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 double-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 Detroit Tigers. Draw a bar graph that illustrates the data. Baldy Louden 5 Bobby Veach 10 Del Gainer 8 Donie Bush 10 Paddy Baumann 4 Red McKee 4 Sam Crawford 23 Ty Cobb 16 2.) This chart shows some of the career statistics for Jimmie Foxx. 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 hit more than 50 homers (denoted HR)? In what year(s)? c.) What is the most consecutive years Foxx slugging percentage (denoted SLG) was at least .600? d.) How many home runs did Babe Ruth 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.