Name ______Date ______
Mr. SchlanskyMath 235
Algebra II Mega Regents Review Packet
1. Which equation is represented by the accompanying graph?
(1) (3)
(2) (4)
2. What are the coordinates of the turning point of the parabola whose equation is
(1) (-2,-11)(3) (2,5)
(2) (-2,-3)(4) (2,13)
3. The graph of the equation will contain no points in Quadrants
(1) I and II(3) III and IV
(2) II and III(4) I and IV
4. What is the value of
(1) 15(3) 21
(2) 19(4) 43
5. Expressed in simplest form, is equivalent to
(1) -2i(3)
(2) 2i(4)
6. On a graph, if point A represents and point B represents which quadrant contains
(1) I(3) III
(2) II(4) IV
7. Which functions are positive for angles terminating in Quadrant II?
(1) sine and cosine(3) sine and tangent
(2) sine and secant(4) sine and cosecant
8. What is expressed in simplest form?
(1) 1(3)
(2) 0(4)
9. Banks use the formula when they compound interest annually. If P represents the amount of money invested and r represents the rate of interest, which expression represents where A represents the amount of money in the account after x years?
(1) (3)
(2) (4)
10. If the equation of the axis of symmetry of a parabola is at which pair of points could the parabola intersect the x-axis?
(1) (3,0) and (5,0)(3) (3,0) and (1,0)
(2) (3,0) and (2,0)(4) (-3,0) and (-1,0)
11. What is the third term in the expansion of
(1) (3)
(2) (4)
12. If and which expression is equivalent to
(1) (3)
(2) (4)
13. What is the inverse of the function
(1) (3)
(2) (4)
14. If which function represents the reflection of in the y-axis?
(1) (3)
(2) (4)
15. The number of degrees equal to radians is
(1) 45(3) 100
(2) 90(4) 900
16. What is the value of
(1) 1(3) 3
(2) 2(4) 0
17. If which statement must be true?
(1) (3)
(2) (4)
18. The accompanying graph shows the curves of best fit for data points comparing temperature to altitude in four different regions, represented by the relations A, B, C, and D.
Which relation is not a function?
(1) A(3) C
(2) B(4) D
19. When the sum of -4 + 8i and 2 - 9i is graphed, in which quadrant does it lie?
(1) I(3) III
(2) II(4) IV
20. The expression is equivalent to
(1) (3)
(2) (4)
21. What is the solution of the inequality
(1) (3)
(2) (4)
22. The accompanying diagram represents the
biological process of cell division.
If this process continues, which expression
best represents the number of cells at any time, t?
(1) (3)
(2) (4)
23. The roots of the equation are
(1) real, rational, and unequal
(2) real, rational, and equal
(3) real, irrational, and unequal
(4) imaginary
24. Which expression is equivalent to
(1) (3)
(2) (4)
25. The expression is equivalent to
(1) (3)
(2) (4)
26. The accompanying graph shows the average daily readership, in thousands, of the newspaper “El Diario La Prensa.”
Which type of function best represents this graph?
(1) exponential(3) trigonometric
(2) logarithmic(4) quadratic
27. What is the solution set of the equation
(1) { }(3) {-4,4}
(2) {2}(4) {4}
28. What is the third term in the expansion of
(1) (3)
(2) (4)
29. The accompanying table shows the scores on a classroom test.
What is the population standard deviation for this set of scores?
(1) 10.2(3) 25
(2) 10.4(4) 88
30. The expression is equivalent to
(1) (3)
(2) (4)
31. The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle?
(1) 5(3) 3
(2) 6(4) 10
32. The expression is equivalent to
(1) (3)
(2) (4)
33. What is the solution of the inequality
(1) -3 < x < -2(3) 1 < x < 6
(2) -2 < x < 3(4) -3 < x < 2
34. If the probability that the Islanders will beat the Rangers in a game is which expression represents the probability that the Islanders will win exactly four out of seven games in a series against the Rangers?
(1) (3)
(2) (4)
35. Which expression is equivalent to
(1) 1(3) i
(2) -1(4) –i
36. If and which expression is equivalent to
(1) (3)
(2) (4)
37. A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius of the garden?
(1) 8 ft(3) 100 ft
(2) 50 ft(4) 125 ft
38. What is a value of
(1) (3)
(2) (4)
39. Given the relation A: {(3,2), (5,3), (6,2), (7,4)}
Which statement is true?
(1) Both A and are functions.
(2) Neither A nor are functions.
