Mathematics for the Liberal Arts Exam File Spring 2018

Exam #1

In exercises #1 - 5, an argument or advertisement is given. For each exercise, identify one and only one of our fallacies that is exhibited in that argument or advertisement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. Some of these exercises come from http://www2.sjsu.edu/depts/itl/graphics/main.html. 1.) Are you going to major in history or are you going to major in mathematics? 2.) Gosh, officer, I know I made an illegal left turn, but please don't give me a ticket. I've had a hard day, and I was just trying to get over to my aged mother's hospital room, and spend a few minutes with her before I report to my second full-time minimum-wage job, which I have to have as the sole support of the seventeen members of my family. 3.) "I can't believe you don't support the President's health care plan. You must want all poor people to die." 4.) "Buy a Yugo. It is more popular in Lithuania than any other car." 5.) "Theodore Kaczynski, Georg Cantor and Kurt Godel were all mathematicians and crazy. Dr. Worth is a mathematician so he must be crazy, too."

6.) Draw a Venn diagram to illustrate the following proposition. All senators eat turnip greens and some are left-handed. 7.) For each of the following, write "Yes" if it is a proposition (statement) or "No" if it is not. a.) Grab that fish! b.) Arkansas is larger than Rhode Island. c.) It's a beautiful day. d.) Bob is 25 years old and Dave's dog is plaid. e.) Arkansas is north of Missouri. f.) 3 + 9 = 10 and the name of this course is advanced underwater basket weaving. 8.) The following Venn diagram illustrates the makeup of a particular group of students. "M" denotes "mathematics major," "P" denotes "plays piano," and "G" denotes "refuses to eat grits." "x" and "y" represent particular students. The numbers represent the number of students who fit the categories.

a.) How many students are in the group? b.) How many students are mathematics majors who play the piano? c.) What do we know about student "x?" d.) What do we know about student "y?"

9.) A Canadian company is advertising a jacket for $59.99 (Can.). They also list a price of $42.25 (U.S.). Are those prices the same? If not, which one is cheaper? Be sure to show the use of units. 10.) Tom was driving 20.3 meters per second in a 45 mile per hour zone. Was Tom speeding? Be sure to show the use of units. 11.) Bob weighs 110 kg. In order to participate in a backpacking trip at Philmont Scout Ranch he must weigh no more than 215 pounds. Does he qualify for the hike? If not, how much weight must he lose in order to qualify? Be sure to show the use of units. 12.) How many centimeters are there in a mile? Be sure to show the use of units. 13.) There are 14 blue apples, 12 plaid apples and 5 green apples in a basket. a.) What is the smallest number of apples you would have to take out to be sure of getting at least three of one kind? b.) What is the smallest number of apples you would have to take out to be sure of getting at least four plaid apples? 14.) There are 10 rectangular tables in a rectangular room. You must set up the tables so there are exactly 3 tables against each wall. 15.) You have a four minute hourglass and a five minute hourglass. You need to cook something for exactly seven minutes. Give a detailed explanation of how you would use the two hourglasses to time the seven minutes. (Note: You cannot tell by looking if an hourglass is half empty.)

