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Sample Problems for Exam 2
Math 365

  1. Write the numbers 125, 3,255 and 1,002,334 in Roman, Egyptian and Mayan notation.
  2. Add tex2html_wrap_inline68 to tex2html_wrap_inline70 .
  3. Find tex2html_wrap_inline72 .
  4. Compare and contrast the Egyptian or the Mayan (Choose one!) to our (Hindu-Arabic) notational system.
  5. Suppose you have an abacus with five beads on each wire. How would you represent the number 723 on this abacus? 125? 30?
  6. Write the base twelve representation for each of tex2html_wrap_inline74 , tex2html_wrap_inline76 , tex2html_wrap_inline78 , tex2html_wrap_inline80 and tex2html_wrap_inline82 .
  7. What is the base sixty notation for 255? 360? 725?
  8. Write the numbers from one to 17 in base two, and in base seven.
  9. Sketch a solution, using either maps and strips OR place value cards, for tex2html_wrap_inline84 . Aside: In this question, how many units are there on a strip? a mat? what is the value of each place card?
  10. Describe, with mats and strips OR place cards, the problem 231-152.
  11. Do the same for tex2html_wrap_inline88 .
  12. Use a non-standard algorithm to solve the problem 125+779 and 1355+7992.
  13. Use an instructional algorithm to solve the problem 561- 279.
  14. Multiply tex2html_wrap_inline96 and tex2html_wrap_inline98 . (Leave the answer in base six.)
  15. Find tex2html_wrap_inline100 and tex2html_wrap_inline102 .
  16. Solve both tex2html_wrap_inline104 and tex2html_wrap_inline106 using an instructional (so non-standard) algorithm.
  17. Draw a number line representation of 4, 7, -2 and -6.
  18. Draw a number line representation of 4 + (-3), 7 - 5 -7-2, -3+ 3 and -5-(-4).
  19. Write a word problem for which 460-120 is a valid representation. Do the same for 55+(150-23).
  20. Suppose you begin the day with $333 and when you go get the mail you have a bill for $531 AND a check from your favorite relative for $200. Write an equation for this situation, then find the solution.
  21. Describe the Cartesian product model for multiplication.
  22. Define division of integers.
  23. What is (-a)(-b)=? why? a(-b)=? Again, why?
  24. What (if anything) is the additive inverse of -s, where s is an integer? Does -s have a multiplicative inverse? Why or why not?
  25. Are the integers closed under addition? subtraction? multiplication? division? Why or why not?
  26. What (if anything) is the additive identity for the integers? the multiplicative identity?


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Next: About this document

Andrew Diener
Tue Oct 26 18:39:02 CDT 1999