Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 Final Exam Review

Solve the absolute value equation.

1. 4a + 4| | = 5

Solve the absolute value inequality.

2. g + 1|| || > 9

3. z− 3| | ≤ 2

4. Graph the function defined by y = −x + 6| |.

5. Without using graphing technology, sketch the parent graph and translate it to obtain a graph of y + 5 = x + 4| |.

____ 6. Which ordered triple is a solution of the system of equations?

−6x + 4y + 6z = 194x + 2y + 2z = 18x + 8y − 4z = −6

a. (−1, 1, 32

) c. (−1, −1, 32

)

b. (1, −1, 32

) d. (− 12

, 1, 2)

7. Graph y = − 14

x 2 .

Graph.

8. y = − 3x 2 + x + 1

Graph.

9. y = − x − 3( ) 2 − 1

10. How would you translate the graph of y = −x 2 to produce the graph of y = − x − 6( ) 2 ?

11. Graph the function. Label the vertex, axis of symmetry, and x-intercepts.

y = − 2 x + 2( ) x + 5( )

Graph.

12. y = − 3 x + 5( ) x + 4( )

13. y = x + 2( ) 2 − 2

Name: ________________________ ID: A

2

Factor the expression.

14. x 2 + 14x + 48

15. What are the solutions of the equation?

x 2 = 9x − 14

16. Solve using factoring: x 2 − 2x − 8 = 0

Factor the expression.

17. 36x 2 + 79x + 28

18. 64x 2 − 9

Solve.

19. 6x 2 − 19x + 14 = 0

Find the zeros of the function if y is a function of x.

20. 4x 2 + 27x = −35 + y

Solve for x.

21. 6x 2 = 54

Solve.

22. 4 x + 3( ) 2 − 17 = 63

Write the expression as a complex number in standard form.

23. (−9 − 2i) − (−6 + 9i)

24. 1 − 8i8 − 9i

Solve.

25. x 2 − 10x + 41 = 0

Solve by completing the square.

26. 2x 2 + 20x = 14

Name: ________________________ ID: A

3

Find the maximum value of the quadratic equation.

27. y = −x 2 + 4x + 77

28. Use the quadratic formula to solve: x 2 + 7x − 1 = 0

Solve.

29. 9x 2 − 24x = −16

30. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d = − 16t2 − 2t + 733. How long after the rock is thrown is it 400 feet from the ground?

31. Use synthetic substitution to evaluate f(k) = 2k 3 − 2k 2 + 9k − 3 when k = 4.

Find the product.

32. n + 4( ) n 2 + 3n + 5Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

Divide.

33. 2x 4 − 4x 3 − 12x − 15Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ÷ x − 3( )

List the possible rational zeros of the function using the rational zeros theorem.

34. g(x) = x 5 − 4x 3 + 2x + 12

35. Simplify 8 4 / 3 .

36. Which is equivalent to 125 −2/3 ?

Simplify:

37. 2 7 + 9 7 − 5 7

38. 8 5 − 2 4 + 8 45

39. Let g(x) = −2x 2 . Find g(g(−1)).

40. Let f(x) = x 2 + 2 and g(x) = 2x 2 . Find g(f(x)).

41. Which is an equation for the inverse of the relation y = 4x − 4?

42. Which gives the solution(s) of the equation x − 73

= 2?

Name: ________________________ ID: A

4

43. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound annual rate, r, is given by A=P 1+r( ) n . If a person invests $180 in an account that pays 9% interest compounded annually, find the balance after 10 years.

Graph:

44. f(x) = 3 14

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

x

45. Graph f x( ) = − 1 − ex .

46. If $6500 is invested at a rate of 6% compounded continuously, find the balance in the account after 3 years. Use the formula A=Pert .

Evaluate:

47. log2 8

Graph:

48. y = log6 x

49. Express as a single logarithm: logr 15 + logr 35

Solve:

50. 18

= 4 5x+ 8

51. Solve for x to the nearest hundredth: 1.95 x = 26

52. Solve. e−0.07t= 8

Solve the equation. Check for extraneous solutions.

53. log5 3x + 9( ) = 2

Name: ________________________ ID: A

5

____ 54. Which is the graph of f x( ) = x − 2x − 1

?

a. c.

b. d.

