Further Mathematics Past Questions and Answers

(a) Three vectors a, b and c are \(\begin{pmatrix} 8 \\ 3 \end{pmatrix}, \begin{pmatrix} 6 \\ -5 \end{pmatrix}\) and \(\begin{pmatrix} 2 \\ -3 \end{pmatrix}\) respectively. Find the vector d such that \(|d| = \sqrt{41}\) and d is in the direction of \(a + b - 2c\).
(b) The coordinates of A and B are (3, 4) and (3, n) respectively. If AOB = 30°, find, correct to 2 decimal places, the values of n.

A particle is under the action of forces \(P = (4N, 030°)\) and \(R = (10N, 300°)\). Find the force that will keep the particle in equilibrium.

Solve: 8\(^{x - 2}\) = 4\(^{3x}\)

Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously

Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)