(a) In an A.P, the difference between the 8th and 4th terms is 20 and the 8th term is \(1\frac{1}{2}\) times the 4th term. What is the:

(i) common difference ; (ii) first term of the sequence?

(b) The value of a machine depreciates each year by 5% of its value at the beginning of that year. If its value when new on 1st January 1980 was N10,250.00, what was its value in January 1989 when it was 9 years old? Give your answer correct to three significant figures.

(a) A pair of fair dice each numbered 1 to 6 is tossed. Find the probability of getting a sum of at least 9.

(b) If the probability that a civil servant owns a car is \(\frac{1}{6}\), find the probability that:

(i) two civil servants, A and B, selected at random each owns a car ; (ii) of two civil servants, C and D selected at random, only one owns a car ; (iii) of three civil servants, X, Y and Z, selected at random, only one owns a car.

(a) Triangle PQR is right-angled at Q. PQ = 3a cm and QR = 4a cm. Determine PR in terms of a. 

(b) Ayo travels a distance of 24km from X on a bearing of 060° to Y. He then travels a distance of 18km to a point Z  and Z is 30km from X.

(i) Draw the diagram to show the positions of X, Y and Z ; (ii) What is the bearing of Z from Y ; (iii) Calculate the bearing of X from Z.

(a) Derive the smallest equation whose coefficients are integers and which has roots of \(\frac{1}{2}\) and -7. 

(b) Three years ago, a father was four times as old as his daughter is now. The product of their present ages is 430. Calculate the ages of the father and daughter. 

The number of items produced by a company over a five- year period is given below:

(i) Plot a bar chart for this information; (ii) What is the average production for the five- year period.