Further Mathematics

Advanced Mathematics is a comprehensive and challenging subject for ordinary students. The content of advanced mathematics includes three parts: pure mathematics, statistics and mechanics. The modules are consistent with mathematics, but its content is more extensive and in-depth. According to the syllabus for 2020-2022, the reformed advanced mathematics is less difficult than before. Before choosing, take Cambridge International AS & A Level Mathematics (9709).


Course targets:

On the basis of basic mathematics, students will learn more difficult mathematics knowledge, develop mathematical thinking, and easily pass the A-level advanced mathematics examination.




课程内容 Content

Part1:Further Pure Mathematics (1) A-Level: 高阶数学

Session1:Roots of polynomial equations 多项式方程求根

Session2:Rational function and graphs 有理函数和图

Session3:Summation of series 级数求和

Session4:Matrices 矩阵

Session5:Polar coordinates 极坐标

Session6:Vectors 向量

Session7:Proof by the induction 归纳证明


Part2:Further Pure Mathematics (2) A-Level: 高阶数学

Session8:Hyperbolic functions 双曲线函数

Session9Matrices 矩阵

Session10:Differentiation 微分

Session11:Integration 积分

Session12:Complex numbers 附属

Session13:Differential equations 微分方程

Session14:Differential equations continued 微分方程


Part3: Further Mechanics A-Level: 高阶力学

Session15:Motion of a projectile 抛物线运动

Session16:Equilibrium of a rigid body 刚体平衡

Session17:Circular motion 圆周运动

Session18:Hookes law 胡克定律

Session19:Linear motion under a variable force 变力下的线性运动

Session20:Momentum 动量


Part4:Further Probability & Statistics 统计学

Session21:Continuous random variables 连续随机变量

Session22:Inference using normal and t-distributions 正态分布和t分布的推理

Session23: tests

Session24:Non-parametric test 非参数检验

Session25:Probability generating functions 概率生成函数

Session26:Mock exam 模拟考试

Session27:Past paper review 过去的论文回顾