Year 13 CCEA Further Mathematics: Intensive Christmas Revision Plan | Year 13 CCEA 进阶数学：寒假强化复习计划

📚 Year 13 CCEA Further Mathematics: Intensive Christmas Revision Plan | Year 13 CCEA 进阶数学：寒假强化复习计划

The Christmas holiday offers a vital opportunity for Year 13 students to consolidate the first term of CCEA Further Mathematics. With the AS Pure Mathematics unit (FP1) and possibly an applied module already under way, a well-structured intensive revision plan can transform shaky foundations into confident understanding. This plan combines topic-focused review, exam-style practice, and well-being strategies to help you return in January fully prepared for the challenges ahead.

寒假为 Year 13 学生提供了一个巩固 CCEA 进阶数学第一学期内容的关键机会。由于 AS 纯数学单元（FP1）和可能的应用模块已经展开，一份精心设计的强化复习计划能把薄弱的基础转化为扎实的理解。本计划将主题复习、真题训练和健康策略结合在一起，帮助你在开学时做好充分准备，迎接下学期的挑战。

1. Designing Your Revision Timetable | 制定复习时间表

During the short Christmas break, it is essential to create a structured revision timetable that balances relaxation with focused study. Map out the days available, set aside 2–3 hours per day for Further Mathematics, and rotate topics to avoid fatigue. Break each session into 45-minute blocks with short breaks, and designate specific days for tackling past paper questions under timed conditions.

在短暂的寒假期间，制定一个结构化的复习时间表至关重要，既要平衡休息与专注学习，也要规划好可利用的天数，每天为进阶数学安排2–3小时，并轮换不同主题以避免疲劳。将每个学习时段分成45分钟的学习块并搭配短暂休息，安排专门的日子用于限时完成历年真题。

A sample weekly plan may look like this:

下面是一个周计划示例：

Adjust the plan to your own pace, but always include a review of the previous day’s topic before moving on.

根据自己的节奏调整计划，但一定要在开始新内容前复习前一天的主题。

2. Complex Numbers: Polishing the Basics | 复数：巩固基础

Review the fundamental operations with complex numbers in the form a + bi, including addition, subtraction, multiplication, and division using the conjugate. Ensure you can convert between Cartesian and modulus-argument form. The modulus r and argument θ are given by:

回顾复数 a + bi 的基本运算，包括加减乘除以及利用共轭进行除法。确保你能在笛卡尔形式和模-辐角形式之间转换。模长 r 和辐角 θ 的计算公式如下：

r = √(a² + b²),   θ = arctan(b/a) (with correct quadrant)

Master De Moivre’s theorem and use it to find powers and roots of complex numbers:

精通棣莫弗定理，并运用它求复数的幂次和根：

(cos θ + i sin θ)ⁿ = cos nθ + i sin nθ

Practice solving equations like z³ = 8i and represent all roots on an Argand diagram. Pay attention to loci problems, such as |z − 2i| = 3 or arg(z − 1) = π/4, which test your geometric understanding.

练习解方程如 z³ = 8i，并将所有根绘制在阿尔冈图上。注意轨迹

Published by TutorHao | Year 13 进阶数学 Revision Series | aleveler.com

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