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MATH 1332
Final Exam Study Guide (Spring 2019)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
1) If a menu has a choice of 4 appetizers, 5 main courses, and 5 desserts, how many
dinners are possible if each includes one appetizer, one main course, and one dessert?
A) 100 B) 3 C) 40 D) 29
1)
2) A middle school student passes out leaflets to the adults at a school function. The
leaflets ask the recipient to indicate whether they believe in anthropogenic global
warming. The bottom of the leaflet indicates that the completed leaflet should be
returned to the student. Identify the kind of sample that is being used.
A) cluster sample B) stratified sample
C) systematic sample D) sample of convenience
2)
3) The grades for the trigonometry exam are listed below. Find the range.
85, 76, 93, 82, 84, 90, 75
A) 76 B) 11 C) 9 D) 18
3)
4) Indicate which student has the higher z score.
Art Major X = 46 X = 50.5 s = 5.2
Theater Major X = 70 X = 75.1 s = 7.3
A) The art major has a higher score than the theater major.
B) Neither student received a positive score; therefore, the higher score cannot be
determined.
C) The theater major has a higher score than the art major.
D) Both students have the same score.
4)
5) How many ways can a student select five questions from an exam containing 12questions, if one of the five must be the last question?
A) 7920 B) 95,040 C) 40,320 D) 330
5)
6) A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1
gallon with a standard deviation of 0.05 gallons. The paint volumes are approximately bell-shaped. Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.
A) almost all (greater than 95%) B) 95%
C) 68% D) 32%
6)
1
Express the set using the roster method.
7) {x | x ∈ N and x is greater than 13}
A) {14,15,16} B) {14,15,16,...}
C) {13,14,15,...} D) {14,16,18,...}
7)
Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units.
8) The graph shows the total cost y (in dollars) of owning and operating a mini-van where x is the
number of miles driven.
x5000 10000 15000 20000 25000
y10000
8000
6000
4000
2000
Miles
Cost
(dollar
s)
(5000, 2333.3)
(9000, 4200)
x5000 10000 15000 20000 25000
y10000
8000
6000
4000
2000
Miles
Cost
(dollar
s)
(5000, 2333.3)
(9000, 4200)
A) $0.47 per mile B) cannot be determined
C) $2.14 per mile D) $22.00 per mile
8)
Given that p and q each represents a simple statement, write the indicated symbolic statement in words.
9) p: The air freshener is working.
q: The basement is smelly.
p → ~ q
A) If the air freshener is working then the basement is not smelly.
B) The air freshener is working if and only if the basement is not smelly.
C) Either the air freshener is working or the basement is smelly.
D) If the air freshener is not working then the basement is smelly.
9)
2
Solve the problem.
10) The cost of a home is financed with a $240,000, 30-year fixed-rate mortgage at 7%. The buyer will
make 360 payments of $1596.00. Prepare a loan amortization schedule for the first three months of the mortgage. Round to the nearest cent.
Payment
Number
Interest
Payment
Principal
Payment
Balance
of Loan
1
2
3
A) Payment
Number
Interest
Payment
Principal
Payment
Balance
of Loan
1 $1400.00 $196.00 $239,860.00
2 $1399.18 $196.82 $239,483.86
3 $1397.71 $198.29 $239,408.57
B) Payment
Number
Interest
Payment
Principal
Payment
Balance
of Loan
1 $1400.00 $196.00 $239,804.00
2 $1398.86 $197.14 $239,606.86
3 $1497.54 $98.46 $239,508.40
C) Payment
Number
Interest
Payment
Principal
Payment
Balance
of Loan
1 $1400.00 $196.00 $239,804.00
2 $1398.86 $197.14 $239,606.86
3 $1397.71 $198.29 $239,408.57
D) Payment
Number
Interest
Payment
Principal
Payment
Balance
of Loan
1 $1400.00 $196.00 $239,804.00
2 $1398.86 $197.14 $239,802.86
3 $1397.71 $198.29 $239,408.57
10)
11) Lonnie needs extra money to buy a truck to start up a delivery service. He takes out a simple interest loan for $6000.00 for 7 months at a rate of 7.25% . How much interest must he pay, and what is the future value of the loan?
A) interest: $253.75 ; future value: $6266.75
B) interest: $3045.00 ; future value: $9045.00
C) interest: $276.82 ; future value: $6276.82
D) interest: $253.75 ; future value: $6253.75
11)
3
Solve the problem. Round up to the nearest dollar.
12) You would like to have $52,000 in 5 years for the down payment on a new house
following college graduation by making deposits at the end of every three months in an annuity that pays 4.25% compounded quarterly. How much should you deposit at the end of every three months? How much of the $52,000 comes from deposits and how much comes from interest?
