Region definition with inequalities

A question is this type if and only if it asks to define a region bounded by curves and lines using a system of inequalities.

2 questions · Standard +0.3

1.02c Simultaneous equations: two variables by elimination and substitution1.02q Use intersection points: of graphs to solve equations
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Edexcel P1 2022 January Q4
7 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c320b71-8793-461a-a078-e4f64c144a3a-10_689_917_264_507} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \section*{In this question you must show all stages of your working.} \section*{Solutions relying on calculator technology are not acceptable.} Figure 1 shows a line \(l\) with equation \(x + y = 6\) and a curve \(C\) with equation \(y = 6 x - 2 x ^ { 2 } + 1\) The line \(l\) intersects the curve \(C\) at the points \(P\) and \(Q\) as shown in Figure 1.
  1. Find, using algebra, the coordinates of \(P\) and the coordinates of \(Q\). The region \(R\), shown shaded in Figure 1, is bounded by \(C , l\) and the \(x\)-axis.
  2. Use inequalities to define the region \(R\).
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Edexcel P1 2024 June Q6
7 marks Standard +0.3
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 \(R\).