algebra domain (approximately 36% of test) 1.which function is shown on the graph? a. y = x 2 b. y =...

ALGEBRA DOMAIN (approximately 36% of test)

1. Which function is shown on the graph?

a. y = x2 b. y = x3

c. y = | x | d. y = 1/x

2. Sam observes that the data he collected falls in a V-shaped pattern when he graphs it. What type of function would best represent Sam’s data?

a. absolute value b. cubicc. inverse d. quadratic

3. Which function is shown on the graph?

a. y = x2 b. y = x3

c. y = | x | d. y = 1/x

4. Anne observes that the data she collected falls in a parabola-shaped pattern when she graphs it.

What type of function would best represent Anne’s data?

a. absolute value b. cubic

c. inverse d. quadratic

5. The graph of f(x) = x2 is transformed to produce the graph shown at the right. Which function would produce this transformation?a. g(x) = (x + 3)2 b. g(x) = (x – 3)2

c. g(x) = x2 + 3 d. g(x) = x2 – 3

6. The graph of f(x) = | x | is transformed to produce the graph shown at the right. Which function would produce this transformation?a. g(x) = | -x | b. g(x) = | 2x |c. g(x) = - | x | d. g(x) = | 1/x |

7. The graph of f(x) = x2 istransformed to produce thegraph shown at the right.Which function would produce this transformation?

a. g(x) = 2x2 b. g(x) = 0.5x2

c. g(x) = -x2 d. g(x) = (-x)2

8. A section of Bill’s graphic design for a client’s logo is represented in his computer graphic program as a cubicfunction, f(x) = x3. He needs to modify his design by copyingthat part of the design 5 units to the left. Which functionshould he use to create this transformation of his originalfunction?

a. g(x) = 5x3 b. g(x) = x8

c. g(x) = (x – 5)3 d. g(x) = (x + 5)3

11. For the function f(x) = x3, which statement below is true?a. As x approaches ∞, f(x) approaches ∞,

and as x approaches -∞, f(x) approaches ∞.b. As x approaches ∞, f(x) approaches ∞,

and as x approaches -∞, f(x) approaches -∞.c. As x approaches ∞, f(x) approaches -∞,

and as x approaches -∞, f(x) approaches ∞.d. As x approaches ∞, f(x) approaches -∞,

and as x approaches -∞, f(x) approaches -∞.

12. What are the zeros of function shown on the graph at the right?

a. 2 and -3b. -2 and 3c. -6c. 0

9. What is the range of the function in the graph shown at the right?

a. ( -∞, ∞) b. ( 3, -2 )

c. [ -2, ∞) d. [ 0, ∞)

10.What is the domain of the function in the graph shown at the right?

a. all real numbers except 0b. all real numbers except 1c. all real numbersd. all integers

13. Colin is developing a catapult for a contest in which the participants compete to see which team’s pumpkin will

stay in the air the longest and which will travel the longest distance. As he considers adjustments to his catapult, he uses computer simulations to track the distance the pumpkin travels as a function of time in the air for each test throw. Should Colin’s graphs show a continuous function, or discrete points?

a. continuous b. discrete

14. Dexter monitors the mosquito population in a certain region by counting the number of mosquitoes in a

mosquito trap at the end of each day. During a particularly wet fourteen-day period, he notices that the mosquito population numbers are increasing in a quadratic pattern. If he wants to prepare a graph to show the population growth for that period, what would be an appropriate domain for his graph?

a. real numbers from -∞ to ∞ b. real numbers from 0 to ∞c. integers from 1 to 14

d. integers from 1 to ∞

Use the graph below for problems 15 and 16. Company Profit

15. According to the graph, during what year did the company earn its maximum profit?

a. 2003 b. 2006 c. 2009 d. 2020

Years Since Business Opened in 2001

16. Between what years did the company see the largest increase in profits?

a. between the first and second years of businessb. between the fifth and sixth years of businessc. between the sixth and seventh years of businessd. between the eighth and ninth years of business

17. What is an explicit formula for the sequence shown?

4, 9, 14, 19, 24, . . .

a. an = 4n + 5 b. an = 4n + 9

c. an = 5n + 4 d. an = 5n – 1

18. Figure 1 Figure 2

Figure 3 Figure 4

If the pattern continues, which formula shows the number of squares that will be on the bottom row of the nth figure?

a. an = n b. an = n + 2

c. an = 2n – 1 d. an = n2

19. Which of the following sequences is best defined by a recursive rather than explicit formula?

a. 2, 5, 8, 11, 14, . . . b. 3, 6, 12, 24, 48, . . .

c. 32, 28, 24, 20, 16, . . . d. 0, 1, 1, 2, 3, 5, 8, 11, . . .

20. Which of the following could be the domain of the sequence below?

1, 7, 13, 19, 25

a. real numbers from 1 to 5b. integers greater than 0c. integers from 1 to 5d. all real numbers

Use the following graph for problems 21 and 22.

21. During which interval of hours is the rate of change constant?

a. 1 to 3 hours b. 3 to 5 hoursc. 5 to 7 hours d. 7 to 9 hours

0 1 2 3 4 5 6 7 8 9 100

Bicycle Trip

Number of Hours Since Start of Trip

22. What was the average rate of change in the number of miles between the sixth and ninth hours?

a. approximately 1.7 miles per hourb. approximately 3.5 miles per hourc. approximately 1.2 miles per hourd. approximately 6 miles per hour

0 1 2 3 4 5 6 7 8 9 100

Bicycle Trip

Number of Hours Since Start of Trip

Which function has the greatest average rate of change between x = 0 and x = 3?

a. y = 2x b. y = x2

c. y = .25x3 d. The rates of change are equal.