Exam #2

1.) Calculate (6.2 x 10-3) x (4 x 107) without using your calculator. Be careful to show ALL of your work and express your final answer in scientific notation. 2.) Bob made $40,000 in 2004. For 2005, his salary went up 5%. For 2006, his salary went up 5% again. What is his salary in 2006? 3.) Bob has a bad cold. He is trying to take some cough syrup. He is pouring the cough syrup into a measuring spoon while coughing. The spoon is chipped so that it can't hold as much as it is supposed to hold. Discuss sources of random error and systematic error in this situation. 4.) Do the following. a.) Write 0.00000034 in scientific notation. b.) Write 45,000,000,000 in scientific notation 5.) You start putting money in your retirement fund at age 23. You put in $500 each month. The interest of 10.25% is compounded monthly. You retire at age 65. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have when you retire. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) How much interest did your money earn? 6.) Maher-Shalal-Hash-Baz started putting money in a college savings account. He wants to have $120,000 in 18 years when his son will be ready for college. The interest rate of 9.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money Maher-Shalal-Hash-Baz will have to put in the account each quarter. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will he have to pay each quarter? d.) What is the total of all of his payments? 7.) Billy Bob is borrowing $34,000 to buy a new -wide. The interest rate for his 10 year mortgage is 6.45%. Throughout the problem we will ignore the escrow payments that would normally be added to the mortgage payment to cover insurance and taxes. a.) Without inserting any numbers, write out the formula that will figure out the amount of Billy Bob's monthly payments. b.) Without doing any simplification, insert all of the numbers into the formula. c.) What will be his monthly payment? d.) What will be the total of all of his monthly payments? e.) How much interest will he pay over the life of the loan? 8.) You put $2500 in a certificate of deposit account for 3 years. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have after 3 years. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have after 3 years? 9.) Jay Leno told the following joke on "The Tonight Show." (I've made a slight change in the numbers.) "When they closed Denver's old Stapleton Airport, the gift shop had a big clearance sale - everything was 94 percent off. This was great! You could get a bottle of aspirin for $15!" Assuming he is giving correct data, how much did the aspirin cost before the sale? 10.) The price of a sofa was $780. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now? 11.) Billy Bob is now making $629.30 per week. That is a raise of 8.5% over what he was making before. How much was he making per week before the raise? 12.) Bob bought a house worth $120,000. Now, after five years he was told the house's value had gone up 26%. What is the house worth now? 13.) You are buying a house. After the down payment, you need to borrow $115,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 6.15%. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? Exam #3

1.) The following table gives the leaders in triples for the 1913 Tigers. Draw a bar graph that illustrates the data. Baldy Louden 5 10 Del Gainer 8 10 Paddy Baumann 4 Red McKee 4 23 16

2.) This chart shows some of the career statistics for . Year Team G AB R H 2B 3B HR RBI AVG OBP SLG 1925 Athletics 10 9 2 6 1 0 0 0 .667 .667 .778 1926 Athletics 26 32 8 10 2 1 0 5 .313 .333 .438 1927 Athletics 61 130 23 42 6 5 3 20 .323 .393 .515 1928 Athletics 118 400 85 131 29 10 13 79 .328 .416 .548 1929 Athletics 149 517 123 183 23 9 33 118 .354 .463 .625 1930 Athletics 153 562 127 188 33 13 37 156 .335 .429 .637 1931 Athletics 139 515 93 150 32 10 30 120 .291 .380 .567 1932 Athletics 154 585 151 213 33 9 58 169 .364 .469 .749 1933 Athletics 149 573 125 204 37 9 48 163 .356 .449 .703 1934 Athletics 150 539 120 180 28 6 44 130 .334 .449 .653 1935 Athletics 147 535 118 185 33 7 36 115 .346 .461 .636 1936 Red Sox 155 585 130 198 32 8 41 143 .338 .440 .631 1937 Red Sox 150 569 111 162 24 6 36 127 .285 .392 .538 1938 Red Sox 149 565 139 197 33 9 50 175 .349 .462 .704 1939 Red Sox 124 467 130 168 31 10 35 105 .360 .464 .694 1940 Red Sox 144 515 106 153 30 4 36 119 .297 .412 .581 1941 Red Sox 135 487 87 146 27 8 19 105 .300 .412 .505 1942 Red Sox/Cubs 100 305 43 69 12 0 8 33 .226 .320 .344 1944 Cubs 15 20 0 1 1 0 0 2 .050 .136 .100 1945 Phillies 89 224 30 60 11 1 7 38 .268 .336 .420 20 Years 2,317 8,134 1,751 2,646 458 125 534 1,922 .325 .428 .609 a.) What was Foxx's highest batting average (denoted AVG)? b.) How many times did Foxx more than 50 homers (denoted HR)? In what year(s)? c.) What is the most consecutive years Foxx (denoted SLG) was at least .600? d.) How many home runs did hit in 1931? 3.) The following chart shows the doubles, triples and home runs for all National Leaguers with at least 10 triples in 1937. Answer the questions below.

