November 2021 Paper 2 Q6
6 Rearrange \(\quad y = \sqrt{\dfrac{x + 2w}{3}} \quad\) to make \(w\) the subject. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(y^2 = \dfrac{x + 2w}{3}\) | M1 | |
| \(3y^2 - x = 2w\) or \(\dfrac{3y^2 - x}{2}\) or \(\dfrac{3y^2}{2} - \dfrac{x}{2}\) | M1dep | |
| \(w = \dfrac{3y^2 - x}{2}\) or \(w = \dfrac{3y^2}{2} - \dfrac{x}{2}\) | A1 | |
| Alternative method 2 | ||
| \(y^2 = \dfrac{x}{3} + \dfrac{2w}{3}\) | M1 | |
| \(y^2 - \dfrac{x}{3} = \dfrac{2w}{3}\) or \(\dfrac{3}{2}\left(y^2 - \dfrac{x}{3}\right)\) or \(\dfrac{3y^2}{2} - \dfrac{3x}{6}\) | M1dep | |
| \(w = \dfrac{3}{2}\left(y^2 - \dfrac{x}{3}\right)\) or \(w = \dfrac{3y^2}{2} - \dfrac{3x}{6}\) | A1 | |
Additional guidance
| Condone eg \(w = \dfrac{3y^2 - x}{2}\) seen in working with \(\dfrac{3y^2 - x}{2}\) on answer line | M2A1 |
| \(w = \dfrac{3}{2}y^2 - \dfrac{1}{2}x\) etc | M2A1 |