1 2 3 4

y=.25x3

24. Which of the following would have a constant rate of change throughout the function? a. an absolute value function b. a cubic function

c. a linear function d. a quadratic function

25. Which of the following functions is symmetric with respect to the origin?

a. y = x3 b. y = x2 c. y = | x | d. y = x

26. Which statement describes the function f(x) = x2 – 3?

a. The function is symmetric with respect to the origin. b. The function is symmetric with respect to the y-axis. c. The axis of symmetry for the function is y = -3. d. The function has no symmetry.

27. Which statement describes the function shown on the graph below?

a. The function is symmetric with respect to the origin. b. The function is symmetric with respect to the y-axis. c. The axis of symmetry for the function is x = 2. d. The function has no symmetry.

28. Which statement describes the function f(x) = 4x3?

a. The function is symmetric with respect to the origin.b. The function is symmetric with respect to the y-axis.c. The axis of symmetry for the function is y = -3.d. The function has rotational symmetry about the point (0, 3).

29. To solve the equation x2 = 2x, Evan graphed f(x) = x2 and g(x) = 2x. What are the solutions for the equation?

a. 0 and 4b. all real numbersc. all integersd. 0 and 2

30. To solve the equation ½ x + 1 = 2x + 7, Fred graphed f(x) = ½ x + 1 and g(x) = 2x + 7. What is the solution for the equation?

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

31. To solve the equation x3 = -x2 + 2, Greg graphed f(x) = x3 and g(x) = -x2 + 2. What is the solution for the equation?

a. 2 b. 0 c. -1 d. 1

-6 -4 -2

32. The functions f(x) = x2 – 4x + 3 and g(x) = -x2 + 4x – 3 are graphed on the coordinate grid at the right. What is the value of x in the equation x2 – 4x + 3 = -x2 + 4x – 3?

a. 3 or -3 b. 1 or 3c. 0 d. no solution

33. What is the inverse of the function f(x) = 5x2 + 8?

a. f-1(x) = b. f-1(x) =

c. f-1(x) = d. f-1(x) =

34. Given the function shown in the table below, what is the domain of the inverse of the function?

X 1 3 5 7Y 2 10 26 50

a. { 1, 3, 5, 7 } b. { -1, -3, -5, -7 }c. {2, 10, 26, 50 } d. {-2, -10, -26, -50 }

35. The graph of f(x) has a restricted domain.

Its inverse, f-1(x), and the dashed line y = x are also graphed . Which set of values indicates the restricted domain of f-1(x)?

a. -5 < x < 8 b. -5 < x < 2 c. 1 < x < 8 d. 1 < x < 2

f-1(x)

36. If f(x) = x3 and f-1(x) = , what is the value of f(f-1(8))?

a. 2 b. 8 c. 16 d. 512

37. Write as a complex number in standard form.

a. 3 b. -3 c. 3i d. -3i

38. Which is equivalent to ?

a. 4 b. 4i c. d.

39. Which is equivalent to ?

a. 9 b. 9i c. d.

40. Write as a complex number in standard form.

a. 7 b. 2 + 5i c. 2 – 5i d. -3

22 22i

23i 23

41. Add: (3 + 2i) + (-5 + 7i).

a. -2 + 9i b. -16 c. -2 – 5i d. 14

42. Simplify: i25

a. -1 b. 1 c. –i d. i

43. Multiply: (3 – 4i)(2 + 5i)

a. 26 b. 6 – 20i2 c. 5 + i d. 26 + 7i

44. Simplify:

45. Simplify: a. b. c. d.

46. Simplify:

a. 6a2b4 b. 6ab2 c. d.

47. Simplify: a. b.

48. Simplify:

106 610 152 215

4236 ba

426 ba ab365320 nm

4252 nmmn mnmn 25 2

mnmn 52 2 mnmn 210

322250 zyx

zxyz 105 xyzxyz 105

zxyz125 xyz5

49. Simplify: a. b. c. 39 d.

50. For which expression below should the denominator berationalized?

I. II. III.

a. I only b. I and II c. II and III d. I and III

51. Simplify: a. b. c. 420 d.

52. Which expression is equivalent to ?

5424 78 65 136

670 617 645

157102

112412

53. Add: (x2 + 7x + 5) + (2x – 9)a. x2 + 9x + 4 b. 10x2 – 4c. 10x2 + 4 d. x2 + 9x – 4

54. Multiply: (x – 6)(x + 4)a. x2 – 2x – 24 b. x2 – 24c. 2x – 24 d. x2 + 2x – 24

55. Multiply: (x – 6)(x2 – 2x + 5)a. x3 + 12x + 5 b. x3 – 8x2

+ 17x – 30c. x3 – 2x2 – 30 d. –x2 – 30

56. Simplify: (2x2 – 3x + 4) + (3x2 – 6) – (x + 11)a. 5x2 – 4x – 13 b. 5x 2‑ – 2x – 13c. 5x2 – 9x – 7 d. 5x2 – 4x + 9

57. Simplify:

a. b. c. d.

58. Simplify:

a. b. c. d.

