A Level Further Maths, Core Pure 1, Chapter 4 · exam-style questions with mark schemes and worked solutions · shadows of past-paper questions and new questions in the style of Edexcel, Edexcel iAL, AQA, OCR A and MEI · the sum and product of the roots of a quadratic, $\sum\alpha$, $\sum\alpha\beta$ and $\alpha\beta\gamma$ for a cubic and $\alpha\beta\gamma\delta$ for a quartic, expressions such as $\alpha^{2} + \beta^{2} + \gamma^{2}$, $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ and $(\alpha + 2)(\beta + 2)(\gamma + 2)$, roots with a given relationship, and new equations whose roots are $2\alpha - 1$, $\alpha^{2}$ or $\frac{1}{\alpha}$