(3) Only A is a function.
(4) Only is a function.
40. The expression is equivalent to
(1) (3)
(2) (4)
41. If and in which quadrant does the graph of lie?
(1) I(3) III
(2) II(4) IV
42. The accompanying graph illustrates the
presence of a certain strain of bacteria at various
pH levels.
What is the range of this set of data?
(1) (3)
(2) (4)
43. Juan has been told to write a quadratic equation where the sum of the roots is equal to -3 and the product of the roots is equal to -9. Which equation meets these requirements?
(1) (3)
(2) (4)
44. Tanner and Robbie discovered that the means of their grades for the first semester in Mrs. Merrell’s mathematics class are identical. They also noticed that the standard deviation of Tanner's scores is 20.7, while the standard deviation of Robbie's scores is 2.7. Which statement must be true?
(1) In general, Robbie's grades are lower than Tanner's grades.
(2) Robbie's grades are more consistent than Tanner's grades.
(3) Robbie had more failing grades during the semester than Tanner had.
(4) The median for Robbie's grades is lower than the median for Tanner's grades.
45. If then is equal to
(1) (3)
(2) (4)
46. The expression is equivalent to
(1) (3)
(2) (4)
47. Which inequality is represented by the accompanying graph?
(1) (3)
(2) (4)
48. If the expression is equal to
(1) (3)
(2) (4)
49. The roots of the equation are
(1) real, rational, and unequal(3) real, irrational, and unequal
(2) real, rational, and equal(4) imaginary
50. The family of curves shown in the accompanying
graph illustrates the transformations of a function.
Which type of function could be the original function?
(1) linear(3) exponential
(2) tangent(4) sinusoidal
51. The expression is equivalent to
(1) (3)
(2) (4)
52. Which equation is not a function?
(1) (3)
(2) (4)
53. The expression is equivalent to
(1) (3)
(2) (4)
54. The expression is equivalent to
(1) -5i(3) 5i
(2) -5(4) 5
55. What is the value of
(1) (3)
(2) (4)
56. One root of the equation is
(1) (3)
(2) (4)
57. Which graph represents a sound wave that follows a curve whose period is π and that is in the form
58. If what does x equal?
(1) only(3) and
(2) only(4) and
59. For which value of x is undefined?
(1) 1(3) 3
(2) 0(4) -3
60. Kathy deposits $25 into an investment account with an annual rate of 5%, compounded annually. The amount in her account can be determined by the formula where P is the amount deposited, R is the annual interest rate, and t is the number of years the money is invested. If she makes no other deposits or withdrawals, how much money will be in her account at the end of 15 years?
(1) $25.75 (3) $51.97
(2) $43.75 (4) $393.97
61. If and what is the value of f(g(-3))?
(1) (3) 8
(2) 2 (4) 13
62. The accompanying graph shows the relationship between kinetic energy, y, and velocity, x.
The reflection of this graph in the line is
63. The accompanying graph shows the elevation
of a certain region in New YorkState as a hiker
travels along a trail.
What is the domain of this function?
(1) (3)
(2) (4)
64. Which relation is a function?
(1) (3)
(2) (4)
65. Which expression represents the sum of the sequence 3, 5, 7, 9, 11?
(1) (3)
(2) (4)
66. Which value of a does not satisfy the inequality
(1) -1 (3) 3
(2) 0 (4) -5
67. What is the sum of and the conjugate of
(1) 2 + 5i(3) 8 + 5i
(2) 2 – 5i(4).8 – 5i
68. The expression is equivalent to
(1) 1 (3)
(2) 2 (4)
69. The value of is a real and irrational number when x is equal to
(1) 5 (3) -3
(2) 0 (4) 4
70. If which expression is equivalent to x?
(1) (3)
(2) (4)
71. The expression is equivalent to
(1) (3)
(2) (4)
72. Al is standing 50 yards from a maple tree and 30 yards
from an oak tree in the park. His position is shown in the
accompanying diagram. If he is looking at the maple tree,
he needs to turn his head 120° to look at the oak tree.
How many yards apart are the two trees?
(1) 58.3 (3) 70
(2) 65.2 (4) 75
73. A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB=20 feet.
What is the length of arc AC, in feet?
