Winter Intensive Revision Plan for CAIE IGCSE Additional Mathematics | CAIE IGCSE 进阶数学寒假强化复习计划

📚 Winter Intensive Revision Plan for CAIE IGCSE Additional Mathematics | CAIE IGCSE 进阶数学寒假强化复习计划

The CAIE IGCSE Additional Mathematics (0606) winter break is a valuable window to convert weak topics into strengths. A focused four-week plan should combine syllabus review, targeted skills practice, timed past papers and an error log.

CAIE IGCSE 进阶数学（0606）寒假是查漏补缺、强化提分的关键窗口。一份高效的四周计划应包含考纲梳理、专项训练、限时真题和错题整理。

1. Know the Syllabus and Exam Structure | 明确考纲与试卷结构

Start by printing the CAIE 0606 syllabus. The course is assessed through two 2-hour papers, each worth 80 marks, both allowing calculators. Major areas include functions, quadratic functions, equations, inequalities, surds, logs, trigonometry, permutations and combinations, binomial expansion, vectors, matrices, differentiation and integration.

首先打印 CAIE 0606 考纲。考试由两份 2 小时试卷组成，每份 80 分，均允许使用计算器。主要板块包括函数、二次函数、方程与不等式、根式、对数、三角学、排列组合、二项式定理、向量、矩阵、微分与积分。

2. Take a Diagnostic Mock Before the Plan | 计划前先做一套诊断性模拟

Take one full past paper under exam conditions before you begin. Mark it using the official mark scheme and sort every mistake into three groups: concept gap, algebra slip, or notation/time error. This tells you which topics deserve most of the two-week core phase.

在正式开始前，请限时完成一套完整真题。按官方评分方案批改，并把每个错误归为三类：概念漏洞、代数粗心、或符号/时间问题。这样你就能清楚哪些专题需要在两周核心阶段投入最多时间。

3. Week 1: Core Algebra Rescue | 第一周：代数核心补救

Rebuild the algebraic toolkit first. For quadratics, be fluent with completing the square, the discriminant and quadratic inequalities. For polynomials, revise the factor theorem and remainder theorem; for simultaneous equations, practise one linear and one quadratic system.

首先重建代数工具。二次函数必须熟练配方、判别式与二次不等式。多项式部分复习因式定理与余式定理；方程组重点练习一个一次与一个二次联立。

For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a

Δ = b² − 4ac

4. Week 1 Extension: Surds, Indices, Logarithms and Exponentials | 第一周拓展：根式、指数、对数与指数函数

Revise laws of indices and surds as one linked set: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ. Then connect logs to indices: logₐ x = y means aʸ = x. Practise solving equations such as e²ˣ = 5 and log₃(x − 1) = 4.

将指数律与根式作为一组相关工具复习：aᵐ × aⁿ = aᵐ⁺ⁿ、aᵐ ÷ aⁿ = aᵐ⁻ⁿ、(aᵐ)ⁿ = aᵐⁿ。再把对数与指数联系起来：logₐ x = y 等价于 aʸ = x。练习求解 e²ˣ = 5 与 log₃(x − 1) = 4 等方程。

5. Week 2: Functions and Graph Transformations | 第二周：函数与图像变换

Be precise with domain and range, one-to-one functions, inverse functions and composite functions. For f(x) = 2x + 3, write y = 2x + 3, swap x and y, then solve to get f⁻¹(x) = (x − 3)/2. For composite functions, remember gf(x) = g(f(x)).

对定义域、值域、一一函数、反函数与复合函数要精确掌握。例如 f(x) = 2x + 3，令 y = 2x + 3，交换 x 与 y，解得 f⁻¹(x) = (x − 3)/2。复合函数注意 gf(x) = g(f(x))。

6. Week 2: Trigonometry and Circular Measure | 第二周：三角学与弧度制

Use radians by default in 0606. Memorise arc length s = rθ and sector area A = ½ r² θ. Revise the exact values of sin, cos, tan for 0, π/6, π/4, π/3, π/2 and the two core identities sin² θ + cos² θ = 1 and tan θ = sin θ / cos θ.

0606 中默认使用弧度制。牢记弧长公式 s = rθ 与扇形面积公式 A = ½ r² θ。复习 0、π/6、π/4、π/3、π/2 的特殊角三角函数值，以及两个核心恒等式 sin² θ + cos² θ = 1 和 tan θ = sin θ / cos θ。