al ii h final review pdf

7/23/2019 Al II H Final Review PDF

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

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Algebra II Honors Final Exam Review

Short Answer

1. Evaluate the series 5nn = 3

8

.

2. Evaluate the series (n + 4)n = 1

4

.

What is the sum of the finite arithmetic series?

3. 29 + 32 + 35 + 38 + 41 + + 59

4. 26 + 29 + 32 + 35 + 38 + 41 + 44

5. Divide 4x3 + 2x2 + 3x + 4byx + 4.

6. Divide 3x3 2x2 x 2byx 2.

7. Determine which binomial is nota factor of 4x4 21x3 46x2 + 219x + 180.

8. Is (x 2)a factor ofP(x)=x3

+ 2x2

6x 4? If it is, writeP(x)as a product of two factors.

Divide using synthetic division.

9. Divide 4x3

+ 21x2

23x + 6by (x 4).

10. Divide 14x3

840 + 14xby (x + 4).

11. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation

x3 6x2 + 4x + 9 = 0. Do not find the actual roots.

Find the roots of the polynomial equation.

12. x3 2x2 + 10x + 136 = 0

13. x3

3x2

5x 15= 0

14. A polynomial equation with rational coefficients has the roots 3 + 6, 2 5 . Find two additional roots.

15. Find a quadratic equation with roots 1 + 4iand 1 4i.


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Find all the zeros of the equation.

16. 2x4 5x3 + 53x2 125x + 75 = 0

17. x3

x2

13x 13= 0

18. 7x2

144= x4

Use Pascals Triangle to expand the binomial.

19. (s + 2v)5

20. (d 2)6

21. Find all the real square roots of 9

16.

22. Find all the real cube roots of 0.000027.

Find the real-number root.

23. 125

3433

What is a simpler form of the radical expression?

24. 36g6

25. 81x20y84

26. The formula for the volume of a sphere is V = 4

3r3 . Find the radius, to the nearest hundredth, of a sphere

with a volume of 15 in.3.

Multiply and simplify if possible.

27. 6 2

What is the simplest form of the expression?

28. 128a13b 63


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What is the simplest form of the product?

29. 7x73

9x 43

What is the simplest form of the quotient?

30.162

3

23

31.400

4

54

32.90x 18

2x

What is the simplest form of the radical expression?

33. 2 2x4

+ 6 2x4

34. 3 2a 6 2a

What is the simplest form of the expression?

35. 20+ 45 5

What is the product of the radical expression?

36. 7 2

8+ 2

37. 5 3

2

38. 2 + 10

2 10

Simplify.

39. 20

1

2 20

1

2

40. 16

1

2


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41. Write the exponential expression 3x

3

8 in radical form.

What is the simplest form of the number?

42. 27

2

3

What is the solution of the equation?

43. x + 10 7 = 5

44. 2x + 8 6 = 4

45. 10+ x + 8 = 4

46. x + 6( )35 = 8

47. 5x = 10+ 15x

48. 3x+ 28 8=x

49. Let f(x) = 5x 4andg(x) = 6x 7. Findf(x) +g(x).

50. Let f(x) = 4x 5andg(x) = 6x 3. Findf(x) g(x).

51. Let f(x) = 3x 6andg(x) = x 2. Findf

gand its domain.

52. Let f(x) = 2x 7andg(x) = 4x + 3. Find (f g)(5).

53. Let f(x) = x2 + 6and g(x) = x + 8

x. Find g f

7( ).

What is the inverse of the given relation?

54. y= 3x + 9

55. For the function f(x) = x + 9, find (f f1 )(5).

Graph the equation.

56. y = x + 1


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57. y = x 3

58. y = x 3

59. You can model the population of a certain city between the years 1965 and 1995 by the radical function

P(x)= 55000 x 1950 . Using this model, in what year was the population of that city 235,000?

Graph the exponential function.

60. y = 4x

61. An initial population of 820 quail increases at an annual rate of 23%. Write an exponential function to model

the quail population. What will the approximate population be after 3 years?

62. The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361

kg. Write an exponential function that models the decay of this material. Find how much radioactive material

remains after 5 days. Round your answer to the nearest thousandth.

63. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you

have in the account after 4 years?

Write the equation in logarithmic form.

64. 25 = 32

65. 125

4

3 = 625

Evaluate the logarithm.

66. log51

625

67. log3 243

Graph the logarithmic equation.

68. y = log5 (x 2)

Write the expression as a single logarithm.

69. 3 logbq + 6 logbv

70. log3 4 log3 2


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Expand the logarithmic expression.

71. log3d

12

72. log3

11p3

73. Use the Change of Base Formula to evaluate log4 20.

74. Use the Change of Base Formula to evaluate log7 28.

Solve the exponential equation.

75.1

16 = 644x 3

76. 44x

= 8

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

77. 3log2x = 4

78. Solve log(4x + 10) = 3.

79. log(x + 9) logx = 3

80. Solve log3x + log9 = 0. Round to the nearest hundredth if necessary.

Write the expression as a single natural logarithm.

81. 3ln3+ 3 lnc

82. Simplify ln e 3 .

Use natural logarithms to solve the equation. Round to the nearest thousandth.

