4MA0 Higher January 2016 Paper 4R Q11

EdexcelHigherOld spec3 marks2D Area & Perimeter Circles & Sectors

Rectangle ABCF, 20 cm by 10 cm, with a semicircle cut from the side FC between E and D; FE = DC = 4 cm

Diagram NOT accurately drawn

The shaded shape is made by cutting a semicircle from a rectangular piece of card, \(ABCF\), as shown in the diagram.
\(FEDC\) is a straight line.
The centre of the semicircle lies on \(ED\).
\(AF = BC = 10\) cm, \(AB = 20\) cm, \(FE = DC = 4\) cm.

Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.

(3)

Mark scheme

Scheme	Marks
\(\pi \times (20 - 2 \times 4)\) oe or \(\pi \times 12\) oe or \(2 \times \pi \times 6\) or 37.6... or 37.7 or \(\dfrac{1}{2} \times \pi \times (20 - 2 \times 4)\) oe or \(\dfrac{1}{2} \times \pi \times 12\) oe or \(\pi \times 6\) or 18.8…	M1
\(4 + 10 + 20 + 10 + 4 + \dfrac{1}{2} \times\) “37.6…” or 4 + 10 + 20 + 10 + 4 + “18.8…”	M1
66.8	A1
	(3)

Notes

M1: for a correct method to find the circumference or half of the circumference

M1: (dep on previous M1) for complete method

A1: 66.8 – 66.9