Further Mathematics Past Questions and Answers

The table shows the age distribution in years of a group of people

Age(in years)	1 - 5	6 - 10	11 - 15	16 - 20	21 - 25	26 - 30
Number of people	18	12	25	15	20	10

Using an assume mean of 13 years, find the mean age of the people.

Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw.

The curve y = 7 - \(\frac{6}{x}\) and the line y + 2x - 3 = 0 intersect at two point. Finf the;
(a) coordinates of the two points
(b) equation of the perpendicular bisector of the line joining the two points

(a) Find the range of value of p for which 4x\(^2\) - px + 1 = 0
(b)(i) Expand (1 + 3x)\(^6\) in ascending powers of x
(ii) Using the expression in 10
(ii) find, correct to four significant figures, the value of (1.03)\(^6\)

In an examination, 60% of the candidates passed. If 10 candidates are selected at random, find the probability that;
(1) at least two of the, failed
(2) exactly half of them passed
(3) at most two of them failed