Further Mathematics Past Questions and Answers

(a) Find the coordinates of the point which divides the line joining (7, -5) and (-2, 7) externally in the ration 3 : 2.
(b) Without using calculators or mathematical tables, evaluate \(\frac{2}{1 + \sqrt{2}}\) - \(\frac{2}{2 + \sqrt{2}}\), leaving the answer in the form p + q\(\sqrt{n}\), where p, q and n are integers.

How many terms of the series -3 -1 + 1 +..... add up to 165?

If sin x \(\frac{P - Q}{P + Q}\), where 0\(^o\) \(\leq\) x \(\leq\) 90\(^o\), find 1 - tan\(^2\)x

Three forces N, 14N and 16N acting on a particle keep it in equilibrium. Find the angle between the forces 10N and 16N.

A uniform beam, WX, of length 90 cm and weight 50N is suspended on a pivot, 35 cm from W. It is kept in equilibrum by a means of forces T and 20N applied at Y and Z respectively. |WY| = 10cm and |XZ| = 10cm. Find the value of T