Choose any 10 problems for Home Work ( Keep in mind at least one problem on each model)
GEOMETRY ASU
34. | Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. y2 = x + 3 | |
Ans: | Symmetric with respect to the x-axis | |
Difficulty Level: Difficult Objective: 3 Section: 1 |
35. | Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. y + 1 = x2 | |
Ans: | Symmetric with respect to the y-axis | |
Difficulty Level: Difficult Objective: 3 Section: 1 |
Use the following to answer questions 36-37: 9x2 + y2 = 36 |
36. | Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. | |
A) | Symmetric with respect to the x-axis | |
B) | Symmetric with respect to the y-axis | |
C) | Symmetric with respect to the origin | |
D) | Symmetric with respect to the x-axis, the y-axis, and the origin | |
37. | Sketch the graph of the equation. | |||
A) | C) | |||
B) | D) | |||
38. | Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. y2 = | x | + 2 | |
Ans: | Symmetric with respect to the x-axis, the y-axis, and the origin | |
39. | Find the distance between (–6, 4) and (0, –4). | |
Ans: | 10 | |
40. | Find the midpoint of the line segment with endpoints (–5, –2) and (7, 6). | |
Ans: | (1, 2) | |
41. | Find the distance between (–3, –2) and (1, 4). | |
A) 27 B) | ||
42. | Find the midpoint of the line segment with endpoints (–5, –5) and (7, 9). | |
A) (2, 4) B) (–12, –14) C) (1, 2) D) (–6, –7) | ||
43. | Write the equation of a circle with center (0, 0) and radius 6. | |
44. | Write the equation of a circle with center (0, 0) and radius 4. | |
45. | Write the equation of a circle with center (0, 2) and radius | |||
46. | Write the equation of a circle with center (–5, –5) and radius | |||
47. | Write an equation for the given set of points. Graph your equation. The set of all points that are two units from (–3, 1) | |
48. | The midpoint of the line segment with endpoints (10, 1) and (b1, b2) is (6, 5). Find b1 and b2. | |
49. | Find x such that (x, 5) is 10 units from (–2, 11) | |
50. | Write the equation of the circle. |
51. | Write the equation of the circle. |
52. | Write the equation of the circle. | |||
53. | Write the equation of the circle. | |||
54. | Find the center and radius of the circle. x2 + y2 = 25. | |
55. | Find the center and radius of the circle. x2 + y2 = 31 | |
56. | Find the center and radius of the circle. x2 + (y + 1)2 = 25. | |
57. | Find the center and radius of the circle. (x + 5)2 + (y – 3)2 = 49. | |
58. | Find the center and radius of the circle. x2 + y2 – 2y = 15 | |
59. | Find the center and radius of the circle. x2 + y2 – 6x + 8y = 14 | |
60. | Find the center and radius of the circle. 3x2 + 3y2 – 18x + 6y – 162 = 0 | |||
61. | Graph the circle by finding the center and radius. x2 + y2 = 16 | |
62. | Graph the circle by finding the center and radius. (x – 2)2 + (y – 1)2 = 9 | |
Ans: | Center (2, 1), radius 3 | |
Difficulty Level: Moderate Objective: 3 Section: 2 |
63. | Graph the circle by finding the center and radius. (x – 2)2 + (y + 3)2 = 16 | |
64. | Graph the circle by finding the center and radius. x2 + 6x + y2 = 7 | |
65. | Graph the circle by finding the center and radius. x2 – 4x + y2 = 12 | |||
A) | C) | |||
B) | D) | |||
66. | Graph the circle by finding the center and radius. x2 + 4x + y2 = 0 | |||
A) | C) | |||
B) | D) | |||
67. | Graph the circle by finding the center and radius. x2 + y2 – 4x + 6y = 3 | |||
Difficulty Level: Difficult Objective: 3 Section: 2 |
