Edexcel PMT Mocks — Question 11

Exam BoardEdexcel
ModulePMT Mocks (PMT Mocks)
TopicSimultaneous equations

11. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f9a252-61a2-491d-94d0-8470aee96942-16_1123_1031_280_511} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} The figure 5 shows part of the curves \(C _ { 1 }\) and \(C _ { 2 }\) with equations $$\begin{array} { c c } C _ { 1 } : y = x ^ { 3 } - 2 x ^ { 2 } & x > 0
C _ { 2 } : y = 9 - \frac { 5 } { 2 } ( x - 3 ) ^ { 2 } & x > 0 \end{array}$$ The curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect at the points \(P\) and \(Q\).
a. Verify that the point \(Q\) has coordinates \(( 3,9 )\)
b. Use algebra to find the coordinates of the point \(P\).