📚 Year 9 Edexcel Further Maths: Terminology Quick Memorisation Guide | 九年级爱德思进阶数学：词汇术语速记指南
Mastering the precise vocabulary of Further Mathematics is the first step towards solving problems with confidence. This guide breaks down essential Year 9 Edexcel terms into clear definitions, paired with memory aids to help you recall them swiftly during lessons and exams.
掌握进阶数学的精确词汇是自信解题的第一步。本指南将九年级爱德思课程的核心术语分解为清晰的定义，并配以记忆技巧，帮助你在课堂和考试中快速回想。
1. Algebraic Expressions | 代数表达式
A term is a single number, a variable, or numbers and variables multiplied together. For example, 5x, -3y, and 7 are all terms.
项是单个数字、单个变量或数字与变量的乘积。例如 5x、-3y 和 7 都是项。
A coefficient is the numerical factor in a term. In 4x², 4 is the coefficient.
系数是项中的数值因数。在 4x² 中，4 是系数。
A constant is a term without a variable, such as 9 in 3x + 9.
常数是不含变量的项，如 3x + 9 中的 9。
Like terms have identical variable parts; only like terms can be combined. 2x and -5x are like terms.
同类项具有完全相同的变量部分；只有同类项可以合并。2x 和 -5x 是同类项。
To expand means to remove brackets by multiplying each term inside by the factor outside. To factorise is the reverse — writing an expression as a product of its factors.
展开是通过将括号外的因数乘以括号内的每一项来去除括号。因式分解则相反——将表达式写成其因式的乘积。
Memory tip: Think of a term as a 'package' that stays together; a coefficient is the 'number label' on the package. Saying 'like terms, like family' helps you remember they can be grouped.
记忆提示：把项想象成一个保持完整的“包裹”；系数是包裹上的“数字标签”。记住“同类项，像家人”，意味着它们可以被归为一组。
2. Equations and Inequalities | 方程与不等式
An equation states that two expressions are equal, using the = sign. An inequality shows a relationship using <, >, ≤ or ≥.
方程用等号 = 表示两个表达式相等。不等式用 <、>、≤ 或 ≥ 表示大小关系。
The solution (or root) of an equation is the value that makes the equation true.
方程的解（或根）是使方程成立的数值。
Solving an equation means finding all its solutions. A linear equation has variables to the power of 1, while a quadratic equation contains a term like x².
解方程就是找出它的所有解。线性方程的变量次数为 1，而二次方程包含像 x² 这样的项。
When multiplying or dividing an inequality by a negative number, you must reverse the inequality sign.
当对不等式乘以或除以一个负数时，必须反转不等号。
Quick recall: 'Equal' means balance; an equation is a balanced scale. For inequalities, picture an open mouth of a crocodile eating the larger quantity.
快速记忆：“相等”意味着平衡；方程好比一架平衡的天平。对于不等式，想象一张张大的鳄鱼嘴正在吞食较大的量。
3. Coordinate Geometry | 坐标几何
A coordinate (x, y) gives a point's position on the Cartesian plane. The x-axis is horizontal, the y-axis vertical, and they intersect at the origin (0, 0).
坐标 (x, y) 给出点在笛卡尔平面上的位置。x 轴水平，y 轴垂直，它们相交于原点 (0, 0)。
The gradient (slope) of a line measures its steepness: m = (change in y) / (change in x).
直线的斜率（梯度）衡量其倾斜程度：m = (y 的变化量) / (x 的变化量)。
The intercept is where a line crosses an axis. The y-intercept occurs when x = 0.
截距是直线与坐标轴的交点。y 轴截距出现在 x = 0 时。
The midpoint of a segment is found by averaging the x‑coordinates and y‑coordinates: ((x₁+x₂)/2, (y₁+y₂)/2).
线段的中点通过将 x 坐标和 y 坐标分别取平均值得到：((x₁+x₂)/2, (y₁+y₂)/2)。
Memory aid: 'Gradient' and 'graph' both start with 'gr' — think of a graph going up a gradually steep hill. 'Intercept' sounds like 'interrupt' — the line interrupts the axis.
记忆辅助：“Gradient”和“graph”都以“gr”开头——想象图表沿山坡逐渐陡峭而上。“Intercept”听起来像“interrupt”——直线中断了坐标轴。
4. Sequences and Series | 数列与级数
A sequence is an ordered list of numbers. Each number is called a term, often denoted un or Tn.
数列是一列有序的数。每个数称为一个项，通常记作 un 或 Tn。
The nth term formula generates any term based on its position n.
第 n 项公式可以根据位置 n 生成任意一项。
An arithmetic progression (AP) increases or decreases by a fixed common difference d. A geometric progression (GP) multiplies by a fixed common ratio r.
等差数列 (AP) 按固定的公差 d 增加或减少。等比数列 (GP) 按固定的公比 r 相乘。
To quickly spot an AP, check if the differences are constant. For a GP, check if the ratio of consecutive terms is constant.
