📚 Year 13 Edexcel Maths: A Rapid Vocab & Terminology Guide | Year 13 Edexcel 数学：词汇术语速记指南
Mastering mathematical vocabulary is essential for A Level success. This guide focuses on the key terms you will encounter in Year 13 Edexcel Pure, Statistics, and Mechanics. Each term is explained clearly in English and Chinese, with memory hooks to speed up your recall for exams.
掌握数学词汇是 A Level 成功的关键。本指南聚焦 Year 13 Edexcel 纯数、统计和力学中你将会遇到的核心术语。每个术语用清晰的中英双语解释，并配有记忆钩子，助你在考试中快速回忆。
1. Algebraic Expressions & Functions | 代数表达式与函数
Partial fractions: A technique for breaking a rational function into simpler ‘partial’ fractions to make integration or summation easier. Usually expressed as sum of terms like A/(ax+b).
部分分式：将一个有理函数分解成更简单的“部分”分式的技巧，以便于积分或求和。通常表示为像 A/(ax+b) 这样的项之和。
Modulus function |x|: Returns the absolute value or magnitude of x, ignoring its sign. It creates a V-shaped graph, representing distance from zero.
模函数 |x|：返回 x 的绝对值或大小，不考虑其符号。它产生 V 形图像，表示到零的距离。
Composite function fg(x): Applying one function to the result of another, read as ‘f of g of x’. The domain must be checked to ensure g(x) lies within f’s domain.
复合函数 fg(x)：将一个函数作用于另一个函数的结果，读作“f of g of x”。需检查定义域以确保 g(x) 的值在 f 的定义域内。
Inverse function f⁻¹(x): Reverses the effect of f(x). Graphically, it is a reflection in the line y = x. Only one-to-one functions have inverses.
反函数 f⁻¹(x)：逆转 f(x) 的作用。在图像上，它是关于直线 y = x 的反射。只有一一对应的函数才有反函数。
2. Coordinate Geometry & Graphs | 坐标几何与图像
Parametric equations: Represent x and y in terms of a third variable, t. They trace a curve as t varies. To find a Cartesian equation, eliminate the parameter t.
参数方程：用第三个变量 t 表示 x 和 y。随着 t 变化，它们描绘出一条曲线。要找到笛卡尔方程，需消去参数 t。
Asymptote: A line that a curve approaches infinitely closely but never touches. Vertical asymptotes occur where a rational function’s denominator is zero, horizontal ones relate to end behaviour.
渐近线：一条曲线无限接近但永远不会触及的直线。垂直渐近线出现在有理函数分母为零处，水平渐近线与末端行为有关。
Turning point: A point where the gradient changes sign, i.e., local maximum or minimum. Found by setting dy/dx = 0 and using the second derivative test to classify.
驻点：梯度改变符号的点，即局部极大值或极小值。通过令 dy/dx = 0 找到，并用二阶导数检验进行分类。
3. Sequences & Series | 数列与级数
Arithmetic sequence: A sequence with a constant difference d between consecutive terms. The nth term is a + (n-1)d, and the sum to n terms is Sₙ = n/2 (2a + (n-1)d).
等差数列：相邻项之间具有常数差 d 的数列。第 n 项为 a + (n-1)d，前 n 项和为 Sₙ = n/2 (2a + (n-1)d)。
Geometric sequence: A sequence with a constant ratio r between terms. The nth term is arⁿ⁻¹, and the sum to infinity exists if |r| < 1, given by S∞ = a/(1-r).
等比数列：项之间具有常数比 r 的数列。第 n 项为 arⁿ⁻¹，当 |r| < 1 时无穷和存在，为 S∞ = a/(1-r)。
Binomial expansion: Expressing (a+b)ⁿ as a sum of terms using binomial coefficients. For rational n, the expansion is infinite and valid for |x| < 1 in (1+x)ⁿ.
二项式展开：利用二项式系数将 (a+b)ⁿ 表示为各项之和。对于有理数 n，展开式是无穷的，且对 (1+x)ⁿ 在 |x| < 1 时成立。
4. Trigonometry | 三角学
Radian measure: An angle subtended by an arc equal in length to the radius. π radians = 180°, and it is essential for calculus with trig functions.
弧度制：弧长等于半径的弧所对的圆心角。π 弧度 = 180°，它对三角函数的微积分运算至关重要。
Secant, cosecant, cotangent: Reciprocal trig functions: sec x = 1/cos x, csc x = 1/sin x, cot x = 1/tan x. They appear in identities and calculus.