4)5)(3(

)3(2 2

2)5( xx

59. Simplify:

60. Simplify:

)2()3(

)3)(4()2)(3(

)3)(4()2( 2

)3)(4()3( 2

)2)(3(113

)2)(3(193

61. Find the complete factorization of 2x5 – 6x3.

a. 2x3(x2 – 4x) b. 2x5(1-3x2)c. -4x2 d. 2x3(x2 – 3)

62. Factor: 9x2 – 16

a. (9x-16)(x+1) b. (3x + 8)(3x – 8)c. (9x – 4)(x + 4) d. (3x – 4)(3x + 4)

63. Factor: 16x2 + 9

a. (4x + 3)(4x + 3) b. (4x + 3i)(4x – 3i)c. (8x + 3)(8x + 3) d. (8x + 3i)(8x – 3i)

64. Factor: 2x2 + 9x – 5

a. (2x + 1)(x – 5) b. (2x – 1)(x + 5)c. (2x – 5)(x + 1) d. (2x + 5)(x – 1)

65. Simplify: a. b. c. d.

66. Simplify:

a. x2 b. c. d. 2x2

67. Simplify:

a. b. c. d.

68. Simplify:

a. 4 b. c. 2 d.

69. Solve for x:

a. 65 b. 63 c. 9 d. 7

70. Solve for x:

a. 1 b. 121 c. 11 d. -1

71. Solve for x:

a. b. c. -2 d. 4

72. Solve for x:

a. 2 b. -2 c. 4 d. -10

9532 xx

5614 xx

73. Solve for x:

a. -1 b. 1 c. -2 d. 2

74. Solve for x:

a. -2 or 10 b. -6 or 40 c. -10 or 4 d. no solution

75. Solve for x:

a. -8 b. 4 c. 10 d. -3

76. Solve for x:

a. -2 or 6 b. 2 or -6 c. -3 or -4 d. 3 or 4

2512 xx

77. What is the range of the following function?

a. (-∞, ∞) b. all whole numbersc. all integers d. [1, ∞)

78. What is the vertex of y = 4 | x – 3 | – 6?

a. (-12, 6) b. (3, -6) c. (-3, -6) d. (3, 6)

79. Over what interval is f(x) increasing?

a. (5, ∞) b. (-∞, 5) c. (-∞,∞) d. (0, ∞)

80. Find the x-intercept and y-intercept of the function:

a. x-intercept = -2; y-intercept = 2b. x-intercept = -2; y-intercept = -2c. x-intercept = 2; y-intercept = -2d. x-intercept = 2; y-intercept = 2

81. Solve: | 2x + 3 | = 11

a. 4, 7 b. , c. 4, -7 d. -4, 7

82. Solve: | a + 5 | > 3

a. a < -8 or a > -2 b. -8 < a < -2

c. a < -3 or a > 3 d. -3 < a < 3

83. According to the graph, for what value(s) of x does f(x) = 4?a. x = 3 or x = 0

b. x = -1 or x = 7

c. x = -4 or x = 4

d. x = 4 or x = 3

84. According to the graph, what is the solution for theinequality | x + 2 | > 3?

a. x < -5 or x > 1

b. -3 < x < 3

c. -5 < x < 1

d. all real numbers

-6 -4 -2 2

85. Which is equivalent to (2x2)-3?a. b. c. d.

86. Simplify: (n3p4)8

a. n11p12 b. n24p32 c. (np)56 d. (np)96

87. Simplify:

a. b. c. d.

88. For a planned mission, a spacecraft will travel 8.2 x 108 miles to Saturn. The craft will travel at a speed of 7.4 x 104 miles per hour. How many hours will it take the craft to reach Saturn?

a. 1.1 x 1012 hours b. 6.1 x 1013 hoursc. 1.1 x 104 hours d. 6.1 x 104 hours

661x 68

89. What is the y-intercept of the graph of the function y = 3(2)x?a) (0, 1) b. (0, 2) c. (0, 6) d. (0, 3)

90. Which statement is true about the end behavior of the graph of f(x) = -3(0.5)x?

a. As x approaches infinity, f(x) approaches 0. As x approaches –∞, f(x) approaches –∞.

b. As x approaches ∞, f(x) approaches ∞. As x approaches –∞, f(x) approaches 0. c. As x approaches ∞, f(x) approaches – ∞. As x approaches – ∞, f(x) approaches 0. d. As x approaches ∞, f(x) approaches 0. As x approaches –∞, f(x) approaches ∞.

91. Which function has a graph that is increasing over the entire domain?

a. f(x) = (0.25)x b. f(x) = -2(3)x

c. f(x) = 3(2)x d. f(x) = 3x2

92. The declining population of wolves in a particular region is modeled by the exponential function shown.

What does the x-intercept represent in the context of the problem? a. the number of wolves at the beginning of the study b. the number of years after which there would be no wolves left if the pattern continues c. the maximum number of wolves during the period of the study d. the year 2005

Number of Years Since Beginning of Study in 2005

93. Which function does the graph represent?

a. f(x) = 2x

b. f(x) = 2-x

c. f(x) = -x2

d. f(x) = -2x

94. Which table can be modeled by the equation y = 2(0.6)x?

a. x -2 0 1 2y 1/18 2 12 72

b. x -2 0 1 2 y -2.4 0 1.2 2.4

c. x -2 0 1 2y 0.6 0.6 0.6 0.6

d. x -2 0 1 2y 5.55… 2 1.2 0.72

a. f(x) = 2x + 3

b. f(x) = 2x – 3

c. f(x) = 2x-3

d. f(x) = 2x+3

a. f(x) = 2x + 3

b. f(x) = 2x – 3

c. f(x) = 2x-3

d. f(x) = 2x+3

97. Solve for x: 3x + 2 = 81a. 25 b. 2 c. 27 d. -5

98. Use the graph of y = 3x – 5 to solve for x when y = -2.

a. -5 b. -4 c. 1 d. 1.5

99. Solve: 4x + 3 > 19

a. x > 2 b. x < 3 c. x > 0 d. x < -2

100. If there are initially 20 bacteria in a sample, and the number of bacteria is increasing by 50% every hour, the number of bacteria after t hours can be found using the formula N = 20(1.5)t. A model of the function isshown on the graph below. After approximately how many hours will the number of bacteria exceed 100?