A) $2796; $27,960 from deposits and $24,040 from interest
B) $2597; $51,940 from deposits and $60 from interest
C) $2347; $46,940 from deposits and $5060 from interest
D) $1746; $34,920 from deposits and $17,080 from interest
12)
Use De Morgan's laws to write a negation of the statement.
13) Roger or Emil will attend the game.
A) Roger will not attend the game and Emil will not attend the game.
B) Roger will not attend the game and Emil will attend the game.
C) Roger or Emil will not attend the game.
D) Roger and Emil will attend the game.
13)
Use the 2012 FICA tax rates in the table below to solve the problem.
14) If you are not self-employed and earn $128,000, what are your FICA taxes?
A) $2612 B) $7232 C) $15,152 D) $6476
14)
Use the following advice from most financial advisors to solve the problem.
· Spend no more than 28% of your gross monthly income for your mortgage payment.
· Spend no more than 36% of your gross monthly income for your total monthly debt.
Round all calculations to the nearest dollar, if necessary.
15) Suppose that your gross annual income is $36,000.
(a) What is the maximum amount you should spend each month on a mortgage payment?
(b) What is the maximum amount you should spend each month for total credit obligations?
(c) If your monthly mortgage payment is 90% of the maximum amount you can afford, what is the
maximum amount you should spend each month for all other debt?
A) (a) $10,080; (b) $12,960; (c) $3888 B) (a) $840; (b) $1080; (c) $756
C) (a) $840; (b) $1080; (c) $324 D) (a) $840; (b) $1080; (c) $132
15)
4
Use the theoretical probability formula to solve the problem. Express the probability as a fraction
reduced to lowest terms.
16) This problem deals with eye color, an inherited trait. For purposes of this problem, assume that
only two eye colors are possible, brown and blue. We use b to represent a blue eye gene and B a
brown eye gene. If any B genes are present, the person will have brown eyes. The table shows the
four possibilities for the children of two Bb (brown-eyed) parents, where each parent has one of
each eye color gene.
Second Parent
B b
First Parent B BB Bb
b Bb bb
Find the probability that these parents give birth to a child who has blue eyes.
A) 1 B)1
2C)
1
4D) 0
16)
17) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1,
3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3,
4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5,
5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two
numbers whose sum is less than 13.
A) 0 B)1
4C) 1 D) ghjvcx
1
2
17)
Write the compound statement in symbolic form. Let letters assigned to the simple statements represent
English sentences that are not negated. Use the dominance of connectives to show grouping symbols
(parentheses) in symbolic statements.
18) If I do not like the song and I change the station then the DJ is not entertaining or I look
for a CD to play.
A) (~p ∧ r) → (~q ∨ s) B) ~p ∧ [(r → ~q) ∨ s]
C) (p ∧ ~r) → (q ∨ ~s) D) [~p ∧ (r → ~q)] ∨ s
18)
5
19) The following bar graph presents the average amount a certain family spent, in
dollars, on various food categories in a recent year.
On which food category was the most money spent?
19)
20) The amount of time needed to run the Boston marathon is an example of which
type of variable?
20)
21) A recent statistics exam yielded the following 25 scores. Construct a grouped
frequency distribution with the class limits shown below.
63 86 77 51 67 55 89 63 68 96 81 82 44 80 90 77 87 74 91 59
77 79 45 87 97
Class Limits Tally Frequency41-50
51-60
61-70
71-80
81-90
91-100
21)
6
22) Find the class with the greatest number of data values 22)
23) Construct a stem-and-leaf plot for the following data. 23)
24) The table below lists the populations, in thousands, of several rural western
counties. What is the median population?
County Population (thousands)
Aldridge 12
Cleveland 8
McCarthy 20
Pope 25
Sorrell 16
Wilson 27
24)
25)25) Out of 733 items checked out of a public library, 269 were fiction books, 222 were non-fiction books, and 242 were videos (of any genre). What is the probability that a randomly4selected item was not a video?
26) A population has a mean µ = 21 and standard deviation σ = 11. Find the
z-score for a population value of 40.
26)
7
27) Following are the closing prices (in dollars) of a certain stock for the past 20trading days.
153.21 151.33 155.74 147.55 123.45 151.24 145.02 127.33 157.17 125.64
145.78 142.76 125.17 126.34 153.05 130.41 141.26 137.18 147.74 147.19
Find the population standard deviation for the closing prices.
27)
28) If one card is drawn from an ordinary deck of cards, what is the probability that
the card will be an ace, a king of hearts, or a spade?
28)
29) A poll was taken of 14,876 working adults aged 40-70 to determine their level of
education. The participants were classified by sex and by level of education. The
results were as follows.
Education Level Male Female Total High School or Less 3590 2523 6113
Bachelor's Degree 3772 3858 7630
Master's Degree 547 483 1030
Ph.D. 51 52 103
Total 7960 6916 14,876
A person is selected at random. Compute the probability that the person is female and has a bachelor's degree.
