Find the lowest common multiple of 12 and 16.

Ben drove from Town A to Town B, a distance of \( 60 \) km, at an average speed of \( 80 \) km/h. He cycled back at an average speed of \( 20 \) km/h. Find his average speed for the whole journey.
Note that it is not \( \textit{50} \) km/h.

Calculate the compounded value of investment:
$7200 for 9 months at 6% per annum with interest compounded quarterly.

Find \(A \) and \(B \), if \(\dfrac{{x + 3}}{{x + 2}} – \dfrac{{x – 4}}{{x – 1}} = \dfrac{{Ax + B}}{{\left( {x + 2} \right)\left( {x – 1} \right)}}\) in its simplest form of a fraction.

Find the maximum \(y\)-value given   \(y = – 2{x^2} + 8x + 10\)  for  \(3 \le x \le 5\).

The equation of a straight line perpendicular to \(y = – \dfrac{x}{2} + 4\) and passing through \(\left( {3,1} \right)\) is \(y = Ax + B\).

Solve  \(\cos x = \dfrac{1}{2}\)  for  \(-360^\circ \le x \le 360^\circ \).  Write four answers in ascending order.

Find scalars  \(a\), \(b\) and \(c\),   if  \(a\left( {\begin{array}{*{20}{c}}
1\\
0\\
3
\end{array}} \right) + b\left( {\begin{array}{*{20}{c}}
0\\
4\\
6
\end{array}} \right) + c\left( {\begin{array}{*{20}{c}}
3\\
6\\
0
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{ – 2}\\
2\\
{15}
\end{array}} \right)\).

Find the probability that a randomly chosen student plays tennis known that he plays rugby.

Find the interquartile range of the data represented in the box-and-whisker plot.

\( \begin{array}{c|cccccc}
1 & 1 & 2 &&&& \\
2 & 2 & 5 & 6 & 9 && \\
3 & 0 & 2 & 3 &&& \\
4 & 1 & 4 &&&& \\
\end{array} \)