MGF 1106 Math for Liberal Arts I Final Exam Review, Multiple Choice Section
Lake City Community College
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1) A school has just purchased new computer equipment for $25,000.00. Write a linear equation in
slope-intercept form that models the value of the equipment, y, x years after purchase. Use the
model to predict the value of the equipment after 2 years.
25000
1)
y
22500
20000
17500
15000
12500
10000
7500
5000
2500
2.5
5
x
A) y = - 5000x + 25,000;
value after 2 years is $15,000.00;
C) y = 25,000x + 5;
value after 2 years is $15,000.00
B) y = 5000x - 25,000;
value after 2 years is $15,000.00
D) y = - 25,000x + 25,000;
value after 2 years is $-25,000.00
Identify a pattern in the list of numbers. Then use this pattern to find the next number.
2) 37, 31, 25, 19, 13
A) 0
B) 2
C) 7
D) 6
3) 7, -28, 112, -448, 1792
A) -3136
3)
B) -7168
C) 3136
D) 7168
Calculate the number of subsets and the number of proper subsets for the set.
1 1 1 1
4) { , , , }
6 7 8 9
A) 15; 14
B) 15; 16
5) {x | x is a day of the week}
A) 127; 126
B) 64; 65
List all the subsets of the given set.
6) {4}
A) {4}, { }
2)
4)
C) 16; 15
D) 14; 15
C) 128; 127
D) 128; 129
C) { }
D) {4}
5)
6)
B) {0}, {4}, { }
7) {m, n}.
A) {m}, {n}, {m, n}, ∅
C) {m}, {n}
7)
B) {m}, {n}, ∅
D) {m}, {n}, {m, n}
1
Decide whether ⊆, ⊂, both, or neither can be placed in the blank to make a true statement.
8) {15, 16, 17} {15, 16, 17}
A) ⊂
B) ⊆
C) Both ⊂ and ⊆
D) Neither
9) {a, b} {z, a, y, b, x, c}
A) Both ⊂ and ⊆
9)
B) ⊆
C) ⊂
Are the sets equivalent?
10) A = {14, 15, 16, 17, 18}
B = {13, 14, 15, 16, 17}
A) Yes
D) Neither
10)
B) No
Are the sets equal?
11) {16, 18, 20, 22, 24} = {18, 20, 22, 24}
A) Yes
11)
B) No
Use the formula for the cardinal number of the union of two sets to solve the problem.
12) Set A contains 12 letters and 8 numbers. Set B contains 7 letters and 8 numbers. Four letters and 5
numbers are common to both sets A and B. Find the number of elements in set A or set B.
A) 29
B) 26
C) 44
D) 35
13) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A ∪ B) then
how many elements are in (A ∩ B)?
A) 5
B) 8
C) 13
D) 17
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
14) (Aʹ ∩ B) ∪ (Aʹ ∩ Cʹ)
A) {r, t, z}
B) {r, s, t, y, z}
15) (A ∪ B)ʹ ∩ C
A) {v, x}
8)
12)
13)
14)
C) {q, s, u, v, x, y}
D) {q, r, t, y, z}
C) {q, v, x}
D) {r, w}
15)
B) {s, u, v, z}
Write the negation of the quantified statement. (The negation should begin with ʺall,ʺ ʺsome,ʺ or ʺno.ʺ)
16) All uncles are males.
A) Some uncles are not males.
B) All males are not uncles.
C) No uncles are not males.
D) Some males are not uncles.
17) No medicines have made people well.
A) Some medicines have not made people well.
B) All medicines have not made people well.
C) Some medicines have made people well.
D) All medicines have made people well.
16)
17)
Use grouping symbols to clarify the meaning of the symbolic statement.
18) p ↔ r ∧ q → p ∨ r
A) [(p ↔ r) ∧ q] → (p ∨ r)
B) p ↔ [(r ∧ q) → (p ∨ r)]
C) [p ↔ (r ∧ q)] → (p ∨ r)
D) (p ↔ r) ∧ [q → (p ∨ r)]
2
18)
Given that p, q, and r ea ch represent a simple statement, write the indicated compound statement in its symbolic form.
