Download Foundations of Arithmetic Exam 2 - Spring 2009 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! M316K – Foundations of Arithmetic Spring 2009 Exam 2 – Version Y You have 50 minutes to take this exam. No books, notes, calculators, or other electronic devices are allowed. Please write everything you want me to grade in your blue book; you will be allowed to take these questions with you when you are done. On the front of your blue book, please indicate which five questions you want graded. If you don’t choose which questions I should grade, then I will choose for you at random. Also, please sign the upper right corner of your blue book; by your signature, you affirm the following Honor Pledge: “I pledge that I will neither give nor receive any unauthorized help on this exam. I will not use any books, notes, calculators, or other electronic devices while taking this exam. I will not attempt to look at any other student’s paper, nor will I engage in behavior that will put me at risk of accidentally seeing another student’s paper. I will stop working immediately when time is called.” ♠ ♠ ♠ PART A: Reading. Please answer one of the following questions. Keep in mind that your goal is to demonstrate that you have read the material and understood the important points, so don’t spend time trying to craft an exquisitely written essay. There is no length limit for this question, but you should easily be able to fit your response on one page. A1. Define each of the following terms or phrases as precisely as you can: a divides b, prime number, unique prime factorization (be sure to explain what the word “unique” means here), least common multiple. On the definition of “a divides b,” please say something more than “a is a factor of b” or “b is divisible by a”; explain what these ideas mean. A2. What is the difference between a model for an operation and an algorithm for an operation? Give an example of a model for multiplication (don’t just give me the name; show me what it is) and an algorithm for multiplication (again, I want more than the name). PART B: Explorations. Please answer two of the following questions. Do not mix-and-match parts of different questions; if you choose to answer a question, you are expected to answer all parts of that question. B1. Show three different ways, other than the standard subtraction algorithm, to perform the subtraction 711− 458. You don’t have to write any explanation on these, as long you write enough work for me to see what you are doing. Which of these methods do you believe is easiest, and why? B2. Answer the following questions. On each question, show your work. (a) Gina and Harry are obsessive e-mail checkers. Gina checks her e-mail regularly every 40 min- utes, and Harry checks his e-mail regularly every 36 minutes. If Gina and Harry both check their e-mail at exactly 9:34 AM, when will be the next time that they simultaneously check their e-mail? (Tell me what time it will be, not just how long it will take.) (b) Suppose Kirsten wants to tile a 54-inch-by-78-inch rectangle with square tiles. All the square tiles are to be the same size, with side length a whole number of inches. Kirsten isn’t allowed to overlap or break the tiles, or leave tiles hanging off the edges of the rectangle. What is the largest possible side length the tiles can have? How many of these tiles would she need? (See the diagram on the board.) 1
