📚 Year 13 OCR Maths: Quick Memorisation Guide to Key Terminology | Year 13 OCR 数学：关键术语速记指南
Mastering the vocabulary of Year 13 OCR Mathematics is just as important as solving the problems themselves. Whether you are tackling Pure, Statistics or Mechanics, a clear grasp of terminology helps you interpret questions correctly and communicate your reasoning in exams. This guide distils the most frequently tested terms across the syllabus and provides memorable hooks, word origins and visual cues to lock them into your long‑term memory.
掌握 Year 13 OCR 数学的词汇与解题本身同等重要。无论你面对的是纯数学、统计学还是力学，清晰理解术语将帮助你准确解读题意，并在考试中有条理地表达推理过程。这份指南提炼了考纲中最常出现的术语，并通过助记钩子、词源线索和视觉提示，帮助你把这些词汇转化为长期记忆。
1. Algebra & Functions Terminology | 代数与函数术语
Discriminant (Δ = b² – 4ac) – The discriminant of a quadratic ax² + bx + c tells us about the nature of its roots. Think of the word ‘discriminate’: it discriminates between two real distinct roots (Δ > 0), one repeated root (Δ = 0) and no real roots (Δ < 0). Remember the rhyme 'positive two, zero one, negative none'.
判别式 (Δ = b² – 4ac) – 二次函数 ax² + bx + c 的判别式揭示了根的性质。回想单词 ‘discriminate’ (区分)，它区分了三种情况：Δ > 0 两个不等实根，Δ = 0 一个重根，Δ < 0 无实根。记住口诀：“正二，零一，负零”。
Completing the square – Writing ax² + bx + c in the form a(x + p)² + q reveals the vertex of the parabola. The expression ‘complete the square’ is literal: you are making a perfect square trinomial. Use the phrase ‘half the x‑coefficient, square it, balance it’ to recall the procedure.
配方法 – 将 ax² + bx + c 写成 a(x + p)² + q 的形式，可以直接读出抛物线的顶点。字面上就是“完成平方”：取出 x 系数的一半，平方，然后平衡等式。记住顺口溜：“半系数，平方，再平衡”。
Modulus function |x| – The modulus gives the absolute value, essentially the distance from zero on the number line. Visualise it as ‘everything becomes positive’; the graph is a V‑shape. When solving equations, split into ± cases.
绝对值函数 |x| – 模长给出数的绝对值，可以理解为数轴上到零的距离。想象所有输入都变成正值，图像为 V 形。解方程时拆分成正负两种情形。
2. Trigonometry & Radians | 三角学与弧度
Radian (rad) – One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. The link between ‘radian’ and ‘radius’ is a built‑in reminder. Since the circumference is 2πr, a full circle contains 2π radians. For quick conversions, recall π rad = 180°.
弧度 (rad) – 一弧度是圆心角所对的弧长等于半径时的角度。“弧度 (radian)” 与 “半径 (radius)” 词形相近，是最好的提醒。圆周长为 2πr，因此一整圈为 2π 弧度。快速转换时记住 π rad = 180°。
CAST diagram – This quadrant diagram tells you which trig ratios are positive. Starting from the fourth quadrant (C for Cosine), moving anticlockwise: All, Sin, Tan, Cos. A mnemonic: ‘All Students Take Calculus’ or ‘CAST’ itself. Use it to find related acute angles.
CAST 象限图 – 用于判断各象限三角比的正负。从第四象限 (C 为余弦) 逆时针数：全正 (All)、正弦 (Sin)、正切 (Tan)、余弦 (Cos)。记忆口诀：“All Students Take Calculus” 或直接记 CAST。用它来寻找相关锐角。
Reciprocal trig functions – sec θ = 1/cos θ, cosec θ = 1/sin θ, cot θ = 1/tan θ. Notice the third letter: sec goes with cos, cosec with sin. Cot is the odd one out, related to tan. Think ‘co‑’ means complement, but here just pair them by the first letter for speed.
倒数三角函数 – sec θ = 1/cos θ，cosec θ = 1/sin θ，cot θ = 1/tan θ。观察第三个字母：sec 对应 cos，cosec 对应 sin。cot 是个例外，与 tan 相关。记忆技巧是快速配对首字母。
3. Exponentials & Logarithms | 指数与对数
Exponential function eˣ – The constant e ≈ 2.718 is Euler’s number, the unique base where the rate of growth equals the value itself. Think of ‘e’ as the natural choice for continuous growth. The derivative of eˣ is itself, an elegant property that links directly to ‘e’ for ‘easy calculus’.
