(a) Given that \(\log_{10} 2 = 0.3010, \log_{10} 7 = 0.8451\) and \(\log_{10} 5 = 0.6990\), evaluate without using logarithm tables:

(i) \(\log_{10} 35\); (ii) \(\log_{10} 2.8\).

(b) Given that \(N^{0.8942} = 2.8\), use your result in (a)(ii) to find the value of N.

(a) The value of the expression \(2Ax - Kx^{2}\) is 7 when x = 1 and 4 when x = 2. Find the values of the constants A and K.

(b) Solve the equation \(x^{2} - 3x - 1 = 0\), giving your answers correct to 1 decimal place.

The area of a rectangular floor is 13.5m\(^{2}\). One side is 1.5m longer than the other.

(a) Calculate the dimensions of the floor ;

(b) If it costs N250.00 per square metre to carpet the floor and only N2,000.00 is available, what area of the floor can be covered with carpet?

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

(b) 

In the diagram, ABCD is a circle. DAE, CBE, ABF and DCF are straight lines. If y + m = 90°, find the value of x.

The third term of a Geometric Progression (G.P) is 360 and the sixth term is 1215. Find the 

(a) common ratio;

(b) first term ;

(c) sum of the first four terms.