Higher November 2019 Paper 1 Q16
16
(a) Rationalise the denominator of \(\dfrac{22}{\sqrt{11}}\)
Give your answer in its simplest form. (2)
Give your answer in its simplest form. (2)
(b) Show that \(\dfrac{\sqrt{3}}{2\sqrt{3} - 1}\) can be written in the form \(\dfrac{a + \sqrt{3}}{b}\) where \(a\) and \(b\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(2\sqrt{11}\) | M1 | for method to multiply numerator and denominator by \(\sqrt{11}\) or a multiple of \(\sqrt{11}\), eg \(\dfrac{22}{\sqrt{11}} \times \dfrac{\sqrt{11}}{\sqrt{11}}\) |
| A1 | for \(2\sqrt{11}\) |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{6 + \sqrt{3}}{11}\) | M1 | for method to multiply numerator and denominator by \(2\sqrt{3} + 1\) or a multiple of \(2\sqrt{3} + 1\), eg \(\dfrac{\sqrt{3}}{2\sqrt{3} - 1} \times \dfrac{2\sqrt{3} + 1}{2\sqrt{3} + 1}\) |
| M1 | (dep) for \(\sqrt{3} \times 2\sqrt{3} = 6\) or \(2\sqrt{3} \times 2\sqrt{3} = 12\) | |
| A1 | for \(\dfrac{6 + \sqrt{3}}{11}\) (accept \(a = 6\) and \(b = 11\)) |