Foundation November 2020 Paper 2 Q23

23 The diagram shows an isosceles triangle.

Diagram NOT accurately drawn

Work out the area of the triangle.

(4)

Mark scheme

Scheme	Marks
\(8.5^2 - (8 \div 2)^2\) (= 56.25) or \(\cos x = \dfrac{4}{8.5}\)	M1
\(\sqrt{\text{“56.25”}}\) (= 7.5) or \(x = \cos^{-1}\left(\dfrac{4}{8.5}\right)\) (= 61.927...)	M1
8 × “7.5” ÷ 2 oe or 0.5 × 8 × 8.5 × sin “61.927...”	M1
30	A1
	(4)
	(4 marks)

M1: or eg \(\cos A = \dfrac{8^2 + 8.5^2 - 8.5^2}{2 \times 8 \times 8.5}\)

M1: or eg (\(A\) =) \(\cos^{-1}\left(\dfrac{8^2 + 8.5^2 - 8.5^2}{2 \times 8 \times 8.5}\right)\) (61.927...)

(other angle = 56.144...)

M1: or eg 0.5 × 8.5 × 8 × sin61.927...oe