Solve the following equation for values of $\theta$ between $0 ^ { \circ }$ and $360 ^ { \circ }$.

$$2 - 3 \cos ^ { 2 } \theta = 2 \sin \theta$$

\begin{center}
\begin{tabular}{ | l | l | }
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0 & 4 \\
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\end{tabular}
\end{center} a) Given that $y = \frac { 5 } { x } + 6 \sqrt [ 3 ] { x }$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ when $x = 8$.

b) Find $\int \left( 5 x ^ { \frac { 3 } { 2 } } + 12 x ^ { - 5 } + 7 \right) \mathrm { d } x$.

\begin{center}
\begin{tabular}{ | l | l | }
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0 & 5 \\
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\end{tabular}
\end{center}

The diagram below shows a sketch of $y = f ( x )$.\\
\includegraphics[max width=\textwidth, alt={}, center]{805df86d-3115-4311-982a-263e114a9722-3_659_828_445_639}\\
a) Sketch the graph of $y = 4 + f ( x )$, clearly indicating any asymptotes.\\
b) Sketch the graph of $y = f ( x - 3 )$, clearly indicating any asymptotes.\\
□\\
0 6\\
\includegraphics[max width=\textwidth, alt={}, center]{805df86d-3115-4311-982a-263e114a9722-3_609_869_1491_619}

The sketch shows the curve $C$ with equation $y = 14 + 5 x - x ^ { 2 }$ and line $L$ with equation $y = x + 2$. The line intersects the curve at the points $A$ and $B$.\\
a) Find the coordinates of $A$ and $B$.\\
b) Calculate the area enclosed by $L$ and $C$.

\begin{center}
\begin{tabular}{ | l | l | }
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0 & 7 \\
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\end{tabular}
\end{center}

Prove that

$$\frac { \sin ^ { 3 } \theta + \sin \theta \cos ^ { 2 } \theta } { \cos \theta } \equiv \tan \theta$$

\hfill \mbox{\textit{WJEC Unit 1 2018 Q3}}