Further Mathematics Past Questions and Answers

The normal to the curve \(y = 2x^{2} + x - 3\) at the point (2, 7) meets the x- axis at the point P. Find the coordinates of P.

(a) Write down the first four terms of the binomial expansion of \((2 - \frac{1}{2})^{5}\) in ascending powers of x.
(b) Use your expansion in (a) above to find, correct to two decimal places, the value of \((1.99)^{5}\).

Five digit numbers are formed from digits 4, 5, 6, 7 and 8.
(a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed?
(b) How many of the numbers are odd, if repetition of digits is not allowed?

Four boys participated in a competition in which their respective chances of winning prizes are \(\frac{1}{5}, \frac{1}{4}, \frac{1}{3}\) and \(\frac{1}{2}\). What is the probability that at most two of them win prizes?

Forces \(F_{1} = (10 N, 090°), F_{2} = (20 N, 210°)\) and \(F_{3} = (4 N, 330°)\) act on a body at rest on a smooth table. Find, correct to one decimal place, the magnitude of the resultant force.