# A-level Mathematics/OCR/C4/Formulae

< A-level Mathematics‎ | OCR‎ | C4

## Formulae

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

### Differentiation

If $y = \sin kx,\,$ then $\frac{dy}{dx} = k\cos kx$.
If $y = \cos kx,\,$ then $\frac{dy}{dx} = -k\sin kx$.

### Integration

$\int \cos kx\, dx = \frac{1}{k}\sin kx +c$
$\int \sin kx\, dx = -\frac{1}{k}\cos kx +c$
$\int f^'[g(x)].g^'(x)\, dx = f[g(x)] +c$

### Vectors

$\left| x\mathbf{i}+y\mathbf{j}+z\mathbf{k} \right| = \sqrt{x^2+y^2+z^2}$
$(a\mathbf{i}+b\mathbf{j}+c\mathbf{k})\cdot(x\mathbf{i}+y\mathbf{j}+z\mathbf{k})=ax+by+cz$
$\mathbf{a}\cdot\mathbf{b} = \left|\mathbf{a}\right|\left|\mathbf{b}\right|\cos \theta$
The vector equation of a line through point $\mathbf{a}$ with direction $\mathbf{b}$ is $\mathbf{r} = \mathbf{a} + t\mathbf{b}$