指数函数 eˣ – 常数 e ≈ 2.718 是欧拉数，它是唯一增长率等于函数值本身的底数。把 e 想象为描述连续增长的自然之选。eˣ 的导数仍是自身，这一优雅性质让微积分变得更容易。
Natural logarithm ln x – ln x is the inverse of eˣ, so ln(eˣ) = x and e^(ln x) = x. ‘ln’ stands for logarithmus naturalis. A visual anchor: if eˣ takes you forward, ln x brings you back. Remember the key values: ln 1 = 0, ln e = 1.
自然对数 ln x – ln x 是 eˣ 的反函数，因此 ln(eˣ) = x 且 e^(ln x) = x。’ln’ 代表自然对数。形象记忆：若 eˣ 是前进，ln x 就是归途。关键值牢记：ln 1 = 0，ln e = 1。
Exponential growth/decay model – The general form A = A₀ e^(kt). If k > 0, it’s growth; if k < 0, decay. 'k' can be remembered as the 'konstant' that either fills up or drains out. The time constant is 1/|k|.
指数增长与衰减模型 – 一般形式 A = A₀ e^(kt)。k > 0 为增长，k < 0 为衰减。k 可以理解为“增长/衰减常数”。时间常数为 1/|k|。
4. Differentiation Terminology | 微分术语
Derivative f'(x) or dy/dx – The derivative measures the instantaneous rate of change, the gradient of a curve. A rough memory hook: ‘derive’ from the original function to get its slope function. The notation dy/dx reminds us it’s a small change in y over a small change in x.
导数 f'(x) 或 dy/dx – 导数衡量瞬时变化率，即曲线的斜率。粗略记忆：从原函数“导出”一个斜率函数。记号 dy/dx 直观表示为 y 的微小变化除以 x 的微小变化。
Chain rule – For y = f(g(x)), dy/dx = f'(g(x)) × g'(x). Think of peeling an onion: ‘derivative of the outside, keep the inside, then multiply by derivative of the inside’. A common mnemonic: ‘outer derivative × inner derivative’.
链式法则 – 对于 y = f(g(x))，dy/dx = f'(g(x)) × g'(x)。像剥洋葱一样：“外函数求导，保留内层，再乘内函数的导数”。口诀：“外导乘内导”。
Stationary points – Points where f'(x) = 0. They can be local maxima, local minima or points of inflection. The word ‘stationary’ suggests the graph is briefly still. Use the second derivative f”(x) to classify: positive → minimum, negative → maximum. If f”(x) = 0, check the sign change of f'(x).
驻点 – 满足 f'(x) = 0 的点。它们可能是极大值点、极小值点或拐点。“驻”字暗示图像在此处暂时停顿。用二阶导数 f”(x) 判别：f”(x) > 0 为极小值，f”(x) < 0 为极大值。若 f''(x) = 0，则需检查 f'(x) 的符号变化。
5. Integration Terminology | 积分术语
Indefinite integral ∫ f(x) dx – The reverse process of differentiation; it finds the family of antiderivatives. The symbol ∫ is an elongated S, standing for ‘sum’. Always add the constant of integration +c. Link the word ‘integrate’ with ‘entire’, as you bring parts together to restore the whole function.
不定积分 ∫ f(x) dx – 微分的逆运算，用来寻找原函数族。积分号 ∫ 是拉长的 S，代表“总和”。切勿遗漏积分常数 +c。将 ‘integrate’ 与 ‘entire’（完整的）关联，意味着将部分整合回整体。
Definite integral ∫ₐᵇ f(x) dx – Gives the net area between the curve and the x‑axis from a to b. Areas below the x‑axis count as negative. Think of the limits a and b as ‘doors’ that enclose the area. The Fundamental Theorem of Calculus connects it to the antiderivative: F(b) – F(a).
定积分 ∫ₐᵇ f(x) dx – 计算曲线与 x 轴在 a 到 b 之间的净面积。x 轴下方的面积为负。将上下限 a 和 b 想象成闭合面积的两扇“门”。微积分基本定理将定积分与原函数联系起来：F(b) – F(a)。
Integration by parts – Based on the product rule: ∫ u dv = uv – ∫ v du. The mnemonic ‘LIATE’ (Logarithmic, Inverse trig, Algebraic, Trig, Exponential) helps choose u. A simple chant: ‘u v minus swap and integrate’.
