Name: 
 

Precalc Practice Semester Test


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
How many 5-digit numbers can be made with the numbers 1, 2 and 3?
a.
243
c.
125
b.
15
d.
32
 

 2. 
How many 3-digit numbers can be made with the numbers 1, 2, 3 and 4?
a.
64
c.
81
b.
12
d.
27
 

 3. 
A coin is tossed 3 times. How many different outcomes are possible?
a.
8
c.
9
b.
6
d.
16
 

 4. 
A six-sided die is tossed 3 times. How many different outcomes are possible?
a.
216
c.
729
b.
18
d.
1296
 

 5. 
A pizzeria has six choices of toppings: pepperoni, sausage, mushrooms, onions, peppers, and extra cheese. How many different pizzas can be ordered with 6 toppings?
a.
1
c.
6
b.
720
d.
36
 

 6. 
A pizzeria has seven choices of toppings: pepperoni, sausage, ham, mushrooms, onions, peppers, and extra cheese. How many different pizzas can be ordered with 4 toppings?
a.
35
c.
4
b.
840
d.
28
 

 7. 
How many 10-digit numbers can be made with the numbers 1, 2 and 3?
a.
310
c.
mc007-1.jpg
b.
103
d.
mc007-2.jpg
 

 8. 
How many 27-digit numbers can be made with the numbers 1, 2, 3 and 4?
a.
427
c.
mc008-1.jpg
b.
274
d.
mc008-2.jpg
 

 9. 
A coin is tossed 46 times. How many different outcomes are possible?
a.
246
c.
mc009-1.jpg
b.
462
d.
mc009-2.jpg
 

 10. 
A six-sided die is tossed 40 times. How many different outcomes are possible?
a.
640
c.
mc010-1.jpg
b.
406
d.
mc010-2.jpg
 

 11. 
How many 10-digit numbers can be made with the numbers 1 through 9?
a.
910
c.
mc011-1.jpg
b.
109
d.
mc011-2.jpg
 

 12. 
How many 16-character “words” can be made with the letters A, B, C, D, E, F, G and H?
a.
816
c.
mc012-1.jpg
b.
168
d.
mc012-2.jpg
 

 13. 
How many functions are there from a 3 element set to a 6 element set?
a.
216
c.
18
b.
729
d.
36
 

 14. 
How many functions are there from a 3 element set to a 7 element set?
a.
343
c.
21
b.
2,187
d.
49
 

 15. 
How many functions are there from a 6 element set to a 6 element set?
a.
46,656
c.
36
b.
279,936
d.
7,776
 

 16. 
Of all the functions from a 3 element set to a 7 element set, how many are one-to-one?
a.
210
c.
133
b.
343
d.
49
 

 17. 
Of all the functions from a 7 element set to a 7 element set, how many are one-to-one?
a.
5,040
c.
818,503
b.
823,543
d.
117,649
 

 18. 
Of all the functions from a 5 element set to a 5 element set, how many are not one-to-one?
a.
120
c.
3,005
b.
3,125
d.
625
 

 19. 
Of all the functions from a 8 element set to a 7 element set, how many are not one-to-one?
a.
5,764,801
c.
4,941,258
b.
0
d.
823,543
 
 
Simplify.
 

 20. 
mc020-1.jpg
a.
12
b.
24
c.
4
d.
2
 

 21. 
mc021-1.jpg
a.
10
b.
604,800
c.
3,628,800
d.
120
 

 22. 
9!
a.
362,880
c.
40,320
b.
3,628,800
d.
181,440
 

 23. 
mc023-1.jpg
a.
6
c.
720
b.
7
d.
120
 

 24. 
mc024-1.jpg
a.
56
b.
8
c.
1
d.
6,720
 

 25. 
mc025-1.jpg
a.
330
b.
7,920
c.
1
d.
11
 

 26. 
mc026-1.jpg
a.
8
b.
7
c.
1
d.
36
 

 27. 
How many 7-digit numbers have all unique digits?
a.
604,800
c.
6
b.
5,040
d.
9,395,200
 

 28. 
How many 3-digit numbers have repeated digits?
a.
720
c.
5,040
b.
6
d.
280
 

 29. 
How many different anagrams can be created from the letters M, N, N, N, N, N, O, P, Q, R, S?
a.
332,640
c.
7,983,360
b.
39,916,800
d.
39,916,680
 

 30. 
In how many ways can 3 singers be selected from 5 who came to an audition?
a.
1
b.
10
c.
5
d.
60
 

 31. 
You own 6 hats and are taking 4 on vacation. In how many ways can you choose 4 hats from the 6?
a.
360
b.
720
c.
1
d.
15
 

 32. 
9 students volunteer for a committee. How many different 7-person committees can be chosen?
a.
181,440
b.
362,880
c.
1
d.
36
 

 33. 
In how many ways can 12 basketball players be listed in a program?
a.
479,001,600
b.
1
c.
665,280
d.
12
 

 34. 
Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny?
a.
24
b.
720
c.
14
d.
696
 

 35. 
In how many different orders can you line up 8 cards on a shelf?
a.
8
b.
1
c.
1,680
d.
40,320
 

 36. 
There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?
a.
1 way
c.
3,628,800 ways
b.
90 ways
d.
45 ways
 

 37. 
There are 6 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0¸ 1¸ 2¸ 3¸ or 4 judges. In how many different ways can a person vote?
a.
57
b.
5
c.
15
d.
6
 

 38. 
6 marbles are to be selected from a group of 8. In how many ways can this be done?
a.
28
b.
1
c.
40,320
d.
20,160
 

 39. 
Find the coefficient of the mc039-1.jpg term in the expansion of mc039-2.jpg.
a.
–250
c.
–25
b.
10
d.
1,250
 

 40. 
What term shares its coefficient with the mc040-1.jpg term in the expansion of mc040-2.jpg?
a.
mc040-3.jpg
c.
mc040-5.jpg
b.
mc040-4.jpg
d.
mc040-6.jpg
 

 41. 
Do any terms share their coefficient with the mc041-1.jpg term in the expansion of mc041-2.jpg?
a.
yes
b.
no
 
 
Use the binomial theorem to expand.
 

 42. 
mc042-1.jpg
a.
mc042-2.jpg
b.
mc042-3.jpg
c.
mc042-4.jpg
d.
mc042-5.jpg
 

 43. 
mc043-1.jpg
a.
mc043-2.jpg
b.
mc043-3.jpg
c.
mc043-4.jpg
d.
mc043-5.jpg
 

 44. 
mc044-1.jpg
a.
mc044-2.jpg
b.
mc044-3.jpg
c.
mc044-4.jpg
d.
mc044-5.jpg
 

 45. 
A manufacturer of shipping boxes has a box shaped like a cube. The side length is
5a + 4b. What is the volume of the box in terms of a and b?
a.
mc045-1.jpg
c.
mc045-3.jpg
b.
mc045-2.jpg
d.
mc045-4.jpg
 
 
Find each element in Pascal’s triangle.
 

 46. 
mc046-1.jpg
a.
20
c.
15
b.
10
d.
35
 

 47. 
mc047-1.jpg
a.
1
c.
45
b.
10
d.
11
 

 48. 
mc048-1.jpg
a.
1
c.
28
b.
8
d.
36
 
 
Find the value of m.
 

 49. 
mc049-1.jpg
a.
10
c.
12
b.
11
d.
15
 

 50. 
mc050-1.jpg
a.
17
c.
19
b.
18
d.
14
 
 
Write a recursive definition for a function that fits each table.
 

 51. 

Input
Output
0
–3
1
–8
2
–13
3
–18
4
–23
a.
mc051-1.jpg
b.
mc051-2.jpg
c.
mc051-3.jpg
d.
mc051-4.jpg
 

 52. 

Input
Output
0
–9
1
–5
2
3
3
15
4
31
a.
mc052-1.jpg
b.
mc052-2.jpg
c.
mc052-3.jpg
d.
mc052-4.jpg
 

 53. 

Input
Output
0
2
1
6
2
12
3
20
4
30
a.
mc053-1.jpg
b.
mc053-2.jpg
c.
mc053-3.jpg
d.
mc053-4.jpg
 
 
Write a recursive definition for a function that fits each table. Use that definition to find a closed form definition that fits each table.
 

 54. 

Input
Output
0
–2
1
–10
2
–24
3
–44
4
–70
a.
mc054-1.jpg
b.
mc054-2.jpg
c.
mc054-3.jpg
d.
mc054-4.jpg
 

 55. 

Input
Output
0
–9
1
–4
2
1
3
6
4
11
a.
mc055-1.jpg
b.
mc055-2.jpg
c.
mc055-3.jpg
d.
mc055-4.jpg
 

 56. 
Jeff deposits $700 in a savings account every year, and leaves it there. Each year the account’s balance grows by 5% of its previous value, plus the $700 of Jeff’s new deposit. Write a recursive definition for the balance of Jeff’s savings account after n years, and use the definition to calculate the balance after 5 years.
a.
$4,761.34
c.
$3,867.94
b.
$5,699.41
d.
$4,061.34
 

 57. 
Suppose you have a credit card balance of $3000 at 18% APR calculated monthly. If you pay $100 per month, how much do you owe at the end of 2 years?
a.
$1425.16
c.
$399.82
b.
$1346.53
d.
$1103.52
 

 58. 
Suppose you have a credit card balance of $2000 and can afford to pay $50 per month. How much lower would your balance be with a rate of 12% APR compared with a rate of 16% APR at the end of 3 years?
a.
$223.13
c.
$930.83
b.
$707.69
d.
$80.00
 
 
Find a closed-form and a recursive function that fits the table below.
 

 59. 

Input
Output
0
–5
1
–8
2
–11
3
–14
4
–17
5
–20
a.
mc059-1.jpg
mc059-2.jpg
c.
mc059-5.jpg
mc059-6.jpg
b.
mc059-3.jpg
mc059-4.jpg
d.
mc059-7.jpg
mc059-8.jpg
 

 60. 

Input
Output
0
–2
1
0
2
6
3
16
4
30
5
48
a.
mc060-1.jpg
mc060-2.jpg
c.
mc060-5.jpg
mc060-6.jpg
b.
mc060-3.jpg
mc060-4.jpg
d.
mc060-7.jpg
mc060-8.jpg
 

 61. 

Input
Output
0
0
1
–9
2
–26
3
–51
4
–84
5
–125
a.
mc061-1.jpg
mc061-2.jpg
b.
mc061-3.jpg
mc061-4.jpg
c.
mc061-5.jpg
mc061-6.jpg
d.
mc061-7.jpg
mc061-8.jpg
 

 62. 

Input
Output
0
–9
1
–12
2
–11
3
–6
4
3
5
16
a.
mc062-1.jpg
mc062-2.jpg
b.
mc062-3.jpg
mc062-4.jpg
c.
mc062-5.jpg
mc062-6.jpg
d.
mc062-7.jpg
mc062-8.jpg
 

 63. 

Input
Output
0
2
1
10
2
50
3
250
4
1250
5
6250
a.
mc063-1.jpg
mc063-2.jpg
c.
mc063-5.jpg
mc063-6.jpg
b.
mc063-3.jpg
mc063-4.jpg
d.
mc063-7.jpg
mc063-8.jpg
 
 
Find the degree of the function by making a difference table.
 

 64. 
InputOutput
0
–3
1
–11
2
–241
3
–2,247
4
–11,447
5
–41,083
6
–117,621
7
–287,591
a.
6
c.
5
b.
7
d.
8
 
 
Find a function that agrees with the difference table.
 

 65. 

Input
Output
mc065-1.jpg
mc065-2.jpg
0
–4
4
8
1
  
8
2
  
8
3
  
8
4
   
5
   
a.
mc065-3.jpg
c.
mc065-5.jpg
b.
mc065-4.jpg
d.
mc065-6.jpg
 

 66. 

