Higher January 2020 Paper 1 Q17

EdexcelHigherCurrent spec6 marksSurds

(a) Show that \(\;\left(6 + 2\sqrt{12}\right)^2 = 12\left(7 + 4\sqrt{3}\right)\)
Show each stage of your working. (3)

(b) Simplify fully \(\;\left(\dfrac{27a^{12}}{t^{15}}\right)^{-\frac{2}{3}}\) (3)

Mark scheme (a)

Scheme	Marks
\(6 \times 6 + 6 \times 2\sqrt{12} + 6 \times 2\sqrt{12} + \left(2 \times \sqrt{12}\right)^2\) or \(36 + 12\sqrt{12} + 12\sqrt{12} + 4\sqrt{12}\sqrt{12}\) or \(36 + 12\sqrt{12} + 12\sqrt{12} + (4 \times 12)\) or \(36 + 24\sqrt{3} + 24\sqrt{3} + 48\) or \(36 + 2 \times 24\sqrt{3} + 48\) or \(36 + 6 \times 2 \times 2\sqrt{12} + 48\)	M1
\(84 + 48\sqrt{3}\)	M1
Shown	A1
	(3)

M1: for correct expansion of brackets showing four terms (need not be simplified)

for the use of \((a + b)^2 = a^2 + 2ab + b^2\)

for showing or stating \(\sqrt{12} = 2\sqrt{3}\) oe

M1: (dep on M1)

A1: for fully correct working leading to given expression

Mark scheme (b)

Scheme	Marks
E.g. \(\left(\dfrac{3a^4}{t^5}\right)^{-2}\) or \(\left(\dfrac{t^{15}}{27a^{12}}\right)^{\frac{2}{3}}\) or \(\left(\dfrac{729a^{24}}{t^{30}}\right)^{-\frac{1}{3}}\)	M1
E.g. \(\left(\dfrac{9a^8}{t^{10}}\right)^{-1}\) or \(\dfrac{3^{-2}a^{-8}}{t^{-10}}\) or \(\dfrac{\frac{1}{9}a^{-8}}{t^{-10}}\) or \(\left(\dfrac{t^5}{3a^4}\right)^2\) or \(\left(\dfrac{t^{30}}{729a^{24}}\right)^{\frac{1}{3}}\) or \(\dfrac{a^{-8}}{9t^{-10}}\)	M1
\(\dfrac{t^{10}}{9a^8}\)	A1
	(3)
	(6 marks)

M1: for one of

cube rooting or inverting or squaring

or \(\dfrac{ka^{-8}}{t^{-10}}\) where \(k\) is an integer \(\neq 0\)

M1: for two of

cube rooting or inverting or squaring

or \(\dfrac{t^{10}}{ka^8}\) where \(k\) is an integer \(\neq 0\)

A1: Allow \(\dfrac{t^{10}a^{-8}}{9}\) or \(\dfrac{1}{9}t^{10}a^{-8}\)