(a) An open rectangular tank is made of a steel plate of area 1440\(m^{2}\). Its length is twice its width . If the depth of the tank is 4m less than its width, find its length.

(b) A man saved N3,000 in a bank P, whose interest rate was x% per annum and N2,000 in another bank Q whose interest rate was y% per annum. His total interest in one year was N640. If he had saved N2,000 in P and N3,000 in Q for the same period, he would have gained N20 as additional interest. Find the values of x and y.

 The diagram is a portion of a right circular solid cylinder of radius 7 cm and height 15 cm. The centre of the base of the cylinder is Q, while that of the top is B, where \(\stackrel\frown{ABC} = \stackrel\frown{PQR} = 120°\). Calculate, correct to one decimal place:

(a) The volume 

(b) the total surface area of the solid. [Take \(\pi = \frac{22}{7}\)].

Using ruler and a pair of compasses only, 

(a) construct, (i) triangle XYZ with |XY| = 8cm, < YXZ = 60° and < XYZ = 30° ; (ii) the perpendicular ZT to meet XY in T ; (iii) the locus \(l_{1}\) of points equidistant from ZY and XY.

(b) If \(l_{1}\) and ZT intersect at S, measure |ST|.

In the diagram, /PQ/ = 8m, /QR/ = 13m, the bearing of Q from P is 050° and the bearing of R from Q is 130°.

(a) Calculate, correct to 3 significant figures, (i) /PR/ ; (ii) the bearing of R from P.

(b) Calculate the shortest distance between Q and PR, hence the area of triangle PQR.

The following data gives the lengths, in cm, of 30 pieces of iron rods :

45 55 65 60 61 68 59 54 64 76 50 68 72 68 80 67 70 62 79 67 64 63 71 59 64 53 57 74 55 57

(a) Using class intervals of 45 - 49, 50 - 54, 55 - 59, ... construct a frequency table of the data.

(b) Draw the histogram for the distribution

(c) Calculate the mean of the distribution

(d) What is the probability of selecting  an iron rod whose length is in the modal class?