📚 Year 10 WJEC Maths: Key Vocabulary and Terms Quick Memory Guide | Year 10 WJEC 数学：核心词汇术语速记指南
Mastering the specific language of mathematics is one of the most effective ways to improve your performance in WJEC Year 10 exams. Many questions test your ability to interpret terminology such as 'expression', 'coefficient', or 'congruent'. This guide will help you lock these terms into your memory by pairing clear definitions with bilingual explanations and simple memory hooks.
掌握数学的专属语言是提高 WJEC Year 10 考试成绩最有效的方法之一。很多题目其实是在考查你对 “表达式”、“系数” 或 “全等” 等术语的理解。这篇指南通过清晰的定义、双语解释和简单的记忆技巧，帮助你将这些术语牢牢印在脑海中。
1. Expressions, Equations and Identities | 表达式、方程与恒等式
An expression is a mathematical 'phrase' made of terms, numbers and operators, but it never contains an equals sign. For example, 3x + 5 is an expression.
表达式是由项、数字和运算符号组成的数学“短语”，它从不包含等号。比如 3x + 5 就是一个表达式。
, always shown with an equals sign. It is like a balanced scale. For example, 3x + 5 = 11.
方程是陈述两个表达式相等的语句，总有等号，就像一台平衡的天平。例如 3x + 5 = 11。
An identity is a special equation that is true for all values of the variable, often written with a triple bar ≡. For instance, (x + 1)² ≡ x² + 2x + 1.
恒等式是一种对方程变量取任何值都成立的等量关系，常用三条横线的恒等号 ≡ 表示。例如 (x + 1)² ≡ x² + 2x + 1。
pression = no equal, Equation = equal, Identity = always identical. Remember the initial E's: Ex– (no), Eq– (balance), Id– (identical).
记忆挂钩：Expression（表达式）没有等号，Equation（方程）带等号，Identity（恒等式）始终相等。记住英文首字母联想：Ex- “出去”（排除等号），Eq- “平衡”（等号象征天平），Id- “同一性”。
2. Linear and Quadratic Terms | 线性与二次项
A linear expression has a variable raised only to the power of 1 and produces a straight line when graphed. For example, 2x + 7 is linear because the highest power of x is 1.
线性表达式中变量的最高指数为 1，画图时是一条直线。例如 2x + 7 是线性的，因为 x 的最高次幂是 1。
A quadratic expression contains a variable squared (power 2) as its highest power, like x² + 3x − 4. Its graph is a smooth U-shaped curve called a parabola.
二次表达式含有平方项（指数为 2）作为最高次幂，如 x² + 3x − 4。它的图像是一条平滑的 U 形曲线，称为抛物线。
The word 'quadratic' comes from the Latin 'quadratus' meaning 'square'. Think of the prefix 'quad-' as in 'quad bike' (4 wheels), but here it refers to the square of a variable, not the number 4.
Quadratic 一词源自拉丁语 “quadratus”，意为“正方形”。尽管前缀 “quad-” 让人想起 “quad bike”（四轮摩托车），但这里特指变量的平方，而非数字 4。
To quickly identify the type: look for the highest exponent. 1 means linear, 2 means quadratic.
快速区分的方法：看最高指数。指数为 1 是线性 (linear)，指数为 2 是二次 (quadratic)。
3. Inequalities | 不等式
≥ (greater than or equal to). It states that one side is not strictly equal to the other.
不等式使用 <（小于）、>（大于）、≤（小于等于）和 ≥（大于等于）等符号来比较两个表达式的关系，表明两边并不严格相等。
point is not included (< or >), while a closed circle means it is included (≤ or ≥).
在解不等式时，得到的解通常是一个数值范围，可在数轴上表示。空心圆表示端点不包含在内（对应 < 或 >），实心圆则表示端点包含在内（对应 ≤ 或 ≥）。
Memory tip: The inequality sign always "points" to the smaller number. Think of the greater side as the open mouth of a hungry crocodile that always wants to eat the bigger portion.
