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:

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

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Contents

Formulae

Differential Equations

Vectors

Complex Numbers