A-level Mathematics/OCR/FP3

This is the Futher 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:

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