Further Mathematics Past Questions and Answers

Given that \(p = 4i + 3j\), find the unit vector in the direction of p.

A particle is projected vertically upwards with a speed of 40 m/s. At what times will it be 35m above its point of projection? \(\text{Take g} = 10 ms^{-2}\)

Three students are working independently on a Mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. What is the probability that at least one of them solves the problem?

Given that \(R = (4, 180°)\) and \(S = (3, 300°)\), find the dot product.

Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.