正割、余割、余切：倒数三角函数：sec x = 1/cos x，csc x = 1/sin x，cot x = 1/tan x。它们出现在恒等式和微积分中。
Harmonic form R sin(x ± α): Rewriting a sin x + b cos x as R sin(x + α) where R = √(a²+b²) and α = arctan(b/a). Useful for solving equations and finding maximums.
辅助角形式 R sin(x ± α)：将 a sin x + b cos x 重写为 R sin(x + α)，其中 R = √(a²+b²)，α = arctan(b/a)。用于解方程和求最大值。
5. Exponentials & Logarithms | 指数与对数
Natural logarithm ln x: The logarithm to base e, where e ≈ 2.71828. It is the inverse of eˣ, so ln(eˣ) = x and e^(ln x) = x.
自然对数 ln x：以 e 为底的对数，e ≈ 2.71828。它是 eˣ 的反函数，因此 ln(eˣ) = x 且 e^(ln x) = x。
Exponential growth model: A function of the form P(t) = P₀ e^(kt). If k > 0 it represents growth; if k < 0 it represents decay. Used in population and radioactive contexts.
指数增长模型：形式为 P(t) = P₀ e^(kt) 的函数。若 k > 0 表示增长；若 k < 0 表示衰减。用于人口和放射性环境。
Logarithmic differentiation: Taking ln of both sides before differentiating, helpful for complicated products, quotients, or functions of the form xˣ.
对数求导法：在求导前对等式两边取自然对数，对于复杂的乘除或形如 xˣ 的函数很有帮助。
6. Differentiation | 微分
Chain rule: If y = f(u) and u = g(x), then dy/dx = (dy/du) × (du/dx). Essential for differentiating composite functions like sin(2x).
链式法则：若 y = f(u) 且 u = g(x)，则 dy/dx = (dy/du) × (du/dx)。对 sin(2x) 这样的复合函数求导至关重要。
Product rule: For y = u v, dy/dx = u’ v + u v’. Used when two functions are multiplied. Keep the rhythm: derivative-first times second, plus first times derivative-second.
乘积法则：对于 y = u v，dy/dx = u’ v + u v’。当两个函数相乘时使用。记住节奏：导第一个乘第二个，加第一个乘导第二个。
Quotient rule: For y = u/v, dy/dx = (u’ v – u v’) / v². Best for rational functions where numerator and denominator are both non-constant.
商法则：对于 y = u/v，dy/dx = (u’ v – u v’) / v²。最适合分子分母都非常数的有理函数。
Implicit differentiation: Differentiating an equation where y is not explicitly solved. Treat y as a function of x and use chain rule on y terms, then solve for dy/dx.
隐函数微分：对一个未显式解出 y 的方程进行微分。将 y 视为 x 的函数并对 y 项使用链式法则，然后解出 dy/dx。
7. Integration | 积分
Integration by substitution: Reversing the chain rule. Replace part of the integral with u, change dx to du, integrate, and substitute back. Essential when a derivative of a function appears in the integrand.
换元积分法：链式法则的逆过程。用 u 替换积分的一部分，将 dx 转换为 du，积分后再代回。当被积函数中包含某函数的导数时至关重要。
Integration by parts: From the product rule, ∫ u dv = uv – ∫ v du. Use the LIATE rule to choose u (Log, Inverse trig, Algebraic, Trig, Exponential).
分部积分法：源自乘积法则，∫ u dv = uv – ∫ v du。利用 LIATE 规则选择 u（对数、反三角、代数、三角、指数）。
Definite integral: The signed area between a curve and the x-axis from a to b. It is evaluated using the Fundamental Theorem: ∫ₐᵇ f(x) dx = F(b) – F(a).
定积分：曲线与 x 轴之间从 a 到 b 的有符号面积。它使用基本定理计算：∫ₐᵇ f(x) dx = F(b) – F(a)。
Differential equation: An equation involving derivatives. Solving means finding the family of functions that satisfy it. In Year 13 you often separate variables: dy/dx = f(x)g(y) becomes ∫ 1/g(y) dy = ∫ f(x) dx.
微分方程：包含导数的方程。求解意味着找出满足它的函数族。在 13 年级你常使用分离变量法：dy/dx = f(x)g(y) 转化为 ∫ 1/g(y) dy = ∫ f(x) dx。
8. Vectors | 向量
Unit vector: A vector with magnitude 1, often used to represent direction. Found by dividing a vector by its magnitude: â = a/|a|.
单位向量：大小为 1 的向量，常用于表示方向。通过向量除以其模长得到：â = a/|a|。
Dot product (scalar product): a·b = |a||b| cos θ, where θ is the angle between vectors. If a·b = 0, the vectors are perpendicular. Used to find angles and for vector proofs.
