📚 Year 8 Edexcel Further Maths: Vocabulary & Terminology Quick Reference Guide | Year 8 Edexcel 进阶数学：词汇术语速记指南
Mastering mathematical language is the first step to solving problems with confidence. This guide covers the key terms you will meet in Year 8 Edexcel Further Maths, grouped into easy‑to‑review sections. Each term is explained in English and Chinese to help you build a solid bilingual foundation.
掌握数学语言是自信解题的第一步。本指南涵盖你在 Year 8 Edexcel 进阶数学中会遇到的关键术语，并按主题分组，方便复习。每个术语均用中英双语解释，帮助你打下扎实的双语基础。
1. Algebraic Expressions & Equations | 代数表达式与方程
Algebraic expression is a combination of numbers, letters and operation symbols without an equals sign, such as 3x + 2y − 5. An equation states that two expressions are equal, using ‘=’, for example 2x + 1 = 7.
代数表达式是由数字、字母和运算符号组成的式子，没有等号，例如 3x + 2y − 5。方程则用等号连接两个表达式，说明它们相等，如 2x + 1 = 7。
A variable (often x or y) represents an unknown number, while a coefficient is the number multiplying the variable, like the 3 in 3x. A constant term is a number on its own, such as −5.
变量（常为 x 或 y）代表未知数，系数是乘在变量前的数字，如 3x 中的 3。常数项是单独的数字，例如 −5。
When we simplify an expression we collect like terms: terms with exactly the same variable parts (e.g. 2x and 3x). Expanding brackets means multiplying each term inside by the term outside, while factorising is the reverse process.
化简表达式时，我们合并同类项：变量部分完全相同的项（如 2x 与 3x）。展开括号是将括号外的项乘以括号内的每一项，而因式分解是相反的步骤。
A linear equation has the variable raised only to the power of 1. To solve an equation we find the value of the variable that makes the statement true.
线性方程中变量的最高次数为 1。解方程就是求出使等式成立的变量值。
2. Indices & Standard Form | 指数与标准形式
An index (or exponent) tells you how many times a number, the base, is multiplied by itself. For example, in 5³, 5 is the base and 3 is the index, meaning 5 × 5 × 5.
指数（或幂）表示一个数（底数）自身相乘的次数。例如 5³ 中，5 是底数，3 是指数，表示 5 × 5 × 5。
The index laws help us work with powers efficiently: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, and (aᵐ)ⁿ = aᵐⁿ. Any number to the power 1 is itself, and any non‑zero number to the power 0 equals 1.
指数运算法则帮助我们高效处理幂：aᵐ × aⁿ = aᵐ⁺ⁿ；aᵐ ÷ aⁿ = aᵐ⁻ⁿ；(aᵐ)ⁿ = aᵐⁿ。任何数的 1 次方是其本身，任何非零数的 0 次方等于 1。
Standard form writes very large or very small numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. For instance, 3.2 × 10⁴ = 32 000.
标准形式将极大或极小的数写成 A × 10ⁿ，其中 1 ≤ A < 10，n 为整数。例如 3.2 × 10⁴ = 32 000。
Significant figures and decimal places are ways to round numbers. The first significant figure is the first non‑zero digit from the left.
有效数字和小数位数是舍入数字的方式。第一个有效数字是左边第一个非零数字。
3. Fractions, Decimals & Percentages | 分数、小数与百分数
A fraction has a numerator (top) and a denominator (bottom). Equivalent fractions represent the same value, like ½ and ²⁄₄. An improper fraction has a numerator larger than the denominator; a mixed number combines a whole number and a fraction.
分数由分子（上）和分母（下）组成。等价分数表示相同的值，如 ½ 和 ²⁄₄。假分数的分子大于分母；带分数由整数和分数组合而成。
To add or subtract fractions, write them with a common denominator. Multiplying fractions is straightforward: multiply numerators together and denominators together. Dividing by a fraction means multiplying by its reciprocal.
加减分数时要先化成公分母。分数乘法直接：分子相乘，分母相乘。除以一个分数等于乘以它的倒数。
A decimal is another way to show part of a whole. Terminating decimals end, while recurring decimals have a repeating pattern. Percentage means ‘out of 100’; to change a fraction to a percentage, multiply by 100.
