(a) With the aid of four- figure logarithm tables, evaluate \((0.004592)^{\frac{1}{3}}\).

(b) If \(\log_{10} y + 3\log_{10} x = 2\), express y in terms of x.

(c) Solve the equations : \(3x - 2y = 21\)

                                        \(4x + 5y = 5\).

(a) A cylinder with radius 3.5 cm has its two ends closed, if the total surface area is \(209 cm^{2}\), calculate the height of the cylinder. [Take \(\pi = \frac{22}{7}\)].

(b)  In the diagram, O is the centre of the circle and ABC is a tangent at B. If \(\stackrel\frown{BDF} = 66°\) and \(\stackrel\frown{DBC} = 57°\), calculate, (i) \(\stackrel\frown{EBF}\) and (ii) \(\stackrel\frown{BGF}\).

(a) Using a ruler and a pair of compasses only, construc :

(i) a triangle PQR such that /PQ/ = 10 cm, /QR/ = 7 cm and < PQR = 90° ; (ii) the locus \(l_{1}\) of points equidistant from Q and R ; (iii) the locus \(l_{2}\) of points equidistant from P and Q.

(b) Locate the point O equidistant from P, Q and R.

(c) With O as centre, draw the circumcircle of the triangle PQR.

(d) Measure the radius of the circumcircle.

(a) Simplify : \(\frac{x^{2} - y^{2}}{3x + 3y}\)

(b) 

In the diagram, PQRS is a rectangle. /PK/ = 15 cm, /SK/ = /KR/ and <PKS = 30°. Calculate, correct to three significant figures : (i) /PS/ ; (ii) /SK/ and (iii) the area of the shaded portion.

(a) 

In the diagram, AOB is a straight line. < AOC = 3(x + y)°, < COB = 45°, < AOD = (5x + y)° and < DOB = y°. Find the values of x and y.

(b) From two points on opposite sides of a pole 33m high, the angles of elevation of the top of the pole are 53° and 67°. If the two points and the base are on te same horizontal level, calculate, correct to three significant figures, the distance between the two points.