A-level Mathematics/FP1/Appendix A: Formulae

Formulae

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

Series

• $\sum _{r=1}^{n}r=\frac{1}{2}n(n+1)$
• $\sum _{r=1}^n{r}^2=\frac{1}{6}n(2n+1)(n+1)$
• $\sum _{r=1}^n{r}^3=\frac{1}{4}{n}^2{(n+1)}^2$

Roots of Polynomials

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

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

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

Matrices

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

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