4MA0 Higher June 2017 Paper 3 Q16

EdexcelHigherOld spec3 marksSurds

16 \(\left(5\sqrt{2} - e\right)\left(3\sqrt{2} + e\right) = f\sqrt{2} - 6\)

Given that \(e\) and \(f\) are positive integers,

find the value of \(e\) and the value of \(f\).

(3)

Mark scheme

Scheme	Marks
E.g. \(5\sqrt{2} \times 3\sqrt{2} + 5e\sqrt{2} - 3e\sqrt{2} - e^2\) or \(30 + 2e\sqrt{2} - e^2\)	M1
\(5\sqrt{2} \times 3\sqrt{2} - e^2 = -6\) oe or rational terms correct and \(e = 6\) or \(5\sqrt{2}\,e - 3\sqrt{2}\,e = \sqrt{2}f\) oe or \(5e - 3e = f\) oe	M1
\(e = 6\) \(f = 12\)	A1
	(3)
	(3 marks)

M1: for rational terms correct (\(5\sqrt{2} \times 3\sqrt{2} - e^2\))

irrational terms correct (\(5e\sqrt{2} - 3e\sqrt{2}\))

NB: \(5\sqrt{2} \times 3\sqrt{2}\) may be fully or partially simplified

M1: dep on M1