Overview for Exam 1
Included is a list of main topics you should know for the exam. To see how these might be asked, study your class notes and review your HW problems.
· Know that our number system, base 10, is Hindu-Arabic, and is positional, not additive.
· Egyptian: Base 10, I will remind you of the symbols, is not positional but additive.
· Babylonian: Base 60 (meaning??) is positional. It is vague without a 0 the two-stack of small triangles so you will also use these. As the symbols are only < (for 10) and Ñ (for 1), you should remember these.
· Roman: Base 10, not positional, additive and subtractive as long as you use only powers of 10 in front of a symbol to subtract. Remember all symbols from 1 (I) to 1000 (M).
· Be able to covert numbers in other bases to base 10 and vice-versa.
· Understand all set notations and definitions, including
o Listing vs. set-builder notation
o Is an element of symbol
o Equal sets is wrong in the book. Equivalent sets uses the tilde notation, and equivalent sets are in one-to-one correspondence.
o Cardinality of a set
o Empty set (check over properties from class)
o Subset of a set meaning and usage. Note how we showed one set was a subset of another set.
o Venn diagrams and how to use them
o The complement of a set and its meaning and usage
o A-B as the complement of B relative to A, its meaning and usage
· Know how to use the fundamental counting principle as in class: Total number of ways an event (that is a succession of events) can happen, the number of one-to-one correspondences between sets, and so on.
Dr. Lunts Materials Word Problems
Be able to put together a word problem from each of the following categories, or change from one sub-category to another in a given category.
o Join Problems: End Unknown, Start Unknown, Change Unknown (action involved)
o Separate Problems: End Unknown, Start Unknown, Change Unknown (action involved)
o Comparison Problems: Difference Unknown, Referent Unknown, Compared Set Unknown (no action involved)
o Part-Part-Whole Problems: Part Unknown, Whole Unknown (no action involved)
o Know the definitions of intersection (with an and) and union (with an or) and how to find them for given sets.
o Know how to use Venn diagrams to show equality of sets.
o Know how to use (and why using Venn diagrams) n(AB) = n(A) + n(B) n(A∩B)
o Know that addition and subtraction approaches mostly follow from either sets (objects, fingers, blocks, etc.) or number line reasoning.
o Know the following properties described by
o Closure of a set under an operation
o Commutative property of addition
o Associate property of addition
o Additive identity is 0