A-level Mathematics/OCR/FP3

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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 ${\displaystyle {\frac {dy}{dx}}+P(x)y=Q(x)}$ is ${\displaystyle e^{\int P(x)\,dx}}$

Vectors

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

Complex Numbers

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

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