Simplify the rational expression, if possible.

55. n 2 + 2n − 24n 2 − 11n + 28

Multiply the expressions. Simplify the result.

56. d 2

ef•

5e 5 f4d

57. x − 8( ) ⋅ x − 7x 2 − 64

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

58. n 2 − 9n + 3

• n2n − 6

Divide the expressions. Simplify the result.

59. x 2 − 36x + 5

÷ x + 6( )

Name: ________________________ ID: A

6

60. x 2 + 10x + 21x 2 − 9

÷ x + 7x − 7

Perform the indicated operation(s) and simplify.

61. −2x + 315x

+ −x − 315x

62. 4x + 8

+ 1x − 8

Solve the equation. Check for extraneous solutions.

63. 5w2 − 9

= 5w+ 3

64. x − 2x − 6

= x + 5x − 4

65. x 2

x + 4 = 16

x + 4

66. x + 24x

− 32x

= 18

67. g

g + 1+

gg + 9

= 1

68. ee + 3

+ 3e − 3

= 4e + 5e + 3( ) e − 3( )

Write a rule for the nth term of the arithmetic sequence.

69. 35, 41, 47, 53, . . .

70. Find the sum of the first 12 terms of the arithmetic series. −7 + 1 + 9 + 17 + . . .

71. Give the first four terms of the geometric sequence for which a 1 = −2 and r = 3.

Evaluate.

72. 12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

j

j = 1

5

∑

73. Find the sum of the infinite geometric series −3 − 13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

k = 1

∞

∑k− 1

.

Name: ________________________ ID: A

7

Find the sum of the geometric series.

74. 35 − 21 + 635

− 18925

+ . . .

Solve the given system of equations.

75. 5a + 2c = 4–2a = 203b + 12c = 18

Factor the polynomial completely.

76. 34xy − 51y − 40x + 60

Solve the given equation.

77. 10 7n−11 =1

10,000

78. Solve log32 n = 15

.

79. Use log4 3 ≈ 0.7925 and log4 4 = 1 to approximate the value of the expression log4 384.

Solve the given equation. If necessary, round to four decimal places.

80. log2 3 + log2 a = log2 18

81. 9 9x = 19

82. Evaluate the expression e ln4.

Solve the given equation. Round to the nearest ten-thousandth, if necessary.

83. 7ex − 7 = 6

84. 7 + 2e 8x = 22

Find the sum of the given arithmetic series.

85. (10n + 23)k = 5

20

∑

86. Factor y3 − 64 completely.

87. Factor 27x3 − 1 completely.

Name: ________________________ ID: A

8

Simplify each expression.

88. 6nn 2 − 9

− 3n + 3

Write a function g whose graph represents the indicated transformation of the graph of f.

____ 89. f(x) = 3x + 8| | − 7; reflection in the x-axisa. g(x) = 3x + 8| | + 7 c. g(x) = − 3x + 8| | + 7b. g(x) = − 3x + 8| | − 7 d. g(x) = − 3x − 8| | − 7

____ 90. f(x) =|x| ; a translation 4 units to the right followed by a reflection in the x-axisa. g(x) = − x − 4| | c. g(x) = x| | − 4b. g(x) = − x| | − 4 d. g(x) = x − 4| |

Write a rule for g described by the transformations of the graph of f. Then identify the vertex.

____ 91. f x( ) = x 2 ; vertical stretch by a factor of 2 and a reflection in the x-axis, followed by a translation 1 unit right.a. g x( ) = −2 x − 1( ) 2 ; 1,0Ê

ËÁÁˆ¯̃̃ c. g x( ) = 2x 2 − 1; 0,−1Ê

ËÁÁˆ¯̃̃

b. g x( ) = 2 x − 1( ) 2 ; 1,0ÊËÁÁ

ˆ¯̃̃ d. g x( ) = − 1

2x − 1( ) 2 ; 1,0Ê

ËÁÁˆ¯̃̃

____ 92. f x( ) = 6x 2 − 5; horizontal shrink by a factor of 13

and a translation 2 units down, followed by a

reflection in the y-axis.

a. f x( ) = 6 3x( ) 2 − 7; 0,−7ÊËÁÁ

ˆ¯̃̃ c. f x( ) = 6 1

3x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

2

− 7; 0,−7ÊËÁÁ

ˆ¯̃̃

b. f x( ) = 18x 2 − 7; 0,−7ÊËÁÁ

ˆ¯̃̃ d. f x( ) = 2x 2 − 7; 0,−7Ê

ËÁÁˆ¯̃̃

Find the minimum or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing.

