Higher June 2017 Paper 6 Q18
18 Alvin has a crate in the shape of a cuboid.
The crate is open at the top.
The internal dimensions of the crate are 46 cm long by 46 cm wide by 55 cm high.
Alvin has a stick of length 95 cm.
Alvin places the stick in the crate so that the shortest possible length extends out above the top of the crate.
(a) Calculate the length of the stick that extends out of the crate. [4]
(b) Calculate the angle the stick makes with the base of the crate. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 9.8[1…] nfww | 4 | Accept answers rounding to 9.8 if correct working seen Condone for full marks minor inaccuracies from rounding, such as \(\sqrt{7256}\) seen | |
| M3 for \(\sqrt{46^2 + 46^2 + 55^2}\) or 85.18 to 85.2 or \(\sqrt{7257}\) OR M2 for \(46^2 + 46^2 + 55^2\) or 7257 or \(\sqrt{46^2 + 46^2}\) or \(\sqrt{4232}\) or 65.05 to 65.1 or \(\sqrt{46^2 + 55^2}\) or \(\sqrt{5141}\) or 71.7[…] OR M1 for \(46^2 + 46^2\) or 4232 or \(46^2 + 55^2\) or 5141 | May be done in steps | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 40.2 nfww | 3 | M2 for sin […] = \(\dfrac{55}{\mathit{their}\,85.18 \text{ to } 85.2}\) or tan […] = \(\dfrac{55}{\mathit{their}\sqrt{46^2 + 46^2}}\) or cos […] = \(\dfrac{\mathit{their}\sqrt{46^2 + 46^2}}{\mathit{their}\,85.18 \text{ to } 85.2}\) OR M1 for indication of required angle | Accept 40° and answers rounding to 40.2 if correct working seen 0 for tan […] = \(\frac{55}{46}\) M2 for cosine rule with cos as subject eg diagram showing angle |