📚 IGCSE CAIE Additional Mathematics: Speaking & Listening Exam Preparation | IGCSE CAIE 进阶数学：口语/听力备考专项
The CAIE IGCSE Additional Mathematics 0606 syllabus is a written paper, but many high-scoring candidates use ‘speaking and listening’ techniques to sharpen their accuracy. In this context, speaking means explaining every mathematical step in clear English, and listening means reading each question as if it were being read to you.
CAIE IGCSE 进阶数学 0606 是笔试科目，但许多高分考生会使用“口语和听力”技巧来提高准确性。在这里，“口语”是指用清晰的英语解释每一个数学步骤，“听力”是指像听到题目一样去读每一道题。
This guide turns verbal and aural skills into practical revision tools for functions, algebra, trigonometry, calculus, vectors and kinematics. No microphone or recorded audio is required; the goal is better attention, reasoning and checking.
本指南将口语与听力技能转化为函数、代数、三角、微积分、向量和运动学的实用复习工具。你不需要麦克风或录音，目标只是提高注意力、推理能力和检查能力。
1. What Speaking & Listening Means in 0606 | 0606 中口语与听力的含义
In Additional Mathematics 0606 there is no speaking interview and no audio recording. ‘Speaking and listening preparation’ means training yourself to read a question as if it were spoken and to explain every step in your own words.
进阶数学 0606 没有口语面试，也没有音频录音。“口语与听力备考”是指训练自己像听到题目一样读题，并用自己的话解释每一个步骤。
When you verbalise a problem, you activate a different part of your working memory. Saying ‘I need the gradient, so I differentiate’ makes it harder to skip a step or misread a condition such as ‘x is positive’ or ‘give your answer in exact form’.
当你把问题说出来时，会调动工作记忆的不同部分。说出“我需要斜率，所以先求导”会让你很难跳步或误读“x 为正数”或“答案保留精确形式”等条件。
Listening to yourself is also a check. If your spoken sentence sounds wrong, it usually means the mathematics is wrong. Practise this in revision, not for the first time in the exam hall.
聆听自己的声音也是一种检查。如果你说出的句子听起来不对劲，通常意味着数学过程出了问题。要在复习中练习，而不是第一次在考场里才这样做。
2. Reading Notation Aloud | 大声读出数学符号
Notation errors are very common in 0606. Learners misread f⁻¹(x) as f(x) or confuse gf(x) with fg(x). Reading notation aloud builds precision and reveals whether you truly understand the order of operations.
符号错误在 0606 中非常常见。考生会把 f⁻¹(x) 误读成 f(x)，或者混淆 gf(x) 与 fg(x)。大声读符号可以建立精确性，并检验你是否真正理解运算顺序。
| Symbol | 符号 | Say | 读法 | Meaning | 含义 |
| f(x) | ‘f of x’ | a function named f applied to x |
| f⁻¹(x) | ‘f inverse of x’ | the inverse function, not 1 ÷ f(x) |
| gf(x) | ‘g of f of x’ | apply f first, then g |
| fg(x) | ‘f of g of x’ | apply g first, then f |
| domain | ‘domain’ | set of possible x values |
| range | ‘range’ | set of possible y values |
For example, say aloud: ‘y equals f of x equals two x squared plus three x minus five.’ This forces you to notice the squared term before you start simplifying.
例如，大声读出：“y 等于 f(x) 等于 2x² 加 3x 减 5。”这会迫使你在化简之前注意到平方项。
y = f(x) = 2x² + 3x – 5
3. Listening for Command Words | 聆听题目中的指令词
Command words tell you what kind of answer is expected. Listening carefully to these words prevents wasted working and lost marks. In 0606, ‘show that’ is not the same as ‘find’.
指令词告诉你答案需要什么形式。仔细“聆听”这些词可以避免无效作答和丢分。在 0606 中，“证明”和“求”并不相同。
When a question says ‘show that’, you must produce a given result with clear steps. When it says ‘hence’, you must use the previous result, even if another method would work. ‘Exact value’ means a surd, fraction or logarithm, not a decimal approximation.
当题目说“证明”时，你必须用清晰的步骤得到给定结果。当题目说“因此”时，你必须使用前面得出的结果，即使其他方法也行得通。“精确值”意味着根式、分数或对数，而不是小数近似。
| Command word | 指令词 | What it asks you to do | 要求你做什么 |
| Show that | Prove the given result with full working |
| Hence | Use the previous answer as your starting point |
| Exact value | Leave the answer as a surd, fraction or log |
| Sketch | Show shape and key features, not a plotted graph |
| Express in the form | Rearrange into the exact requested structure |
Before you pick up your pen, read the command word aloud once. This tiny habit reduces misreading in multi-part questions.
在你动笔之前，把指令词大声读一遍。这个小习惯能减少多步骤题目中的误读。
4. Verbalising Algebraic Manipulation | 口头表达代数运算
Algebra in 0606 includes expanding, factorising, completing the square, simplifying rational expressions and solving inequalities. Saying each step aloud helps you avoid sign errors and missing factors.
0606 的代数包括展开、因式分解、配方法、化简有理式以及解不等式。大声说出每一步有助于避免符号错误和漏掉因式。
When completing the square, say: ‘Take x² + 6x, halve the 6 to get 3, square it to get 9, add 9 and subtract 9.’ This turns a memorised process into a heard sequence.
