4MA0 Higher June 2013 Paper 3R Q10

EdexcelHigherOld spec4 marks2D Area & Perimeter Circles & Sectors

10 The diagram shows the path of an athlete on a running track.

Running track: a rectangle 85 m long with a semicircle of radius 36.6 m at each end

Diagram NOT accurately drawn

The path consists of two straight lengths and a semicircle at each end.
Each straight length is 85 metres.
Each semicircle has a radius of 36.6 metres.
Calculate the area enclosed by the path.
Give your answer correct to 3 significant figures.

(4)

Mark scheme

Scheme	Marks
\(\pi \times 36.6^2\;(= 4208.35..)\)	M1
85 x 2 x 36.6 (=6222)	M1
“4208.35..” + “6222” (=10430.35..)	M1
10400	A1
	(4)

Notes

M1: or \(\pi \times 36.6^2 \div 2\;(= 2104.17..)\)

M1: dep on both previous method marks

A1: awrt 10400
(accept correct answers given in an alternative form eg. \(1.04 \times 10^4\) ; \(104 \times 10^2\))
SC: B2 for an awrt 7320