4400 Higher June 2007 Paper 3 Q7

EdexcelHigherOld spec6 marksCompound Measures

7 A tunnel is 38.5 km long.

(a) A train travels the 38.5 km in 21 minutes.
Work out the average speed of the train.
Give your answer in km/h. (3)

(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled.
The radius of the cylindrical hole was 4.19 m.
Work out the volume of earth, in m³, which was removed to make the hole.
Give your answer correct to 3 significant figures. (3)

Mark scheme (a)

Scheme	Marks
\(\dfrac{38.5}{21} \times 60\) or \(\dfrac{21}{60} = 0.35\); \(\dfrac{38.5}{0.35}\)	M1
	M1
110	A1
	(3)

Notes

M1: for \(\dfrac{38.5}{21}\) or 1.83 or better

or \(\dfrac{38.5}{0.21}\) or 183.3 or better

or \(\dfrac{21}{60}\) or 0.35

M1: for ‘1.8333...’ × 60 or \(\dfrac{38.5}{\text{‘}0.35\text{’}}\)

A1: cao

Mark scheme (b)

Scheme	Marks
\(\pi \times 4.19^2 \times 38500\)	M2
2 120 000	A1
	(3)
	(6 marks)

Notes

M2: M1 for \(\pi \times\) (no with digits 419)\(^2\) × no with digits 385

A1: for 2 120 000 or for answer which rounds to 2 120 000