Higher June 2023 Paper 1 Q21
21. In this question all lengths are in centimetres.
Diagram not drawn to scale
The length of this rectangle is \(\sqrt{5} + 3\).
The perimeter of the rectangle is \(8\sqrt{5} - 2\).
Calculate the exact area of this rectangle. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(\big(8\sqrt{5} - 2 - 2(\sqrt{5} + 3)\big) \div 2\) OR \(4\sqrt{5} - 1 - (\sqrt{5} + 3)\) | M2 | Condone missing brackets if A1 is awarded. M1 for either:
|
| \(3\sqrt{5} - 4\) | A1 | CAO |
| \((3\sqrt{5} - 4)(\sqrt{5} + 3) = 15 + 9\sqrt{5} - 4\sqrt{5} - 12\) | M1 | FT ‘their \(a\sqrt{5} \pm b\)’ providing \(a \ne 0\) and \(b \ne 0\). |
| \(5\sqrt{5} + 3\) (cm2) | A1 | Mark final answer. FT |
| (5) |