Mathematics Past Questions and Answers

<table class='tbn'><tbody><tr><td> Age in years </td><td> 10 - 14 </td><td> 15 - 19 </td><td> 20 - 24 </td><td> 25 - 29 </td><td> 30 - 34 </td></tr><tr><td> Frequency </td><td> 6 </td><td> 8 </td><td> 14 </td><td> 10 </td><td> 12 </td></tr></tbody></table><br/><br/>Find the mean of the distribution.

A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the value of k.

If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x - 3}\), find the value of (P + Q).

Find the derivative of \(\sqrt[3]{(3x^{3} + 1}\) with respect to x.

If \(T = \begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatrix}\), find \(T^{-1}\), the inverse of T.