A-level Mathematics/OCR/FP1/Appendix A: Formulae

Formulae
By the end of this module you will be expected to have learnt the following formulae: Formulae marked † are in the standard OCR Maths Data book (as of 2010)

Series

 * $$ \sum_{r=1}^n r = \frac{1}{2} n(n+1) $$
 * $$\sum_{r=1}^n r^2 = \frac{1}{6}n\left(2n+1\right)\left(n+1\right)$$ †
 * $$\sum_{r=1}^n r^3 = \frac{1}{4}n^2\left(n+1\right)^2$$ †

Roots of Polynomials

 * Let $$\alpha\,$$ and $$\beta\,$$ be the roots of $$ax^2+bx+c=0$$. Then, $$\alpha + \beta = - \frac{b}{a},\quad \alpha\beta = \frac{c}{a}$$
 * Let $$\alpha, \beta\,$$ and $$\gamma\,$$ be the roots of $$ax^3+bx^2+cx+d=0$$. Then, $$\sum\alpha = - \frac{b}{a},\quad \sum\alpha\beta = \frac{c}{a},\quad \alpha\beta\gamma = -\frac{d}{a} $$

Where: $$\sum\alpha = \alpha + \beta + \gamma$$

And: $$\sum\alpha\beta = \alpha\beta + \alpha\gamma + \beta\gamma$$

Matrices

 * $$\mathbf{(AB)^{-1}}=\mathbf{B^{-1}A^{-1}}$$