记忆技巧：不等号总是“指向”较小的数。可以把开口较大的一侧想象成饥饿的鳄鱼嘴巴，总是想吃更大的数。
For strict inequalities < and >, visualize a 'strict' bouncer who says 'you cannot come in' — the boundary is not allowed. For ≤ and ≥, the bouncer allows the boundary number to enter.
对于严格不等式 < 和 >，想象一位严格的保安说“你不能进来”——边界值不允许包含在内。对于 ≤ 和 ≥，保安允许边界值进入。
4. Sequences and the nth Term | 数列与第 n 项
A sequence is an ordered list of numbers following a rule. A term is each number in the sequence. The first term is often called T₁, the second T₂, and so on.
数列是按照某种规则排列的一列数字。项指数列中的每个数。第一项常记作 T₁，第二项 T₂，依此类推。
rence between consecutive terms, called the common difference d. For example, 5, 8, 11, 14… has d = 3.
等差数列中相邻两项的差是固定的，这个差称为公差 d。例如数列 5, 8, 11, 14… 的公差 d = 3。
The nth term formula for an arithmetic sequence is a + (n − 1)d, where a is the first term. In WJEC, you may also write it as dn + (a − d). This formula allows you to find any term without listing all previous ones.
等差数列的第 n 项公式为 a + (n − 1)d，其中 a 是首项。在 WJEC 考试中，也常写成 dn + (a − d)。有了这个公式，你无需列出前面所有项就能求出任意一项。
Memory trick: Think of 'd' as the 'difference' that you keep adding. The nth term is the first term plus (n−1) jumps of the common difference.
记忆窍门：把 d 想象成每次“跳跃”的相同步长 (difference)。第 n 项就是首项加上 (n−1) 次这样的跳跃。
5. Fractions, Decimals and Percentages | 分数、小数与百分比
A proper fraction has a numerator smaller than the denominator (e.g., ⅗). An improper fraction has a numerator larger than or equal to the denominator (e.g., ⁷⁄₄). A mixed number combines a whole number and a fraction (e.g., 1¾).
真分数的分子小于分母（如 ⅗）。假分数的分子大于或等于分母（如 ⁷⁄₄）。带分数由整数和分数共同表示（如 1¾）。
A terminating decimal is one that ends, such as 0.75. A recurring decimal has digits that repeat forever, like 0.333… (written as 0.3̇ in WJEC notation).
有限小数是指小数位数会停止的数字，如 0.75。循环小数是指小数部分有数字永远重复，如 0.333…（WJEC 记法中写作 0.3̇）。
'Percent' means 'out of 100'. Changing a fraction to a percentage means finding an equivalent fraction with denominator 100, or multiplying the decimal form by 100%.
“百分比”的意思是“每一百中的份数”。将分数转换成百分比，就是找到一个分母为 100 的等价分数，或者将小数乘以 100%。
Quick conversions to memorise: ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ¾ = 0.75 = 75%, ⅕ = 0.2 = 20%, ⅓ ≈ 0.333 = 33⅓%.
需要背记的快速转换：½ = 0.5 = 50%，¼ = 0.25 = 25%，¾ = 0.75 = 75%，⅕ = 0.2 = 20%，⅓ ≈ 0.333 = 33⅓%。
6. Ratio and Proportion | 比与比例
A ratio compares the relative sizes of two or more quantities. It is written as a : b (read as 'a to b'). Ratios have no units and can be simplified like fractions.
比用于比较两个或多个量之间的相对大小，写作 a : b（读作 “a 比 b”）。比没有单位，可以像分数一样化简。
Proportion describes a relationship where two quantities change at the same rate. If two quantities are in direct proportion, doubling one doubles the other. If they are in inverse proportion, doubling one halves the other.
比例描述两个量之间以相同速率变化的关系。如果两个量成正比，一个加倍另一个也加倍；如果成反比，一个加倍则另一个减半。
A unitary method is often used to solve ratio and proportion problems: find the value of one unit first, then scale up or down. Think 'Find one, then multiply'.