a. 2 b. 4 c. 6 d. 50

-2 2 4 6

101. A geometric sequence follows the rule an = 100 · 5n-1. What is the domain of the sequence?

a. all real numbers b. all positive numbers

c. all integers d. all positive integers

102. What are the first five terms in the geometric sequence for which a1 = 3 and r = 5?

a. 3, 8, 13, 18, 23 b. 3, 8, 11, 16, 19

c. 5, 15, 45, 135, 405 d. 3, 15, 75, 375, 1875

103. What are the first five terms in the geometric sequence defined by the rule an = 3n-1?

a. 1, 3, 9, 27, 81 b. 3, 6, 9, 12, 15

c. 3, 2, 1, 0, -1 d. 3, 4, 5, 6, 7

104. In a particular geometric sequence, a1 = 7 and a2 = 14. Which answer shows a rule that could be used to find the nth term of that sequence?

a. an = 7n b. an = 2 · 7n

c. an = 7 · 2n – 1 d. an = 14n – 1

105. Which rule below could apply to a geometric sequence that has a common ratio of 6?

a. an = 6 · 2n-1 b. an = 25 · 6n-1

c. an = 6n – 5 d. an = x6

106. Write a rule for the nth term of the geometric sequence.

3, 12, 48, 192, . . .

a. an = 4 · 3n - 1 b. an = 4n – 1

c. an = 3 · 4n – 1 d. a n = 192 · (0.25)n

107. Due to a decreasing number of predators, the population of forest mice in a particular region is doubling every year. If the population of mice was estimated to be 1000 when data was first collected, how many mice would be expected to be in the population 6 years later?

a. 64,000 b. 6,000 c. 12,000 d. 100,000

108. A certain antibiotic is found to reduce the number of germ cells by 75% of each time a dose is given. In a certain sample, if there are originally 2000 germ cells, approximately how many would remain after 4 doses

of the antibiotic?

a. 633 b. 8 c. 122 d. 15

109. Find the domain and range for y = log3(x – 2)

a. domain: all real numbers; range: y > 2b. domain: all real numbers; range: y > 0c. domain: x > 0; range: all real numbersd. domain: x > 2; range: all real numbers

110. What is the y-intercept of y = 4 · 11n – 1?a. 4 b. 11 c. 44 d. 0

111. Which line is an asymptote for y = 3 + log x?a. x = 3 b. y = 0 c. y = 3 d. x = 0

112. Which function increases on the interval (-∞, ∞)?a. y = 0.25x b. y = -(2x) c. y = 4-x d. y = 3x

113. Change y = x2 – 6x + 8 into general (vertex) form.

a. y = (x – 3)2 – 1 b. y = (x – 3)2 + 8

b. y = (x – 6)2 + 8 d. y = (x + 4)2 – 6

114. What are the x-intercepts and vertex of the quadraticfunction y = x2 + 10x + 16?

a. x-intercepts: 10 and 16; vertex (0, 0)

b. x-intercepts: -8 and -2; vertex (-5, -9)

c. x-intercepts: -10 and -16; vertex (-13, -10)

d. x-intercepts: 8 and 2; vertex (5, -9)

115. If the function f(x) = 2(x – 3)2 + 5 is written in the formf(x) = ax2 + bx + c, what are the values of a, b, and c?

a. a = 2, b = -12, c = 23 b. a = 2, b = -3, c = 5

c. a = 2, b = 3, c = 5 d. a = 2, b = 0, c = 5

116. Change y = 2x2 + 16x + 25 to vertex form.

a. y = 2(x + 4)2 + 9 b. y = 2(x + 8)2 + 25

c. y = 2(x + 8)2 + 9 d. y = 2(x + 4)2 – 7

117. Which of the following is the graph of f(x) = (x – 3)2?

118. How would you translate the graph of y = x2 to produce the graph of y = x2 + 7?

a. translate the graph of y = x2 up 7 unitsb. translate the graph of y = x2 down 7 unitsc. translate the graph of y = x2 right 7 unitsd. translate the graph of y = x2 left 7 units

119. Which function shows the reflection of y = x2 over the x-axis?

a. y = (-x)2 b. y = 2x c. y = x-2 d. y = -x2

120. How would you translate the graph of y = 5x2 to produce the graph of y = 5(x – 2)2 + 3?

a. translate y = 5x2 left two units and up three unitsb. translate y = 5x2 left two units and down three unitsc. translate y = 5x2 right three units and up two unitsd. translate y = 5x2 right two units and up three units

121. What is the equation of the axis of symmetry for the quadratic function y = (x – 5)2 + 3?

a. y = 3 b. x = 3 c. y = 5 d. x = 5

122. Which correctly describes the intervals of increase and decrease for the graph of y = (x – 4)2 + 11?

a. increasing (-∞, 0); decreasing (0, ∞)b. decreasing (-∞, 4); increasing (4, ∞)c. decreasing (-∞, 0); increasing (0, ∞)d. increasing (-∞, 4); decreasing (4, ∞)

Use the graph below for problems 123 and 124.

123. The height (in feet) of a ball x seconds after it is thrown is modeled by the equation f(x) = -(x – 3)2 + 16. After how many seconds does the ball reach its maximum height?

a. 0 b. 3 c. 7 d. 16

124. What was the average rate of change in the ball’s height between 0 and 3 seconds after it was thrown?

a. 3 feet per second b. 9 feet per second

c. 2 feet per second d. 16 feet per second

124. What was the average rate of change in the ball’s height between 0 and 3 seconds after it was thrown?

a. 3 feet per second b. 9 feet per secondc. 2 feet per second d. 16 feet per second

125. Change to standard a + bi format.

a. 3 + 4i b. 3 – 4i c. -1 d. 7

126.Change to standard a + bi format.

a. -5 – 14i b.

c. d. -5 + 14i

127. Lily used the quadratic formula to solve a quadratic equation and got the following result: .

Which answer is equivalent to Lily’s answer?

