Further Mathematics Past Questions and Answers

The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).

If \(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix} \), find x.

The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.

What percentage increase in the radius of a sphere will cause its volume to increase by 45%?

Evaluate \(\frac{1}{1 - \sin 60°}\), leaving your answer in surd form.