Further Mathematics Past Questions and Answers

Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and 5 m/s. If they move at 60° to each other, find the distance between them in 2 seconds.

A \(2\sqrt{61}\)
B \(\sqrt{42}\)
C \(2\sqrt{21}\)
D \(2\sqrt{10}\)

Question 427:

Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).

A \((4\sqrt{2} N, 000Â°)\)
B \((4\sqrt{2} N, 045°)\)
C \((4\sqrt{2} N, 090Â°)\)
D \((4\sqrt{2} N, 180Â°)\)

Question 428:

A stone is thrown vertically upwards and its height at any time t seconds is \(h = 45t - 9t^{2}\). Find the maximum height reached.

A 45. 25 m
B 45.50 m
C 56.00 m
D 56.25 m

Question 429:

Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.

A \(x^{3} - 4x - 9\)
B \(x^{3} - 4x + 9\)
C \(x^{3} + 4x - 9\)
D \(x^{3} + 4x + 9\)

Question 430:

If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).

A -1
C \(2a^{3} - \frac{2}{a^{3}}\)
D \(\frac{2}{a^{3}} - 2a^{3}\)