Evaluate the expression.
75)
4C2·4C1
16C13
75)
A)
9
14
B)
3
70
C)
1
70
D)
3
35
D)
Solve the problem.
76)
The bar graph below shows a company’s yearly profits from 1991 to 1999. Let an represent the
company’s profit, in millions, in year n, where n=1 corresponds to 1991, n = 2 corresponds to 1992,
and so on.
Find
7
i =2
ai
76)
A)
$414.1 million
B)
$128.5 million
C)
$400.7 million
D)
$438.3 million
D)
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
77)
4, 12 , 20 , 28 , 36 , . . .
77)
A)
an=8n – 4; a20 =156
B)
an=4n –8; a20 =72
C)
an=8n –1; a20 =159
D)
an=4n –1; a20 =79
D)
Solve the problem.
78)
As part of her retirement savings plan, Patricia deposited $300 in a bank account during her first
year in the workforce. During each subsequent year, she deposited $35 more than the previous
year. Find how much she deposited during her twentieth year in the workforce. Find the total
amount deposited in the twenty years.
78)
A)
$965; $25,300
B)
$1000; $13,000
C)
$965; $12,650
D)
$1000; $26,000
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
79)
(3x + 2)3
79)
A)
27x3+ 54x2+ 54x + 8
B)
9x2+ 12x + 4
C)
9x6+ 6x3+ 64
D)
27x3+ 54x2+ 36x + 8
Find the probability.
80)
A lottery game has balls numbered 1 through 21. What is the probability of selecting an even
numbered ball or a 11?
80)
A)
10
21
B)
10
11
C)
11
21
D)
3
7
Write the first three terms in the binomial expansion, expressing the result in simplified form.
81)
(x2+ 6 )9
81)
A)
x18 + 54 x16 + 1296 x14
B)
x18 + 60 x16 + 2592 x14
C)
x18 + 54 x16 + 2592 x14
D)
x18 + 60 x16 + 1296 x14
22
Express the repeating decimal as a fraction in lowest terms.
82)
0.6=6
10 +6
100 +6
1,000 +6
10,000 …
82)
A)
333
500
B)
33
50
C)
2
3
D)
2
33
Write a formula for the general term (the nth term) of the geometric sequence.
83)
3, 1, 1
3, 1
9, 1
27 , . . .
83)
A)
an=31
3
n + 1
B)
an=31
9
n – 1
C)
an=31
3
n
D)
an=31
3
n – 1
Find the indicated sum.
84)
4
k = 1
(–1)k(k + 3)
84)
A)
–22
B)
14
C)
22
D)
2
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
85)
(x + 8y)5
85)
A)
x5+ 40x4y + 1280x3y2+ 10,240x2y3+ 20,480xy4+ 32,768y5
B)
x5+ 40x4y + 1280x3y2+ 10,240x2y3+ 20,480xy4+ 8y5
C)
x5+ 40x4y + 640x3y2+ 5120x2y3+ 20,480xy4+ 32,768
D)
x5+ 40x4y + 640x3y2+ 5120x2y3+ 20,480xy4+ 32,768y5
23
Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of
summation.
86)
3
4+4
5+5
6+6
7+ . . . +20
21
86)
A)
20
k =4
k + 1
k
B)
20
k =3
k
k + 1
C)
20
k =3
k + 1
k
D)
20
k =4
k
k + 1
Find the probability.
87)
A card is drawn from a deck of 52 cards. What is the probability that it is a diamond or that it is
greater than 3 and less than 10?
87)
A)
7
13
B)
17
26
C)
31
52
D)
37
52
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
88)
Find a11 when a1=6, r =3.
88)
A)
36
B)
354,298
C)
354,294
D)
1,062,882
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
89)
a1=5, d = – 0.7
89)
A)
an= – 0.7n + 5; a20 = – 9
B)
an= – 0.7n + 5.7; a20 = – 8.3
C)
an=5n – 5.7; a20 =94.3
D)
an=5n – 0.7; a20 =99.3
Find the probability.
90)
One digit from the number 1,898,778 is written on each of seven cards. What is the probability of
drawing a card that shows 1 or 7?
90)
A)
2
7
B)
3
7
C)
1
7
D)
8
7
Evaluate the factorial expression.
91)
12!
6!6!
91)
A)
1848
B)
924
C)
665,280
D)
462
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
92)
1
3+1
2+3
5+ . . . +5
6
92)
A)
10
i =2
i
i + 1
B)
10
i = 1
i
i +2
C)
10
i = 0
i
i +2
D)
n
i = 1
i
i +2
Find the indicated sum.
93)
Find the sum of the even integers between 21 and 49.
