Name: ____________________________________ Table #: ___ Period: _______ Date: __________

2

Algebra II Honors: 1st Semester Practice 2010-2011

1. Solve the equation:3x 17 5x 12 6x 3

2. Solve the equation:7x 29 21x 3 12 2x

3. Solve:4b 8 5b 9a. b 17

b. b = 179

c. b 19

d. b –17

4. Solve:8 2x 4 6

5. Solve:x 3 5 or x 4 14a. x 8b. x 8 or x 10c. x 10d. 8 x 10

6. Solve: x - 4 9a. {13, –5}b. {5, –13}c. {–5}d. {–13}

7. Solve: x 1 5a. x 4 or x 6b. 4 x 6c. 4 x 6d. x 4 or x 6

8. Solve:42x 1 16

9. Find the range of the relation 4 2

2 3

1 3

a. {2, –3, 3}b. {4, –2, 1}c. {–2, 3, –3}d. {–4, 2, –1}

10. Determine whether the relation is a function.(0, 4), (1, 4), (2, 5), (3, 6), (4, 6)

11. Determine whether the relation is a function.(4, 0), (4, 1), (5, 2), (6, 3), (6, 4)

12. Use the Vertical Line Test to determine if the graph represents y as a function of x.

2

13. Two cars leave a city and travel in opposite directions. If one car averages 50 miles per hour and the other car averages 60 miles per hour, how long will it take for the cars to be 385miles apart?

14. Write the slope-intercept form of the line that passes through the point (5, 5) and has slope 3.

a. y 3x 10b. y 3x 10c. y 3x 10d. y 3x 10

15. Write an equation of the line that is perpendicular to the given line and passes through the given point. Express your answer in slope-intercept form.y 2x 6; 0 5

16. Tickets to a local movie were sold at $4.00 for adults and $2.50 for students. If 100 tickets were sold for a total of $355.00, how many adult tickets were sold?

17. Graph the linear system and estimate the solution.x + y = 43x – y = –8

a. (1, 3)

b. (2, –2)

c. (–1, 5)

d. (2, 2)

3

18. Solve the linear system.x 2y 8x y 2

a. no solutionb. (5, 7)c. (4, –2)d. 2 5

19. Solve the linear system.4x – 4y = –4x + 4y = –6

a. (–12, –1)b. (–2, –1)c. no solutiond. 0 1

20. Tickets to a local movie were sold at $3.00 for adults and $1.50 for students. If 350 tickets were sold for a total of $630.00, how many adult tickets were sold?

a. 70b. 210c. 280d. 85

21. Solve the linear system.x + y + z 6

2x y + z 8x 2y z 12

a. (–2, 2, 6)b. (–6, –2, 2)c. (6, 2, –2)d. (2, –2, –6)

22. Solve the linear system.2x 3y z 1x y z 33x y z 15

23. Which is equivalent to 6253/4 ?

a. 1125

b. 5c. 125

d. 15

4

24. Simplify:(54 / 5 54 / 5 )10

25. Simplify:403 4 53

26. Simplify:23

543

27. Simplify:

5 6 9 6 2 6

a. 72b. 16 6c. 12 6d. 72

28. Write 16xy 2

27z5 in simplest form. Assume all

variables are positive.

