<p>It is given that</p>
<p style="text-align: center">$\mathrm{f}\left( x \right)=\left\{ \begin{matrix}
&amp; ax,\mathrm{for }0\le x&lt;2, \\
&amp; \frac{12a}{x}-4a,\mathrm{for }2\le x&lt;3, \\
\end{matrix} \right.$</p>
<p>where $a$ is a positive constant and that $\mathrm{f}\left( x \right)=\mathrm{f}\left( x+3 \right)$ for all real values of $x$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the exact value of $\mathrm{f}\left( \frac{44}{3} \right)$ in terms of $a$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Sketch the graph of $y=\mathrm{f}\left( x \right)$ for $-3\le x\le 3$, indicating clearly the coordinates of the maximum points and axial intercepts.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find $\displaystyle\int\nolimits_{-2}^{2}{\mathrm{f}\left( x \right)\,}\mathrm{d}x$ in terms of $a$, leaving your answer in the exact form.</span></div><p style="text-align: right;">[3]</p></li></ol>

$\mathrm{f}\left( x \right)=\left\{ \begin{matrix}
&amp; ax,\mathrm{for }0\le x&lt;2, \\
&amp; \frac{12a}{x}-4a,\mathrm{for }2\le x&lt;3, \\
\end{matrix} \right.$

where $a$ is a positive constant and that $\mathrm{f}\left( x \right)=\mathrm{f}\left( x+3 \right)$ for all real values of $x$.

Find the exact value of $\mathrm{f}\left( \frac{44}{3} \right)$ in terms of $a$.

Sketch the graph of $y=\mathrm{f}\left( x \right)$ for $-3\le x\le 3$, indicating clearly the coordinates of the maximum points and axial intercepts.

Find $\displaystyle\displaystyle \displaystyle\int\nolimits_{-2}^{2}{\mathrm{f}\left( x \right)\,}\mathrm{d}x$ in terms of $a$, leaving your answer in the exact form.

2019 NJC P2 Q1

2019 NJC P2 Q1

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