68. | Write the equation of a circle whose diameter has endpoints (2, –7) and (2, 1). | |||
69. | Find the equation of a circle with center (2, –3) and the graph of which contains the point (3, 4). | |||
A) | (x – 2)2 + (y + 3)2 = 50 | C) | (x – 2)2 + (y + 3)2 = | |
B) | (x + 2)2 + (y – 3)2 = 50 | D) | (x + 2)2 + (y – 3)2 = | |
Use the following to answer questions 70-73: |
70. | Find the x-intercept of the line. | |
71. | Find the y-intercept of the line. |
72. | Find the slope of the line. |
73. | Write the equation of the line in slope-intercept form. |
Use the following to answer questions 74-77: |
74. | Find the x-intercept of the line. | |
A) 3 B) 0 C) –3 D) No x-intercept | ||
75. | Find the y-intercept of the line. | |
A) –3 B) 0 C) 3 D) No y-intercept | ||
76. | Find the slope of the line. | |
A) –3 B) 0 C) 3 D) Undefined | ||
77. | Write the equation of the line. | |
A) y = –3x B) y = 3x C) x = –3 D) y = –3 | ||
78. | Graph y = | |
79. | Graph | |
80. | Graph | |
81. | Graph 6x + 2y = 0. Indicate the slope, if it exists. | |
82. | Graph 2x – 5y = 10. Indicate the slope, if it exists. | |
83. | Graph 4x – 3y = 6. Indicate the slope, if it exists. | |
Use the following to answer questions 84-85: 3x + 4y = 12 |
84. | Graph the line. | |||
A) | C) | |||
B) | D) | |||
85. | Indicate the slope. | |||
A) | ||||
Use the following to answer questions 86-87: 3x + 2y = 6 |
86. | Graph the line. | |||
A) | C) | |||
B) | D) | |||
87. | Indicate the slope. | |||
A) | ||||
88. | Graph | |||
89. | Graph | |||
Use the following to answer questions 90-91: x = 3 |
90. | Graph the line. | |||
A) | C) | |||
B) | D) | |||
91. | Indicate the slope, if it exists. | |||
A) 3 B) 0 C) –3 D) Undefined | ||||
Use the following to answer questions 92-93: y = –3 |
92. | Graph the line. | |||
A) | C) | |||
B) | D) | |||
93. | Indicate the slope, if it exists. | |||
A) 3 B) 0 C) –3 D) Undefined | ||||
94. | Graph y = –1. Indicate the slope, if it exists. | |||
Difficulty Level: Moderate Objective: 1 Section: 3 |
95. | Graph y = 4. Indicate the slope, if it exists. | |
Ans: | Slope = 0 | |
96. | Find the equation of the line with slope –6 and y-intercept 3. Write the equation in standard form Ax + By = C, A ≥ 0. | |
A) 6x – y = 3 B) 6x – y = –3 C) 6x + y = 3 D) 6x + y = –3 | ||
97. | Write the equation of the line with slope | |
98. | Write the equation of the line with slope | |
99. | Write the equation of the line with slope 0 and y-intercept –7. Write the equation in standard form Ax + By = C, A ≥ 0. | |
A) –7x – y = 0 B) –7x + y = 0 C) y = –7 D) x = –7 | ||
100. | Write the equation of the line that passes through point (0, –4) with slope | |
101. | Write the equation of the line that passes through point (–2, 9) with a slope of –2. Give your answer in the slope-intercept form y = mx + b. | |
102. | Sketch a graph of the line that contains the point (0, 3) and has slope –3. Then write the equation of the line in the slope intercept form y = mx + b. | |
103. | Sketch a graph of the line that contains the point (1, –2) and has slope 2. Then write the equation of the line in the slope intercept form y = mx + b. | |
104. | Sketch a graph of the line that contains the point (–3, –4) and has slope | |
105. | Write the equation of the line passing through (–6, –19) and (–2, –11). Write your answer in the slope-intercept form y = mx + b. | |||||||||||||||||
Ans: | y = 2x – 7 | |||||||||||||||||
Difficulty Level: Difficult Objective: 3 Section: 3 | ||||||||||||||||||
