# Core 40 Practice Test - Quia

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```					                                       Algebra 2-2 Core 40 Practice Exam

Follow the directions for each problem.

1. Which of the properties of real numbers is illustrated below?
b  ( b) = 0

[A] associative law       [B] inverse law            [C] distributive law     [D] commutative law

2. State the property that is illustrated. (a  2b)  3c  a  (2b  3c)

3. Evaluate 2e  3 f for e = –3 and f = 1.

[A] –2           [B] 9            [C] 5              [D] –3

1
4. Evaluate (7  5y)  3x when x           when y = 5.
9

5. Simplify:  6  x 6 y  xy  8 x 6 y  2 xy  2

[A] 7 x 6 y  3xy  8     [B]  9 x 6 y  xy  8     [C] 7 x12 y 2  3xy  8 [D]  9 x 6 y  x 2 y 2  8

6. Solve: 10x + 4 = 34

[A] 3            [B] 38           [C] 30             [D] 4

7. Solve the equation. 4(2 x  3)  6  (3  2 x)

8. The literature club is printing a storybook to raise money. The print shop charges \$3 for each book, and \$30
to create the film. How many books can the club print if their budget is \$690?

[A] 223                   [B] 220                    [C] 230                  [D] 227

9. For 1980 through 1990, the average salary, A, (in thousands of dollars), of assistant principals at public high
schools can be modeled by A = 2t + 25, where t = 0 represents 1980. Approximate a high school assistant
principal’s salary in 1986.
5
10. Solve for A: B =      (A  9).
8

8 B  45                  8 B  67               8 B  40                8 B  72
[A]                       [B]                    [C]                     [D]
5                         8                      8                       5

11. Solve for s: r 2 s  5s  7

9
12. Solve for C: F         C  32
5

13. Guess and check: Which of the numbers 5, 6, or 7 is the solution of 81 = 87 – x?

14. Which of the numbers is the solution of 108 = 121 – x?

[A] 12           [B] 11              [C] 13      [D] none of the above

15. Jeff earns \$4.00 an hour baby-sitting. He is saving to buy a pair of in-line skates that costs \$116.00. If Jeff
already has \$60.00 saved, how many hours must he baby-sit in order to buy the skates?

16. The length and width of the floor of a room are each 11 meters. The height is 4 meters. A spider, on the
floor in a corner, sees a fly on the ceiling in the corner diagonally opposite. If the fly does not move, what is the
shortest distance the spider can travel to reach the fly, to the nearest tenth of a meter?

[A] 18.6 m                [B] 16.1 m             [C] 26.0 m              [D] 19.6 m

17. Solve: 9b  11  10b  6

[A] b  –17               [B] b  17             [C] b  20              [D] b = 5

5
18. Is x =     a solution of the inequality 5x  4  3( x  7) ?
2

19. Solve: –6  3x  15  12
20. On a road in the city of Wilsonville, the maximum speed is 55 miles per hour and the minimum speed is 30
miles per hour. If x represents speed, which sentence best expresses this condition?

[A] 55  x  30         [B] x  30 < 55           [C] 55  x  30        [D] 55  x  30

21. Solve: x  3  3

[A] x < –6 or x > 0              [B] –6  x  0          [C] x  –6 or x  0           [D] –6 < x < 0

22. Solve the inequality. Then graph your solution. 2 x  3  5

1
23. For a door to meet specifications at a carpentry shop the width must be within       inch of the expected width
2
1
of the door. The shop gets an order for doors that are 3      feet wide. Which of the following is an inequality that
2
expresses the range of widths for acceptable doors?

1                      1               1    1               1      1
[A] x  42            [B] x  42            [C] x  3          [D] x       3
2                      2               2    2               2      2
24. You have \$20,000 available to invest in two stocks, A and B. Write an inequality stating the restriction on A
if at least \$3000 must be invested in each stock.

25. Find the range of the relation {(– 2, – 3), (1, 0), (5, – 2)}.

[A] {–2, 1, 5}          [B] {2, –1, –5}                  [C] {3, 0, 2}         [D] {–3, 0, –2}

26. Determine whether the relation is a function.
(4, 0), (4, 1), (5, 2), (6, 3), (6, 4)

27. Find f F 1I. f ( x)  18x
G3J                  2
 12 x  3
HK

3
28. Graph f ( x)       x 5.
4
[A]            y                                          [B]           y
                                                       

                     x                                              x

                                                      

[C]            y                                          [D]           y
                                                       

                     x                                              x

                                                      

29. Find the slope of the line.
y
10

–10                             10 x

–10

2                 10                           9                       5
[A]                [B]                         [C]                      [D]
5                  9                          10                       2

7             5
30. Which line is steeper, y          x  5 or y  x  2 ?
4             3

31. In 1983 the pollution in a local lake was rated at 1.4 parts per million. By 1987 it had risen to 2.6 parts per
million. Which of the following expresses the rate of change in parts per million from 1983 to 1987?

1                 5                 6                     3
[A]                [B]               [C]                  [D]
4                 6                 5                    10

32. Graph the linear equation by finding x- and y-intercepts. 3x  3y = 9
[A]           y                                [B]           y
                                             

                 x                                      x

                                            

[C]           y                                [D]           y
                                             

                 x                                       x

                                            

33. Find the slope and y-intercepts of the line. 4 x  3y  36

34. Graph: 9 x  7 y  63

[A]           y                                [B]           y
                                             

                 x                                      x

                                            

[C]           y                                [D]           y
                                             

                 x                                       x

                                            

35. Write the equation in slope-intercept form. Then identify the slope and y-intercept. 15x  3y  7
36. Write an equation to model the following situation.
A candle is 6 in. tall and burns at a rate of 2.50 in./h.

