Further Mathematics Past Questions and Answers

The distribution of the masses of a group of persons is shown in the following table

Mass/kg	10.5 - 14.4	14.5 - 24.4	24.5 - 44.4	44.5 - 47.4	47.5 - 49.4
Number of Persons	2	6	18	2	1

Draw a histogram for the distribution

Find the angle between \(\over {OP}\) = (\(^{-3}_{-4}\)) and \(\over{OQ}\) = (\(^8_{-15}\))

In the diagram, a mass of 12kg hanging from a light inextensible string is pulled aside by a horizontal force, R, such that the string is inclined at 45\(^o\) to the vertical. If the system is in equilibrium, calculate the;
(a) tension in the string;
(b) value of R

(a). \(\frac{T}{\sin 90^o}\) = \(\frac{120}{sin 135^o}\) and found T = 169.71N
(b) \(\frac{R}{\sin 135^o}\) = \(\frac{120}{\sin 135^o}\)
R = 120N

(a) If sin p = \(\frac{1}{2}\) and cos q = \(\frac{1}{3}\), evaluate sin(p - q), where 0\(^o\) \(\geq\) p \(\geq\) 90\(^o\) and 90\(^o\) \(\geq\) q \(\geq\) 180\(^o\)

b) Using trapezum rule with seven ordinates, evaluate \(\int^4_1\frac{2}{\sqrt{x + 3}}\)dx