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.