(a) The operation (*) is defined on the set of real numbers, R, by \(x * y = \frac{x + y}{2}, x, y \in R\).

(i) Evaluate \(3 * \frac{2}{5}\).

(ii) If \(8 * y = 8\frac{1}{4}\), find the value of y.

(b) In \(\Delta ABC, \overline{AB} = \begin{pmatrix} -4 \\ 6 \end{pmatrix}\) and \(\overline{AC} = \begin{pmatrix} 3 \\ -8 \end{pmatrix}\). If P is the midpoint of \(\overline{AB}\), express \(\overline{CP}\) as a column vector.

(a) Without using Mathematical tables or calculators, evaluate \(\frac{0.09 \times 1.21}{3.3 \times 0.00025}\), leaving the answer in standard form (Scientific Notation).

(b) A principal of GH¢5,600 was deposited for 3 years at compound interest. If the interest earned was GH¢1,200, find, correct to 3 significant figures, the interest rate per annum.

(a) Solve : \(7(x + 4) - \frac{2}{3}(x - 6) \leq 2[x - 3(x + 5)]\)

(b) A transport company has a total of 20 vehicles made up of tricycle and taxicabs. Each tricycle carries 2 passengers while each taxicab carries four passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?

(a) 

In the diagram, < RTS = 28°, < VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find < VUS.

(b) A cylinder tin, 7cm high, is closed at one end. If its total surface area is 462\(cm^{2}\), calculate its radius. [Take \(\pi = \frac{22}{7}\)].

The table shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225;

(a) How many times was the die thrown?

(b) Calculate the probability that a trial chosen at random gives a score of an even number or a prime number.