[A] y = 6 x + 2.5      [B] y = 6x – 2.5       [C] y = 2.5x+6        [D] y = –2.5x + 6

37. The variables x and y vary directly and y = –7 when x = 14. Write an equation that relates the variables.

38. Graph:  y  5x  2

[A]           y                               [B]             y
                                              

                  x                                      x

                                             

[C]           y                               [D]             y
                                              

                  x                                      x

                                             

2
39. Graph the inequality in a coordinate plane. y      x2
3

40. Sally wants to buy her boyfriend a bouquet for his birthday. She wants it to contain both carnations and
roses. She has \$27.60 to spend. Carnations cost \$1.41 each and roses cost \$2.33 each. Which graph below
represents the possible combinations of numbers of carnations and roses Sally can afford to buy?
[A]                                      [B]     

roses                                      roses

carnations                               carnations   

[C]                                      [D]     

roses                                      roses

carnations                               carnations   

41. Graph the function. f ( x)  x  3

42. Graph the function defined by y = x  3 .

[A]             y                          [B]             y
                                         

                  x                                     x

                                        

[C]             y                          [D]             y
                                         

                   x                                     x

                                        
43. The population, P (in thousands), of a town can be modeled by P  2 t  8  4 , where t = 0 represents 1990.
During which two years does the town have a population of 8000?

44. Solve the system by graphing: x  y = 2
y = 2 x  13

[A]           y                               [B]            y
                                             

                 x                                      x

                                            

F ,  13I
G 3J
13                                            F, 4 I
G 3J
2
H K
3                                            H K
3

[C]           y                               [D]            y
                                             

                 x                                      x

                                            
b , 17g
15                                           b, – 3g
5

45. Is (5, –2) a solution of the system?
2x + 6y = –2
2x + y = 6

46. A rental car agency charges \$19 per day plus 10 cents per mile to rent a certain car. Another agency charges
\$26 per day plus 7 cents per mile to rent the same car. How many miles per day will have to be driven for the
cost of a car from the first agency to equal the cost of a car from the second agency?

[A] 2333.33 miles per day       [B] 233.33 miles per day     [C] 1500 miles per day       [D] 150 miles per day

47. The drama club sold 1500 tickets for the end-of-year performance. Admission prices were \$12 for adults
and \$6 for students. The total amount collected at the box office was \$15,600. How many students attended the
play?
48. Solve the linear system: 4 x  4 y  4
3x  4 y  – 25

49. Solve the system.
3     1
y  x
4     4
3     3
y     x
4     4

50. Tickets to a local movie were sold at \$4.00 for adults and \$2.50 for students. If 420 tickets were sold for a
total of \$1155.00, how many student tickets were sold?

[A] 70                  [B] 85                 [C] 350                        [D] 280

51. A group of 65 people attend a ball game. There were four times as many children as adults in the group.
Write a system of equations that you could use to set up this problem, where a is the number of adults and c is
the number of children in the group. Solve the system of equations for c, the number of children in the group.

52. Graph the system of linear inequalities:
x  –4
y  –5

[A]           y                                [B]           y
                                             

                 x                                        x

                                            

[C]           y                                [D]           y
                                             

                 x                                        x

                                            
53. Graph the system of inequalities:
y  –7
y < –4

54. Graph the system of inequalities:
4 x  5y  20
x  y
x 5

[A]           y                               [B]           y
                                            

                    x                                     x

                                           

[C]           y                               [D]            y
                                             

                    x                                     x

                                           

55. Solve the system of equations:
x + y + z = –2
 2x  y + z = – 9
x  2 y  z = 16

[A] (5, –4, –3)            [B] (–5, 4, 3)     [C] (–3, –4, 5)        [D] (3, 4, –5)

56. James sold magazine subscriptions with three prices: \$20, \$27, and \$18. He sold 6 fewer of the \$20
subscriptions than of the \$27 subscriptions and sold a total of 31 subscriptions. If his total sales amounted to
\$678, how many \$18 subscriptions did James sell?

[A] 15            [B] 13           [C] 6      [D] 12
L7   –1 – 4  O          L
–9 –7 –6          O
57. If A = M            P          M             P
M
–3
M
–7      P
2 and B =
P
8  M
M
1            P
7 , find A + B.
P
N5    3   4  Q          N
–8 – 3 –1         Q
L16 6       2  O             L2 – 8 – 10O
–
[A] M – 8           P             M – 6 9P
M– 11
M 6
5  P
P
[B]
M 0 3P
M 5
P
N  13      –5  Q             N3
–          Q
L16 6         2O             L2 – 8 – 10O
–
[C] M – 8           P             M – 6 3P
M– 11
M 6
– 5P         [D]
M 0 9P
M 5
N  13         5P
Q             N3
–          P
Q
L xO L 3OL 6O
4

1
58. Solve for x and y. 3M P2 M P M P

10
N 3Q N 0QN7 9Q
1   y       

59. Don asked the players on two ski teams what new color each team uniform should be: red, blue, or green.
He recorded the results in two matrices. Find the total for the two teams.

R B G                          R B G
L OP
Males 1 6 7                           L OQ
Males 0 8 3
Females M 4 2P                Females M 5 7P
                           
N Q
8                             N Q
9

L 14 1 O
[A] M
10                                L 9 17O
9
N 9 17P
[B] M
9      Q                         N 14 1 P
10    Q
L 14 10O
[C] M
1                                L 10 9O
1
N 9 9P
[D] M
17      Q                         N 17 9P
14    Q
L2O
–
MP B
60. Given A  1 and
MP                1 4 0 , find AB.
MP
N1Q


L1
M
–     2 –2     O
P
[A] 2
M
[B] 2
M
5 1      P
P
N 0    3 1     Q
L2
M
–     –8 0   O
P
M
[C] 1
M
4 0    P
P
[D] not possible
N1
     –4 0   Q
61. Perform the matrix operations, if possible.
L 5O
2
M 7P2              1 4
N Q
1

62. Student Government and the cheerleaders at a local school are ordering supplies. The supplies they need are
listed below.
Paint Paper Tape
Student Government        L12
M       14          5   O
P
N8      17          9   P
Q
If a bottle of paint costs \$5, a roll of paper costs \$12, and a roll of tape costs \$2, which of the following shows
the use of matrices to find the total cost of supplies for each group?

