Higher November 2022 Paper 2 Q24
24 B is 60 miles from A on a bearing of \(170^\circ\)
A ship sails from A on a bearing of \(247^\circ\)
It travels at a constant speed of 23 mph for \(1\dfrac{1}{2}\) hours.
Is the ship now closer to B than it was when it left A?
You must show your working. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(247 - 170\) or 77 | M1 | oe may be on diagram |
| \(23 \times 1\dfrac{1}{2}\) or 34.5 | M1 | oe eg \(23 + 11.5\) or \(23 \times 90 \div 60\) or \(23 \times 1.5\) may be on diagram |
| (their \(34.5)^2 + 60^2 - 2 \times\) their \(34.5 \times 60 \times \cos\) (their 77) or [3858, 3859] | M1dep | oe dep on at least one M scored |
| \(\sqrt{\text{their } [3858, 3859]}\) or 62.1(…) | M1dep | oe eg \(\sqrt{34.5^2 + 60^2 - 2 \times 34.5 \times 60 \times \cos 77}\) dep on 3rd M1 |
| No and 62.1(…) | A1 | oe eg 62.1 and the ship is further away accept No and 62 with M4 scored |
Additional guidance
Up to M2 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts
2nd M1 Do not accept \(23 \times 1.30\) unless recovered