MATH 107 UMUC Simplify Fractions Questionnaire

University of Maryland University CollegeMath 107 – College Algebra
Quiz 4
Free Response and Multiple Choice Problems, 3 Points Each.
You may write answers after problems (you may use Microsoft Equation). If you prefer
handwriting, prepare you answer sheet, scan it, and prepare a file in PDF format. Write exact
answers, using fractions or radicals as needed. Simplify answers if possible.
1. Express in terms of i.
−144
2. Solve.
6
8
=
x+6 x
3. Solve.
5 x 2 = 55
4. Divide and simplify to the form a + bi. Type a and b as fractions.
4 + 5i
5−i
5. Use the quadratic formula to solve the equation. Show your work.
x 2 = 4 x + 10
6. Use the quadratic formula to solve the equation. Show your work.
2 x2 − 9 x = 1
2
7. Determine the nature of the solutions of the equation 4 x 2 − 8 x + 4 = 0 .
A) Two real solutions.
B) One real solution.
C) Two non-real solutions.
8. Sketch the graph of the function f ( x) = x 2 − 8x + 15 . Mark the scale.
9. Multiply (−4 + 3i )(5 − 8i ) .
10. Aki’s Bicycle Designs has determined that when x bicycles are built, the average cost per
bicycle is given by C ( x) = 0.1x 2 − 1.6 x + 9.046 where C ( x ) is in hundreds of dollars. How many
bicycles should the shop build to minimize the average cost per bicycle.
11. Solve
1 1 1
+ = for p.
p s f
3
12. Simplify i 8
13. Solve: x 2 + 64 = 0 .
14. The diagonal of a TV set is 13 inches long. Its length is 7 inches more than the height. Find
dimensions of the TV set.
15. Solve l =
ab
for a.
a+c
2
16. For the quadratic function f ( x) = 2 x − 8 x + 13 find:
A) The vertex:
B) What is the maximum/minimum?
C) What is the range?
D) On what interval is the function increasing?
E) On what interval is the function decreasing?
4
17. Subtract and simplify:
(12 + 9i) − (4 − 5i) .
18. Solve x + 4  5 . Give the answer in interval notation and then graph it.
19. Solve 4 x −1 = 4
4
20. The polynomial P( x) = −6 x − 7 is
A) Linear
B) Quadric
C) Quartic
D) Constant
E) Cubic
21. Solve.
x−7
3
x − 20
22. Determine the horizontal asymptote of the graph of the following function.
x2 − 8
f ( x) = 4
5x + 7
23. List all the asymptotes of the following function.
4×2
f ( x) = 2
x − 25
5
24. Determine the domain of the function. Write the answer in interval notation.
4x − 5
f ( x) =
4 x + 20
25. Find the zeros of the polynomial function, and state the multiplicity of each.
f ( x) = x3 ( x − 2)2
26. Using the Intermediate Value Theorem, show that the function f has a zero between a and b.
f ( x) = x3 + 3x 2 − 9 x − 13; a = −5, b = −4
27. Choose the correct graph of the polynomial function.
1
5
f ( x) = x3 + x 2
2
2
28. Solve
x 2 − 8 x + 21  0 .
6
7
5
29. Choose the end behavior diagram that best describes the function P( x) =  x − x − 5 x + 7 .
30. Solve x + 3 + 1 = 11 .
31. Solve x + 8  8 and choose the correct graph of the solution set.
32. Solve
x 2 + 5 x − 26  x − 5 . Write your answer in interval notation.
33. Solve. Write your answer in interval notation.
−7
0.
4x + 7