小数是表示部分整体的另一种方式。有限小数会终止，循环小数有重复的数字。百分数表示“百分之几”；将分数化为百分数就是乘以 100。
4. Ratio & Proportion | 比与比例
A ratio compares two or more quantities, written as a:b. Ratios can be simplified by dividing all parts by a common factor, just like fractions. For example, 4:6 simplifies to 2:3.
比用于比较两个或多个量，写作 a:b。比可以通过将所有部分除以公因数来化简，和分数类似。例如 4:6 化简为 2:3。
Direct proportion means that as one quantity increases, the other increases at the same rate. The graph is a straight line through the origin. Unitary method finds the value of one unit first.
正比例指一个量增加时，另一个量以相同速率增加。其图像是一条通过原点的直线。单位法先求出单个单位的值。
A scale factor describes how much a shape is enlarged or reduced. In a recipe, ratios help adjust ingredient amounts using the multiplier.
比例因子描述图形放大或缩小的倍数。在食谱中，比可以利用倍数来调整配料用量。
5. Angles & Lines | 角与线
An angle is 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°.
角以度为单位。锐角小于 90°，直角恰好 90°，钝角在 90° 到 180° 之间，优角大于 180°。
When two lines cross, vertically opposite angles are equal. Adjacent angles on a straight line sum to 180°, and angles around a point sum to 360°.
两直线相交时，对顶角相等。一条直线上的邻角之和为 180°，绕点一周的角度之和为 360°。
Parallel lines never meet. When a transversal cuts them, we identify corresponding angles, alternate angles and co‑interior angles, which follow specific angle relationships.
平行线永不相交。一条截线穿过平行线时，会产生同位角、内错角和同旁内角，它们有着特定的角度关系。
6. Properties of 2D Shapes | 平面图形的性质
A polygon is a closed shape made of straight sides. Regular polygons have all sides and angles equal. Triangles are classified by sides: equilateral (3 equal sides), isosceles (2 equal sides), scalene (no equal sides).
多边形是由直边围成的封闭图形。正多边形的所有边和角都相等。三角形按边分类：等边三角形（3边相等）、等腰三角形（2边相等）、不等边三角形（无边相等）。
Quadrilaterals include square (4 equal sides, 4 right angles), rectangle (opposite sides equal, 4 right angles), parallelogram, rhombus, trapezium and kite.
四边形包括正方形（四边相等、四个直角）、长方形（对边相等、四个直角）、平行四边形、菱形、梯形和风筝形。
The sum of interior angles of an n‑sided polygon is (n−2) × 180°. The sum of exterior angles of any convex polygon is always 360°.
n 边形内角和为 (n−2) × 180°。任何凸多边形的外角和恒为 360°。
7. Perimeter, Area & Volume | 周长、面积与体积
Perimeter is the total distance around a shape. Area measures the space inside, expressed in square units. Key formulas: rectangle area = length × width, triangle area = ½ × base × height.
周长是图形一周的总长度。面积衡量图形内部的空间，以平方单位表示。关键公式：长方形面积 = 长 × 宽，三角形面积 = ½ × 底 × 高。
For a parallelogram, area = base × perpendicular height. For a trapezium, area = ½ × (a + b) × h, where a and b are the parallel sides. The circumference of a circle is πd or 2πr, and the area is πr².
平行四边形面积 = 底 × 垂直高。梯形面积 = ½ × (a + b) × 高，其中 a 和 b 是平行边。圆的周长为 πd 或 2πr，面积为 πr²。
Volume measures the space a 3D shape takes up, in cubic units. A prism has a constant cross‑section; its volume = area of cross‑section × length. Surface area is the total area of all faces.
体积衡量立体图形所占空间，以立方单位表示。棱柱的横截面不变；其体积 = 横截面积 × 长。表面积是所有面的面积之和。
8. Statistics: Averages & Charts | 统计：平均数与图表
The mean is the sum of values divided by the number of values. The median is the middle value when data is ordered. The mode is the most frequent value, and the range is the difference between the largest and smallest.
平均数（均值）是总和除以个数。中位数是排序后中间的值。众数是出现次数最多的值，极差是最大值与最小值的差。
A frequency table organises data with counts. A bar chart uses bars for categorical data; a pie chart shows proportions as sectors. Scatter graphs reveal correlation: positive, negative or none.
频数表用计数整理数据。条形图用条形表示分类数据；饼图以扇形显示比例。散点图揭示相关性：正相关、负相关或无相关。
A line graph shows trends over time, and a stem‑and‑leaf diagram keeps original values while showing shape. Remember: ‘stem’ is the leading digit(s), ‘leaf’ is the final digit.