解决比和比例问题时常用归一法：先求出单一单位对应的值，再按所需倍数放大或缩小。记住“先求出一份，再相乘”。
among friends). Proportion = growing together (like two plants that always stay in sync).
记忆挂钩：比是关于“分配”的（想象给朋友分糖果）。比例是关于“同步增长”的（就像两株始终保持同步生长的植物）。
7. Angles and Shapes | 角与形状
An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is between 90° and 180°. A reflex angle is greater than 180° but less than 360°.
锐角小于 90°。直角等于 90°。钝角在 90° 到 180° 之间。优角（反射角）大于 180° 且小于 360°。
A polygon is a 2-D closed shape with straight sides. Regular polygons have all sides and angles equal. Irregular polygons do not.
多边形是由直线段围成的二维封闭图形。正多边形的所有边和角都相等，不规则多边形则不然。
Congruent shapes are identical in shape and size; they can be mapped onto each other by translation, rotation, or reflection. Similar shapes have the same shape but different sizes, with corresponding angles equal and sides in proportion.
全等图形在形状和大小上完全相同，可通过平移、旋转或镜面反射完全重合。相似图形形状相同但大小不同，对应角相等，对应边成比例。
Memory aid: 'Congruent' sounds like 'copy' — same copy. 'Similar' reminds you of 'similar' twins who look alike but are not exactly the same size.
记忆辅助：Congruent（全等）读音像 “copy”，指完全一样的副本。Similar（相似）让人联想到长相相似的双胞胎，他们很像但尺寸可能不同。
8. Transformations | 图形变换
A transformation changes the position or size of a shape. The four main types in WJEC are translation, reflection, rotation, and enlargement.
变换可以改变图形的位置或大小。WJEC 涉及的四种主要变换类型是：平移、镜面反射、旋转和放大。
Translation is sliding a shape without turning or flipping. It is described by a column vector (e.g., (3, −2)) showing the horizontal and vertical movements.
平移是将图形无翻转无旋转地滑动。平移可由一个列向量（如 (3, −2)）描述，表明水平和垂直移动的距离。
Reflection flips a shape over a mirror line. Every point and its image are the same perpendicular distance from the mirror line.
镜面反射是沿一条镜像直线翻转图形。原图形上的任意一点与其镜像点到镜像直线的垂直距离相等。
Rotation turns a shape about a centre of rotation through a given angle (90°, 180°, or 270°). Negative angles indicate clockwise turns, positive anticlockwise.
旋转是让图形绕一个旋转中心转过给定的角度（90°、180° 或 270°）。负角度表示顺时针旋转，正角度表示逆时针旋转。
Enlargement changes the size of a shape by a scale factor relative to a centre of enlargement. If the scale factor is greater than 1, the shape gets larger; if between 0 and 1, it gets smaller.
放大（缩放）是根据一个放大中心按照某个比例因子改变图形的大小。比例因子大于 1 时图形变大，介于 0 和 1 之间时图形缩小。
9. Pythagoras' Theorem | 勾股定理
Pythagoras' quares of the other two sides. This is written as a² + b² = c², where c is the hypotenuse.
勾股定理适用于直角三角形：斜边（直角所对的边）的平方等于另外两条直角边的平方和。可写作 a² + b² = c²，其中 c 为斜边。
The hypotenuse is always the longest side and is opposite the right angle. You can identify it by looking for the side that does not touch the right angle.
斜边始终是三角形中最长的一条边，位于直角的对面。找到不接触直角的边，就能确定斜边。
formula: a² = c² − b². Many students forget that you subtract when finding a leg, not add.
求直角边时需要对公式变式：a² = c² − b²。很多学生容易忘记，求直角边时要用减法而非加法。
Memory phrase: 'The square on the longest side equals the sum of the squares on the other two sides.' Visualise literal squares drawn on each side.