Input
Output
mc066-1.jpg
mc066-2.jpg
0
–15
–17
–6
1
  
–6
2
  
–6
3
  
–6
4
   
5
   
a.
mc066-3.jpg
c.
mc066-5.jpg
b.
mc066-4.jpg
d.
mc066-6.jpg
 

 67. 
Find mc067-1.jpg, mc067-2.jpg, mc067-3.jpg, and mc067-4.jpg.
a.
1, 4, 6, 4
c.
1, 5, 10, 10
b.
4, 6, 4, 1
d.
5, 10, 10, 5
 
 
Use the first row of the difference table to find each value.
 

 68. 

x
f(x)
mc068-1.jpg
mc068-2.jpg
mc068-3.jpg
mc068-4.jpg
mc068-5.jpg
0
1
3
–3
–5
–1
0

Find f(13).
a.
–2339
c.
–3051
b.
–5473
d.
–7812
 

 69. 

x
f(x)
mc069-1.jpg
mc069-2.jpg
mc069-3.jpg
mc069-4.jpg
mc069-5.jpg
0
2
3
–4
5
0
0

Find f(11).
a.
640
c.
874
b.
1177
d.
1817
 

 70. 

x
f(x)
mc070-1.jpg
mc070-2.jpg
mc070-3.jpg
mc070-4.jpg
mc070-5.jpg
0
3
1
4
0
0
0

Find f(10).
a.
193
c.
234
b.
555
d.
748
 
 
Find the degree and leading coefficient of the polynomial represented by the table.
 

 71. 

Input
Output
0
2
1
4
2
–26
3
–298
4
–1430
5
–4688
6
–12226
7
–27326
a.
5, –2
c.
4, –2
b.
5, 15
d.
4, 15
 

 72. 

Input
Output
0
–3
1
–3
2
–83
3
–663
4
–2859
5
–8843
6
–22203
7
–48303
a.
mc072-1.jpg
c.
mc072-3.jpg
b.
mc072-2.jpg
d.
mc072-4.jpg
 

 73. 

Input
Output
0
2
1
1
2
–26
3
–145
4
–470
5
–1163
6
–2434
7
–4541
a.
mc073-1.jpg
c.
mc073-3.jpg
b.
mc073-2.jpg
d.
mc073-4.jpg
 

 74. 

Input
Output
0
–3
1
–6
2
–17
3
–48
4
–111
5
–218
6
–381
7
–612
a.
mc074-1.jpg
c.
mc074-3.jpg
b.
mc074-2.jpg
d.
mc074-4.jpg
 
 
Find a closed form for each sum in terms of n.
 

 75. 
mc075-1.jpg
a.
mc075-2.jpgn2 mc075-3.jpgn
c.
mc075-4.jpgn2 mc075-5.jpgn
b.
n2 – n
d.
mc075-6.jpgn2 + n
 

 76. 
mc076-1.jpg
a.
mc076-2.jpgn3 mc076-3.jpgn2 mc076-4.jpgn
c.
mc076-8.jpgn3 mc076-9.jpgn2 mc076-10.jpgn
b.
mc076-5.jpgn3 mc076-6.jpgn2 mc076-7.jpgn
d.
mc076-11.jpgn3 mc076-12.jpgn2 mc076-13.jpgn
 

 77. 
mc077-1.jpg
a.
mc077-2.jpgn4 mc077-3.jpgn3 mc077-4.jpgn2
c.
mc077-7.jpgn4 mc077-8.jpgn3 mc077-9.jpgn2
b.
n4 mc077-5.jpgn3 mc077-6.jpgn2
d.
n4 mc077-10.jpgn3 mc077-11.jpgn2
 

