Higher June 2024 Paper 1 Q11
11 The diagram shows a roof support.
Diagram NOT accurately drawn
The roof support is made from four lengths of wood, \(AB\), \(AC\), \(BC\) and \(MC\)
\(AC = BC = 9\) m \(\qquad AB = 12\) m
angle \(AMC = 90^\circ\)
Lewis is going to buy lengths of wood to make the roof support.
The wood costs 21.50 euros per metre.
Each length of wood he buys has to be a whole number of metres.
Work out the total cost of the wood Lewis needs to buy.
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| \((CM)^2 + (12 \div 2)^2 = 9^2\) oe or \(9^2 - (12 \div 2)^2\) \((= 81 - 36 = 45)\) | M1 \(AM = MB\) \(CAM = CBM\) |
\(\sqrt{9^2 - (12 \div 2)^2}\) oe \((= \sqrt{81 - 36} = \sqrt{45} = 3\sqrt{5} = 6.7(08...))\) | M1 |
| (“7”+ 9 + 9 + 12) × 21.5(0) or 37 × 21.5(0) | M1 |
| Working required Answer: 795.5(0) | A1 |
| (4) | |
| (4 marks) |
Notes
A1: dep on M2
SC B3 for awrt 789 for using 6.7…
M2 for (first two M1 marks)
\(\big(\cos^{-1}(CAM) =\big)\dfrac{12 \div 2}{9} = 48.1(896...)\)
and
\((CM =)(12 \div 2) \times \tan \text{``}{48.1...}\text{''}(= 6.7…)\)
or
\((CM =)\, 9 \times \sin \text{``}{48.1...}\text{''}(= 6.7…)\)