📚 IGCSE Cambridge Additional Mathematics: High-Scorer Experience and Exam Tips | IGCSE 剑桥进阶数学：学霸高分经验分享
Scoring an A* in IGCSE Cambridge Additional Mathematics (0606) is not about being “naturally gifted” – it is about studying the right concepts in the right order and practising until the methods become automatic. This guide shares the habits and strategies used by high scorers.
IGCSE 剑桥进阶数学（0606）拿 A* 并不是靠“天生聪明”，而是用正确的顺序学透核心概念，并通过练习让方法变成条件反射。本文分享学霸们常用的习惯和策略。
1. Know the 0606 Syllabus Inside Out | 吃透 0606 考纲
Cambridge Additional Mathematics 0606 is very different from Extended Mathematics. It covers functions, quadratic equations, surds, indices, logarithms, binomial expansion, trigonometry, differentiation, integration, kinematics and vectors. High scorers begin by printing the official syllabus and ticking off every bullet point before they start past papers.
剑桥进阶数学 0606 与普通数学 Extended 有很大区别。它涵盖函数、二次方程、根式、指数、对数、二项式展开、三角学、微分、积分、运动学和向量。学霸会先打印官方考纲，在开始做真题前逐条勾掉每个考点。
Core areas: Functions → Quadratics → Surds and Indices → Logarithms → Trigonometry → Calculus → Kinematics → Vectors
The assessment has two papers, each lasting 2 hours and carrying 80 marks. There is no separate formula sheet, so you must know the key results and derivations by heart. Treat the syllabus as your personal checklist, not as a document to ignore.
考试包含两份试卷，每份 2 小时、80 分。考试不会单独提供公式表，所以你必须熟记核心结论和推导过程。把考纲当作你的个人清单，而不是一份可以忽略的文件。
2. Master Functions and Graphs First | 先攻克函数与图像
Functions are the backbone of the whole paper. Make sure you can state domain and range, form composite functions such as fg(x), find inverse functions f⁻¹(x), and sketch modulus graphs such as y = |2x – 3|. These skills appear in almost every session in Paper 1 and Paper 2.
函数是整个试卷的骨架。必须会写出定义域和值域、求复合函数 fg(x)、求反函数 f⁻¹(x)，并能画出 y = |2x – 3| 这类绝对值图像。这些技能几乎每次考试都会在卷一和卷二中出现。
For a one-to-one function f, fg(x) means f(g(x)); the inverse f⁻¹(x) satisfies f(f⁻¹(x)) = x. A common mistake is to forget that the domain of f⁻¹ is the range of f. Always check this when you write your final answer.
对于一一对应的函数 f，fg(x) 表示 f(g(x))；反函数 f⁻¹(x) 满足 f(f⁻¹(x)) = x。一个常见错误是忘记 f⁻¹ 的定义域就是 f 的值域。写最终答案时一定要检查这一点。
Key check: domain of f⁻¹ = range of f
3. Build Rock-Solid Algebra Skills | 打好代数基本功
Algebra speed decides your grade. Practise completing the square, solving quadratic inequalities, simplifying surds, and switching between index and log forms. For example, aˣ = b is equivalent to x = logₐ b. These skills reduce careless errors in later calculus questions.
代数速度决定你的分数段。要熟练配方、解二次不等式、化简根式，并能在指数式和对数式之间切换。例如，aˣ = b 等价于 x = logₐ b。这些技能能减少后面微积分题中的粗心错误。
You should be able to solve any quadratic equation without hesitation. The quadratic formula is given by:
你应该能够毫不犹豫地解出任何二次方程。求根公式为：
x = (-b ± √(b² – 4ac)) ÷ 2a
Also practise handling inequalities such as ax² + bx + c > 0. Sketch the graph first, then read the interval from the correct side of the parabola. Do not just solve the equation and guess the inequality direction.
还要练习 ax² + bx + c > 0 这类不等式。先画图像，再从抛物线的正确一侧读取区间。不要只解方程然后猜测不等号方向。
4. Trigonometry: Do Not Memorise, Derive | 三角函数：不要死记，要会推导
The high-scorer trick is to learn where identities come from. Know the unit circle definitions of sin θ, cos θ and tan θ, then derive sin²θ + cos²θ = 1 and the double-angle formulas. This reduces memory load and helps you spot exam traps.
学霸的诀窍是理解恒等式的来源。先掌握单位圆上 sin θ、cos θ、tan θ 的定义，再推导 sin²θ + cos²θ = 1 以及二倍角公式。这样记忆负担更轻，也更容易发现考题陷阱。
| Identity | Use / 用途 |
| sin²θ + cos²θ = 1 | Simplify or prove / 化简或证明 |
| tan θ = sin θ ÷ cos θ | Convert equations / 转换方程 |
| sin 2θ = 2 sin θ cos θ | Solving and integration / 解方程与积分 |
For radian questions, draw the unit circle and mark the angle. This makes it much easier to decide whether an answer is in quadrant I, II, III or IV. Always check the range given in the question, such as 0 ≤ θ ≤ 2π.
做弧度题时，画出单位圆并标出角度。这能帮助你判断答案位于第 I、II、III 或 IV 象限。一定要检查题目给出的范围，例如 0 ≤ θ ≤ 2π。
5. Differentiation and Integration as One Topic | 把微分与积分当一个整体学
Do not study differentiation and integration separately; they are inverse operations. If you differentiate xⁿ, you get nxⁿ⁻¹. If you integrate xⁿ, you get xⁿ⁺¹/(n+1) + C, provided n ≠ -1. Understanding this link makes exam questions easier.
