GCSE Cambridge Additional Mathematics: Key Terminology Memorisation Guide | GCSE Cambridge 进阶数学：词汇术语速记指南

📚 GCSE Cambridge Additional Mathematics: Key Terminology Memorisation Guide | GCSE Cambridge 进阶数学：词汇术语速记指南

Mastering the specialised vocabulary of Cambridge IGCSE Additional Mathematics (0606) is essential for understanding questions and expressing solutions precisely. This guide pairs each key term with a simple memory hook or mnemonic, helping you build fluency fast. Every entry is bilingual – read the English explanation first, then the Chinese – so you can anchor the meaning in both languages.

掌握剑桥IGCSE进阶数学（0606）的专业词汇是理解题意和精准表达解题过程的关键。本指南为每个核心术语配上了简易记忆法或助记句，帮助你快速积累专业表达。每一条均为中英双语——先读英文解释，再读中文——让您在两种语言中同时扎根。

1. Algebraic Fundamentals | 代数基础

A term is a single mathematical entity separated by + or − signs. Think of a term as a ‘word’ in the language of algebra. The number in front is the coefficient, which literally ‘co-operates’ with the variable.

项是由加号或减号分隔而成的单个数学单位。将项想象成代数语言中的“单词”。前面的数字是系数，字面意思即与变量“共同起作用”。

Like terms share the same variable powers – they are ‘alike’ and can be combined. When we expand, we distribute multiplication over addition: picture expanding a compressed file to see all its parts.

同类项具有相同的变量及指数——它们“相似”，可以合并。展开就是把乘法分配到加法上：想象解压一个压缩文件，看到其中的全部内容。

Factorisation reverses expansion. The word contains ‘factor’ – look for what the terms have in common, just as a factory assembles common parts. A quadratic expression is a polynomial of degree 2; ‘quad’ reminds you of square, though it refers to the second power.

因式分解是展开的逆运算。这个词含有“因子”——寻找各项共有的部分，正如工厂把公用零件组合起来。二次表达式是最高次数为2的多项式；“quad”指向方形，尽管它指代的是二次幂。

2. Equations & Inequalities | 方程与不等式

A quadratic equation has the form ax² + bx + c = 0. The discriminant (Δ = b² − 4ac) ‘discriminates’ between real and complex roots. Recall: if Δ > 0, two real roots exist; Δ = 0 gives one repeated root; Δ < 0 means no real roots. Link discriminant to ‘discriminating’ taste buds – they tell you the nature of what you’re dealing with.

二次方程的一般形式为 ax² + bx + c = 0。判别式（Δ = b² − 4ac）“辨别”实根与复根。记住：Δ > 0 有两个不等实根；Δ = 0 有一个重根；Δ < 0 无实根。联系“判别”一词——就像灵敏的味蕾告诉你正在品尝什么口味。

Completing the square transforms a quadratic into vertex form by building a perfect square trinomial. Imagine drawing a square and filling in the missing corner piece. This directly leads to the quadratic formula, a one-size-fits-all root-finder.

配方法通过构造完全平方三项式将二次式转化为顶点式。想象画一个正方形并补上缺失的角块。这直接引出求根公式，一个通用的求根利器。

An inequality shows a relation where one side is greater or smaller than the other. When multiplying or dividing by a negative, the sign reverses – visualise flipping the inequality symbol like a reflection in a mirror.

不等式表示两边的大小关系。当乘或除以负数时，不等号方向反转——想象不等号像镜子里的像一样被翻转。

3. Functions & Graphs | 函数与图形

A function maps each input to exactly one output – think of a vending machine: each button (input) dispenses one specific snack (output). The domain is the set of allowed inputs; the range is the set of outputs produced. Remember ‘d’ before ‘r’ alphabetically – you set the domain, you observe the range.

函数将每个输入映射到唯一输出——想象一台自动售货机：每个按钮（输入）只吐出一种特定的零食（输出）。定义域是允许输入值的集合；值域是输出值的集合。按字母顺序，d在r之前——先定义域，再得出值域。

Composite functions combine two functions: (f ∘ g)(x) = f(g(x)). Say ‘apply g, then apply f’. The chain runs from inside out. Think of a factory line: g does the first operation, f finishes the product.

复合函数将两个函数组合：(f ∘ g)(x) = f(g(x))。遵循“先g后f”的顺序，由内向外运算。想象一条流水线：g完成第一道工序，f完成成品。

The inverse function f⁻¹(x) reverses the effect of f(x). Graphically, it’s a reflection in the line y = x. Swap x and y in the equation and solve for y – that’s the mental algorithm.