93)
A)
455
B)
560
C)
525
D)
490
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
94)
(3x + 5)4
94)
A)
81x3+ 540x2+ 1350x + 1500
B)
81x4+ 540x3+ 1350x2+ 1500x + 625
C)
81x4+625x4
D)
405x4+ 2700 x3+ 1350x2+ 7500x + 625
Find the probability.
95)
Two 6–sided dice are rolled. What is the probability that the sum of the two numbers on the dice
will be greater than 9?
95)
A)
1
4
B)
6
C)
1
6
D)
1
12
Find the sum of the infinite geometric series, if it exists.
96)
144 + 24 + 4 +2
3+ . . .
96)
A)
172
B)
864
5
C)
–144
5
D)
does not exist
Solve the problem.
97)
A combination lock has 40 numbers on it. How many different 3–digit lock combinations are
possible if no digit can be repeated?
97)
A)
9880
B)
19,760
C)
59,280
D)
1560
Write the first five terms of the geometric sequence.
98)
a1=7; r =4
98)
A)
7, 28, 112, 448, 1792
B)
28, 112, 448, 1792, 7168
C)
4, 28, 196, 1372, 9604
D)
7, 11, 15, 19, 23
Find the probability.
99)
Give the probability that the roll of a die will show a number less than 6.
99)
A)
5
6
B)
0
C)
1
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
100)
a + ar + ar2+ . . . + ar14
100)
A)
14
i = 1
(ar)i
B)
15
i = 1
ari – 1
C)
14
i = 1
ari
D)
14
i = 1
(ar)i – 1
Solve the problem.
101)
Ron finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how
many ways can he make his selection? How many ways can he make his selection if he decides that
one of the books is a must?
101)
A)
7560; 840
B)
126; 70
C)
3024; 1680
D)
15,120; 1680
Solve the problem. Round to the nearest dollar if needed.
102)
Looking ahead to retirement, you sign up for automatic savings in a fixed–income 401K plan that
pays 7% per year compounded annually. You plan to invest $3000 at the end of each year for the
next 20 years. How much will your account have in it at the end of 20 years?
102)
A)
$122,986
B)
$124,284
C)
$121,443
D)
$124,756
Find the probability.
103)
A bag contains 5 blue marbles, 10 green marbles, and 8 red marbles. One marble is drawn from the
bag. What is the probability that the marble drawn is not blue?
103)
A)
18
23
B)
5
23
C)
18
5
D)
5
18
Solve the problem. Round to the nearest hundredth of a percent if needed.
104)
Use of the internet for shopping is increasing dramatically, but still is somewhat age dependent.
When a popular web site that sells books asked the age of users who bought products from them
over the internet, they obtained the following data. What is the probability that a buyer on this web
site is aged 60–69?
Age Group Number
10–19 1951
20–29 3611
30–39 2982
40–49 656
50–59 324
60–69 296
70–79 78
104)
A)
3.30%
B)
2.99%
C)
3.08%
D)
3.27%
Write the first five terms of the geometric sequence.
105)
an=3an–1; a1= – 5
105)
A)
–5, –15, –45, –135, –405
B)
–5, –2, 1, 4, 7
C)
–15, –45, –135, –405, –1215
D)
3, 15, –45, –135, –405
Use the formula for the sum of the first n terms of a geometric sequence to solve.
106)
Find the sum of the first 13 terms of the geometric sequence: 6, –12, 24, –48, 96, . . . .
106)
A)
16,380
B)
16,393
C)
16,384
D)
16,386
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
107)
(x2+5y)4
107)
A)
x6+20x5y +30x4y2+20x2y3+5y4
B)
x8+15x6y +150x4y2+375x2y3+625y4
C)
x8+20x6y +150x4y2+500x2y3+625y4
D)
x6+15x5y +150x4y2+375x2y3+625y4
Solve the problem.
108)
A deposit of $8000 is made in an account that earns 9% interest compounded quarterly. The balance
in the account after n quarters is given by the sequence
an=8000 1 +0.09
4
n n = 1, 2, 3, …
Find the balance in the account after 32 quarters.
108)
A)
$16,304.82
B)
$16,358.82
C)
$16,362.82
D)
$16,192.82
Find the indicated sum.
109)
5
i = 1
(–1)i – 1
(i – 1)!
109)
A)
–3
8
B)
–5
12
C)
3
8
D)
5
12
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
110)
5
i = 1
4
3·4i
110)
A)
5495
3
B)
5498
3
C)
5486
3
D)
5456
3
Solve the problem. Round to the nearest dollar if needed.
111)
Yvette invests $300 each quarter in a fixed–interest mutual fund paying annual interest of 7%
compounded quarterly. How much will her account have in it at the end of 11 years?
111)
A)
$19,636
B)
$59,243
C)
$19,765
D)
$4735
Write the first five terms of the geometric sequence.
