Higher June 2022 Paper 1R Q16

EdexcelHigherCurrent spec6 marksExpanding Brackets Indices

(a) Expand and simplify \((3x - 1)(x + 2)(3x + 1)\) (3)

(b) Simplify fully \(\left(\dfrac{2x^5}{8xy^2}\right)^{-2}\) (3)

Mark scheme (a)

Scheme	Marks
\((3x - 1)(x + 2) = 3x^2 + 6x - x - 2\;(= 3x^2 + 5x - 2)\) or \((3x - 1)(3x + 1) = 9x^2 + 3x - 3x - 1\;(= 9x^2 - 1)\) or \((x + 2)(3x + 1) = 3x^2 + x + 6x + 2\;(= 3x^2 + 7x + 2)\)	M1
\([(3x^2 + 5x - 2)(3x + 1) =]\;9x^3 + 15x^2 - 6x + 3x^2 + 5x - 2\) or \([(9x^2 - 1)(x + 2) =]\;9x^3 + 18x^2 - x - 2\) or \([(3x^2 + 7x + 2)(3x - 1) =]\;9x^3 + 21x^2 + 6x - 3x^2 - 7x - 2\)	M1
\(9x^3 + 18x^2 - x - 2\)	A1
	(3)

M1: for a correct intention to multiply all 3 factors by multiplying 2 factors only, allow one error

M1: (dep)ft for expanding by the third factor, allow one error

Scheme	Marks
\(9x^3 + 3x^2 + 18x^2 + 6x - 3x^2 - x - 6x - 2\)	M2
\(9x^3 + 18x^2 - x - 2\)	A1

M2: for a complete expansion with 8 terms present, at least 4 of which must be correct

Mark scheme (b)

Scheme	Marks
\(\left(\dfrac{8xy^2}{2x^5}\right)^2\) or \(\left(\dfrac{x^4}{4y^2}\right)^{-2}\) or \(\left(\dfrac{4x^{10}}{64x^2y^4}\right)^{-1}\)	M1
\(\left(\dfrac{4y^2}{x^4}\right)^2\) or \(\left(\dfrac{x^8}{16y^4}\right)^{-1}\) or \(\dfrac{64x^2y^4}{4x^{10}}\) or \(\dfrac{\frac{1}{4}x^{-10}}{\frac{1}{64}x^{-2}y^{-4}}\)	M1
\(\dfrac{16y^4}{x^8}\)	A1
	(3)
	(6 marks)

M1: for one of reciprocating or simplifying or squaring

M1: for two of reciprocating or simplifying or squaring

A1: accept \(16y^4x^{-8}\) or \(\dfrac{16}{y^{-4}x^8}\) or \(\dfrac{16x^{-8}}{y^{-4}}\) oe

Scheme	Marks
	M2
\(\dfrac{16y^4}{x^8}\)	A1

M2: for 2 correct terms
(M1 for 1 correct term)

A1: accept \(16y^4x^{-8}\) or \(\dfrac{16}{y^{-4}x^8}\) or \(\dfrac{16x^{-8}}{y^{-4}}\) oe