Higher January 2022 Paper 2 Q3

EdexcelHigherCurrent spec3 marksSimilar Shapes

Two similar triangles: triangle ABC with AB = 4 cm and AC = x cm, and the larger triangle PQR with PQ = 12 cm, PR = y cm and RQ = 16.5 cm; the angles at A and P are marked equal and the angles at C and R are marked equal

Diagram NOT accurately drawn

Triangle \(ABC\) is similar to triangle \(PQR\)

\(AB = 4\) cm \(PQ = 12\) cm \(RQ = 16.5\) cm \(AC = x\) cm \(PR = y\) cm

(a) Calculate the length of \(BC\) (2)

(b) Write down an expression for \(y\) in terms of \(x\) (1)

Mark scheme (a)

Scheme	Marks
\(\dfrac{12}{4}\;(= 3)\) or \(\dfrac{4}{12}\;(= 0.\dot{3})\) or \(\dfrac{BC}{4} = \dfrac{16.5}{12}\) or \(BC \div 16.5 = 4 \div 12\) or \((BC =)\;16.5 \div \dfrac{12}{4}\) oe	M1
5.5	A1
	(2)

Notes

M1: correct scale factor (given as 3 or a fraction or a ratio) or correct equation using \(BC\) or a correct expression for \(BC\)
(award for SF even if not used)

Scheme	Marks
\(3x\)	B1
	(1)
	(3 marks)