106. | Write the equation of the line passing through (–3, –5) and (3, 0). Write your answer in the slope-intercept form y = mx + b. | |||||||||||||||||
A) | ||||||||||||||||||
Ans: B Difficulty Level: Difficult Objective: 3 Section: 3 | ||||||||||||||||||
107. | Write the equation of the line passing through (–1, –1) and (1, –1). Write your answer in the slope-intercept form y = mx + b. | |||||||||||||||||
Ans: | y = –1 | |||||||||||||||||
Difficulty Level: Moderate Objective: 3 Section: 3 | ||||||||||||||||||
108. | Sketch a graph of the line that contains the points (3, 2) and (–3, 6) . Then write the equation of the line in the slope intercept form y = mx + b. | |||||||||||||||||
109. | Write the equation of the line passing through (0, –5) and (0, 1). | |||||||||||||||||
A) x = 0 B) y = 0 C) y = x + 0 D) y = 6x | ||||||||||||||||||
110. | Write the equation of the line with x-intercept (4, 0) and y-intercept (0, 1). Write your answer in the slope-intercept form y = mx + b. | |||||||||||||||||
111. | Write an equation of the line passing through (6, 3), and parallel to y = 2x + 8. Write your answer in standard form Ax + By = C, A ≥ 0. | |||||||||||||||||
112. | Write an equation of the line passing through (–8, –3), and perpendicular to y = | |||||||||||||||||
A) 4x + y = –35 B) 4x – y = –35 C) x + 4y = –20 D) x – 4y = –20 | ||||||||||||||||||
113. | Write the equation of the line passing through (–7, 1) and parallel to the y-axis. Write your answer in standard form Ax + By = C, A ≥ 0. | |||||||||||||||||
A) y = –7 B) y = 1 C) x = –7 D) x = 1 | ||||||||||||||||||
114. | Write the equation of the line passing through (0, 6) and perpendicular to x – 6y = 30. Write your answer in standard form Ax + By = C, A ≥ 0. | |||||||||||||||||
115. | Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 3y – x = 1. | |||||||||||||||||
A) 3x + y = 5 B) 3x – y = 7 C) x + 3y = –1 D) x – 3y = 5 | ||||||||||||||||||
Use the following to answer questions 127-129: The regression model for the data shown in the table is y = 2.3x + 3.9.
|
127. | Plot the data and the model on the same axes. | |
Ans: | ||
Difficulty Level: Moderate Objective: 3 Section: 4 |
128. | Use the model to estimate y when x = 3.5. | |||||||||||||||
Ans: | 11.95 | |||||||||||||||
129. | Use the model to estimate y when x = 50. | |||||||||||||||
Use the following to answer questions 130-132: The regression model for the data shown in the table is y = –3.0x + 134.6.
|
130. | Plot the data and the model on the same axes. |
131. | Use the model to estimate y when x = 11.5. |
A) 99.7 B) 99.9 C) 100.1 D) 100.3 | |
132. | Use the model to estimate y when x = 45. |
A) –0.5 B) –0.4 C) –0.3 D) –0.2 | |
Use the following to answer questions 133-135:
|
133. | Plot the data from the table. | ||||||||||||||||||||||||||
134. | Find a linear regression model for the data. Round regression coefficients to two significant digits. | ||||||||||||||||||||||||||
135. | Plot the data from the table and the linear regression model on the same axes. | ||||||||||||||||||||||||||
Use the following to answer questions 136-138: The data in the table show the height x (in inches) compared to the shoe size y worn for a random sample of 12 males.
|
136. | Find a linear regression model for the data. | |||
A) | y = 0.48x – 1.15 | C) | y = 0.28x – 1.35 | |
B) | y = 0.38x – 1.25 | D) | y = 0.18x – 1.45 |
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