29. Simplify the expression. Assume all variables are positive.

18x 8 y 9 z34

30. Simplify

5 3

2

a. 28 10 3b. 28 10 3c. 13 5 3d. 25 10 3

31. Simplify7 10

7 10

a. 3 10b. –3c. 17d. 3 7

32. Simplify90x18

2x

a. 3x8 5xb. 18x 17

c. 5x 3x8

d. none of the above

33. Let g x 3x and h x x3 1. Find h(g(2)).

5

34. Let f x x2 1 and g x 3x 2 . Find f (g(x)).

a. 3x 4 6x 2 3b. 9x4 1c. 3x4 1d. 3x4 3

35. Solve the equation. Check for extraneous solutions.3x 8 1 / 2 5

36. Which gives the solution(s) of x 6 = x?

a. 3, –2b. 3c. no solutiond. –2

37. Which gives the solution of 5x 43 5 6?

a. 35

b. 37

c. 1d. none of the above

38. Solve the equation. Check for extraneous solutions.

4(3 x)43 5 59

a. –5, 11b. 5c. 11d. –11

39. Solve4x 2 x 3?

40. Express as a single logarithm: loga 13 loga 60

a. loga 780b. loga 1360

c. loga1360

d. loga 1360

41. Condense the expression. 12 log5 16 3log5 x 4log5 y

42. Expand the expression. ln 2xy4

6

43. Solve the equation. Check for extraneous solutions.log5 3x 9 2

a. 233

b. 163

c. 13

d. 343

44. Solve the equation. Check for extraneous solutions.log4 x 6 log4 x 2

45. Solve the equation. Check for extraneous solutions.ln x 7 ln 3x 5

46. Write the equation in logarithmic form.64 1, 296a. log6 1, 296 4b. log 1, 296 4c. log 1, 296 4 6d. log4 1, 296 6

47. Evaluate the logarithm.

log51

625a. –3b. 5c. –4d. 4

48. Evaluate the logarithm.log 0.01a. –10b. –2c. 2d. 10

49. Which of the following is equivalent tolog3 11p 3

a. log3 11 3 log3 pb. log 3 11 3 log 3 pc. log3 11 3 log3 pd. 11 log 3 p 3

50. Solve ln 2 ln x 5.a. 50,000b. 74.2c. 10d. 3

51. Rewrite using the change of base formula.4x 7

52. If log10 x 3 what is the value of x?

7

53. Which is the first incorrect step in simplifying

log214?

Step 1: log214 log2 1 log24

Step 2: 12 2

Step 3: 32

a. Step 1b. Step 2c. Step 3d. Every step is correct.

54. A student showed the following steps in his solution of the equation below, but his answer was not correct.

log(6x2 13x 5) log(3x 1) log2 16 3

Step 1:log(3x 1)(2x 5) log(3x 1) 4 3Step 2:log(3x 1)(2x 5) log(3x 1) 1 Step 3: log(3x 1) 1Step 4:

3x – 1 = 110

Step 5:

x = 1130

In which step did he make his first error?

a. Step 1b. Step 2c. Step 3d. Step 4

55. Solvelog5 (2x 5) 0

56. Which of the following is not equivalent to log3 16?

a. ln16ln3

b.log3log16

c. 2log3 4d. log3 8 log3 2

8

57. Graph y = x2 3

a.

b.

c.

d.

58. Does the parabola open up or down? y 7 5x 3x2

59. Graph y x 3 2 1

a.

b.

c.

d.

9

60. Graph the parabola: y x 1 2 3

a.

b.

c.

d.

61. Factor completelyx2 14x 48a. x 8 x 6 b. x 24 x 2 c. x 24 x 2 d. x 8 x 6

62. What are the factors of x2 4x 4?

63. Write as the product of two factors: x2 3x 40a. x 5 x 8 b. x 5 x 8 c. x 5 x 8 d. x 5 x 8

64. What are the solutions to the equation?x 2 3x 54

a. x = 1 or x = 54b. x = 54 or x = 1c. x = 6 or x = 9d. x = 9 or x = 6

65. What are the solutions to the equation?x2 2x 24 = 0

a. x = 6 or x = 4b. x = 12 or x = 2c. x = 8 or x = 3d. x = 1 or x = 24

10

66. Find the x-intercepts of the graph of y = x 2 11x 18.a. -3, -5

b. 2, 9

c. -2, -9

d. 3, 5

67. Factor3x2 x 14

a. x 7 3x 2 b. 3x 7 x 2 c. x 7 3x 2 d. 3x 7 x 2

68. Factor4x 2 36

a. 4x 1 x 36 b. 2x 6 2x 6 c. 2x 6 2x 6 d. 4x 1 x 36

69. Write as the product of two factors: 49k 2 21k 4

a. 7k 1 7k 4 b. 7k 1 7k 4 c. 7k 1 7k 4 d. 7k 1 7k 4

70. Solve3x2 = x 14

11

71. Find the x-interceptsy = 3x2 13x 14

72. Write the expression as a complex number in standard form.2 4i 3 9i

73. Write the expression as a complex number in standard form.2 4i 3 9i

a. 5 13ib. 30 30ic. 1 5id. 1 5i

74. Write the expression as a complex number in standard form.3i 6 5i

75. Plot the number in a complex plane. 2 4i

a.

b.

c.

d.

