Algebra 1B Final Exam Review: 2019-20

Name: ______________________ Teacher: _________________ Hour: ________ ID: A

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Algebra 1B Final Exam Review: 2019-20

Short Answer Part 1Complete each question on a separate sheet of paper. You must show work for each question in order to recieve full credit.

____ 1. Which system has infinitely many solutions?

a.x + 2 = y

4 = 2y − x

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c.y + 3 = 2x

4x = 2y − 3

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b.2y + 6 = 4x

−3 = y − 2x

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d.y = 2x − 5

−2 = y − 2x

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____ 2. Solve 2x + 5y = 4

3x + 5y = 1

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.

a. - b. -

____ 3. Which equation would make this system have an infinite number of solutions?

y = x + 2Ï

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a. 2y = 2x + 2 c. y = 2xb. y − 2 = x d. y = 3x − 1

____ 4. Which is the best first step in solving the system shown using the elimination method?7x − 10y = 12

8y − x = 11

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a. Multiply each term in 8y − x = 11 by –10.b. Rewrite the equations so like variable terms are in the same order.c. Multiply each term in 8y − x = 11 by 10.d. Add the corresponding sides of each equation.

Name: ______________________ ID: A

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____ 5. What can be done to eliminate the x-variable in the system shown?3x − 3y = 11

3x + 10y = 3

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a. Divide each term in each equation by 3.b. Add the corresponding sides of each equation. c. Subtract the corresponding sides of each equation. d. Multiply each term in 3x − 3y = 11 by 10 and multiply each term in 3x + 10y = 3 by 3.

____ 6. Mr. Frankel bought 7 tickets to a puppet show and spent $33. He bought a combination of child tickets for $3 each and adult tickets for $9 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?a. - b. -

____ 7. The cost of 2 notebooks and 4 folders is $2.50. What is the cost of a notebook? What is the cost of a folder?a. - b. -

____ 8. Subtract.

x3 − 2x + 3Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ – 3x2 + 4x − 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. - b. -

____ 9. Subtract.

x3 − 2x + 5Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ – 2x3 − 3x2 + 4x − 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. - b. -

____ 10. A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial 9000 + 3.2d. The revenue generated from the sale of d dog leashes will be given by the polynomial d(15 – 0.00005d). Write a polynomial expression that represents the profit earned from producing and selling d dog leashes.a. - b. -

____ 11. Write an expression that represents the perimeter of the triangle below?

a. - b. -

Name: ______________________ ID: A

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____ 12. What is the vertex of the quadratic function f x( )? Is it a maximum or a minimum?

a. - b. -

____ 13. Solve 4x2 = 14x + 8.a. - b. -

____ 14. Solve (7x + 6) 2 = 35.a. - b. -

____ 15. Use the Quadratic Formula to solve −4x2 = 5x + 9.a. - b. -

____ 16. Use the Quadratic Formula to solve x2 + 10x = 39.a. - b. -

____ 17. Use the Quadratic Formula to solve 24x = −16x2 − 2.a. - b. -

____ 18. Solve 49x2 + 169 = 0.a. - b. -

____ 19. Use the discriminant to find the number of solutions of the equation 3x2 + 2x + 1a. - b. -

____ 20. Solve x − 10( ) 2 = 49.a. - b. -

____ 21. Use the discriminant to find the number of solutions of the equation x2 + 4x − 3 = 0a. - b. -

____ 22. Solve using the quadratic formula. y = 3x2 − 5x − 2a. - b. -

Name: ______________________ ID: A

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____ 23. The discriminant of a quadratic equation is 0. How many solutions are there? a. - b. -

____ 24. The height in feet of a rock above the ground is given by the equation h = −16t2 + 24t + 16, where t is the time in seconds after a rock is thrown. It is 16 feet above the ground. How long does it take the rock to reach the ground? a. - b. -

____ 25. Solve x + 2( ) 2 = 36.a. - b. -

____ 26. Solve 2x2 − 18 = 0.a. - b. -

____ 27. Solve 2 x − 3( ) 2 = 8.a. - b. -

____ 28. Simplify x

15

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˜̃̃˜̃̃˜̃̃˜̃̃˜̃̃˜

5

.

