Name___________________________________
Math 101 – All sections- Fall, 2013
Final Exam
Make sure that your scantron matches the color of this page. Be sure to encode your name, student number and put
section # in the last two columns under special code (O and P). The formula sheet is the last page of this exam, feel
free to tear it off.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the preference table to answer the question.
1) Which vertices are adjacent to vertex B?
A) F and G only
B) D and E only
C) A and C only
D) A,C,E,D only
E) all vertices in this graph
2) Please refer to the graph in problem 1). Use Kruskal’s Algorithm to find the weight of the minimal spanning tree.
A) 38
B) 40
C) 32
D) 90
E) 39
3) The nearest-neighbor tour starting with vertex E is given by:
A) EABCDE
B) ECDBAE
C) ECBADC
D) EADCBE
E) ECDABE
4) The scores of seven students in a mathematics test with a maximum possible mark of 20 are given below. Find the
mean score:
16 13 19
A)
B)
C)
D)
E)
16
14
17
11
16.0
15.1
14.9
15.9
17.7
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5) Given the histogram, which statement is true?
A) graph is skewed to the left
B) graph is skewed to the right
C) graph is bimodal
D) graph is approximately symmetric
E) none of the above
6) Two marbles are drawn without replacement from a box with 4 yellow, 2 red, 7 pink, and 5 purple marbles. Find the
probability that the first is purple and the 2nd is yellow.
A) 4/17
B) 10/153
C) 5/17
D) 5/81
E)157/306
7) Find the remainder if 75 is divided by 8
A) 1
B) 2
C) 3
D) 4
E) none of these
8) Luke takes out a conventional installment loan for six years at 6.3% compounded monthly. What are his monthly
payments if he borrows $18,000?
A) $300.87
B) $250.00
C) $296.54
D) $285.26
E) $206.37
9) Suppose that the generator matrix for a (4,8) – code is as follows. Find the codeword corresponding to: 1010
A)
B)
C)
D)
E)
10101001
10101010
10001000
10101000
none of these
1
0

0

0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0

1
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10) Which of the following algorithms will guarantee the Minimum Cost Hamiltonian Circuit
A)
B)
C)
D)
E)
Brute Force Algorithm.
Nearest Neighbor Algorithm.
Sorted Edges Algorithm.
Kruskal's Algorithm.
Cheapest Link Algorithm
11)
A) I only
B) II only
C) both I and II
D) Neither I nor II
12) The number of edges in a tree with 20 vertices is
A) 19
B) 20
C) 20!
D) 19!
13)
E) 220
The table shows the number of college students (out of 209) who prefer a given pizza topping.
Find the probability that a randomly selected student chose cheese pizza, given that the student was a junior
A) 25/71
B) 25/209
C) 25
D) 10/209
E) 25/58
14) Jessica borrows $3000 at 6.2% simple interest for 5 years. What is the total amount due at the end of 5 years?
A) $4052.69
B) $4087.01
C) $3930.00
D) $4021.18
E) $930.00
15) Perform the indicated calculation in Z6: [8] + [7]
A) [1]
B) [6]
C) [3]
D) [4]
E) [5]
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16) Find the median of the following: 18, 30, 49, 85, 40, 30
A) 49
B) 67
C) 40
D) 35
E) 30
17) The first nine digits of an ISBN are 1-613-03281. What is the correct check digit?
A) 1
B) 2
C) 5
D) 7
E) 9
18)
An optimal Eulerization of this graph can be obtained by duplicating how many edges?
A) 1
B) none, it has an Euler circuit
C) 2
D) 3
E) 4
19) Find the standard deviation of the following set of numbers: 8, 7, 4, 2. Round your final answer to 2 decimal places.
A)
B)
C)
D)
E)
2.75
3.01
2.09
5.25
2.38
20) Determine the effective annual yield for 6.5% compounded semi-annually. Round to the nearest tenth of a percent.
A) 6.5%
B) 6.6%
C) 6.7%
D) 6.4%
E) 6.8%
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21) A bag contains 5 red marbles, 7 blue marbles, 12 yellow marbles and 4 green marbles. What is the probability that a
randomly selected marble is not blue?
A) 1 1/3
B) 5/6
C) 3/4
D) 7/11
E) 1/4
22) The numbers on the edges represent distances in miles between locations 1, 2, 3, and 4. Find the total distance for the
Hamilton circuit found using the cheapest-link algorithm.
A)
B)
C)
D)
E)
183
185
187
196
175
23)
Find the value of the 1st quartile (lower quartile): 3, 5, 7, 7, 9, 10, 12, 12, 14, 16, 16, 18, 19, 20 ,24
A) 3
B) 12
C) 7
D) 12
E) 18
24) How many check digits are in a (4,7) matrix code?
A) 4
B) 7
C) 3
D) 11
E) none of these
25) How much money should be deposited today into an account that earns 4% compounded quarterly so that it will
accumulate to $5,000 in 10 years? (Round to the nearest cent.)
A) $ 4101.24
B) $ 3353.84
C) $ 7444.32
D) $ 3571.43
E) $ 3358.27
26) 33) What is the Hamming distance between the codewords: 11101 and 10100
A) 1
B) 5
C) 2
D) 3
E) 4
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27) Suppose that a fifteen-person committee needs to select one of the alternatives A, B, or C. Their votes are
summarized in the following preference table.
Number of Votes
7
5
2
3
First Choice
B
A
C
A
Second Choice
C
B
A
C
Third Choice
A
C
B
B
Which choice is the winner using the plurality method?
A) A
B) B
C) C
D) Tie between A and B
E) Tie between C and A
28) What are the odds of spinning a number more than 5?
A)
B)
C)
D)
E)
3:8
3:5
4:4
8:3
5:3
29) Jennifer deposits $100 at the end of each month for six years into an account that pays 4.1% compounded monthly.
How much will Jennifer have accumulated in the account at the end of six years? (Round to the nearest cent.)
A) $8147.22
B) $127.84
C) $8412.46
D) $9024.33
E) $7200.00
30) What type of study would be most appropriate? A pharmaceutical company wants to know the effects of a drug and
the test administrators gave half the participants the drug and then the other half a placebo. The administrators and
participants do not know who has the placebo and who has the drug.
A) Experiment without blinding
B) Observational study
C) Experiment with double blinding
D) Experiment with single blinding
E) Case-control study
31) Suppose the check matrix for a (2,6) matrix code is as follows. Decode the word 101011 if it is a codeword or if it
differs from a codeword in a single digit. The decoded message is:
A) cannot be decoded
B) 11
C) 10
D) 00
E) 01
1
1

