Edexcel P1 2021 June — Question 7

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicCircles

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-22_775_837_251_557} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The line \(l _ { 1 }\) has equation \(4 y + 3 x = 48\)
The line \(l _ { 1 }\) cuts the \(y\)-axis at the point \(C\), as shown in Figure 3.
  1. State the \(y\) coordinate of \(C\). The point \(D ( 8,6 )\) lies on \(l _ { 1 }\)
    The line \(l _ { 2 }\) passes through \(D\) and is perpendicular to \(l _ { 1 }\) The line \(l _ { 2 }\) cuts the \(y\)-axis at the point \(E\) as shown in Figure 3.
  2. Show that the \(y\) coordinate of \(E\) is \(- \frac { 14 } { 3 }\) A sector \(B C E\) of a circle with centre \(C\) is also shown in Figure 3. Given that angle \(B C E\) is 1.8 radians,
  3. find the length of arc \(B E\). The region \(C B E D\), shown shaded in Figure 3, consists of the sector \(B C E\) joined to the triangle \(C D E\).
  4. Calculate the exact area of the region \(C B E D\).