128. Violet used the quadratic formula to solve a quadratic equation and got the following result: .

Which answer is equivalent to Violet’s answer?a. b. c. d.

ix 523 ix 25

i102 i52 i52 i202

129. Solve: x2 + 3x – 10 = 0a. x = 5 or x = -2 b. x = -5 or x = 2c. x = 3 or x = -10 d. x = -3 or x = 10

130. Solve: x2 – 16 = 0a. x = 16 or x = 1 b. x = -16 or x = -1c. x = 8 or x = -8 d. x = 4 or x = -4

131. Solve: x2 – 20 = 0a. b.

132. Solve: x2 – 11x + 24 = 0a. x = -11 or x = 24 b. x = 11 or x = -24c. x = -8 or x = -3 d. x = 8 or x = 3

52x 25x

10x 54x

133. The table shows some ordered pairs that result from a quadratic function. Which of the following is an x-interceptof the function?a. -1 b. -6 c. 3 d. 1

134. The height (in feet) of a ball x seconds after it is thrown is modeled by the equation f(x) = -(x – 3)2 + 16. At which time below would the ball be at a height of 12 feet?a. 1 second after it is thrown b. 6 seconds after it is thrownc. 2 seconds after it is thrown d. 7 seconds after it is thrown

x y-2 0-1 -40 -61 -62 -43 0

135. An object thrown downward from a height of 50 feet at a velocity of 30 feet per second. The height of the

object after t seconds can be modeled by the function h(t)=16t2–30t + 50. If this function was displayed on a graph, what would the x-intercept of the graph represent in the context of the problem?

a. the initial height of the object before it was dropped b. the maximum height of the object c. the number of seconds it takes the object to get halfway to the ground d. the number of seconds it takes the object to reach the ground

136. The graph of f(x) = x2 – 2x – 4 is shown. Based on the graph, for what approximate values of x does the function equal 0?

a. -3 and 7 b. -2.5 and 5.4

c. -1.2 and 3.2 d. -4.9 and 1.3

137. Use the quadratic formula to solve: x2 + 4x + 5 = 0.

a. x = 1 or x = -5 b. x = -2 ± I

c. x = -1 or x = 5 d. x = -2 ± 2i

138. A building covering a 20 meter by 25 meter rectangle of land is to be surrounded by a garden so that the total area of land covered by the building and garden is 800 square meters. If the width of the garden is consistent around the building, then the width can be determined by solving the equation 4x2 + 90x – 300 = 0. What is the approximate width of the garden?

a. 1.5 meters b. -12.7 meters

c. 2.7 meters d. -11.4 meters

139. Three quadratic equations and three methods of solving are listed below. Which equation would be best suited to each method? Quadratic Equations Method A. x2 + 8x + 12 = 0 1. Taking square roots of both sides B. (x – 2)2 = 36 2. Using the quadratic formula C. x2 – 5x + 11 = 0 3. Factoring and using zero

product property a. Equation A with Method 2; Equation B with Method 3; Equation C with Method 1 b. Equation A with Method 2; Equation B with Method 1; Equation C with Method 3c. Equation A with Method 1; Equation B with Method 2; Equation C with Method 3d. Equation A with Method 3; Equation B with Method 1; Equation C with Method 2

140. Solve: x2 – 7x – 30 = 0.

a. x = 7 or x = -30 b. x = -7 or x = -30

c. x = -10 or x = 3 d. x = -3 or x = 10

141. Which matrix equation is equivalent to the system of equations above?

wyrxmy kx

y x wr

142. If the matrix below is the coefficient matrix for a system of equations with two variables, x and y, in that order, what are the coefficients of the y terms?

a. -4 and 12 b. 1 and -4 c. -5 and 12 d. 1 and -5

143. A bakery is preparing packages with a mixture of large chocolate chip cookies, which weigh 1.5 ounces each, and large peanut butter cookies, which weigh 2 ounces each. Each box is to contain a total of 24 cookies, and the total weight of the cookies is to be 39 ounces. To determine the number of chocolate chip and the number of peanut butter cookies to be included in each box, a system of equationsmay be written. If the system is written as a matrix equation, what number will be part of the answer side of the original matrix equation? a. 1.5 b. 2 c. 39 d. 17

144. The total number of students in Mr. Euclid’s and Ms. Lovelace’s first period classes is 50. The difference between the number of students in Mr. Euclid’s first period class and Ms. Lovelace’s first period class is 6. Which matrix equation shows a system that could be solved to determine the number of students in each teacher’s class?

1- 11- 1

GEOMETRY DOMAIN (approximately 36% of test)

145. What is the length of the line segment with endpoints(-4, 5) and (1, 11)?

a. 7 b. 3 c. d.

