Question 11 - A-Level Maths

\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e5ac28f3-d61a-4b40-8b47-28c930761a28-4_775_768_260_733} \captionsetup{labelformat=empty} \caption{Fig. 11.1}
\end{figure} A boat travels from P to Q and then to R . As shown in Fig. 11.1, Q is 10.6 km from P on a bearing of \(045 ^ { \circ }\). R is 9.2 km from P on a bearing of \(113 ^ { \circ }\), so that angle QPR is \(68 ^ { \circ }\). Calculate the distance and bearing of R from Q .
Fig. 11.2 shows the cross-section, EBC, of the rudder of a boat. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e5ac28f3-d61a-4b40-8b47-28c930761a28-4_531_1490_1509_363} \captionsetup{labelformat=empty} \caption{Fig. 11.2}
\end{figure} BC is an arc of a circle with centre A and radius 80 cm . Angle \(\mathrm { CAB } = \frac { 2 \pi } { 3 }\) radians.
EC is an arc of a circle with centre D and radius \(r \mathrm {~cm}\). Angle CDE is a right angle.
1. Calculate the area of sector ABC .
2. Show that \(r = 40 \sqrt { 3 }\) and calculate the area of triangle CDA.
3. Hence calculate the area of cross-section of the rudder. \begin{figure}[h]
  \includegraphics[alt={},max width=\textwidth]{e5ac28f3-d61a-4b40-8b47-28c930761a28-5_881_1378_255_379} \captionsetup{labelformat=empty} \caption{Fig. 12}
  \end{figure} A branching plant has stems, nodes, leaves and buds.
  - There are 7 leaves at each node.
From each node, 2 new stems grow.
At the end of each final stem, there is a bud.