不要把微分和积分分开学；它们互为逆运算。对 xⁿ 微分得到 nxⁿ⁻¹。对 xⁿ 积分得到 xⁿ⁺¹/(n+1) + C，前提是 n ≠ -1。理解这层关系，考试题会简单很多。
d/dx (xⁿ) = nxⁿ⁻¹
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ -1
Practise applying these rules to real functions such as y = 4x³ – 2x⁻² + 5√x. First rewrite √x as x½, then differentiate or integrate term by term. Never forget the constant of integration in indefinite integrals.
练习将这些规则应用到真实函数上，例如 y = 4x³ – 2x⁻² + 5√x。先把 √x 写成 x½，再逐项微分或积分。不定积分千万不要漏掉积分常数 C。
6. Vectors, Kinematics and Applications | 向量、运动学与应用题
Applied problems often decide the A* boundary. In kinematics, link displacement s, velocity v and acceleration a using differentiation and integration: v = ds/dt, a = dv/dt. In vectors, know magnitude, unit vector and relative position.
应用题常常决定 A* 分数线。运动学中，要用微分和积分联系位移 s、速度 v 和加速度 a：v = ds/dt，a = dv/dt。向量部分要掌握模长、单位向量和相对位置。
v = ds/dt, a = dv/dt
For a vector v = xi + yj, the magnitude is |v| = √(x² + y²). A unit vector in the same direction is v ÷ |v|. Many exam questions combine vector position with velocity and ask for the speed or the distance travelled.
对于向量 v = xi + yj，模长为 |v| = √(x² + y²)。同方向的单位向量为 v ÷ |v|。很多考题会把向量位置与速度结合，要求计算速率或运动距离。
7. Exam Paper Strategy: Timing and Marks | 试卷策略：时间与分值
Paper 1 and Paper 2 each last 2 hours and carry 80 marks. Aim to finish the first 60% of marks in about 50 minutes, leaving time for the harder later questions. Never spend more than 1.5 minutes per mark.
卷一和卷二各 2 小时、80 分。目标是在约 50 分钟内拿下前 60% 分值，留出时间攻克后面难题。不要在每分上花超过 1.5 分钟。
| Paper | Duration | Marks | High-yield focus |
| Paper 1 | 2 hours | 80 | Functions, algebra, trigonometry |
| Paper 2 | 2 hours | 80 | Calculus, kinematics, vectors |
Read the whole question before you start writing. Sometimes a later part gives a hint about the method needed earlier. Write clear working because method marks can save your grade even if the final answer is wrong.
开始答题前先通读整道题。有时后面的小题会提示前面需要的方法。书写清晰完整，因为即使最终答案错误，过程分也能保住你的分数。
8. The 80/20 Mistake Log | 80/20 错题本
Keep a mistake log, but do not copy every error. Record only the 20% of mistakes that cause 80% of your lost marks: sign errors, forgotten +C, domain restrictions, or calculator mode errors. Review this log weekly.
错题本不要抄所有错误，只记录导致 80% 失分的 20% 错误：符号错误、漏掉 +C、忽略定义域限制、计算器模式设错等。每周复盘一次。
For each mistake, write the question, your wrong approach, the correct approach, and a one-line rule to prevent repetition. For example: “When integrating x⁻¹, the answer is ln|x| + C, not x⁰/0 + C.” This rule-based memory is much stronger than re-reading notes.
每道错题写出题目、错误做法、正确做法和一句防错规则。例如：“积分 x⁻¹ 时，答案是 ln|x| + C，而不是 x⁰/0 + C。”这种规则记忆比反复看笔记更牢固。
9. Calculator Use: Sharp and Fast | 计算器使用：又准又快
A scientific calculator is allowed, but it cannot replace method marks. Always show the exact form, such as √3 or π, before rounding to 3 significant figures. Check your calculator is in degree mode for angle questions unless radians are stated.
科学计算器可以使用，但不能替代步骤分。先写出精确形式，如 √3 或 π，再按要求保留三位有效数字。除非题目说明用弧度，否则角度题要检查计算器是否在角度模式。
Use the calculator to check, not to think. After solving by hand, you can verify numerically by substituting a value into the original equation. This is a powerful way to catch sign and bracket errors in the final minutes of the exam.
计算器用于检查，而不是代替思考。手算求解后，可以把一个数值代回原方程进行验证。这是在考试最后几分钟发现符号和括号错误的有力方法。
10. Final Revision Plan and Past Papers | 最终复习计划与真题
In the last 30 days, spend 50% of time on past papers under timed conditions, 30% on targeted weak topics, and 20% on rewriting model solutions. Do every paper from 2019 onward twice: once normally, once with a mark scheme to improve working.
最后 30 天，50% 时间做限时真题，30% 专攻薄弱专题，20% 重写标准答案。2019 年以后的每套试卷至少做两遍：第一遍正常作答，第二遍对照评分标准优化书写。
When marking, be strict with yourself. If you did not show a required step, do not award yourself the method mark. Use the mark scheme to learn how examiners award marks for working, then practise writing answers in that style.
批改时要对自己严格。如果没有写出必要步骤，就不要给自己过程
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