146. What is the length of the line segment with endpoints(3, 8) and (3, -2)?

a. 10 b. 6 c. 14 d. 16

147. Charlotte is traveling to visit her friend Emily and is unfamiliar with the region where Emily lives. Studying a map of the town obtained at a gas station in the area, Charlotte is able to determine that she is currently at coordinates (5 in, 8 in) on the map, and Emily’s house is at coordinates (9 in, 4 in) on the map. If she could travel straight from the gas station to Emily’s house, approximately how far would she have to travel? Each inch on the map represents 3 miles of real-world distance.

a. 6 miles b. 8 miles c. 12 miles d. 17 miles

148. What is the distance between points A and B on the grid?

a. 5 b. 6

c. 7 d. 4.5

B(2, 3)

A(5, 7)

149. What is the midpoint of the segment that has endpoints at (1, 11) and (5, -3)?

a. (2, -7) b. (3, 4) c. (-2, 7) d. (6, 8)

150. What is the midpoint of side VW in the triangle?

a. (3.5, 4) b. (3, 6)

c. (5.5, 2.5) d. (6, 3)

151. The midpoint of a segment is (3, -2). If one of the endpoints is located at (7, -6), where is the other endpoint?

a. (-1, -10) b. (5, -4) c. (2, -2) d. (10, -8)

152. The midpoint of a segment is (-4, -8). If one of the endpoints is located at (6, -10), where is the other endpoint?

a. (5, -1) b. (-10, -18) c. (-8, 20) d. (-14, -6)

153. Which answer correctly shows how the Pythagorean Theorem could be used to find the distance from A to C?

a. 72 + 52 = c2

b. 32 + 52 = c2

c. 22 + 22 = c2

d. 42 + 72 = c2

154. When the distance formula is used to find the distance from A to B, part of the calculation involves finding the difference between the x-coordinates of points A and B. When the x-coordinates are being subtracted, what length is being found?

a. the perimeter of the triangleb. the length of segment ACc. the length of segment BCd. the sum of the lengths of segments AC and BC

155. When the distance formula is used to find the distance from A to B, part of the calculation involves finding the difference between the y-coordinates of points A and B. When the y-coordinates are being subtracted, what length is being found?

a. the perimeter of the triangle b. the length of segment BC c. the length of segment AC d. the sum of the lengths of segments AC and BC

156. To find the distance from A to B, what point could form the third corner of a right triangle to relate the distance formula to the Pythagorean theorem?

a. (6, 1) b. (6, 2) c. (1, 2) d. (4, 1)

157. In quadrilateral ABCD, and bisect each other. What must be congruent to ? a. b. c. d. Congruency among the sides cannot be determined

based on the given information.

158. Quadrilateral EFGH is a rhombus. What information below would be sufficient to show that quadrilateral EFGH and quadrilateral JKLM are similar? a. and are perpendicular bisectors of each other. b. EFG JKL c. Neither a nor b contains sufficient information, but together they are sufficient to determine that EFGH is similar to JKLM. d. Even if a and b were both known, the information would not be sufficient to determine similarity of the figures.

AD BC DC

159. In the figures below, AB = DE and AC = DF. Which other information would be sufficient to prove that ABC DEF?

a. mA = mDb. mC = mFc. mB = mE

d. none of the above

160. ABC includes two sides and one diagonal of a parallelogram. If the ordered pairs for the vertices of ABC are A(-2, 2), B(3, -3), and C(3, 1), which of the following could be the fourth vertex of the parallelogram?

a. (2, 2) b. (-2, 0) c. (5, 1) d. (8, -4)

161. The vertices of a quadrilateral are (3, 3), (1, 2), (5, 2), and (3, -1). Which of the following describes the quadrilateral?

a. parallelogram that is not a rectangle b. isosceles trapezoid c. rhombus that is not a square d. kite

162. ABC is an isosceles right triangle. If two of the vertices are A(-5, 2) and B(-1, -2), what is a possible location for point C?

a. (-1, 2) b. (-2, 1) c. (-4, -1) d. (-7, -4)

163. If Matthew’s father does not have to work over the weekend, then Matthew and his father go fishing on Saturday. Matthew and his father did not go fishing on Saturday this weekend. Assuming that these two statements are true, what conclusion can be drawn?

a. Matthew had to work this weekend.

b. Matthew’s father had to work this weekend.

c. Matthew’s father works every weekend.

d. Matthew’s mother does not like to fish.

164. Bela knows that the angles inside a triangle always have measures that have a sum of 180°. She knows that in ABC, A measures 75° and B measures 65°. She concludes that C must measure 40°. Which word or phrase best describes Bela’s reasoning?

a. counterexample b. deductive reasoning

c. inductive reasoning d. indirect proof

165. Istvan knows that in quadrilateral WXYZ, mW = 110°, mX = 70°, and mY = 110°. Based on this information, which of the following can Istvan prove?

a. WXYZ is a parallelogram.

b. WXYZ is an isosceles trapezoid.

c. WXYZ is a rectangle.

d. WXYZ is a scalene quadrilateral.

166. A geometric flow proof is shown below:

Given : M is the midpoint of . M is the midpoint of . Prove: DMA BMC. M is the midpoint of Given Def. of midpoint M is the midpoint of DMA BMC Given Def. of midpoint ?

DMA BMC Vertical angles are congruent.

What reason may be used to justify the final statement?

a. Given b. AAS c. SAS d. Def. of midpoint

167. What is the hypothesis in the statement below?

If two angles form a linear pair, then the angles are supplementary.

a. Two angles do not form a linear pair.b. The angles are not supplementary.c. The angles are supplementary.d. Two angles form a linear pair.

168. Which two related statements are logically equivalent?

a. original statement and contrapositiveb. original statement and conversec. original statement and inversed. converse and contrapositive

169.What is the inverse of the statement below?

If x3 = 8, then x = 2.

a. If x3 8, then x = 2. b. If x3 8, then x 2.c. If x = 2, then x3 = 8. d. If x 2, then x3 8.

170.What is the converse of the statement below?

