📚 Year 8 CCEA Further Maths: Quick Terminology Memorisation Guide | CCEA 八年级进阶数学：词汇术语速记指南
Welcome to your rapid-revision toolkit for Year 8 CCEA Further Mathematics. Mastering the language of maths is half the battle – when you know what 'coefficient', 'circumference' or 'congruent' really mean, problem solving becomes far less scary. This guide gives every key term a clear definition, a memory hook, and a paired Chinese translation so you can lock it into long-term memory. Use the tips, say them aloud, and you will soon speak fluent maths.
欢迎使用 CCEA 八年级进阶数学快速复习工具包。掌握数学语言是成功的一半——当你真正明白“系数”、“周长”或“全等”的含义时，解题就不再可怕。本指南为每个关键术语提供清晰的定义、记忆技巧，以及对应的中文翻译，帮助你牢牢记住。大声说出这些技巧，你很快就能流利地“说数学”了。
1. Algebraic Expressions | 代数表达式
Algebra uses letters (like x, y, n) to stand for unknown numbers. An expression is a combination of numbers, letters and operation signs – for example 3x + 2 or 5a – 7b. Expressions do not contain an equals sign. The tiny number in front of a letter is called the coefficient: in 4y the coefficient is 4. A constant term is a number on its own, such as the 2 in x + 2. Remember: 'coefficient' co-stars with the variable; 'constant' stands alone without any letter.
代数使用字母（如 x, y, n）代表未知数。表达式是由数字、字母和运算符号组成的组合——例如 3x + 2 或 5a – 7b。表达式中不含等号。字母前面的那个数字叫做系数：在 4y 中，系数为 4。常数项是单独出现的数字，比如 x + 2 中的 2。记忆窍门：系数（coefficient）像“合演”一样与变量一起出现；常数（constant）则独自站着，不跟任何字母。
2. Equations and Inequalities | 方程与不等式
An equation Solving an equation means finding the value of the unknown that makes the statement true. An inequality greater than or equal to). Think of the inequality symbol as a hungry crocodile that always eats the bigger number – this helps you read it correctly every time.
方程是用等号（=）表示两个表达式相等的陈述。解方程就是找到使等式成立的未知数的值。不等式用 <（小于）、>（大于）、≤（小于或等于）或 ≥（大于或等于）等符号比较两个表达式。想象不等号是一只饥饿的鳄鱼，它总是吃掉较大的那个数——这个联想能帮你每次都读对符号方向。
3. Number Types | 数的类型
A prime number has exactly two distinct factors: 1 and itself. (So 1 is NOT prime.) A composite number has more than two factors. Square numbers result from multiplying a whole number by itself (1, 4, 9, 16...). Cube numbers come from multiplying a whole number by itself three times (1, 8, 27, 64...). The square root (√) undoes squaring; the cube root (³√) undoes cubing. A quick way to remember: 'prime' sounds like 'first', and primes are the building blocks of all whole numbers.
素数有且仅有两个不同的因数：1 和它本身。（因此 1 不是素数。）合数的因数多于两个。平方数是将一个整数自乘一次得到的结果（1, 4, 9, 16……）。立方数是将一个整数自乘两次（即乘三次）得到的结果（1, 8, 27, 64……）。平方根（√）是平方的逆运算；立方根（³√）是立方的逆运算。速记法：“prime”（素数）听起来像“first”（第一），素数正是所有整数的搭建基石。
4. Factors and Multiples | 因数与倍数
A factor divides a number exactly without leaving a remainder. A multiple is the result of multiplying a number by any whole number. The highest common factor (HCF) is the largest factor shared by two or more numbers. The lowest common multiple factors you divide down; with multiples you multiply up. To remember which is which, think 'Factor → Fits into' and 'Multiple → Many times'.
因数能整除一个数而不留余数。倍数是一个数乘任意整数得到的结果。最大公因数（HCF）是两个或多个数共有的最大的因数。最小公倍数（LCM）是两个或多个数共有的最小的倍数。因数是往下除的；倍数是往上乘的。要记住哪个是哪个，可以这样想：Factor → Fits into（能装进去），Multiple → Many times（很多次）。
5. Fractions, Decimals and Percentages | 分数、小数与百分比
A fraction has a numerator (top) and a denominator (bottom). An improper fraction has a numerator larger than its denominator; a mixed number combines a whole number and a proper fraction. Decimals use a decimal point to show parts of a whole. A percentage is a fraction out of 100 – the % symbol means 'per hundred'. When you see %, think of two little zeros hugging a slash, just like /100. To convert between them, remember: fractions to decimals means dividing; decimals to percentages means multiplying by 100.
分数由分子（上方）和分母（下方）组成。假分数的分子比分母大；带分数由一个整数和一个真分数组合而成。小数用小数点表示整体的一部分。百分比是分母为 100 的分数——% 符号本身就代表“每百”。看到 % 时，想象两个小零圈抱着一道斜杠，就像 /100。转换时记住：分数化小数用除法；小数化百分比乘以 100。
6. Ratio and Proportion | 比和比例
A ratio compares two or more quantities in the same order and can be written as a : b or a/b. The ratio does not tell the actual amounts, only the relative size. Proportion describes a relationship where two quantities change together. In direct proportion, as one quantity doubles, the other doubles too. In inverse proportion, as one doubles, the other halves. Memory tip: 'direct' = both go the same direction; 'inverse' = one goes up while the other goes down. Always simplify ratios like fractions.
