MGF 1107-Math for Liberal Arts II-Final Exam Study Guide
Spring 2015
The final exam will consist of three parts: both a multiple choice and free response section allowing a scientific
calculator, and a free response section that must be completed without the use of a calculator. The study guide is divided
into those three sections. A formula bank is given below. Be advised that not every formula you will need is given.
Make sure you have learned all formulas required to work the problems below that are not given in the bank.
Formulas Given:
r nt
A=P 1+
n
A = Pert
r n
Y= 1+
-1
n
PMT =
P r
n
-nt
1- 1+ r
n
Part I. Multiple Choice (Scientific Calculators Allowed)
Express the expanded form as a Hindu-Arabic numeral.
1) (8 × 106) + (4 × 105) + (9 × 104) + (8 × 103) + (3 × 102) + (6 × 101) + (8 × 1)
A) 8,498,368
2) (7 × 108) + (2 × 104) + (9 × 1)
A) 7,002,009
B) 460
C) 46
D) 331,776
B) 70,002,009
C) 70,020,009
D) 700,020,009
3) (8 × 10-1) + (5 × 10-3) + (7 × 10-5) + (6 × 10-7) + (2 × 10-8) + (2 × 10-9)
A) 0.805070622
B) 0.8057622
C) 0.80507060202
D) 0.857622
Write the Babylonian numeral as a Hindu-Arabic numeral.
4)
A) 1083
B) 18
C) 11,523
D) 903
A) 44
B) 3300
C) 2,200,271
D) 2,416,271
C) 4325
D) 725
C) 560
D) 44,004
5)
Convert the numeral to a numeral in base ten.
6) 3205six
A) 125
B) 43
7) BAE4sixteen
A) 47,844
B) 52,196
1
Write the Egyptian numeral as a Hindu-Arabic numeral using the table below.
Hindu-Arabic Egyptian
Numeral
Numeral Description
1
Staff
10
Heel bone
100
Spiral
1000
Lotus blossom
10,000
Pointing finger
100,000
Tadpole
1,000,000
Astonished person
8)
A) 13,420
B) 132,042
C) 13,242
D) 132,402
A) 23,223
B) 2,300,223
C) 2,030,223
D) 2,003,223
9)
Write the Hindu-Arabic numeral as an Egyptian numeral using the table above.
10) 32,457
A)
B)
C)
D)
2
11) 1,235,042
A)
B)
C)
D)
Write the Roman numeral as a Hindu-Arabic numeral.
12) XIII
A) 103
B) 53
13) MDCXXXI
A) 1631
B) 1831
Write the Hindu-Arabic numeral as a Roman numeral.
14) 139
A) CXXXVIIII
B) CXXLVIIII
C) 13
D) 30
C) 1591
D) 15,131
C) CXXXIX
D) CXXLIX
15) 4758
A) IVDCCLVIII
B) IVDCCLVIII
C) VIDCCLVIII
D) MMMMDCCLVIII
Write the Ionic Greek numeral as a Hindu-Arabic numeral using the table below.
Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek
Numeral
Numeral
Numeral
Numeral
Numeral
Numeral
1
α
20
κ
200
σ
2
β
30
λ
300
τ
3
γ
40
µ
400
υ
4
δ
50
ν
500
φ
5
ε
60
ξ
600
χ
6
70
ο
700
ψ
7
ζ
80
π
800
ω
8
η
90
Q
900
9
θ
100
ρ
10
ι
16) ια
A) 10
B) 21
C) 1
3
D) 11
17) φξβ
A) 762
B) 572
Evaluate the function at the given values of the variable.
18) f(x) = 5x2 + 5
a. f(-1)
b. f(-7)
A) 30, 1230
B) 10, 250
19) f(x) = 6x2 + 4x + 5
A) 960, 8640
a. f(-2)
b. f(6)
B) 21, 245
C) 562
D) 672
C) -5, -65
D) -50, -350
C) -27, 101
D) 141, 1325
The figure shows the percentage of the U.S. population, f(x), made up of teachers
as a function of time, x, where x is the number of years after 1900. Use the graph to solve the problem.
20) Use the graph to estimate f(50).
A) 2%
B) 50%
C) 1%
D) 3%
Provide an appropriate response.
21) The cost, in millions of dollars, for a company to manufacture x thousand automobiles is given by the
function C(x) = 5x2 - 40x + 144. Find the number of automobiles that must be produced to minimize cost.
Cost to Manufacture Automobiles
y
200
175
150
125
100
75
50
25
1 2 3 4 5 6 7
Number of Autos (thousands)
8
x
A) 4 thousand automobiles
C) 20 thousand automobiles
B) 8 thousand automobiles
D) 64 thousand automobiles
4
Express the fraction as a percent.