60

50

40

30 2B 20 3B HR 10

0

Al Todd Al

GusSuhr

Billy Jurges Billy

AugieGalan

LeeHandley

Jo-Jo MooreJo-Jo

GeneMoore

Billy Herman Billy

JoeMedwick

ArkyVaughan IvalGoodman DonGutteridge

a.) Of these players, which one had the most doubles in 1937? How many did he have? b.) Who led the in home runs in 1937? c.) Who led the National League in triples in 1937? d.) How many of these players had at least 10 home runs in 1937? 4.) You flip three coins. a.) Draw a tree diagram to illustrate tossing the three coins. b.) Find the probability that at least two of the coins came up tails. 5.) The following table shows the leaders in triples for the 1962 New York Mets.

Charlie Neal 9 Without using your calculator, find the following. Be Elio Chacon 3 sure to show or explain how you got each answer. Felix Mantilla 4 Frank Thomas 3 a.) mean Marv Throneberry 3 3

b.) median

c.) mode

6.) In 1988, the New York Mets hit 152 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by Lenny Dykstra, Mookie Wilson, Kevin Elster, , Keith Hernandez, Howard Johnson, Kevin McReynolds, and "other" players. Other

Strawberry Dykstra

Wilson

Elster

Carter

McReynolds Hernandez

Johnson a.) The portion of the pie for Darryl Strawberry has an angle of 92.36842. How many home runs did he hit? b.) Three players hit more than 20 home runs. Who were they? c.) How many home runs did Wally Backman hit? d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez? 7.) You roll two standard, six-sided dice. What is the probability that the sum of the numbers on the dice is greater than 9? 8.) The following are the major league leaders in from 1932. 367 Jack Burns 270 Find the following: 312 Jimmie Foxx 438 Babe Ruth 302 274 a.) mean Ben Chapman 275 Joe Vosmik 287 373 John Stone 283 b.) median Bruce Campbell 273 Lefty O'Doul 330 307 370 c.) mode 420 340 Don Hurst 317 321 359 Pinky Whitney 280 269 Smead Jolley 273 Hal Lee 296 282 325 9.) A box contains eight jelly beans, five peeps, and three Tasmanian Devils. a.) You reach into the box and remove an item. You reach into the box again and remove another item. What is the probability you got two jelly beans? b.) You reach into the box and remove an item. You note what it is and put it back. Then you reach into the box again and remove another item. What is the probability you got a peep first, then a Tasmanian Devil? 10.) You go to a restaurant. The menu lists five kinds of cold appetizers, seven kinds of warm appetizers, four kinds of bread, 10 kinds of beverage, 11 kinds of dessert, 28 kinds of entrée, 12 kinds of pasta, 12 kinds of vegetables, nine kinds of salad, and eight kinds of soup. You order one of each kind of item. How many different meals are possible? 11.) You have a class of 25 second graders. Fifteen are boys, ten are girls. You are going to have them form a committee consisting of three boys and two girls. How many different committees can you form? 12.) Explain the difference between a linear model and an exponential model. 13.) Bubbaville had a population of 2400 in 1910. In 1925, its population had fallen to 1200. Assuming that exponential rate of decline continued, what would the population of Bubbaville be in 2006? 14.) You are making a license plate. It has 3 letters followed by 4 numbers. How many different license plates can be made if letters may not be repeated? 15.) If f(x) = 2x2 + 3x - 4, find the following. a.) f(-1) b.) f(2) c.) f(a) d.) f(x + 1)

