📚 Year 10 WJEC Mathematics: A Quick Memorisation Guide to Key Terms and Vocabulary | Year 10 WJEC 数学：核心词汇术语速记指南
Mastering the vocabulary of mathematics is just as important as practising calculations. In WJEC Year 10, you will encounter many technical terms across algebra, geometry, statistics and probability. This guide provides simple memory hooks, visual links and word association tricks to help you embed these terms firmly and recall them under exam pressure.
掌握数学词汇与练习计算同等重要。在 WJEC Year 10 的课程中，你会接触到代数、几何、统计和概率等领域的众多专业术语。本指南提供简单的记忆钩子、图像联想和词语关联技巧，帮助你牢牢记住这些术语并在考试中顺利回想起来。
1. Number Types, Factors and Multiples | 数的类型、因数与倍数
An integer is any whole number, including negatives and zero. Think of the word ‘integral’ – it suggests wholeness. Positive integers are greater than zero, negative integers are less than zero, and absolute value strips away the sign, so |-5| = 5. The term factor refers to a number that divides another exactly; you can picture factors fitting perfectly into a larger block. A multiple is the result of multiplying a number by an integer, like the multiples of 3: 3, 6, 9…
整数 (integer) 是任意完整的数，包括负数和零。可以联想 ‘integral’（完整的）一词，强调整体性。正整数大于零，负整数小于零，绝对值 (absolute value) 则去掉符号，因此 |-5| = 5。因数 (factor) 表示能整除另一个数的数；你可以想象因数完美地嵌入一个更大的积木块。倍数 (multiple) 是一个数乘以整数得到的结果，例如 3 的倍数有 3、6、9……
Prime numbers have exactly two distinct factors: 1 and themselves. A memory trick is to think of primes as the ‘primary’ building blocks of all numbers. Composite numbers have more than two factors. The highest common factor (HCF) is the largest factor shared by two or more numbers – remember ‘H’ for ‘highest’. The lowest common multiple (LCM) is the smallest multiple they share – ‘L’ for ‘lowest’.
质数 (prime number) 恰好有两个不同的因数：1 和它本身。记忆技巧是把质数看作所有数的 ‘primary’（基本）构建块。合数 (composite number) 的因数多于两个。最大公因数 (HCF) 是两个或多个数共有的最大因数——请记住 ‘H’ 代表 ‘最高 (highest)’。最小公倍数 (LCM) 是它们共有的最小倍数——’L’ 代表 ‘最低 (lowest)’。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
The top part of a fraction is the numerator – it counts how many parts we have. The bottom part is the denominator – it names the type of part. A quick memory aid: ‘Numerator’ sounds like ‘number’ and ‘counter’; ‘denominator’ shares a root with ‘name’. A proper fraction has a smaller numerator, an improper fraction has a larger numerator, and a mixed number combines a whole and a fraction.
分数上方的部分是分子 (numerator)，数出我们拥有多少份。下方的部分是分母 (denominator)，说明每份的类型。快速记忆法：’Numerator’ 听上去像 ‘number’ 和 ‘counter’；’denominator’ 与 ‘name’ 有相同词根。真分数 (proper fraction) 的分子较小，假分数 (improper fraction) 的分子较大，带分数 (mixed number) 则是整数与真分数的组合。
Decimals use place value to show parts of a whole; the word ‘decimal’ comes from ‘decem’, Latin for ten. Percentage literally means ‘per hundred’. To convert between these forms, remember that the fraction bar means division. Visualising a whole as a 100-square grid can lock in the connection: 1/4 = 0.25 = 25%.
小数 (decimal) 利用数位表示整体的一部分；’decimal’ 源自拉丁语 ‘decem’，意为十。百分数 (percentage) 字面意思是 ‘每百 (per hundred)’。在三种形式之间转换时，请记住分数线表示除法。将整体想象成一个百格图表，可以牢固地联结关系：1/4 = 0.25 = 25%。
3. Indices and Standard Form | 指数与标准形式
Indices (or exponents) tell you how many times a number is multiplied by itself. In 5³, 5 is the base and ³ is the index. A common memory phrase: ‘An index points upward, showing repeated multiplication.’ The index laws include multiplying by adding indices (a² × a³ = a⁵) and power of a power ( (a²)³ = a⁶ ).
指数 (indices/exponents) 表示一个数自乘的次数。在 5³ 中，5 是底数 (base)，³ 是指数 (index)。常用记忆口诀：’指数向上指，显示连续乘。’ 运算法则包括同底数相乘指数相加 (a² × a³ = a⁵) 和幂的乘方 ( (a²)³ = a⁶ )。
Standard form writes very large or very small numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. For the Earth's diameter ~ 12 742 000 m, the standard form is 1.2742 × 10⁷ m. The index n counts how many places the decimal point moves. Think of 'standard form' as a neat, compact way to package bulky numbers.
