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.

Contents

1. More About Differential Equations
2. More About Vectors
3. Hyperbolic Functions
4. Complex Numbers
5. Groups

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^iθ then:

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