Further Mathematics Past Questions

Which of the following is a singular matrix?

Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

The mean age of n men in a club is 50 years. Two men aged 55 and 63 years left the club, and the mean age reduced by 1 year. Find the value of n.

Evaluate \(\lim \limits_{x \to 1} \frac{1 - x}{x^{2} - 3x + 2}\)

Evaluate \(\log_{0.25} 8\)

Find the sum of the exponential series \(96 + 24 + 6 +...\)

The roots of the equation \(2x^{2} + kx + 5 = 0\) are \(\alpha\) and \(\beta\), where k is a constant. If \(\alpha^{2} + \beta^{2} = -1\), find the values of k.

Find the equation of the line passing through (0, -1) and parallel to the y- axis.

Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).

If \(f(x) = \frac{1}{2 - x}, x \neq 2\), find \(f^{-1}(-\frac{1}{2})\).

Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q.

Given that \(\frac{1}{8^{2y - 3y}} = 2^{y + 2}\).

Two functions f and g are defined by \(f : x \to 3x - 1\) and \(g : x \to 2x^{3}\), evaluate \(fg(-2)\).

If \((x - 3)\) is a factor of \(2x^{3} + 3x^{2} - 17x - 30\), find the remaining factors.

A binary operation ♦ is defined on the set R, of real numbers by \(a ♦ b = \frac{ab}{4}\). Find the value of \(\sqrt{2} ♦ \sqrt{6}\).

Simplify \(\sqrt{(\frac{-1}{64})^{\frac{-2}{3}}}\).

Solve the inequality \(2x^{2} + 5x - 3 \geq 0\).

\(P = {x : 1 \leq x \leq 6}\) and \(Q = {x : 2 < x < 9}\) where \(x \in R\), find \(P \cap Q\).