配方法时可以说：“取 x² + 6x，把 6 除以 2 得到 3，平方得到 9，加上 9 再减去 9。”这把记忆中的过程变成可听见的步骤。
x² + 6x + 1 = (x + 3)² – 9 + 1 = (x + 3)² – 8
For factorising a quadratic, say: ‘I need two numbers that multiply to c and add to b.’ Then test the pair mentally before writing the brackets.
因式分解二次式时可以说：“我需要两个数，它们相乘得 c，相加得 b。”然后在写出括号之前先在心里检验这一对数。
When solving an inequality, say: ‘If I multiply or divide by a negative number, I must reverse the inequality sign.’ This rule is one of the most frequently forgotten in CAIE 0606.
解不等式时可以说：“如果乘以或除以一个负数，我必须反转不等号。”这是 CAIE 0606 中最常被遗忘的规则之一。
5. Speaking the Laws of Indices and Logarithms | 说出指数与对数法则
Indices and logarithms are tested in 0606 nearly every series. Saying the laws aloud builds instant recall and helps you spot when a question is asking you to change base or remove a logarithm.
指数与对数几乎每套 0606 试卷都会考查。大声说出法则可以建立即时回忆，并帮助你识别题目是否要求换底或去掉对数。
xᵐ × xⁿ = xᵐ⁺ⁿ
xᵐ ÷ xⁿ = xᵐ⁻ⁿ
(xᵐ)ⁿ = xᵐⁿ
Say this sentence before any log question: ‘A logarithm is the power to which the base must be raised to produce the number.’ For example, log₂ 8 = 3 because 2³ = 8.
在做对数题之前先说这句话：“对数就是为使底数变成某个数所需要的幂。”例如，log₂ 8 = 3，因为 2³ = 8。
logₐ(xy) = logₐ x + logₐ y
logₐ(x ÷ y) = logₐ x – logₐ y
logₐ(xⁿ) = n logₐ x
When you change base, say: ‘log base a of b equals log b over log a.’ This prevents the inverse error of writing log a over log b.
换底时可以说：“以 a 为底 b 的对数等于 log b 除以 log a。”这可以防止写成 log a 除以 log b 的反向错误。
6. Explaining Trigonometry and Angles | 解释三角学与角度
Trigonometry in 0606 uses radians as well as degrees, so speaking about angles helps you remember which mode is required. A common listening cue is the word ‘radians’ or the absence of a degree symbol.
0606 的三角学使用弧度制和角度制，因此说出角度可以帮助你记住需要哪种模式。一个常见的“听力”线索是“弧度”一词或度符号的缺失。
Say: ‘In radian mode, π is 180 degrees, so π ÷ 2 is 90 degrees.’ This stops you from entering degree values into a radian calculation and getting wildly wrong answers.
可以说：“在弧度模式下，π 是 180 度，所以 π ÷ 2 是 90 度。”这可以防止你在弧度计算中输入角度值而得到完全错误的答案。
sin²θ + cos²θ = 1
tan θ = sin θ ÷ cos θ
When solving a trigonometric equation, say: ‘I need the principal value first, then I use the CAST diagram or graph symmetry to find all solutions in the given interval.’ This verbal plan prevents missing solutions.
解三角方程时可以说：“我需要先求主值，然后利用 CAST 图或图像对称性找出给定区间内的所有解。”这个口头计划可以防止漏解。
For graphs of y = sin x, y = cos x and y = tan x, say the period and amplitude aloud. For example: ‘y = 3 sin 2x has amplitude 3 and period π.’
对于 y = sin x、y = cos x 和 y = tan x 的图像，大声说出周期和振幅。例如：“y = 3 sin 2x 的振幅为 3，周期为 π。”
7. Talking Through Differentiation | 口头演练微分
Differentiation questions in 0606 often ask for gradients, turning points, tangents, normals and rates of change. A spoken routine helps you decide what to find first.
0606 的微分题通常考查斜率、驻点、切线、法线和变化率。一套口头流程可以帮助你决定先求什么。
For the power rule, say: ‘Multiply by the power, then reduce the power by one.’ For y = xⁿ, this gives dy/dx = nxⁿ⁻¹.
对于幂函数法则，可以说：“乘以幂，然后把幂减一。”对于 y = xⁿ，得到 dy/dx = nxⁿ⁻¹。
y = xⁿ ⇒ dy/dx = nxⁿ⁻¹
When a question says ‘find the equation of the normal’, say: ‘The normal gradient is the negative reciprocal of the tangent gradient.’ This prevents the common mistake of using the tangent gradient in the normal equation.
当题目说“求法线方程”时，可以说：“法线斜率是切线斜率的负倒数。”这可以防止把切线斜率误用在法线方程中。
For a stationary point, say: ‘Set dy/dx equal to zero, solve for x, then use the second derivative or sign test to decide maximum or minimum.’
对于驻点，可以说：“令 dy/dx 等于零，解出 x，然后用二阶导数或符号测试判断极大值还是极小值。”
d²y/dx² > 0 ⇒ minimumPublished by TutorHao | IGCSE 进阶数学 Revision Series | aleveler.com
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