1MA0 Higher June 2013 Paper 2 Q20
*20 The diagram shows a ladder leaning against a vertical wall.
Diagram NOT accurately drawn
The ladder stands on horizontal ground.
The length of the ladder is 6 m.
The bottom of the ladder is 2.25 m from the bottom of the wall.
A ladder is safe to use when the angle marked \(y\) is about \(75^\circ\).
Is the ladder safe to use?
You must show all your working. (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\cos y = 2.25 \div 6\) \(y = \cos^{-1}(2.25 \div 6)\) OR \(6\cos 75 = 1.55\ldots\) | The ladder is not safe because \(y\) is not near to 75 | 3 | M1 for \(\cos y = 2.25 \div 6\) oe M1 for \(\cos^{-1}(2.25 \div 6)\) C1 for sight of 67-68 and a statement eg this angle is NOT (near to) 75° and so the ladder is not steep enough and so not safe. OR M1 for \(\cos 75 = x \div 6\) M1 for \(6\cos 75\) C1 for sight of 1.55(29…) and a statement eg that 2.25 NOT (near to) 1.55 and so the ladder is not steep enough and so not safe. |