Mathematics Past Questions and Answers

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 \(y = 3x^{2} - x - 6\).

The radius of a circle increases at a rate of 0.5\(cms^{-1}\). Find the rate of change in the area of the circle with radius 7cm. \([\pi = \frac{22}{7}]\)