(a)  Without using Mathematical tables or calculators, simplify:

\(3\frac{4}{9} \div (5\frac{1}{3} - 2\frac{3}{4}) + 5\frac{9}{10}\)

(b) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3 and less than 7.

(a) Solve the inequality : \(4 + \frac{3}{4}(x + 2) \leq \frac{3}{8}x + 1\)

(b) 

The diagram shows a rectangle PQRS from which a square of side x cm has been cut. If the area of the shaded portion is 484\(cm^{2}\), find the values of x.

(a) The ratio of the interior angle to the exterior angle of a regular polygon is 5 : 2, Find the number of sides of the polygon.

(b) 

The diagram shows a circle PQRS with centre O, < UQR = 68°, < TPS = 74° and < QSR = 40°. Calculate the value of < PRS.

(a) By how much is the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) less than 7?

(b) The height, h m, of a dock above sea level is given by \(h = 6 + 4\cos (15p)°, 0 < p < 6\). Find :

(i) the value of h when p = 4 ; (ii) correct to two significant figures, the value of p when h = 9 m.

A trapezium PQRS is such that PQ // RS and the perpendicular P to RS is 40 cm. If |PQ| = 20 cm, |SP| = 50 cm and |SR| = 60 cm. Calculate, correct to 2 significant figures, the

(a) Area of the trapezium ; (b) < QRS.