ACE College Algebra II Name ____________________________________Final Exam Review – Semester 2Please do all your work on another sheet of paper. Period _____

1. Find the x-value of the ordered pair that solves the system:

[A] [B] [C] [D]

2. Find the x-value of the ordered triple that solves the system:

[A] [B] [C] [D]

3. Find the x-value(s) of the ordered pair(s) that solve the system:[A] [B] [C] [D]

4. Which point is a solution to the inequality:[A] [B] [C] [D]

5. Determine which point is a solution for the system of inequalities:[A] [B] [C] [D]

6. Find the dimensions of matrix A.

[A] [B] [C] [D]

7. Write the system of equations for which the given matrix is the augmented matrix.

[A] [B] [C] [D]

8. Given

[A] [B] [C] [D]

9. Given

[A] [B] [C] [D]

10. Find the determinant of the matrix:

[A] [B] [C] [D]

11. Find the inverse of the matrix .

[A] [B] [C] [D]

12. Write out the form of the partial fraction decomposition of .

[A] [B] [C] [D]

13. Find the partial fraction decomposition of .

[A] [B]

[C] [D]

14. Find the vertex, focus and directrix of the parabola: .

[A] [B]

[C] [D]

15. Find the vertex and directrix of the parabola: . [A] [B] [C] [D]

16. Find the vertices and foci for the ellipse:

[A] [B]

[C] [D]

17. Find the lengths of the major and minor axes for the ellipse:

[A] [B]

[C] [D]

18. Find the vertices for the hyperbola: ?[A] [B] [C] [D]

19. Find the foci for the hyperbola:

[A] [B] [C] [D]

20. Find the foci for the hyperbola:

[A] [B] [C] [D]

21. Find an equation for the conic whose graph is shown:

[A] [B]

[C] [D]

22. Find an equation for the conic whose graph is shown:

[A] [B]

[C] [D]

23. Find an equation for the conic whose graph is shown:

[A] [B]

[C] [D]

24. Complete the square to determine the type of curve represented by the equation:

[A] [B]

[C] [D]

25. Complete the square to determine the type of curve represented by the equation:

[A] [B]

[C] [D]

26. Find an equation of a parabola with horizontal axis and vertex at the origin that passes through the point [A] [B] [C] [D]

27. Find an equation for the ellipse with center at the origin, major axis of length , minor axis of length

, and whose foci lie on the y-axis.

[A] [B] [C] [D]

28. Find the 1000th term of the sequence:

[A] [B] [C] [D]

29. Find the first five terms of the sequence

[A] [B]

[C] [D]

30. Find the nth term of the sequence whose first several terms are

[A] [B] [C] [D]

31. The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference. If the sequence is geometric, find the common ratio. [A] [B] [C] [D] [E] neither

32. The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference. If the sequence is geometric, find the common ratio.

[A] [B] [C]

[D] [E] neither

33. Given that the 50th term of an arithmetic sequence is 259 and the common difference is 5, find the first three terms.[A] [B] [C] [D]

34. The first term of an arithmetic sequence is and the common difference is . Which term of the

sequence is ?

[A] [B] [C] [D]

35. Find the fourth term of the geometric sequence given .

[A] [B] [C] [D]

36. Find the values for a and b for which the sequence 2, a, b, 17, . . . is arithmetic.[A] [B] [C] [D]

37. Find the sum: . [A] [B] [C] [D]

38. Write the sum using sigma notation:

[A] [B] [C] [D]

39. Find the sum: [A] [B] [C] [D] [E] none of these

40. Find the sum: [A] [B] [C] [D] [E]

41. The seventh term of an arithmetic sequence is -16 and the tenth term is -31. Find the twenty-fourth term.

[A] [B] [C] [D]

