运算、运算顺序与因数
Sum, difference, product and quotient: the sum is the answer to an addition, the difference comes from a subtraction, the product from a multiplication, and the quotient from a division.
和、差、积、商：和是加法的结果，差是减法的结果，积是乘法的结果，商是除法的结果。
ition and Subtraction, working left to right within each level. So 2 + 3 × 4 = 14, not 20.
运算顺序（BIDMAS）：先括号、再指数、再乘除、最后加减，同一级从左到右计算。所以 2 + 3 × 4 = 14，而不是 20。
Factor: a number that divides exactly into another number with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.
因数：能整除另一个数且没有余数的数。12 的因数是 1、2、3、4、6 和 12。
Multiple: the result of multiplying a number by an integer. Multiples of 7 are 7, 14, 21, 28 … and they never end.
倍数：一个数乘以整数所得的结果。7 的倍数是 7、14、21、28……可以无限延续。
Prime number: a number with exactly two factors, 1 and itself. Prime, composite and square numbers are three different categories you must keep apart.
质数：恰好只有 1 和它本身两个因数的数。质数、合数与平方数是三组必须分清的类别。
- Prime 质数: 2, 3, 5, 7, 11, 13 … (2 is the only even prime | 2 是唯一的偶质数)
- Composite 合数: 4, 6, 8, 9, 10, 12 … (has more than two factors | 因数多于两个)
- Square number 平方数: 1, 4, 9, 16, 25 … (n × n | n × n)
HCF and LCM: the highest common factor is the largest factor shared by two numbers, while the lowest common multiple is the smallest multiple they share. HCF is used for simplifying, LCM for adding fractions.
最大公因数与最小公倍数：最大公因数是两个数共有的最大因数；最小公倍数是它们共有的最小倍数。最大公因数用于约分，最小公倍数用于通分。
er by itself, so 5³ = 5 × 5 × 5 = 125; the square root of 125 is not exact, but √144 = 12.
指数（幂）与根：指数表示一个数自乘的次数，所以 5³ = 5 × 5 × 5 = 125；125 的平方根不是整数，而 √144 = 12。
4. Algebra Basics | 代数基础
Variable: a letter standing for a number that can change, such as x or n. Think 'variable' equals 'varies'.
变量：代表可变化的数的字母，如 x 或 n。记住 "variable" 就是"会变的"。
Term, coefficient and constant: a term is a single part of an expression separated by + or − signs; the coefficient is the number multiplying a letter; the constant is the term with no letter at all. In 5x + 7, the coefficient is 5 and the constant is 7.
项、系数与常数：项是用加号或减号分隔开的单个部分；系数是乘在字母前面的数；常数是不含字母的项。在 5x + 7 中，系数是 5，常数是 7。
uch as 3x + 4; an equation contains an equals sign and can be solved, such as 3x + 4 = 19.
表达式与方程：表达式没有等号，只能化简，如 3x + 4；方程含有等号，可以求解，如 3x + 4 = 19。
tter part, which can be collected together. 4a + 7a = 11a, but 4a + 7b cannot be combined.
同类项：字母部分完全相同的项，可以合并。4a + 7a = 11a，但 4a + 7b 不能合并。
with given numbers and then calculating carefully. If x = 3, then 2x + 5 = 2 × 3 + 5 = 11.
代入：把字母换成给定的数值再仔细计算。若 x = 3，则 2x + 5 = 2 × 3 + 5 = 11。
Expand and factorise: expanding removes brackets by multiplying each term inside, while factorising puts brackets back by taking out common factors. They are opposite processes.
展开与因式分解：展开是用括号外的数去乘括号内每一项从而去掉括号；因式分解是提取公因式把括号加回去。两者互为逆过程。
3(x + 4) = 3x + 12 (expand 展开) ⇌ 3x + 12 = 3(x + 4) (factorise 因式分解)
5. Equations, Formulae & Inequalities | 方程、公式与不等式
Solve and solution: to solve means to find the value of the unknown that makes the equation true; that value is called the solution. Always check by substituting your answer back in.
求解与解：求解就是找出使方程成立的未知数的值，这个值叫解。一定要把答案代回原方程检验。
Inverse operation: the operation that undoes another one. Addition undoes subtraction, multiplication undoes division - use inverses to isolate the unknown.
逆运算：能抵消另一种运算的运算。加法是减法的逆运算，乘法是除法的逆运算——用逆运算把未知数单独留在一边。
ea of a rectangle. The subject of a formula is the letter on its own, usually on the left.