要快速识别等差数列，检查差是否恒定。对于等比数列，检查连续两项的比值是否恒定。
Memory tip: 'Arithmetic' has 'met' in the middle — think of adding a 'metre' repeatedly. 'Geometric' has 'metric' — think of multiplying by a 'metric' scale.
记忆提示：“Arithmetic”中间有“met”——想象重复增加“一米”。“Geometric”中有“metric”——想象乘以一个公制的刻度。
5. Sets and Logic | 集合与逻辑
A set is a collection of distinct objects, called elements. We write x ∈ A to say x is an element of set A.
集合是一组互不相同的对象，称为元素。我们写作 x ∈ A 表示 x 是集合 A 的元素。
A subset is a set whose elements all belong to another set: B ⊆ A. The universal set (ξ or U) contains all elements under consideration.
如果集合中所有元素都属于另一个集合，则它是子集：B ⊆ A。全集 (ξ 或 U) 包含所考虑的所有元素。
The empty set (∅) has no elements. Intersection (A ∩ B) contains elements in both sets; union (A ∪ B) contains elements in either set.
空集 (∅) 没有元素。交集 (A ∩ B) 包含同时在两个集合中的元素；并集 (A ∪ B) 包含至少在一个集合中的元素。
The complement of A (A') is everything in the universal set not in A.
A 的补集 (A') 是全集里不在 A 中的一切。
Visual aid: Use Venn diagrams — the overlap is intersection, the combined region is union, and the outside is complement. Link '∩' to 'and' both having the shape of an 'n', and '∪' to 'or' having the shape of a 'u'.
视觉辅助：使用文氏图——重叠区域是交集，合并区域是并集，外部是补集。把“∩”与“and”联系起来，两者都含字母 n 的形状；把“∪”与“or”联系起来，呈 u 的形状。
6. Functions | 函数
A function h input exactly one output. Notation: f(x) = 2x + 3. The set of all possible inputs is the domain; the set of outputs is the range.
函数是一种规则，为每个输入值指定唯一的输出值。记法：f(x) = 2x + 3。所有可能输入值的集合是定义域；输出值的集合是值域。
A mapping shows how inputs are linked to outputs. If each input has exactly one output, the mapping is a function.
映射表示输入如何与输出关联。如果每个输入恰好对应一个输出，这个映射就是函数。
An inverse function, f⁻¹(x), reverses the effect of f. A composite function combines two functions: (g ∘ f)(x) = g(f(x)).
反函数 f⁻¹(x) 逆转 f 的作用。复合函数是将两个函数组合：(g ∘ f)(x) = g(f(x))。
Memory trick: The domain is the 'door' through which values enter the function; the range is the 'roof' of possible results. The inverse 'undoes' the function, like unwrapping a gift.
记忆窍门：定义域是值进入函数的“门”；值域是可能结果的“屋顶”。反函数“撤销”原函数的作用，就像拆开礼物。
7. Matrices | 矩阵
A matrix is a rectangular array of numbers arranged in rows and columns. Each number is an element.
矩阵是按行和列排列的数字矩形阵列。每个数字是一个元素。
The order of a matrix is given as rows × columns. A 2 × 3 matrix has 2 rows and 3 columns.
矩阵的阶数表示为 行数 × 列数。2 × 3 矩阵有 2 行和 3 列。
The identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. For a 2 × 2 matrix, I =
单位矩阵 I 是一个方阵，主对角线上为 1，其余位置为 0。对于 2 × 2 矩阵，I =
| 1 | 0 |
| 0 | 1 |
The inverse matrix, A⁻¹, satisfies AA⁻¹ = I. The determinant of A = (a b; c d) is calculated as ad – bc. If the determinant is 0, the inverse does not exist.
逆矩阵 A⁻¹ 满足 AA⁻¹ = I。矩阵 A = (a b; c d) 的行列式计算为 ad – bc。如果行列式为 0，逆矩阵不存在。
Recall aid: 'Order' starts with 'O' for 'organisation' — describe matrix size like room dimensions (rows by columns). The identity matrix 'I' acts like multiplying by 1 in algebra; its inverse is the reciprocal.
记忆辅助：“Order”以“O”开头，代表“组织”——像描述房间尺寸那样描述矩阵大小（行乘列）。单位矩阵“I”就像代数中的乘 1；其逆矩阵就是倒数。
8. Transformations | 变换
A translation moves every point of a shape by the same vector. It is described as a shift (x + a, y + b).
平移将形状的每个点按相同向量移动。它被描述为位移 (x + a, y + b)。
A reflection flips a shape over a mirror line. The key words are 'reflect in the line y = x' or the x‑axis.
反射将形状沿一条镜面线翻转。关键术语为“关于直线 y = x 反射”或关于 x 轴反射。
A rotation turns a shape around a centre by a given angle, typically 90°, 180° or 270°. The direction can be clockwise or anticlockwise.
旋转将形状绕一个中心旋转给定角度，通常为 90°、180° 或 270°。方向可以为顺时针或逆时针。
An enlargement changes the size of a shape by a scale factor k from a centre of enlargement. If k > 1, it grows; if 0 < k < 1, it shrinks.
