Moderate -0.8 This is a multiple-choice question worth 1 mark requiring students to recognize that the set A excludes x=0 and consists of values where -√2 < x < √2 (x≠0). Testing the boundary values x=±√2 gives |x²-1|=1, and x=0 gives |x²-1|=1, so the strict inequality |x²-1|<1 is needed. While it involves absolute values and requires careful checking of boundaries, it's a straightforward recognition task with no extended working required, making it easier than average for Further Maths.
The set \(A\) is defined by \(A = \{x : -\sqrt{2} < x < 0\} \cup \{x : 0 < x < \sqrt{2}\}\)
Which of the inequalities given below has \(A\) as its solution?
Circle your answer.
[1 mark]
\(|x^2 - 1| > 1\) \quad\quad \(|x^2 - 1| \geq 1\) \quad\quad \(|x^2 - 1| < 1\) \quad\quad \(|x^2 - 1| \leq 1\)
The set $A$ is defined by $A = \{x : -\sqrt{2} < x < 0\} \cup \{x : 0 < x < \sqrt{2}\}$
Which of the inequalities given below has $A$ as its solution?
Circle your answer.
[1 mark]
$|x^2 - 1| > 1$ \quad\quad $|x^2 - 1| \geq 1$ \quad\quad $|x^2 - 1| < 1$ \quad\quad $|x^2 - 1| \leq 1$
\hfill \mbox{\textit{AQA Further Paper 2 2019 Q3 [1]}}