MA 201 - Math for Elementary TeachersExam 219 October 2006Name: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 use a graphing calculator on this exam.• The use of electronic equipment such as mp3 players, ipods, cell phones andother electronic devices (besides your calculator) 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. Write down the defintions of the following terms: (5 points each)• Greatest common divisor• Least common multiple• A prime number32. After the second exam a group of MA201 students: Molly, Thor, and Gargomel,decided to go out for pizza. They each ordered a two slices of pizza. Thesix slices ordered were one cheese, one pepperoni, one olive, one spinach, onemushroom, and one chicken. Given the information below, who ate which slices?(15 points)• Molly is a vegetarian.• Thor’s favorite cartoon is Popeye and ordered a slice of spinach pizza tohonor him.• Gargomel hates vegetables.• Thor has a weak stomach and can not eat olives or pepp eroni.• Someone ordered a slice of mushroom pizza and a slice of pizza with meat.43. Draw an array diagram to show that 5 does not divide 32. Be sure to explainyour diagram. (5 points)4. Construct a factor tree for the number 6930. (5 points)55. Compute the sum 1 + 4 + 7 + . . . + 73 + 76 + 79 while showing all work andexplain the steps you used to do this. Minimal partial credit will be given ifyou only give an answer. (10 points)66. Answer the following question concerning divisibility. (10 points)Is there a digit d so that 87, 543, 24d is divisible by 8 but not 16? Explain.77. (5 points each)• How many people must be in a room to ensure at least 2 of them have abirthday in the same month?• How many people must be in a room to ensure at least 3 of them have abirthday in the same month?88. Compute the following: (5 p oints each)• Find the GCD(1050, 1540) using prime-power representations.• Find the LCM(8, 14) using set intersection.• Find the GCD(210, 615) using the Euclidean Algorithm.• If the GCD(2268, 77175) = 63, then what is the LCM (2268, 77175)?99. Show 127 is a prime number. Be sure to explain your reasoning. State anydivisibility tests that you use. (Hint: First use a theorem that makes thisproblem shorter. Then use the divisibility tests.) (10 points)1010. Extra Credit:A checkerboard is composed of 64 squares, colored red or black arranged in 8rows and 8 columns. The color of each square is different from all four neigh-boring squares. We can cover the checker board with 32 dominos, where eachdomino covers two adjacent squares, one red and one black, of the checkerboard.Now suppose we remove the two opposite corners of the checkerboard that arered. Explain why you can or can not cover the remaining 62 squares with 31dominos. (5
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