📚 Edexcel Year 9 Further Maths: Key Vocabulary & Terminology Quick-Reference Guide | Year 9 Edexcel 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is just as important as solving problems. This guide provides the essential terms you will encounter in the Edexcel Year 9 Further Mathematics curriculum, explained clearly in both English and Chinese to help you memorise them faster and build a solid foundation for advanced topics.
掌握数学词汇与解题同样重要。本指南为你整理了 Edexcel Year 9 进阶数学课程中必会的核心术语，并用中英双语清晰解释，帮助你快速记忆，为学习更高阶内容打下坚实基础。
1. Basic Algebraic Terminology | 基础代数术语
Variable – A letter or symbol used to represent an unknown number or a quantity that can change.
变量 – 用字母或符号代表未知数或可变的数量。
Coefficient – The number placed in front of a variable to show how many times it is being multiplied. In 4x, the coefficient is 4.
系数 – 放在变量前面的数字，表示该变量被乘的次数。例如 4x 中系数为 4。
Constant – A value that does not change; a term without a variable.
常数 – 不发生变化的值；不含变量的项。
Term – A single number, variable, or the product of numbers and variables, separated by '+' or '−' in an expression.
项 – 单独的数字、变量，或数字与变量的积，在表达式中由 '+' 或 '−' 隔开。
Expression – A mathematical phrase made up of numbers, variables and operators, but without an equals sign.
表达式 – 由数字、变量和运算符组成的数学短语，不含等号。
Equation – A statement that two expressions are equal, shown by using an equals sign.
方程 – 表示两个表达式相等的关系，使用等号连接。
Identity – An equation that is true for all values of the variable, often written with the ≡ symbol.
恒等式 – 对变量的所有取值都成立的等式，常用 ≡ 符号表示。
Simplify – To collect like terms within an expression to make it as short as possible.
化简 – 合并表达式中的同类项，使其尽可能简短。
Expand – To remove brackets by multiplying each term inside by the factor outside.
展开 – 通过将括号外的因数与括号内每一项相乘来去掉括号。
Factorise – To write an expression as a product of its factors; the reverse process of expanding.
因式分解 – 将表达式写成其因子的乘积；与展开互为逆运算。
2. Equations and Inequalities | 方程与不等式
Linear equation – An equation where the highest power of the variable is 1, producing a straight line when graphed.
线性方程 – 变量的最高次幂为 1 的方程，图像是一条直线。
Quadratic equation – An equation where the highest power of the variable is 2, such as x² + 3x − 4 = 0.
二次方程 – 变量的最高次幂为 2 的方程，例如 x² + 3x − 4 = 0。
Solving – The process of finding the value (or values) of the variable that satisfy an equation.
求解 – 找出使方程成立的变量值的过程。
Root / Solution – A value that makes an equation true when substituted into the variable.
根 / 解 – 代入变量后使方程成立的值。
Inequality – A mathematical statement comparing two expressions using signs like <, >, ≤ or ≥.
不等式 – 使用 <、>、≤ 或 ≥ 符号比较两个表达式的数学语句。
Solution set – The range of values that satisfy an inequality, often shown on a number line.
解集 – 满足不等式的所有值的集合，常在数轴上表示。
3. Coordinate Geometry and Linear Graphs | 坐标几何与直线图
Coordinates – An ordered pair (x, y) that shows the exact position of a point on a grid.
坐标 – 表示网格上一个点准确位置的有序数对 (x, y)。
Origin – The point (0, 0) where the x-axis and y-axis intersect.
原点 – x 轴与 y 轴相交的点 (0, 0)。
Gradient – A measure of steepness of a line; often calculated as rise over run or (change in y) / (change in x).
梯度（斜率） – 直线倾斜程度的度量，通常用铅垂变化与水平变化之比计算：Δy / Δx。
y-intercept – The point where a line crosses the y-axis; its x-coordinate is always 0.
y 轴截距 – 直线与 y 轴相交的点，其 x 坐标恒为 0。
Midpoint – The point exactly halfway between two given points, found by averaging x- and y-coordinates.
中点 – 两点正中间的坐标，通过分别取 x 坐标和 y 坐标的平均值求得。
Line segment – A part of a straight line with two distinct endpoints.
线段 – 一条直线上两个不同端点之间的部分。
4. Sequences | 序列
Sequence – An ordered list of numbers that follows a specific pattern or rule.
序列 – 按特定模式或规则排列的一列有序数字。
Term – Each individual number in a sequence.
项 – 序列中的每个具体数字。
Term-to-term rule – A rule that tells you how to get from one term to the next in a sequence.
逐项规则 – 描述如何从一项得到下一项的规则。
Position-to-term rule (nth term) – A formula that allows you to find any term directly from its position number n.
位置规则（第 n 项） – 允许你直接从项的位置编号 n 求出该项数值的公式。
Arithmetic sequence – A sequence where the difference between consecutive terms is constant.
