Edexcel P1 2019 January — Question 4

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJanuary
TopicCurve Sketching
TypeArea between curve and line

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-08_857_857_251_548} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a line \(l _ { 1 }\) with equation \(2 y = x\) and a curve \(C\) with equation \(y = 2 x - \frac { 1 } { 8 } x ^ { 2 }\) The region \(R\), shown unshaded in Figure 1, is bounded by the line \(l _ { 1 }\), the curve \(C\) and a line \(l _ { 2 }\) Given that \(l _ { 2 }\) is parallel to the \(y\)-axis and passes through the intercept of \(C\) with the positive \(x\)-axis, identify the inequalities that define \(R\).