____ 93. h x( ) = −x 2 + 4x − 2a. The minimum value is 2. The domain is all real numbers and the range is y ≥ 2. The

function is decreasing to the left of x = 2 and increasing to the right of x = 2.b. The minimum value is –14. The domain is all real numbers and the range is y ≥ −14.

The function is decreasing to the left of x = −2 and increasing to the right of x = −2.c. The maximum value is –14. The domain is all real numbers and the range is y ≤ −14.

The function is increasing to the left of x = −2 and decreasing to the right of x = −2.d. The maximum value is 2. The domain is all real numbers and the range is y ≤ 2. The

function is increasing to the left of x = 2 and decreasing to the right of x = 2.

Name: ________________________ ID: A

9

Solve the equation.

____ 94. x 2 + 10x + 25 = −5a. x = −5 ± i 5 c. x = −30b. x = −5 and x = 5 d. x = −5 ± 5

Graph the polynomial function.

____ 95. h x( ) = −x 5 + x 2 − x

a. c.

b. d.

Name: ________________________ ID: A

10

____ 96. h x( ) = −x 5 + x 2 − x + 2

a. c.

b. d.

Use synthetic division to evaluate the function for the indicated value of x.

____ 97. f x( ) = −5x 2 + 26x; x = 5a. f 5( ) = −255 c. f 5( ) = −5b. f 5( ) = 5 d. f 5( ) = 255

Factor the polynomial completely.

____ 98. n 3 + 1000a. n + 10( ) (n 2 − 10n + 100) c. n + 10( ) (n 2 + 100)b. n − 10( ) (n 2 + 10n + 100) d. n + 10( ) (n 2 + 10n + 100)

____ 99. 9r3 − 63r2 − 4r+ 28a. (9r2 − 4) r− 7( ) c. r(9r− 4) r− 7( )

b. (9r2 − 7) r− 4( ) d. (3r+ 2)(3r− 2) r− 7( )

Name: ________________________ ID: A

11

____100. b 3 − 10b 2 − 25b + 250a. (b 2 − 25) b − 10( ) c. b(b − 25) b − 10( )

b. (b 2 − 10) b − 25( ) d. (b + 5)(b − 5) b − 10( )

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.

____101. x + 8( ) 3 = 525a. x ≈ ± 8.03 c. x ≈ 8.03b. x ≈ −16.07 d. x ≈ 0.07

Write the expression in simplest form. Assume all variables are positive.

____102. 64r25 s18 t176

a. 323

r4 s3 t2 r t56c. 2r4 s3 t2 r t56

b. 323

r24 s18 t12 r t56d. 2r24 s18 t12 r t56

Write a rule for g described by the transformations of the graph of f.

____103. Let g be a vertical stretch by a factor of 5, followed by a translation 4 units up of the graph of f(x) = x − 1.a. g(x) = 5x + 3 c. g(x) = 5 x + 3b. g(x) = 5 x − 1 d. g(x) = 5x − 1

____104. Let g be a reflection in the x-axis, followed by a translation 4 units down of the graph of f(x) = 5 x − 33

.

a. g(x) = −5 x + 33

− 4 c. g(x) = 5 −x − 33

− 4

b. g(x) = −5 x − 33

− 4 d. g(x) = 5 −x + 33

− 4

____105. Let g be a horizontal shrink by a factor of 37

, followed by a translation 5 units left of the graph of

f(x) = 21x a. g(x) = 49x + 5 c. g(x) = 9x + 5b. g(x) = 9x + 45 d. g(x) = 49x + 245

____106. Let g be a translation 1 unit down and 4 units left, followed by a reflection in the x-axis of the graph of

f(x) = − 23

x4

+ 43

a. f(x) = − 23

−x + 44

+ 13

c. f(x) = − 23

−x − 44

+ 13

b. g(x) = 23

x + 44

− 13

d. g(x) = 23

x + 44

+ 13

Name: ________________________ ID: A

12

____107. Use log7 4 ≈ 0.712 and log7 5 ≈ 0.827 to evaluate log7 25. a. 1.54 c. 0.589b. 0.827 d. 1.654

Expand the logarithmic expression.

