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

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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)


  •  \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[edit]

  • 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


  • \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.