标准形式 (standard form) 把很大或很小的数写成 A × 10ⁿ，其中 1 ≤ A < 10 且 n 为整数。地球直径约为 12 742 000 米，标准形式为 1.2742 × 10⁷ 米。指数 n 就是小数点移动的位数。可以将 '标准形式' 想象成打包庞大数字的整齐压缩包。
4. Algebraic Expressions | 代数表达式
An expression is a combination of numbers, letters and operation symbols without an equals sign, such as 3x + 2y – 7. Each part separated by + or – is a term. A variable (often x, y) can change its value; a constant stays fixed. The coefficient is the number multiplying the variable – in 5x, 5 is the coefficient. Link ‘coefficient’ with ‘co-pilot’: it works alongside the variable.
表达式 (expression) 是由数字、字母和运算符组合而成，没有等号，例如 3x + 2y – 7。由 ‘+’ 或 ‘-‘ 分隔的每一部分称为项 (term)。变量 (variable)（常用 x、y）可以改变数值；常量 (constant) 保持不变。系数 (coefficient) 是乘以变量的数——在 5x 中，5 就是系数。将 ‘coefficient’ 与 ‘co-pilot’（副驾驶）联系：它与变量协同工作。
Like terms have exactly the same variable part, so 4a and -2a can be combined. Simplify expressions by collecting like terms. When faced with an identity (using ≡), it means true for all values, whereas an equation is true only for particular solutions. The triple bar ≡ resembles three equal lines, emphasising ‘identical’.
同类项 (like terms) 拥有完全相同的变量部分，因此 4a 和 -2a 可以合并。通过合并同类项简化表达式。当遇到恒等式 (identity)（使用 ≡）时，表示对所有值都成立；而方程 (equation) 只对特定解成立。三横符号 ≡ 像是三条等号，强调 ‘完全相同 (identical)’。
5. Equations, Inequalities and Sequences | 方程、不等式与序列
An equation states that two expressions are equal using the ‘=’ sign. To solve an equation means to find the value of the unknown that makes it true. The unknown is typically denoted by a letter. Memory aid: ‘Equation has “equa” like equal.’ An inequality uses signs such as , ≤ or ≥. The symbol points to the smaller quantity; think of it as a hungry mouth eating the larger number.
方程 (equation) 使用 ‘=’ 表达两个表达式相等。解 (solve) 方程就是找出使等式成立的未知数的值。未知数 (unknown) 通常用字母表示。记忆技巧：’Equation 含有 “equa”，就像 equal。’ 不等式 (inequality) 使用 、≤ 或 ≥ 等符号。符号的开口指向较大的数；可以想象成一张饥饿的嘴，总是朝向更大的数。
A sequence is an ordered list of numbers following a rule. Each value is a term. An arithmetic sequence increases or decreases by a constant difference, e.g., 2, 5, 8, 11… The nth term formula lets you find any term directly: for that sequence it is 3n − 1. Think of ‘nth term’ as the ‘any-term formula’. A geometric sequence multiplies by a constant ratio, though it is less common at Year 10.
序列 (sequence) 是按规律排列的有序数字列表。每一个值是一个项 (term)。等差数列 (arithmetic sequence) 以恒定差值增减，如 2, 5, 8, 11…… 第n项 (nth term) 公式可让你直接求出任意一项：该序列的公式是 3n − 1。把 ‘nth term’ 看作是 ‘任意项公式’。等比数列 (geometric sequence) 以恒定比值相乘，Year 10 阶段较少见。
6. Geometry Fundamentals | 几何基础
A point has position but no size. A line extends infinitely in both directions, while a line segment has two endpoints. Parallel lines never meet – picture railway tracks. Perpendicular lines intersect at right angles (90°); ‘perpendicular’ contains the root ‘pend’ like ‘pendant’ hanging straight down. An angle is formed by two rays sharing a vertex.
点 (point) 有位置但无大小。直线 (line) 向两端无限延伸；线段 (line segment) 则有两个端点。平行线 (parallel lines) 永不相交——想象铁轨。垂直线 (perpendicular lines) 相交成直角 (90°)；’perpendicular’ 包含词根 ‘pend’，如同 ‘pendant (垂饰)’ 竖直下垂。角 (angle) 由两条射线共享一个顶点 (vertex) 组成。
Symmetry means a shape can be reflected or rotated onto itself. A line of symmetry divides a shape into mirror images. Rotational symmetry is the number of times a shape matches itself in one full turn. The order of rotational symmetry helps classify shapes: a square has order 4. Use tracing paper in the exam to visualise this.