L 14
12
[A] M
5OO L O
L P 238
M
5
P P M P                                 L 14 5O 12
12
M 17 9P               2 
LO
238
MP
N 17
8         9M 262
12
QP N Q
MQ
[B]
N8
5
Q                     NQ
262
N 2

L 14
12
LO5
5O P
MP 500                                  L 14 5O 12
12
[C]   M 17
N        9P
M12
QP
[D]   M 17 9P
N     5
Q               2  500
8
MQ
N 2
8

2 3 1
63. Evaluate the determinant of the matrix. 4 1 3
5 5 2

[A] 10                 [B] –18                               [C] –10             [D] 18

10    7
64. Evaluate the determinant of the matrix.
 5 12

65. Use Cramer’s Rule to solve for x:
R  5y = 6
3
Sx  3y = 1
Tx
3

13                     5                23                           7
[A]                    [B]              [C]                        [D] 
24                     8                24                           8

66. Find the coefficient matrix and evaluate its determinant.
R  8x  5y  7
S x  7y   4
T
12
67. Find the inverse of
L 7O
4
M 8P
.
N Q
9

68. Use the inverse of the matrix A =
L2 – 1O decode the message –9, –5, 54, 17, 24, 3.
–
M 1P   to
N Q
3
1   =   A 8 = H      15   =    O   22   =   V
2   =   B 9 = I      16   =    P   23   =   W
3   =   C 10 = J     17   =    Q   24   =   X
4   =   D 11 = K     18   =    R   25   =   Y
5   =   E 12 = L     19   =    S   26   =   Z
6 = F 13 = M 20 = T
7 = G 14 = N 21 = U

[A] CIRCLE             [B] DEGREE                 [C] MEDIAN          [D] FACTOR

69. Graph: y  4 x 2  x  1

[A]             y                                 [B]           y
                                              

                x                                        x

                                             

[C]             y                                 [D]           y
                                              

                x                                        x

                                             

70. Find the vertex of the parabola and determine if it opens up or down. y  7  8 x  2 x 2
b
b g g
71. Write in standard form and graph: y  – 2 x  3 x  4

[A] y  –2 x 2 – 14 x – 24                         [B] y  –2 x 2  14 x  24
y                                                y
                                               

                     x                                            x

                                              

[C] y  –24 x 2 – 14 x – 2                         [D] – 2 y  x 2  7 x  12
y                                                y
                                               

                     x                                            x

                                              

72. Graph: y  2 x 2  x  2

73. The surface area of a cube is 380 square inches. How long is each edge? (Round to two decimal places.)

x

x
x

74. Solve by factoring: x 2  18x  81  0
75. A restaurant’s aquarium is destroyed in an earthquake. The insurance company is willing to replace the
aquarium with one of the same dimensions. The owner can only remember that the diagonal of the front was 68
inches, the length was 28 inches more than the height of the front, and the depths was the same as the height of
the front. Find the dimensions of the aquarium.

[A] 61 in.  33 in.  33 in.                    [B] 59 in.  31 in.  31 in.

[C] 58 in.  30 in.  30 in.                    [D] 60 in.  32 in.  32 in.

76. Find the x-intercepts of the graph of y = x 2  2 x  15 .

[A] –2, 3                                       [B] 3, –5
y                                               y
                                              

                   x                                            x

                                              

[C] 2, –3                                                [D] –3, 5
y                                                     y
                                                    

                   x                                                   x

                                                      

77. Find the zeros of the equation. x 2  2 x  15 = y

78. Solve for x: 6 x 2 = 24

[A] 2            [B] 12          [C] 144                 [D] 18

1 2
79. Solve the equation.       x  1  33
3
80. The distance, d (in meters), travelled by a falling object is given by the equation d  4.9t 2 , where t is the
time in seconds. From what height was the object originally dropped if it took 5.27 seconds to hit the ground?
Round answers to the nearest whole number.

[A] 666 meters            [B] 25.81 meters       [C] 136 meters           [D] 27.76 meters

81. Solve: (6 x  4) 2 = 77

 4  77  4 + 77                                 4  77  4 + 77
[A]           ,                                  [B]           ,
12       12                                       6        6

– 4  77 – 4 + 77                                – 4  77 – 4 + 77
[C]           ,                                  [D]           ,
6        6                                      12       12

82. Write the expression as a complex number in standard form. (1  i )  (8  3i )

5
83. Write the expression as a complex number in standard form.
1 i

8  5i
84. Write the expression as a complex number in standard form.
6  4i

17   1                           17 31                   7   31                         7   1
[A]         i                   [B]        i          [C]          i                 [D]        i
5 10                             5 10                   13 26                          13 26

85. Find the absolute value of the complex number. 2  5 i

[A] 29           [B] 21          [C] 4.58               [D] 5.39

86. Solve by completing the square: x 2  6x  40 = 0

[A] 10, 4                 [B] 10, –4             [C] –10, –4              [D] –10, 4

87. Solve by completing the square: 7 x 2  28x  21  0
4 2
88. Write the quadratic equation in vertex form: y                  x  40x  294
3

89. Find the maximum value of the quadratic equation: y   2 x 2  24 x  87

[A] max = –129                             [B] max = 6            [C] max = –87           [D] max = –15

90. Solve by the quadratic formula: x 2  5x  1 = 0

5        21       5        21                  – 5  29 – 5  29
[A]                  ,                           [B]           ,
2                  2                            2        2

5        29       5        29                    – 5  21 – 5  21
[C]                  ,                           [D]             ,
2                  2                              2        2

91. State the discriminant of the quadratic. 3x 2  4 x  4  0

92. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t
seconds after it is thrown is given by d   16t 2  2t  405 . How long after the rock is thrown is it 300 feet
from the ground?

21                                 5                      29                      7
[A]      sec                       [B]     sec            [C]      sec            [D]     sec
8                                  2                       8                      2

93. Graph: y >  x 2  5x  6

94. Which is the graph of y   1  3x  x 2 ?
[A]             y                              [B]               y
                                               

                    x                                    x

                                            

[C]             y                              [D]               y
                                               

                    x                                     x

                                            

95. Solve the inequality algebraically: ( x  5)(9 x  8)  0

96. An arrow shot into the air is 144t  4.9t 2 meters above the ground t seconds after it is released. During what
period(s) of time is the arrow below 68.6 meters? Round your answer to the nearest .01 second.

