📚 Year 13 WJEC Maths: A Rapid Memorisation Guide to Key Vocabulary | Year 13 WJEC 数学：关键术语速记指南
Mastering the precise terminology of Year 13 WJEC Mathematics builds confidence and accuracy in exams. This guide covers the essential vocabulary from pure mathematics, statistics and mechanics, pairing clear English definitions with bilingual explanations and memory tips. Use it for quick revision, active recall, and to ensure you never lose marks through misinterpreting a keyword.
掌握 Year 13 WJEC 数学的精确术语，能为考试带来自信与准确。本指南涵盖了纯数学、统计和力学的核心词汇，将清晰的英文定义与双语解释和记忆技巧相结合。用它来快速复习、主动回忆，确保你不会因为误解关键词而失分。
1. Algebra and Functions | 代数与函数
A polynomial function has the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₀, with non‑negative integer powers. The highest power n is the degree.
多项式函数 形如 aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₀，指数为非负整数，最高次幂 n 称为次数。
The domain is the set of all possible input values (x), and the range is the set of all possible outputs (y). Think: domain = x going 'in', range = y coming 'out'.
定义域 是所有可能输入值 x 的集合，值域 是所有可能输出值 y 的集合。记住：定义域对应 x，值域对应 y。
A composite function fg(x) means apply g first, then f. Order matters – 'fog' is f of g.
复合函数 fg(x) 表示先作用 g 再作用 f。顺序很重要——fg 意味着 f(g(x))。
The inverse function graph is a reflection of y = f(x) in the line y = x. The domain of f⁻¹ is the range of f.
反函数 f⁻¹(x) 逆转 f 的作用；它的图像是 y = f(x) 关于直线 y = x 的对称。f⁻¹ 的定义域就是 f 的值域。
The modulus function |x| gives the absolute value, always non‑negative. Think 'mod = modify sign to positive'. It creates a V‑shaped graph.
模函数 |x| 返回绝对值，结果恒为非负。联想 “模 — 将符号修正为正”。图像呈 V 形。
For a quadratic ax² + bx + c, the discriminant the roots: Δ > 0 two distinct real roots; Δ = 0 one repeated root; Δ < 0 no real roots.
二次方程 ax² + bx + c 的判别式 Δ = b² − 4ac 决定根的性质：Δ > 0 两个不等实根；Δ = 0 一个重根；Δ < 0 无实根。
Partial fractions decompose an algebraic fraction into simpler fractions that are easier to integrate or expand. For repeated linear factors, include denominators up to the highest power.
部分分式 将一个代数分式分解为更简单的分式之和，便于积分或展开。遇到重复线性因子时，分母必须包含从一次到最高次幂的所有项。
2. Trigonometry | 三角学
Radian measure to radians, multiply by π/180. A radian is the angle subtended by an arc equal to the radius.
弧度制：π 弧度 = 180°。角度转弧度乘以 π/180。一弧度就是弧长等于半径时所对的圆心角。
θ and sector area A = ½r²θ, with θ in radians. Picture a pizza slice: area scales with r².
弧长公式 s = rθ，扇形面积 A = ½r²θ，θ 必须用弧度。想象披萨片：面积与 r² 成正比。
Reciprocal trig functions: secant secθ = 1/cosθ, cosecant cosecθ = 1/sinθ, cotangent cotθ = 1/tanθ. Mnemonic: third letter tells you the reciprocal of – sec → cos, cosec → sin, cot → tan.
倒数三角函数：正割 secθ = 1/cosθ，余割 cosecθ = 1/sinθ，余切 cotθ = 1/tanθ。记忆法：第三个字母提示它是谁的倒数—— sec 对 cos，cosec 对 sin，cot 对 tan。
sec²θ and 1 + cot²θ = cosec²θ. Derived from dividing sin²θ + cos²θ = 1 by cos²θ or sin²θ.
关键恒等式：1 + tan²θ = sec²θ 和 1 + cot²θ = cosec²θ，均可由 sin²θ + cos²θ = 1 除以 cos²θ 或 sin²θ 得到。
Compound angle formulae: sin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB. Notice the sign flip in cosine formulas.
和差角公式：sin(A±B) = sinA cosB ± cosA sinB；cos(A±B) = cosA cosB ∓ sinA sinB。注意余弦公式中的符号相反。
Double angle formulae 2cos²θ − 1 = 1 − 2sin²θ. These are used extensively in integration and solving equations.
倍角公式：sin2θ = 2 sinθ cosθ；cos2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ，在积分和解方程中广泛应用。
Expressing a sinθ + b cosθ in the form R sin(θ + α) or R cos(θ − α), where R = √a² + b². This simplifies finding maximum/minimum values and solving equations.
将 a sinθ + b cosθ 化为 R sin(θ + α) 或 R cos(θ − α) 的形式，其中 R = √a² + b²。这可以简化求最值和解方程的过程。
3. Calculus | 微积分
Differentiation from first principles: f ' = limₕ→₀ [f(x+h) − f(x)]/h. It reinforces that the derivative is the limit of a gradient.
从第一原理求导：f '(x) = limₕ→₀ [f(x+h) − f(x)]/h，强调导数就是割线斜率的极限。
Chain rule: dy/dx = (dy/du) × (du/dx). Think of it as peeling an onion – differentiate the outer function, then multiply by the derivative of the inner function.
链式法则：dy/dx = (dy/du) × (du/dx)。可以想象剥洋葱——先对外层函数求导，再乘以内层函数的导数。
Product rule: (uv)' = u'v + uv'. Quotient rule: (u/v)' = (u'v − uv')/v². For the quotient, remember the rhyme 'low d high minus high d low, square the bottom and away you go'.
乘法法则：(uv)' = u'v + uv'。除法法则：(u/v)' = (u'v − uv')/v²。记住口诀 “下导上不导减上导下不导，除以下平方”。
Implicit differentiation is used when y cannot be easily made the subject. Differentiate every term with respect to x, treating y as a function of x and adding dy/dx whenever differentiating y.
隐函数求导 用于 y 难以显式表示的情况。对 x 逐项求导，将 y 视为 x 的函数，每次对 y 求导时都要乘以 dy/dx。
For parametric curves x = f(t), y = g(t), the gradient is dy/dx = (dy/dt)/(dx/dt). Visualise as chain rule: dy divided by dx equals (dy/dt) divided by (dx/dt).
参数曲线 x = f(t), y = g(t) 的斜率为 dy/dx = (dy/dt)/(dx/dt)。可理解为链式法则：dy 除以 dx 等于 (dy/dt) 除以 (dx/dt)。
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