4MA0 Higher January 2015 Paper 4R Q17

EdexcelHigherOld spec4 marksSurds

(a) Show that \((3 + 2\sqrt{2})(4 - \sqrt{2}) = 8 + 5\sqrt{2}\)
Show your working clearly. (2)

(b) Rationalise the denominator and simplify fully \(\dfrac{10 + 3\sqrt{2}}{\sqrt{2}}\)
Show your working clearly. (2)

Mark scheme (a)

Scheme	Marks
\(12 - 3\sqrt{2} + 8\sqrt{2} - 2\sqrt{2} \times \sqrt{2}\) or \(12 - 3\sqrt{2} + 8\sqrt{2} - 2 \times 2\) or \(12 - 3\sqrt{2} + 8\sqrt{2} - 4\)	M1
\(8 + 5\sqrt{2}\)	A1
	(2)

M1: for any 3 terms correct of a 4 term expansion

A1: dep on M1 with all necessary steps shown

Mark scheme (b)

Scheme	Marks
\(\dfrac{10 + 3\sqrt{2}}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\) or \(\dfrac{10}{\sqrt{2}} + 3 = \dfrac{10}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} + 3\)	M1
\(5\sqrt{2} + 3\)	A1
	(2)
	(4 marks)

M1: for a correct method to rationalise denominator

A1: dep on M1 with all necessary steps shown