Higher November 2021 Paper 2 Q17
17 Express \(\dfrac{8}{\sqrt{5} - 1}\) in the form \(\sqrt{a} + b\) where \(a\) and \(b\) are integers.
Show each stage of your working clearly.
(3)
| Scheme | Marks |
|---|---|
\(\left(\dfrac{8}{\sqrt{5} - 1}\right) \times \dfrac{\sqrt{5} + 1}{\sqrt{5} + 1}\) or \(\dfrac{8\left(\sqrt{5} + 1\right)}{4}\) or \(\dfrac{8\sqrt{5} + 8}{4}\) oe | M1 |
Working required Answer: \(2\sqrt{5} + 2\) | A1 |
| \(\sqrt{20} + 2\) | B1ft |
| (3) | |
| (3 marks) |
Notes
M1: for rationalising the denominator – award for seeing intention to multiply by \(\dfrac{\sqrt{5} + 1}{\sqrt{5} + 1}\) or \(\dfrac{-\sqrt{5} - 1}{-\sqrt{5} - 1}\)
A1: from correct working
B1ft: for \(k\sqrt{5} + c = \sqrt{5k^2} + c\) where \(5k^2\) is a single integer
Accept \(a = 20\) and \(b = 2\)