(a) Using the method of completing the square, solve, correct to 2 decimal places, \(\frac{x - 2}{4} = \frac{x + 2}{2x}\).

(b) 

In the diagram, PQRST is a circle with centre O. If PS is a diameter, RS//QT, and < QTS = 52°, find :

(i) < SQT ; (ii) < PQT.

(a) 

In the diagram, < KLM = x, < LMK = y, < KJH = r and < KGF = 110°. If 2x = r = y, find the value of x.

(b) Ten boys and twelve girls collected donations for a project. The total amount collected by the boys was N600.00 gretaer than that collected by the girls. If the average collection of the boys was N100.00 greater than the average collection of the girls, how much was collected by the two groups?

The weight (in kg) of 50 contestants at a competition is as follows:

65 66 67 66 64 66 65 63 65 68 64 62 66 64 67 65 64 66 65 67 65 67 66 64 65 64 66 65 64 65 66 65 64 65 63 63 67 65 63 64 66 64 68 65 63 65 64 67 66 64.

(a) Construct a frequenct table for the discrete data.

(b) Calculate, correct to 2 decimal places, the;

(i) mean ; (ii) standard deviation of the data.

Using ruler and a pair of compasses only, 

(a) construct : 

(i) \(\Delta\)XYZ such that |XY| = 10cm, < XYZ = 30° and < YXZ = 45°.

(ii) locus, \(l_{1}\), of points equidistant from Y and Z.

(iii) locus, \(l_{2}\), of points parallel to XY through Z.

(b) Locate M, the point of intersection of \(l_{1}\) and \(l_{2}\).

(c) Measure < ZMY.

(a) If \(\frac{3p + 4q}{3p - 4q} = 2\), find \(p : q\).

(b)  

The diagram shows the cross section of a bridge with a semi-circular hollow in the middle. If the perimeter of the cross section is 34 cm, calculate the :

(i) length PQ; (ii) area of the cross section. 

[Take \(\pi = \frac{22}{7}\)].