If Jenny is wearing her glasses, then she can see clearly.

a. If Jenny can see clearly, then she is wearing her glasses. b. If Jenny can’t see clearly, then she is not wearing her

glasses. c. If Jenny is not wearing her glasses, then she can’t see

clearly. d. If Jenny is not wearing her glasses, then she can see

clearly.

171. Given the statement below, state the contrapositive. If you have finished your homework, then you may text Eoin. a. If you may not text Eoin, then you have not finished your homework. b. If you have not finished your homework, then you may not text Eoin. c. If you may text Eoin, then you have finished your homework. d. If you have not finished your homework, then you may text Eoin.

172. Ani knows that if an angle is a right angle, then its measure is 90°. She measures an angle and finds its measure to be 110°. What can she conclude?

a. It is a right angle. b. It is in an isosceles triangle.

c. It is acute. d. It is not a right angle.

173. What are the measures of the interior and exterior angles of a regular octagon?

a. interior: 157.5°; exterior: 22.5°b. interior: 135°; exterior: 45°c. interior: 112.5°; exterior: 67.5°d. interior: 70°; exterior: 110°

174. Solve for x:a. 54°b. 59°c. 66°d. 72°

102(2x)

175. Find the measure of ABC in the figure below:

a. 80°b. 92°c. 130°d. 134°

176. Solve for x.

a. 90°b. 110°c. 85°d. 75°

(x+19)144

(2x-58)127

(x+50)

(x-23)

97(x+37)

177. The direct distance between the towns of Askel and Bodil is 50 miles. The direct distance between the towns of Bodil and Havelock is 72 miles. Which could be the direct distance between Havelock and Askel?

a. 110 miles b. 130 milesc. 15 miles d. 150 miles

178. In the triangle below, which angle is the smallest angle?a. Cb. Bc. Ad. There is not

enough information to determine which angle

is smallest.

3.8 cm3.3 cm

4.4 cm

179. Solve for x:a. 120°b. 24°c. 144°d. 36°

180. Which of the following could be the measures of three sides of a triangle?

a. 3 cm, 5 cm, 8 cm b. 2 cm, 6 cm, 10 cmc. 11 cm, 12 cm, 25 cm d. 5 cm, 12 cm 14 cm

180. Which of the following could be the measures of three sides of a triangle?

a. 3 cm, 5 cm, 8 cm b. 2 cm, 6 cm, 10 cm

c. 11 cm, 12 cm, 25 cm d. 5 cm, 12 cm 14 cm

181. Which of the following would be enough information to show that two triangles are congruent? a. congruence of two pairs of angles and one pair of sides b. congruence of the hypotenuses of two right triangles c. congruence of one pairs of legs in two right triangles d. congruence of all three pairs of angles in two triangles

182. Which pair of triangles below can be proved congruentusing the given information?

183. The two legs of a right triangle measure 8 units and 12 units. A leg and the hypotenuse of another right triangle measure 8 units and 17 units, respectively. What conclusion can be drawn about these two triangles?

a. They are both isosceles triangles.b. They are both equilateral triangles.c. They are not congruent triangles.d. They are congruent triangles.

184. Given that bisects ADC and , which method can be used to proved that ABD CBD?

a. Angle-Angle-Side (AAS)b. Angle-Side-Angle (ASA)c. Side-Angle-Side (SAS)d. There is not enough information

given to prove that the triangles are congruent.

185. In parallelogram MATH, mM = 3x – 40 and mA = 2x + 70. What is the value of x?

a. 130° b. 50° c. 30°d. 25°

186. In rhombus LMNO, mLMO = 28°. Find mMNO.

a. 28° b. 56°c. 124° d. 152°

187. In an isosceles trapezoid, the two diagonals are represented by 2x + 1 and 3x – 7. How long is each diagonal?

a. One is 7units and the other is 2 units.b. Each one is 8 units long.c. One is 11 units and the other is 8 units.d. Each one is 17 units long.

188. Quadrilateral DEFG has congruent diagonals. What type of quadrilateral is DEFG?

a. a rectangle b. isosceles trapezoidc. square d. There is not enough information

to determine the type.

189. A school system wants to build a science center so that it is equidistant from it’s three elementary schools. If a triangle is drawn on a map so that the three elementary schools positions are at the vertices, which point of concurrency would be equidistant from the vertices?

a. orthocenter b. incenterc. centroid d. Circumcenter

190. In which type of triangle would the orthocenter be located on the outside of the triangle?

a. acute b. rightc. obtuse d. The orthocenter is never

outside the triangle.

191. To find the incenter of the triangle, which intersection could be found?

a. the intersection of the perpendicular bisectors of the triangle’s sides

b. the intersection of the angle bisectors of the triangle’s vertex angles

c. the intersection of the triangle’s medians

d. the intersection of the triangle’s altitudes

192. In ABC below, M , N, and P are the midpoints of , , and , respectively. Which point of concurrency

is at point Z?

a. the triangle’s center of gravity

b. the point equidistant from the vertices

c. the point equidistant from the sides

d. the orthocenter

ABBC CA

193. Given that the length of the long leg of a 30°-60°-90° is , what is the length of the hypotenuse?

a. 7 b. 10 c. 14 d. 21

194. Find the value of x.

a. 5b. 10c. d. 15

195. Find the value of x.a. b. 6c.

196. Given that an equilateral triangle has sides of length 8, what is the height of the triangle?

a. b. 4 c. d. 16

197. Given that the length of the hypotenuse of a 45-45-90 triangle is 22, find the length of a leg.

a. 11 b. c. d.

198. Given that the length of a leg in a 45°-45°-90° triangle is 6 units long, what is the length of the hypotenuse?

a. 6 b. c. d.

199. Find the length of the diagonal of a square with sides of length 10.

a. 5 b. 10 c. d.

