This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level further maths exams.

You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:

* Fluency â€“ selecting and applying correct methods to answer with speed and efficiency

* Confidence â€“ critically assessing mathematical methods and investigating ways to apply them

* Problem solving â€“ analysing the â€˜unfamiliarâ€™ and identifying which skills and techniques you require to answer questions

* Constructing mathematical argument â€“ using mathematical tools such as diagrams, graphs, the logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others

* Deep reasoning â€“ analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied

Over eight modules, you will be introduced to

- Analytical and numerical methods for solving first-order differential equations
- The nth roots of unity, the nth roots of any complex number, geometrical applications of complex numbers.
- Coordinate systems and curve sketching.
- Improper integrals, integration using partial fractions and reduction formulae
- The area enclosed by a curve defined by parametric equations or polar equations, arc length and the surface area of revolution.
- Solving second-order differential equations
- The vector product and its applications
- Eigenvalues, eigenvectors, diagonalization and the Cayley-Hamilton Theorem.

Your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A -level further mathematics course. Youâ€™ll also be encouraged to consider how what you know fits into the wider mathematical world.