Name Date Alg2 Common Core Midterm Review

Part I QuestionsEach correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet.

1. Which values of x are solutions of the equation ?1)2)3)4)

2. What is the fifteenth term of the sequence ?1)2)3) 81,9204) 327,680

3. Over what interval is the average rate of change the greatest?

1) -3 < x < -1 2) -1 < x < 6 3) 6 < x < 9 4) -3 < x < 6

4. When is subtracted from , the difference is1)

2)

3)4)

5. If is solved by completing the square, an intermediate step would be1)2)3)4)

6. Which equation represents the circle shown in the graph below that passes through the point ?

1)2)3)4)

7. The product of and is1)2)3) 144) 4

8. The expression is equivalent to1)2)3)4)

9. What is a formula for the nth term of sequence B shown below?

1)2)3)4)

10. Which values of x are in the solution set of the following system of equations?

1)2)3)4)

11. Which function is not one-to-one?

1) (1, 0), (2, 1), (3, 2), (4, 3)2) (1, 1), (2, 2), (3, 3), (4, 4)3) (1, -1), (2, -2), (3, -3), (4, -4)4) (1, 1), (2, 1), (3, 1), (4, 1)

12. The value of the expression is1) 122) 223) 244) 26

13. What is the domain of the function ?

1)2)3)4)

14. When expressed as a monomial in terms of i,

1) 2) 03) 4)

15. If k is a constant, what is the value of k such that the polynomial is divisible by x – 1?

1) 12) 33) 94) 3

16. What is the remainder when is divided by x + 2 ?

1) 42) 123) 44) 16

17. The graph of y = is shown below. What is the product of the roots of the equation

y = ?

1) 02) 63) 6.0044) 6

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28. The following function, is:

1) even 2) odd

3) neither even or odd 4) even and odd

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49. The expression is the factorization of which of the following?

(1) (2) (2) (2)

50. The product of and is equivalent to:(1) 1 (2) i (3) -1 (4) -i

51. What is the end behavior of the function:

(1) As and as

(2) As and as

(3) As and as

(4) As and as

Part II, III and IVClearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.

52. Find the roots of 3 x2−4 x−5=0 in simplest radical form.

53. If (5, ) is a solution to the system:px – qy = 16

px + qy = 24

find the values of p and q.

54. Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house?

55. Two mechanics were working on your car. Steve can complete the given job in six hours, together they can complete it in 4 hours. How long does it take David, the other mechanic to complete the job alone?

56. Given the length and width of a rectangle are and , find the area of the rectangle in simplest form.

57. Find the inverse of the function f(x) = 3x + 5

58. Evaluate:

59. The graph below represents the function .

State the domain and range of this function.

60. Factor completely:

61. Express the sum using sigma notation.

62. Express in simplest form:

63. Express as a trinomial.

64. Solve algebraically for x:

65. Simplify the expression

66. Write an equation of the circle shown in the graph below.

67. Solve for x:

68. Solve and express the result in simplest radical form.

69. Solve the equation algebraically for all values of x.

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72. What are the coordinates of the point(s) of intersection of the graphs of and y = x + 2

73. What is the total number of points of intersection of the graphs of and y = 2?

74. Write the equation of the parabola that is equidistant from the point (2,8) and the line y = 10.

75. Write the equation of the parabola with a focus of (3,5) and where the directrix is the x-axis.

76. The equation: has:(1) no real root(2) one positive root only(3) two positive roots(4) one positive and one negative root.

77. Solve:

78.Factor:

79. What is the product of and in simplest form?80. Consider the graph of . It is slid 4 units left, then reflected in the x-axis, stretched vertically by a factor of ½ and slid 4 units up. What is the resulting equation?

81. Using the equation: List each of the transformations that have occurred when compared to the graph of .

82. Find the product of and express in simplest form.

83. Stu factors f(x) to find the zeros of a function. If Stu comes up with f(x) = (x+7)(x – 3) and states that the zeros are 7, 0, and -3, what errors has he made?

84. Write a cubic function in intercept form for the given graph whose intercepts are integers. Assume that the leading coefficient is either +1 or -1.

85. Write a quartic function in intercept form for the given graph whose intercepts are integers. Assume that the leading coefficient is either +1 or -1.

86. What is the solution set of the equation ?

87. Find the quotient: by long division or tabular method.

88. Solve for x:

89. Algebraically determine the values of x that satisfy the system of equations below:

90. Given:

State the solutions to the equation , rounded to the nearest hundredth.

91. Algebraically prove that the difference of the squares of any two consecutive integers is an odd integer.

92. Algebraically prove that , and are Pythagorean triples for all values of x > 1.

93. Algebraically prove that the product of two odd integers is an odd integer.

94. Express as a monomial in terms of i,

95. Express as a monomial in terms of i,

96. Simplify:

97. Solve the system of equations:

98. Simplify:

99. Simplify: (3gm – 8m2) – [(gm – m2) +(4m2 – 5gm)]

100. Factor: