June 2023 Paper 1 Q9
9 Rearrange \(\quad w = \dfrac{y^2 + 5}{y^2 - 2} \quad\) to make \(y\) the subject. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(w(y^2 - 2) = y^2 + 5\) | M1 | |
| \(wy^2 - 2w = y^2 + 5\) | M1dep | |
| \(y^2(w - 1) = 2w + 5\) or \(y^2 = \dfrac{(2w + 5)}{(w - 1)}\) or \(y^2(-w + 1) = -2w - 5\) or \(y^2 = \dfrac{(-2w - 5)}{(-w + 1)}\) | M1dep | rearranges and factorises |
| \(y = (\pm)\sqrt{\dfrac{(2w + 5)}{(w - 1)}}\) or \(y = (\pm)\sqrt{\dfrac{(-2w - 5)}{(-w + 1)}}\) | A1 |
Additional guidance
| Root must cover the whole function for final mark (or separate roots over both numerator and denominator) | |
| Must be \(y =\) If correct answer in working then \(y =\) lost on the answer line then transcription error so A1 can be awarded | |
| Penalise incorrect further working |