Exam #4 1.) Middle C has a frequency of 260 cycles per second. Find the frequency of the note that is a.) two octaves below middle C. b.) one octave above middle C. c.) three octaves above middle C. d.) two half-steps below middle C. e.) five half-steps above middle C. 2.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 111 members, find the standard divisor and fill in the table below. Standard Divisor = State Population Standard Quota # of reps the state "should" get # of reps you'll give A 2,450,000 B 2,450,001 C 5,231,000 D 5,646 E 4,454,000 Total Population 14,590,647 3.) A Fibonacci-like sequence has 1st term 3, 2nd term 7. Find the next four terms. 4.) Explain the difference between majority and plurality voting. 5.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Also draw walls. Identify the principal vanishing point and two other vanishing points. 6.) Give examples of two votes that require a super-majority vote. GIVE THE PERCENTAGE OR FRACTION OF VOTES REQUIRED FOR EACH ONE. 7.) Explain how a Borda count works. Give an example of a vote done with a Borda count. 8.) A basketball has a diameter of 12 inches. Find the volume and surface area. Show at least four decimal places. 9.) Consider the following shapes.

1 2 3 4 5

6 7 8 9 10 For each type of symmetry below, list the numbers of the shapes that have that kind of symmetry. Some may fit more than one symmetry. a.) symmetry around a horizontal line through the middle of the shape b.) symmetry around a vertical line through the middle of the shape c.) rotational symmetry d.) none of the above symmetries 10.) A cylinder has a height of 4 feet and a diameter of one yard. Find the volume and surface area. Show at least four decimal places. 11.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

12.) Find the area and perimeter of the following shape. Show at least four decimal places.

Final Exam

For each of #1 - 3, identify one AND ONLY ONE of our logical fallacies that is exhibited. Give a brief explanation for your choice. 1.) "I saw five people on the way to school today who didn't use their turn signals. Folks in Arkansas must not know how to use turn signals." 2.) "Titanic must be the best movie of all time since it has the highest box office receipts of all time." 3.) "You shouldn't eat meat because eating meat is wrong." 4.) What year was it 2,000,000,000 seconds ago? 5.) You are driving 100 feet per second. The speed limit is 70 miles per hour. Are you speeding? You must show the use of units and conversion factors. 6.) The main dining room at Bubba's All You Can Stomach Eatery is 45 feet by 52 feet. What is the area if you convert all measurements to centimeters? 7.) You are borrowing $120,000 to buy a house. The interest rate for your 30 year mortgage is 4.15%. Throughout the problem we will ignore the escrow payments that would normally be added to the mortgage payment to cover insurance and taxes. a.) Without inserting any numbers, write out the formula that will figure out the amount of your monthly payments. b.) Without doing any simplification, insert all of the numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? 8.) You put $3200 in a certificate of deposit account. It receives 1.25% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Write out the formula that will figure out the amount of money you will have after 3 years without any of the numbers inserted. b.) Write out the formula that will figure out the amount of money you will have after 3 years with all of the numbers inserted. c.) How much money will you have after 3 years? 9.) Bubba is borrowing $16,500 to buy a new four wheeler. The interest rate for his 5 year loan is 1.85%. a.) Without inserting any numbers, write out the formula that will figure out the amount of Bubba's monthly payments. b.) Without doing any simplification, insert all of the numbers into the formula. c.) What will be his monthly payment? d.) What will be the total of all of his monthly payments? e.) How much interest will he pay over the life of the loan? 10.) The price of gasoline was $2.40 per gallon. Two weeks ago the price went up 15%. This week it went up 10%. What is the price now? 11.) A car was on sale for $11,745. That was 13% off the original price. What was the original price? 12.) Bubba's All You Can Stomach Eatery has a buffet price of $82.99. They give a 42% discount to college students. Once you get the discount, you have to pay 8.45% sales tax. How much will it cost for you to eat at Bubba's? 13.) The following table shows the number of wins for , and from 1961 through 1966. Draw a time series plot that represents this data. Be sure to label your graph so I can determine who is represented by each part of the graph. (data from www.baseball-reference.com) Koufax Drysdale Marichal 1961 18 13 13 1962 14 25 18 1963 25 19 25 1964 19 18 21 1965 26 23 22 1966 27 13 25 14.) The following graph shows the number of complete games thrown by Christy "Big Six" Mathewson each year during his career. (source: sabermetric baseball encyclopedia")

