(a) Simplify, without using tables or calculator : \(\frac{\frac{3}{4}(3\frac{3}{8} + 1\frac{5}{8})}{2\frac{1}{8} - 1\frac{1}{2}}\).

(b) Given that \(\log_{10} 2 = 0.3010\) and \(\log_{10} 3 = 0.4771\), evaluate, correct to 2 significant figures and without using tables or calculator, \(\log_{10} 1.125\). 

(a) Solve : \(7x + 4 < \frac{1}{2}(4x + 3)\).

(b) Salem, Sunday and Shaka shared a sum of N1,100.00. For every N2.00 that Salem gets, Sunday gets 50 kobo and for every N4.00 Sunday gets, Shaka gets N2.00. Find Shaka's share.

(a) The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be 2 : 1?

(b) The arithmetic mean of x, y and z is 6 while that of x, y, z, l, u, v and w is 9. Calculate the arithmetic mean of l, u, v and w.

The area of a circle is \(154cm^{2}\). It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. [Take \(\pi = \frac{22}{7}\)].

A boy 1.2m tall, stands 6m away from the foot of a vertical lamp pole 4.2m long. If the lamp is at the tip of the pole,

(a) represent this information in a diagram ;

(b) calculate the (i) length of the shadow of the boy cast by the lamp ; (ii) angle of elevation of the lamp from the boy, correct to the nearest degree.