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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 1

This homework was originally designed to motivate some lecture topics and set up some information for later reference (problems 1-7). Also, it can take a week or more for such matters as buying or borrowing a graphing calculator to be resolved.

  1. (4 points) Count to ten by ones.
    1. Write these numbers down in order both with names (words) and in symbols (digits).
    2. What number did you start with? Why?
    3. What number comes next after ten?
    4. How many numbers come before ten?

     

  2. (3 points) Suppose you have two egg cartons each filled with a dozen eggs. However, the egg cartons are not the same shape--i.e. one is long and skinny, the other is short and fat. (i.e. is an abbreviation for the Latin term id est meaning that is (to say).)
    1. What are the two most likely configurations of eggs in these cartons?
    2. What is another possible, but unlikely configuration?
    3. What are two ways to show that each carton has the same number of eggs?

     

  3. Repeat problem one, part one, but instead of assuming arabic numbers, write your results using roman numerals.

     

  4. (2 points) Begin with the number two.

     

  5. Suppose a new toy costs a hundred clams, but you only have eighty-nine clams. After you buy the toy, how many clams do you have (i.e. you may have borrowed)? Show your work.

     

  6. By long division and showing your work, determine how many times six goes into one million. If it did not go evenly, what is the remainder?

     

  7. Preferably using the process of long division and showing your work, determine how many times seven goes into one million. If it did not go evenly, what is the remainder?
  8. Name a counting song.

    For problems 9 - 11: Given A = {m,a,t,h} and B = {e,a,s,y}.

  9. Find AB.

  10. Find AB.

  11. Find A'.

     

  12. Given A = {-2, 0, 4, 7} and B = {-4, -2, 0}, show both A B and A B using Venn Diagrams.

     

  13. Given A = {x > 4} and B = {x < 3}, find A B and A B using real number lines.

     

  14. Given M = {residents of Michigan} and N = {residents of Niles, Michigan},
    describe in words M N and M N.

     

  15. Given B = {youths attending BCYF} and C = {BCM&SC students},
    describe in words B C and B C.

     

  16. Draw a Venn Diagram of the previous exercise. What might the Universal Set be?

     

  17. (3 points) Use Venn Diagrams to prove whether these statements are true.
    1. Complement of (A B) = complement of A complement of B.
    2. (A B) C = A (B C)
    3. A (B C) = (A B) (A C)

  18. (2 points) Given: X = {1,3,5,7,9},       Y = {1,6,11,16...},      Z = {0,2,4,6,8...}.
    Find:
    1. (X Z) Y
    2. (X Y) Z

  19. When you get your Geometry textbook, read section 2.5 and look carefully at problems 2, 9, 14, 15, and 19. Note the application of unions and intersections to geometric figures.

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