40 35 30 25 20 15 10 5

0

1900 1902 1904 1906 1908 1910 1912 1914 1916

a.) How many seasons did Mathewson have at least 25 complete games? b.) What is the most consecutive years Mathewson had at least 25 complete games? c.) What is the most complete games Mathewson had in one season? What season? d.) How many complete games did Joe "Iron Man" McGinnity have in 1904? 15.) The following chart shows who hit all of the home runs for the 1915 and how many they hit. George Burns, other, 4 5

Ty Cobb, 3

Sam Crawford, 4 Bobby Veach, 3 Marty Kavanagh, 4 Answer the following questions. All questions refer to the 1915 Detroit Tigers.

a.) Who hit the most home runs? b.) How many home runs did the Tigers hit? c.) What is the angle for the portion of the chart representing Bobby Veach? d.) How many players hit home runs? 16.) The following are the Major League leading totals for 1957. 583 577 644 650 574 594 576 634 611 594 579 615 624 617 609 575 619 648 626 585 Using your calculator, find the following. a.) mean b.) median c.) mode d.) minimum 17.) The following are the leaders in triples for the 1986 . 7 6 5 4 6 4 Without your calculator, find the following. Show how you got each answer. a.) mean b.) median c.) mode d.) maximum 18.) A cylindrical storage drum has a height of 4 feet and a diameter of one yard. Find the volume and surface area. 19.) The window below is shaped like a rectangle with a semi-circle on top. What are the area and perimeter of the window?

20.) You flip three coins. a.) Draw a tree diagram to illustrate tossing the three coins. b.) Find the probability that you got more heads than tails. 21.) The poisonous snakes that can be found in Australia are the Australian Copperhead, Death Adder, Taipan and Tiger Snake. A box contains five Australian Copperheads, seven Death Adders, eight Taipans, and four Tiger Snakes. a.) You reach into the box and randomly choose a snake. You put it back, shake the box and then reach in and take another snake. What is the probability that the first snake was a Death Adder and the second was a Taipan? b.) You reach into the box and randomly choose a snake. You then reach in and take another snake. What is the probability that the first snake was a Taipan and the other was a Tiger Snake? 22.) You go to a restaurant. The menu lists five kinds of cold appetizers, seven kinds of warm appetizers, 10 kinds of beverage, 11 kinds of dessert, 28 kinds of entrée, 12 kinds of pasta, nine kinds of salad, and eight kinds of soup. You order one of each kind of item. How many different meals are possible? 23.) Consider the eight letters G, H, I, J, K, M, L, and N. For our purposes, a "word" is ANY arrangement of letters. a.) How many four letter "words" can be made from these letters if repetitions are allowed? b.) How many four letter "words" can be made from these letters if no repetitions are allowed? 24.) In 1870, Searcy, Arkansas had a population of 874. By 1880 the population had dropped to 840 (that's a drop of 3.8902% over the 10 year period). If that rate had remained the same, what would the population of Searcy be in 2005?

25.) A.) You have a basket with apples in it. There are 23 green apples, 14 red apples and 8 plaid apples. You are going to take some apples out of the basket. (1) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of apples? (2) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of plaid apples? (3) How many apples must you take out of the basket to be absolutely certain you have removed four apples of the same color? B.) You have a four minute hourglass and a five minute hourglass. You need to cook something for exactly seven minutes. Give a detailed explanation of how you would use the two hourglasses to time the seven minutes. (Note: You cannot tell by looking if an hourglass is half empty.)