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/ Template:Stage short
2. /More About Vectors/ Template:Stage short
3. /Hyperbolic Functions/ Template:Stage short
4. /Complex Numbers/ Template:Stage short
5. /Groups/ Template:Stage short

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 $𝐚$ with normal vector $𝐧$ is $(𝐫-𝐚)\cdot 𝐧=0$

Complex Numbers

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

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