(1) 63 (3) 20
(2) 31 (4) 10
74. The expression equals
(1) 1(3) -i
(2) -l(4) i
75. Which equation has roots whose sum is 3 and whose product is -4?
(1) (3)
(2) (4)
76. Which equation is represented by the accompanying graph?
(1) (3)
(2) (4)
77. What is the value of x in the equation
(1) 46 (3) 3
(2) 12 (4) 6
78. A wave displayed by an oscilloscope is represented by the equation What is the period of this function?
(1) 2π(3) 3
(2) 2 (4) 3π
79. Sean tells prospective clients that the probability of rain at the dive location is .2 each day. Which expression can be used to calculate the probability that it will rain on exactly 5 days of the 7 days at the dive location?
(1) (3)
(2) (4)
80. Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures radians, what is the length, in yards, of the border?
(1) 0.5(3) 5
(2) 2(4) 7.5
81. Mayken collected data about the size of the honors classes in her school building. This set of data is shown in the accompanying table.
Which statement about the range of this sample is true?
(1) range = mean (3) range < mean
(2) range > mean (4) range < standard deviation
82. The accompanying diagram shows a resultant force vector, R.
Which diagram best represents the pair of component force
vectors, A and B, that combined to produce the resultant force vector R?
83. On a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4. What is the best approximation of the percent of scores that fell between 61.6 and 75.1?
(1) 38.2% (3) 68.2%
(2) 66.8% (4) 95%
84. The expression is equivalent to
(1) (3)
(2) (4)
85. A radioactive substance has an initial mass of 100 grams and its mass halves every 4 years. Which expression shows the number of grams remaining after t years?
(1) (3)
(2) (4)
86. The accompanying tables define functions
f and g.
What is (g o f )(3)?
(1) 6(3) 8
(2) 2(4) 4
87. Which method of collecting data would most likely result in an unbiased random sample?
(1) selecting every third teenager leaving a movie theater to answer a survey about entertainment
(2) placing a survey in a local newspaper to determine how people voted in the 2004 presidential election
(3) selecting students by the last digit of their school ID number to participate in a survey about cafeteria food
(4) surveying honor students taking Mathematics B to determine the average amount of time students in a school spend doing homework each night
88. In the physics lab, Thelma determined the kinetic energy,
KE, of an object at various velocities, V, and found the linear
correlation coefficient between KE and V to be +0.8. Which
graph shows this relationship?
89. Which equation has roots that are real, rational, and unequal?
(1) (3)
(2) (4)
90. The expression cos(π – x) is equivalent to
(1) sin x(3) cos x
(2) -sin x(4) -cos x
91. If what is the value of x?
(1) 81(3) 3
(2) (4)
92. What is the coefficient of the fifth term in the expansion of
(1) 8(3) 56
(2) 28 (4) 70
93. If then f(3) is equal to
(1) (3) -21
(2) (4) -22
94. The expression is equivalent to
(1) (3)
(2) (4)
95. The expression is equivalent to
(1) (3)
(2) (4)
96. If what is the value of
(1) -2(3)
(2) 2(4)
97. What is 235°, expressed in radian measure?
(1) (3)
(2) (4)
98. The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the equations of the jets' flight paths are represented by and The best approximation of the intersection of the flight paths is
(1) (-1.72,3.3) (3) (-1.50,2.82)
(2) (0,1) (4) (-2,-1)
99. Which expression is equivalent to the complex fraction
(1) +1(3)
(2) -1(4)
100. Which equation represents the function shown in the
accompanying graph?
(1) (3)
(2) (4)
101. A meteorologist drew the accompanying graph to
show the changes in relative humidity during a 24-hour
period in New York City.
What is the range of this set of data?
(1) (3)
(2) (4)
102. The equation used to determine the time it takes a swinging pendulum to return to its starting point is where T represents time, in seconds, represents the length of the pendulum, in feet, and g equals How is this equation expressed in logarithmic form?
(1)
(2)
(3)
(4)
103. Which type of function could be used to model the data
shown in the accompanying graph?
(1) exponential(3) trigonometric
(2) quadratic(4) linear
104. Which graph has an inverse that is a function?
105. What is the solution set of the inequality
(1) (3)
(2) (4)
106. The accompanying graph represents a portion of a sound wave.
Which equation best represents this graph?
(1) (3)
(2) (4)
107. Which equation has the complex number as a root?
(1) (3)
(2) (4)
108. If what is the value of a?
(1) 1 (3) 3
(2) 2 (4) 4
109. During a single day at radio station WMZH, the probability that a particular song is played is .38. Which expression represents the probability that this song will be played on exactly 5 days out of 7 days?