公式：连接两个或多个量的规则，例如长方形面积 A = l × w。公式的主元是单独位于等号一侧（通常左侧）的字母。
rforming the same inverse operations, for example turning v = u + at into t = (v − u) ÷ a.
公式变形：通过相同的逆运算改变主元，例如把 v = u + at 变成 t = (v − u) ÷ a。
Inequality: a statement comparing quantities that are not necessarily equal. Learn the four symbols and how to read them from the variable side.
不等式：比较两个不一定相等的量的表达式。要记住四个符号，并学会从变量一侧去读。
- < less than 小于 | > greater than 大于
- ≤ less than or equal to 小于或等于 | ≥ greater than or equal to 大于或等于
- 2 < x ≤ 9 means x is greater than 2 but no more than 9 | 2 < x ≤ 9 表示 x 大于 2 且不超过 9
Linear equation: an equation where the unknown appears only to the power 1 and is not multiplied by itself, so its graph is a straight line.
线性方程：未知数只出现一次幂、且不与自身相乘的方程，其图像是一条直线。
6. Coordinates, Sequences & Graphs | 坐标、数列与图像
Axes and origin: the x-axis is horizontal and the y-axis is vertical; they meet at the origin, which has coordinates (0, 0).
坐标轴与原点：x 轴水平，y 轴竖直，两轴相交于原点，坐标为 (0, 0)。
Coordinates: an ordered pair (x, y) telling you how far to move across and then up. Always go along the corridor before climbing the stairs.
坐标：有序数对 (x, y)，表示先横向移动多少、再纵向移动多少。记住"先走走廊，再上楼梯"。
Quadrant: one of the four regions the axes divide the plane into, numbered anticlockwise from the top right. Signs of coordinates change in each quadrant.
象限：坐标轴把平面分成的四个区域之一，从右上角起逆时针编号。各象限中坐标的正负号不同。
Sequence and term: a sequence is an ordered list of numbers, and each number in it is called a term. 4, 7, 10, 13 … is a linear sequence because it increases by the same amount each time.
数列与项：数列是有序排列的一串数，其中的每一个数叫做项。4、7、10、13……是线性数列，因为每次增加的量相同。
Term-to-term rule and nth term: the term-to-term rule describes how to get from one term to the next (+3 above); the nth term is a formula that jumps straight to any term, here 3n + 1.
相邻项规律与第 n 项：相邻项规律描述如何从前一项得到后一项（上例为 +3）；第 n 项则是能直接求出任意一项的公式，此处为 3n + 1。
Gradient and intercept: the gradient measures steepness, found by dividing the vertical change by the horizontal change; the y-intercept is where the line crosses the y-axis.
斜率与截距：斜率衡量倾斜程度，用纵向变化量除以横向变化量求得；y 轴截距是直线与 y 轴的交点。
Midpoint: the point exactly halfway between two coordinates, found by averaging the x values and averaging the y values.
中点：恰好位于两个坐标正中间的点，求法是把两个 x 值取平均、两个 y 值取平均。
Midpoint of (x₁, y₁) and (x₂, y₂) = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
7. Angles & Basic Geometry | 角与几何基础
Acute, right, obtuse and reflex: an acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle lies between 90° and 180°, and a reflex angle is greater than 180°.
锐角、直角、钝角与优角：锐角小于 90°，直角正好 90°，钝角在 90° 与 180° 之间，优角大于 180°。
Complementary and supplementary: complementary angles add to 90°, supplementary angles add to 180°. Remember 'c' for corner (90°) and 's' for straight line (180°).
互余与互补：互余两角之和为 90°，互补两角之和为 180°。记 "c" 对应拐角（90°），"s" 对应直线（180°）。
Vertically opposite angles: the two angles formed on opposite sides when two straight lines cross. They are always equal.
对顶角：两条直线相交时，位于交点两侧相对位置的两个角。对顶角永远相等。
Parallel and perpendicular lines: parallel lines never meet and stay the same distance apart; perpendicular lines meet at exactly 90°.
平行线与垂直线：平行线永不相交、间距恒定；垂直线相交成 90°。
Alternate, corresponding and co-interior angles: these are the three key angle pairs created when a transversal cuts through parallel lines.
