Standard +0.3 This is a straightforward inequality problem involving a cuboid volume constraint. Students must form the inequality (3)(2x+1)(x-2) ≤ 9, expand to get a quadratic inequality, solve it, then apply the physical constraint x > 2 (since DC must be positive). While it requires multiple steps and careful attention to inequality direction, it uses standard GCSE/AS-level techniques with no novel insight required, making it slightly easier than average.
In this question you must show detailed reasoning.
\includegraphics{figure_5}
The diagram shows the cuboid \(ABCDEFGH\) where \(AD = 3\) cm, \(AF = (2x + 1)\) cm and \(DC = (x - 2)\) cm.
The volume of the cuboid is at most 9 cm³.
Find the range of possible values of \(x\). Give your answer in interval notation. [5]
In this question you must show detailed reasoning.
\includegraphics{figure_5}
The diagram shows the cuboid $ABCDEFGH$ where $AD = 3$ cm, $AF = (2x + 1)$ cm and $DC = (x - 2)$ cm.
The volume of the cuboid is at most 9 cm³.
Find the range of possible values of $x$. Give your answer in interval notation. [5]
\hfill \mbox{\textit{SPS SPS SM 2025 Q5 [5]}}