Name__________________________ Section______________ MATH100 Final Exam A Fall 2011 Turn off all cell phones and electronic devices. Remove all headphones. NO CALCULATORS!!!! Each problem is worth 4 points. You must show all work to receive credit. All fractions should be left in lowest terms. 
2 3
1. Simplify: 2 x y
  2x y  4
5
Answer__________________________________ 2
2
1
0
2. Evaluate:    4  4 3
 
Answer__________________________________ 3. Simplify the expression below, assuming all variables represent nonzero numbers. Your final answer should contain only positive exponents. 3
1
x3 y 5   4 xy 2 
2
3x 4 y 3
1
Answer_______________________________ 4. Perform the indicated operation and simplify:  2 x  6  3x  1 Answer_____________________________ 


5. Perform the indicated operation and simplify: 2 p 2  3 3 p 4  4 p 2  2 Answer___________________________________________ 3 y5  2 y3  y 2
6. Perform the indicated operation and simplify: . Assume y  0. 6y
Answer________________________________________ 7. Factor completely: 14k 3  7k 2  70k Answer_____________________________________ 8. Factor completely: 49t 4  25 s 2 Answer_______________________________________ Solve the equations in problems 9‐13. If there are no solutions, indicate that this is so and explain why . 9.  7 x  11 23 x  45   0 x =______________________________ 10. x  x  3  10 x =______________________________ 11. x 2 
4
4
  x 15
15
x =______________________________ 12. x 2  6 x  10  0 x =______________________________ 13. x 2  8 x  1  0 x =______________________________ 14. Solve for x: 2  x  5   3  x  2   12 x = _______________________ 
15. Expand and simplify as much as possible: 2 x  15
 x  5  Answer____________________________________ 16. Solve for x: 10 x  14  2 3 x . Be sure to check that your answer works. x=____________________________________ 17. Evaluate the expression below for x 
1
3
and y  . Simplify your answer as much as possible. 3
5
xy  1
y2
Answer_______________________ 2
3 2
18. Evaluate and simplify as much as possible:    4 5
Answer________________________________ 19. Solve for F in terms of C if C 
5
 F  32  9
F=________________________________________ 20. If 5 times the lesser of two consecutive integers is added to three times the greater, the result is 59. Find the integers. You must set up and solve an algebraic equation to get credit for this problem. Answer____________________________ 21. Solve for t: 1
1
25
 2t  1   3t  2   6
4
12
t =__________________________ 22. Give an example of a polynomial of degree 3 whose constant term is 5 and whose x coefficient is ‐2. Answer_________________________________ 23. Expand and simplify:  2 x  3 3
Answer________________________________ 24. Solve for x. Put your answer in interval notation. 31  4  5 x  24 Answer_____________________________________ 25. The area of a rectangle is 65. The length of one side is 5 13 . What is the length of the other side? Simplify your answer as much as possible. Answer___________________________________