反函数 f⁻¹(x) 逆转 f(x) 的效果。图像上，它是关于直线 y = x 的对称。在原方程中交换 x 和 y，再解出 y——这就是思考的口诀。

Transformations include translation (shift), stretch (pull), and reflection (flip). Translate by vector (h, k); stretch vertically by factor a. Use hand gestures: slide for translation, pull apart for stretch, flip hand for reflection.

变换包括平移（滑动）、伸缩（拉伸）和反射（翻转）。按向量 (h, k) 平移；竖直伸缩因子为 a。用手势辅助记忆：平移时手掌平移，伸缩时双手拉开，反射时翻转手掌。

4. Exponentials & Logarithms | 指数与对数

An exponential function has form aˣ where a > 0. The base a is raised to the power x. When a = e (≈ 2.718), the function eˣ is its own derivative – a unique property. ‘E’ for ‘exponential’ and ‘Euler’.

指数函数形如 aˣ，其中 a > 0。底数 a 自乘 x 次。当 a = e（≈ 2.718）时，eˣ 的导数等于它自身——独一无二的特性。“E” 代表指数，也代表欧拉（Euler）。

A logarithm answers “to what power?” The equation logₐ N = x means aˣ = N. Think of logs as the ‘power detective’. The natural logarithm, ln, uses base e. Its memory aid: ‘ln’ stands for ‘logarithmus naturalis’.

对数回答“多少次方？” logₐ N = x 意味着 aˣ = N。把对数想象成“幂的侦探”。自然对数 ln 以 e 为底。助记：ln 代表拉丁语“自然对数”。

Key properties: log(AB) = log A + log B (product → sum), log(A/B) = log A − log B (division → subtraction). The change of base formula: logₐ b = log_c b / log_c a. Role-play: you are changing the ‘language’ of the log.

关键性质：log(AB) = log A + log B（积变和），log(A/B) = log A − log B（商变差）。换底公式：logₐ b = log_c b / log_c a。角色扮演：你正在转换对数的“语言”。

5. Trigonometry | 三角学

Radian measure ties angles to arc length: π rad = 180°. 1 radian is the angle when arc length equals radius. The symbol ‘rad’ is often omitted in calculations. Remember: radians feel ‘radial’.

弧度制将角与弧长挂钩：π 弧度 = 180°。当弧长等于半径时，所对的圆心角为 1 弧度。计算中“rad”常被省略。记住：弧度与半径（radius）同源。

The three basic ratios – sine, cosine, tangent – are memorised with SOH CAH TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Say it as a nonsense word: soh-cah-toa.

三种基本比——正弦、余弦、正切——用 SOH CAH TOA 记忆：正弦 = 对边/斜边，余弦 = 邻边/斜边，正切 = 对边/邻边。把它当成一个顺口溜：soh-cah-toa。

The sine rule a/sin A = b/sin B = c/sin C works for any triangle. Visualise equal ratios across the triangle. The cosine rule a² = b² + c² − 2bc cos A extends Pythagoras to non-right triangles; it is the ‘fudge factor’ rule.

正弦定理 a/sin A = b/sin B = c/sin C 适用于任意三角形。想象三角形内贯通的对边-正弦比相等。余弦定理 a² = b² + c² − 2bc cos A 将勾股定理推广到非直角三角形；可以看作带“修正项”的勾股。

Important identities: sin²θ + cos²θ = 1 (the Pythagorean identity). To remember, think of a right triangle with hypotenuse 1. Also, tan θ = sin θ / cos θ.

重要恒等式：sin²θ + cos²θ = 1（毕达哥拉斯恒等式）。联想斜边为1的直角三角形。还有 tan θ = sin θ / cos θ。

6. Sequences & Series | 序列与级数

An arithmetic progression (AP) adds a constant common difference (d) each step. ‘D’ for difference, like the steady steps of a ladder. The nth term: uₙ = a + (n−1)d. Sum of n terms: Sₙ = n/2 [2a + (n−1)d] or n/2 (first + last).

等差数列每一步加上常数的公差 d。“差”就是每步的阶梯高度。第 n 项：uₙ = a + (n−1)d。前 n 项和：Sₙ = n/2 [2a + (n−1)d] 或 n/2 (首项+末项)。

A geometric progression (GP) multiplies by a constant common ratio (r). ‘R’ for ratio, like a photocopier enlarging or reducing. nth term: uₙ = arⁿ⁻¹. The sum to infinity exists only when |r| < 1: S∞ = a/(1−r). Remember: if the ratio is a fraction, the sum converges.