1

0
0

0
1 1 0
0 0 1
0 0 0

1 0 0
0 1 0

0 0 1
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32) A distribution of scores of 19 year-old students who take an IQ test is normally distributed with a mean of 450 and a
standard deviation of 25. Approximately what percent of 19 year-old students should score between 400 and 500?
A) 68% B) 95% C) 99.7% D) 15% E) 34%
33) In a poll of 5056 adults, 54% said they planned to vote yes on a school bond referendum. Find the 95% confidence
interval for the proportion of adults who plan to vote yes.
A) 51.3% to 56.7%
B) 54.99% to 55.01%
C) 55.98% to 65.02%
D) 53.5% to 54.5%
E) 52.59% to 55.41%
34) A probability distribution is given as follows. The random variable x represents the number of cars registered per
household. Find the mean number of registered cars per household. Do not round.
X P(x)
0 0.20
1 0.30
2 0.25
3 0.15
4 0.10
A) 1.65
B) 0.5
C) 2.12
D) 1.94
E) 1.76
35) Suppose that an eleven-person committee needs to select one of the alternatives A, B, or C. Their votes are
summarized in the following preference table. Which choice is the Borda Count Winner?
Number of Votes
5
3
3
First Choice
B
C
A
Second Choice
C
A
C
A
B
B
Third Choice
A) A
B) B
C) C
D) There is a tie
36) Determine the sampling method: Randomly selecting every 5th phone number on a list of 1000 students to call and
ask his or her opinion about global warming.
A) Simple Random Sampling
B) Stratified Random Sampling
C) Systematic Sampling
D) Cluster sampling
E) none of these
37) The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan's simple interest
rate, r, to the nearest tenth of a percent. P = $ 4000; A = $ 4800; t = 3 years
A) 6.7%
B) 6.8%
C) 7.2%
D) 5.8%
E) 7.4%.
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Use the table for problem 38)
38) Heights of college women have a distribution that can be approximated by a normal curve with a mean of
65 inches and a standard deviation equal to 3 inches. About what proportion of college women are taller than
69 inches tall?
A)
B)
C)
D)
E)
90.32%
61.79%
9.68%
88.49%
none of these
39) A savings account pays 6.5% compounded monthly. If you make a deposit of $800 into this account, how much will
you have after 9 years? Round to the nearest cent.
A) $116996.87
B) $7200.00
C) $1410.06
D) $1433.73
E) $1268.00
40) Nineteen voters must choose between alternatives A, B, C, or D. Their votes are summarized in the following
preference table.
Number of Votes
7
5
5
First Choice
Second Choice
2
B
C
D
A
C
D
C
D
Third Choice
D
B
B
C
Fourth Choice
A
A
A
B
Which candidate is eliminated 3rd using the plurality with elimination method?
A) A B) B C) C D) D E) none of the candidates
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PLEASE TEAR THIS OFF TO USE AS YOU ARE TAKING YOUR FINAL
Simple Interest:
Effective Annual Yield (EAY):
P…the principal amount
r…the interest rate (as a decimal)
t…time (in years)
r…the interest rate (as a decimal)
Future Value (with Simple Interest):
A…the accumulated amount
P…the principal amount
r…the interest rate (as a decimal)
t…time (in years)
Compound Interest -finite # of compound periods:
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + 𝑛)
A…the accumulated amount
P…the principal amount
r…the interest rate (as a decimal)
t…time (in years)
n…number of compounding periods in 1 year
n…number of compounding periods in 1 year
*Note: Effective Annual Yield is the same as
Annual Percentage Yield (APY)
Savings Formula
A…the accumulated amount
d…deposit made at the end of each period
r…the interest rate (as a decimal)
n…number of compounding periods in 1 year
t…time (in years)
Loan Formula (Amortization Formula):
Compound Interest –continous
𝐴 = 𝑃𝑒 𝑟𝑡
A…the accumulated amount
P…the principal amount
r…the interest rate (as a decimal)
t…time (in years)
A…the accumulated amount
P…the principal amount
d…deposit made at the end of each period
r…the interest rate (as a decimal)
n…number of compounding periods in 1 year
t…time (in years)
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