4400 Higher June 2006 Paper 4 Q4
4
(a) The diagram shows triangle \(PQR\).
\(PQ = 4\) cm.
\(PR = 8\) cm.
Angle \(PQR = 90^\circ\).
\(PQ = 4\) cm.
\(PR = 8\) cm.
Angle \(PQR = 90^\circ\).
Diagram NOT accurately drawn
Calculate the value of \(x\).
(3)
(b) The diagram shows triangle \(LMN\).
\(MN = 12\) cm.
Angle \(LMN = 32^\circ\).
Angle \(MLN = 90^\circ\).
\(MN = 12\) cm.
Angle \(LMN = 32^\circ\).
Angle \(MLN = 90^\circ\).
Diagram NOT accurately drawn
Calculate the length of \(ML\).
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
| 4/8 or 0.5 oe | M1 |
| \(\sin x^\circ = 4/8\) oe | M1 |
| 30 | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(\cos 32^\circ = ML/12\) | M1 |
| \(12 \times \cos 32^\circ\) | M1 |
| 10(.17..) or 10.2 | A1 |
| (3) | |
| (6 marks) |
Notes
M1: May be implied \(\quad\) or \(12^2 - (12\sin 32)^2\)
M1: or \(\sqrt{12^2 - (12\sin 32)^2}\)
A1: Allow 10 with working