等比数列每一步乘以常数的公比 r。“比”如同复印机的缩放比例。第 n 项：uₙ = arⁿ⁻¹。当 |r| < 1 时，无穷级数和 S∞ = a/(1−r) 存在。记住：公比为真分数时，无穷和收敛。

7. Basic Calculus | 微积分基础

Differentiation finds the gradient of a curve. The derivative dy/dx is the rate of change. Think of ‘differentiate’ as separating a curve into infinitesimal straight pieces. For polynomials, multiply by the power and reduce the power by 1. The phrase “down you go, one less” helps.

微分求曲线在某点的梯度。导数 dy/dx 表示变化率。将“微分”理解为把曲线分割成无限小的直线段。对多项式而言，乘以原指数，再将指数减1。口诀“指数降下来，再减1”。

Stationary points occur where dy/dx = 0. Use the second derivative to classify: positive means minimum (smile shape), negative means maximum (frown shape), zero may be a point of inflection. Visualise a roller coaster: at the top or bottom, the slope is momentarily zero.

驻点出现在 dy/dx = 0 处。用二阶导数分类：二阶导数为正时是极小值点（微笑形状），为负时是极大值点（皱眉形状），为零时可能是拐点。想象过山车：在顶点或低谷处，坡度瞬时为零。

Integration reverses differentiation. The indefinite integral adds a constant ‘+C’ because many functions share the same derivative. The definite integral between limits gives the area under the curve. Think of integration as ‘summing up’ slices to find area.

积分是微分的逆运算。不定积分要加常数“+C”，因为无数函数有相同的导数。定积分在给定上下限之间计算，得到曲线下的面积。把积分想象成“累加”薄片来求总面积。

8. Vectors | 向量

A vector has both magnitude and direction, unlike a scalar which has only size. Represent a vector as a column or using i, j notation. The magnitude (modulus) of vector v = √(x² + y²). It’s the length of the arrow.

向量既有大小又有方向，而标量只有大小。向量可用列向量或 i, j 表示。模（大小）为 √(x² + y²)，即箭头的长度。

A unit vector has magnitude 1. To find it, divide the vector by its magnitude. A position vector starts from the origin. The dot product a·b = |a||b| cos θ gives a scalar; use it to find the angle between vectors. If a·b = 0, they are perpendicular.

单位向量的模为1。求法：将向量除以其模。位置向量从原点出发。点积 a·b = |a||b| cos θ 得出一个标量；用于求两向量的夹角。若 a·b = 0，则两向量垂直。

9. Permutations & Combinations | 排列与组合

Factorial n! = n × (n−1) × … × 1 counts arrangements of n distinct objects. ‘!’ is the shock of how fast it grows. A permutation cares about order: the word ‘perm’ suggests a particular arrangement. The formula is nPr = n!/(n−r)!.

阶乘 n! = n × (n−1) × … × 1 计算 n 个不同物品的排列数。“!” 感叹其增长速度之快。排列考虑顺序：“排列”暗示特定的次序，公式为 nPr = n!/(n−r)!。

A combination ignores order; ‘comb’ selects a group. nCr = n!/(r!(n−r)!). Remember: r! dividing in the combination removes the order counted in permutations. Mnemonic: “Permutation – Position matters; Combination – Choose a Committee.”

组合不计顺序；“组合”只选出群体。nCr = n!/(r!(n−r)!)。记住：组合多除以 r! 是为了消除排列中计重的顺序。口诀：“排列关心位置，组合只管选人。”

10. Statistics & Probability | 统计与概率

Mean (average) is sum of values divided by number of values. Median is the middle value when data is ordered. Mode is the most frequent value. Think ‘Mean is mean to calculate (arithmetic), Median is the middleman, Mode is the most.’

平均数是总和除以个数。中位数是排序后中间的值。众数是出现频率最高的值。联想：“平均要算，中位在中间，众数出现最多。”

Variance measures spread: average of squared deviations from the mean. Standard deviation is its square root, bringing units back to original scale. Formula: σ² = Σ(x − μ)² / N. Remember: standard deviation is the ‘typical distance’ from the mean.

方差衡量离散程度：各数据与均值之差的平方的平均。标准差是方差的算术平方根，使量纲复原。公式：σ² = Σ(x − μ)² / N。记忆：标准差即偏离均值的“典型距离”。

In probability, events are mutually exclusive if they cannot occur together – their Venn diagrams don’t overlap. Independent events don’t influence each other. For independent events, P(A∩B) = P(A)×P(B). Use the phrase “independent means multiply.”

概率中，若两事件不能同时发生，则它们互斥——韦恩图无交集。独立事件互不影响。对于独立事件，P(A∩B) = P(A)×P(B)。口诀：“独立即相乘”。

Published by TutorHao | Additional Mathematics Revision Series | aleveler.com

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