Further Mathematics Past Questions and Answers

The remainder when \(x^{3} - 2x + m\) is divided by \(x - 1\) is equal to the remainder when \(2x^{3} + x - m\) is divided by \(2x + 1\). Find the value of m.

If (2t - 3s)(t - s) = 0, find \(\frac{t}{s}\).

If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).

Express \(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).

An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If the identity element is 0, find the value of p for which the operation has no inverse.