[A] 14  x  1539 seconds
.                               [B] x  0.48 and x  28.90 seconds

[C] x  14 and x  1539 seconds
.                         [D] 0.48  x  28.90 seconds

F 6 I5
b
97. Simplify: G9 J
G J
G J
H K
c

ch
98. Simplify: xy 3     5

[A] x 5 y 3                [B] x 6 y15         [C] x 6 y 8           [D] x 5 y15

99. According to figures from 1995, the population of the United Kingdom is 58,295,119. The land mass of the
United Kingdom is 94,251 square miles. If the land mass of the United Kingdom is divided evenly amongst the
population, how many people live in each square mile?

[A] 61.85                  [B] 0.16            [C] 618.5             [D] 0.0016
100. Evaluate the polynomial when d = 5: 7d 3  6d 2  5d  12

bg
101. Use synthetic substitution to evaluate f c  9c3  2c2  5c  7 when c = 2.

bg
[A] f c  64                      bg
[B] f c  49                       bg
[C] f c  75                       bg
[D] f c  67

102. Graph: y = x 6

[A]            y                                     [B]             y
                                                    

                   x                                               x

                                                   

[C]            y                                     [D]              y
                                                     

                   x                                                x

                                                   

103. Decide whether the function is a polynomial function. If it is, state its degree, type, and leading
coefficients.
f ( x)  x 4  x 2  3x  7.

104. Multiply: ( x  4)( x 2  x  4)

[A] x 3  x 2  16        [B] x 3  5x 2  8x  16         [C] x 3  3x 2  8x  16     [D] x 3  5x 2  16

105. The sides of a rectangle have lengths x  9 and widths x  5 . Which equation below describes the
perimeter, P, of the rectangle in terms of x?

[A] P = x 2  14 x  45           [B] P = 4 x  8             [C] P = x 2  4 x  45         D] P = x  4

106. Factor: 9 y 2  25
[A] (3y  5)(3y  5)      [B] (3y  5)(3y  5)      [C] (3y  5)(3y  5)   [D] (9 y  1)( y  25)

107. Solve: x 3  6x 2 = 0

[A] 0, –6          [B] 6, –7      [C] 6, –6         [D] 0, 6

108. Find all real-number solutions. x 3  9 x 2  27 x  27  0

109. Divide: ( x 3  5x  3 )  ( x  3 )

21                                          45
[A] x 2  2 x  6 –                         [B] x 2  3x  14 –
x3                                         x3

27                                         14
[C] x 2  2 x  9 +                         [D] x 2  3x  4 +
x3                                        x3

c                 h                                  b g
110. A rectangle has an area of x 3  x 2  10 x  8 square meters, and a width of x  4 meters. Find its
length.

c           h
[A] x 2  x  10 meters                         c              h
[B] x 2  3x  10 meters

c              h
[C] x 2  3x  2 meters                         c           h
[D] x 2  x  2 meters

111. Estimate the real zeros of the function graphed below.
y
10

–10                           10 x

–10

[A] 12, 1, 3, 5           [B] 1, 3, 5               [C] –5, –3, –1         [D] 12

112. Find all real zeros of the function. g ( x)  2 x 3  x 2  6 x  3

113. For 1985 through 1996, the number, C (in thousands), of videos rented each year in Moose Jaw can be
modeled by C = 0.079( t 3  2t 2  31t  600 ), where t = 0 represents 1990. During which year are 99.4 thousand
movies projected to be rented?

[A] 2002                [B] 1996                  [C] 1994          [D] 1997

114. Write a polynomial function that has the zeros 2, –2, and –1 and has a leading coefficient of 1. Then graph
the function to show that 2, –2, and –1 are solutions.

[A]            y                 y =  x3  x2  4x  4


                  x



[B]            y                 y = x3  x2  4x  4


                  x



[C]            y                 y =  2x2  2x  1


                  x



[D]            y                 y = x2  x  2


                  x


115. Solve for x: x 4  12 x 2  11 = 0
116. Evaluate: 12961/ 4

1                                                1
[A]                            [B] 6             [C]                    [D] 36
36                                               6

117. Use a calculator to evaluate 9 1/ 3 to three decimal places.

118. Evaluate the expression using a calculator. Round the result to three decimal places when appropriate.
3
128

[A] 23 4                       [B] 163 8         [C] 43 2               [D] 43 8

5
119. Evaluate        1540 to three decimal places using a calculator.

120. The volume of a sphere can be given by the formula V = 418879r 3 . You have to design a spherical
.
container that will hold a volume of 55 cubic inches. What should the radius of your container be?

[A] 2.36 in.                   [B] 2.49 in.      [C] 3.62 in.           [D] 13.13 in.

495/ 6
121. Simplify:
491/ 3

FI
v
122. Simplify: G J
25    3/ 5

HK
w        15

123. The surface area of a baseball is 23.75 in 2 . The surface area of a softball is 53.78 in 2 . Find the ratio of the
4
volumes of a baseball to a softball. Surface Area = 4  r 2 and Volume =  r 3 .
3

[A] 0.665                      [B] 0.293         [C] 0.442              [D] 0.193
124. Let f ( x )  1  x 2 and g( x)  1  x . Find f ( x)  g( x) .

125. Sara bought 3 fish. Every month the number of fish she has doubles. After m months she will have F fish,
where F  3 2 m . How many fish will Sara have after 3 months if she keeps all of them and the fish stay
healthy?

[A] 24          [B] 216                   [C] 30                   [D] 11

126. Find an equation for the inverse of the relation y = 5x  2 .

x2                      5x  2                   x2
[A] y =                   [B] y =                  [C] y =                  [D] y =  2 x  5
5                         5                       5

127. Are f and g inverses of each other?
bg   2     1
f x  x , g x  x
3     2
bg 2
3     3
4

128. Sketch the graph of the function. Is the inverse of f(x) a function? f ( x )  2  x 2

129. Describe how to obtain the graph of y          x  3  3 from the graph of y      x.

130. Graph: f(x) =   3
x3  2
[A]            y                              [B]            y
                                            

                   x                                         x

                                           

[C]            y                              [D]            y
                                            

                   x                                         x

                                           

131. Refer to the function g( x)  1  x  3 . What is the range of g(x)?

132. The sales of a certain product after an initial release can be found by the equation s  14 7t  45 ,
where s represents the total sales and t represents the time in weeks after release. How many weeks will pass
before the product sells about 200 units? Round your answer to the nearest week.

