Practice Quiz 1 covering Chapters 1 and 2

Quiz 1 Friday January 26 will consist of 6 questions. Each one will be like one of the 9 questions below. Each question is 5 points (for a total of 30 points on Quiz 1).

Instructions: Answer each question, and explain your answer. An answer alone is not enough for full credit. Your explanation must be clear and show how to get the answer. The actual exam will have a selection of 6 of the following problems, with some changes in the details of the problem.

  1. The UPC code on a Kleenex cents off coupon is 5 36000 51031 "?" (the 5 means it's a coupon, the 36000 gives the manufacturer, the 51031 is item specific and the "?" is supposed to be the check digit). What should the check digit be? (Remember: the UPC code is such that when you add every other digit starting with the first, triple the result and then add the remaining digits, you get an even multiple of 10.)
  2. Determine the remainder when 2637583736455264957563 is divided by 9.
  3. The Postnet bar code shown here has a single error in which either one vertical bar which should be long is short or vice versa:


    Express the correct zip code in ordinary characters. (Remember: the outside bars are framing bars which you ignore; also, the digit Postnet bar codes are as follows:
    1: ...|| 2: ..|.| 3: ..||. 4: .|..| 5: .|.|. 6: .||.. 7: |...| 8: |..|. 9: |.|.. 0: ||... Also, the digits in a valid Postnet code must sum to an even multiple of 10.)
  4. What is the sum of the measures of the vertex angles of a regular polygon with 41 sides?
  5. What is n for a regular n-gon if the sum of the measures of all but one of the n vertex angles is 3078 degrees?
  6. Show how to tile the plane with the following quadrilateral:

    Do this with a drawing in which the given polygonal tile is surrounded by 8 additional tiles, one for each vertex and side. (Use a separate piece of paper, tracing the given tile by placing the paper over it, and sliding the paper to a new position and tracing again, etc.)
  7. Determine the symmetries of the following strip pattern (which you should imgain as extending indefinitely to the right and left), and use crystallographic notation to classify the pattern:
           8              8              8              8              8              8
                  8              8              8              8              8              8
  8. Problem 7 on page 125 of the text: Find the value of the 26th Fibonacci number if the 25th is 75025 and the 27th is 196418.