The solid is a cylinder surmounted by a hemispherical bowl. Calculate its

(a) total surface area ;

(b) volume (Take \(\pi = \frac{22}{7}\))

Above is the graph of the quadratic function \(y = ax^{2} + bx + c\) where a, b and c are constants. Using the graph, find :

(a)(i) the scales on both axes ; (ii) the equation of the line of symmetry of the curve ; (iii) the roots of the quadratic equation \(ax^{2} + bx + c = 0\)

(b) Use the coordinates of D, E and G to find the values of the constants a, b and c hence write down the quadratic function illustrated in the graph.

(c) Find the greatest value of y within the range \(-3 \leq x \leq 5\).

(a)  PQRST is a circle with centre C. PCS is a straight line, RS // QT, |QR| = |RS| and < QTS = 56°. Find (i) SQT (ii) PQT.

(b)    In the diagram, points B and C are on a horizontal plane and |BC| = 30cm. A and D are points vertically above B and C respectively. |DC| = 40 cm and |AB| = 26 cm. Calculate the angles of depression of : (i) B from D ; (ii) A from D ; correct to the nearest degree.

The table below shows the mark distribution of candidates in an aptitude test for selection into the public service.

(a) Make a cumulative frequency for the distribution

(b) Draw the cumulative frequency curve.

(c) From your graph, estimate the median mark.

(d) The cut-off mark was 63%. What percentage of the candidates was selected?

A shopkeeper buys 40 kg of fruits for N120.00. He sells 20 kg at N5.00 per kg, 10 kg at N3.00 per kg, 5 kg at N2.00 per kg and the remaining 5 kg at 50k per kg. Calculate the :

(a) amount he realises from the sales ;

(b) total profit / loss ;

(c) percentage profit/ loss on his outlay of N120.00.