Further Mathematics Past Questions and Answers

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

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

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