83. 6e4x 2 = 3

84. ex = 34

85. e2x = 1.4


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Is the relationship between the variables in the table a direct variation, an inverse variation, or

neither? If it is a direct or inverse variation, write a function to model it.

86.

x 7 10 14 18

y 14 20 28 36

87.

x 9 4 3 1

y 13 12 9 21

88. Suppose thatxandyvary inversely, andx= 2 wheny= 8. Write the function that models the inverse

variation.

Graph the function.

89. y =2

x

Sketch the asymptotes and graph the function.

90. y =5

x 3+ 2

91. Write an equation for the translation of y =4

x

that has the asymptotesx= 7 andy= 6.

92. This graph of a function is a translation of y = 2

x. What is an equation for the function?


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Find any points of discontinuity for the rational function.

93. y =(x + 6)(x + 2)(x + 8)

(x + 9)(x + 7)

94. Describe the vertical asymptote(s) and hole(s) for the graph of y = (x + 2)(x + 4)

(x + 4)(x + 1).

95. Find the horizontal asymptote of the graph of y =4x6 + 6x + 3

8x6 + 9x + 3

.

Simplify the rational expression. State any restrictions on the variable.

96.p

2 4p 32

p + 4

97.q

2 + 11q + 24

q2 5q 24

What is the product in simplest form? State any restrictions on the variable.

98.4a

5

7b4

2b

2

2a4

99. z2

z+ 1 z

2

+ 3z+ 2z

2 + 3z

What is the quotient in simplified form? State any restrictions on the variable.

100.x + 2

x 1

x + 4

x2 + 4x 5

Simplify the sum.

101.

7

a + 8 +

7

a 2 64

Simplify the difference.

102.b

2 2b 8

b2 + b 2

6

b 1


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Simplify the complex fraction.

103.

2

5t

3

3t

1

2t+

1

2t

Solve the equation. Check the solution.

104.2

x + 4=

4

x + 3

105.5

6w+

1

w= 4

What are the solutions of the rational equation? Use a graphing calculator to solve.

106.3.66

4c+

4

3c= 4

Generate the first five terms in the sequence using the explicit formula.

107. yn = 5n 5

108. What is the 15th

term in the sequence using the given formula?

cn =3n 1

109. Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term.

110. Write a recursive formula for the sequence 7, 4, 1, 2, 5, .... Then find the next term.

111. Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a14

.

112. Suppose you drop a tennis ball from a height of 8 feet. After the ball hits the floor, it rebounds to 80% of its

previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

Is the sequence arithmetic? If so, identify the common difference.

113. 13, 20, 27, 34, ...

114. 14, 21, 42, 77, ...

115. Find the 50th term of the sequence 5, 2, 9, 16, ...


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116. Find the 2nd and 3rd term of the sequence 7, ___, ___, 22, 27, ...

117. Find the missing term of the arithmetic sequence 22, , 34, ...

Is the sequence geometric? If so, identify the common ratio.

118. 6, 12, 24, 48, ...

119. 2, 4, 16, 36, ...

What is the fifth term of the geometric sequence?

120. 5, 15, 45, ...

Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.

121. a1 = 4, a2 = 8, a3 = 16

What is a possible value for the missing term of the geometric sequence?

122. 50, , 450, ...

123. 1250, , 50, ...


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34. 3 2a

35. 4 5

36. 54 2

37. 28+ 10 3

38. 8 39. 20

40. 4

41. 3 x38

42. 9

43. 6

44. 2

45. 28

46. 26

47. 1

48. 4

49. x 11

50. 2x 2

51. 3; all real numbers exceptx=2

52. 53

53.63

55

54. y= 1

3x 3

55. 5

56.


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57.

58.

59. 1968

60.

61. f(x) = 820(1.23)x ; 1526

62. y = 3611

2

1

32x

; 323.945 kg

63. $1,923.23


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64. log2 32 = 5

65. log125 625 = 4

3

66. 4

67. 5

68.

69. logb(q3v6 )

70. log3 2

71. log3d log3 12

72. log3 11+ 3 log3p

73. 2.161

74. 1.712

75.7

12 76.

3

8

77. 10.7722

78.495

2

79. 0.0090

80. 0.04

81. ln 27c3

82. 3

83. 0.046

84. 0.288 85. 0.168

86. direct variation;y = 2x

87. neither

88. y =16

x


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89.

90.

91. y =4

x 7+ 6

92. y= 2

x 3 6

93. x= 9,x= 7

94. asymptote:x = 1 and hole:x= 4

95. y = 1

2

96. p 8;p 4

97.q + 8

q 8; q 3,q 8

98.4a

7b2

, a 0, b 0

99.z

2 + 2z

z+ 3, z 1, 0, 3


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100.(x + 2)(x + 5)

x + 4, x 1, 4

101.7a 49

(a 8)(a + 8)

102. b 10b 1

103. 3

5

104. 11

3

105. 11

24

106. 0.562

107. 10, 15, 20, 25, 30

108. 44

109. an = a n 1 + 6,where a1 = 7; 37

110. an = a n 1 3,where a1 = 7; 8

111. an = 2n + 10; 18

112. 4.1 feet

113. yes; 7

114. no

115. 338

116. 12, 17

117. 28

118. yes; 2

119. no 120. 405

121. an = 4 (2)n 1 ; 64

122. 150

123. 250

al ii h final review pdf

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