Mathematics Past Questions and Answers

If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27)

Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)

\(\begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\1 & 3 & -1 \end{vmatrix}\) = 23

If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.

In a triangle XYZ, < YXZ = 44° and < XYZ = 112°. Calculate the acute angle between the internal bisectors of < XYZ and < XZY.