(a) The first term of an Arithmetic Progression(AP) is 3 and the common difference is 4. Find the sum of the first 28 terms.

(b) Given that \(x = \frac{2m}{1 - m^{2}}\) and \(y = \frac{2m}{1 + m}\), express 2x - y in terms of m in the simplest form.

(c) The angles of pentagon are x°, 2x°, 3x°, 2x° and (3x - 10)°. Find the value of x.

(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.