# 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

• $\mathbf {(AB)^{-1}} =\mathbf {B^{-1}A^{-1}}$ This is part of the FP1 (Further Pure Mathematics 1) module of the A-level Mathematics text.