133. A certain gas will escape from a storage tank according to the formula e  170 p , where e represents
the amount escaping per minute in gallons, and p represents the pressure in pounds per square inch. What is the
pressure on the gas when about 250 gallons per minute are escaping? Round your answer to the nearest tenth.

[A] 20.5 lb/in. 2      [B] 2.2 lb/in. 2       [C] 0.7 lb/in. 2          [D] 1.5 lb/in. 2

134. Solve the equation. Check for extraneous solutions.    3    x  5  –5

[A] 130         [B] –120          [C] 30      [D] –120, 130

135. The velocity of sound in air is given by the equation v = 20 273  t where v is the velocity in meters per
second and t is the temperature in degrees Celsius. Find the temperature when the velocity of sound in air is 348
meters per second. Round the answer to the nearest degree.

[A] –14°C              [B] 22°C               [C] 6°C                   [D] none of these
136. Graph f ( x) =  2  e x .

[A]               y                          [B]                   y
10                                                10

–10                         10 x             –10                         10 x

–10                                            –10

[C]               y                                    [D]                y
10                                                      10

–10                         10 x                       –10                       10 x

–10                                                     –10

137. Is f ( x)  7e 2t an example of exponential growth or decay?

138. If \$5000 is invested at a rate of 7% compounded continuously, find the balance in the account after 2
years. Use the formula A  Pert .

[A] \$5724.50             [B] \$5751.37        [C] \$36945.28              [D] \$6168.39

139. Evaluate: log 3 9

1                                            1
[A]            [B] 6           [C] 2         [D]
2                                            6

140. Evaluate without using a calculator. log 7 343
141. Graph: y  log 4 x

[A]              y                            [B]            y
                                          

                    x                                    x

                                         

[C]              y                            [D]            y
                                          

                    x                                    x

                                         

142. Express as a single logarithm: logb 6  logb 45

[A] logb 645                                              FI
GJ
6
[D] logb (6  45)
[B] logb 270       [C] log b
HK
45

143. Expand the expression. log 4 3x 1 y 3

144. Use the formula R  log10 I , where R is the measurement of the Richter scale and I is the intensity, to find
the Richter scale measurement of an earthquake with intensity 120,000,000.

[A] 8.0792                 [B] 0.80792        [C] 18.603             [D] 1.8603

145. Solve for x correct to four decimal places: e–4 x = 58
.

1
146. Solve:      = 273x5
9

13               1                            17
[A]              [B]               [C] 1      [D]
9                3                             9
147. Solve the equation. 60.2 x  3  7

148. It takes a train 7 h to get from Capital City to Johnson City when it travels 55 mi/h. How long would it take
the train to go the same distance when it travels 77 mi/h?

7                        5
[A] 5 h          [B]     h                [C]     h                [D] 11 h
5                        7

149. The variable z varies jointly with the product of x and y. z = 3.6 when x = 8 and y = 90. Find an equation
that relates the variables.

150. The wattage rating of an appliance, W, varies jointly as the square of the current, I, and the resistance, R. If
the wattage is 4.5 watts when the current is 0.3 ampere and the resistance is 50 ohms, find the wattage when the
current is 0.2 ampere and the resistance is 100 ohms.

[A] 40 watts             [B] 20 watts             [C] 2000 watts              [D] 4 watts

n 2  2n  24
151. Simplify the rational expression. 2
n  11n  28

n6              n6             n6              n4
[A]              [B]             [C]              [D]
n7              n4             n7              n7

2x  3      x2  4x  3
152. Multiply and simplify.            
( x  3) 2    4x2  9

9                       2
153. The length of a rectangle is          m, while its width is m. Which of the following is true?
y4                      y

18                                 18
[A] perimeter:               m            [B] area:             m2
y ( y  4)                          y( y  4)

11y  8                                36
[C] perimeter:               m            [D] area:             m2
y ( y  4)                          y( y  4)
11         1
6( x  4) 6( x  4)

4     1
x2   x2

5x  6                     5                 5x  6                   5
[A]                       [B]                [C]                    [D]
5                       x2                x2  4                 x 4
2

4
1 +
156. Simplify:     5
3
2 +
7

85                        63                                        7
[A]                       [B]                [C] 5355               [D]
63                        85                                        55

4     2

157. Simplify the complex fraction. x  3 3
5
x3

x2      36
158. Solve:         
x6     x6

[A] {6}           [B] {–6, 6}          [C] {–6}             [D] 

4x       8
159. Is x = –2 a solution of         1     ?
x2      x2

160. The number of in-line skates sold between 1982 and 1991 can be modeled by the equation
1375       1
I =          + x . The number of roller skates sold during the same period can be modeled by
4        4
11,835       3
S =             – x , where x is the year. Use a graph to determine what year sales of in-line skates will exceed
7        7
sales of roller skates.
[A] 1985         [B] 1987         [C] 1986    [D] 1984

161. Find the distance between the points (5, 8) and (5, 5) .

[A] 23           [B] 10           [C] 13      [D] 3

162. Write the standard form of the equation of the parabola with its vertex at (0, 0) and directrix y  –4 .

1
[A] x 2  16 y            [B] y  16 x 2      [C] y 2       x        [D] x  –4 y 2
16

163. Identify the focus and directrix of the parabola given by y 2  4 x.

164. In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall
and 80 cm wide. Find an equation of the parabola.
80 cm

40 cm

165. Graph: 3x 2  3 y 2 = 75

166. The pool at a park is circular. You want to find the equation of the circle that is the boundary of the pool.
Find the equation if the area of the pool is 900 square feet and (0, 0) represents the center of the pool.

