MOUNT HOLYOKE COLLEGE

ELEMENTARY ALGEBRA

Time: Two Hours

1. Factor the following expressions:

1. (a)

1. (b)

1. (c)

2. (a) Simplify

2. (b) Extract the square root of

3. Solve the following equations:

3. (a)

3. (b)

3. (c)

4. Simplify:

4. (a)

4. (b)

4. (c) Find

5. Plot the graphs of the following system, and determine the solution from the point of intersection:

6. (a) Derive the formula for the solution of

6. (b) Determine the value of m for which the roots of are (i) equal, (ii) real, (iii) imaginary.

6. (c) Form the quadratic equation whose roots are

and

7. A page is to have a margin of 1 inch, and is to contain 35 square inches of printing. How large must the page be, if the length is to exceed the width by 2 inches?

8. (a) In an arithmetical progression the sum of the first six terms is 261, and the sum of the first nine terms is 297. Find the common difference.

8. (b) Three numbers whose sum is 27 are in arithmetical progression. If 1 is added to the first, 3 to the second, and 11 to the third, the sums will be in geometrical progression. Find the numbers.

8. (c) Derive the formula for the sum of n terms of a geometrical progression.

9. (a) Expand and simplify

9. (b) For what value of x will the ratio be equal to the ratio ?