Further Maths Past Questions and Answers

If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.

If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.

Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).

If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).