折线图展示随时间变化的趋势，茎叶图保留原始数据同时显示分布形态。记住：“茎”是前导数字，“叶”是最后一位数字。
9. Probability | 概率
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). A probability experiment has outcomes; the set of all possible outcomes is the sample space.
概率衡量事件发生的可能性，范围从 0（不可能）到 1（一定）。概率实验产生结果；所有可能结果的集合称为样本空间。
The probability of an event is: number of favourable outcomes ÷ total number of outcomes. Mutually exclusive events cannot happen at the same time; their probabilities add up correctly.
事件概率 = 有利结果数 ÷ 总结果数。互斥事件不可能同时发生，其概率可直接相加。
Relative frequency is the number of times an event occurs divided by the number of trials — it estimates probability from experiment. The expected number of successes in n trials is probability × n.
相对频率是事件发生次数除以试验次数——通过实验估算概率。期望成功次数在 n 次试验中为概率 × n。
10. Sequences & Patterns | 数列与模式
A sequence is a list of numbers following a rule. An arithmetic sequence has a constant difference, called the common difference, between terms. The nth term formula lets you find any term without listing all previous ones.
数列是按规律排列的一列数。等差数列的项与项之间的差为常数，这个差称为公差。第 n 项公式让你无需列出前面所有项即可求出任意一项。
For a sequence with first term a and common difference d, the nth term is a + (n−1)d. Term‑to‑term rule tells you how to get from one term to the next; position‑to‑term rule (nth term) links the position number directly to the value.
对于首项为 a、公差为 d 的等差数列，第 n 项为 a + (n−1)d。项间递推规则说明如何从一项得到下一项；位置公式（第 n 项）直接将位置序号与数值挂钩。
Triangular numbers (1, 3, 6, 10, …) are an example of a sequence generated by adding consecutive integers. Square numbers and cube numbers are also common patterns to recognise.
三角形数（1, 3, 6, 10, …）是通过连续整数相加生成的数列例子。平方数和立方数也是需要识别的常见模式。
11. Transformations & Symmetry | 变换与对称
A transformation changes the position or size of a shape. Translation slides a shape by a vector; reflection flips it across a mirror line; rotation turns it around a centre by an angle; enlargement changes its size by a scale factor.
变换改变图形的位置或大小。平移通过向量滑动图形；反射让图形沿镜面线翻转；旋转绕中心点转动一定角度；放大通过比例因子改变大小。
A shape has line symmetry if you can fold it along a line so that the two halves match. Rotational symmetry is when a shape looks the same more than once in a full turn; the order tells how many times.
若图形可沿一条线对折使两部分重合，则它具有线对称（轴对称）。旋转对称指图形在旋转一圈内会与自己重合多次；重合次数称为对称阶数。
The column vector for a translation shows horizontal and vertical movement: (x above y). A mirror line can be described with an equation, e.g. x = 2 or y = x.
平移的列向量表示水平和垂直移动量，形式为 (x 在上，y 在下)。镜面线可用方程描述，如 x = 2 或 y = x。
12. Coordinates & Graphs | 坐标与图像
The Cartesian plane has an x‑axis (horizontal) and y‑axis (vertical). A point is located by its coordinates (x, y). The origin is (0, 0).
笛卡尔坐标平面有 x 轴（水平）和 y 轴（垂直）。一个点由其坐标 (x, y) 确定位置。原点为 (0, 0)。
A linear graph is a straight line with equation y = mx + c, where m is the gradient (slope) and c is the y‑intercept. To find the gradient, use: (change in y) ÷ (change in x).
一次函数图像是一条直线，方程为 y = mx + c，其中 m 是斜率，c 是y 轴截距。斜率计算方法为：y 的变化量 ÷ x 的变化量。
Parallel lines have the same gradient. To find the midpoint of a line segment, average the x‑coordinates and average the y‑coordinates.
平行直线的斜率相等。求线段的中点，只需将两端点的 x 坐标取平均，y 坐标取平均。
Quadratic graphs are U‑shaped (parabolas); a cubic graph has an S‑like shape. Substituting x‑values into an equation generates a table of values for plotting.
二次函数图像呈 U 形（抛物线）；三次函数图像呈 S 形。将 x 值代入方程可生成用于绘图的数值表。
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