12

76. Use the quadratic formula to solve: x2 3x 1 = 0

a.3 5

2 ,3 5

2

b.3 5

2 ,3 5

2

c.3 13

2 ,3 13

2

d.3 13

2 ,3 13

2

77. Use the quadratic formula to solve the equation. x2 2x 1 0

78. Solve5x2 3x 4

a.3 i 89

10 ,3 i 89

10

b.3 i 71

10 ,3 i 71

10

c.3 i 89

10 ,3 i 89

10

d.3 i 71

10 ,3 i 71

10

79. Which of the following most accurately describes the translation of y (x 1)2 5 to the graph ofy x2 4?

a. down 9, left 1b. down 9, right 0c. down 4, right 1d. down 4, left 1

80. Raul correctly solved the equation x 2 8x 10 by completing the square. Which equation is part of the solution?

a. (x 4)2 26b. (x 8)2 26c. (x 8)2 18d. (x 8)2 90

13

81. Factor the polynomial completely.36y 2 25

a. 36y 1

y 25

b. 6y 5

6y 5

c. 6y 5

6y 5

d. 6y 5

6y 5

82. Factor the polynomial completely. 64x3 27y3

83. Factor the polynomial completely.x 3 8y 3

84. Divide k 3 8

k 2

a. k 2 2k 4b. k 2 2k 4c. k 2 4d. k 2 4

85. Divide 2x3 5x 4

x 3

a. 2x2 6x 23 – 70x 3

b. 2x2 x 7 + 21x 3

c. 2x2 6x 13 + 43x 3

d. 2x2 x 3 – 5x 3

86. Divide using synthetic division 4x 4 12x 3 48x 60

x 4

a. 4x 3 4x 2 16x 16 + 4x 4

b. 4x2 4x 16 + 4x 4

c. 4x 2 4x 16 + 4d. 4x3 4x2 16x 16 + 4

14

87. Divide using long division. 2x 2 4x 3 4 10x

2x 3

a. 2x2 2x 2 + 22x 3

b. 2x2 2x 1 12x 3

c. 2x2 2x 1 12x 3

d. 2x2 2x 2 + 22x 3

88. Simplify the given expression. Assume that no variable equals 0.14x 4xy14

4x10 y7

a. 224x11 y110

b.224y21

x9

c.14y21

x 9

d. 224x9 y21

89. Simplify the given expression. Assume that no variable equals 0.

32x 18 y 10

16x 9 y 20

2

a. 2x 9 y 20

b. 4x18

y20

c. 4x 9

y 10

d. 4x 18 y20

90. Simplify 2x2 14x 14

2x2 7

a. 4x2 14x 21b. 4x2 14x 7c. 4x 2 21d. 4x2 14x 21

91. Simplify 2x 2 9x 17

16x 2 17x 1

a. 18x2 8x 18b. 18x2 26x 16c. 18x2 26x 18d. 18x2 25x 16

92. Simplify the given expression.2xy(3xy 3 5xy 7y 2 )

a. 6x2 y4 10x2y2 14xy3

b. 6x 2y 4 5xy 7y 2

c. 6x2 y4 5x2 y2 7x2 y3

d. 6x 2 y4 10xy 14y 2

15

93. A Honda Accord depreciates exponentially at an annual rate of 11%. The out-of-the-door price for a brand new Accord is $24,250. Which of the following is the best model for the scenario?

a. y 24,250(.11) t

b. y 24,250(.89) t

c. y 24,250(1.11) t

d. y 24,250(1.89) t

94. A certain radioactive element decays over time

according to the equation y A 12

t300

where A =

the number of grams present initially and t = time in years. If 1000 grams were present initially, how many grams are left after 1500 years?

95. Bacteria in a culture are growing exponentially with time, as shown in the table below.

Bacteria GrowthDay Bacteria0 3001 6002 1200

Find an equation that represents the number of bacteria, y, present at any time, t.

