Sample Test II MATH 3032


 1. How many triangles are there in the following figure? (6 points)

            

 2. In each case below, determine the pattern and continue for the next three terms. (4 points each)

    a) 1, 8, 27, 64, ...

    b) 1, 4, 16, 64, ...

    c) 2, 2, 4, 6, 10, 16, ,,,

 3. Which of the following arrow diagrams are functions?

Explain each answer. (4 points each)

    a)

    b)

    c)

 4. What are the two numbers before and after each of the following? (5 points each)

    a) _____, _____, 387nine, _____, _____

    b) _____, _____, 400twelve, _____, _____

    c) _____, _____, 601eight, _____, _____

 5. Convert 426nine to base ten. (6 points)

 6. Convert 13421five to base ten. (6 points)

 7. Convert 437nine to base ten. (6 points)

 8. Convert 526 to base twelve. (6 points)

 9. Convert 978 to base five. (6 points)

10. Convert 1987 to base eleven. (6 points)

11. Compute the following subtraction problem in base six by the equal addition method. (6 points)

       3  3  4six

    - 1  5  5six

12. Compute the following subtraction problem in base eight. (6 points)

       4  1  6  2eight

    - 1  2  4  6eight

13. Compute the following subtraction problem in base twelve. (6 points)

       3  7  4  3twelve

    - 1  9  6  8twelve

14. Compute the following multiplication problem by the lattice method in base five. (6 points)

3 2 4 x 4 2five

15. Compute the following multiplication problem in base eleven by any method. (6 points)

2 9 8 x 3 2eleven

16. Compute the following division problem in base seven. (8 points)

4 3 4 4seven divided by 5 2seven

52 x 1 =    5 2seven

52 x 2 = 1 3 4seven

52 x 3 = 2 1 6seven

52 x 4 = 3 0 1seven

52 x 5 = 3 5 3seven

52 x 6 = 4 3 5seven

17. Mark each of the following as either TRUE or FALSE. (4 points each)

    a) For all numbers the GCF is less than or equal to the LCM.

    b) The cube of any number has a prime decomposition with only odd exponents.

    c) The square of any number has a prime decomposition with only even exponents.

18. Write each of the following with only one exponent. (3 points each)

    a) 7 2 9 divided by 32

    b) 4 x 83 x 642

19. Which is larger 810 or 168? And why. (4 points)

20. What is the digit in the ones place of 350? (5 points)

21. Given the following values:

     L  = 55 x 7 x 114 x 134

    M = 53 x 74 x 112 x 132

    N  = 56 x 72 x 115

what are each of the following numbers? You do not need to multiply them out. (6 points each)

    a) The G C F of M and N.

    b) The L C M of M and N.

    c) The G C F of L and N

    d) The L C M of L and M

22. What is the GCF of 64 x 73 x 83 and 66 x 72 x 82. (6 points)

23. What are the G C F and L C M of 96 and 72? (4 points each)

    a) G C F

    b) L C M

24. How many factors are there in each of the following? (4 points each)

    a) 32 x 53 x 72

    b) 62 x 74 x 82

25. Dr. Xiadies has 104 students in his classes. The ratio of math majors to non math majors is 4 to 9. How many math majors does he have? (4 points)

26. Suppose that you drive an average of 4460 miles every six months in your car. At the end of 2 3/4 years how far will you have driven your car? (4 points)


This page updated by Frank Matthews Nov. 13, 2003