200. Find the perimeter of a square if the diagonal is 6 units.a. 24 b. 12 c. d.

211 322 222

26 36 23

25 210

224 212

201. A road rises at an angle of 8° above horizontal. When a car has traveled 5 miles up the road, how far has it traveled horizontally?

a. 3.66 miles b. 4.95 miles

c. 0.70 miles d. 5.75 miles

202. A tower that is 200 feet tall casts a shadow that is250 feet long. Determine the angle at which the sun’s rays hit the ground, to the nearest degree.

a. 14° b. 39° c. 43° d. 51°

203. Two buildings are 50 feet apart. The top of the taller building is at a 20° angle of elevation from the top of the shorter building. If a wire is extended from the top of the taller building to the top of the shorter building, how long must the wire be?

a. 53 feet 20°?

50 ft. b. 60 feet

c. 62 feet

d. 65 feet

204. In the figure below, M is the midpoint of . What is the approximate perimeter of ABC?

a. 60 m

b. 50 m

c. 48 m

d. 44 m

205. Given circle O shown at the right, find the measure of ABC.

a. 55° b. 110°

c. 27.5° d. 152.5°

206. In circle D shown at the right, mABC = 78° and the measure of arc AC is 30°. Find the measure of arc GF.

a. 66° b. 78°

c. 93° d. 102°

207. Two friends are eating dinner in a revolving restaurant. As the restaurant revolves counterclockwise during their meal, the friends are able to spot various local landmarks from their table at the restaurant’s glass exterior wall. If it takes 60 minutes for the restaurant to complete one rotation, approximately how long will it take the friends to rotate from their current position to the position facing the stadium?

a. 37 minutes

b. 45 minutes

c. 50 minutes

d. 53 minutes

Stadium

City park

Tallest buildingin city

Currentposition

208. In circle A below, the measure of arc BD is 40°, and the measure of arc ED is 112°. Segment CD is tangent to circle A at point D. What is the measure of BCD?

a. 20°

b. 36° c. 56°

d. 72°E

209. In circle V, the radius is 6 cm and mUVW = 135°. Find the length of arc UW.

a. 6 cm b. 11.2 cm

c. 13.5 cm d. 14.1 cm

210. A building is designed with a curved front. A circular garden in front of the building follows the front curve. The builders are installing glass panels along the curved front of the building to give a view of the garden. How many feet long will the glass front of the building be?

a. 30 feet

b. 188 feet

c. 59 feet

d. 72 feetGarden

Building

211. Find the area of the shaded sector.

a. 36.6 square feet

b. 73.2 square feet

c. 96.3 square feet

d. 101.7 square feet

212. A 12-inch-diameter pizza is cut into six equal slices. If Brian eats two slices, how many square inches of pizza does he eat?

a. 18.8 square inches

b. 37.7 square inches

c. 75.4 square inches

d. 12.6 square inches

213. Find the equation of a circle with its center at (3, 4) and a radius of 9.

a. (x – 3)2 + (y – 4)2 = 3 b. (x + 3)2 + (y + 4)2 = 3

c. (x + 3)2 + (y + 4)2 = 3 d. (x – 3)2 + (y – 4)2 = 81

214. Find the equation of the circle shown on the graph below.

a. (x + 3)2 + (y + 2)2 = 2

b. (x + 3)2 + (y + 2)2 = 4

c. (x – 3)2 + (y – 2)2 = 2

d. (x – 3)2 + (y – 2)2 = 4

215. Find the equation of a circle with its center at the origin and a radius of 10.

a. (x – 10)2 + (y – 10)2 = 0b. x2 + y2 = 100

c. x2 + y2 = 10 d. x2 + y2 = 20

216. Find the equation of the circle with its center at (-5, 3) and a radius of 4.

a. (x – 5)2 + (y + 3)2 = 4 b. (x + 5)2 + (y – 3)2 = 2

c. (x + 5)2 + (y – 3)2 = 4 d. (x + 5)2 + (y – 3)2 = 16

217. A sphere has a volume of 905 cubic inches. What is the approximate radius of the sphere?

a. 11 b. 6 c. 4 d. 2

218. A sphere has a surface area of 324π square centimeters. What is the approximate volume of the sphere?

a. 324π cubic centimeters b. 972π cubic centimeters

c. 729π cubic centimeters d. 288 cubic centimeters

219. Find the approximate surface area of the sphere shown below.

a. 314 square inches

b. 1257 square inches

c. 3142 square inches

d. 4189 square inches

10 inches

220. Find the volume of the sphere shown below.

a. 2304π cm3

b. 576π cm3

c. 144π cm3

d. 576 cm3

221. The radius of a volleyball is approximately 10.5 cm. The radius of a tennis ball is approximately 3.2 cm. How would the surface area of a volleyball compare to the surface area of a tennis ball?

a. The surface area of a volleyball is about 3.3 times the surface area of a tennis ball.

b. The surface area of a volleyball is about 10.8 times the surface area of a tennis ball.

c. The surface area of a volleyball is about 13.7 times the surface area of a tennis ball.

d. The surface area of a volleyball is about 17.5 times the surface area of a tennis ball.

222. If the radius of a sphere is doubled, how will the surface area be affected?

a. The surface area will double.b. The surface area will be halved.c. The surface area will be four times the original surface area.d. The surface area will be eight times the original surface area.

223. If the ratio of the radii of two spheres is 7:10, what is the ratio of their volumes?

a. 343:1000 b. 49:100 c. 7:10 d. 33 10:7

224. How many clay spheres of radius 5 cm could be made from a clay sphere that is 15 cm?

a. 3 b. 9 c. 27 d. 81

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