Forming Equations: Eduqas GCSE Higher November 2022 Paper 2 Q15

Higher November 2022 Paper 2 Q15

15. In this question all lengths are in metres.

Diagram not drawn to scale

This shape is made from two rectangles.
The area of this shape is 10 m².

(a) Show that \(3x^2 + 2x - 1 = 0\). [3]

(b) Calculate the value of the perimeter of this shape.

You must show all your working. [5]

Mark scheme (a)

Scheme	Marks	Comments
\(2x(3x + 2) + 4 \times 2\) or \(2(2x + 4) + 3x(2x)\) or \(2 \times 4 + 2x \times 2 + 2x \times 3x\)	B1
\(6x^2 + 4x + 8 = 10\) or better	M1
\(6x^2 + 4x - 2 = 0\) leading to \(3x^2 + 2x - 1 = 0\)	A1

Mark scheme (b)

Scheme	Marks	Comments
		The work for M2 A1 may be seen in (a). Allow the marks if this is the case.
\((3x - 1)(x + 1) = 0\)	M2	Allow ‘= 0’ to be omitted If not M2, award M1 for \((3x \ldots 1)(x \ldots 1) = 0\)
\(x = \dfrac{1}{3}\)	A1	Strict FT from ‘their pair of brackets’ provided equivalent level of difficulty, with at least one answer a positive fraction; ignore any negative solution if stated
Correct perimeter calculation or expression e.g. \(\dfrac{2}{3} + 4 + 1 + 2 + \dfrac{2}{3} + 1 + 4 + 2\) oe or \(2x + 4 + 3x + 2 + 2x + 3x + 4 + 2\) or \(10x + 12\) oe	M1	FT ‘their \(x\)’ providing at least M1 previously awarded and \(x\) > 0. Also, if M0 previously awarded, allow the use of \(x = \dfrac{1}{3}\) (from calculator use) for this M1 and possible A1.
\(15\dfrac{1}{3}\) (m) oe	A1	FT

Scheme	Marks	Comments
		The work for M2 A1 may be seen in (a). Allow the marks if this is the case.
\((x =)\ \dfrac{-2 \pm \sqrt{2^2 - 4(3)(-1)}}{2(3)}\)	M1	Substitution into the formula must be seen for M1, otherwise award M0 M0 A0.
\((x =)\ \dfrac{-2 \pm \sqrt{16}}{6}\)	m1	Can be implied from at least one correct value of \(x\) evaluated.
\(x = \dfrac{1}{3}\)	A1	ignore any negative solution if stated
Correct perimeter calculation or expression e.g. \(\dfrac{2}{3} + 4 + 1 + 2 + \dfrac{2}{3} + 1 + 4 + 2\) oe or \(2x + 4 + 3x + 2 + 2x + 3x + 4 + 2\) or \(10x + 12\) oe	M1	FT ‘their \(x\)’ providing M1 previously awarded and \(x\) > 0 or allow \(x = \dfrac{1}{3}\) without working.
\(15\dfrac{1}{3}\) (m) oe	A1	FT

(8)