Algebra from A to Z 

An Introduction to Algebra


Constants – Finding the Numbers
Variables and Identities

A


Absolute Value


The Basics
Solving Equations
Graphing

Applications


Investing in the Stock Market
Number Word Problems
Applications of Quadratic Equations
Average Velocity

B


Binomial Theorem
Binomials

C


Circles


Pre-Algebra Level
Algebra Level
Graphing with Center At the Origin
Graphing with Center Off the Origin
Combining Like Terms

Completing the Square


Completing the Square – Preparing
Completing the Square – Solving Quadratics

Consecutive Integers


Linear Equations
Quadratic Equations
Coins
Coordinate Plane (also called the Cartesian Plane)
Counting – Factorials and Combinations

D


[Distance/Rate/Time: See Motion Problems.]

Distance on the Line and in the Plane

Distributive Property


The Basics
Double Distributing
Solving Equations

E


Ellipses

Equations


Introduction
Cubic (3rd Degree) and Quartic (4th Degree)
Containing Square Roots
Exponential Functions

Exponents


An Introduction
More
The Five Laws
Negative
Fractional

F


Factoring


The GCF (Greatest Common Factor)
Introduction to Factoring Quadratics
The Real Deal – Factoring Quadratics
Complete Factoring (Reducing Fractions, Solving Quadratics)
Advanced Factoring (Quartic, GCF, 4 Terms, Grouping, Substitution
The Sum and Difference of Cubes (Using Long Division)

Formulas


Using
Solving
Creating

Fractional Equations


Solving
Applications
Fractions and Decimals

Fractions


An Introduction
Signed Fractions, Powers, Roots, and Equations
Reducing with the GCF
Reducing Quadratics
Adding and Subtracting, Part I
Adding and Subtracting, Part II
Multiplying and Dividing

Functions


Tables and Mappings
Formulas and Graphs
Function Notation
Piecewise (Branch)

G


GCF - Solving Equations and Formulas

Geometry


A Non-Algebra Intro to Rectangles and Circles
Squares and Circles Using Algebra
Triangles and Angles
Triangles and Perimeter

Graphing


Graphing Lines
Graphing Lines - Revisited
Graph to Equation
Growth and Decay Formula

H


Horizontal Lines

I


Inequalities


Solving
Graphing in the Plane
Intercepts – Lines

[Intercepts for a Parabola: See Parabolas.]

Interval Notation

L


Like Terms


Combining
Solving Equations

Lines


Creating the Slope-Intercept Form: y = mx + b
Using the Slope-Intercept Form
Using the Point-Slope Form: yy1 = m(xx1)

Linear Modeling


Using Given Information
Using the Equation of a Line
Literal Equations
Logarithms
Logic

M


Midpoint on the Line and in the Plane

Mixture Problems


Coins
Nuts
Percent, Part I
Percent, Part II
Producing Widgets
Monomials

Motion Problems


An Introduction
Opposite Direction
Pursuit
Round Trip
Same Direction
Two-Part Journey

O


Order of Operations

P


Parabolas


Graphing
Intercepts (Factorable)
Intercepts (Non-Factorable)
Vertex
Parallel and Perpendicular Lines
Percents

Polynomials


Adding and Multiplying
Dividing
Proportions

Pythagorean Theorem


Finding the Hypotenuse
Finding a Leg
Radicals

Q


Quadratic Equations


Quadratic Equations by Factoring
Quadratic Equations by Taking Square Roots

Quadratic Formula


Preparing
Deriving
Rational Solutions
Irrational Solutions
Applications
Quadratic Modeling – Finding Maximums and Minimums

R


Radicals


Square Roots
Higher Roots
Adding, Subtracting, Multiplying, and Dividing
Ratios
Real Numbers and Their Properties

Radicals


Perimeter
Area

S


Scientific Notation
Sequences
Series
Sets

Signed Numbers


An Introduction
Adding and Subtracting
Multiplying and Dividing
Division by 0, Exponents, Equations
More on Signed Numbers and Equations

Systems of Equations


An Introduction
Substitution
Elimination
Graphing
Three Variables

Slope


Rise/Run
Δy/Δx
Special Lines

T


Temperature Formulas
Triangles and Angles
Triangles and Perimeter
Trinomials

V


Variation – Direct and Inverse
Velocity
Vertical Lines

Z


Zero



George Washington:

"Ninety-nine percent of the failures come from people who have the habit of making excuses."

 

Thomas Jefferson:
“I'm a great believer in luck, and I find the harder I work, the more I have of it.”

Extensive research has shown that 3 out of 4 people make up 75% of the population.

How come you can tune a piano, but you can't tuna fish?

A thief stole a calendar. He got twelve months.