19)
19) p: The outside humidity is low.
q: The central humidifier is running.
r: The air in the house is getting dry.
The air in the house is getting dry, if and only if the outside humidity is low and the
central humidifier is not running.
A) r ↔ (p ∧ q)
B) (p ∧ q) → r
C) r ↔ (p ∧ ~ q)
D) (r ↔ p) ∧ ~ q
20) It is not the case that if the air in the house is getting dry, then the central humidifier is not
running.
A) ~ (r ∧ ~ q)
B) ~ r → ~ q
C) ~ (r → q)
D) ~ (r → ~ q)
Write the equivalent contrapositive of the statement.
21) If I am in the city of Jokdrifa, then I am on the planet Plochus.
A) If I am not in the city of Jokdrifa, then I am on the planet Plochus.
B) If I am not on the planet Plochus, then I am not in the city of Jokdrifa.
C) If I am not in the city of Jokdrifa, then I am not on the planet Plochus.
D) If I am not on the planet Plochus, then I am in the city of Jokdrifa.
22) If he is not working in China, then he is vacationing in England.
A) If he is working in China, then he is not vacationing in England.
B) If he is not vacationing in China, then he is working in England.
C) If he is not vacationing in England, then he is working in China.
D) If he is vacationing in China, then he is not working in England.
Use De Morganʹs laws to write a negation of the statement.
23) She is not older than 21 and he is older than 21.
A) She is older than 21 but he is not older than 21.
B) She is older than 21 or he is not younger than 21.
C) It is not true that she is older than 21 or he is not older than 21.
D) She is older than 21 or he is not older than 21.
24) Roger or Emil will attend the game.
A) Roger and Emil will attend the game.
B) Roger or Emil will not attend the game.
C) Roger will not attend the game and Emil will not attend the game.
D) Roger will not attend the game and Emil will attend the game.
20)
21)
22)
23)
24)
Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound
statement.
25) [(~p ∧ ~q) ∨ ~q]
25)
A) True
B) False
Given p is true, q is true, and r is false, find the truth value of the statement.
26) ~[(~q → r) →(q ∨ r)]
A) True
B) False
3
26)
Complete the truth table by filling in the required columns.
27) ~ p ∨ ~ q
27)
p q ~ p ~ q ~ p ∨ ~ q
T T
T F
F T
F F
A)
p q ~ p ~ q ~ p ∨ ~ q
T T F F T
T F F T F
F T T F F
F F T T F
B)
C)
p q
T T
T F
F T
F F
~ p
F
F
T
T
~ q
F
T
F
T
~ p ∨ ~ q
F
T
T
T
p q
T T
T F
F T
F F
~ p
F
F
T
T
~ q
F
F
T
F
~ p ∨ ~ q
F
T
T
T
D)
p q
T T
T F
F T
F F
~ p
F
F
T
T
~ q
F
T
F
T
~ p ∨ ~ q
F
F
F
T
Construct a truth table for the given statement.
28) (p ↔ q) → ~ q
A)
p q p ↔ q ~ q (p ↔ q) → ~ q
T T T
F F
T F F
T T
F T T
F F
F F T
T T
28)
B)
C)
p q
T T
T F
F T
F F
p ↔ q
T
F
F
T
~ q
F
T
F
T
(p ↔ q) → ~ q
F
T
T
T
p q
T T
T F
F T
F F
p ↔ q
T
F
F
T
~ q
F
T
F
T
(p ↔ q) → ~ q
T
F
F
F
D)
p q
T T
T F
F T
F F
p ↔ q
T
F
F
T
~ q
F
T
F
T
(p ↔ q) → ~ q
F
F
T
T
Convert the given measurement to the unit indicated.
