📚 Year 12 Edexcel Maths: Vocabulary & Terminology Quick Memorisation Guide | 爱德思12年级数学：词汇术语速记指南
Mastering key terminology is essential for success in Year 12 Edexcel Mathematics. Understanding the precise language of Pure, Statistics and Mechanics not only helps you interpret exam questions correctly but also allows you to communicate your reasoning with clarity. This guide presents the most important terms alongside simple memory aids, making them stick faster.
掌握关键术语是攻克爱德思12年级数学的基石。无论是纯数、统计还是力学，准确理解题目中的词汇才能规范作答、避免失分。本篇指南为你精选高频术语，配以中文释义和速记妙招，让记忆不再枯燥。
1. Algebraic Expressions and Equations | 代数表达式与方程
A coefficient is the number multiplying a variable. Think of ‘co-‘ (together) and ‘efficient’ (working) — the number that works together with the variable. In 7x, the coefficient is 7.
系数是乘在变量前的数字。速记：co- 表示“共同”，efficient 表示“有效的”，系数就是与变量共同起作用的数，如 7x 的系数是 7。
A variable is a symbol (usually a letter) that can take different values. Memory aid: ‘vary-able’ — able to vary. In 3y + 2, y is the variable.
变量是取值可变的符号，通常用字母表示。速记：vary-able，“能变的”。在 3y + 2 中，y 就是变量。
A term is a single mathematical unit in an expression, separated by + or − signs. Think of it as one ‘piece’ of the whole; just like a school term is one block of the year.
项是由加号或减号分隔的单个数学单元。速记：像学期一样，一个“项”是整体中的一块，例如 4x²、-3x 和 +5 分别是三项。
A polynomial is an expression with many terms. Break it down: ‘poly-‘ means many, and ‘-nomial’ comes from Latin ‘nomen’ (name/part) — so many parts.
多项式是由多个项构成的表达式。速记：poly- 多 + nomial 项 → 多项组成，如 x³ + 2x² – 5x + 1。
In a quadratic expression the highest power of x is 2. The word comes from the Latin ‘quadratum’ meaning square, because x² is a square term. x² + 3x – 4 is quadratic.
二次表达式中 x 的最高次是 2。速记：quadratic 源于“正方形”一词，x² 代表平方项，形如 ax² + bx + c。
The discriminant Δ = b² – 4ac tells you the nature of the roots for ax² + bx + c = 0. To memorise: ‘discriminant’ sounds like ‘discriminate’ — it helps you distinguish between two real, one repeated, or no real roots.
判别式 Δ = b² – 4ac 用于判断二次方程根的情况。速记：“判别”二字就是区分，Δ 能区分有两个不等实根、一个重根还是没有实根。
A root (or solution) of an equation is the x-value that makes the equation true, where the graph crosses the x-axis. Imagine a plant’s root touching the ground — the solution ‘touches’ the axis.
根（或解）是使方程成立的 x 值，也是图像与 x 轴的交点。速记：像树根扎入地面一样，根就是函数图像与 x 轴的接触点。
2. Functions and Graphs | 函数与图像
A function is a rule that maps each input x to exactly one output f(x). Picture a machine: you feed in x, it processes and spits out f(x).
函数是一种映射规则，每个输入 x 只对应一个输出 f(x)。速记：把函数想象成一台机器，放进 x，就得到唯一的 f(x)。
The domain is the set of all possible inputs for a function. Think ‘do-‘ as in ‘do main’ — the main x-values you are allowed to use.
定义域是函数所有可能输入的集合。速记：域里规定“你能用的 x”，就像领地一样。
The range is the set of all possible outputs f(x). After you run the x-inputs, the range is the ‘range’ of results you can get.
值域是函数所有可能输出的集合。速记：输入决定后，输出的“范围”就是值域，看 y 能取哪些值。
An asymptote is a line that a graph gets arbitrarily close to but never touches. Break it: a- (not) + sym- (together) + ptote (fall) — they never fall together. E.g. y = 1/x has asymptotes x = 0 and y = 0.
渐近线是图像无限接近但永不触及的直线。速记：a- 不 + sym 同 + ptote 落，永远不同时落下，即永不相交。如 y = 1/x 的渐近线是 x = 0 和 y = 0。
The gradient of a straight line measures its steepness, often the coefficient m in y = mx + c. Remember ‘grad’ like a grade of a slope — how steep the climb is.
斜率（梯度）衡量直线的倾斜程度，通常是 y = mx + c 中的 m。速记：grad 让人想到坡度分级，斜率就是爬坡的陡峭程度。
A tangent to a curve is a straight line that touches the curve at one point without crossing it (locally). The word tangent also means ‘touching’. In trigonometry, tan is related to a tangent line to the unit circle.
切线是与曲线在某一点“刚好接触”且不横向穿越的直线。速记：tangent 意为“触碰”，三角中的正切也与单位圆的切线有关。
3. Sequences and Series | 数列与级数
A sequence is an ordered list of numbers following a rule. Think ‘se-QUENCE’ like a sequence of events — one after another. An arithmetic sequence adds a fixed common difference d. Arithmetic operations are about adding/subtracting; that is why it adds d each time.
数列是按一定规则排列的一串数。速记：像事件发生的顺序，数一个接一个。等差数列每次加上固定的公差 d。算术运算是加减，所以等差就是反复加 d。
A geometric sequence multiplies by a fixed common ratio r. Geometric growth multiplies, just like geometric scaling. E.g. 2, 6, 18, … has r = 3.