记忆口诀：“最长边上的正方形面积等于其他两边上正方形面积之和。”你可以想象在三角形每条边上画了实实在在的正方形。
10. Statistics: Averages and Spread | 统计：平均数与离散程度
The mean is the sum of all values divided by the number of values. It is the most commonly used average but can be affected by extreme values.
平均数（均值）是所有数值之和除以数值的个数。它是最常用的集中趋势量度，但容易受到极端值的影响。
The median is the middle value when data are arranged in order. If there is an even number of data values, the median is the mean of the two middle numbers.
中位数是将数据按顺序排列后位于中间的数值。如果数据的个数是偶数，中位数就是中间两个数的平均数。
The mode is the value that occurs most frequently. A data set can have one mode, more than one mode (bimodal), or no mode at all.
众数是出现频率最高的数值。一组数据可能有一个众数、多个众数（双众数），也可能没有众数。
The range is a simple measure of spread: largest value minus smallest value. It shows how spread out the data are.
极差（范围）是一个简单的离散程度量度：最大值减最小值。它能体现数据的分散程度。
Memory aid: Mean = average (think 'mean teacher averages your grades'), Median = middle (both start with 'med'), Mode = most (both start with 'mo').
记忆帮助：Mean（平均数）对应平均（想象一位严厉的老师计算你的平均分）；Median（中位数）对应中间（英文都以 'med' 开头）；Mode（众数）对应最多（英文都以 'mo' 开头）。
11. Probability Basics | 概率基础
Probability is a measure of how likely an event is to happen, expressed as a fraction, decimal, or percentage between 0 and 1 (or 0% and 100%). 0 means impossible, 1 means certain.
概率是用来衡量事件发生可能性的数值，常用分数、小数或百分比表示，取值在 0 到 1（或 0% 到 100%）之间。0 表示不可能发生，1 表示必然发生。
The sample space is the set of all possible outcomes. For a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间是指所有可能结果的集合。对于一个均匀的六面骰子，样本空间是 {1, 2, 3, 4, 5, 6}。
le outcomes / Total number of possible outcomes, assuming all outcomes are equally likely.
事件 A 的理论概率为 P(A) = 有利结果的数量 / 所有可能结果的总数，前提是每种结果出现的可能性相等。
Mutually exclusive events cannot happen at the same time. The sum of their individual probabilities gives the probability that one or the other occurs.
互斥事件不能同时发生。它们各自概率之和等于其中某个事件发生的概率。
Experimental probability is based on actual trials or experiments, while theoretical probability is based on equally likely outcomes. As the number of trials increases, experimental probability tends to approach theoretical probability.
实验概率是基于实际试验或实验得出的频率，而理论概率是基于等可能结果计算得出。随着试验次数增加，实验概率会越来越接近理论概率。
12. Coordinates and Straight Lines | 坐标与直线
The Cartesian coordinate system uses an x-axis (horizontal) and a y-axis (vertical). A point is written as (x, y). The origin is (0, 0).
平面直角坐标系由水平的 x 轴和竖直的 y 轴构成。一个点的坐标写作 (x, y)。原点为 (0, 0)。
is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
直线方程常写作 y = mx + c，其中 m 是斜率（坡度），c 是 y 轴截距（直线与 y 轴的交点）。
The gradient m is calculated as change in y divided by change in x, often remembered as 'rise over run'. A positive gradient slopes upwards, a negative gradient slopes downwards.
斜率 m 的计算方式为 y 的变化量除以 x 的变化量，常记作 “垂直变化 vs 水平变化” (rise over run)。斜率为正时直线向上倾斜，斜率为负时向下倾斜。
as equation x = constant, gradient undefined. These are exceptions to the y = mx + c form.
水平线的方程为 y = 常数，斜率为 0。垂直线的方程为 x = 常数，斜率无定义。它们都是 y = mx + c 形式的特例。
Memory tip: 'm' for mountain — how steep the line climbs. 'c' for crossing point — where the line cuts the y-axis.
记忆技巧：'m' 联想到 mountain（山），代表直线爬升的坡度；'c' 联想到 crossing（穿越点），表示直线与 y 轴的交点。
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