4MA0 Higher June 2012 Paper 4 Q20
20 Show that \((6 - \sqrt{8})^2 = 44 - 24\sqrt{2}\)
Show each stage of your working clearly.
(3)
| Scheme | Marks |
|---|---|
| \(36 - 6\sqrt{8} - 6\sqrt{8} + 8\) or \(36 - 12\sqrt{8} + 8\) | M2 |
\(44 - 12\sqrt{(4 \times 2)}\) \(44 - 12\sqrt{4} \times \sqrt{2}\) Answer: \(44 - 24\sqrt{2}\)* | M1 |
| (Total 3 marks) |
Notes
M2: M1 for \(6^2 + (\sqrt{8})^2\) or 36 + 8 or \(6^2 + \sqrt{64}\) or \(-12\sqrt{8}\) or \(-6\sqrt{8} - 6\sqrt{8}\)
M1: for \((-)12\sqrt{8} = (-)12 \times 2\sqrt{2}\) or \(\sqrt{8} = 2\sqrt{2}\) or \(6\sqrt{8} = 6 \times 2\sqrt{2}\)
Must see \(\sqrt{8}\) stated as \(2\sqrt{2}\) for final M1
Alt
| Scheme | Marks |
|---|---|
| LHS = \((6 - 2\sqrt{2})^2\) or \(\sqrt{8} = 2\sqrt{2}\) | M1 |
| \(6^2 - 12\sqrt{2} - 12\sqrt{2} + 4 \times 2\) or \(36 - 24\sqrt{2} + 8\) | M2 |
Notes
M2: M1 for \(6^2 + 4 \times 2\) or 36 + 8