• 3.1 - Graphing Inequalities

Graphing Lines

Labeling lines (EQUALITIES!)

Shading the FALSE region

Finding corner points

Bounded - can enclose feasible region in a circle

Unbounded - cannot enclose feasible region in a

circle

**• 3.2 - Setting-up LP Problems**

Defining variables correctly

OBJ Function (Max or Min statement)

Constraints (Almost always inequalities)

**• 3.3 - Graphical Solutions to LP Problems**

Graph constraints to find feasible region -

including corner points

Look at the placement of the feasible region -

decide if a max or min exists in that region

Set up chart with corner points and evaluate OBJ

function at each corner point

Locate the max or min value depending on the

problem

If solving a word problem, be able to give answer

in terms the problem. Be able to determine

leftover resources.

**• 6.1 - Sets and Set Operations**

Know how to read both roster and set-builder no-

tation

Know the meaning of and U

Know DeMorgan’s Laws

Be able to shade portions of Venn diagrams

Be able to use set notation to describe regions

Be able to read set notation to describe sets in

words

**• 6.2 - The Number of Elements in a Set**

n(A) = the number of elements in a set

If disjoint, n(A ∪ B) = n(A) + n(B)

For any sets, n(A ∪ B) = n(A)+n(B)−n(A∩B)

Be able to fill in the sections of a Venn diagram

with the number of elements in each section

**• 6.3 - The Multiplication Principle
**

he total # of ways to perform a large task is

the product of the # of ways to perform each

subtask

Be able to draw a tree diagram

**• 6.4 - Permutations and Combinations**

Permutations - ORDER MATTERS!

Things in a Line or Row, Titles for Group

Members, etc.

n! ways to permute n distinct objects

ways to permute n non-distinct obj.

Combinations - ORDER DOES NOT MATTER!

Groups where people have no titles, etc.

Know how to use calc. to find the # of perm. and

comb.

Mixed Problems - counting with both perm. and

comb. in the same problem

**• Counting Handouts**

**• 7.1 - Experiments, Sample Spaces, and
Events**

Sample Points - outcomes of an exp.

Sample Space (S) - all possible sample points

A common sample space is that of rolling two

fair dice.

Events - subsets of S

- impossible event

S - certain event

Simple Events - contain exactly one sample

point

There are 2^{n} total events for an exp. having

n sample points.

Mutually Exclusive Events - don’t occur at the

same time

A ∩ B =

P(A ∪ B) = P(A) + P(B)

**• 7.2 - Definition of Probability**

P(E) denotes the prob. that event E occurs

P(E) is a NUMBER such that 0 ≤ P(E) ≤ 1

Uniform Sample Space - all outcomes are equally

likely; the prob. of each simple event is 1/n

where n=the number of outcomes

Probability Distribution - a TABLE giving the

prob. associated with each simple event

**• 7.3 - Rules of Probability**

P(S) = 1

0 ≤ P(E) ≤ 1 for every event E

P(E ∪ F) = P(E) + P(F) − P(E ∩ F)