167. Graph: 9 x 2  y 2 = 9
[A]             y                             [B]           y
                                          

                 x                                        x

                                         

[C]            y                              [D]            y
                                            

                x                                         x

                                           

x2 y2
168. Sketch the graph of         1.
4 16

169. A skating park has a track shaped like an ellipse. If the length of the track is 80 m and the width of the
track is 44 m, find the equation of the ellipse.

x2   y2
170. Graph:           1
9    25
[A]            y                               [B]             y
                                              

                    x                                      x

                                             

[C]           y                                [D]             y
                                               

                    x                                      x

                                             

bg b g                         bg b g
171. Write the equation of the hyperbola with vertices at 2, 0 and  2, 0 and foci at 8, 0 and  8, 0 .

172. Find the center and radius of x 2  y 2  8 x  6 y  9  0.

[A] center (4, 3); r = 4                [B] center (4, 3); r = 16

[C] center (–4, –3); r = 16             [D] center (–4, –3); r = 4

173. Find an equation of the hyperbola with vertices at (–3, 2) and (3, 2) and foci at (–5, 2), (5, 2).

174. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola.
144 x 2  64  64 y 2

[A] hyperbola              [B] circle          [C] parabola            [D] ellipse

175. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola.
x 2  9 y  3x  7  0
x 2  y 2  16
176. Solve:
x y 4

[A] {(0, 0), (4,  4 )}                  [B] {(4,  4 ), (  4 ,  4 )}

[C] {(0,  4 ), (  4 , 0)}              [D] {(0, 4), (4, 0)}

177. Solve the system by substitution: 3x  4 y  10
y 2 x  3

178. The cost, C, of manufacturing and selling x units of a product is C  23x  73 , and the corresponding
revenue, R, is R  x 2  35 . Find the break-even value of x.

[A] 4           [B] 31           [C] 31 and 4            [D] 27

179. Find the first four terms of the sequence tn  n(3n  7) .

180. Find the first four terms of the sequence tn  n(6n  2) .

[A] 4, 20, 48, 88         [B] 4, 20, 46, 84      [C] 6, 2, 0, –2          [D] 6, 22, 52, 94

181. Write the series with summation notation. 2  5  8  11  . . .

182. Find the common difference of the arithmetic sequence.
3      7
 , 1, , 6, . . .
2      2

183. Find the sum of the first 14 terms of the arithmetic series.
– 13  8  3  2  . . .

[A] 268         [B] 273          [C] 278         [D] 546
1                             1
184. Write a rule for the nth term of the arithmetic sequence with a1      and the common difference of .
2                             6

185. Evaluate the sum.
F I
G J
30 2
 i4
H K
i 1 3

186. The number of lilies a large nursery can sell each day after April 1 is modeled by a sequence whose
general term is an = 1700  75n , where n is the number of days after April 1. Find the number of lilies that can
be sold on April 5th, 6th, and 7th.

[A] 1250, 1325, 1250                   [B] 1400, 1325, 1250

[C] 1325, 1250, 1175                   [D] 1475, 1400, 1325

187. The distance (in feet) that a free-falling body falls in each second, starting with the first second, is given by
the arithmetic progression 21, 63, 105, 147, . . . . Find the distance that the body falls in the 7th second.

188. Give the first four terms of the geometric sequence for which a1 = 4 and r  3.

4 4 4
[A] 4, 12, 36, 108                     [B] 4 ,    , ,
3 9 27

[C] 12, 36, 108, 324                   [D] 7, 10, 13, 16

189. Find the common ratio of the geometric sequence.
2, –8, 32, –128, . . .

64     128
190. Write a rule for the nth term of the geometric sequence. 48,  32,        ,      , ...
3      9
191. In a financial deal, you are promised \$700 the first day and each day after that you will receive 65% of the
previous day’s amount. When one day’s amount drops below \$1, you stop getting paid from that day on. What
day is the first day you would receive no payment and what is your total income?

[A] 17th day; \$1997.26 total income                         [B] 16th day; \$1999.39 total income

[C] 17th day; \$1997.97 total income                         [D] 21st day; \$1997.97 total income

192. A lunch menu consists of 6 different sandwiches, 4 different soups, and 4 different drinks. How many
choices are there for ordering a sandwich, a bowl of soup, and a drink?

193. Eleven people are entered in a race. If there are no ties, in how many ways can the first two places come
out?

[A] 6            [B] 220                    [C] 78                 [D] 110

9!
194. Evaluate the factorial expression.
4!

[A] 362,880               [B] 0             [C] 24                 [D] 15,120

195. Find the number of permutations.         10       P6

196. You own 9 sweaters and are taking 4 on vacation. In how many ways can you choose 4 sweaters from the
9?

[A] 362,880               [B] 36            [C] 126                         [D] 504

197. A four-person committee is chosen at random from a group of 15 people. How many different committees
are possible?

198. Expand ( p  2q ) 4 .

[A] p 4  8 p 3q  24 p 2 q 2  32 pq 3  16q 4                    [B] p 4  2 p 3q  2 p 2 q 2  2 pq 3  2q 4
[C] p 4  8 p 3q  12 p 2 q 2  8 pq 3  2q 4           [D] p 4  2 p 3q  4 p 2 q 2  8 pq 3  16q 4

b
199. Expand A  2 B .     g4

200. A card is drawn from a standard deck of playing cards. Find the probability that it is not a face card (J, Q,
or K) or an ace.

201. A student fails to study for a 9 question true/false test. What is the probability that the student gets 6
questions correct?

