**Freshman Year Math Concept Map**

**Area of plane figures**

Counting, sets, & Probability

Euclidean geometry

linear systems

Circles

Area of disc sectors

scale factors

advanced objectives

basics

n-Gon Video

circumference & diameter

chord, secant, arc, sector

the definition of a circle

circle equations

tangent segments

circle proofs with tangents

basic probability with dice

How many different rolls where order

does

matter?

How many ways can the sum be 5 or less?

Probability you roll a sum of 6 or more?

3 dice roll permutations

3 dice 5 or less sum

3 dice p(sum =6+)

6*6*6 = 6^3

probability trees

unions and intersections

set complements

harder trees

combinations and permutations

Combinations:

n!/(n-r)! * (r!)

(rid duplicates)

Permutations:

n!/(n-r)!

(don't rid duplicates)

simple problems

Expected value

independent and conditional/dependent events

Independent Events are not influenced by another event happening; their likelihood never changed based on previous events. Picking multiple cards from a deck are NOT independent events; they are dependent because as you pick, the number of total cards in the deck changes. However, picking cards with replacement are independent events because the total number of cards in the deck doesn't change. Dependent Events only happen

given another circumstance. For example, a problem that asks you to find P(A|B) is dependent because you are finding the probability A happens given that B happened.

mutually exclusive events

sets within sets

at least problems

baye's theorem

P(A|B)=P(B|A)*P(A)/P(B)

quadrilateral proofs

congruency types

diagonals of square congruent & bisect each other

shortest distance to...

constructions: bisectors

different forms

inequalities

midpoints of segments

parallel & perpendicular

reflections

Reflecting across the axes

simple ones

graphing

absolute value inequalities

number line solutions

graphing

generalizations

piecewise functions

inverses

systems of equations

advanced coordinate geometry

similar and right triangles

special triangles

clinometer problems

trigonometry

problems

coordinate geometry

advanced trig

oblique triangles