Edexcel P1 2024 June — Question 6

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2024
SessionJune
TopicSimultaneous equations

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7e2b7c81-e678-4078-964b-8b78e3b63f43-14_899_901_251_584} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} \section*{In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.} Figure 3 shows
  • the line \(l\) with equation \(y - 5 x = 75\)
  • the curve \(C\) with equation \(y = 2 x ^ { 2 } + x - 21\)
The line \(l\) intersects the curve \(C\) at the points \(P\) and \(Q\), as shown in Figure 3 .
  1. Find, using algebra, the coordinates of \(P\) and the coordinates of \(Q\). The region \(R\), shown shaded in Figure 3, is bounded by \(C , l\) and the \(x\)-axis.
  2. Use inequalities to define the region \(R\).