等差数列 – 相邻两项的差为常数的序列。
Geometric sequence – A sequence where each term is found by multiplying the previous term by a constant ratio.
等比数列 – 每一项由前一项乘以一个固定的比值得到的序列。
Fibonacci sequence – A sequence where each term is the sum of the two preceding terms (1, 1, 2, 3, 5, ...).
斐波那契数列 – 每一项都是前两项之和的序列（如 1, 1, 2, 3, 5, …）。
5. Pythagoras' Theorem and Trigonometry | 勾股定理与三角学
Hypotenuse – The longest side of a right-angled triangle, always opposite the right angle.
斜边 – 直角三角形中最长的边，始终对着直角。
Opposite – The side directly across from a given angle in a right-angled triangle.
对边 – 直角三角形中给定角正对的边。
Adjacent – The side next to a given angle that is not the hypotenuse.
邻边 – 直角三角形中给定角旁边且不是斜边的边。
Pythagoras' theorem – uare of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
勾股定理 – 直角三角形中，斜边的平方等于两条直角边的平方和：a² + b² = c²。
Sine (sin) – Trigonometric ratio: sin θ = Opposite / Hypotenuse.
正弦（sin） – 三角函数比：sin θ = 对边 / 斜边。
Cosine (cos) – Trigonometric ratio: cos θ = Adjacent / Hypotenuse.
余弦（cos） – 三角函数比：cos θ = 邻边 / 斜边。
Tangent (tan) – Trigonometric ratio: tan θ = Opposite / Adjacent.
正切（tan） – 三角函数比：tan θ = 对边 / 邻边。
Angle of elevation – The angle measured upwards from the horizontal line of sight to an object above.
仰角 – 从水平视线向上测量到上方物体的角。
Angle of depression – The angle measured downwards from the horizontal line of sight to an object below.
俯角 – 从水平视线向下测量到下方物体的角。
6. Measures, Perimeter, Area and Volume | 测量、周长、面积与体积
Perimeter – The total distance around the outside of a 2D shape.
周长 – 二维图形外边界的总长度。
Circumference – The perimeter of a circle.
圆周长 – 圆的周长。
Diameter – A straight line passing through the centre of a circle, touching two points on the circumference.
直径 – 通过圆心且两端在圆周上的直线段。
Radius – The distance from the centre of a circle to its circumference; half the diameter.
半径 – 从圆心到圆周的距离，等于直径的一半。
π (pi) – The constant ratio of a circle's circumference to its diameter, approximately 3.142.
π (圆周率) – 圆的周长与直径的恒定比值，约等于 3.142。
Area – The amount of space inside a 2D shape, measured in square units.
面积 – 二维图形内部空间的大小，以平方单位度量。
Volume – The amount of space a 3D object occupies, measured in cubic units.
体积 – 三维物体所占空间的大小，以立方单位度量。
Prism – A 3D solid with a constant cross-section along its length.
棱柱 – 横截面沿长度方向不变的直柱体。
Cross-section – The face you see when you cut through a solid at right angles to its length.
横截面 – 垂直于柱体长度方向切割后所看到的面。
7. Statistics and Data Handling | 统计与数据处理
Data – Collected facts or figures used for analysis.
数据 – 收集用于分析的事实或数字。
Mean – The average of a data set, calculated by summing all values and dividing by the number of values.
平均数（均值） – 数据集的平均值，将所有数值相加后除以数值个数。
Median – The middle value when the data is ordered from smallest to largest.
中位数 – 将数据从小到大排列后位于中间的值。
Mode – The value that appears most frequently in a data set.
众数 – 数据集中出现频率最高的值。
Range – A measure of spread: the difference between the largest and smallest values.
极差（范围） – 衡量数据分散程度的量：最大值与最小值的差。
Quartile – Values that divide an ordered data set into four equal parts; the lower quartile (Q1) and upper quartile (Q3).
四分位数 – 将有序数据集等分成四份的值，如下四分位数 (Q1) 和上四分位数 (Q3)。
Interquartile range (IQR) – The difference between the upper and lower quartiles; a measure of spread that ignores extremes.
四分位距 (IQR) – 上四分位数与下四分位数之差；一种剔除极端值的离散度量。
Scatter graph – A graph displaying pairs of values to reveal a possible relationship between two variables.
散点图 – 显示成对数值的图形，用于揭示两个变量之间可能存在的关系。
Correlation – The degree to which two variables are connected; can be positive, negative or none.
相关性 – 两个变量相互关联的程度，可分为正相关、负相关或无相关。
Outlier – A data point that lies far away from the general pattern of the data.
异常值 – 远离整体数据模式的个别数据点。
8. Probability | 概率
Outcome – A possible result of a probability experiment.
结果 – 概率试验中可能发生的结果。
Event – A set of one or more outcomes sharing a common property.
事件 – 具有共同属性的一组一个或多个结果。
Sample space – The set of all possible outcomes of an experiment.
样本空间
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