29) 58.09 m to dm
A) 5.809 dm
B) 0.581 dm
C) 5809 dm
D) 580.9 dm
Use dimensional analysis to convert the unit indicated.
30) 18 cm to in.
A) 0.02 cm
B) 45.72 cm
C) 0.14 cm
D) 7.09 cm
29)
30)
4
31) 1.7 dam to in.
A) 669.29 in.
31)
B) 4.32 in.
Convert the given unit of weight to the unit indicated.
32) 42 kg to g
A) 0.42 g
B) 4200 g
33) 7 g to cg
A) 0.07 cg
C) 0.23 in.
D) 0.67 in.
C) 42,000 g
D) 0.042 g
C) 70 cg
D) 7000 cg
32)
33)
B) 700 cg
Convert the given Celsius temperature to its equivalent temperature on the Fahrenheit scale. Where appropriate, round
to the nearest tenth of a degree.
34) -4°C
34)
A) 24.8°F
B) -39.2°F
C) -20°F
D) 29.8°F
Convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. Where appropriate, round
to the nearest tenth of a degree.
35) 536°F
35)
A) 996.8°C
B) 315.6°C
C) 907.2°C
D) 280°C
Solve the problem. Use 3.14 for π.
36) A wicker basket has a circular rim with a diameter of 11 inches. How many inches of ribbon are
needed to go once around the rim? Round results to the nearest tenth of a unit.
A) 69.1 in.
B) 34.5 in.
C) 32.5 in.
D) 121.0 in.
37) A circular fountain has a statue in its center, 8 m from the edge. What is the distance around the
fountain? Round results to the nearest tenth of a unit.
A) 48.2 m
B) 25.1 m
C) 50.2 m
D) 64.0 m
36)
37)
Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to
the nearest tenth.
38) A square sheet of paper measures 28 centimeters on each side. What is the length of the diagonal
38)
of this paper?
A) 28 cm
B) 56 cm
C) 1568 cm
D) 39.6 cm
39) If you drive 8 miles south, then make a left turn and drive 6 miles east, how far are you, in a
straight line, from your starting point?
A) 10 mi
B) 5.3 mi
C) 1.4 mi
D) 3.7 mi
Solve the problem by applying the Fundamental Counting Principle with two groups of items.
40) There are 5 roads leading from Bluffton to Hardeeville, 7 roads leading from Hardeeville to
Savannah, and 3 roads leading from Savannah to Macon. How many ways are there to get from
Bluffton to Macon?
A) 105
B) 210
C) 15
D) 35
5
39)
40)
41) An apartment complex offers apartments with four different options, designated by A through D.
41)
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available?
A) 120
B) 240
C) 14
D) 16
Evaluate the factorial expression.
600!
42)
597!
A) 600
43)
42)
B) 597
C) 214,561,800
D) 359,400
10!
5! 5!
A) 1
43)
B) 720
C) 252
D) 10
Find the indicated probability.
44) Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue
marble. Find the probability that both marbles are white.
3
3
3
9
B)
C)
D)
A)
32
28
8
56
Solve the problem that involves probabilities with events that are not mutually exclusive.
45) Consider a political discussion group consisting of 4 Democrats, 7 Republicans, and 9
Independents. Suppose that two group members are randomly selected, in succession, to attend a
political convention. Find the probability of selecting an Independent and then a Democrat.
1
9
9
9
B)
C)
D)
A)
95
95
100
380
Solve the problem.
46) A service that repairs televisions sells maintenance agreements for $11 a year. The average cost for
repairing a television is $34 and 5 in every 100 people who purchase maintenance agreements
have televisions that require repair. Find the serviceʹs expected profit per maintenance agreement.
A) $10.95
B) $9.64
C) $9.30
D) $10.66
47) An insurance company will insure a $220,000 home for its total value for an annual premium of
$510. If the company spends $30 per year to service such a policy, the probability of total loss for
such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is
the companyʹs expected annual gain (or profit) on each such policy?
