4MA0 Higher June 2011 Paper 4 Q23
23 Express \(\sqrt{48} + \sqrt{108}\) in the form \(k\sqrt{6}\) where \(k\) is a surd.
(3)
| Scheme | Marks |
|---|---|
\(\sqrt{(8 \times 6)} + \sqrt{(18 \times 6)}\) Answer: must see intention to add | M1 |
| \((2\sqrt{2} \times \sqrt{6}) + (3\sqrt{2} \times \sqrt{6})\) | M1 |
| (\(k\)=) \(\sqrt{50}\) or \(5\sqrt{2}\) or \(\dfrac{10}{\sqrt{2}}\) | A1 |
| (Total 3 marks) |
Notes
M1: or \(\sqrt{(16 \times 3)} + \sqrt{(36 \times 3)}\) (= \(10\sqrt{3}\)) or \(\sqrt{(4 \times 12)} + \sqrt{(9 \times 12)}\) (= \(5\sqrt{12}\))
M1: \(10\sqrt{3} \times \dfrac{\sqrt{2}}{\sqrt{2}}\) or \(\dfrac{10\sqrt{3}}{\sqrt{6}}\) or \(5\sqrt{12} \times \dfrac{\sqrt{2}}{\sqrt{2}}\) or \(5 \times \sqrt{(6 \times 2)}\)
A1: dep on at least 1 M1
sight of decimals used in working loses M marks at that stage and A mark