(1) (3)
(2) (4)
110. A function, f, is defined by the set {(2,3), (4,7), (-1,5)}. If f is reflected in the line y = x, which point will be in the reflection?
(1) (5,-1) (3) (1,-5)
(2) (-5,1) (4) (-1,5)
111. Which equation is best represented by the accompanying graph?
(1) (3)
(2) (4)
112. The accompanying graph represents the equation
Which graph represents if
113. Jack is planting a triangular rose garden. The lengths of two sides of the plot are 8 feet and 12 feet, and the angle between them is 87°. Which expression could be used to find the area of this garden?
(1) (3)
(2) (4)
114. What could be the approximate value of the correlation
coefficient for the accompanying scatter plot?
(1) -0.85(3) 0.21
(2) -0.16(4) 0.90
115. What is one solution of the accompanying system of equations?
(1) (3,5)(3) (-2,1)
(2) (0,5)(4) (0,3)
116. Which inequality is represented by the accompanying graph?
(1) (3)
(2) (4)
117. The volume of a soap bubble is represented by the equation where A represents the surface area of the bubble. Which expression is also equivalent to V?
(1) (3)
(2) (4)
118. The fraction is equivalent to
(1) (3)
(2) (4)
119. Which equation is represented by the accompanying graph?
(1) (3)
(2) (4)
120. Which expression is in simplest form?
(1) (3)
(2) (4)
121. The expression is equivalent to
(1) (3)
(2) (4)
122. The expression is equivalent to
(1) (3)
(2) (4)
123. Which set of ordered pairs does not represent a function?
(1) {(3,-2), (-2,3), (4,-1), (-1,4)}
(2) {(3,-2), (3,-4), (4,-1), (4,-3)}
(3) {(3,-2), (4,-3), (5,-4), (6,-5)}
(4) {(3,-2), (5,-2), (4,-2), (-1,-2)}
124. Cerise waters her lawn with a sprinkler that sprays water in a circular
pattern at a distance of 15 feet from the sprinkler. The sprinkler head
rotates through an angle of 300°, as shown by the shaded area in the
accompanying diagram.
What is the area of the lawn, to the nearest square foot,that receives
water from this sprinkler?
(1) 79 (3) 589
(2) 94 (4) 707
125. Which number is the discriminant of a quadratic equation whose roots are real, unequal, and irrational?
(1) 0 (3) 7
(2) -5 (4) 4
126. If 2 + i and 2 – iarethe roots of the equation what is the value of c?
(1) -5(3) -4
(2) 5(4) 4
127. The expression is equivalent to
(1) 1(3)
(2) (4)
128. The formula is used to determine the speed of sound, S, in meters per second, near Earth’s surface, where t is the surface temperature, in degrees Celsius. Which graph best represents this function?
129. Which equation best represents the accompanying graph?
(1) (3)
(2) (4)
130. The accompanying diagram shows the approximate
linear distances traveled by a sailboat during a race.
The sailboat started at point S, traveled to points E and A,
respectively, and ended at point S.
Based on the measures shown in the diagram, which
equation can be used to find x, the distance from point
A to point S?
(1) (3)
(2) (4)
131. If which expression is equivalent to x?
(1)(3)
(2) (4)
132. The expression is equivalent to
(1) 1(3) i
(2) -1(4) –i
133. The expression is equivalent to
(1) (3)
(2) 2(4)
134. The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6
What are the mean and population standard deviation for these data, to the nearest hundredth?
(1) mean = 9.46; standard deviation = 3.74
(2) mean = 9.46; standard deviation = 3.85
(3) mean = 9.45; standard deviation = 3.74
(4) mean = 9.45; standard deviation = 3.85
135. The expression is equivalent to
(1) (3)
(2) (4)
136. What is the value of b in the equation
(1) (3)
(2) (4)
137. What is the solution set of the inequality
(1) (3)
(2) (4)
138. Which transformation could be used to make the graph of the equation coincide with the graph of the equation
(1) translation(3) dilation
(2) rotation(4) point reflection
139. Data collected during an experiment are shown in the
accompanying graph.
What is the range of this set of data?
(1) (3)
(2) (4)
140. Which is a true statement about the graph of the equation
(1) It is tangent to the x-axis.
(2) It does not intersect the x -axis.
(3) It intersects the x-axis in two distinct points that have irrational coordinates.
(4) It intersects the x-axis in two distinct points that have rational coordinates.
141. Which quadratic equation has the roots and
(1) (3)
(2) (4)
142. What is the amplitude of the function shown in the accompanying graph?
(1) 1.5(3) 6
(2) 2(4) 12
143. Which equation represents the circle shown in
the accompanying graph?