分部积分法 – 源于乘积法则：∫ u dv = uv – ∫ v du。口诀 ‘LIATE’ (对数、反三角、代数、三角、指数) 辅助选择 u。记忆歌谣：“u v 减去交换再积分”。
6. Sequences & Series | 数列与级数
Arithmetic progression (AP) – A sequence with a common difference d. The nth term is a + (n-1)d. Think ‘add’ – arithmetic has ‘add’ in its sound. Sum to n terms: Sₙ = n/2 [2a + (n-1)d]. The formula mimics ‘first + last × number of terms over 2’.
等差数列 (AP) – 具有公差 d 的数列。第 n 项为 a + (n-1)d。联想：“等差”意味着依次“加”一个固定差值。前 n 项和：Sₙ = n/2 [2a + (n-1)d]。公式可理解为（首项+末项）×项数÷2。
Geometric progression (GP) – A sequence with a common ratio r. The nth term is arⁿ⁻¹. The sum of the first n terms is a(1 – rⁿ)/(1 – r) for |r| < 1. A visual link: 'geo' like 'multiply by the ratio'. For infinite convergent GP (|r| < 1), S∞ = a/(1 - r).
等比数列 (GP) – 具有公比 r 的数列。第 n 项为 arⁿ⁻¹。前 n 项和为 a(1 – rⁿ)/(1 – r) (|r| < 1)。形象联想：“等比”即反复乘以同一比例。对于收敛的无穷等比级数 (|r| < 1)，S∞ = a/(1 - r)。
Binomial expansion – (1 + x)ⁿ = 1 + nx + n(n-1)x²/2! + … . For any rational n, valid for |x| < 1. Remember the pattern: 'n choose r' coefficients. The phrase 'binomial' means two terms, linking to the two parts (1 + x).
二项式展开 – (1 + x)ⁿ = 1 + nx + n(n-1)x²/2! + …，对任意有理数 n 成立，要求 |x| < 1。记住系数模式：“n 选 r”。‘binomial’ 本身意指两项，与 (1 + x) 的两个部分呼应。
7. Numerical Methods | 数值方法
Change of sign method – If f(a) and f(b) have opposite signs and f is continuous on [a,b], there is at least one root in the interval. A simple memory: ‘sign change guarantees a root’ – but only for continuous functions.
符号改变法 – 若 f(a) 与 f(b) 异号且 f 在 [a,b] 上连续，则该区间内至少存在一个根。简单记忆：“符号改变必有根”——但前提是函数连续。
Newton‑Raphson method – An iterative formula xₙ₊₁ = xₙ – f(xₙ)/f'(xₙ). It uses the tangent to hunt the root. Pronounce it as ‘Newton wraps on’ the curve. Visualise: you slide down the tangent until you hit the x‑axis. It converges quadratically when close to the root.
牛顿‑拉弗森法 – 迭代公式 xₙ₊₁ = xₙ – f(xₙ)/f'(xₙ)，利用切线逐步逼近根。想象沿着切线滑行直至与 x 轴相交。靠近根时具有二次收敛速度。
Cobweb diagram – A graphical way to visualise iterations like xₙ₊₁ = g(xₙ). Draw the curve y = g(x) and the line y = x. The path bounces between them. A ‘cobweb’ shape appears when converging. Remember: ‘cobweb’ catches the solution.
蛛网图 – 可视化迭代过程 (xₙ₊₁ = g(xₙ)) 的图示法。画出 y = g(x) 和 y = x，轨迹在两者之间弹跳。收敛时呈现“蛛网”形状。记忆：“蛛网”网住解。
8. Statistics: Distributions & Hypothesis Testing | 统计：分布与假设检验
Binomial distribution B(n, p) – Models the number of successes in n independent trials, each with probability p. ‘Bi‑’ means two outcomes. The parameter n is number of trials, p is success probability. Mean = np, variance = np(1-p). Use ‘binomial’ to think of ‘binary outcomes’.
二项分布 B(n, p) – 对 n 次独立试验中成功次数的建模，每次成功概率为 p。“二项”代表两种结果。参数 n 为试验次数，p 为成功概率。均值 = np，方差 = np(1-p)。由 ‘binary’ 联想二元结果。
Normal distribution N(μ, σ²) – The bell‑shaped continuous distribution defined by mean μ and variance σ². About 68% of data lies within 1σ, 95% within 2σ. Remember ‘normal’ because many natural phenomena follow it. Use the standardised value z = (x – μ)/σ.
