📚 WJEC Year 12 Maths: Quick Vocabulary Memorisation Guide | WJEC 12年级数学：词汇术语速记指南
Mastering the precise vocabulary of mathematics is crucial for understanding concepts, following examination instructions, and communicating solutions effectively in WJEC Year 12 Mathematics. This guide collects the essential terms from Pure Mathematics, Statistics and Mechanics, presenting each in English with a parallel Chinese explanation. Use it for quick daily review, self‑testing and reinforcing the language that underpins your AS‑level success.
掌握精确的数学词汇对于理解概念、遵循考试指令以及有效交流解题过程至关重要。本指南汇集了WJEC 12年级数学中纯数学、统计和力学的关键术语，每个术语先给出英文解释，再配以对应的中文阐述。你可以用它进行每日快速复习、自测，并巩固支撑你AS阶段成功的数学语言。
1. Functions and Graphs | 函数与图像
Function: A rule that assigns to each input exactly one output. Written as f(x), it maps elements from the domain to the range.
函数：一种将每个输入对应到唯一输出的规则，记作 f(x)，它将定义域中的元素映射到值域。
Domain: The set of all possible input values (x) for which a function is defined.
定义域：使函数有定义的所有可能输入值 (x) 的集合。
Range: The set of all possible output values (f(x)) that the function actually produces.
值域：函数实际产生的所有可能输出值 (f(x)) 的集合。
One‑one function: A function where each output comes from exactly one input. It passes both the vertical and horizontal line tests and has an inverse that is also a function.
一一对应函数：每个输出仅由唯一输入产生的函数。它同时满足垂直线检验和水平线检验，且其逆关系也是一个函数。
Inverse function: The reversal of a function, denoted f⁻¹(x), which maps outputs back to original inputs. It exists only if f is one‑one; its graph is the reflection of y=f(x) in the line y=x.
反函数：函数的逆，记作 f⁻¹(x)，将输出映回最初输入。仅当 f 为一一对应时才存在；其图像是 y=f(x) 关于直线 y=x 的反射。
Composite function: A combination of two functions where the output of one becomes the input of the other, written as fg(x) meaning f(g(x)).
复合函数：两个函数的组合，其中一个的输出作为另一个的输入，写法 fg(x) 表示 f(g(x))。
Graph transformations: Changes to the curve y=f(x) caused by replacing x with ax, x+a, or adding a to f(x), resulting in translations, stretches and reflections.
图像变换：通过将 y=f(x) 中的 x 替换为 ax、x+a，或对 f(x) 加减常数所引起的曲线变化，形成平移、拉伸和反射。
2. Algebra and Polynomials | 代数与多项式
Polynomial: An expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₁x + a₀, where n is a non‑negative integer and coefficients aᵢ are constants.
多项式：形如 aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₁x + a₀ 的表达式，其中 n 是非负整数，系数 aᵢ 为常数。
Degree of a polynomial: The highest power of the variable in the polynomial. For example, 3x⁴+2x²−1 has degree 4.
多项式的次数：多项式中变量的最高次幂。例如 3x⁴+2x²−1 的次数为 4。
Factor theorem: For a polynomial f(x), if f(a)=0 then (x−a) is a factor. Conversely, if (x−a) is a factor then f(a)=0.
因式定理：对于多项式 f(x)，若 f(a)=0 则 (x−a) 是其因式。反之，若 (x−a) 是因式，则 f(a)=0。
Remainder theorem: When a polynomial f(x) is divided by (x−a), the remainder is f(a).
余数定理：当多项式 f(x) 除以 (x−a) 时，余数等于 f(a)。
Discriminant: For the quadratic ax²+bx+c, the discriminant is b²−4ac. It determines the nature of the roots: two real distinct if >0, one real repeated if =0, and no real roots if <0.
判别式：对于二次式 ax²+bx+c，判别式为 b²−4ac。它决定根的性质：>0 有两个不等实根，=0 有一个重实根，<0 无实根。
Completing the square: Rewriting a quadratic in the form a(x+p)²+q to identify the vertex and solve equations.
