June 2023 Paper 3 Q2

OCR MEICurrent spec4 marksFunctions (including |mod|)Quadratics

2 The straight line \(y = 5 - 2x\) is shown in the diagram.

Axes with origin O; a dashed straight line with negative gradient crossing the positive y-axis and the positive x-axis

(a) On the copy of the diagram in the Printed Answer Booklet, sketch the graph of \(y = |5 - 2x|\). [1]

(b) Solve the inequality \(|5 - 2x| < 3\). [3]

V-shaped graph: the given line above the x-axis, reflected in the x-axis where it would go below it, vertex on the positive x-axis; the original line below the x-axis shown dashed — Mark scheme (a)

Scheme	Marks	AO
	B1	1.1
	[1]

Mark scheme (b)

Scheme	Marks	AO
\(-3 < 5 - 2x < 3\)	M1	1.1a
\(2 < 2x < 8\) \(1 < x < 4\) oe e.g. ‘\(1 < x\) and \(x < 4\)’	A2	1.1 1.1
	[3]

Notes

M1: Could be treated as two separate inequalities (at least one correct) in \(x\) not \(|x|\)
OR \((5 - 2x)^2 < 9\)
If only one linear inequality in \(x\) stated scores M0 A0 A0
OR \(4x^2 - 20x + 16 < 0\) or \(x^2 - 5x + 4 < 0\)
OR \((x-1)(x-4) < 0\)
Allow M1 if treated as equations in \(x\) not \(|x|\)

A2: A1 if only one inequality correct
OR for \(1 \leqslant x \leqslant 4\)
OR for \(1 < x\), \(x < 4\)
OR for ‘\(1 < x\) or \(x < 4\)’