4MA0 Higher June 2013 Paper 3 Q21

EdexcelHigherOld spec6 marksAdvanced Trigonometry Circles & Sectors

21 Here is a shape.

Shape made from triangle ABC and a major sector of a circle centre C, radius 7 cm; CA = 7 cm, angle ACB = 150°, and the 9 cm part of CB lies outside the circle

Diagram NOT accurately drawn

The shape is made from triangle \(ABC\) and a sector of a circle, centre \(C\) and radius \(CA\).
\(CA = 7\) cm.
\(CB = 16\) cm.
Angle \(ACB = 150^\circ\)

Calculate the area of the shape.
Give your answer correct to 3 significant figures.

(6)

Mark scheme

Scheme	Marks
\(\tfrac{1}{2} \times 7 \times 16 \times \sin 150^\circ\)	M1
	M1
\(\dfrac{210}{360} \times \pi \times 7^2\) or \(\pi \times 7^2 - \dfrac{150}{360} \times \pi \times 7^2\)	M2
	A1
118	A1
	(6)

Notes

M1: for \(\tfrac{1}{2} \times 7 \times 16 \times \sin 150^\circ\)

M1: for \(\pi \times 7^2\) or \(49\pi\) or for value rounding to 153.9

M2: correct method for sector of circle

M1 for \(\dfrac{210}{360}\) oe inc 0.5833... rounded or truncated to at least 3 decimal places

or for \(\dfrac{360}{210}\) oe inc 1.714... rounded or truncated to at least 2 decimal places

A1: for value rounding to 89.8 or \(\dfrac{343\pi}{12}\) for area of sector

or 28 for area of triangle

A1: for value rounding to 118