1. Express 3/10¹/2 as a decimal of a £. Hence find the price of 2500 articles at £2. 3. 10 ¹/2 each.

2. During the war a manufacturer made a profit of 20 per cent on the sale of his goods. After the war his cost of manufacture came down 10 per cent and the manufacturer reduced his selling price by 5 per cent. What was his new gain per cent?

3. Find the value of the cube root of a² - b² when a = 21.2 and b = 3.87 as closely as your logarithm tables permit.

4. State and prove the Remainder Theorem. If 6x⁴ - 13x³ + ax² + bx = 12 is exactly divisible by 6x² + 5x - 6, find the values of a and b and completely factorise the expression.

5. Solve the equations,

(1) (x-2)/(x+1) + (x+1)/(x-2) = 4

(2) 2x - 3y = 5 ; 2x² + 2xy + 3y² + x -3y =7

6. When the price of goods goes up 10/- per ton, 3 tons less can be bought for £5. 12. 6 than formerly. What is the present price per ton?

7. Find the largest angle of the triangle whose sides are 27.31, 37.85, and 12.36 ins respectively.

8. If p = tanA + cot A and q = sinA + cosA prove that p(q² - 1) = 2