正态分布 N(μ, σ²) – 由均值 μ 和方差 σ² 决定的钟形连续分布。约 68% 的数据落在 μ±σ，95% 落在 μ±2σ。记住“正态”即自然界中常见形态。使用标准化值 z = (x – μ)/σ。
Hypothesis testing vocabulary – Null hypothesis H₀: the default assumption (e.g. p = 0.5). Alternative hypothesis H₁: what you suspect (one‑tailed or two‑tailed). Significance level α: probability of rejecting H₀ when it is true (Type I error). The p‑value is the probability of obtaining a result at least as extreme as the observed one, assuming H₀ is true. A rhyme: ‘If p is low, H₀ must go.’
假设检验术语 – 原假设 H₀：默认假设 (如 p=0.5)。备择假设 H₁：怀疑的命题 (单尾或双尾)。显著性水平 α：当 H₀ 为真时拒绝它的概率 (第 I 类错误)。p 值是在 H₀ 为真的情况下，得到至少如观测值般极端结果的概率。口诀：“p 值小，H₀ 跑。”
9. Statistics: Correlation & Regression | 统计：相关与回归
Product moment correlation coefficient (PMCC, r) – Measures the strength and direction of a linear relationship between two variables. Values range from -1 to 1. r close to 1 means strong positive correlation, r close to -1 strong negative. Think ‘r for relationship’.
积矩相关系数 (PMCC, r) – 衡量两个变量间线性关系的强度和方向，取值范围 -1 到 1。r 接近 1 表示强正相关，接近 -1 表示强负相关。将 r 联想为 ‘relationship’。
Spearman’s rank correlation coefficient (rₛ) – Used when data is ranked or not linear. It assesses monotonic relationships. ‘Spearman’ sounds like ‘spear’ – it points to the direction of association. It’s based on the differences in ranks.
斯皮尔曼等级相关系数 (rₛ) – 用于等级数据或非线性关系，衡量单调相关。’Spearman’ 听起来像 ‘spear’ (矛)，指向关联方向。基于等级之差计算。
Least squares regression line – The line of best fit y = a + bx minimises the sum of squared residuals. The gradient b = Sxy/Sxx. ‘Least squares’ is a visual: we minimise the squares of the vertical distances. This line passes through the mean point (x̄, ȳ).
最小二乘回归直线 – 最佳拟合线 y = a + bx 使残差平方和最小。斜率 b = Sxy/Sxx。“最小二乘”形象地表示使垂直距离的平方之和最小。该直线必过均值点 (x̄, ȳ)。
10. Mechanics: Kinematics & Forces | 力学：运动学与受力
Displacement, velocity, acceleration – Displacement is a vector from origin to position (s). Velocity is the rate of change of displacement (v = ds/dt). Acceleration is rate of change of velocity (a = dv/dt). The ladder of motion: differentiate going down, integrate going up. ‘Acceleration’ has ‘accelerate’, imagine a car speeding up.
位移、速度、加速度 – 位移是从原点到位置的矢量 (s)。速度是位移的变化率 (v = ds/dt)。加速度是速度的变化率 (a = dv/dt)。运动阶梯：向下求导，向上积分。想象汽车加速来记 acceleration。
SUVAT equations – For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u+v)t, s = vt – ½at². The mnemonic ‘SUVAT’ stands for s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). Each equation misses one variable – the ‘menu’ approach: choose the equation that omits the unknown you don’t need.
SUVAT 方程 – 匀加速运动公式：v = u + at，s = ut + ½at²，v² = u² + 2as，s = ½(u+v)t，s = vt – ½at²。’SUVAT’ 分别代表位移 s、初速度 u、末速度 v、加速度 a、时间 t。每个方程忽略一个变量——采用“菜单法”：选择不包含多余未知量的方程。
Moment of a force – The turning effect: moment = force × perpendicular distance from pivot. The unit is Nm. If an object is in equilibrium, total clockwise moments = total anticlockwise moments. The phrase ‘moment matters’ reminds you it depends on the distance as well as the force.
力矩 – 力的转动效应：力矩 = 力 × 到支点的垂直距离，单位为 Nm。物体平衡时，顺时针力矩之和等于逆时针力矩之和。记住“力矩扣距离”，转动效果既看力也看力臂。
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