配方法：将二次式改写为 a(x+p)²+q 的形式，以便确定顶点并求解方程。
Quadratic formula: The solutions to ax²+bx+c=0 are given by x = (−b ± √(b²−4ac)) / (2a).
二次公式：方程 ax²+bx+c=0 的解为 x = (−b ± √(b²−4ac)) / (2a)。
3. Differentiation | 微分
Derivative: The instantaneous rate of change of a function, denoted by f'(x) or dy/dx. It is defined as the limit of the gradient chord as h→0.
导数：函数的瞬时变化率，记作 f'(x) 或 dy/dx，定义为当 h→0 时弦的梯度之极限。
Differentiation from first principles: Using the limit definition f'(x)=limₕ→₀ [f(x+h)−f(x)]/h to find the derivative.
基本原理求导法：利用极限定义 f'(x)=limₕ→₀ [f(x+h)−f(x)]/h 来求导数。
Stationary point: A point on a curve where dy/dx=0. It can be a local maximum, a local minimum, or a point of inflection.
驻点：曲线上满足 dy/dx=0 的点，它可能是局部极大值、局部极小值或拐点。
Turning point: A stationary point where the gradient changes sign; it is either a maximum or a minimum.
转折点：梯度变号的驻点，即极大值点或极小值点。
Point of inflection: A point where the curve changes curvature (concavity) but may have non‑zero gradient. If dy/dx=0 it is a stationary point of inflection.
拐点：曲线改变弯曲方向（凹性）的点，但其梯度可以不为零。若 dy/dx=0，则为驻拐点。
Chain rule: Used to differentiate a composite function: if y=f(u) and u=g(x), then dy/dx = dy/du × du/dx.
链式法则：用于对复合函数求导：若 y=f(u) 且 u=g(x)，则 dy/dx = dy/du × du/dx。
Product rule: If y=u(x)v(x), then dy/dx = u·dv/dx + v·du/dx.
乘法法则：若 y=u(x)v(x)，则 dy/dx = u·dv/dx + v·du/dx。
Quotient rule: If y=u(x)/v(x), then dy/dx = (v·du/dx − u·dv/dx) / v².
除法法则：若 y=u(x)/v(x)，则 dy/dx = (v·du/dx − u·dv/dx) / v²。
4. Integration | 积分
Indefinite integral: The reverse of differentiation, giving a family of functions whose derivative is the integrand. It includes a constant of integration +C.
不定积分：微分的逆运算，得到一族函数，其导数等于被积函数。它包含积分常数 +C。
Definite integral: The integral with limits a and b, written ∫ₐᵇ f(x) dx. It represents the signed area between the curve and the x‑axis.
定积分：带有上下限 a 和 b 的积分，记作 ∫ₐᵇ f(x) dx。它表示曲线与 x 轴之间的带符号面积。
Constant of integration: The arbitrary constant C added when finding an indefinite integral, reflecting the loss of absolute position during differentiation.
积分常数：求不定积分时添加的任意常数 C，体现了微分过程中绝对位置信息的丢失。
Area under a curve: Calculated by the definite integral. Areas below the x‑axis give negative contributions, so total area often requires splitting the interval.
曲线下方区域：由定积分计算。x 轴下方的区域贡献负值，因此总面积通常需要分割积分区间。
Fundamental theorem of calculus: Connects differentiation and integration: if F'(x)=f(x), then ∫ₐᵇ f(x) dx = F(b)−F(a).
微积分基本定理：联系微分与积分：若 F'(x)=f(x)，则 ∫ₐᵇ f(x) dx = F(b)−F(a)。
Trapezium rule: A numerical method to approximate a definite integral using trapezia. With n strips, ∫ₐᵇ f(x) dx ≈ h/2 [y₀ + 2(y₁+y₂+…+yₙ₋₁) + yₙ].
梯形法则：用梯形近似定积分的数值方法。n 个条纹下，∫ₐᵇ f(x) dx ≈ h/2 [y₀ + 2(y₁+y₂+…+yₙ₋₁) + yₙ]。
5. Exponentials and Logarithms | 指数与对数
Exponential function: A function of the form y=aˣ, where a>0. The natural exponential function is y=eˣ, with e≈2.718.
