Further Mathematics Past Questions and Answers

The table gives the distribution of heights in metres of 100 students.

Height	1.40-1.42	1.43-1.45	1.46-1.48	1.49-1.51	1.52-1.54	1.55-1.57	1.58-1.60	1.61-1.63
Freq	2	4	19	30	24	14	6	1

(a) Calculate the : (i) mean height ; (ii) mean deviation of the distribution.
(b) What is the probability that the height of a student selected at random is greater than the mean height of the distribution?

(a) Two items are selected at random from four items labelled (p, q, r, s).
(i) List the sample space if sampling is done (1) with replacement ; (2) without replacement.
(ii) Find the probability that r is at least one of the two objects selected : (1) in a(i)1 ; (2) in a(i)2.
(b) How many whole numbers from 100 to 999 are divisible by (i) 4 ; (ii) both 3 and 4?

(a) A body P of mass 5kg is suspended by two light inextensible strings AP and BP attached to a ceiling. If the strings are inclined at angles 40° and 30° respectively to the downward vertical, find the tension in each of the strings. [Take \(g = 10 ms^{-2}\)].
(b) A constant force F acts on a toy car of mass 5 kg and increases its velocity from 5 ms\(^{-1}\) to 9 ms\(^{-1}\) in 2 seconds. Calculate :
(i) the magnitude of the force ; (ii) velocity of the toy car 3 seconds after attaining a velocity of 9 ms\(^{-1}\).

(a) Given that \(p = (4i - 3j)\) and \(q = (-i + 5j)\), find r such that \(|r| = 15\) and is in the direction \((2p + 3q)\).
(b)
Forces of magnitude 8N, 6N and 4N act at the point P, as shown in the above diagram. Find the : (i) magnitude ; (ii) direction of the resultant force.

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).