📚 Year 7 WJEC Further Maths: Vocabulary Memorisation Guide | 七年级 WJEC 进阶数学：词汇术语速记指南
Mastering new mathematical vocabulary can feel like learning a secret code. This guide breaks down the essential terms you will meet in Year 7 WJEC Further Maths, giving you clear explanations and clever memory tricks to make them stick.
掌握新的数学词汇有时就像学习一套密码。这份指南将为你拆解七年级 WJEC 进阶数学中会遇到的核心术语，提供清晰的解释和巧妙的记忆诀窍，帮助你牢牢记住它们。
1. Algebraic Expressions | 代数表达式
An algebraic expression uses letters, called variables, to stand for unknown numbers that can change. Think of the letter as an empty box waiting to be filled.
代数表达式用称为变量的字母来代表可以变化的未知数。把这些字母想象成一个等待被填满的空盒子。
A term is a single part of an expression, like 3x or 5. When terms are separated by '+' or '−' signs, each chunk counts as a separate term. For a quick memory aid, imagine each term as a separate piece of a jigsaw puzzle.
项是表达式中的一个单独部分，比如 3x 或 5。当各部分被 '+' 或 '−' 号隔开时，每一块都算作一个独立的项。为了方便记忆，可以把每一项想象成拼图的一块独立拼片。
| Expression | Terms | Memory Tip |
| 4a + 2b − 7 | 4a, 2b, −7 | Pieces of a sandwich: bread, filling, sauce |
| 表达式 | 项 | 记忆提示 |
| 4a + 2b − 7 | 4a, 2b, −7 | 三明治的组成部分：面包、馅料、酱汁 |
A coefficient is the number attached to the front of a variable. In 4a, the coefficient is 4. Remember it as the 'co-pilot' steering the variable.
系数是变量前面附带的数字。在 4a 中，系数是 4。把它记成“副驾驶”，负责引导变量。
2. Equations and Inequalities | 方程与不等式
An equation states that two expressions are equal, using the equals sign '=' y balanced seesaw. Whatever you do to one side, you must do to the other to keep it level.
方程是用等号 '=' 表示两个表达式相等的关系。你可以把它想象成一个完全平衡的跷跷板。对一边做的任何事情，都必须对另一边做同样的事以保持水平。
An inequality shows that one quantity is greater than or less than another. The wide-open mouth of the sign always points to the bigger number. Think of a hungry crocodile who always wants to eat the larger meal.
不等式表示一个量大于或小于另一个量。不等号张开的大口始终对着较大的数。想象一条饥饿的鳄鱼，它总想吃更丰盛的那份餐。
| Symbol | Meaning | Crocodile Says |
| x > 5 | x is greater than 5 | Mouth eats x |
| y < 10 | y is less than 10 | Mouth eats 10 |
| 符号 | 含义 | 鳄鱼说 |
| x > 5 | x 大于 5 | 嘴巴吃掉 x |
| y < 10 | y 小于 10 | 嘴巴吃掉 10 |
3. Sequences and Pattern Spotting | 序列与规律识别
A sequence is an ordered list of numbers that follows a rule. Each number in the sequence is called a term. To remember the difference between term-to-term and position-to-term rules, use the 'next-door' and 'street-address' trick: term-to-term tells you how to get from one neighbour to the next, while position-to-term gives the number for any house number.
序列是按照某种规则排列的一列有序数字。序列中的每一个数字都称为项。要记住递推规则和位置规则的区别，可以用“邻居”和“门牌”的窍门：递推规则告诉你如何从一位邻居走到下一位，而位置规则则给出任意门牌号对应的号码。
An arithmetic sequence adds or subtracts the same value each time. This constant difference is the common difference. Use the rhythm 'add d, add d, add d' like a drum beat to lock it in your memory.
