MA 202 - Math for Elementary TeachersExam 1February 6 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 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. Let f be the function given by the formula f (x) = 7 − 2x on the domainD = {x | x = 1, 3, 5, 7}.(a) Make a table of the x− and y−values. (5 points)(b) Using set notation, what is the range of f? (5 points)(c) Graph the function f on a Cartesian coordinate system. Remember tolabel and give a scale to your axis. (5 points)32. Consider the two sets of data from seperate MA201 classes’ final exam scores:CLASS 1 : = {40, 52, 65, 66, 68, 71, 72, 73, 77, 77, 78, 78, 80, 81, 81, 83, 86, 87, 92, 99}CLASS 2 : = {55, 65, 66, 68, 72, 72, 73, 74, 76, 78, 79, 79, 80, 81, 85, 85, 85, 87, 90, 95}.(a) Give Box and Whiskers plots for both classes on a single axis. (10 points)(b) Compare the two classes using statistical measures discussed in class.Which class’ scores seem the “best” to you? (5 points)43. Your pal Freddy has done a survey and collected data concerning 100 UK stu-dents and claims to have ground breaking results. He claims the mean of hisdata set is 64.37 and the standard deviation is just 4.28. However you peak athis actual data set and see the data values 22, 31, 89, and 93. What should youtell Freddy of his calculations? What assumptions are being made? Answer inthe form of a paragraph. (6 points)4. (a) Find the equation of the line that passes through the points (4, −2) and(1, 2). Show all work. (5 points)(b) Does the point (10, −9) lie on the line? Justify your answer. (5 points)(c) Find the equation of the line through (−3, −4) that is parallel to the linethrough part a. Write you answer in slope-intercept form. (5 points)55. Below is a list of basketball scores by the Boston Celtics during their first 25home games last year.114 81 99 82 102100 100 90 83 110102 85 96 109 101109 98 102 103 9991 87 84 94 81(a) Give a physical representation of the data using one of the graphical repre-sentation techniques we have discussed this semester. Please explain yourrepresentation and why it is a good choice for this data set. (10 points)(b) The average for the basketball scores above is 96.08 points per game.Would the corresponding standard deviation for the data be closest to5, 10, or 15? Be sure to explain your reasoning and you may use yourrepresentation from part a. (5 points)66. Give definitions for the following terms. (5 points each)(a) Algebraic Expression -(b) The 68-95-99.7 rule -7. Your friend Marc Rosenbaum is studying the population of racoons in CentralPark, New York. One night Marc is able to capture, tag, and release 75 racoons.A month later, Marc catches 100 racoons in one night and notices that only 5of them were tagged from the previous month. Estimate the size of the racoonpopulation in Central Park using this information. (7 points)78. (a) Please give an example where the mean is a po or measure of central ten-dency for a set of data with at least 10 data values. You must give aspecific set of data and be sure to explain your example. (5 points)(b) Please give an example where the mode is a poor measure of central ten-dency for a set of data with at least 10 data values. You must give aspecific set of data and be sure to explain your example. (5 points)9. In your 4rth grade classroom, Nyki claims that “you could generate a randomsequence of numbers 2, 3, . . . , 12, by repeatedly tossing a pair of six-sided diceand adding up the two numbers facing up on the dice”. Is Nyki correct? If not,what is the problem with her theory? (7 points)810. EXTRA CREDIT: Suppose you have the two sets below:A = {a1, a2, . . . , a30}B = {b1, b2, . . . , b45}.If the mean of set A is 45, and the mean of set B is 65, what is the mean of thecombined data set:A ∪ B = {a1, a2, . . . , a30, b1, b2, . . . , b45}?(5