A) $290
B) -$220
C) $260
D) $210
6
44)
45)
46)
47)
For the given data set, find the mean, median, mode (or state that there is no mode), and midrange.
48) A company advertised that, on the average, 98% of their customers reported ʺvery high
satisfactionʺ with their services. The actual percentages reported in 15 samples were the following:
98, 98, 93, 55, 76, 98, 93, 76, 98, 98, 55, 93, 93, 98, 55
Find the mean, median, mode and midrange.
A) mean = 85.13, median = 93, mode = 98, midrange = 76.5
48)
B) mean = 85.13, median = 93, mode = 98, midrange = 76.5
C) mean = 85.13, median = 93, mode = 98, midrange = 76.5
D) mean = 85.13, median = 93, mode = 98, midrange = 76.5
Find the standard deviation for the group of data items (to the nearest hundredth).
49) 13, 13, 13, 16, 19, 19, 19
A) 8.14
B) 9
C) 2.85
D) 3
Find the standard deviation for the group of data items.
50) 14, 19, 14, 19, 14, 19, 14, 19
5
A)
B) 25
2 7
25
D)
4
49)
50)
5 2
C)
7
Solve the problem.
51) Martin scored 40 points on a quiz. The average score for his class was 39 with a standard
deviation of 2.4. Martinʹs brother Jeff who is in a different class also had a quiz. He scored 29. The
average score in Jeffʹs class was 26 with a standard deviation of 1.9. Find the z-score for each
person. Relatively speaking, who did better?
B) 1.0, 3.0, Martin
A) 1.0, 3.0, Jeff
D) 0.42, 1.58, Martin
C) 0.42, 1.58, Jeff
52) Which score has the better relative position: a score of 49 on a test for which the mean is 41 and
the standard deviation is 8, a score of 5.8 on a test for which the mean is 5 and the standard
deviation is 0.7 or a score of 491.6 on a test for which the mean is 467 and the standard deviation
is 41?
A) A score of 49
B) A score of 491.6
C) The scores have the same relative position.
D) A score of 5.8
51)
52)
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the
68-95-99.7 rule to find the percentage of buyers who paid:
53)
53) between $149,200 and $150,800 if the standard deviation is $800.
A) 68%
B) 99.7%
C) 95%
D) 34%
54) between $150,000 and $153,600 if the standard deviation is $1800.
A) 68%
B) 34%
C) 47.5%
7
54)
D) 99.7%
The scatter plot shows the relationship between average number of years of education and births per woman of child
bearing age in selected countries. Use the scatter plot to determine whether the statement is true or false.
55)
55)
10
9
8
Births per Woman
7
6
5
4
3
2
1
2
4
6
8
10 12 14
Average number of years of education
of Married Women of Child-Bearing Age
There is a strong negative correlation between years of education and births per woman.
A) False
B) True
56)
56)
10
9
8
Births per Woman
7
6
5
4
3
2
1
2
4
6
8
10 12 14
Average number of years of education
of Married Women of Child-Bearing Age
There is a causal relationship between years of education and births per woman.
A) False
B) True
8
Answer Key
Testname: MGF 1106 FINAL EXAM REVIEW MULTIPLE CHOICE SECTION
1) A
2) C
3) B
4) C
5) C
6) A
7) A
8) B
9) A
10) A
11) B
12) B
13) D
14) A
15) A
16) A
17) C
18) B
19) C
20) D
21) B
22) C
23) D
24) C
25) A
26) B
27) B
28) B
29) D
30) D
31) A
32) C
33) B
34) A
35) D
36) B
37) C
38) D
39) A
40) A
41) A
42) C
43) C
44) C
45) C
46) C
47) C
48) B
49) D
50) C
9
Answer Key
Testname: MGF 1106 FINAL EXAM REVIEW MULTIPLE CHOICE SECTION
51) C
52) D
53) A
54) C
55) B
56) A
10