Applied Algebra II Semester 2 Practice Exam B
DRAFT
1. What is the solution set of ?
A.
B.
C.
D.
2. Write the expression in exponential notation.
3. Simplify .
A. 2
B. 4
C. 8
D. 12
4. Let and . Find .
5. Given and , what is .
A. –80
B. –8
C. 32
D. 640
6. Let and . Find .
7. Which is the inverse of the function for ?
A. , x ≥ 0
B. , x ≥ 0
C. , x ≥ 0
D. , x ≥ 0
8. The graph below is the function .
What is the value of k?
A.
B.
C.
D.
9. Solve for x:
A. x = 5
B. x =
C. x =
D. x =
10. To compete in a sailboat race, a boat must satisfy the rule
,
where l is the length of the boat (in meters), s is the area of the sails (in square meters), and d is the volume of water displaced by the boat (in cubic meters).
A boat has a length of 21 meters and sail area of 400 square meters. What is its displacement?
11. Simplify the expression where .
A.
B.
C.
D. –4 + 7i
12. Which equation is an exponential function?
A.
B.
C.
D.
13. Sketch the graph of .
14. Solve for x:
A. x = 2
B. x = 4
C. x = 9
D. x = 27
15. Solve for x:
16. What is the solution to the given system of linear equations?
A.
B.
C.
D.
17. The value of z varies jointly with x and y. If z = 4 when x = 1 and y = 12, what is the value of z when x = 5 and y = –6?
A. –90
B. –10
C. 2
D. 8
18. Sketch the graph of .
19. What is the domain of the function ?
A.
B.
C.
D.
20. Which best describes all asymptotes of the function ?
A. x = 1, x = 2
B. x = 2, y = 0
C. x = 2, y = 1
D. x = 2, y = x
21. Simplify .
22. Simplify the expression .
A.
B.
C.
D.
23. Solve for x:
A. x = –3
B. x = 1
C. x = 2
D. x = 3
24. What is the solution set of ?
A. {3, –1}
B. {0, 4}
C.
D. {–1}
25. What is the minimum or maximum of the quadratic function ?
A.
B.
C.
D.
26. Graph the circle .
27. What is the equation of the graph below?
28. Graph the circle .
29. What is the radius of the circle ?
A.
B.
C. 8
D. 13
30. A circle has the equation . The circle is translated 3 units down and 4 units right. What is its new equation?
A.
B.
C.
D.
31. Given the system of linear equations
find the solution to the system using matrices by:
(1) writing in the form ,
(2) then computing ,
(3) and finally computing .
32. How many terms are in the geometric sequence , , 2, … , 162?
A. 6
B. 7
C. 9
D. 18
33. Expand the expression .
A.
B.
C.
D.
34. Use the information below:
3, 9, 15, 21, 27
What best describes the information?
A. arithmetic sequence
B. arithmetic series
C. geometric sequence
D. geometric series
35. What is the series when written in summation notation?
36. Given and are terms of a geometric sequence, what is ?
A. 48
B. 192
C. 384
D. 576
37. Write the formula of an arithmetic sequence when and .
38. A box of paper clips begins with 270 clips. A person takes one-third of the clips and passes the box to a second person who takes one-third of the remaining clips. Another person then takes one third of the remaining clips. How many clips remain when a fourth person receives the box?
A. 10
B. 80
C. 90
D. 120
39. Write a recursive rule for the sequence
1, 2, 5, 14, 41, 122, …
40. Write the first six terms of the sequence with the definition:
41. Graph the function:
42. Postal codes in Canada consist of three letters and three digits, in an alternating pattern, beginning with a letter. For example, T1J4A5.
Any digit is allowed in the 2nd, 4th, and 6th places. The letters D, F, I, O, Q, and U are not allowed in the 1st, 3rd, or 5th places. Additionally, the letters W and Z are not allowed in the 1st place.
How many possible Canadian postal codes exist?
A.
B.
C.
D.
43. Three students are chosen at random from a group of five. How many different combinations of three students are possible?
A. 10
B. 20
C. 60
D. 120
44. There are twelve basketball players on a team. One is randomly selected to shoot free throws, one to do jump shots, and one to do layups. How many different permutations of players could be chosen for the activities?
A. 3!
B. 12!
C.
D.
45. What is the expanded form of ?
46. What is the coefficient of in the expansion of ?
A. 12
B. 18
C. 36
D. 54
47. Two marbles are selected randomly from a bag containing 4 red and 6 blue marbles. Which events are independent?
A. Selecting two red marbles in one pick.
B. Selecting a red and blue marble in one pick.
C. Selecting one red and one blue marble in two picks with replacement.
D. Selecting one red and one blue marble in two picks without replacement.
2008–2009 1 GO ON
Clark County School District Revised 07/22/2009
Applied Algebra II Semester 2 Practice Exam B
DRAFT
48. A group of students consists of
3 freshmen, 4 sophomores, 5 juniors, and 2 seniors. If two students are chosen at random from the group, what is the probability that neither student is a junior?
49. Which measure(s) of central tendency are generally affected by outliers?
50. The list below shows the low temperatures for a North Dakota city over a 10-day period.
11, 17, 17, 12, 1, 2, 18, 17, 26, 28
Create a box-plot that represents the data.
2008–2009 7
Clark County School District Revised 07/22/2009
Applied Algebra II Semester 2 Practice Exam B
Free Response
DRAFT
1. Use the function to answer the questions below.
A. What are the domain and range of ?
B. Derive .
C. Sketch the graph of on the same set of axes.
D. If , find .
2. The equation of a circle is .
A. Sketch a graph of the circle on the grid provided.
B. Sketch a graph of the line y = x on the same axes.
C. For what values of x is the line in the interior of the circle?
2008–2009 1 GO ON
Clark County School District Revised 07/22/2009
Applied Algebra II Semester 2 Practice Exam B
Free Response
DRAFT
3. Use the functions and to answer the questions below.
A. Let . Find .
B. Solve .
C. Sketch the graph of on the grid provided. Be certain to note any asymptotes and intercepts on the graph.
2008–2009 2
Clark County School District Revised 07/22/2009