点积（数量积）：a·b = |a||b| cos θ，其中 θ 是两向量夹角。若 a·b = 0，则向量垂直。用于求角度和向量证明。
Vector equation of a line: r = a + λ d, where a is a point on the line and d is the direction vector. λ is a scalar parameter.
直线的向量方程：r = a + λ d，其中 a 是直线上的一点，d 是方向向量。λ 是标量参数。
9. Kinematics (Mechanics) | 运动学（力学）
SUVAT equations: Constant acceleration formulae: v = u + at, s = ut + ½at², s = vt – ½at², s = ½(u+v)t, v² = u² + 2as. Applicable only in one direction with constant a.
SUVAT 方程：匀加速度公式：v = u + at, s = ut + ½at², s = vt – ½at², s = ½(u+v)t, v² = u² + 2as。仅适用于一个方向上有恒定加速度 a。
Variable acceleration: When acceleration changes with time, use calculus. Velocity v = ∫ a dt, displacement s = ∫ v dt, and a = dv/dt = d²s/dt².
变加速度：当加速度随时间变化时，使用微积分。速度 v = ∫ a dt，位移 s = ∫ v dt，且 a = dv/dt = d²s/dt²。
Displacement-time graph: Slope gives velocity. A negative slope indicates motion in the opposite direction. Curvature shows acceleration.
位移-时间图：斜率给出速度。负斜率表示反方向运动。曲率显示加速度。
10. Forces & Newton’s Laws | 力与牛顿定律
Resultant force: The single force that has the same effect as all forces acting on a particle. Found by vector addition, represented as components F = Fₓ i + Fᵧ j.
合力：与作用在质点上所有力效果相同的单个力。通过向量加法求得，用分量表示为 F = Fₓ i + Fᵧ j。
Resolving forces: Splitting a force into perpendicular components, typically horizontal and vertical. Makes equilibrium or motion calculations possible.
力的分解：将一个力拆分为垂直的分量，通常是水平和垂直分量。使平衡或运动计算成为可能。
Friction: A force opposing motion, Fₘₐₓ = μR, where μ is the coefficient of friction and R is the normal reaction. It acts parallel to the surface.
摩擦力：阻碍运动的力，Fₘₐₓ = μR，其中 μ 是摩擦系数，R 是法向反作用力。它平行于接触面作用。
Moment: The turning effect of a force about a pivot: moment = force × perpendicular distance. Equilibrium requires both resultant force zero and total moment zero.
力矩：力绕支点的转动效果：力矩 = 力 × 垂直距离。平衡要求合力为零且总力矩为零。
11. Statistical Distributions | 统计分布
Probability density function (PDF): For a continuous random variable, the area under the curve between a and b gives P(a ≤ X ≤ b). Total area = 1.
概率密度函数（PDF）：对于连续随机变量，曲线下 a 到 b 的面积给出 P(a ≤ X ≤ b)。总面积为 1。
Binomial distribution B(n, p): Models number of successes in n independent trials, each with success probability p. E(X) = np, Var(X) = np(1-p).
二项分布 B(n, p)：模拟 n 次独立试验中成功的次数，每次成功概率为 p。E(X) = np，Var(X) = np(1-p)。
Normal distribution N(μ, σ²): A bell-shaped continuous distribution defined by mean μ and variance σ². The standard normal Z = (X – μ)/σ allows use of tables for probability.
正态分布 N(μ, σ²)：由均值 μ 和方差 σ² 定义的钟形连续分布。标准正态 Z = (X – μ)/σ 便于使用表格查找概率。
12. Hypothesis Testing | 假设检验
Null hypothesis H₀: The statement being tested, usually assuming no effect or no difference. In a binomial test for proportion p it is H₀: p = claimed value.
零假设 H₀：被检验的陈述，通常假设无效应或无差异。在比例 p 的二项检验中为 H₀: p = 声称值。
Significance level α: The probability of rejecting H₀ when it is true. Typical values are 0.05 or 0.01. It defines the critical region.
显著性水平 α：当 H₀ 为真时拒绝 H₀ 的概率。通常取 0.05 或 0.01。它定义了拒绝域。
p-value: The probability of obtaining a result at least as extreme as the observed, assuming H₀ is true. If p-value < α, reject H₀.
p 值：假设 H₀ 为真时，获得至少等于观测值极端程度的概率。若 p 值 < α，拒绝 H₀。
Critical region: The set of values of the test statistic that leads to rejection of H₀. In a two-tailed test it is split into both tails.
拒绝域：导致拒绝 H₀ 的检验统计量取值集合。在双尾检验中，拒绝域分在两侧尾部。
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