对称 (symmetry) 指形状经过反射或旋转后能与自身重合。对称轴 (line of symmetry) 将形状分为镜像的两部分。旋转对称 (rotational symmetry) 指形状在旋转一周过程中与自身重合的次数。旋转对称阶数 (order) 有助于分类：正方形的阶数为 4。考试时可用描图纸辅助观察。
7. Angles and Polygons | 角与多边形
Acute angles are less than 90° – think of ‘a cute little angle’. Right angles are exactly 90°, obtuse angles between 90° and 180°, and reflex angles between 180° and 360°. A straight angle is exactly 180°. Polygons are closed shapes with straight sides. Naming uses Greek prefixes: pentagon (5 sides), hexagon (6), heptagon (7), octagon (8) and so on.
锐角 (acute) 小于 90°——联想 ‘a cute little angle’（一个可爱的小角）。直角 (right angle) 恰好 90°，钝角 (obtuse) 在 90° 到 180° 之间，优角 (reflex) 在 180° 到 360° 之间。平角 (straight angle) 恰好 180°。多边形 (polygon) 是由直线段围成的闭合图形。命名使用希腊前缀：五边形 (pentagon) (5 边)、六边形 (hexagon) (6)、七边形 (heptagon) (7)、八边形 (octagon) (8) 等。
Interior angles are inside a polygon. The sum of interior angles of an n-sided polygon is (n − 2) × 180°. Exterior angles are formed by extending one side; they always sum to 360° for any convex polygon. A simple memory trick: imagine walking along the edges – the total turn you make is one full circle, 360°. Regular polygons have equal sides and equal angles.
内角 (interior angle) 位于多边形内部。n 边多边形内角和为 (n − 2) × 180°。外角 (exterior angle) 由延长一条边形成；任何凸多边形的外角和总是 360°。一个简单的记忆技巧：想象沿边行走——你转过的总角度刚好是一整个圆，360°。正多边形 (regular polygon) 拥有相等的边和相等的角。
8. Circle Terminology | 圆的术语
The circumference is the perimeter of a circle. To remember it, link ‘circum’ with ‘around’. The radius (r) goes from the centre to the edge; it looks like a spoke. The diameter (d) cuts through the centre and equals 2r – think ‘dia’ meaning ‘across’. A chord joins two points on the circle; the diameter is the longest chord.
圆周 (circumference) 是圆的周长。为记住它，将 ‘circum’ 与 ‘around (环绕)’ 联系。半径 (radius) (r) 从圆心到边缘，形如辐条。直径 (diameter) (d) 穿过圆心，等于 2r——联想 ‘dia’ 意为 ‘穿过 (across)’。弦 (chord) 连接圆上两点；直径是最长的弦。
A tangent is a straight line that touches the circle at exactly one point without crossing it. The word shares a root with ‘tangible’, meaning ‘touching’. An arc is part of the circumference. A sector is a ‘slice’ bounded by two radii and an arc, like a pizza slice. A segment is the region between a chord and an arc, resembling a filled half-moon.
切线 (tangent) 是一条仅接触圆于一点但不穿过的直线。该词与 ‘tangible (可触摸的)’ 同源，意为 ‘触碰’。弧 (arc) 是圆周的一部分。扇形 (sector) 是由两条半径和一条弧围成的 ‘切片’，如比萨块。弓形 (segment) 是弦与弧之间的区域，形如填满的半月。
9. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the total distance around a 2D shape; ‘peri’ means around, ‘meter’ measures. Area is the amount of space inside a shape, measured in square units (cm², m²). Volume measures the space a 3D object occupies, in cubic units (cm³, m³). Surface area is the total area of all faces of a 3D solid.
周长 (perimeter) 是围绕二维形状的总长度；’peri’ 意为周围，’meter’ 测量。面积 (area) 是形状内部的空间大小，以平方单位 (cm², m²) 度量。体积 (volume) 衡量三维物体占有的空间，以立方单位 (cm³, m³) 度量。表面积 (surface area) 是立体所有面的总面积。
Key formulas include rectangle area = length × width; triangle area = ½ × base × height; circle area = πr² and circumference = 2πr or πd. For volume, a prism’s volume = area of cross-section × length. The symbol π (pi) is roughly 3.14 or 22/7. A mnemonic for the circle formulas: ‘Fudge it: Curved area is πr², boundary is 2πr.’ Imagining the two ‘r’s in ‘area’ can remind you of the square.
关键公式包括矩形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高；圆面积 = πr²，周长 = 2πr 或 πd。体积方面，棱柱体积 = 横截面积 × 长度。符号 π (派) 约等于 3.14 或 22/7。圆公式的记忆口诀：’Fudge 一下：弯曲面积是 πr²，边界是 2πr。’ 想象 ‘area’ 中有两个 ‘r’，可以提醒你面积有平方。
10. Statistics | 统计
Data can be qualitative (descriptive) or quantitative (numer
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