112)
a1= – 5; r = – 4
112)
A)
–5, –20, –80, 320, –1280
B)
–5, –9, –13, –17, –21
C)
–4, 20, –80, 320, –1280
D)
–5, 20, –80, 320, –1280
Write the first four terms of the sequence whose general term is given.
113)
an=(–3)n
113)
A)
–3, 9, –27, 81
B)
3, –9, 27, –81
C)
3, –9, –27, –81
D)
–3, –9, –27, –81
Solve the problem.
114)
A restaurant offers a choice of 3 salads, 10 main courses, and 4 desserts. How many possible
choices for a meal are there (including single items)?
114)
A)
137 possible meals
B)
202 possible meals
C)
179 possible meals
D)
219 possible meals
The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the
sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
115)
an=3n –2
115)
A)
arithmetic, d =3
B)
arithmetic, d = – 2
C)
geometric, r =3
D)
neither
Solve the problem.
116)
A stack of 8 different cards are shuffled and spread out face down. If 5 cards are turned face up,
how many different 5–card combinations are possible?
116)
A)
3360
B)
336
C)
6720
D)
56
Use the formula for nCr to evaluate the expression.
117)
11C4
117)
A)
9,979,200
B)
7920
C)
330
D)
1,663,200
Write the first four terms of the sequence whose general term is given.
118)
an=(–1)n + 1(n +7)
118)
A)
8, –18, 30, –44
B)
–8, 9, –10, 11
C)
–9, 10, –11, 12
D)
8, –9, 10, –11
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
119)
a1= – 4
5, d = – 3
5
119)
A)
an= – 3
5n –4
5; a20 = – 64
5
B)
an= – 4
5n +1
5; a20 = – 79
5
C)
an= – 3
5n –1
5; a20 = – 61
5
D)
an= – 4
5n –3
5; a20 = – 83
5
Find the common difference for the arithmetic sequence.
120)
7, 11, 15, 19, . . .
120)
A)
7
B)
4
C)
3
D)
12
Find the probability.
121)
What is the probability that a card drawn from a deck of 52 cards is not a 2?
121)
A)
1
13
B)
9
10
C)
1
10
D)
12
13
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
122)
Find a8 when a1=70,000, r = – 0.1.
122)
A)
0.007
B)
–0.07
C)
–0.007
D)
0.0007
Use the formula for nPr to evaluate the expression.
123)
9P3
123)
A)
362,880
B)
120,960
C)
504
D)
60,480
Write the first five terms of the arithmetic sequence.
124)
a1=13; d = – 4
124)
A)
13, 9, 5, 1, –3
B)
9, 5, 1, –3, –7
C)
13, 9, 4, 1, –3
D)
17, 13, 9, 5, 1
Express the repeating decimal as a fraction in lowest terms.
125)
0. 77 =77
100 +77
10,000 +77
1,000,000 + ...
125)
A)
7700
999
B)
7777
10000
C)
7
9
D)
7777
999
Evaluate the expression.
126)
10C6
8C4
–43!
41!
126)
A)
–40
B)
1803
C)
–1803
D)
–1889
Express the repeating decimal as a fraction in lowest terms.
127)
0.5
127)
A)
1
20
B)
1
2
C)
50
9
D)
5
9
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
128)
(x2+ 5y)4
128)
A)
x4+ 20x3y + 150x2y2+ 500xy3+ 625y4
B)
x8+ 5x6y + 150x4y2+ 250x2y3+ 625y4
C)
x8+ 20x6y + 150x4y2+ 20x2y3+ 625y4
D)
x8+ 20x6y + 150x4y2+ 500x2y3+ 625y4
33
129)
an=an–1–2, a1=36
129)
A)
an= – 2n +34, a20 = – 6
B)
an= – 2n +38, a20 = – 2
C)
an=36n +38, a20 =758
D)
an=34n +36, a20 =716
D)
Find the probability.
130)
A spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on
an even number or a multiple of 3?
130)
A)
1
3
B)
2
3
C)
1
D)
15
D)
Solve the problem.
131)
A club elects a president, vice–president, and secretary–treasurer. How many sets of officers are
possible if there are 10 members and any member can be elected to each position? No person can
hold more than one office.
131)
A)
720
B)
360
C)
5040
D)
240
D)
Evaluate the given binomial coefficient.
132)
8
8
132)
A)
40,320
B)
1
C)
2
D)
0
D)
34
Solve the problem.
133)
How many 4–digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can
be used more than once.
133)
A)
151,200
B)
302,400
C)
5040
D)
210
The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the
sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
134)
an=5n
134)
A)
geometric, r =5
B)
geometric, r =6
C)
arithmetic, d =5
D)
neither
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
135)
(x + 2y)6
135)
A)
x6+ 12x5y + 64x4y2+ 40x3y3+ 64x2y4+ 12xy5+ 2y6
B)
x6+ 12x5y + 48x4y2+ 144x3y3+ 192x2y4+ 192xy5+ 64y6
C)
x6+ 12x5y +24x4y2+ 36x3y3+24x2y4+ 12x y5+2y6
D)
x6+ 12x5y +60x4y2+ 160x3y3+240x2y4+ 192xy5+64y6
Find the common difference for the arithmetic sequence.
