Pre-U Pre-U 9794/3 (Pre-U Mathematics Paper 3) 2014 June

The masses, in kilograms, of 100 chickens on sale in a large supermarket were recorded as follows.

Mass (\(x\) kg)	\(1.6 \leq x < 1.8\)	\(1.8 \leq x < 2.0\)	\(2.0 \leq x < 2.2\)	\(2.2 \leq x < 2.4\)	\(2.4 \leq x < 2.6\)
Number of chickens	16	27	28	18	11

Calculate estimates of the mean and standard deviation of the masses of these chickens. [5]

A stone is projected vertically upwards from ground level at a speed of \(30 \mathrm{~m} \mathrm{~s}^{-1}\). It is assumed that there is no wind or air resistance. Find the maximum height it reaches and the total time it takes from its projection to its return to ground level. [5]

A particle \(P\) is free to move along a straight line \(Ox\). It starts from rest at \(O\) and after \(t\) seconds its acceleration \(a \mathrm{~m} \mathrm{~s}^{-2}\) is given by \(a = 12 - 6t\).

1. Find an expression in terms of \(t\) for its velocity \(v \mathrm{~m} \mathrm{~s}^{-1}\). Hence find the velocity of \(P\) when \(t = 4\). [4]
2. Find the displacement of \(P\) from \(O\) when \(t = 4\). [3]
3. Find the velocity of \(P\) when it returns to \(O\). [3]