Question 3 - A-Level Maths

Exam Board	OCR MEI
Module	C3 (Core Mathematics 3)
Year	2013
Session	January
Marks	2
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Modulus function
Type	Express interval using modulus notation
Difficulty	Easy -1.2 This is a straightforward application of the modulus inequality formula requiring students to recognize that the midpoint gives 'a' and half the width gives 'b'. It's a routine 2-mark question testing basic understanding of modulus notation with minimal calculation: a = 2, b = 1.
Spec	1.02l Modulus function: notation, relations, equations and inequalities

Express \(1 < x < 3\) in the form \(|x - a| < b\), where \(a\) and \(b\) are to be determined. [2]

Answer	Marks	Guidance
\(1 < x < 3 \Rightarrow -1 < x - 2 < 1\)	B1, B1 [2]	o.e. [or \(a = 2\) and \(b = 1\)]
\(\Rightarrow	x - 2	< 1\)

$1 < x < 3 \Rightarrow -1 < x - 2 < 1$ | B1, B1 [2] | o.e. [or $a = 2$ and $b = 1$]

$\Rightarrow |x - 2| < 1$ |  |  

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Express $1 < x < 3$ in the form $|x - a| < b$, where $a$ and $b$ are to be determined. [2]

\hfill \mbox{\textit{OCR MEI C3 2013 Q3 [2]}}