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Mathematics for the Liberal Arts Exam File Fall 2015 Exam #1 for Each Of

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Mathematics for the Liberal Arts Exam File Fall 2015 Exam #1 for Each Of Mathematics for the Liberal Arts Exam File Fall 2015 Exam #1 For each of #1-5, identify one of our logical fallacies that is exhibited. Give a brief explanation for your choice. DO NOT USE THE SAME ANSWER MORE THAN ONCE. 1.) If you aren't sure why you should vote for Senator Kadiddlehopper, then think of the children! 2.) "Buy a Yugo. It is more popular in Lithuania than any other car." 3.) I understand why you think Obama should be president, but what about the corruption charges against Illinois Governor Blagojevich? 4.) "I can't believe you don't support the President's health care plan. You must want all poor people to die." 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.) Construct the truth table for the following proposition. (not p q ) p → q 7.) For each of the following, tell whether or not it is a proposition. 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.) Donald Duck is the president. f.) 3 + 9 = 10 and the name of this course is advanced underwater basket weaving. 8.) Draw a Venn Diagram to illustrate the following categorical proposition. All dogs eat acorns and some dogs ride skateboards. 9.) The following Venn diagram represents how a college class is broken down in the categories of female students (denoted "F"), students from Arkansas (denoted "A") and mathematics majors (denoted "M"). Answer the questions below the diagram. [Note that "x" and "y" represent students. Those students are already included in the numbers given in the diagram and should not be counted in addition to the numbers.] a.) How many students are in the class? b.) How many of the students are mathematics majors from Arkansas? c.) How many female students are in the class? d.) How many psychology majors are in the class? e.) What do we know about student "x?" f.) What do we know about student "y?" 10.) Tom was driving 20.1 meters per second in a 45 mile per hour zone. Was Tom speeding? Be sure to show the use of units. 11.) The part of a baseball diamond inside the base paths is a square that is 90 feet on each side. Find the area inside the base paths and convert it to meters. 12.) Suppose "Gerhard's Combination Motor Oil/Salad Dressing" is on sale at a store in Austria 2.60 shillings per liter. What is the price in dollars per gallon? State your answer to the nearest $0.01 per gallon. 13.) Your French friend Maurice is coming to visit. You want to tell him the temperatures he should expect. The high temperatures are expected to be around 44 Fahrenheit. If you want to tell Maurice the temperature in Celsius, what will you tell him? Show the details of the formula you use. 14.) Methusaleh was 969 years old when he died. How many seconds old was Methusaleh when he died? 15.) You are considering buying 13 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale? (A balance scale just indicates which of two items is heavier.) 16.) You have a basket with apples in it. There are 13 green apples, 18 red apples and 11 plaid apples. You are going to take some apples out of the basket. a.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of apples? b.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of plaid apples? c.) How many apples must you take out of the basket to be absolutely certain you have removed four apples of the same color? 17.) Complete the following Sudoku. Each number 1, 2, 3, 4, 5, 6, 7, 8 and 9 must appear once in each row, once in each column and once in each 3-by-3 subsquare (the ones enclosed by the thicker lines)(a correctly completed example is below) Exam #2 1.) The price of a coat was $210. Yesterday it was reduced 30%. What is the price now? 2.) In 2004, Jose Reyes of the New York Mets earned a salary of $307,500. For 2005, he received a raise of 7.967479675%. For 2006, he received a raise of 20.93373494%. WITHOUT ROUNDING OFF EITHER PERCENTAGE, determine his 2006 salary. (source: www.baseball-reference.com) 3.) The price of a coat was $210. Last week it was reduced 20%. This week it was reduced another 10%. Sales tax is 8%. With tax included, what is the price of the coat now? 4.) David Wright of the New York Mets earned a salary in 2006 of $374,000. That was a 15.968992248% raise from his 2005 salary. What was his 2005 salary? (source: www.baseball-reference.com) 5.) Use reasonable estimations to approximate the total number of slices of bread eaten each year by all people in the United States. 6.) a.) Write 5.3 x 1012 in regular notation. b.) Write 2.2 x 10-6 in regular notation. c.) Write 302,000,000,000 in scientific notation. d.) Write 0.00000000425 in scientific notation. e.) Use the scientific notation from parts a.) and b.). Multiply the two numbers together, SHOWING ALL NECESSARY WORK AND WITHOUT USING YOUR CALCULATOR, and write your final answer in scientific notation. 7.) You put $2550 in the bank. The account gets an annual percentage rate of interest of 1.4% compounded monthly. The money is left in the account for 4 years. Throughout the problem, we assume no other money is added or removed from the account. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of four years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of four years. c.) How much money will you have at the end of four years? 8.) You put $5525 in the bank. The account gets an annual percentage rate of interest of 1.25% compounded continuously. The money is left in the account for 6 years. Throughout the problem, we assume no other money is added or removed from the accounts. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of six years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of six years. c.) How much money will you have at the end of six years? 9.) You start putting money in your retirement fund at age 23. You put in $215 each month. The interest of 10.15% is compounded quarterly. You will retire when you turn 65. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money in your fund when you retire. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct 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.) Find the amount of interest you will receive. 10.) Consider the following question. How do doctors' salaries compare to lawyers' salaries? Which type of study (experimental, observational, double-blind) would best answer the question? Give a reason for your answer. 11.) You are buying a house. After the down payment, you need to borrow $105,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 4.85%. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. 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? 12.) A person is interested in finding out the average income of people in Arkansas. In order to do that, he does a survey by asking the annual income of Arkansas residents in line at the Chenal Valley Country Club in Little Rock. Are his results likely to be representative of Arkansas? Why or why not? 13.) You start putting money in a college savings account. You want to have $135,000 in 18 years when your daughter will be ready for college. The interest rate of 8.35% is compounded monthly. a.) WITHOUT INSERTING ANY NUMBERS, write the formula that will figure out the amount of money you will have to put in the account each month. b.) WITHOUT DOING ANY SIMPLIFICATION, insert all of the numbers into the formula. c.) How much money will you have to pay each month? d.) What is the total of all of your payments? 14.) At a doctor's office a piece from a tongue depressor has gotten under the weighing surface of a scale, keeping the surface from being able to go down all the way.
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