等差数列每次加上或减去相同的值。这个不变的差值就是公差。用“加 d，加 d，加 d”的节奏像打鼓点一样把它刻进记忆里。
The nth term formula for a linear sequence is often written as:
nth term = dn + (a − d)
where d is the common difference and a is the first term. Think of d as the 'step size' and a as the 'starting number'.
线性序列的第 n 项公式通常写作：
第 n 项 = dn + (a − d)
其中 d 是公差，a 是首项。把 d 想象成“步长”，把 a 想象成“起始数”。
4. Coordinates and Straight-Line Graphs | 坐标与直线图形
A coordinate pair (x, y) tells you where a point sits on the grid. Remember to 'go along the corridor, then up the stairs': x first, then y. The horizontal axis is x, the vertical axis is y.
坐标对 (x, y) 告诉你点在网格上的位置。记住“先沿着走廊走，再上楼”：先 x 后 y。横轴是 x 轴，纵轴是 y 轴。
The equation of a straight line is often written as:
y = mx + c
where m stands for the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). A fun mnemonic is 'Moves x, Cuts y': m multiplies x and tells you how steep, c tells you where it cuts the y-axis.
直线方程通常写成：
y = mx + c
其中 m 代表斜率（陡峭程度），c 是 y 轴截距（直线与 y 轴交点的纵坐标）。一个有趣的口诀是“M 移动 x，C 切割 y”：m 乘以 x 决定倾斜度，c 告诉你直线与 y 轴相交的位置。
Parallel lines have exactly the same gradient. You can spot them because they never meet, just like railway tracks. Perpendicular lines intersect at right angles (90°) and their gradients multiply to give −1. Picture a capital 'T' to recall perpendicular.
平行线具有完全相同的斜率。你能认出它们，因为它们永不相交，就像铁轨一样。垂直线相交成直角（90°），它们的斜率乘积为 −1。回想大写字母“T”来记住垂直。
5. Angles and Lines | 角与线
Angles are measured in degrees (°). A full turn is 360°, a straight line is 180°, and a right angle is exactly 90°. To keep these values in mind, use the rhyme 'half a turn, flat and straight, 180 on the slate'.
角度以度（°）为单位。一整圈是 360°，一条直线是 180°，一个直角恰好是 90°。为了记住这些数值，可以使用口诀：“半圈翻转，平又直，石板上写 180。”
Acute angles are less than 90° — think of 'a cute little angle'. Obtuse angles are between 90° and 180° — 'obtuse' sounds like 'obese', so it is a bigger, wider angle. Reflex angles are between 180° and 360°, the 'reflex' of bending your arm back.
锐角小于 90°——想象一个“小巧可爱”的角。钝角在 90° 到 180° 之间——“钝”听起来像“胖”，因此它是一个较大、较宽的角。优角（反射角）在 180° 到 360° 之间，就如同把手臂向后弯的“反射”动作。
When two lines cross, vertically opposite angles are equal. Adjacent angles on a straight line sum to 180°. Around a point, angles sum to 360°. Use the phrase 'V for vertical, V for equal' to link vertically opposite angles to equality.
当两条直线相交时，对顶角相等。直线上相邻的角之和为 180°。围绕一个点的角之和是 360°。用“V 是 vertical，V 是 equal”这句话把对顶角与相等联系起来。
6. 2D Shapes and Symmetry | 二维图形与对称
A polygon is a closed flat shape with straight sides. The name comes from Greek: 'poly' means many, 'gon' means angle. Regular polygons have all sides equal and all angles equal; irregular ones do not.
多边形是由直边围成的封闭平面图形。这个名字来自希腊语：“poly”意思是多，“gon”意思是角。正多边形的所有边相等、所有角相等；不规则多边形则不然。
Line symmetry means you can fold the shape exactly in half. The fold line is called the line of symmetry. Rotational symmetry means the shape looks the same more than once during a full turn. A square has rotational symmetry of order 4. Think of spinning a badge on your shirt — it matches up four times in one rotation.
线对称意味着你可以将图形完全对折。折线叫做对称轴。旋转对称意味着图形在完整旋转一圈的过程中，不止一次地恢复原样。正方形的旋转对称阶数为 4。想象旋转你衬衫上的徽章——它旋转一圈会重合 4 次。
| Shape | Lines of Symmetry | Order of Rotational Symmetry |
| Equilateral Triangle | 3 | 3 |
| Square | 4 | 4 |
| Regular Pentagon | 5 | 5 |
| 图形 | 对称轴条数 | 旋转对称阶数 |
| 等边三角形 | 3 | 3 |
| 正方形 | 4 | 4 |
| 正五边形 | 5 | 5 |
7. Fractions, Decimals and Percentages | 分数、小数与百分数
the whole is split into). Picture a chocolate bar: denominator = total pieces, numerator = pieces you eat.
分数代表整体的一部分。上面的数是分子（你有几份），下面的数是分母（整体被分成多少等份）。想象一块巧克力：分母 = 总块数，分子 = 你吃掉的块数。
A terminating decimal ends after a finite number of digits, like 0.25. A recurring decimal has a pattern that repeats forever, marked with a dot or bar. Remember 'terminating terminates, recurring repeats'. Convert fractions to decimals by dividing the numerator by the denominator.
有限小数在小数点后有有限的位数，如 0.25。循环小数的小数位有永远重复的模式，用点或横线标出。记住“terminating 会终止，recurring 会重现”。分数化小数用分子除以分母。
Percentage means 'out of 100'. The symbol % has two zeros, reminding you of 100. To convert a decimal to a percentage, multiply by 100; to convert a fraction to a percentage, find an equivalent fraction with denominator 100, or multiply by 100.
百分数意为“每一百份中的几份”。符号 % 有两个圆圈，提醒你它和 100 有关。小数化百分数乘 100；分数化百分数则找分母为 100 的等价分数，或乘 100。
8. Data Handling and Statistics | 数据处理与统计
s the average found by adding all values and dividing by how many there are. Use the rhyme 'Mean, add them up, then split between the team'. The median is the middle value when data is ordered. Think 'median = middle, like the central reservation on a motorway'.
平均数（均值）是把所有数值加起来再除以个数得到的。用这句口诀：“平均数，加起来，团队里面分一分”。中位数是数据排序后的中间值。联想“median = 中间，就像高速公路上的中央隔离带”。
The mode is the value that appears most often — 'mode' sounds like 'most'. The range is the difference between the largest and smallest values, a measure of spread. A larger range means the data is more spread out.
众数是出现次数最多的值——“mode”听起来像“most”（最多）。极差是最大值和最小值之间的差，用来度量数据的分散程度。极差越大，数据越分散。
- Mean: sensitive to every value, good for symmetric data.
- Median: not affected by extreme values, good for skewed data.
- Mode: easy to find, useful for non-numerical data.
- 平均数：受每个值影响，适合对称数据。
- 中位数：不受极端值影响，适合偏态数据。
- 众数：容易找到，适合非数值数据。
9. Probability and Chance | 概率与机会
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). A probability of 0.5 means an even chance. Think of a number line: 0 is 'never', 1 is 'always', and 0.5 is 'maybe'.
概率用于衡量事件发生的可能性，范围从 0（不可能）到 1（必然发生）。概率为 0.5 表示机会均等。想象一条数轴：0 是“从不”，1 是“总是”，0.5 是“也许”。
ossible outcomes. An outcome is a single result. An event is a set of outcomes. The mantra 'All outcomes = sample space' helps you remember. When you roll a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间是所有可能结果的集合。结果是指单个结果。事件是一组结果的集合。口诀“所有结果 = 样本空间”能帮到你。当你掷一个均匀的六面骰子时，样本空间是 {1, 2, 3, 4, 5, 6}。
s / total number of outcomes. The fraction should always be as simple as possible. Imagine you are picking a red ball from a bag of coloured balls: count the reds, count the total, and simplify.
对于等可能的结果，概率 = 有利结果的数量 / 总结果数量。得到的分数应尽可能化简。想象你从一个装有彩色球的袋子里摸出一个红球：数出红球数量，数出总数，再化简。
10. Units, Length and Perimeter | 单位、长度与周长
(÷ 100) and milli- (÷ 1000). Use the ladder method: to go from a larger unit to a smaller, multiply; from smaller to larger, divide.
公制单位基于 10 的幂，因此换算很简单。关键的前缀有 kilo-（× 1000）、centi-（÷ 100）和 milli-（÷ 1000）。使用阶梯法：从大单位化为小单位要乘；从小单位化为大单位要除。
| Length | Conversion |
| 1 km = 1000 m | × 1000 |
| 1 m = 100 cm | × 100 |
| 1 cm = 10 mm | × 10 |
| 长度 | 换算 |
| 1 km = 1000 m | × 1000 |
| 1 m = 100 cm | × 100 |
| 1 cm = 10 mm | × 10 |
th + width). A simple walk-around-the-garden image works: imagine you are building a fence — you need the length of the entire boundary.
周长是围绕图形外缘的总长度。对于长方形，它是 2 ×（长 + 宽）。想象一个“绕花园走一圈”的画面：假设你要建一道篱笆——你需要整条边界的长度。
11. Ratio and Proportion | 比与比例
A ratio compares parts of a whole, using a colon. The order matters: a ratio of 2:3 is not the same as 3:2. A memory phrase is 'Ratio respects order — first comes first'.
比用冒号来比较整体的各部分。顺序很重要：2:3 和 3:2 不一样。一句记忆短句是“比尊重顺序——先说先写”。
Equivalent ratios are found by multiplying or dividing both sides by the same number. This is the same as finding equivalent fractions. When simplifying, divide by the highest common factor until you cannot go further. The simplified ratio 1:4 is in its simplest form.
等价比可以通过将两边同乘或同除相同的数得到。这与寻找等值分数的道理一样。化简时，除以最大公因数，直到不能再除为止。最简比 1:4 就是最简单的形式。
A proportion describes how one quantity changes in relation to another. If two amounts are in direct proportion, doubling one doubles the other. The twin-word 'double-double' reminds you of the effect.
比例描述一个量如何随另一个量变化。如果两个量成正比例，其中一个翻倍，另一个也会翻倍。用“一倍一倍”这个叠词来提醒自己这种效应。
12. Money, Finance and Time | 金钱、理财与时间
Profit is the money made after covering costs. Use the formula:
Profit = Selling price − Cost price
A loss happens when selling price is less than cost price. Visualise a shop: if you sell a toy for more than you paid, you gain; if less, you lose.
利润是收回成本之后赚的钱。使用公式：
利润 = 售价 − 成本价
当售价低于成本价时就会亏损。想象一家商店：如果你卖玩具的价格高于进价，你就赚钱；如果低于进价，你就亏本。
Discount is a reduction on the original price. A 20% discount means you pay 80% of the original. Break it into 'dis-count' — ated using I = PRT (Interest = Principal × Rate × Time). Repeat the letters like a beat: P‑R‑T.
折扣是在原价基础上的减价。20% 的折扣意味着你支付原价的 80%。把它拆成“dis‑count”——从原价往下减。单利计算用 I = PRT（利息 = 本金 × 利率 × 时间）。像打节拍一样重复这三个字母：P‑R‑T。
Time can be read on both 12‑hour and 24‑hour clocks. 24‑hour time avoids confusion between am and pm. A day has 24 hours, an hour has 60 minutes. The key conversion is: times after 12:00 noon add 12 to the hour to switch to 24‑hour format.
时间既可以用 12 小时制也可以用 24 小时制读取。24 小时制避免了上午和下午的混淆。一天有 24 小时，一小时有 60 分钟。关键换算是：中午 12:00 之后的时间，将小时数加上 12 即可转换为 24 小时制。
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