ELEMENTARY ALGEBRA

Time: One Hour and a Half

Arrange your work neatly and clearly, beginning each question on a separate page.

1. Simplify the following expression:

2. (a) Write the middle term of the expansion of

by the binomial theorem.

2. (b) Find the value of

and

2. (b) and reduce the result to a form having only positive exponents.

3. Find correct to three significant figures the negative root of the equation

4. Prove the rule for finding the sum of n terms of a geometrical progression of which the first term is a and the constant ratio is r.

4. Find the sum of 8 terms of the progression

5. A goldsmith has two alloys of gold, the first being

pure gold, the second

pure gold. How much of each must he take to produce 100 ounces of an alloy which shall be

pure gold?