136)
–7, –9, –11, –13, . . .
136)
A)
–2
B)
6
C)
–4
D)
–6
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
137)
Find a8 when a1=4000, r =1
3.
137)
A)
4000
19683
B)
12007
3
C)
4000
2187
D)
4000
6561
Solve the problem.
138)
The finite sequence whose general term is
an=0.18n2–1.08n +7.07
where n = 1, 2, 3, …, 9 models the total operating costs, in millions of dollars, for a company from
1991 through 1999.
Find
5
i = 1
ai
138)
A)
$22.88 million
B)
$30.85 million
C)
$29.05 million
D)
$24.68 million
Write the first four terms of the sequence whose general term is given.
139)
an= n – 6
139)
A)
–24, –18, –12, –6
B)
–6, –5, –4, –3
C)
1, 2, 3, 4
D)
–5, –4, –3, –2
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
140)
1, 5, 9, 13 , 17 , . . .
140)
A)
an= n +4; a20 =24
B)
an=3n –4; a20 =56
C)
an=4n –3; a20 =77
D)
an=4n + 3; a20 =83
Find the probability.
141)
A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue when one marble is drawn from the bag?
141)
A)
6
B)
2
3
C)
3
2
D)
1
3
Write the first four terms of the sequence whose general term is given.
142)
an=3n
(n +1)!
142)
A)
3
2, 3, 27
4, 81
5
B)
2
3, 3, 27
4, 5
81
C)
3
2, 3
2, 9
4, 27
20
D)
3
2, 3
2, 9
8, 27
40
Solve the problem. Round to the nearest hundredth of a percent if needed.
143)
A traffic engineer is counting the number of vehicles by type that turn into a residential area. The
table below shows the results of the counts during a four–hour period. What is the probability that
the next vehicle passing is an SUV?
Type of vehicle Number
Car 268
SUV 428
Van 66
Small truck 289
Large truck 222
Dump truck 25
Other 77
143)
A)
32.97%
B)
31.13%
C)
19.49%
D)
31.70%
Find the probability.
144)
Two 6–sided dice are rolled. What is the probability that the sum is odd and the number on one of
the dice is a 3?
144)
A)
3
36
B)
1
12
C)
1
6
D)
1
2
D)
Find the indicated sum.
145)
8
i =3
8
145)
A)
240
B)
40
C)
264
D)
48
D)
Solve the problem.
146)
A deposit of $8000 is made in an account that earns 6% interest compounded quarterly. The balance
in the account after n quarters is given by the sequence
an=8000 1 +0.06
4
n n = 1, 2, 3, …
Find the balance in the account after 5 years.
146)
A)
$10,825.84
B)
$10,626.84
C)
$10,774.84
D)
$10,871.84
D)
Evaluate the factorial expression.
147)
8!
7!
147)
A)
1
B)
8
7
C)
8!
D)
8
D)
Use the formula for the sum of the first n terms of a geometric sequence to solve.
148)
Find the sum of the first 11 terms of the geometric sequence: 2, 4, 8, 16, 32, . . . .
148)
A)
4096
B)
4074
C)
4131
D)
4094
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
149)
Find a4 when a1=4, r =3.
149)
A)
27
B)
324
C)
36
D)
108
Solve the problem.
150)
In a student government election, 5 seniors, 2 juniors, and 3sophomores are running for election.
Students elect four at–large senators. In how many ways can this be done?
150)
A)
5040
B)
151,200
C)
30
D)
210
Evaluate the factorial expression.
151)
8!
6! 2!
151)
A)
28
B)
8
C)
1
D)
0!
Use the formula for nCr to evaluate the expression.
152)
6C0
152)
A)
1
B)
0
C)
60
D)
720
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
153)
70
i = 1
5i
153)
A)
12,248
B)
12,603
C)
12,425
D)
12,420
Find the probability.
154)
A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2–10) or
a club?
154)
A)
33
52
B)
10
13
C)
23
52
D)
53
52
Write the first four terms of the sequence whose general term is given.
155)
an=(–1)n + 1
n +5
155)
A)
1
6, –1
7, 1
8, –1
9
B)
–1
6, 1
7, –1
8, 1
9
C)
–1
7, 1
8, –1
9, 1
10
D)
1
6, –1
14 , 1
24 , –1
36
Evaluate the given binomial coefficient.
156)
90
88
156)
A)
4005
88
B)
352,440
C)
45
44
D)
4005