a. - b. -

____ 29. Write the radical expression in rational exponent form.

a5

a. - b. -

____ 30. Write the radical expression in rational exponent form.

k 73

a. - b. -

Name: ______________________ ID: A

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____ 31. A website allows its users to submit and edit content in an online encyclopedia. The graph shows the number of articles a t( ) in the encyclopedia t months after the website went live. How many articles were in the encyclopedia when it went live?

a. - b. -

____ 32. Give the first four terms of the geometric sequence for which a 1 = −5 and r = −4.a. - b. -

____ 33. The table below shows the balance b, in dollars, of Daryl’s savings account t years after he made an initial deposit. What is an explicit formula for the geometric sequence that represents this situation?

Time t(years)

Balance b(dollars)

1 $12182 $1236.273 $1254.814 $1273.64

a. - b. -

____ 34. Which of the following is a geometric sequence?

a. 3, 6, 12, 24, . . . b. -


a. 4, 8, 12, 16, . . . b. -


a. 2, 4, 16, 256, . . . b. -

Name: ______________________ ID: A

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a. 2, 3, 5, 8, . . . b. -

____ 38. What is the explicit rule for the geometric sequence 3, 12, 48, . . . a. - b. -

Short Answer Part 2Complete each question on a separate sheet of paper. You must show work for each question in order to recieve full credit.

39. Solve 2x − y = 13

3x + y = 12

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.

40. Solve y = x + 3

2x + y = −6

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.

41. Solve y = 4x − 1

y = 3x + 6

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.

42. Solve x + y = −1

x − y = −7

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.

Name: ______________________ ID: A

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43. The graph of a system of linear equations is shown below. What is the solution of the system?

44. Solve 4x = 2y + 6

y = 2x − 3

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.

45. Solve 2x + 3y = 4

3x − 3y = −9

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.

46. Zahra spent $20.50 on 10 party favors for her party. The boys each received a puzzle book that cost $1.75 each. The girls each received a magic trick that cost $2.25 each. How many boys and how many girls attended the party?

47. Use a graph to solve the system y = 5

4x + 3

2

y = 3x − 2

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48. Two gyms offer a two-month “boot camp” training program. One gym charges $4 per session plus a one-time $50 fee. The other charges $6 per session plus a one-time $30 fee. For what number of sessions is the cost of the program the same for each gym?

49. A coin purse contains d dimes and q quarters. There are 20 coins in the purse and the total value of the coins is $4.25. Which system of equations represents this situation?

Name: ______________________ ID: A

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50. Two gyms offer a two-month “boot camp” training program. One gym charges $4 per session plus a one-time $50 fee. The other charges $6 per session plus a one-time $30 fee. For what number of sessions is the cost of the program the same for each gym?

51. Write 5x − 12 − 2x2 in standard form. Identify the leading coefficient.

52. What is the degree of 3x3 y2 ?

53. What is the degree of 4xy2 + 2x6 ?

54. What name best describes 6x3 − 2x2 + 3x

55. Add.6p 3 + 2p − p 3 + 7

56. Add.

2x3 − 5Ê

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ˆ

¯

˜̃̃˜̃̃ + x3 + 3

Ê

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ˆ

¯

˜̃̃˜̃̃

57. Add.(–7r3 s – 4rs) + (–3r3 s – 2rs – 3) + (8rs + 8)

58. Subtract (7a 2 − 3a) − (5a 2 − 5a).

59. Multiply (x + 2)(3x2 − 4x + 5).

60. Multiply (3x − 2)(2x + 6).

61. Multiply.(r + 5)(r – 5)

62. What is the product of x4 y and 4x2

63. What is the product of 4 11x + 3( )

64. Multiply x + 3( ) x − 5( )

65. Multiply 5 5x2 + 2x − 4Ê

Ë

ÁÁÁÁÁÁ

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¯

˜̃̃˜̃̃

Name: ______________________ ID: A

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66. Multiply 21x6 ⋅ 3x2

67. Celesete has a garden that has a length of x + 7 feet and a width of 3x − 5 feet. What is the area of the garden? A = lw

