Higher June 2024 Paper 2 Q15
15 Given that \(a\) is a prime number, rationalise the denominator of \(\dfrac{1}{\sqrt{a} + 1}\)
Give your answer in its simplest form. (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{\sqrt{a} - 1}{a - 1}\) | M1 | for a correct method to rationalise the denominator, eg, \(\dfrac{1}{\sqrt{a} + 1} \times \dfrac{\sqrt{a} - 1}{\sqrt{a} - 1}\) or \(\dfrac{1}{\sqrt{a} + 1} \times \dfrac{1 - \sqrt{a}}{1 - \sqrt{a}}\) |
| A1 | for \(\dfrac{\sqrt{a} - 1}{a - 1}\) or \(\dfrac{1 - \sqrt{a}}{1 - a}\) |
Additional guidance
Condone use of a prime number in place of \(a\) for the M1
Do not ISW