放大通过比例因子 k 从放大中心改变形状的大小。若 k > 1，形状变大；若 0 < k < 1，形状缩小。
Simple link: Translation is like sliding a book; reflection is its mirror image; rotation is spinning a wheel; enlargement is like a zoom lens.
简单联想：平移像是滑动一本书；反射是它的镜像；旋转如同转动轮子；放大就像变焦镜头。
9. Probability Terminology | 概率术语
An experiment is a repeatable process with observable results. Each possible result is an outcome.
试验是一个可重复的具有可观察结果的过程。每个可能的结果是一个结果。
An event is a set of one or more outcomes. The sample space is the set of all possible outcomes.
事件是一个或多个结果的集合。样本空间是所有可能结果的集合。
Probability ent = (number of favourable outcomes) / (total number of outcomes), often written as P(A).
事件的概率 = (有利结果的数目) / (结果的总数)，常写作 P(A)。
Events are mutually exclusive if they cannot happen at the same time. They are independent if one does not affect the probability of the other.
如果事件不能同时发生，则它们是互斥的。如果一个事件不影响另一个事件的概率，则它们相互独立。
Memory: 'Sample space' is like the full menu; an 'event' is your chosen dish. Mutually exclusive means 'cannot share the same plate'. Independence means the first course does not decide the dessert.
记忆：“样本空间”就像完整的菜单；“事件”是你选择的菜肴。互斥意味着“不能共享同一盘子”。独立意味着前一道菜不决定甜点。
10. Statistics Basics | 统计基础
| Term (术语) | Meaning (含义) | Memory Aid (记忆法) |
|---|---|---|
| Mean (平均数) | Sum of values divided by number of values. | 'Mean' is 'average' — both have 'a'. |
| Median (中位数) | Middle value when data is ordered. | 'Median' as in 'medium' — right in the middle. |
| Mode (众数) | Value that appears most often. | 'Mode' and 'most' both start with 'mo'. |
| Range (极差) | Largest value minus smallest value. | 'Range' sounds like 'change' — it measures spread. |
| Quartile (四分位数) | Values dividing data into four equal parts: Q1, Q2 (median), Q3. | 'Quart' as in quarter — four parts. |
| Interquartile range (IQR) (四分位距) | Q3 – Q1; measures spread of the middle 50%. | IQR = Inner Quartile Range — think of the 'inner half'. |
| Frequency (频数) | How often a value occurs. | 'Frequent' means often. |
| Histogram (直方图) | Diagram where area of bars represents frequency (for unequal widths, frequency density is used). | 'Histo' means tissue or web; a histogram is a visual web of bars. |
When you see 'average', check which measure is needed: mean for all data, median to avoid outliers, mode for most common. The range and IQR tell you about spread.
当你看到“平均”，确认需要哪个度量：平均数用到所有数据，中位数避免异常值影响，众数找出最常见。极差和四分位距告诉你分散情况。
11. Key Algebraic Operations: Expand, Factorise, Simplify | 关键代数运算：展开、因式分解、化简
These three words appear frequently. Simplify means to combine like terms and reduce an expression to its simplest form. For instance, 3x + 5x simplifies to 8x.
这三个词频繁出现。化简是指合并同类项并将表达式化为最简形式。例如，3x + 5x 化简为 8x。
Expand istributive law: a(b + c) = ab + ac. Double brackets use FOIL (First, Outer, Inner, Last).
展开是指使用分配律去除括号：a(b + c) = ab + ac。双括号使用 FOIL（先外内后）法则。
Factorise is the reverse process; it extracts a common factor or rewrites a quadratic as a product of two binomials. Always look for the highest common factor first.
因式分解是逆过程；它提取公因式或将二次式写为两个二项式的乘积。始终首先寻找最大公因式。
Tip: 'Simplify' — make it simple. 'Expand' — spread out. 'Factorise' — find the factors, like tearing down to building blocks.
提示：“Simplify”——使其简单。“Expand”——铺展开来。“Factorise”——找出因式，就像拆解回积木块。
12. Geometry Circle Terms | 几何圆术语
A quick overview of circle vocabulary often needed: radius (plural radii) — distance from centre to circumference. Diameter — twice the radius, passing through the centre.
快速回顾常需的圆术语：半径——圆心到圆周的距离。直径——两倍半径，通过圆心。
Chord — a line segment joining two points on a circle. Arc — part of the circumference. Sector — region between two radii and an arc. Segment — region between a chord and an arc.
弦——连接圆上两点的线段。弧——圆周的一部分。扇形——两条半径与一段弧围成的区域。弓形——一条弦与一段弧围成的区域。
A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.
切线与圆恰好在一个点接触，并在该点与半径垂直。
Memory: 'Arc' is part of 'arch'; 'sector' like a slice of pie; 'segment' is the piece cut off by a chord. The tangent just 'taps' the circle lightly.
记忆：“Arc”是“arch”的一部分；“sector”像一块派的切片；“segment”是被弦切下的一块。切线只是轻轻“拍”一下圆。
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