22) 1
4
A) 2.5%
B) 25%
C) 80%
D) 31.3%
A) 6.15 %
B) 16.25 %
C) 1.63 %
D) 61.54 %
B) 0.000952%
C) 0.0952%
D) 0.476%
B) 4.2%
C) 4200%
D) 0.42%
B) 79,200
C) 792
D) 79.2
B) 0.374
C) 374
D) 37.4
B) 3560
C) 356
D) 35,600
29) 0.24 is 48% of what number?
A) 0.5
B) 0.1152
C) 0.05
D) 0.005
30) What percent of 110 is 40.7?
A) 0.37%
B) 37%
C) 370%
D) 3.7%
31) 522.5 is what percent of 55?
A) 9.5%
B) 1.05%
C) 10.53%
D) 950%
23) 13
80
Write the decimal as a percent.
24) 0.00952
A) 0.952%
25) 42
A) 2100%
Solve the problem.
26) What number is 88% of 90?
A) 7920
27) What number is 22% of 17?
A) 3.74
28) 329.3 is 9 1 % of what number?
4
A) 35.6
The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of
the money. Round answer to the nearest cent.
32) P = $6700
r = 4.5%
t = 21 months
A) $6331.50
B) $7227.63
C) $575.59
D) $527.63
33) P = $180
r = 4%
t = 2 years
A) $14.40
B) $8.00
C) $7.20
5
D) $194.40
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value (the total
amount due at time t). Round answer to the nearest cent.
34) P = $160
r = 8%
t = 3 years
A) $184.00
B) $1038.40
C) $198.40
D) $172.80
35) P = $300
r = 7.25%
t = 8 months
A) $474.00
B) $314.50
C) $319.50
D) $315.82
Solve the problem.
36) A passbook savings account has a rate of 6.1%. Find the effective annual yield if the interest is compounded
semiannually.
A) 6.1%
B) 6.2%
C) 6.3%
D) 6%
37) A passbook savings account has a rate of 6%. Find the effective annual yield if the interest is compounded
quarterly.
A) 6.2%
B) 6.1%
C) 6.3%
D) 6%
38) Find the accumulated value of an investment of $7000 at 7% compounded continuously for 6 years.
A) $10,505.11
B) $9940.00
C) $10,753.73
D) $10,653.73
39) Find the accumulated value of an investment of $8000 at 9% compounded continuously for 6 years.
A) $13,416.80
B) $12,320.00
C) $13,728.05
D) $13,828.05
40) How much money should be deposited today in an account that earns 10% compounded semiannually so
that it will accumulate to $1000 in 12 years?
A) $318.63
B) $689.93
C) $3225.10
D) $310.07
41) James and Susan wish to have $10,000 available for their wedding in 2 years. How much money should they
set aside now at 6% compounded monthly in order to reach their financial goal?
A) $10,616.78
B) $8871.86
C) $9419.05
D) $5000.00
6
Which of the following is a possible representation for the graph with the given edges.
42) QR, RS, RT, and SS
A)
B)
Q
R
Q
S
R
T
S
C)
T
D) None of these
Q
R
T
S
The graph models the football schedule for 5 area high schools. The vertices represent the teams and each game
played is represented as an edge between two teams. Use the information in the graph to answer the question.
43) How many games are scheduled for West?
A) 5
B) 7
C) 4
7
D) 6
Use the weighted graph shown to answer the question.
44) Find the weight of edge CE.
A) 22
B) 42
45) Find the total weight of the circuit A, B, F, G, D, E, C, A.
A) 111
B) 110
C) 441
D) 21
C) 87
D) 174
Determine if the graph must have Hamilton circuits. If so, determine the number of such circuits.
46)
A) No
B) Yes, 7
C) Yes, 5040
D) Yes, 720
A) Yes, 720
B) Yes, 6
C) Yes, 5040
D) No
47)
Determine the number of Hamilton circuits in a complete graph with the given number of vertices.
48) 6
A) 5040
B) 120
C) cannot be determined
D) 720
8
49) 15
A) 15!
C) 16!
B) cannot be determined
D) 14!
Find a spanning tree for the connected graph.
50)
A)
B)
C)
51)
A)
B)
C)
D)
9
D)
Part II. Free Response (Scientific Calculators Allowed) Work MUST be shown for credit in this section.
Write the Hindu-Arabic numeral in expanded form.
52) 7179
53) 820,005,004
Use the table below to write the Mayan numeral as a Hindu-Arabic numeral.