29)
30) A certain system has two components. There are 6 different models of the first
component and 11 different models of the second. Any first component can be
paired with any second component. A salesman must select 2 of the first
component and 3 of the second to take on a sales call. How many different sets
of components can the salesman take?
30)
31) A ______________ variable assumes values that can be counted. 31)
32) If five cards are drawn from a deck of cards without replacement, what is the
probability that at least one of the cards is a heart?
32)
A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that
corresponds to the given z-score.
33) z = -3 , if the standard deviation is 20. 33)
8
Calculate the number of subsets and the number of proper subsets for the set.
34)1
6,
1
7,
1
8,
1
934)
Complete the truth table by filling in the required columns.
35) p ∧ ~ q
p q ~ q p ∧ ~ q
T T
T F
F T
F F
35)
Construct a truth table for the statement.
36) (r ∧ q) ∨ (~r ∧ ~q) 36)
Find a. the mean b. the deviation from the mean for each data item: and c. the sum of the deviations in
part b.
37) 162, 169, 171, 176, 177 37)
Find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the
greater of a standard deduction or an itemized deduction.
38) Suppose your friend earned wages of $93,260, received $1340 in interest from a
savings account, and contributed $6300 to a tax-deferred retirement plan. She is entitled to a personal exemption of $3500 and a standard deduction of $7800. The interest on her home mortgage was $4500, she contributed $2500 to charity, and she paid $1359 in state taxes.
38)
Find the gross income, the adjusted gross income, and the taxable income.
39) A taxpayer earned wages of $65,800, received $890 in interest from a savings
account, and contributed $2900 to a tax-deferred retirement plan. He was entitled to a personal exemption of $3500 and had deductions totaling $5940.
39)
For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange.
40) Ages of teachers in the mathematics department of a certain high school:
27, 53, 35, 60, 27, 53, 27, 50, 50, 42
40)
9
Given that p and q each represents a simple statement, write the indicated compound statement in its
symbolic form.
41) p: The outside humidity is low.
q: The central humidifier is running.
r: The air in the house is getting dry.
The outside humidity is low and the central humidifier is running, or the
air in the house is getting dry.
41)
In the following exercises, does the problem involve permutations or combinations? Explain your answer.
It is not necessary to solve the problem.
42) How many different user ID's can be formed from the letters W, X, Y, Z if no
repetition of letters is allowed?
42)
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.
43) C' ∩ A' 43)
Provide an appropriate response.
44) In a normal distribution, approximately what percent of data items fall within 1
standard deviation of the mean (in both directions)?
44)
Solve the problem using the strategy of your choice.
45) Find the number of squares in the figure. 45)
Solve the problem.
46) A physics exam consists of 9 multiple-choice questions and 6 open-ended
problems in which all work must be shown. If an examinee must answer 6 of
the multiple-choice questions and 4 of the open-ended problems, in how many
ways can the questions and problems be chosen?
46)
10
47)47) Lonnie needs extra money to buy a truck to start up a delivery service. He takes out a simple interest loan for $5000.00 for 9 months at a rate of 5.25% . How much interest must he pay, and what is the future value of the loan?
48) There are 777,859 physicians in the United States.
177,030 are women.
33,947 physicians have cardiology as their specialty.
6,817 women physicians specialize in cardiology.
Identify the Venn diagram in which U is the set of all physicians, W is the set of all women physicians, and C is the set of all U.S. physicians specializing in cardiology. Fill in each of the four regions of the Venn diagram with the number of physicians who belong to that region.
Use your Venn diagram to answer the questions.
How many physicians in the United States are there who are men specializing in
cardiology?
How many male physicians in the United States do not specialize in cardiology?
48)
49)
50)
49) A student scores 68 on a geography test and 267 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 10. The mathematics test has a mean of 300 and a standard deviation of 22. If the data for both tests are normally distributed, on which test did the student score better?
50) The price of an item is reduced by 40% of its original price. A week later it is reduced by 30% of the reduced price. The cashier informs you that there has been a total reduction of 70%. Is the cashier using percentages correctly? If not, what is the actual percent reduction from the original price?
51) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (1 through 50). The order in which the selections is made does not matter. How many different selections are possible?
51)
11
Solve the problem.
A = P 1 + r
n
ntP =
A
1 + r
n
ntA = Pert Y = 1 +
r
n
n- 1
52) James and Susan wish to have $10,000 available for their wedding in 4 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
52)
53) How much money should be deposited today in an account that earns 8%
compounded semiannually so that it will accumulate to $3000 in 4 years?
53)
The graph shows that the cost of the average college mathematics textbook has been rising steadily since 1990.