____108. log6 7x4

a. 74

log6 x c. −4 log6 7 − 4 log6 x

b. 4 log6 x + 7 log6 x d. 14

log6 7 + 14

log6 x

Condense the logarithmic expression.

____109. 5 logx − 2 log4

a. log x 5 − 16Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ c. log 5x − 8( )

b. log 5x8

d. log x 5

16

Describe the transformation of f represented by g. Then graph each function.

110. f(x) = 15

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

x

; g(x) = 15

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

x− 5

111. f(x) = 0.3 x; g(x) = 0.3 4x− 1

112. f(x) = log8 x; g(x) = 2 log8 (−x)

113. f(x) = log 1 2 x; g(x) = log1 / 212

xÊ

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ − 4

ID: A

1

Algebra 2 Final Exam ReviewAnswer Section

1. 14

, − 94

2. g < −10 or g > 8 3. 1 ≤ z ≤ 5

4.

5.

6. A 7.

ID: A

2

8.

9.

10. translate the graph of y = −x 2 right 6 units

11.

vertex: (− 72

, 92

)

axis of symm: x = − 72

x-intercepts: –5, –2

ID: A

3

12. y = −3x 2 − 27x − 60

13. y = x 2 + 4x + 2

14. x + 8( ) x + 6( ) 15. x = 7 or x = 2 16. −2, 4 17. (9x + 4)(4x + 7) 18. 8x + 3( ) 8x − 3( )

19. 76

, 2

20. x = −5 and x = − 74

21. ±3 22. –3 ± 2 5 23. −3 − 11i

24. 1629

− 1129

i

25. 5 + 4i, 5 − 4i 26. –5 + 4 2 and –5 – 4 2 27. max = 81

28. −7 + 532

, −7 − 532

ID: A

4

29. x = 43

30. 92

sec

31. f(k) = 129

32. n 3 + 7n 2 + 17n + 20

33. 2x 3 + 2x 2 + 6x + 6 + 3x − 3

34. ±1,±2,±3,±4,±6,±12 35. 16

36. 125

37. 6 7 38. 32 5 − 4 39. –8 40. 2x 4 + 8x 2 + 8

41. y = x + 44

42. 15 43. $426

44.

45.

46. $7781.91 47. 3

ID: A

5

48.

49. logr 525

50. − 1910

51. 4.88 52. –29.7063

53. 163

54. D

55. n + 6n − 7

56. 5de 4

4

57. x − 7x + 8

58. n2

59. x − 6x + 5

60. x − 7x − 3

61. − 15

62. 5x − 24x 2 − 64

63. 4

64. 385

65. 4 66. 8 67. 3, –3 68. 2 69. a n = 6n + 29

70. 444

ID: A

6

71. –2, –6, –18, –54

72. 3132

73. − 94

74. 1758

75. a = –10, b = –102, c = 27 76. (17y − 20)(2x − 3) 77. n = 1 78. 2 79. 4.2925 80. 6 81. 0.1489 82. 4 83. 0.619 84. 0.2519 85. 2368 86. ( y − 4)( y2 + 4y + 16) 87. (3x − 1)(9x2 + 3x + 1)

88. 3n − 3

89. C 90. A 91. A 92. A 93. D 94. A 95. D 96. D 97. B 98. A 99. D 100. D 101. D 102. C 103. B 104. B 105. D 106. B 107. D 108. D 109. D

ID: A

7

110. The graph of g is a translation 5 units right of the graph of f.

111. The graph of g is a translation 1 unit right followed by a horizontal shrink by a factor of 14

of the graph

of f.

ID: A

8

112. The graph of g is a reflection in the y-axis and a vertical stretch by a factor of 2 of the graph of f.

113. The graph of g is a horizontal stretch by a factor of 2 and a translation 4 units down of the graph of f.