等比数列每次乘以固定的公比 r。速记：几何级数的增长方式是乘法，正如几何相似放大，例 2, 6, 18 的公比是 3。
A series is the sum of the terms of a sequence. The sum to infinity for a convergent geometric series (|r|<1) is S∞ = a/(1 - r). Picture the total adding up smaller and smaller pieces until they settle at a finite limit.
级数是数列各项的和。当 |r|<1 时，无穷等比级数收敛，其无穷和为 a/(1 – r)。想象越来越小的块拼成一个有限总量，永远加下去也不会超过这个值。
4. Differentiation | 微分
Differentiation is the process of finding the derivative or gradient function f'(x). The derivative measures the instantaneous rate of change. Remember: differentiate means ‘tell the difference’ — you are finding how the function differs from point to point.
微分是求导数的过程，导数也称为梯度函数 f'(x)，表示瞬时的变化率。速记：differentiate 原义是“区分”，微分正是寻找函数在不同点的微小差异。
A stationary point occurs where f'(x) = 0, meaning the gradient is zero. These can be maximum, minimum or point of inflection. A point of inflection is where the tangent crosses the curve and the concavity changes.
当 f'(x) = 0 时出现驻点，梯度为零。驻点可以是极大值、极小值或拐点。拐点是切线穿越曲线且凹向改变的地方。
The chain rule is used to differentiate a function of a function: dy/dx = dy/du × du/dx. Think of it as a chain of derivatives linked together; you break the function into inner and outer parts.
链式法则用于复合函数求导。速记：像链条一样一环扣一环，dy/dx = dy/du × du/dx，把外层和内层拆开分别求导再相乘。
5. Integration | 积分
Integration is the reverse process of differentiation, often called the anti-derivative. The indefinite integral ∫ f(x) dx gives a family of functions plus a constant of integration +c. Think of it as ‘putting together’ the small changes to recover the original function.
积分是微分的逆运算，也称为反导数。不定积分 ∫ f(x) dx 得到一族函数并加上积分常数 +c。速记：把微小的变化“积”起来，恢复原来的函数。
A definite integral ∫ₐᵇ f(x) dx calculates the exact area between the curve and the x-axis from x = a to x = b. The limits a and b define the boundaries of the area. No +c is needed because the constant cancels.
定积分 ∫ₐᵇ f(x) dx 计算的是曲线下从 a 到 b 的精确面积。因为有上下限，常数 +c 会被抵消，所以不需要写积分常数。
6. Trigonometry | 三角学
Radian measure relates the arc length to the radius. One radian is the angle subtended when the arc length equals the radius. π rad = 180°. To memorise: a full circle has 2π radii along its circumference, so there are 2π radians in 360°.
弧度用弧长与半径的比值度量角。当弧长等于半径时所对的圆心角就是 1 弧度。整圆的周长是 2π 个半径，所以 360° = 2π rad。
The basic trigonometric ratios are sine, cosine and tangent. The key identity is sin²θ + cos²θ ≡ 1. Remember the word ‘SOHCAHTOA’ for right-angled triangles, and extend to the unit circle for all angles.
基本三角比是正弦、余弦和正切。核心恒等式为 sin²θ + cos²θ ≡ 1。速记：直角三角形用 SOHCAHTOA，单位圆可推广到任意角。
7. Vectors | 向量
A vector has both magnitude (size) and direction, whereas a scalar only has magnitude. The magnitude of vector a is written |a| or a. Think of a vector as an arrow: its length is magnitude, its orientation is direction.
向量既有大小又有方向，而标量只有大小。向量的模记为 |a|。速记：把向量想象成一支箭，箭的长度是模，指向是方向。
A unit vector has magnitude 1 and is often used to describe direction. The vectors i and j are unit vectors along the x- and y-axes. A position vector specifies the location of a point relative to the origin.
单位向量的模为 1，用来表示方向，如 i 和 j 分别是沿 x、y 轴的单位向量。位置向量则从原点指向某个点。
The resultant of two or more vectors is their sum. Graphically, it is the single vector that has the same effect as the combined vectors. Tip: the resultant ‘results’ from adding them together.
合向量是几个向量的和，可以起到完全等效的作用。速记：resultant 即“结果”，把它们加起来得到的结果。
8. Statistics: Data and Measures | 统计：数据与度量
The mean is the arithmetic average: sum of values divided by the number of values. Median is the middle value when ordered. Mode is the most frequent value. Think ‘Mean = average (Mean), Median = Middle, Mode = Most’ — all starting with M.
平均数是算术平均值：总和除以个数。中位数是排序后居中的值。众数是出现次数最多的值。速记：三个 M——Mean 平均，Median 中位，Mode 众数（Most frequent）。
The range (max − min) and interquartile range (IQR = Q₃ − Q₁) measure spread. The IQR focuses on the middle 50% of data. Variance is the average squared deviation from the mean; standard deviation is its square root. To memorise: standard deviation is the typical distance from the mean, variance is that value squared.
极差（最大值–最小值）和四分位距（IQR = Q₃ − Q₁）衡量离散程度。方差是各数据与均值偏差平方的平均，标准差是方差的平方根。速记：标准差就是与均值的“标准”距离，方差将它平方。
An outlier is an extreme value that lies far from the rest of the data. A common rule: any value below Q₁ − 1.5×IQR or above Q₃ + 1
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