内错角、同位角与同旁内角：当一条截线穿过两条平行线时，形成的三种关键角关系。
- Alternate angles 内错角: equal 相等 (Z shape | Z 形)
- Corresponding angles 同位角: equal 相等 (F shape | F 形)
- Co-interior angles 同旁内角: add to 180° 互补 (C or U shape | C 形或 U 形)
Bearings: an angle measured clockwise from north, always written with three digits, for example 045°. North lines are drawn in and bearings are never given as negative values.
方位角：从正北方向顺时针测量的角，必须写成三位数，例如 045°。作图时要画出正北线，方位角不会取负值。
8. Triangles, Quadrilaterals & Circles | 三角形、四边形与圆
Triangle types: equilateral triangles have three equal sides and three 60° angles; isosceles triangles have two equal sides and two equal base angles; scalene triangles have all sides different.
三角形种类：等边三角形三边相等、三个角都是 60°；等腰三角形有两边相等、两个底角相等；不等边三角形三边都不相等。
Angle facts: angles in any triangle add to 180°, angles in any quadrilateral add to 360°, and angles on a straight line add to 180°.
角度定理：任意三角形内角和为 180°，任意四边形内角和为 360°，直线上的邻补角之和为 180°。
Polygon and regular polygon: a polygon is any closed shape with straight sides; a regular polygon has all sides and all angles equal. The exterior angles of any polygon add to 360°.
多边形与正多边形：多边形是由直线边围成的封闭图形；正多边形所有边、所有角都相等。任意多边形的外角和为 360°。
Quadrilateral family: a parallelogram has two pairs of parallel sides, a rhombus is a parallelogram with four equal sides, a trapezium has exactly one pair of parallel sides, and a kite has two pairs of adjacent equal sides.
四边形家族：平行四边形有两组对边平行；菱形是四边相等的平行四边形；梯形恰有一组平行对边；风筝形有两组相邻边相等。
ord joins two points on the circle, and a tangent touches the circle at exactly one point.
圆的术语：半径连接圆心与圆周；直径穿过圆心，等于半径的 2 倍；弦连接圆上两点；切线只与圆相交于一点。
Arc, sector and segment: an arc is part of the circumference, a sector is the 'pizza slice' bounded by two radii and an arc, and a segment is the region cut off by a chord.
弧、扇形与弓形：弧是圆周的一部分；扇形是由两条半径和一段弧围成的"披萨块"；弓形是被弦切出的区域。
- Circumference 周长 = π × diameter = 2πr
- Area of a circle 圆面积 = π × r²
- π ≈ 3.142 or use the π key on your calculator | π ≈ 3.142，或直接使用计算器上的 π 键
9. Perimeter, Area, Volume & Surface Area | 周长、面积、体积与表面积
Perimeter: the total distance around the outside of a 2D shape, found by adding all the side lengths. Units are lengths such as cm or m.
周长：二维图形外边界一周的总长度，把所有边长相加即可。单位是长度单位，如 cm 或 m。
Area: the amount of surface a 2D shape covers, measured in square units such as cm². Perimeter is a length, area is a surface - never mix the two labels.
面积：二维图形所覆盖的表面大小，用平方单位如 cm² 表示。周长是长度，面积是表面——两者标签绝不能混用。
h as cm³; capacity is how much a container holds, often in ml or litres, and 1 cm³ = 1 ml.
体积与容积：体积是三维立体所占的空间，用立方单位如 cm³ 表示；容积是容器能容纳的量，常用 ml 或升表示，且 1 cm³ = 1 ml。
Surface area: the total area of all the faces of a solid. For a cuboid, add the areas of the six rectangular faces, remembering opposite faces are identical.
表面积：立体所有面的面积之和。对长方体而言，把六个长方形面的面积相加，注意相对的两个面完全相同。
Area of a triangle 三角形面积 = ½ × base 底 × perpendicular height 垂直高
Volume of a cuboid 长方体体积 = length × width × height
Compound shape: a shape made by joining simpler shapes together. Split it into rectangles, triangles or circles, work out each part, then add or subtract as needed.
复合图形：由较简单的图形拼合而成的图形。把它拆成矩形、三角形或圆，分别计算，再根据需要相加或相减。
10. Units, Measures & Scales | 单位、度量与比例尺
ndredth and milli- means one thousandth. So 1 km = 1 000 m, 1 m = 100 cm and 1 cm = 10 mm.
公制词头：kilo- 表示 1 000，centi- 表示百分之一，milli- 表示千分之一。所以 1 km = 1 000 m，1 m = 100 cm，1 cm = 10 mm。
Mass, length and capacity:
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