Higher June 2018 Paper 1 Q13
13. Rearrange \(x + y = \sqrt{2(xy + w)}\) to make \(x\) the subject. [5]
| Scheme | Marks | Comments |
|---|---|---|
| For squaring both sides e.g \((x + y)^2 = 2(xy + w)\) or equivalent, seen or implied | B1 | FT until second error where possible; a first line of \(x^2 + y^2 = 2(xy + w)\) implies the first B1 |
| \(x^2 + y^2 + xy + yx = 2xy + 2w\) or better | B2 | FT B1 FT for 3 out of 4 terms correct in \((x + y)^2 = x^2 + xy + yx + y^2\) or for \(x^2 + y^2 + 2xy = 2xy + w\) or for \(x^2 + y^2 + 2xy = 4xy + 2w\) Omission of (2)\(xy\) in expansion of \((x + y)^2\) counts as one error |
| \(x^2 = 2w - y^2\) | B1 | FT for collection of ‘their \(x\) terms’ to one side and all other terms to the other |
| \(x = \pm\sqrt{2w - y^2}\) CAO | B1 | Mark final answer Allow \(x = \sqrt{2w - y^2}\); the final subject must be \(x\) If B1 B2 B0, allow SC1 for a final answer of \(x = \pm\sqrt{2w + y^2}\) |
| (5) |