| Syllabus | Contact Info |

Herbert J. Bernstein Professor of Computer Science
Dept. of Mathematics and Computer Science, 150 Idle Hour Blvd., KSC 121, Oakdale, NY 11769-1999

## 90092 MTH 1002 A -- Fundamentals of Mathematics -- Fall 2012 Online Course Quiz 1

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1002F12/MTH1002_Quiz_1.html

This is the weekly quiz for 11 September 2012 for the MTH 1002 course. Please do this quiz after you have completed the rest of assignment 1. It should take between one half hour and 2 1/2 hours to complete if you are well prepared, longer if not.

<==== Do this AFTER you've answered all the questions

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Notes:
• A fraction is of the form a/b, where a and b are integers and b is not zero.
• The number on top of a fraction is called the numerator.
• The number on the bottom is called the denominator.
• In a proper fraction, the magnitude of the numerator is less than the magnitude of the denominator.
• In order to add or subtract fractions we need to have a common denominator.
• When we multiply fractions, we just multiply the two numerators and multiply the two denominators.
• To divide two fractions, we turn the second fraction over and then multiply.

• A set is a collection of elements (objects in the set).
• We need to know the Universe (or universal set), U, from which elements of sets may be drawn.
• We list the elements of a set in curly brackets, or something similar.
• The empty set {} is often shown as ∅
• Order does not matter in a set.
• No duplicates are allowed in a set.
• We use the word "or" or the symbol ∪ ("cup") to get all the elements that are in one set or the other or both.
• We use the word "and" the symbol ∩ ("cap") to get only those elements that are in one set and are in the other set.
• We use the symbol ¬ ("not") to get those elements in the complement of the set, those elements from U that are not in the set. We also can use an apostrophe (') or a bar over the set to mean the complement. However, in this class, for quizzes and homeworks, please use the word "not".
• We use the symbols ∈, ⊂ and ⊃, to say that an element is contained in a set, that one set is contained in another or that one set contains another. The symbols ⊆ and ⊇ are sometimes used when it is important to emphasize the possibility that one set might be equal to the other, but in general every set is a subset of itself.
• When describing a set we use a vertical bar (∣) or the symbol (like element inclusion backwards and depressed) to say "such that".
For fraction problems, do not give the decimal fractions from a calculator when a propoer fraction reduced to lowest terms is requested.

1. Convert the following to a whole number and a proper fraction in lowest terms: 303/45

2. Convert the following to a whole number and a proper fraction in lowest terms: -785/103

3. Convert the following to a whole number and a proper fraction in lowest terms: 17/11

4. Convert the following to a whole number and a proper fraction in lowest terms: 87/17

5. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 4/12 + 7/28

6. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 11/13 + 5/39

7. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 38/17 + 4/51

8. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 55/72 - 11/6

9. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 1/3 + 3/6 - 1/5

10. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: ((1/3)*(3/6))/(1/5)

11. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∩ { 2, 4, 6, 8 }

12. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∪ { 2, 4, 6, 8 }

13. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∪ ( not { 2, 4, 6, 8 } ). Assume the universe is the set of non-negative whole numbers (0, 1, 2, ...)

14. For the following combination of sets, perform the indicated operations: { n | n2 < 36 } ∩ { m | 5m + 3 > 27 }. Assume the universe is the set of non-negative whole numbers (0, 1, 2, ...)

15. Simplify (x2 - x + 1) • (x + 1)

16. Factor 16x2 - 25

17. Simplify (x+y-z)2 - (x-y+z)2 + x*(4*z -4*y)

<==== Do this AFTER you've answered all the questions

You probably DON'T want to do this ===>

Updated 30 September 2012.