Expanding Brackets: Eduqas GCSE Higher November 2022 Paper 1 Q7

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Higher November 2022 Paper 1 Q7

EduqasHigherCurrent spec7 marksExpanding Brackets Factorising

(a) Expand and simplify \((3x - 4)(5x + 7)\). [3]

(b) Factorise each of the following.

(i) \(2x^2y + 12xy^2\) [3]

(ii) \(x^2 - 64\) [1]

Mark scheme (a)

Scheme	Marks	Comments
\(15x^2 + 21x - 20x - 28\)	B2	B1 for any three terms correct. \(mx^2 + x + n\) implies middle two terms correct if not from wrong working
\(15x^2 + x - 28\)	B1	Mark final answer. Implies previous B2. FT their expression, provided it is a quadratic with 4 terms to consider and there are like terms to collect.

Mark scheme (b)

Scheme	Marks	Comments
(b)(i) \(2xy(x + 6y)\)	B3	Mark final answer. B2 for any one of the following: A correct answer seen then spoiled \(2x(xy + 6y^2)\) \(2y(x^2 + 6xy)\) \(xy(2x + 12y)\) \(2xy(x + my)\) where \(m \neq 0\) or \(m \neq 6\) \(2xy(nx + 6y)\) where \(n \neq 1\) or \(n \neq 0\) B1 for any one of the following: \(2(x^2y + 6xy^2)\) \(x(2xy + 12y^2)\) \(y(2x^2 + 12xy)\) \(2x(xy + my^2)\) where \(m \neq 0\) or \(m \neq 6\) \(2y(x^2 + mxy)\) where \(m \neq 0\) or \(m \neq 6\) \(xy(2x + my)\) where \(m \neq 0\) or \(m \neq 12\) \(2x(nxy + 6y^2)\) where \(n \neq 1\) or \(n \neq 0\) \(2y(nx^2 + 6xy)\) where \(n \neq 1\) or \(n \neq 0\) \(xy(nx + 12y)\) where \(n \neq 2\) or \(n \neq 0\) \(2xy(x + \ldots)\) \(2xy(\ldots + 6y)\)
(b)(ii) \((x - 8)(x + 8)\)	B1
	(7)

Scheme

Marks

Comments

(b)(i)
\(2xy(x + 6y)\)

Mark final answer.
B2 for any one of the following:

A correct answer seen then spoiled
\(2x(xy + 6y^2)\)
\(2y(x^2 + 6xy)\)
\(xy(2x + 12y)\)
\(2xy(x + my)\) where \(m \neq 0\) or \(m \neq 6\)
\(2xy(nx + 6y)\) where \(n \neq 1\) or \(n \neq 0\)

B1 for any one of the following:

\(2(x^2y + 6xy^2)\)
\(x(2xy + 12y^2)\)
\(y(2x^2 + 12xy)\)
\(2x(xy + my^2)\) where \(m \neq 0\) or \(m \neq 6\)
\(2y(x^2 + mxy)\) where \(m \neq 0\) or \(m \neq 6\)
\(xy(2x + my)\) where \(m \neq 0\) or \(m \neq 12\)
\(2x(nxy + 6y^2)\) where \(n \neq 1\) or \(n \neq 0\)
\(2y(nx^2 + 6xy)\) where \(n \neq 1\) or \(n \neq 0\)
\(xy(nx + 12y)\) where \(n \neq 2\) or \(n \neq 0\)
\(2xy(x + \ldots)\)
\(2xy(\ldots + 6y)\)

(b)(ii)
\((x - 8)(x + 8)\)

(7)

Corrected by Westie's Workshop

The board's mark scheme printed “\(xy(2x + my)\) where \(m \neq 0\) or \(m \neq 6\)”. Changed to “\(xy(2x + my)\) where \(m \neq 0\) or \(m \neq 12\)” because \(xy(2x + 12y)\) is the correct answer (worth B2), so the value to leave out here is \(m = 12\), not 6.
The board's mark scheme printed “\(xy(nx + 12y)\) where \(n \neq 1\) or \(n \neq 0\)”. Changed to “\(xy(nx + 12y)\) where \(n \neq 2\) or \(n \neq 0\)” because \(xy(2x + 12y)\) is the correct answer (worth B2), so the value to leave out here is \(n = 2\), not 1.

Original: see the board's mark scheme PDF (link above).