# A-level Mathematics/OCR/FP3

This is the Further Pure Mathematics 3 module of the A-level Mathematics book. This module assumes that you are familiar with the C1, C2, C3, C4 and FP1 modules. Please post all questions to A-level Mathematics/Discussion.

## Formulae

By the end of this module you will be expected to have learnt the following formulae:

### Differential Equations

• An integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x)\, dx}$

### Vectors

• The vector equation of a plane through point $\mathbf{a}$ with normal vector $\mathbf{n}$ is $(\mathbf{r}-\mathbf{a})\cdot\mathbf{n} = 0$

### Complex Numbers

If $z = e^{i\theta}$ then:

• $\cos \theta = \frac{1}{2}\left(z+\frac{1}{z}\right)$
• $\sin \theta = \frac{1}{2i}\left(z-\frac{1}{z}\right)$