October 2020 Paper 3 Q2

OCR MEICurrent spec4 marksFunctions (including |mod|)

2 The graph of \(y = |1 - x| - 2\) is shown in Fig. 2.

Fig. 2: V-shaped graph of y = |1 − x| − 2, crossing the x-axis once to the left of O and once to the right, with its vertex below the x-axis just to the right of the y-axis — Fig. 2

Determine the set of values of \(x\) for which \(|1 - x| > 2\). [4]

Mark scheme

Scheme	Marks	AO
Attempt to find where graph crosses \(x\)-axis	M1	3.1a
Both \(x = -1\) and \(x = 3\) seen	A1	1.1
\(x < -1\) or \(x > 3\) OE	B2	2.2a 2.2a
	[4]

Notes

M1: E.g. \(x = -1\) or \(x = 3\) seen or \((1 - x)^2 > 2^2\)

A1: May be in final answer

B2: B1 if equals included in inequalities but otherwise correct
(both inequalities needed for B1 or B2)
Allow , (comma) for ‘or’ but do not allow ‘and’