54) a. What is the y-intercept?
b. What is the slope?
c. What is the equation of this line, in slope-intercept form?
d. Predict the cost of an average college mathematics textbook in 2017.
54)
12
The graph shows the level of subsidized daycare spending in a foreign country for the period 1995-1999.
Use the graph to answer the question.
55) Find the percent increase in daycare spending from 1997 to 1998. Round to the
nearest percent.
55)
The problem describes procedures that are to be applied to numbers. Represent the original number as n
and use deductive reasoning to prove a conjecture that relates the result of the process to the number n.
56) Select a number. Multiply the number by 96. Add 96 to the product. Divide this
sum by 48. Subtract two from the quotient.
56)
Use PMT =
Pr
n
1 - 1 + r
n
-nt to determine the regular payment amount, rounded to the nearest dollar.
57) The price of a home is $390,000. The bank requires a 20% down payment. After
the down payment, the balance is financed with a 20-year fixed-rate mortgage at
7%. Determine the monthly mortgage payment (excluding escrowed taxes and
insurance) to the nearest dollar.
57)
Use De Morgan's laws to write a negation of the statement.
58) Roger or Emil will attend the game. 58)
Use a truth table to determine whether the symbolic form of the argument is valid or invalid.
59) p → q
~ p
∴ ~ q
59)
13
Use grouping symbols to clarify the meaning of the symbolic statement.
60) p ∨ q → p ↔ q ∧ ~p 60)
Use set notation to identify the shaded region.
61) 61)
Use the Fundamental Counting Principle to solve the problem.
62) There are 8 performers who are to present their acts at a variety show. One of
them insists on being the first act of the evening. If this request is granted, how
many different ways are there to schedule the appearances?
62)
Use the following definition to place the indicated natural number in the correct region of the Venn
diagram.
A palindromic number is a natural number whose value does not change if its digits are reversed.
U = the set of natural numbers
A = the set of palindromic numbers
B = the set of odd numbers
63) 100 63)
Use the four-step method in problem solving to solve the problem.
64) A store received 300 containers of milk to be sold by February 1. Each container
cost the store $0.79 and sold for $1.55. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 270 containers were sold by February 1, how much profit did the store make?
64)
Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.")
65) No entertainers have gone on tour. 65)
14
Answer Key
Testname: 1332_ FINAL EXAM STUDY GUIDE
1) A
2) D
3) D
4) C
5) D
6) C
7) B
8) A
9) A
10) C
11) D
12) C
13) A
14) D
15) C
16) C
17) C
18) A
19) Dairy products
20) continuous
21)
Class Limits Frequency
41-50 2
51-60 3
61-70 4
71-80 6
81-90 7
91-100 3
22) 55-65
23)
24) 18 thousand
25) 0.67
26) 1.7
27) $11.10
15
Answer Key
Testname: 1332_ FINAL EXAM STUDY GUIDE
28)17
52
29) 0.259
30) 6C2 · 11C3
31) discrete
32) 0.778
33) 440
34) 16; 15
35)
p q ~ q p ∧ ~ q
T T F F
T F T T
F T F F
F F T F
36) r q (r ∧ q) ∨ (~r ∧ ~q)
T T T
T F F
F T F
F F T
37) a. 171 b. -9, -2, 0, 5, 6 c. 0
38) $94,600; $88,300; $76,441
39) $66,690; $63,790; $54,350
40) a. 42.4
b. 46
c. 27
d. 43.5
41) (p ∧ q) ∨ r
42) Permutations, because the order of the letters matters.
43) {r, t}
44) 68%
45) 55
46) 1260
47) interest: $196.88 ; future value: $5196.88
16
Answer Key
Testname: 1332_ FINAL EXAM STUDY GUIDE
48)
27,130 male physicians in the United States specialize in cardiology.
573,699 male physicians in the United States do not specialize in cardiology.
49) The student scored better on the geography test.
50) The cashier is not using percentages correctly. The actual percent reduction from the original price is 58%.
51) 15,890,700
52) $7870.98
53) $2192.0754) a. 46
b. 6
c. y = 6x + 46
d. 208
55) 10%
56)96n + 96
48 - 2 = 2n + 2 - 2 = 2n
57) $2419
58) Roger will not attend the game and Emil will not attend the game.59)
p q p→q ~ p (p → q) ∧ ~ p ~ q [ (p → q) ∧ ~ p ] → ~ q
T T T F F F T
T F F F F T T
F T T T T F F
F F T T T T T
The argument is invalid.
60) [(p ∨ q) → p] ↔ (q ∧ ~p)
61) A' ∩ C' ∩ B
62) 5040
17
Answer Key
Testname: 1332_ FINAL EXAM STUDY GUIDE
63)
100
64) $196.50
65) Some entertainers have gone on tour.
18
