Moderate -0.8 This is a straightforward inequality question requiring students to identify where a cubic expression is negative given three roots in order (1, 2, a with a>2). The cubic opens upward, so it's negative between odd pairs of roots. This is a standard technique tested at AS level with minimal steps, making it easier than average despite being Further Maths content.
Given \((x - 1)(x - 2)(x - a) < 0\) and \(a > 2\)
Find the set of possible values of \(x\).
Tick \((\checkmark)\) one box.
[1 mark]
\(\{x : x < 1\} \cup \{x : 2 < x < a\}\)
\(\{x : 1 < x < 2\} \cup \{x : x > a\}\)
\(\{x : x < -a\} \cup \{x : -2 < x < -1\}\)
\(\{x : -a < x < -2\} \cup \{x : x > -1\}\)
Given $(x - 1)(x - 2)(x - a) < 0$ and $a > 2$
Find the set of possible values of $x$.
Tick $(\checkmark)$ one box.
[1 mark]
$\{x : x < 1\} \cup \{x : 2 < x < a\}$
$\{x : 1 < x < 2\} \cup \{x : x > a\}$
$\{x : x < -a\} \cup \{x : -2 < x < -1\}$
$\{x : -a < x < -2\} \cup \{x : x > -1\}$
\hfill \mbox{\textit{AQA Further AS Paper 1 2020 Q3 [1]}}