(1)
(2)
(3)
(4)
144. A black hole is a region in space where objects seem to disappear. A formula used in the study of black holes is the Schwarzschild formula,
Based on the laws of logarithms, log R can be represented by
(1) (3)
(2) (4)
145. In the unit circle shown in the accompanying diagram, what are the coordinates of
(1) (3)
(2) (4)
146. In and Which type of angle is
(1) It must be an acute angle.
(2) It must be a right angle.
(3) It must be an obtuse angle.
(4) It may be either an acute angle or an obtuse angle.
147. The expression is equal to
(1) (3) 16
(2) (4) 4
148. What is the solution of the equation
(1) 42 (3) 3
(2) 39 (4) 6
149. What is the minimum point of the graph of the equation
(1) (2,33) (3) (-2,-15)
(2) (2,17) (4) (-2,1)
150. If x is a positive acute angle and what is the exact value of
(1) (3)
(2) (4)
151. Which equation does not represent a function?
(1) (3)
(2) (4)
152. The expression is equivalent to
(1) (3)
(2) (4)
153. The function is equivalent to
(1) (3)
(2) (4)
154. A solution set of the equation contains all multiples of
(1) 45° (3) 135°
(2) 90° (4) 180°
155. What is the total number of points of intersection for the graphs of the equations and
(1) 1 (3) 3
(2) 2 (4) 0
156. For which equation is the sum of the roots equal to the product of the roots?
(1) (3)
(2) (4)
157. Jonathan’s teacher required him to express the sum using sigma notation. Jonathan proposed four possible answers. Which of these four answers is not correct?
(1) (3)
(2) . (4)
158. What is the period of the graph of the equation
(1) (3)
(2) (4)
159. What is the solution set of the equation
(1) {2,±3} (3) {±3}
(2) {2} (4) {2,3}
160. The expression is equivalent to
(1) (3)
(2) (4)
161. The accompanying diagram shows unit circle O, with radius OB = 1.
Which line segment has a length equivalent to
(1) (3)
(2) (4)
162. The expression is equivalent to
(1) (3)
(2) (4)
163. Which graph represents a quadratic function
with a negative discriminant?
164. , what is the value of x?
(1) 11(3) 45
(2) 18(4) 53
165. What is the value of ?
(1) 10(3) 30
(2) 13(4) 60
166. An equation of a parabola that has as its axis of symmetry is
(1) (3)
(2)(4)
167. What is the solution set for the equation ?
(1) (3)
(2) (4)
168. A central angle of radians intercepts an arc whose degree measure is
(1) 48(3) 96
(2) 72(4)
169. If , a value of is
(1) 45º(3) 180º
(2) 90º(4) 270º
170. If and , the terminal side of angle x is located in Quadrant
(1) I(3) III
(2) II(4) IV
171. In the binomial expansion of , what is the coefficient of the term containing ?
(1) 15(3) 56
(2) 28(4) 70
172. What is the inverse of the function ?
(1) (3)
(2) (4)
173. Which expression is equivalent to ?
(1) (3)
(2)(4)
174. If , then x is equal to
(1) (3)
(2)(4)
175. Which expression is equivalent to b in the equation ?
(1)(3)
(2) (4)
176. If , , and , how many different triangles can be constructed?
(1) No triangles can be constructed.(3) one right triangle, only
(2) two triangles(4) one obtuse triangle, only
177. If zero is the value of the discriminant of the equation , which graph best represents ?
(1) (2) (3) (4)
178. The expression is equivalent to
(1) -40 + 0i(3) 58 + 0i
(2) -40 – 42i(4) 58 – 42i
179. If and , what is the value of ?
(1) -13(3) 3
(2) 3.5(4) 6
180. What are the values of in the interval that satisfy the equation ?
(1) 60º, 240º(3) 72º, 108º, 252º, 288º
(2) 72º, 252º(4) 60º, 120º, 240º, 300º
181. A survey completed at a large university asked 2,000 students to estimate the average number of hours they spend studying each week. Every tenth student entering the library was surveyed. The data showed that the mean number of hours that students spend studying was 15.7 per week. Which characteristic of the survey could create a bias in the results?
(1) the size of the sample(3) the method of analyzing the data
(2) the size of the population(4) the method of choosing the students who were surveyed
182. Which graph represents the solution set of ?
(1) (3)
(2)(4)