Edexcel P1 2023 January — Question 10

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJanuary
TopicCurve Sketching
TypeDeduce inequality solutions from sketch

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-26_902_896_248_587} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of part of the curve \(C\) with equation \(y = \mathrm { f } ( x )\), where $$f ( x ) = ( 3 x + 20 ) ( x + 6 ) ( 2 x - 3 )$$
  1. Use the given information to state the values of \(x\) for which $$f ( x ) > 0$$
  2. Expand \(( 3 x + 20 ) ( x + 6 ) ( 2 x - 3 )\), writing your answer as a polynomial in simplest form. The straight line \(l\) is the tangent to \(C\) at the point where \(C\) cuts the \(y\)-axis.
    Given that \(l\) cuts \(C\) at the point \(P\), as shown in Figure 4,
  3. find, using algebra, the \(x\) coordinate of \(P\)
    (Solutions based on calculator technology are not acceptable.)