Further Mathematics Past Questions and Answers

A box contains 14 white balls and 6 black balls. Find the probability of first drawing a black ball and then a white ball without replacement.

Given that \(r = 3i + 4j\) and \(t = -5i + 12j\), find the acute angle between them.

Find \(\lim\limits_{x \to 3} \frac{2x^{2} + x - 21}{x - 3}\).

Find the gradient to the normal of the curve \(y = x^{3} - x^{2}\) at the point where x = 2.

Find the minimum value of \(y = 3x^{2} - x - 6\).