Further Mathematics Past Questions and Answers

The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation.

Given \(\sin \theta = \frac{\sqrt{3}}{2}, 0° \leq \theta \leq 90°\), find \(\tan 2\theta\) in surd form.

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

Which of the following binary operations is not commutative?

Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.