3                 945               21          21
[A]               [B]               [C]         [D]
256               2048              128         256

202. Half of a circle is inside a square and half is outside, as shown. If a point is selected at random inside the
square, find the probability that the point is also inside the circle.

r

2r
Reference: [1.1.2.11]
[1] [B]

Reference: [1.1.2.16]
[2] Associative property of addition

Reference: [1.2.1.19]
[3] [D]

Reference: [1.2.1.28]
[4] 96

Reference: [1.2.2.37]
[5] [A]

Reference: [1.3.1.40]
[6] [A]

Reference: [1.3.1.45]
5
[7] x 
2

Reference: [1.3.2.49]
[8] [B]

Reference: [1.3.2.51]
[9] \$37,000

Reference: [1.4.1.58]
[10] [A]

Reference: [1.4.1.60]
7
[11] s  2
r 5

Reference: [1.4.2.63]
5
[12] C  ( F  32)
9

Reference: [1.5.1.65]
[13] 6

Reference: [1.5.1.66]
[14] [C]

Reference: [1.5.2.72]
[15] 14 hours

Reference: [1.5.2.76]
[16] [A]

Reference: [1.6.1.79]
[17] [A]

Reference: [1.6.1.83]
[18] No

Reference: [1.6.2.87]
[19] 3  x  9

Reference: [1.6.2.89]
[20] [C]

Reference: [1.7.1.91]
[21] [C]

Reference: [1.7.1.95]
[22]  1  x  4

–2 –1 0 1 2 3 4 5 6   x

Reference: [1.7.2.98]
[23] [A]

Reference: [1.7.2.101]
[24] 3,000  A  17,000

Reference: [2.1.1.2]
[25] [D]

Reference: [2.1.1.6]
[26] It is not.

Reference: [2.1.2.10]
[27] 3

Reference: [2.1.2.13]
[28] [A]

Reference: [2.2.1.17]
[29] [B]
Reference: [2.2.1.24]
7
[30] y  x  5
4

Reference: [2.2.2.28]
[31] [D]

Reference: [2.3.1.31]
[32] [A]

Reference: [2.3.1.34]
4
[33] slope  ; y-intercept = (0, –12)
3

Reference: [2.3.2.42]
[34] [D]

Reference: [2.4.1.48]
7                             7
[35] y  5x  ; Slope: 5; y-intercept: (0,  )
3                             3

Reference: [2.4.1.55]
[36] [D]

Reference: [2.4.2.63]
1
[37] y   x
2

Reference: [2.6.1.75]
[38] [A]

Reference: [2.6.1.82]
[39]                y
5
4
3

1

–3 –2 –1      1 2   x

Reference: [2.6.2.88]
[40] [C]

Reference: [2.8.1.109]
[41]                          f(x )

5
4

1

–6 –5 –4 –3 –2           x
–1

Reference: [2.8.1.113]
[42] [D]

Reference: [2.8.2.122]
[43] 1996, 2000

Reference: [3.1.1.4]
[44] [D]

Reference: [3.1.1.11]
[45] No

Reference: [3.1.2.17]
[46] [B]

Reference: [3.1.2.19]
[47] 400

Reference: [3.2.1.23]
[48] (–3, –4)

Reference: [3.2.1.29]
2F I
G J
, 
1
[49]
3H K  4

Reference: [3.2.2.36]
[50] [C]

Reference: [3.2.2.39]
[51] Sample Acceptable Response:
a  c = 65
c = 4a
by substitution:
a  4a = 65
5a     65
=
5      5
a = 13
c = 4(13) = 52 children
Reference: [3.3.1.42]
[52] [A]

Reference: [3.3.1.47]
[53]              y
10

–10               10 x

–10

Reference: [3.3.2.59]
[54] [A]

Reference: [3.6.1.78]
[55] [A]

Reference: [3.6.2.83]
[56] [B]

Reference: [4.1.1.4]
[57] [B]

Reference: [4.1.1.10]
[58] x = 4, y = 2

Reference: [4.1.2.19]
[59] [C]

Reference: [4.2.1.21]
[60] [C]

Reference: [4.2.1.25]
[61] Not possible

Reference: [4.2.2.29]
[62] [A]

Reference: [4.3.1.35]
[63] [A]
Reference: [4.3.1.38]
[64] 155

Reference: [4.3.2.48]
[65] [C]

Reference: [4.3.2.52]

[66]
L O
8 5
M P       ,
8 –5
= 116
N Q
12 7          12 7

Reference: [4.4.1.67]
L
M
8     7 O
P
[67] M
M
31
9

31
4P
P
N  31     31Q
Reference: [4.4.2.71]
[68] [D]

Reference: [5.1.1.4]
[69] [B]

Reference: [5.1.1.8]
[70] Vertex: (–2, 15); Opens down

Reference: [5.1.1.17]
[71] [A]

Reference: [5.1.1.22]
[72]              y
10

–10                     10 x

–10

Reference: [5.1.2.24]
[73] 7.96 in.

Reference: [5.2.1.30]
[74] 9

Reference: [5.2.1.34]
[75] [D]

Reference: [5.2.2.38]
[76] [D]

Reference: [5.2.2.39]
[77] –5, 3

Reference: [5.3.1.45]
[78] [A]

Reference: [5.3.1.50]
[79]  4 6

Reference: [5.3.2.55]
[80] [C]

Reference: [5.4.1.62]
[81] [C]

Reference: [5.4.1.71]
[82]  7  2i

Reference: [5.4.1.82]
5 5
[83]  i
2 2

Reference: [5.4.1.87]
[84] [C]

Reference: [5.4.2.93]
[85] [D]

Reference: [5.5.1.100]
[86] [D]

Reference: [5.5.1.108]
[87] x = –1 and –3

Reference: [5.5.2.113]
4
b g
[88] y  x  15  6
3
2

vertex = (15, –6)
Reference: [5.5.2.115]
[89] [D]

Reference: [5.6.1.120]
[90] [A]

Reference: [5.6.1.129]
[91] –32

Reference: [5.6.2.135]
[92] [B]

Reference: [5.7.1.138]
[93]              y
10

–10                      10 x

–10

Reference: [5.7.1.143]
[94] [D]

Reference: [5.7.2.147]
F
G
[95] – , 
8O
P   5,    g
H        9Q
Reference: [5.7.2.149]
[96] [B]

Reference: [6.1.1.2]
b 30
[97] 45
c

Reference: [6.1.1.6]
[98] [D]

Reference: [6.1.2.16]
[99] [C]
Reference: [6.2.1.18]
[100] 688

Reference: [6.2.1.20]
[101] [D]

Reference: [6.2.2.22]
[102] [C]

Reference: [6.2.2.27]
[103] The function is a quartic polynomial with degree 4 and leading coefficient 1.

