A-level Mathematics/OCR/FP3

From Wikibooks, open books for an open world
Jump to: navigation, search

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[edit]

  1. More About Differential Equations 0% developed
  2. More About Vectors 0% developed
  3. Hyperbolic Functions 0% developed
  4. Complex Numbers 0% developed
  5. Groups 0% developed

Formulae[edit]

By the end of this module you will be expected to have learnt the following formulae:

Differential Equations[edit]

  • An integrating factor of \frac{dy}{dx} + P(x)y = Q(x) is   e^{\int P(x)\, dx}

Vectors[edit]

  • 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[edit]

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)