Basic Trigonometry: Eduqas GCSE Foundation November 2023 Paper 2 Q25

Foundation November 2023 Paper 2 Q25

EduqasFoundationCurrent spec6 marksBasic Trigonometry

25. 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: a straight track sloping down from Vaughan at the top of the track to the bottom of the track at ground level, at 48 degrees below the horizontal; the vertical height is 800 feet

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]

(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]

Mark scheme (a)

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 equivalent full method. M1 for \(\cos(42)=\dfrac{800}{h}\) or \(\sin(48)=\dfrac{800}{h}\)
(\(h\) = ) 1076(.5….) or 1077 (feet)	A1	Allow 1076 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).

Mark scheme (b)

Scheme	Marks	Comments
(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°’
(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)