4400 Higher November 2006 Paper 4 Q14
14

Diagram NOT accurately drawn
Triangle \(LMN\) is right-angled at \(N\).
\(MN = 5.4\) cm and \(LN = 9.3\) cm.
(a) Work out the size of angle \(LMN\).
Give your answer correct to 1 decimal place. (3)
Give your answer correct to 1 decimal place. (3)
The length of \(MN\) is 5.4 cm, correct to 2 significant figures.
(b)
(i) Write down the upper bound of the length of \(MN\).
(ii) Write down the lower bound of the length of \(MN\). (2)
The length, 5.4 cm, of \(MN\) and the length, 9.3 cm, of \(LN\), are each correct to 2 significant figures.
The line \(MN\) is horizontal and the line \(LN\) is vertical.
(c) Work out the upper bound for the gradient of the line \(LM\). (2)
| Scheme | Marks |
|---|---|
| \(\tan \angle LMN = \dfrac{9.3}{5.4}\) | M1 |
| \(\frac{9.3}{5.4}\) or 1.722... | A1 |
| 59.9 | A1 |
| (3) |
Notes
M1: \(\sin LMN = \dfrac{9.3}{\sqrt{9.3^2 + 5.4^2}}\) or cos etc M1A1
A1: for 59.85 − 59.9
| Scheme | Marks |
|---|---|
| (i) Answer: 5.45 | B1 |
| (ii) Answer: 5.35 | B1 |
| (2) |
Notes
B1: Accept \(5.44\dot{9}\), 5.4499...
B1: cao
| Scheme | Marks |
|---|---|
| \(\dfrac{9.35}{\text{“}5.35\text{”}}\) | M1 |
| 1.74766... | A1 |
| (2) | |
| (7 marks) |
Notes
A1: for 1.74 or 1.75 or better