4MA0 Higher January 2016 Paper 4 Q19
19
Diagram NOT accurately drawn
\(PSR\) is a straight line.
Angle \(PSQ\) = 90°
\(PS\) = 8.4 cm
Angle \(QPS\) = 38°
Angle \(SQR\) = 44°
Work out the length of \(QR\).
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\tan 38 = \dfrac{QS}{8.4}\) or \(\tan 52 = \dfrac{8.4}{QS}\) or \(\dfrac{QS}{\sin 38} = \dfrac{8.4}{\sin 52}\) | M1 |
(\(QS\) =) 8.4tan38 or (\(QS\) =) 8.4/tan52 or (\(QS\) =) \(\dfrac{8.4\sin 38}{\sin 52}\) (=6.56…) | M1 |
| (\(QR\) =) \(\dfrac{\text{‘6.56’}}{\cos 44}\) or (\(QR\) =) \(\dfrac{\text{‘6.56’}}{\sin 46}\) | M1 |
| \(QR\) = 9.12(336459) Answer: 9.12 | A1 |
| (4) |
Notes
M1: Must be a correct equation
M1: A correct calculation for \(QS\) or 6.56…
M1: A correct calculation with their \(QS\) for length \(QR\)
A1: Awrt 9.12
Alternative
| Scheme | Marks |
|---|---|
| \(\cos 38 = \dfrac{8.4}{PQ}\) or \(\sin 52 = \dfrac{8.4}{PQ}\) | M1 |
| (\(PQ\) =) \(\dfrac{8.4}{\cos 38}\) or (\(PQ\) =) \(\dfrac{8.4}{\sin 52}\) (=10.65…) | M1 |
| (\(QR\) =) \(\dfrac{\text{‘10.65..’}}{\sin 46} \times \sin 38\) | M1 |
| \(QR\) = 9.12(336459) Answer: 9.12 | A1 |
Notes
M1: Must be a correct equation
M1: A correct calculation for \(PQ\) Or 10.65…
M1: A correct calculation with their \(PQ\) for length \(QR\)
A1: Awrt 9.12