42. Find the sum of the infinite geometric series: . [A] [B] [C] [D] [E] 18

43. A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from 3 ft above the ground, until it comes to rest.

[A] 5 ft [B] 5.25 ft [C] 4.125 ft [D] 3.5 ft [E] 3.25 ft

44. Evaluate the expression: [A] 1940 [B] 1950 [C] 3920 [D] 980 [E] none of these

45. Expand the expression: . [A] [B] [C] [D]

46. Find the coefficient of in the expansion of . [A] -28 [B] 28 [C] -56 [D] 56 [E] 70

47. In how many ways can a first, second, and third baseman be selected from eight players? [A] 40320 [B] 28 [C] 56 [D] 336 [E] none of these

48. What is the probability of rolling a 6 on a fair number cube and flipping a coin and getting tails?

[A] [B] [C] [D] [E] none of these

49. The table shows the number of male and female freshmen who chose to play one of the three intramural sports offered at a small college. What is P(soccer|female)?

[A] [B] [C] [D]

50. A student compiled the following table comparing the amounts of land area and water area, in square miles, in various U.S. states. What is the probability that a point chosen at random on a map is water, given that the map is of Florida?

[A] [B] [C] [D]

51. The chance of rain for the next evening is 60%. If it rains, the chance of lightening is 80%. If it does not rain, the chance of lightening is 5%. What is the probability that it will not rain and there will be no lightening?

[A] [B] [C] [D] [E] none of these

52. A spinner has five equal sections. Each section is a different color; red, blue, green, yellow, and orange. You spin the spinner four times. What is the probability that at least two of the spins will land on the red section?

[A] [B] [C] [D] [E] none of these

53. The frequency table shows the number of textbooks in several students’ book bags. What are the mean, median, and mode for textbooks per student?

[A] [B]

[C] [D]

54. Which is an outlier for this data set: 22 35 12 28 46 30 31 15 19?

[A] [B] [C] [D]

55. The table shows population density by square mile for counties in three of Florida’s eight regions, according to the 2000 U.S. Census. What are the quartiles of the Central East Region population density data in the preceding table?

[A]

[B]

[C]

[D]

56. The data shows the number of hours in a week that students in a class spent doing homework. What value is at the 45th percentile?

0 3 4 4 4 4.25 4.5 4.5 4.75 5 5.25 5.5 5.5 6 6.25 6.25 6.5 7 7 9

[A] [B] [C] [D] [E] 5

57. The table to the right displays the number of sales a salesperson made each month during the past 15 months. Within how many standard deviations of the mean do all of the values fall?

[A] 1 [B] 2 [C] 3 [D] 4 [E] 5

58. What are the mean, variance, and standard deviation of the sample values below? 6.5 5.8 3.9 5.7 4.2

[A] [B] [C] [D]

59. For the following situation, what sampling method is used? Does the sample have a bias? The manager of a grocery store wants to determine what percent of shoppers are using the store coupons printed in the Sunday paper. He has an employee ask every tenth

shopper who passes through the store’s door for the next week if he or she intends to use a store coupon on their visit.

[A] [B] [C] [D]

60. You track the number of words in your text messages for a month and sketch the bar graph shown. The number of words is normally distributed about a mean of 10. About what percent of your text messages are between 9 and 11 words long?

[A] 34% [B] 13.5% [C] 26% [D] 68% [E] 95%

61. The yields of apples trees in an orchard have Normal distribution with mean 42.4 pounds and standard deviation 6.1 pounds. Compute the z-score for a tree yielding 35 pounds of apples.

[A] -1.04 [B] 1.04 [C] -1.21 [D] 1.21 [E] none of these

Solutions for the Multiple Choice Review Worksheet:1. A2. B3. C4. B5. C6. A7. D8. C9. D10. D11. D12. D13. A14. D15. B16. C17. A

18. C19. B20. D21. D22. D23. C24. D25. A26. B27. A28. D29. A30. B31. C32. E33. D34. B

35. D36. A37. B38. C39. C40. E41. A42. A43. A44. E45. B46. E47. D48. C49. D50. A51. A

52. C53. C54. B55. C56. D57. B58. B59. D60. D61. C