Further Mathematics Past Questions

A man of mass 80kg stands in a lift. If the lift moves upwards with acceleration 0.5\(ms^{-2}\), calculate the reaction from the floor of the lift on the man. \([g = 10ms^{-2}]\)

A force 10N acts in the direction 060° and another force 6N acts in the direction 330°. Find the y component of their resultant force.

A body of mass 10kg moving with a velocity of 5\(ms^{-1}\) collides with another body of mass 15kg moving in the same direction as the first with a velocity of 2\(ms^{-1}\). After collision, the two bodies move together with a common velocity v\(ms^{-1}\).

Find the unit vector in the direction of \(-2i + 5j\).

Given that \(r = 3i + 4j\) and \(t = -5i + 12j\), find the acute angle between them.

A box contains 14 white balls and 6 black balls. Find the probability of first drawing a black ball and then a white ball without replacement.

A fair coin is tossed 3 times. Find the probability of obtaining exactly 2 heads.

Find the variance of 11, 12, 13, 14 and 15.

Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman's rank correlation coefficient.

Find an expression for y given that \(\frac{\mathrm d y}{\mathrm d x} = x^{2}\sqrt{x}\)

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. \([\pi = \frac{22}{7}]\)

Find the minimum value of \(y = 3x^{2} - x - 6\).

Find the gradient to the normal of the curve \(y = x^{3} - x^{2}\) at the point where x = 2.

Find \(\lim\limits_{x \to 3} \frac{2x^{2} + x - 21}{x - 3}\).

The lines \(2y + 3x - 16 = 0\) and \(7y - 2x - 6 = 0\) intersect at point P. Find the coordinates of P.

Points E(-2, -1) and F(3, 2) are the ends of the diameter of a circle. Find the equation of the circle.

Find the equation of the line which passes through (-4, 3) and parallel to line y =  2x + 5.

Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\).

Evaluate \(\cos 75°\), leaving the answer in surd form.