Reference: [6.3.1.40]
[104] [B]

Reference: [6.3.2.47]
[105] [B]

Reference: [6.4.1.50]
[106] [A]

Reference: [6.4.2.60]
[107] [D]

Reference: [6.4.2.63]
[108] 3

Reference: [6.5.1.66]
[109] [B]

Reference: [6.5.2.80]
[110] [C]

Reference: [6.6.1.82]
[111] [C]

Reference: [6.6.1.84]
1
[112]  ,  3
2

Reference: [6.6.2.86]
[113] [D]

Reference: [6.7.1.90]
[114] [B]
Reference: [6.7.2.97]
[115]  1,  11

Reference: [7.1.1.3]
[116] [C]

Reference: [7.1.1.10]
[117] 0.481

Reference: [7.1.1.13]
[118] [C]

Reference: [7.1.1.17]
[119] 4.340

Reference: [7.1.2.21]
[120] [A]

Reference: [7.2.1.28]
[121] 7

Reference: [7.2.1.34]
v 15
[122] 9
w

Reference: [7.2.2.38]
[123] [B]

Reference: [7.3.1.39]
[124]  x 2  x

Reference: [7.3.2.44]
[125] [A]

Reference: [7.4.1.47]
[126] [C]

Reference: [7.4.1.58]
[127] No

Reference: [7.4.2.63]
[128] No
f(x )

3

1

–3         1      3   x

–2
–3

Reference: [7.5.1.65]
[129] You move the graph left 3 units and down 3 units.

Reference: [7.5.1.69]
[130] [A]

Reference: [7.5.1.74]
[131] g( x)  1

Reference: [7.5.2.79]
[132] 18 weeks

Reference: [7.5.2.80]
[133] [B]

Reference: [7.6.1.84]
[134] [B]

Reference: [7.6.2.90]
[135] [D]

Reference: [8.3.1.28]
[136] [B]

Reference: [8.3.1.35]
[137] Decay

Reference: [8.3.2.42]
[138] [B]

Reference: [8.4.1.44]
[139] [C]

Reference: [8.4.1.50]
[140] 3

Reference: [8.4.2.55]
[141] [D]

Reference: [8.5.1.63]
[142] [B]

Reference: [8.5.1.68]
[143] log4 3  log 4 x  3 log4 y

Reference: [8.5.2.73]
[144] [A]

Reference: [8.6.1.76]
[145] –0.4395

Reference: [8.6.2.80]
[146] [A]

Reference: [8.6.2.84]
[147] x = –6.425

Reference: [9.1.1.4]
[148] [A]

Reference: [9.1.2.10]
1
[149] z      xy
200

Reference: [9.1.2.13]
[150] [D]

Reference: [9.4.1.28]
[151] [A]

Reference: [9.4.1.36]
x 1
[152]
( x  3)(2 x  3)

Reference: [9.4.2.44]
[153] [B]

Reference: [9.5.1.47]
2
[154]
x4

Reference: [9.5.1.48]
[155] [C]

Reference: [9.5.2.53]
[156] [B]

Reference: [9.5.2.56]
2( x  3)
[157]
15

Reference: [9.6.1.63]
[158] [A]

Reference: [9.6.1.68]
[159] It is not.

Reference: [9.6.2.73]
[160] [A]

Reference: [10.1.1.1]
[161] [D]

Reference: [10.2.1.10]
[162] [A]

Reference: [10.2.1.18]
[163] Directrix: x = 1
Focus: (–1, 0)

Reference: [10.2.2.24]
1 2
[164] Answers may vary. Sample answer: y        x  40
40

Reference: [10.3.1.27]
[165]                  y
10

–10                    10 x

–10

Reference: [10.3.2.35]
900
[166] x 2  y 2 =


Reference: [10.4.1.38]
[167] [C]

Reference: [10.4.1.43]
y
[168]
6

–6 –4          4   6   x

–6

Reference: [10.4.2.46]
x2        y2
[169]        +       = 1
1600      484

Reference: [10.5.1.48]
[170] [A]

Reference: [10.5.1.53]
x2 y2
[171]        1
4 60

Reference: [10.6.1.61]
[172] [D]

Reference: [10.6.1.68]

[173]
x2

b g
y2
2

1
9       16

Reference: [10.6.2.74]
[174] [D]

Reference: [10.6.2.80]
[175] Parabola

Reference: [10.7.1.86]
[176] [D]

Reference: [10.7.1.87]
[177] (  2 ,  1 )
Reference: [10.7.2.88]
[178] [D]

Reference: [11.1.1.1]
[179] –4, –2, 6, 20

Reference: [11.1.1.2]
[180] [A]

Reference: [11.1.2.6]

a f
[181]  3i  1
i 1

Reference: [11.2.1.11]
5
[182]
2

Reference: [11.2.1.16]
[183] [B]

Reference: [11.2.1.22]
1    1
[184] an  n 
6    3

Reference: [11.2.1.29]
[185] 430

Reference: [11.2.2.33]
[186] [B]

Reference: [11.2.2.34]
[187] 273 ft

Reference: [11.3.1.37]
[188] [A]

Reference: [11.3.1.45]
[189] –4

Reference: [11.3.1.52]

[190] an  48 
FI
GJ
2
n 1

HK3

Reference: [11.3.2.59]
[191] [C]
Reference: [12.1.1.3]
[192] 96

Reference: [12.1.1.5]
[193] [D]

Reference: [12.1.2.9]
[194] [D]

Reference: [12.1.2.12]
[195] 151,200

Reference: [12.2.1.20]
[196] [C]

Reference: [12.2.1.25]
[197] 1365

Reference: [12.2.2.29]
[198] [A]

Reference: [12.2.2.33]
[199] A4  8 A3 B  24 A2 B2  32 AB3  16B4

Reference: [12.3.1.39]
36 9
[200]    
52 13

Reference: [12.3.1.44]
[201] [C]

Reference: [12.3.2.52]

[202]
8

Department of Education Core 40 Website

http://doe.state.in.us/core40eca/welcome.html

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