54)
55)
Convert the base ten numeral to a numeral in the given base.
56) 2,874 to base eight
57) 125 to base three
Add in the indicated base.
58)
8765nine
+5864nine
10
59)
64Asixteen
+593sixteen
Subtract in the indicated base.
60)
564 eight
- 236 eight
61)
653seven
- 154seven
Multiply in the indicated base.
62)
34six
× 5six
63)
32four
×13four
Divide in the indicated base.
64) 3four 210four
65) 4five 112five
Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate
whether the line rises, falls, is horizontal, or is vertical.
66) (9, 6), (8, 9)
67) (1, 8), (1, 6)
11
In the following problem: a. Put the equation in slope-intercept form.
b. Identify the slope and y-intercept. c. Graph the line.
68) 2y + x = 0
y
10
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10 x
2
4
6
8
10 x
1
2
-2
-4
-6
-8
-10
69) 3x + 8y = 24
y
10
8
6
4
2
-10 -8
-6
-4
-2
-2
-4
-6
-8
-10
Graph the line.
70) x = 2
y
4
3
2
1
-4
-3
-2
-1
-1
3
4
x
-2
-3
-4
12
71) y = 5
y
8
6
4
2
-8
-6
-4
-2
-2
2
4
6
8
x
-4
-6
-8
Solve by the method of your choice.
72) x - 5y = 7
2x - 4y = 14
73) x + 2y = 25
-7x + 2y = -31
74) 3x + y = 10
12x + 4y = 40
Graph the linear inequality.
75) x + y ≤ 6
y
10
5
-10
-5
5
10 x
-5
-10
13
76) y < - 1 x
4
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
First, create a scatter plot for the data in the table. Then, use the shape of the scatter plot given to determine if the data
are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function.
77)
y
x
y
4
0.6 3
1.5 4.2
3
2.2 4
3
2.5
2
4
0.5
2.7 3
1
3.5 1.5
0
2
x
1
2
3
4
78)
x
0.1
1
1.7
2.5
3.5
3.2
y
0.3
0.5
1
2
4
3
y
4
3
2
1
1
2
3
4
x
Solve the problem.
79) The price of a home is $260,000. The bank requires a 20% down payment and one point at the time of closing.
The cost of the home is financed with a 15-year fixed-rate mortgage at 7%.
a. Find the required down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
d. Find the total cost of interest over 15 years, to the nearest dollar.
14
80) The cost of a home on a particular island is $1,000,000. The bank requires a 15% down payment and three
points at the time of closing. The cost of the home is financed with a 30-year fixed rate at 8%.
a. Find the required down payment
b. Find the amount of the mortgage
c. Find the amount that must be paid for the three points at closing
d. Find the monthly payment
e. Find the total cost of interest over 30 years.
Use the preference table to answer the question.
81) Diners at the Rive Gauche restaurant answer a questionnaire about their favorite course in a French meal.
The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following
table.
Number of Votes
First choice
Second choice
Third choice
21
E
A
D
13
D
A
E
7
A
D
E
5
D
E
A
Which course is selected as the most favorite using the plurality method?
82) Four students are running for president of their residence hall: Debra (D), Farah (F), Jorge (J), and Hillary
(H). The votes of their fellow students are summarized in the following preference table.
Number of Votes 52 45 13 9
First choice D F J F
Second choice
F
J F J
Third choice
H H H D
Fourth choice
J D D H
4
H
J
D
F
Who is declared the new president using the plurality method?
83) Diners at the Rive Gauche restaurant answer a questionnaire about their favorite course in a French meal.
The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following
table.
Number of Votes
First choice
Second choice
Third choice
21 13 7 5
E D A D
A A D E
D E E A
Which course is selected as the most favorite using the Borda count method?
15
84) Four students are running for president of their dormitory: Debra (D), Farah (F), Jorge (J), and Hillary (H).
The votes of their fellow students are summarized in the following preference table.
Number of Votes 52 35 22 10
First choice D F J F
Second choice
F
J F J
Third choice
H H H D
Fourth choice
J D D H
4
H
J
D
F
Who is declared the new president using the Borda count method?
Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit), Euler circuit, or
neither. Make sure you can explain WHY!
85) The graph has 102 even vertices and no odd vertices.
86) The graph has 45 even vertices and three odd vertices.
87) The graph has 53 even vertices and two odd vertices.
Use Kruskal's algorithm to find the minimum spanning tree for the weighted graph. Give the total weight of the
minimum spanning tree.
88)
Solve the problem.