指数函数：形如 y=aˣ 的函数，其中 a>0。自然指数函数为 y=eˣ，e≈2.718。
Natural logarithm: The logarithm to base e, written ln x. It is the inverse of eˣ, so ln(eˣ)=x and e^(ln x)=x for x>0.
自然对数：以 e 为底的对数，写作 ln x。它是 eˣ 的反函数，因此对 x>0 有 ln(eˣ)=x 及 e^(ln x)=x。
Laws of logarithms: Product: logₐ(xy)=logₐx+logₐy; Quotient: logₐ(x/y)=logₐx−logₐy; Power: logₐ(xⁿ)=n logₐx. These apply to any base, including ln.
对数运算法则：乘积：logₐ(xy)=logₐx+logₐy；商：logₐ(x/y)=logₐx−logₐy；幂：logₐ(xⁿ)=n logₐx。这些适用于任何底数，包括 ln。
Exponential growth/decay: Models using y=Ae^(kt) (growth if k>0, decay if k<0). They describe continuous change in populations, temperature or radioactive substances.
指数增长/衰减：使用 y=Ae^(kt) 建模（k>0 增长，k<0 衰减）。它们描述人口、温度或放射性物质的连续变化。
Solving exponential equations: Often take natural logs of both sides. For example, e^(2x)=5 becomes 2x=ln 5.
求解指数方程：常对两边取自然对数。例如 e^(2x)=5 变为 2x=ln 5。
6. Sequences and Series | 数列与级数
Arithmetic sequence: A sequence where the difference between consecutive terms is constant, known as the common difference d. The n‑th term is a+(n−1)d.
等差数列：相邻两项之差为常数的数列，该常数称为公差 d。第 n 项为 a+(n−1)d。
Arithmetic series: The sum of terms of an arithmetic sequence. Sₙ = n/2 [2a + (n−1)d] or n/2 (a+l).
等差级数：等差数列各项之和。Sₙ = n/2 [2a + (n−1)d] 或 n/2 (a+l)。
Geometric sequence: A sequence where each term after the first is found by multiplying the previous term by a fixed common ratio r. The n‑th term is arⁿ⁻¹.
等比数列：从第二项起，每一项均为前一项乘以固定公比 r 而得的数列。第 n 项为 arⁿ⁻¹。
Geometric series: Sum of a geometric sequence: Sₙ = a(1−rⁿ)/(1−r) for r≠1.
等比级数：等比数列的和：当 r≠1 时，Sₙ = a(1−rⁿ)/(1−r)。
Sum to infinity: For a geometric series with |r|<1, the infinite sum converges to S∞ = a/(1−r).
无穷和：对于 |r|<1 的等比级数，无穷和收敛于 S∞ = a/(1−r)。
Sigma notation: The Greek letter Σ used to represent a sum. Σ (from i=1 to n) uᵢ means u₁+u₂+…+uₙ.
求和符号 (Σ)：希腊字母 Σ 用于表示总和。Σ (i=1 到 n) uᵢ 意为 u₁+u₂+…+uₙ。
7. Statistics: Data and Probability | 统计：数据与概率
Mean: The arithmetic average of a set of data, calculated as Σx/n. It is a measure of central tendency.
平均数（均值）：一组数据的算术平均值，计算为 Σx/n，是集中趋势的度量之一。
Median: The middle value when data are arranged in order. For n even, it is the average of the two middle numbers.
中位数：将数据按顺序排列后居中的数值。当 n 为偶数时，取中间两数的平均值。
Mode: The most frequently occurring value(s) in a data set.
众数：数据集中出现次数最多的值。
Standard deviation: A measure of the spread of data about the mean. For a sample, s = √[ Σ(x−x̄)² / (n−1) ]. It is the square root of the variance.
标准差：衡量数据关于均值分散程度的指标。对于样本，s = √[ Σ(x−x̄)² / (n−1) ]，它是方差的平方根。
Variance: The square of the standard deviation, denoted σ² or s².
