- Find \(\sum _ { r = 1 } ^ { n } \left( 2 r ^ { 2 } - 1 \right)\), expressing your answer in fully factorised form.
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[BLANK PAGE] - Solve the equation \(2 z - 5 i z ^ { * } = 12\).
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\section*{3. In this question you must show detailed reasoning.}
Fig. 4 shows the region bounded by the curve \(y = \sec \frac { 1 } { 2 } x\), the \(x\)-axis, the \(y\)-axis and the line \(x = \frac { 1 } { 2 } \pi\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d8a4ccd-f88a-4f03-a70f-61864d2e30e2-06_538_723_296_242}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
This region is rotated through \(2 \pi\) radians about the \(x\)-axis.
Find, in exact form, the volume of the solid of revolution generated.
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4. The plane \(\Pi\) has equation
$$\mathbf { r } = \left( \begin{array} { l }
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