 78. 
mc078-1.jpg
a.
mc078-2.jpgn5 mc078-3.jpgn4 mc078-4.jpgn3 mc078-5.jpgn
c.
mc078-10.jpgn5 mc078-11.jpgn4 mc078-12.jpgn3 mc078-13.jpgn
b.
mc078-6.jpgn5 mc078-7.jpgn4 mc078-8.jpgn3 mc078-9.jpgn
d.
mc078-14.jpgn5 mc078-15.jpgn4 mc078-16.jpgn3 mc078-17.jpgn
 

 79. 
mc079-1.jpg
mc079-2.jpg
Find mc079-3.jpg.
a.
256
c.
128
b.
1024
d.
2048
 

 80. 
mc080-1.jpg
mc080-2.jpg
Find K.
a.
–7
c.
–9
b.
14
d.
–5
 

 81. 
mc081-1.jpg
Find mc081-2.jpg.
a.
–192
c.
96
b.
384
d.
–768
 
 
Find a closed form of the function.
 

 82. 
mc082-1.jpg
a.
mc082-2.jpg
c.
mc082-4.jpg
b.
mc082-3.jpg
d.
mc082-5.jpg
 

 83. 
mc083-1.jpg
a.
mc083-2.jpg
c.
mc083-4.jpg
b.
mc083-3.jpg
d.
mc083-5.jpg
 
 
The function in the table below is represented by a two-term recurrence. Find a closed form of f(n).
 

 84. 

n
f(n)
0
2
1
–2
2
–22
3
–98
4
–358
5
–1202
a.
mc084-1.jpg
c.
mc084-3.jpg
b.
mc084-2.jpg
d.
mc084-4.jpg
 

 85. 
The function mc085-1.jpg is satisfied by any function in the form mc085-2.jpg. Two terms of the sequence are –6 and –8. Find A and B.
a.
mc085-3.jpg, mc085-4.jpg
c.
mc085-7.jpg, mc085-8.jpg
b.
mc085-5.jpg, mc085-6.jpg
d.
mc085-9.jpg, mc085-10.jpg
 

 86. 
The function mc086-1.jpg is satisfied by any function in the form mc086-2.jpg. Two terms of the sequence are –3 and –2. Find the next term in the sequence.
a.
8
c.
27
b.
–28
d.
–3
 

 87. 
Suppose you buy a car. The car costs $6000, and the financing is 6% APR, divided into 0.5% every month. A car payment is due every month for 24 months. Find the car payment to the nearest penny.
a.
$265.92
c.
$22.16
b.
$39.84
d.
$478.07
 

 88. 
Suppose you buy a car. The car costs $11000, and the financing is 5% APR, divided into 0.4% every month. A car payment is due every month for 24 months. Find the total car payments made to the nearest penny.
a.
$11582.05
c.
$5791.02
b.
$482.59
d.
$582.05
 
 
Sketch a graph of all points in the plane satisfying the equation.
 

 89. 
mc089-1.jpg
a.
mc089-2.jpg
c.
mc089-4.jpg
b.
mc089-3.jpg
d.
mc089-5.jpg
 

 90. 
Find an equation characterizing the points that are 5 units away from (3, 6).
a.
mc090-1.jpg
c.
mc090-3.jpg
b.
mc090-2.jpg
d.
mc090-4.jpg
 

 91. 
Find an equation for the set of points that are equidistant from (–2, 5) and (8, 7).
a.
mc091-1.jpg
c.
mc091-3.jpg
b.
mc091-2.jpg
d.
mc091-4.jpg
 

 92. 
Find an equation for the set of points that are equidistant from the origin and the line y = –3.
a.
y = mc092-1.jpgx2 mc092-2.jpg
c.
y = mc092-4.jpgx2 mc092-5.jpg
b.
y = –6x2 mc092-3.jpg
d.
y = –6x2 mc092-6.jpg
 

 93. 
Sketch a graph of the set of points that are equidistant from (5, –3) and (7, 9).
a.
mc093-1.jpg
c.
mc093-3.jpg
b.
mc093-2.jpg
d.
mc093-4.jpg
 