比是按相同顺序比较两个或多个数量，可以写成 a : b 或 a/b。比不表示实际数量，只表示相对大小。比例描述的是两个量一起变化的关系。在正比例中，一个量翻倍，另一个也翻倍。在反比例中，一个翻倍，另一个则减半。记忆诀窍：“正比”就是两者同向变化；“反比”就是一个上升另一个下降。比永远要像分数一样化到最简。
7. Geometry Basics | 几何基础术语
Perimeter is the total distance around the outside of a shape – imagine walking along the fence of a field. Area is the amount of surface inside a flat shape, measured in square units. Volume tells how much space a 3D solid occupies, measured in cubic units. A polygon is any closed 2D shape with straight sides – triangles, quadrilaterals, pentagons (5 sides), hexagons (6 sides), heptagons (7 sides) and octagons (8 sides). The Greek prefix tells you the number of sides: 'oct' means eight, like an octopus.
周长是围绕图形外边缘的总长度——想象沿着田地的围栏走一圈。面积是平面图形内部的表面大小，用平方单位度量。体积表示一个三维立体所占据的空间，用立方单位度量。多边形是任何由直边围成的封闭平面图形——三角形、四边形、五边形、六边形、七边形、八边形等。希腊语前缀体现了边数：“oct”指八，就像章鱼（octopus）有八条腿。
8. Angles and Lines | 角与线
An angle is the space between two rays meeting at a vertex, measured in degrees (°). Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are between 90° and 180°, and reflex angles are greater than 180°. On a straight line, angles add up to 180°; around a point they total 360°. Parallel lines never meet, while perpendicular lines intersect at right angles. Link 'parallel' with 'pair of railway lines' – they always stay the same distance apart.
角是两条射线在顶点处相交所形成的空间，用度（°）度量。锐角小于 90°，直角恰好是 90°，钝角在 90° 到 180° 之间，优角大于 180°。在一条直线上，角之和为 180°；围绕一个点，角之和为 360°。平行线永不相交，而垂直线相交成直角。记“平行”可以联想“一对铁轨”——它们始终保持着相同的间距。
9. Triangles and Quadrilaterals | 三角形与四边形
Triangles are classified by sides – equilateral (all sides equal, all angles 60°), isosceles (two equal sides, two equal angles) and scalene (no equal sides). By angles they can be acute, right or obtuse. The interior angles of any triangle always sum to 180°. Among quadrilaterals, a square has four equal sides and four right angles; a rectangle has opposite sides equal; a parallelogram has both pairs of opposite sides parallel; a trapezium has at least one pair of parallel sides. Use the 'equal toes' trick for isosceles – your two big toes are equal, just like the two equal base angles.
三角形按边分类：等边三角形（三边相等，每个角均为 60°）、等腰三角形（两条边相等，两个底角相等），不等边三角形（三边均不相等）。按角可分为锐角三角形、直角三角形和钝角三角形。任何三角形的内角和永远为 180°。四边形中，正方形有四条等边和四个直角；长方形的对边相等；平行四边形的两组对边分别平行；梯形至少有一组对边平行。用“大脚趾等长”来记等腰三角形——你的两个大脚趾一样大，就像等腰三角形的两个相等的底角。
10. Symmetry and Transformations | 对称与变换
A shape has line symmetry (reflective symmetry) if you can fold it along a line and the two halves match exactly. Rotational symmetry tells you how many times a shape looks the same in one full turn. Congruent shapes are identical in shape and size; similar shapes have the same shape but may be different sizes – all corresponding angles are equal and side lengths are in proportion. In transformations, translation slides a shape, reflection flips it over a mirror line, rotation turns it around a point, and enlargement changes its size by a scale factor. Congruent = same everything; similar = same shape, different size.
如果一个图形沿某条直线对折后两部分完全重合，那么这个图形就有线对称（反射对称）。旋转对称描述的是图形在旋转一周的过程中有多少次与自身重合。全等图形形状和大小完全相同；相似图形形状相同，但大小可以不同——所有对应角相等，边长成比例。在变换中，平移是滑移图形，反射是沿对称轴翻转，旋转是绕某一点转动，放大是按比例因子改变大小。全等 = 什么都相同；相似 = 形状相同，大小不同。
11. Statistics and Data | 统计与数据
The three key averages are: mode (most frequent value), median (middle value when ordered) and mean (sum divided by count). The range measures spread: largest minus smallest. A quick way to keep them straight: mode sounds like 'most', median thinks about the 'middle taxi' on a road, and mean is the 'mean (unkind)' one that makes you do all the adding and dividing. Data can be shown in bar charts, pictograms, pie charts and line graphs – always read titles and labels carefully.
三个关键的平均数：众数（出现最多的值），中位数（排序后中间的值），平均数（总和除以个数）。范围衡量分散程度：最大值减去最小值。区分它们的顺口溜：众数（mode）听起来像“most”（最多），中位数想想道路中间的出租车，平均数（mean）则是那个“刻薄的”让你又加又除的家伙。数据可以用条形图、象形图、饼图和折线图表示——一定要仔细阅读标题和标签。
12. Coordinates and Graphs | 坐标与图形
A coordinate pair (x, y) fixes a point on the grid. The first number (x) tells you how far to move horizontally from the origin (0,0); the second (y) tells you the vertical movement. In a linear graph, y = mx + c, m is the gradient (steepness) and c is the y-intercept (where the line cuts the y-axis). Remember 'along the corridor, up the stairs': go along the x-axis first, then go up or down the y-axis. For plotting, choose simple x values and use a sharp pencil.
一个坐标对 (x, y) 在网格上确定一个点。第一个数 (x) 告诉你从原点 (0,0) 沿水平方向移动多远；第二个数 (y) 告诉你垂直方向移动多远。在线性图像中，y = mx + c，m 是斜率（陡峭程度），c 是y 轴截距（直线与 y 轴相交的位置）。记住口诀“先沿着走廊走，再上楼”：先在 x 轴方向上走，然后再沿 y 轴方向上下移动。画图时，选取简单的 x 值，用削尖的铅笔画。
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