MA 202 - Math for Elementary TeachersExam 28 March 2007Name:Score: /100 Points1Instructions:• You may not use any outside assistance on this exam. You may not use books,notebooks, other people’s exams, or any other materials to cheat on this exam.• You may not use a graphing calculator on this exam.• The use of electronic equipment such as mp3 players, ipods, cell phones andother electronic devices during the exam is prohibited.• If you are caught cheating on the exam, you will be given a 0 for a grade.• Write clearly during the exam and fully erase or mark out anything you do notwant graded.• You must show all your work to recieve full credit unless otherwisestated.21. Meg pulls out a standard deck of cards with four suits and 13 cards to a suitand deals herself three cards.(a) What is the probability Meg dealt herself three clubs? (10 points)(b) What is the probability Meg dealt herself three cards of the same suit butthe suit can be hearts, diamonds, clubs or spades? (5 points)32. Forever developing his art skills, Chris decides to practice sketching polygons.Unfortunately he is having trouble remembering what they all are supposed tolook like. Help Chris by drawing the asked for polygon and be sure to tell himwhy your picture is correct.(a) Draw a convex hexagon. (5 points)(b) Draw a concave decagon. (5 points)3. You want to develop a secret language using the letter ‘a’ through ‘j’. Youdecide all “words” in this language will be either 3 or 5 letters long.(a) How many different “words” can you have in this secret language if repi-tition of a letter is allowed in a word? (5 p oints)(b) How many different “words” can you have in this secret language if youdo not allows repititions of letters? (5 points)44. Brian enter a mathematics vocabulary contest. Answer the following questionsfor Brian using complete sentences.(a) What is the “Total-Turn” theorem? (5 points)(b) What is the “Alternate-Interior-Angles” theorem? (5 points)(c) What is the “Law of Large Numbers”? (5 points)5. Tired of sitting in an MA202 exam, you imagine a clock on the front wall of theclassroom.(a) What is the measure of the angle b etween the minute and hour hands at5:00 pm? (5 points)(b) What is the measure of the angle b etween the minute and hour hands at5:45 pm? (5 points)56. Reading the paper you come across the sports page and see that the odds ofthe University of Kentucky winning the SEC tournament this year are 7 to 30.(a) Using the above odds, what is the probability the University of Kentuckywins the SEC tournament this year. (5 points)(b) What is the probability the University of Kentucky does not win the SECtournament this year? (5 p oints)(c) Suppose the Univertsity of Kentucky happens to win the SEC tournamentthis year. The empirical probability they win the SEC tournament in 2007is now equal to 1. How does this compare to the probability you foundin part a? Explain how both answers can be correct by discussing thedifference between empirical probability and the probability you found inpart a. (5 points)67. Voldermort is running a gambling ring in the basement of Patterson OfficeTower and you decide to stop by and see what games he is offering. The gameconsists of rolling two dice one time. If you get the same number on each die ,you win and receive a payout. Otherwise you lose and receive no payout. Theamount of money that Voldermort pays you in each situation is given by thechart below. The game costs $5 to play one time. Should you? You must leaveyour expected value in the form of a reduced fraction. (10 points)Die 1 Die 2 Payout1 1 $52 2 $103 3 $154 4 $205 5 $256 6 $3078. Sophia Venn, a MA202 student on a far away planet decided not to study for thesecond exam and made the following statements concering rectangles, squares,rhombuses, and trapezoids:• Rectangles are always squares.• Rhombuses are never squares.• Trapezoids are sometimes squares.Please help Sophia by answering the following questions.(a) What incorrect statements did Sophia make about squares? (5 points)(b) How would you explain to Sophia the relationship between rectangles,squares, rhombuses, and trapezoids? You may use a diagram to aid inyour explanation if you like. Be sure to label all of your sets. (10 points)89. Extra Credit: Mayor West challenges you to read his mind. He offers a key tothe city of Quahog if you can guess the number of sides of the convex polygonhe is thinking of and gives you the following clue. The average interior anglemeasure of the convex polygon Mayor West is envisioning is 174◦. What is thenumber of sides of the polygon? Explain how you found your answer. (Hint:Use a theorem about the sum of interior angles for convex polygons.) (5