4MA0 Higher January 2017 Paper 3 Q19
19 Make \(e\) the subject of \(\;k = \sqrt{\dfrac{5m + 2e}{3e}}\)
(4)
| Scheme | Marks |
|---|---|
| \(k^2 = \dfrac{5m + 2e}{3e}\) or \(k\sqrt{3e} = \sqrt{5m + 2e}\) | M1 |
| \(3ek^2 = 5m + 2e\) | M1 |
| \(3ek^2 - 2e = 5m\) or \(-5m = 2e - 3ek^2\) \(e(3k^2 - 2) = 5m\) or \(-5m = e(2 - 3k^2)\) | M1 |
| \(e = \dfrac{5m}{3k^2 - 2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Squaring both sides or clearing fraction
M1: Clearing fraction and squaring both sides
M1: Isolating terms in \(e\) in a correct equation
A1: for \(e = \dfrac{5m}{3k^2 - 2}\) or \(e = \dfrac{-5m}{2 - 3k^2}\) oe