Related posts: What is the difference between H1, H2, H3 Maths
From the syllabus, it looks like Further Maths has some overlap with H2 Maths. This is a good thing, since students can reinforce their knowledge by learning it twice. It is also like killing two birds with one stone!
Some new things in Further Math:
- Conic sections in Polar Form
- Arc length of curves
- Integrating factor (Differential Equations)
- Second order recurrence relations
- Matrices and Linear Spaces (This in my opinion is one of the biggest difference between Further Maths and H2 Maths)
- Numerical methods
- Geometric Distribution
- Uniform and exponential distribution
- Non-parametric tests
Further Math is a good subject to take for those intending to enter physical science or engineering in university, since it will cover many of the topics learnt in the first year of university.
Overall, there are quite a lot of advanced topics crammed into Further Math, so I doubt the teachers have time to teach everything in depth in two years. Matrices and Linear Spaces (Linear Algebra) alone will take half a year to teach it properly. Most likely it will be a touch-and-go event and students will get to see the tip of the iceberg. Students wishing to learn more can read up some undergraduate math books listed here.