Further Mathematics Past Questions and Answers

There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys

The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.

If \(B = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}\), find \(B^{-1}\).

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)

Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).