 94. 
ABCD is a rectangle with coordinates A(–8, –2), B(–2, –2), C(–2, 6), and D(–8, 6). Find the length of the diagonals mc094-1.jpg and mc094-2.jpg to the nearest tenth.
a.
10 and 10
c.
8.4 and 8.4
b.
6.6 and 6.6
d.
3.7 and 3.7
 

 95. 
mc095-1.jpg has coordinates A(9, –4), B(–3, 0), and C(8, 8). Find the length of the midsegment joining side mc095-2.jpg and mc095-3.jpg to the nearest tenth.
a.
6.3
c.
4.2
b.
12.6
d.
3.2
 

 96. 
ABCD is a trapezoid with coordinates A(7, 2), B(–3, –3), C(6, –6), and D(0, –9). Find the length of the midsegment joining the mc096-1.jpg and mc096-2.jpg to the nearest tenth.
a.
8.9
c.
11.2
b.
17.9
d.
6.7
 

 97. 
ABCD is a rhombus with coordinates A(–7, 6), B(–3, 15), C(6, 19), and D(2, 10). The slopes of the diagonals to the nearest tenth.
a.
1, –1
c.
2.3, 1
b.
–1, 0.4
d.
2.3, 0.4
 

 98. 
ABCD has coordinates A(–3, 7), B(2, 11), C(10, 17), and D(5, 13). Is ABCD a parallelogram?
a.
yes
b.
no
 

 99. 
Find the center for the circle with equation mc099-1.jpg.
a.
(8, –3)
c.
(–3, 8)
b.
(–8, 3)
d.
(3, –8)
 

 100. 
Find the radius for the circle with equation mc100-1.jpg.
a.
8
c.
16
b.
64
d.
3
 

 101. 
Sketch a graph of an ellipse with foci F1(5, 0) and F2(–5, 0) and total distance 14.
a.
mc101-1.jpg
c.
mc101-3.jpg
b.
mc101-2.jpg
d.
mc101-4.jpg
 

 102. 
Sketch a graph of an hyperbola with foci F1(7, 0) and F2(–7, 0) and total distance 6.
a.
mc102-1.jpg
c.
mc102-3.jpg
b.
mc102-2.jpg
d.
mc102-4.jpg
 

 103. 
Find the foci of the ellipse with the equation mc103-1.jpg.
a.
(0, mc103-2.jpg), (0, mc103-3.jpgmc103-4.jpg)
c.
(mc103-8.jpg, 0), (mc103-9.jpgmc103-10.jpg, 0)
b.
(0, mc103-5.jpg), (0, mc103-6.jpgmc103-7.jpg)
d.
(mc103-11.jpg, 0), (mc103-12.jpgmc103-13.jpg, 0)
 

 104. 
Find the length of the major axis of the ellipse with the equation mc104-1.jpg.
a.
10
c.
2
b.
4
d.
5
 

 105. 
Find the focus and the directrix of the graph of mc105-1.jpg.
a.
focus (0, –6), directrix at y = 6
c.
focus (–6, 0), directrix at y = –6
b.
focus (–6, 0), directrix at y = 6
d.
focus (0, –6), directrix at y = –6
 

 106. 
Sketch a graph of the hyperbola with equation mc106-1.jpg.
a.
mc106-2.jpg
c.
mc106-4.jpg
b.
mc106-3.jpg
d.
mc106-5.jpg
 

 107. 
Sketch a graph of the ellipse with the equation mc107-1.jpg.
a.
mc107-2.jpg
c.
mc107-4.jpg
b.
mc107-3.jpg
d.
mc107-5.jpg
 

 108. 
What is the center of the ellipse with the equation mc108-1.jpg?
a.
(3, –1)
c.
(–1, 3)
b.
(–3, 1)
d.
(1, –3)
 

 109. 
Sketch a graph of the hyperbola with the equation mc109-1.jpg.
a.
mc109-2.jpg
c.
mc109-4.jpg
b.
mc109-3.jpg
d.
mc109-5.jpg
 

 110. 
What is the center of the hyperbola with the equation mc110-1.jpg?
a.
(2, –1)
c.
(–1, 2)
b.
(–2, 1)
d.
(1, –2)
 

 111. 
An ellipse has center (3, 3) and one focus (5, 3). What is the other focus?
a.
(1, 3)
c.
(3, 3)
b.
(7, 3)
d.
(3, 5)
 
 
Find the coordinates of R so that PQRS is a parallelogram.
 

