Without using a calculator, simplify \(\frac{(3 \sqrt{3}-1)^{2}}{2 \sqrt{3}-3}\), giving your answer in the form \(\frac{a \sqrt{3}+b}{3}\), where \(a\) and \(b\) are integers.

Available soon

2013 Oct Nov Paper 21 & 22 Q2

Express \(\frac{(4 \sqrt{5}-2)^{2}}{\sqrt{5}-1}\) in the form \(p \sqrt{5}+q\), where \(p\) and \(q\) are integers.

Available soon

2014 May June Paper 22 Q1

Without using a calculator, express \(\frac{(2+\sqrt{5})^{2}}{\sqrt{5}-1}\) in the form \(a+b \sqrt{5}\), where \(a\) and \(b\) are constants to be found.

Available soon

2016 May June Paper 21 & 23 Q5

Do not use a calculator in this question. (a) Express \(\frac{\sqrt{8}}{\sqrt{7}-\sqrt{5}}\) in the form \(\sqrt{a}+\sqrt{b}\), where \(a\) and \(b\) are integers.

Available soon

2016 Oct Nov Paper 23 Q1

Without using a calculator, show that \(\frac{\sqrt{5}+3 \sqrt{3}}{\sqrt{5}+\sqrt{3}}=\sqrt{k}-2\) where \(k\) is an integer to be found.