If you are studying Further Mathematics alongside Mathematics, in a class with students who are only studying Mathematics, you will need to study some sections of Core 3 and Core 4 independently, earlier than you cover it in your A2 Core classes.

To help you with this independent study, the FMSP has produced a series of short videos. These introduce all the material that you will need to know. Note that the content is common to all examination boards. The videos are divided into 3 sections:

After watching each video, you will need to complete some consolidation work from your own text books. If you need additional help, you should ask your own A level teacher, who will understand your need to get ahead with this work. We suggest that you consult your teacher about which exercises to tackle.

The videos assume that you have already covered some of Core 3 as well as the AS Core, in particular the Chain Rule. (Note that the video on this topic is concerned with increasing fluency in this area, not with studying it from scratch.) You may find that you have also covered some of the other material in section A: Trigonometric Functions and Differentiation.

- New trigonometric functions and pythagorean identities
- Trigonometric addition formulae
- Differentiating the exponential, logarithm and trig functions
- Fluency with the chain rule
- Fluency with the product and quotient rules, implicit and parametric differentiation

- Integrating trigonometric, exponential and reciprocal functions
- Using trigonometric identities to simplify integrals
- Integration by substitution
- Integration by parts and parametric integration
- Differential equations

- Definitions and basics
- Magnitude and unit vectors
- Vector equations of straight lines
- The scalar product and the angle between two lines