68. Use a table to graph the quadratic function f(x) = 5x2 + 4x – 2.

69. Graph the quadratic function f(x) = (x – 3)(x – 2).

70. What are the x-intercepts of the graph of the function (x − 3)(x − 9) = 0

71. What are the x-intercepts of the graph of the function (x + 1)(x + 5) = 0

72. Find the zeros of the quadratic function f x( ) = −x2 + 4x + 5 from the graph.

73. Graph y = 3x2 – 4x – 2.

74. Solve the equation x2 + 4x + 3 = 0 by graphing the related function.

75. Solve the equation −x2 + 6x − 9 = 0 by graphing the related function.

76. A soccer goalie kicks the soccer ball. The quadratic function y = −16x2 + 64x gives the time x seconds when the soccer ball is at height 0 feet. How long does it take for the soccer ball to return to the ground?

77. Use the Zero Product Property to solve the equation x − 4( ) x + 3( ) = −6.

Name: ______________________ ID: A

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78. Use the graph to find the solutions of f x( ) = −x2 − 2x + 3

79. What are the zeros of y = 3x − 9( ) x + 2( )

80. Solve the quadratic equation b 2 + b − 20 = 0 by factoring.

81. Solve 3x = x2 − 4.

82. Find the zeros of the function h x( ) = x2 + 5x − 50.

83. Solve the equation x2 = 64 − 12x.

84. Solve the equation.x2 − 2x − 24 = 0

85. Factor the expression x2 + 6x + 8

86. Factor the expression x2 − 7x − 30

87. Factor the expression 3x2 + 14x + 8

Name: ______________________ ID: A

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88. Factor the expression 5x2 − 2x − 3

89. Factor the expression x2 + 4x − 21

90. Use the Quadratic Formula to solve 4x2 + 5x + 2 = 0.

91. Use the Quadratic Formula to solve x2 + x = −1.

92. Use the Quadratic Formula to solve 2x = x2 − 8.

93. Use the Quadratic Formula to find the zeros of f(x) = x2 + 7x + 9.

94. Use the Quadratic Formula to solve the equation.x2 + 8x − 9 = 0

95. Write the expression 5 911 by using rational exponents.

96. Write the expression 4

32 in radical form, and simplify. Round to the nearest whole number if necessary.

97. Simplify 625

14 .

98. Write y

19 as a radical expression.

99. Write two algebraic expressions for the square root of x.

100. Simplify r

58

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ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜̃̃˜̃̃˜

8

.

101. Write y

311 ⋅ y

311 as a radical expression.

102. Simplify the expression 8x93. Assume that all variables are positive.

Name: ______________________ ID: A

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103. Write the expression 64

43 in radical form, and simplify. Round to the nearest whole number if necessary.

104. Simplify the expression (125)

13 ⋅ (125)

23 .

105. Simplify 625

14 .

106. Simplify 164

Ê

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ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

12 .

107. Simplify 4

52 .

108. Simplify 27

23 .

109. Simplify 64

43 .

110. Simplify 256

34 .

111. Simplify 164

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃−

13 .

112. Simplify 49

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃−

12 .

113. Simplify (−27)43 .

114. Simplify 216

13 + 64

16 .

Name: ______________________ ID: A

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115. Simplify the expression 24 .

116. Simplify z5

4z. All variables represent nonnegative numbers.

117. Which of the following is equivalent to x8 y612 for all values of x and y?

118. Simplify 144

12 .

119. Which expression equals 3?

120. 324

23 is equivalent to which of the following?

121. What is 81

12 + 64

13 simplified?

122. What is x

12 • x

32 simplified?

123. Simplify 6x6

2x3.