96. Describe the transformation of the graph of y log (x 2) 1 compared to its parent function y logx.

a. shift right 2, shift down 1, reflected over the x-axis

b. shift left 2, shift down 1, reflected over the x-axis

c. shift left 2, shift down 1, reflected over the y-axis

d. shift right 2, shift up 1, reflected over the y-axis

97. Identify the domain and range of f(x) 4(3x 1) 2.

a. D: ,

, R: 2,

b. D: ,

, R: 2,

c. D: ,

, R: 1,

d. D: ,

, R: 2,

98. Jason invests $700 into a savings that earns 3.5% annual interest compounded continuously. Write an equation that shows the correct substitution to find the amount of money that Jason has after 8 years?

99. Find the inverse to y log4 (3x 2) 5?

100. Dana invests $5000 into a savings that earns 2.5% annual interest compounded continuously. If Dana wants to have at least $12,000, how many years does Dana need to leave the money in the savings account? (Leave your answer in Log Form.)

16

101. Given the table of an exponential growth function below:x y0 11 22 43 8 Find the new points when the following transformation is performed f(x) 2x 1 5

102. Assume ln2 .6931, ln3 1.0986, ln5 1.6094. (a) Find the approximation for ln18.(a) Find the approximation for ln 3 .(a) Find the approximation for ln150.

103. Write the logarithmic expression as a single logarithm (condense).12 logx 4logy 6 logz 2logw

104. Expand the logarithm.

log3xy5

z

105. Which of the following graph is the inverse of y e x?

a.

b.

c.

d.

17

106. Sketch the graph then state the function’s domain and range. y = –1.3(7)x a.

The domain is all real numbers and the range is all positive numbers.

b.

The domain is all real numbers and the range is all negative numbers.

c.

The domain is all real numbers and the range is all positive numbers.

d.

The domain is all real numbers and the range is all negative numbers.

107. Evaluate the expression e ln 4 .a. lne4

b. e4

c. 4d. ln4e

108. Solve. 10 8n 8 1

10,000

a. n = 4

b. n = 12

c. n = 58

d. n = 32

109. Solve. 5 7n 15 1

625

a. n = 197

b. n = 117

c. n = 127

d. n = 11

ID: A

1

Algebra II Honors: 1st Semester Practice 2010-2011Answer Section

1. –2

2. 53

3. D 4. 1 x 6 5. B 6. A 7. C

8. x 52 or x 3

2 9. C 10. It is. 11. It is not. 12. Function 13. 3.5 hours 14. C

15. y 12 x 5

16. 70 17. C 18. C 19. B 20. A 21. A 22. (4, –2, 1) 23. A

24. 1516

25. 8 253

26. 13

27. C

28. 4y 3xz

9z3

29. x 2 y 2 18yz34

30. A 31. B 32. A 33. 217

ID: A

2

34. B 35. x 11 36. B 37. A 38. A 39. 5/3 40. A

41. log5

4y4

x3

42. ln2 lnx 4lny 43. B 44. 2 45. x = 6 46. A 47. C 48. B 49. C 50. B

51. x log7log4

52. 1/1000 53. B 54. C 55. -3 56. B 57. A 58. Up 59. B 60. C 61. D 62. (x 2)2

63. A 64. D 65. A 66. B 67. B 68. C 69. C

70. 73 , 2

71. 73 , 2

72. 5 5i

ID: A

3

73. C 74. 15 18i 75. C 76. C 77. 1 2 78. D 79. A 80. A 81. C

82. 4x 3y

16x2 12xy 9y2

83. x 2y

x 2 2xy 4y2

84. A 85. C 86. A 87. D 88. B 89. B 90. A 91. C 92. A 93. B 94. 31.25 grams 95. y 300(2t) 96. A 97. A

98. y 700e (0.035)(8)

99. y1 4x 5 23

100. t ln2.4.025

101. {(-1, -4), (0, -3), (1, -1), (2, 3)} 102. (a) 2.8903

(b) .5493(c) 5.0105

103. logz6 xw2 y4

104. 16 logx 5

6 logy 12 logz

105. A 106. B 107. C

ID: A

4

108. B 109. B