Pre-AlgebraAlgebra 1

Algebra 2

OK. So what are you going to learn here?

You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to solve them.

You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind.

With your new skills you will be able to put together mathematical models so you can find good quality solutions to many tricky real world situations.

Near the end of most pages is a "Your Turn" section ... do these! You need to balance your reading with doing. Answering questions helps you sort things out in your mind. And don't guess the answer: use pen and paper and try your best before seeing the solution.


So what is this thing called Mathematics? And how do you go about learning it?

  Welcome to Mathematics Reading Math
  Learning Mathematics
  The Language of Mathematics
  Symbols in Algebra


Next, we need to think about mathematics in terms of sets.

    Introduction to Sets



Now you know what a set is, let us look at different sets of numbers that you will be using:

  The Evolution of Numbers  
  Prime and Composite Numbers  
  Fundamental Theorem of Arithmetic  
  Whole Numbers and Integers  
  Rational Numbers Pi
  Using Rational Numbers
  Irrational Numbers
  0.999... = 1
  Real Numbers
  Imaginary Numbers square root of minus one
  Complex Numbers
  The Complex Plane
  Common Number Sets  


"Equal To" is nice but not always available. Maybe you only know that something is less than, or greater than. So let us learn about inequalities.

  Introduction to Inequalities a≥b
  Properties of Inequalities



You will be using exponents a lot, so get to know them well.

  Exponents 8 to the Power 2
  Using Exponents in Algebra
  Squares and Square Roots
  Squares and Square Roots in Algebra
  nth Root
  Fractional Exponents
  Laws of Exponents
  Exponents of Negative Numbers



Polynomials were some of the first things ever studied in Algebra. They are simple, yet powerful in their ability to model real world situations.

  What is a Polynomial? polynomial example
  Adding And Subtracting Polynomials
  Multiplying Polynomials
  Dividing Polynomials
  Polynomials - Long Division
  Degree (of an Expression)  
  Special Binomial Products  
  Difference of Two Cubes expand vs factor
  Factoring in Algebra
  Solving Polynomials
  Roots of Polynomials: Sums and Products
  Rational Expressions
  Using Rational Expressions  
  Fundamental Theorem of Algebra  
  Remainder Theorem and Factor Theorem  
  General Form of a Polynomial  

Graphing Polynomials

  How Polynomials Behave  
  Polynomials: The Rule of Signs  
  Polynomials: Bounds on Zeros  



And, of course, you need to know about equations ... and how to solve them.

  Equations and Formulas  
  Solving Equations  
  Zero Product Property  
  Implication and Iff  
  Theorems, Corollaries, Lemmas  



Graphs can save you! They are a great way to see what is going on and can help you solve things. But you need to be careful as they may not always give you the full story.

  Cartesian Coordinates Intercepts
  Pythagoras' Theorem
  Distance Between 2 Points
  Graph of an Equation
  Finding Intercepts From an Equation
  Symmetry in Equations


Linear Equations

They are just equations for lines. But they come in many forms.

  Equation of a Straight Line Slope-Intercept Form
  Linear Equations
  Point-Slope Equation of a Line
  General Form of Equation of a Line
  Equation of a Line from 2 Points
  Midpoint of a Line Segment
  Parallel and Perpendicular Lines



A function just relates an input to an output. But from that simple foundation many useful things can be built.

  What is a Function? doman and range
  Domain, Range and Codomain
  Evaluating Functions
  Increasing and Decreasing Functions
  Maxima and Minima of Functions
  Even and Odd Functions
  Set-Builder Notation

Common Functions Reference:

  Function Transformations  
  Equation Grapher  
  Operations with Functions  
  Composition of Functions  
  Inverse Functions  


Equations of Second Degree

"Second degree" just means the variable has an exponent of 2, like x2. It is the next major step after linear equations (where the exponent is 1, like x).

  Quadratic Equations Quadratic Graph
  Factoring Quadratics
  Completing the Square
  Derivation of Quadratic Formula
  Graphing Quadratic Equations
  Circle Equations


You already have experience in solving, but now you can learn more!

  Mathematical Models 3d Box
  Approximate Solutions
  Intermediate Value Theorem
  Solving Radical Equations
  Change of Variables
  Algebra Mistakes


Solving Inequalities

We learned about inequalities above, now let's learn how to solve them.

  Solving Inequalities  
  Graphing Linear Inequalities  
  Solving Quadratic Inequalities  
  Solving Rational Inequalities  
  Absolute Value in Algebra  


Exponents and Logarithms

You know about exponents ... well logarithms just go the other way. And together they can be very powerful.

  Working with Exponents and Logarithms Exponent vs Logarithm
  Exponential Function
  Logarithmic Function
  Exponential Growth and Decay

Systems of Linear Equations

What happens when you have two or more linear equations that work together? They can be solved! It isn't too complicated, but can take quite a few calculations.

  Systems of Linear Equations A Matrix
  How to Multiply Matrices
  Determinant of a Matrix
  Inverse of a Matrix:
  Matrix Calculator
  Solving Systems of Linear Equations Using Matrices  
  Systems of Linear and Quadratic Equations  


Is it likely? You be the judge!

  Probability lock
  The Basic Counting Principle
  Combinations and Permutations

Sequences, Series and Partial Sums

A Sequence is a set of things (usually numbers) that are in order. You can also sum up a series, where Sigma Notation is very useful.

  Sequences sequence term
  Sequences - Finding A Rule
  Sigma Notation
  Partial Sums
  Arithmetic Sequences and Sums
  Geometric Sequences and Sums



These last few subjects use what you have learned above.

  Partial Fractions  
  Mathematical Induction  
  Pascal's Triangle  
  Binomial Theorem  


And that is all!


Other Algebra topics that may interest you now: