KS3 WJEC Further Maths: Vocabulary and Terminology Quick-Memorisation Guide | KS3 WJEC 进阶数学：词汇术语速记指南

📚 KS3 WJEC Further Maths: Vocabulary and Terminology Quick-Memorisation Guide | KS3 WJEC 进阶数学：词汇术语速记指南

Mastering the language of mathematics is the first step to thinking like a mathematician. This revision guide breaks down the essential terminology you will encounter in the KS3 WJEC Further Mathematics curriculum, pairing every term with a clear definition and a memory-friendly trick. Work through each section, and soon the words 'coefficient', 'hypotenuse' or 'standard form' will feel like old friends.

掌握数学的语言是像数学家一样思考的第一步。这份复习指南将你在 KS3 WJEC 进阶数学课程中会遇到的核心术语逐一拆解，每个术语都配有清晰的定义和便于记忆的小窍门。逐节学习，不久之后，'系数'、'斜边'或'标准形式'这些词语就会变得像老朋友一样熟悉。

1. Algebraic Expressions and Terminology | 代数表达式与术语

Variable: A symbol, usually a letter, that stands for a number we do not know yet. In an expression like 5x + 2, x is the variable – its value can vary.

变量： 一个符号，通常是字母，代表我们尚不知道的数字。在像 5x + 2 这样的表达式中，x 就是变量——它的值可以变化。

Constant: A fixed number that never changes its value. In 3y − 7, the number 7 is a constant.

常量： 一个数值固定不变的数字。在 3y − 7 中，数字 7 就是常量。

Coefficient: The number that multiplies a variable. In 4a, the coefficient of a is 4; in −2pq, the coefficient of pq is −2.

系数： 与变量相乘的数字。在 4a 中，a 的系数是 4；在 −2pq 中，pq 的系数是 −2。

Term: A single number, a variable, or numbers and variables multiplied together, separated by + or − signs. 2x², −5y and 7 are all separate terms.

项： 单个数字、单个变量，或数字与变量的乘积，由加号或减号隔开。2x²、−5y 和 7 都是独立的项。

Expression: A collection of terms without an equals sign, like 3x² + 2x − 4. Think of it as a mathematical 'phrase'.

表达式： 一组项的集合，不含等号，如 3x² + 2x − 4。可以把它想象成数学中的'短语'。

Equation: n : Two expressions linked by an equals sign, stating they are equal, e.g. 4x − 3 = 9. An equation is a full mathematical 'sentence'.

方程： 由等号连接的两个表达式，表示它们相等，例如 4x − 3 = 9。方程是一个完整的数学'句子'。

Formula: uation that shows a general rule or relationship, like A = lw for the area of a rectangle.

公式： 一种特殊的方程，展示通用的规则或关系，例如矩形面积公式 A = lw。

Expand: Multiplying out brackets to write an expression as a sum of terms. Expanding 2(x + 3) gives 2x + 6.

展开： 将括号相乘，把表达式写成若干项的和。将 2(x + 3) 展开得到 2x + 6。

Factorise: The reverse of expanding; rewriting an expression as a product of its factors. 6x + 9 factorises to 3(2x + 3).

因式分解： 展开的逆运算；将一个表达式写成它的因子的乘积。6x + 9 因式分解为 3(2x + 3)。

Memory trick: 'Expression' has no 'equals' – you just express a quantity. 'Equation' contains 'equa' for equal. 'Formula' is a little 'form' or recipe.

记忆窍门： '表达式'没有等号——你只是在表达一个量。'方程'中有'等'字。'公式'就像一个小小的配方。

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2. Solving Equations and Inequalities | 解方程与不等式

Solve: ues) of the variable that makes an equation true. When we solve x + 5 = 12, we find x = 7.

解： 找到使方程成立的变量的值。当我们解方程 x + 5 = 12 时，我们得到 x = 7。

Root / Solution: The numerical answer itself. 7 is the root of the equation x − 7 = 0.

根 / 解： 数值答案本身。7 是方程 x − 7 = 0 的根。

Inverse operation: The opposite operation. Addition and subtraction are inverses; multiplication and division are inverses. Squaring and square rooting are inverses.

逆运算： 相反的运算。加和减互为逆运算；乘和除互为逆运算。平方和开平方也互为逆运算。

Balance method: A way of solving equations by doing the same operation to both sides, like keeping a scale balanced. If you add 3 to the left, you must add 3 to the right.

平衡法： 通过对等式两边施加相同运算来解方程的方法，就像维持天平平衡一样。如果你在左边加 3，右边也必须加 3。

Inequality: ss than or equal to), ≥ (greater than or equal to). x > 4 means all numbers larger than 4.

不等式： 使用 < (小于)、> (大于)、≤ (小于等于)、≥ (大于等于) 等符号比较两个表达式的陈述。x > 4 表示所有大于 4 的数。

Solution set: The range of numbers that satisfy an inequality, often shown on a number line with an open or closed circle.

解集： 满足不等式的数的范围，通常用数轴上的空心或实心圆点表示。

Memory trick: The inequality symbol always 'eats' the larger number. The balance method is like a seesaw – you must sit equally on both sides to keep it level.

记忆窍门： 不等式符号总是'吃'掉更大的数。平衡法就像跷跷板——你必须在两边保持同样的行为，它才会平衡。

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3. Sequences and the nth Term | 数列与通项

Sequence: A list of numbers in a specific order, following a rule. 2, 5, 8, 11, ... is a sequence where we add 3 each time.

数列： 按特定顺序排列的一列数，遵循某种规则。2, 5, 8, 11, ... 是一个数列，每次加 3。

Term: Each individual number in a sequence. The first term is often written as U₁, the second as U₂.

项： 数列中的每个单独的数。第一项经常写作 U₁，第二项写作 U₂。

nth term: A formula that allows you to calculate any term directly without listing all the previous ones. For the sequence 5, 8, 11, 14, ..., the nth term is 3n + 2.

通项（第 n 项）： 一个让你能够直接计算任意一项，而不需要列出所有前面项的公式。对于数列 5, 8, 11, 14, ...，通项公式是 3n + 2。

Arithmetic sequence: led the common difference, often denoted by d. 4, 9, 14, 19, ... is arithmetic with d = 5.

等差数列： 相邻两项之差为常数的数列。这个常数称为公差，常用 d 表示。4, 9, 14, 19, ... 是一个公差为 5 的等差数列。

Linear sequence: Any arithmetic sequence; its nth term is of the form an + b, and its graph is a straight line.

线性数列： 任何等差数列；它的通项公式具有 an + b 的形式，其图像是一条直线。

Quadratic sequence (extension): A sequence where the second difference is constant. The nth term contains an n² term, e.g. n² + 1.

二次数列（拓展）： 二阶差分为常数的数列。它的通项中包含 n² 项，例如 n² + 1。

Memory trick: 'Arithmetic' sounds like 'add rhythm' – keep adding the same number. For the nth term, put n = 1 to check it gives the first term.

记忆窍门： '等差数列'就像在跳加法舞——你一直在加同一个数。对于通项公式，代入 n = 1 检查看看是否得到第一项。

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4. Ratio, Proportion and Rates | 比、比例和率

Ratio: A way to compare the sizes of two or more quantities. The ratio 3:2 means for every 3 parts of the first, there are 2 parts of the second.

比： 比较两个或以上数量大小的一种方式。3:2 意味着每 3 份第一个量，就有 2 份第二个量。

Proportion: A statement that two ratios are equal, or the comparison of a part to the whole. Often expressed as a fraction or percentage.

比例： 两个比相等的陈述，或部分与整体的比较。通常用分数或百分数表示。

Direct proportion: ease or decrease together at the same rate. If y is directly proportional to x, we write y ∝ x, and y = kx for some constant k.

正比例： 两个量以相同的比率一同增加或减少。如果 y 与 x 成正比，写作 y ∝ x，并且可表示为 y = kx，其中 k 是常数。

Inverse proportion: One quantity increases as the other decreases, so their product stays constant. y ∝ 1/x means y = k/x.

反比例： 一个量增加时另一个量减少，使得它们的乘积保持不变。y ∝ 1/x 表示 y = k/x。

Rate: A special ratio that compares two quantities with different units, such as speed (metres per second), density (grams per cm³) or unit price (pence per gram).

率： 一种特殊的比，比较具有不同单位的两个量，例如速度（米每秒）、密度（克每立方厘米）或单价（便士每克）。

Unitary method: A technique where you first find the value of one unit, and then multiply to find the required number of units. 'If 5 pens cost £2, one pen costs 40p.'

单位法： 一种先求出一个单位的值，再乘以需要的单位数的技巧。'若 5 支笔 2 英镑，一支笔 40 便士。'

Memory trick: 'Ratio' compares things side by side. 'Rate' has a 'time' flavour – think heart rate or speed. The unitary method is the 'down to 1, then up' approach.

记忆窍门： '比'是并列比较。'率'常带有时间的意味——想想心率或速度。单位法就是'先降到 1，再乘上去'的方法。

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5. Angles and Parallel Lines | 角度与平行线

Acute angle: An angle less than 90°. Obtuse angle: between 90° and 180°. Reflex angle: between 180° and 360°.

锐角： 小于 90° 的角。钝角：90° 到 180° 之间的角。优角：180° 到 360° 之间的角。

Right angle: Exactly 90°, often marked with a small square. Perpendicular lines meet at right angles.

直角： 恰好 90°，常标有小正方形符号。互相垂直的直线相交成直角。

Angles on a straight line: They always add up to 180°. Angles around a point sum to 360°.

平角： 直线上的角之和总是 180°。绕一点一周的角之和是 360°。

Vertically opposite angles: When two lines cross, the opposite pairs of angles are equal.

对顶角： 当两条直线相交时，相对的一对角相等。

Corresponding angles (F-shape): When a transversal cuts parallel lines, corresponding angles in matching corners are equal.

同位角（F 形）： 一条截线与平行线相交时，位于相同角落位置的一对角相等。

Alternate angles (Z-shape): Inside parallel lines, on opposite sides of the transversal, these angles are equal.

内错角（Z 形）： 在平行线内侧、截线两侧的一对角相等。

Co-interior angles (C-shape): Inside the parallel lines, on the same side of the transversal, they sum to 180°.

同旁内角（C 形）： 在平行线内侧、截线同侧的一对角，其和为 180°。

Interior and exterior angles of polygons: terior angle + exterior angle = 180°. For any polygon, the sum of exterior angles is 360°.

多边形的内角和外角： 内角 + 外角 = 180°。任何多边形的外角和都是 360°。

Memory trick: Imagine letters on the diagram: 'F' for corresponding, 'Z' for alternate, 'C' for co-interior (they need to Close to 180°). 'Acute' sounds like 'a cute' little angle.

记忆窍门： 想象图上的字母：'F' 代表同位角，'Z' 代表内错角，'C' 代表同旁内角（它们需要闭合到 180°）。'锐角'让你想起尖锐小巧的角。

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6. Perimeter, Area and Volume | 周长、面积与体积

Perimeter: The total distance around the outside of a 2D shape. For a rectangle it is 2(l + w). Think of a fence around a field.

周长： 二维图形外部一圈的总长度。对于矩形，是 2(长 + 宽)。可以想象是运动场周围的篱笆。

Area: The amount of surface a shape covers, measured in square units. A rectangle's area is length × width; a triangle's area is ½ × base × height.

面积： 一个图形所覆盖的表面大小，以平方单位计量。矩形的面积是长 × 宽；三角形的面积是 ½ × 底 × 高。

Circle geometry: Circumference = 2πr or πd; Area = πr². Here r is the radius and d is the diameter.

圆几何： 周长 = 2πr 或 πd；面积 = πr²。其中 r 是半径，d 是直径。

Composite shape: A shape made up of two or more simpler shapes. To find area, split it into rectangles, triangles or parts of circles and sum the areas.

复合图形： 由两个或以上较简单图形组成的形状。求面积时，将其分割为矩形、三角形或部分圆，再把面积加起来。

Volume: occupies, measured in cubic units (cm³, m³). Volume of a cuboid = length × width × height.

体积： 三维物体占据的空间，以立方单位（厘米³、米³）计量。长方体的体积 = 长 × 宽 × 高。

Prism: A solid with a uniform cross‑section along its length. Volume of a prism = area of cross‑section × length.

棱柱： 沿长度方向具有均匀横截面的立体。棱柱的体积 = 横截面积 × 长度。

Surface area: The total area of all the faces of a 3D shape. For a cuboid you add the areas of the six rectangles.

表面积： 三维图形所有面的总面积。求长方体表面积时，你把六个矩形的面积加起来。

Memory trick: 'Perimeter' has 'rim' inside – it's the rim of the shape. Area is what you'd need to carpet. Volume is what you'd fill with water. πr² sounds like 'pie

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