Higher June 2018 Paper 2 Q21

EdexcelHigherCurrent spec6 marksSurds

(a) Show that \(\sqrt{45} + \sqrt{20} = 5\sqrt{5}\)
Show your working clearly. (2)

(b) Express \(\dfrac{2}{\sqrt{3} - 1}\) in the form \(p + \sqrt{q}\) where \(p\) and \(q\) are integers.
Show your working clearly. (2)

Mark scheme (a)

Scheme	Marks
\(\sqrt{9 \times 5}\) and \(\sqrt{4 \times 5}\)	M1
Working required Answer: \(5\sqrt{5}\) shown	A1
	(2)

Notes

M1: or for 45 = 3 × 3 × 5 and 20 = 2 × 2 × 5

A1: dep on M1 cao with sight of \(3\sqrt{5} + 2\sqrt{5}\) but we must see where these come from

Mark scheme (b)

Scheme	Marks
\(\dfrac{2}{\sqrt{3} - 1} \times \dfrac{\sqrt{3} + 1}{\sqrt{3} + 1}\) or \(\dfrac{2(\sqrt{3} + 1)}{3 - 1}\) or \(\dfrac{2\sqrt{3} + 2}{2}\)	M1
Working required Answer: \(1 + \sqrt{3}\) oe	A1
	(2)

Notes

M1: Rationalise denominator – award for seeing multiplication by \(\dfrac{\sqrt{3} + 1}{\sqrt{3} + 1}\) or \(\dfrac{-\sqrt{3} - 1}{-\sqrt{3} - 1}\)

A1: dep on M1

Scheme	Marks
\((x + 3\sqrt{2})^2 - (3\sqrt{2})^2 - 1\)	M1
\((x + 3\sqrt{2})^2 - 19\)	A1
	(2)
	(6 marks)