124. Simplify −4 0

125. Simplify −3x2Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

0

126. Simplify 4 −2

127. Simplify b 3 • b 4

128. Simplify t6

t3

Name: ______________________ ID: A

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129. Simplify 3y3Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

2

130. Simplify 32

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

3

131. Simplify x5Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4

132. Simplify d −3

133. Simplify 5w8Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

2

134. Simplify a 4b 2Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ a

−1b 6Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

135. Simplify b 2Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃−2b 4Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

5

136. Simplify a4

b 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

−3

137. Simplify 5 −3

138. What is the 16t h term in the following geometric sequence?2, –6, 18, –54, 162, ...

139. An electric can opener is worth 31 dollars when it is new. After each year it is worth half what it was the previous year. What will its worth be after 7 years? Round your answer to the nearest cent.

140. What is the 16t h term in the following geometric sequence?5, 15, 45, 135, 405, ...

Name: ______________________ ID: A

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141. Which ordered pair is the solution of the system graphed below?

y = −x + 2

y = x − 8

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ID: A

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Algebra 1B Final Exam Review: 2019-20Answer Section

MULTIPLE CHOICE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. OBJ: Using Square Roots to Solve Quadratic Equations 19. 20. OBJ: Using Square Roots to Solve Quadratic Equations 21. 22. 23. 24. 25. OBJ: Using Square Roots to Solve Quadratic Equations 26. OBJ: Using Square Roots to Solve Quadratic Equations 27. OBJ: Using Square Roots to Solve Quadratic Equations 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

ID: A

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SHORT ANSWER

39. 40. 41. 42. 43. 44. 45. 46. 47. OBJ: Solving Linear Systems by Using Graphs and Tables 48. OBJ: Application 49. OBJ: Application 50. OBJ: Application 51. OBJ: Adding Polynomials Horizontally 52. OBJ: Adding Polynomials Horizontally 53. OBJ: Adding Polynomials Horizontally 54. OBJ: Adding Polynomials Horizontally 55. OBJ: Adding Polynomials Horizontally 56. OBJ: Adding Polynomials Horizontally 57. OBJ: Adding Polynomials Horizontally 58. 59. 60. 61. OBJ: Special Products of Binomials 62. OBJ: Special Products of Binomials 63. OBJ: Special Products of Binomials 64. OBJ: Special Products of Binomials 65. OBJ: Special Products of Binomials 66. OBJ: Special Products of Binomials 67. OBJ: Special Products of Binomials 68. OBJ: Graphing Quadratic Functions 69. OBJ: Graphing Quadratic Functions 70. 71. 72. OBJ: 8-2.1 Finding Zeros of Quadratic Functions From Graphs 73. OBJ: 8-3.1 Graphing a Quadratic Function 74. OBJ: 8-5.1 Solving Quadratic Equations by Graphing 75. OBJ: 8-5.1 Solving Quadratic Equations by Graphing 76. OBJ: 8-5.2 Application 77. OBJ: 8-6.1 Using the Zero Product Property 78. OBJ: 8-6.1 Using the Zero Product Property 79. OBJ: 8-6.1 Using the Zero Product Property 80. OBJ: 8-6.2 Solving Quadratic Equations by Factoring 81. OBJ: Using the Quadratic Formula 82. OBJ: Finding Zeros by Factoring

ID: A

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83. OBJ: Solving a Quadratic Equation by Completing the Square 84. 85. 86. 87. 88. 89. 90. 91. 92. OBJ: Using the Quadratic Formula 93. OBJ: Quadratic Functions with Real Zeros 94. 95. OBJ: Writing Expressions by Using Rational Exponents 96. OBJ: Writing Expressions in Radical Form 97. 98. 99. 100. 101. 102. OBJ: Simplifying Radical Expressions 103. OBJ: Writing Expressions in Radical Form 104. OBJ: Simplifying Expressions with Rational Exponents 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. OBJ: Using the Product Property of Square Roots 116. OBJ: Using the Quotient Property of Square Roots 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128.

ID: A

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129. 130. 131. 132. 133. 134. 135. 136. 137. 138. OBJ: Finding a Given Term of a Geometric Sequence 139. OBJ: Application 140. 141.

Algebra 1B Final Exam Review: 2019-20

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Transcript of Algebra 1B Final Exam Review: 2019-20