方差：标准差的平方，记作 σ² 或 s²。
Histogram: A diagram used for grouped continuous data. The area of each bar represents frequency, so bar height = frequency ÷ class width.
直方图：用于分组连续数据的图表。每个矩形的面积表示频数，因此条形高度 = 频数 ÷ 组距。
Probability of an event: A measure of likelihood between 0 and 1, defined as number of favourable outcomes / total number of outcomes for equally likely events.
事件的概率：介于 0 和 1 之间的可能性度量，对于等可能事件，定义为有利结果数 / 总结果数。
Mutually exclusive events: Two events that cannot occur at the same time. P(A∩B)=0 and P(A∪B)=P(A)+P(B).
互斥事件：不能同时发生的两个事件，满足 P(A∩B)=0，且 P(A∪B)=P(A)+P(B)。
Independent events: Occurrence of one does not affect the probability of the other. P(A∩B)=P(A)×P(B).
独立事件：一个事件的发生不影响另一个事件发生的概率，满足 P(A∩B)=P(A)×P(B)。
Binomial distribution: Models the number of successes in n independent trials, each with probability p of success. X~B(n,p) with P(X=r)=ⁿCᵣ pʳ (1−p)ⁿ⁻ʳ.
二项分布：对 n 次独立试验中成功次数的建模，每次试验成功概率为 p。X~B(n,p)，P(X=r)=ⁿCᵣ pʳ (1−p)ⁿ⁻ʳ。
8. Mechanics: Kinematics and Forces | 力学：运动学与力
Displacement: A vector quantity giving the distance in a specific direction from a reference point, measured in metres (m). It can be positive or negative.
位移：描述从参考点出发特定方向上的距离的矢量，单位为米(m)，可为正或负。
Velocity: Rate of change of displacement with respect to time, a vector quantity. v = ds/dt, measured in m·s⁻¹.
速度：位移相对于时间的变化率，是矢量，v = ds/dt，单位为 m·s⁻¹。
Acceleration: Rate of change of velocity with respect to time. a = dv/dt, measured in m·s⁻².
加速度：速度相对于时间的变化率，a = dv/dt，单位为 m·s⁻²。
SUVAT equations: Five equations for constant acceleration: v=u+at, s=ut+½at², s=½(u+v)t, v²=u²+2as, s=vt−½at², where s=displacement, u=initial velocity, v=final velocity, a=acceleration, t=time.
匀加速运动方程：用于匀加速运动的五个方程：v=u+at, s=ut+½at², s=½(u+v)t, v²=u²+2as, s=vt−½at²，其中 s=位移, u=初速度, v=末速度, a=加速度, t=时间。
Resultant force: The single force that has the same effect as all the forces acting on a particle. It is the vector sum of all forces.
合力：与作用在质点上的所有力效果相同的力，为所有力的矢量和。
Newton’s second law: The acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass: F=ma.
牛顿第二定律：物体的加速度与所受合力成正比，与质量成反比：F=ma。
Equilibrium: A state where the resultant force on a particle is zero, so it remains at rest or moves with constant velocity.
平衡：作用在质点上的合力为零的状态，因此质点保持静止或匀速直线运动。
9. Vectors | 向量
Vector: A quantity with both magnitude and direction, often written in bold or as an arrowed letter, or using i, j components.
向量：既有大小又有方向的量，常用粗体或带箭头字母书写，或用 i、j 分量表示。
Magnitude of a vector: The length of the vector, calculated for a=xi+yj as |a|=√(x²+y²).
向量的模：向量的长度，对于 a=xi+yj，|a|=√(x²+y²)。
Unit vector: A vector with magnitude 1, often denoted with a hat: â. The unit vector in the direction of a is a/|a|.
单位向量：模为 1 的向量，常加帽标 â。沿 a 方向的单位向量为 a/|a|。
Position vector: A vector that describes the location of a point relative to the origin. The position vector of point P(x,y) is r = xi+yj.
位置向量：描述点相对于原点位置的向量。点 P(x
Published by TutorHao | Year 12 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导