# MATH 15300 Exam 1A

1. Given that x > 0 and y < 0, which of the following expressions must be negative?

2. Simplify. Do not leave negative exponents in your
answer .

3. Simplify. Do not leave negative exponents in your
answer.

4. Rationalize the denominator and simplify.

5. Perform the indicated operations and express as a
polynomial.

6. Which of the following is a factor of x ^{6} - 81x^{2} ?

7. Factor completely . Given:

8. Simplify completely .

9. Perform the indicated operation and simplify .

10. Solve for x . Choose the answer that best describes the
solution(s).

A. x is less than -10.

B. x is between -10 and 0.

C. x is between 0 and 10.

D. x is greater then 10.

E. None of the above.

11. The following equation is an identity in which 5x - 6
= 5x - 6 or 0 = 0.

Choose which of the following describes the solution(s) to this equation .

A. x = 0

B. x is any positive real number.

C. x is any positive real number .

D. There is no solution for x .

E. All real numbers x are solutions except x =
±2.

12. Solve for w.

13. A chemist must create 20 ml of a solution that has an 8% active ingredient. The chemist has a 5% active ingredient and a 10% active ingredient. If x represents the number of ml of the 5% active ingredient to be used, choose the equation that would be used to solve for x.

14. Christopher and Anthony can rake leaves working together in 2 hours. If Christopher works alone, he can do the same job in 5 hours. How long would it take Anthony to do the same job alone?

A. 11/5 hours

B. 10/3 hours

C. 11/3 hours

D. 3 hours

E. None of the above.

15. A barn is to be constructed in the shape of two
rectangles surmounted by a triangle. The given dimensions are shown in the
picture. The first story of the barn is the 12 foot by 40 foot rectangle and the
second story is everything above that (see the figure). The height, h, of the
second story has yet to be determined. Choose the equation that would be used to
find h so that the area of the first story equals the area of the second story.
Simplify your equation.

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