June 2017 Paper 1 Q17
17
(a) Factorise \(\quad 2x^2 + 7x + 5\) [2 marks]
(b) Hence, or otherwise, work out the value of \(\theta\) between \(0^\circ\) and \(360^\circ\) for which\[2\sin^2\theta + 7\sin\theta + 5 = 0\]
[3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((2x + a)(x + b)\) | M1 | \(ab = 5\) or \(a + 2b = 7\) |
| \((2x + 5)(x + 1)\) | A1 |
Additional guidance
\(2(x + 2.5)(x + 1)\) and \((x + 2.5)(2x + 2)\) both score SC1
Ignore subsequent working ... eg solving
| Answer | Mark | Comments |
|---|---|---|
| \((2\sin\theta + 5)(\sin\theta + 1)\) (\(=0\)) or \(2\sin\theta + 5 = 0\) and \(\sin\theta + 1 = 0\) | M1 | ft their factors from part (a) |
| \(\sin\theta = -1\) | M1 | |
| \(270^\circ\) | A1 | only \(270^\circ\) ... no extra (incorrect) solutions |
Additional guidance
In (b) they can work with \(x\) or \(s\) but must eventually use \(\sin\theta = -1\)