 112. 
P(5, 7), Q(0, 8), S(9, 7)
a.
(4, 8)
c.
(14, 22)
b.
(–4, 8)
d.
(–14, –6)
 

 113. 
What is the total number of possible outcomes when you roll a die 4 times?
a.
1296
c.
24
b.
10
d.
6
 

 114. 
A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single spin?
a.
mc114-1.jpg
b.
mc114-2.jpg
c.
mc114-3.jpg
d.
mc114-4.jpg
 

 115. 
A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
a.
mc115-1.jpg
b.
mc115-2.jpg
c.
mc115-3.jpg
d.
mc115-4.jpg
 

 116. 
A coin is tossed 4 times. What is the probability of getting tails 2 times in a row?
a.
mc116-1.jpg
b.
mc116-2.jpg
c.
mc116-3.jpg
d.
mc116-4.jpg
 

 117. 
What is the probability of rolling two dice and getting a sum of at least 9?
a.
mc117-1.jpg
c.
mc117-3.jpg
b.
mc117-2.jpg
d.
mc117-4.jpg
 

 118. 
What is the probability of rolling 4 dice and getting a sum of 21?
a.
mc118-1.jpg
c.
mc118-3.jpg
b.
mc118-2.jpg
d.
mc118-4.jpg
 
 
Find the expected value of each situation.
 

 119. 
The number of heads when you toss 6 coins
a.
3
c.
3.167
b.
6
d.
2.833
 

 120. 
The value of rolling 3 standard 6-sided dice
a.
10.5
c.
11.5
b.
21
d.
9.833
 

 121. 
A spinner has 12 equal sections labeled 1 through 12. You spin the spinner 6 times.
a.
39
c.
39.333
b.
78
d.
38
 

 122. 
A ten-sided die is labeled 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. You roll the die 3 times.
a.
49.5
c.
50.167
b.
99
d.
48.5
 

 123. 
An eight-sided die is labeled 9, 4, 8, 6, 3, 3, 4, and 9. You roll the die 7 times.
a.
40.25
c.
40.679
b.
80.5
d.
39.393
 

 124. 
Find the sample space of a pick-5 lottery with a bonus ball chosen from two sets of 55 balls.
a.
191,331,855
c.
28,989,675
b.
162,342,180
d.
220,321,530
 

 125. 
One lottery is pick-4 lottery with a bonus ball chosen from two sets of 60 balls. Another lottery is a pick-5 lottery with 60 balls. What is the difference in sample space between the two lotteries?
a.
23,796,588
c.
5,461,512
b.
29,258,100
d.
34,719,612
 

 126. 
A pick-6 lottery with 70 balls has the following frequencies and payouts. Find the expected value of a $1 ticket.
Ticket Type
Frequency
Payout
0 matches
131115985
$0
1 matches
72618084
$0
2 matches
13753425
$1
3 matches
1094800
$50
4 matches
36225
$200
5 matches
420
$2,000
6 matches
1
$5,000,000
a.
$0.37
c.
$0.33
b.
$0.35
d.
$0.12
 

 127. 
A $1 scratch ticket game has the following payout frequencies. Find the expected value of each ticket.
Frequency
Payout
959081
$0
156000
$1
60000
$5
19920
$10
4000
$25
400
$50
537
$100
61
$500
1
$2,000
a.
$0.72
c.
$0.7
b.
$0.74
d.
$0.68
 
 
Find the probability of each event.
 

 128. 
65 tails in 140 coin flips
a.
4.72%
c.
1.13%
b.
0.04%
d.
3.08%
 



 
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