SQA Advanced Mathematics: Vocabulary and Terminology Memory Guide | SQA 进阶数学：词汇术语速记指南

📚 SQA Advanced Mathematics: Vocabulary and Terminology Memory Guide | SQA 进阶数学：词汇术语速记指南

Mastering advanced mathematics goes beyond solving problems – it requires a firm grasp of the precise vocabulary used in SQA Higher and Advanced Higher exams. Misinterpreting a single term like ‘discriminant’ or ‘orthogonal’ can cost valuable marks. This guide presents essential terminology paired with memory aids to help you recall definitions quickly under exam pressure.

掌握进阶数学不仅在于解题，还在于牢固掌握 SQA 高等与进阶高等考试中使用的精确词汇。对‘判别式’或‘正交’等术语的误解可能导致失分。本指南提供核心术语并配以记忆辅助，帮助你在考试压力下快速回忆定义。

1. Functions & Mappings | 函数与映射

Function: A relation where each input has exactly one output. Think ‘single-output machine’. Notation: f: x → f(x).

函数：一种每个输入对应唯一输出的关系。可想象成‘单输出机器’。记号: f: x → f(x)。

Domain: The set of all permitted input values. Memory tip: Domain starts with ‘D’ for ‘x-Dimension’.

定义域：所有允许输入值的集合。记忆法：Domain 以 ‘D’ 开头，联想‘x 维度的区域’。

Range: The set of all possible output values obtained from the domain. Imagine ‘Range’ as the ‘reach’ of the function on the y-axis.

值域：由定义域获得的所有可能输出值的集合。可想象‘Range’是函数在 y 轴上的‘延伸范围’。

Inverse function f⁻¹: Reverses the effect of f. Swap x and y, then solve. Graphically, reflection in the line y = x. Memory: f⁻¹ undoes f.

反函数 f⁻¹：逆转 f 的作用。交换 x 与 y 然后解出。图像上关于直线 y = x 的对称。记忆：f⁻¹ 是 f 的逆操作。

Composite function f(g(x)): Applying one function after another. Tip: Read from inside out, like ‘g first, then f’.

复合函数 f(g(x))：先后应用两个函数。技巧：从内向外读，先 g 再 f。

2. Differentiation Foundations | 微分基础

Derivative f'(x): The rate of change of a function, representing the gradient of the tangent. Remember: Derivative → ‘derive’ the slope.

导数 f'(x)：函数的变化率，表示切线的斜率。记忆：导数即‘导出’斜率。

Leibniz notation dy/dx: Emphasises that we are differentiating y with respect to x. Tip: Think ‘change in y over change in x’ as Δx→0.

莱布尼茨记号 dy/dx：强调 y 对 x 求导。提示：可以看作 Δy/Δx 在 Δx→0 时的极限。

Stationary point: Where dy/dx = 0. Could be maximum, minimum or point of inflection. Mnemonic: ‘Stationary’ = graph is ‘standing still’ momentarily.

驻点：dy/dx = 0 的点。可能是极大值、极小值或拐点。助记：‘驻点’意为图像在此‘暂时停留’。

Second derivative d²y/dx²: Rate of change of the gradient. Used to determine nature of stationary points (concavity). Memory: The ‘second’ layer of slope analysis.

二阶导数 d²y/dx²：斜率的变化率。用于判断驻点的性质（凹凸性）。记忆：对斜率进行‘第二次’剖析。

3. Advanced Differentiation | 进阶微分

Chain rule: For composite functions: dy/dx = dy/du × du/dx. Visualise a chain linking the rates. ‘Outside derivative times inside derivative’.

链式法则：用于复合函数：dy/dx = dy/du × du/dx。想象一条链连接变化率。‘外导数乘以内导数’。

Product rule: If y = u v, then dy/dx = u’ v + u v’. Memory: ‘first d second plus second d first’ (udv + vdu).

乘积法则：若 y = u v，则 dy/dx = u’ v + u v’。口诀：‘前导后不导加后导前不导’。

Quotient rule: For y = u/v, dy/dx = (vu’ – uv’) / v². Mnemonic: ‘low d high minus high d low over low squared’.

商法则：y = u/v 时，dy/dx = (vu’ – uv’) / v²。口诀：‘下导上减上导下除以下平方’。

Implicit differentiation: When y is not explicitly written as a function of x, differentiate both sides and apply chain rule to y terms. Tip: Whenever you see y

Published by TutorHao | Year 11 进阶数学 Revision Series | aleveler.com

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