Embed Size (px)
Citation preview
COLLEGE ALGEBRA PRACTICE FINAL(Revised 3/04)
Sketch the following graphs:1. 2. 3.
INCLUDEPICTURE "../../../../../My%20Documents/TIIimagefile29828.gif" \* MERGEFORMATINET
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
Use the graph of to sketch the following graphs:
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
16. 17. 18.
19. Find the solution set for .
a) b) c)
d) e) None of the above
20. Find the solution set for a) b) c)
d) e) None of the above
21. Find the solution set for a) b) c)
d) e) None of the above
22. Find the solution set for
a) b) c)
d) e) None of the above
23. Find the solution set for a) b) c)
d) e) None of the above
24. Find the solution set for . Express your answer in interval notation.a) b) c)
d) e) None of the above
25. Find the solution set for . Express your answer in interval notation.
a) b) c) d) e) None of the above
26. A chemist has an 80% alcohol solution and a 30% alcohol solution. How many liters of each should he use to obtain 5 liters of a 60% alcohol solution?a) 3L 80% , 2L 30% b) 2.5L 80% , 2.5L 30% c) 1L 80% , 4L 30%d) 1.8L 80% , 3.2L 30% e) None of the above
27. If and , find .a) 45 b) 3 c) 14d) 11 e) None of the above
28. Given the two points and , find the equation of the line through and .a) b) c) d) e) None of the above
29. Find the domain of
a) All real numbers b) c)
d) e) None of the above
30. Find the coordinates of the vertex for .
a) b) c)
d) e) None of the above
31. Determine the asymptotes of the graph of
a) b) c) d) e) None of the above
32. What is the set of possible rational zeros for ?
a)
b)
c)
d) e) None of the above
33. Find all the zeros of .
a) b) c)
d) e) None of the above
34. Match the solution region of with a
region of the accompanying graph.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
a) A b) B c) Cd) D e) None of the above
35. Find the center and radius of the circle a) b) c)
d) e) None of the above
36. If then .a) b) c)
d) e) None of the above
37. For the matrices and :
i) Find .a) b) c)
d) Impossible e) None of the above
ii) Find .a) b) c)
d) Impossible e) None of the above
iii) Find the determinant of .
a)
b) 5 c)
d) Impossible e) None of the above
A
B
C
D
38. For the function , find
a) b)
c)
d) 4 e) None of the above
39. Find a polynomial of least degree, with lead coefficient 1, that has for zeros.a) b) c) d) e) None of the above
40. Solve to 2 decimal places: a) 4.59 b) 8.76 c) .123d) 3.14 e) None of the above
41. Write using summation notation with index , starting with .
a) b) c)
d) e) None of the above
42. Find the fourth term in the expansion of
a) b) c) d) e) None of the above
43. Find the solution set for .
a) b) c)
d) e) None of the above
44. Find the inverse of .
a) Does not existb) c)
d) e) None of the above
45. Solve the system of equations . Give the coordinates only.
a) b) c)
d) e) None of the above
46. Let represent a mass of radioactive radium (in grams), whose half-life is 1620 years. The
quantity of radium present after years is given by .
a) Determine the initial quantity (when ).
b) Determine the quantity present after 1000 years.
47. An investment of $5000 is compounded continuously for 20 years, when it is worth $16600.58. What is the interest rate, to the nearest percent?
48. On her 18th birthday a woman planning for retirement invests $25000 in a trust fund that pays 8% interest compounded continuously. How old is she when the account is worth a million dollars?
49. What is the tripling time of an $8000 investment at 4% interest compounded monthly?
50. The population of a town increases according to the model , where is the time in years, with corresponding to 1990.
a) Estimate the population in 2000.
b) Estimate the population in 2010.
51. The work (in foot- pounds) done in compressing a volume of 9 cubic feet at a pressure of 15 pounds per square inch to a volume of 3 cubic feet is . Find .
52. Identify the quotient and remainder when is divided by .
53. Identify the vertex, focus, and directrix of the parabola
54. What is ?
55. Write a formula for the term of the arithmetic sequence and identify the 10th term.
56. Write a formula for the term of the geometric sequence and identify the 10th term.
57. Which is the correct partial fraction decomposition setup for ?
a) b) c)
d) e) None of the above
58. Indicate the correct and in the mathematical induction proof of the proposition
a)
b)
c)
d)
e) None of the above
59. Find the center and foci of the ellipse .
60. What are the asymptotes of the hyperbola ?
COLLEGE ALGEBRA PRACTICE FINAL SOLUTIONS(Revised 3/04)
1.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
2.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
3.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
4.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
5.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
6.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5x=-3
y=0
7.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5x=-1
y=-1
8.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5 y=x+1x=1
9.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
10.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
y=0
11.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
y=0
12.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
y=2
13.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
y=0
14.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5 x=0
15.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5 x=2
16.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
17.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
18.
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
19. D20. B21. C22. B23. D24. C25. B26. A27. C28. E 29. E 30. A31. B32. A33. B34. A35. C36. D37. i) A ii) D iii) B38. D39. A40. D41. C42. B43. B44. D45. B46. a) 25 grams b) 16.3 grams47. 6%48. 6449. 27.5 years50. a) 3351 b) 449251. 21357 foot-pounds
52.
53. Vertex: Focus: Directrix: 54. 33055.
56. 57. D58. C59. Center: Foci: 60.
