Higher November 2023 Paper 2 Q7
7. Vaughan cycles down a track from the top of a mountain to the bottom.
The track goes down at an angle of 48° to the horizontal.
Vaughan is 800 feet above ground level.
Diagram not drawn to scale
(a) Vaughan cycles from the top of the track to the bottom of the track.
What distance has he cycled? [4]
What distance has he cycled? [4]
(b)
(i) State an assumption you have made in answering part (a). [1]
(ii) If your assumption is not correct, what effect would this have on your answer to part (a)? [1]
| Scheme | Marks | Comments |
|---|---|---|
| Use of trigonometry in a right-angled triangle with an angle of 48(°) or 42(°) and a side of 800 (feet) | S1 | Trig ratio used may not be correct at this stage. |
| \((h =)\ \dfrac{800}{\cos(42)}\) or \((h =)\ \dfrac{800}{\sin(48)}\) | M2 | Or alternative full method M1 for \(\cos(42) = \dfrac{800}{h}\) or \(\sin(48) = \dfrac{800}{h}\) |
| (h = ) 1076(.5….) or 1077 (feet) | A1 | Allow 1076 (feet) from correct working |
Corrected by Westie's Workshop
- The board's mark scheme printed “800 (m)”. Changed to “800 (feet)” because the question gives the height as 800 feet, not metres.
Original: see the board's mark scheme PDF (link above).
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) A correct assumption e.g. ‘The (surface of) the slope is smooth (and he cycles the shortest distance).’ | E1 | Allow e.g. ‘He rode in a straight line.’ ‘It was a straight line.’ ‘The track wasn’t bumpy.’ ‘He cycled straight from the top to the bottom.’ ‘He didn’t do any jumps.’ ‘There are no obstructions.’ ‘The surface is flat.’ ‘He cycled the shortest distance.’ ‘That it was 48° the whole way down’. ‘That it is a right-angled triangle’ ‘The track is level’ (assume they mean not bumpy) Do not allow: ‘That it was 48°’ |
| (b)(ii) A correct effect of assumption e.g. ‘If the surface of the slope is not smooth then Vaughan will have cycled further than the calculated value in (a).’ | E1 | If no valid assumption is made, then this mark cannot be awarded. Cannot award E0 E1. Allow e.g. ‘He cycled further.’ ‘The answer would be bigger.’ Do not allow: ‘The answer would be different’ |
| (6) |