Higher June 2018 Paper 1 Q15

EdexcelHigherCurrent spec5 marksAlgebraic Fractions Indices

(a) Simplify fully \(\left(\dfrac{256x^{20}}{y^8}\right)^{-\frac{1}{4}}\) (2)

(b) Express \(\dfrac{1}{9x^2 - 25} - \dfrac{1}{6x + 10}\) as a single fraction in its simplest form. (3)

Mark scheme (a)

Scheme	Marks
E.g. \(\left(\dfrac{y^8}{256x^{20}}\right)^{\frac{1}{4}}\) or \(\left(\dfrac{4x^5}{y^2}\right)^{-1}\) or \(\dfrac{x^{-5}}{4y^{-2}}\) or \(\dfrac{\frac{1}{4}x^{-5}}{y^{-2}}\) or \(k\dfrac{y^a}{x^b}\) or \(\dfrac{ky^a}{x^b}\) with 2 of \(k = \dfrac{1}{4}\) oe, \(a = 2\), \(b = 5\) or \(\dfrac{y^a}{mx^b}\) with 2 of \(m = 4\), \(a = 2\), \(b = 5\)	M1
\(\dfrac{y^2}{4x^5}\)	A1
	(2)

M1: for a correct first step leading to a correct partially simplified expression

A1: for \(\dfrac{y^2}{4x^5}\) or \(\dfrac{\frac{1}{4}y^2}{x^5}\) or \(0.25\dfrac{y^2}{x^5}\) or \(0.25y^2x^{-5}\)

Mark scheme (b)

Scheme	Marks
\(\dfrac{1}{(3x - 5)(3x + 5)} - \dfrac{1}{2(3x + 5)}\)	M1
E.g. \(\dfrac{2}{2(3x - 5)(3x + 5)} - \dfrac{1(3x - 5)}{2(3x - 5)(3x + 5)}\) or \(\dfrac{6x + 10}{(9x^2 - 25)(6x + 10)} - \dfrac{9x^2 - 25}{(9x^2 - 25)(6x + 10)}\)	M1
\(\dfrac{7 - 3x}{2(3x - 5)(3x + 5)}\)	A1
	(3)
	(5 marks)

M1: indep for \((3x + 5)(3x - 5)\)

M1: for two correct fractions with a common denominator
if there is any expansion at this stage then it must be correct

A1: accept equivalents eg. \(\dfrac{7 - 3x}{18x^2 - 50}\)

Mark scheme (b) (Alternative scheme)

M1: for two correct fractions with a common denominator

M1: Numerator expanded and then factorised correctly

A1: accept equivalents