The table shows the distribution of the ages of a group of people in a village.

Using an assumed mean of 24.5, calculate the mean of the distribution.

A body of mass 5 kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4i - j. Calculate the:

(a) velocity of the body

(b) Magnitude of its velocity after 4s.

An object is projected vertically upwards with a velocity of 80 m/s. Find the :

(a) Maximum height reached

(b) Time taken to return to the point of projection. [Take g = \(10 ms^{-2}\)].

(a) Simplify \(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\), leaving your answer in the form \(a + b\sqrt{c}\); where a, b and c are rational numbers.

(b) The points (7, 3), (2, 8) and (-3, 3) lie on a circle. Find the (i) equation and (ii) radius of the circle.

(a) The gradient of the tangent to the curve \(y = 4x^{3}\) at points P and Q is 108. Find the coordinates of P and Q.

(b) Given that \(A = 45°, B = 30°, \sin (A + B) = \sin A \cos B + \sin B \cos A\) and \(\cos (A + B)  = \cos A \cos B - \sin A \sin B\)

(i) Show that \(\sin 15° = \frac{\sqrt{6} - \sqrt{2}}{4}\) and \(\cos 15° = \frac{\sqrt{6} + \sqrt{2}}{4}\)

(ii) hence find \(\tan 15°\).