89) A corporate campus plans to run computer network cable between buildings. Use Krustal's algorithm to find
the minimum spanning tree that allows the network to connect all the buildings. How much cable is needed?
16
Part III. Number Theory (NO Calculators Allowed). Work MUST be shown for credit in this section.
Perform the indicated operation(s). Where possible, reduce the answer to lowest terms.
90) 5 ∙ 2
9 3
91) 3 3
7
25
8
92) - 2 ÷ - 2
13
7
93) 8 + 6
9 11
Perform the indicated operation. Simplify the answer when possible.
94) 2 + 2 98 - 4 8
95) 4
175 - 4
20 - 4
125 -
28
Rationalize the denominator.
96) 4
5
97) 14
18
Write the first six terms of the arithmetic sequence with the first term, a1, and common difference, d.
98) a1 = 17; d = -5
99) a1 = 4.9, d = 0.5
Write the first six terms of the geometric sequence with first term, a1, and common ratio, r.
100) a1 = -7; r = 2
101) a1 = 1 , r = 1
3
2
Use the order of operations to simplify the expression.
102) 96 - 12 ∙ 5 + 140 ÷ (-20)
103) 17 -
32 + 3 ∙ 9
17
104) 22 - [7 - (2 - 7)] + (3-5)3
18
Answer Key
Testname: MGF 1107 FINAL EXAM REVIEW
1) A
2) D
3) A
4) C
5) D
6) D
7) A
8) D
9) C
10) C
11) B
12) C
13) A
14) C
15) A
16) D
17) C
18) B
19) B
20) D
21) A
22) B
23) B
24) A
25) C
26) D
27) A
28) B
29) A
30) B
31) D
32) D
33) A
34) C
35) B
36) B
37) B
38) D
39) C
40) D
41) B
42) C
43) A
44) D
45) B
46) A
47) A
48) B
49) D
50) A
51) C
52) (7 × 103) + (1 × 102) + (7 × 101) + (9 × 1)
53) (8 × 108) + (2 × 107) + ( 0 × 106) + ( 0 × 105) +
( 0 × 104) + (5 × 103) + ( 0 × 102) + ( 0 × 101) + (4 × 1 )
54) 5046
55) 45,366
56) 5,472 eight
57) 11122three
58) 15740nine
59) BDD sixteen
60) 326eight
61) 466seven
62) 302six
63) 1202four
64) 30four
65) 13five
66) - 3, falls
67) undefined, is vertical
68) a. y = - 1 x
2
b. slope = - 1 , y-intercept = 0
2
c.
y
10
8
6
4
2
(0, 0)
-10 -8
-6
-4
-2
2
-2
-4
-6
-8
-10
19
4
6
8
10 x
Answer Key
Testname: MGF 1107 FINAL EXAM REVIEW
74) {(x, y) 3x + y = 10}
75)
69) a. y = - 3 x + 3
8
y
b. slope = - 3 , y-intercept = 3
8
10
c.
5
y
10
8
-10
-5
10 x
5
6
4
-5
(0, 3)
2
-10 -8
-6
-4
-2
2
4
6
-10
10 x
8
-2
76)
-4
y
-6
7
6
5
4
3
2
1
-8
-10
70)
y
4
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
3
2
1
-4
-3
-2
-1
-1
1
2
3
4
x
1 2 3 4 5 6 7
77)
-2
y
-3
4
-4
3
71)
2
y
1
8
6
1
4
2
-8
-6
-4
-2
-2
2
quadratic function
2
4
6
8
x
-4
-6
-8
72) {(7, 0)}
73) {(7, 9)}
20
3
4
x
x
Answer Key
Testname: MGF 1107 FINAL EXAM REVIEW
y
97) 7
3
4
98) 17, 12, 7, 2, -3, -8
99) 4.9, 5.4, 5.9, 6.4, 6.9, 7.4
100) -7, -14, -28, -56, -112, -224
101) 1 , 1 , 1 , 1 , 1 , 1
3 6 12 24 48 96
3
2
1
1
2
3
4
102) 29
103) 11
104) 2
x
78)
exponential function
79) a. down payment: $52,000
b. amount of mortgage: $208,000
c. points paid at closing: $2080
d. total cost of interest over 15 years: $336,521
80) a. $150,000; b. $850,000; c. $25,500;
d. $6237; e. $1,395,320
81) Entree
82) Farah
83) Appetizer
84) Farah
85) Euler circuit
86) neither
87) Euler path
88) 119
89) 526 feet
90) 10
27
91) 9
92) 7
13
93) 142
99
94) 7 2
95) 18 7 - 28
96) 4
2
5
5
5
21