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.

## Language

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

* Welcome to Mathematics
* Learning Mathematics
* The Language of Mathematics
* Symbols in Algebra

## Sets

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

* Introduction to Sets

## Numbers

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
* Using Rational Numbers
* Irrational Numbers
* 0,999... = 1
* Real Numbers

* Imaginary Numbers
* Complex Numbers
* Multiplying Complex Numbers
* The Complex Plane

* Common Number Sets

## Inequalities

"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 **in**equalities.

a≥b

* Introduction to Inequalities
* Properties of Inequalities
* Solving Inequalities
* Solving Inequality Word Questions
* Intervals

## Exponents

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

* Exponents
* Variables with Exponents
* 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

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?
* Adding And Subtracting Polynomials
* Multiplying Polynomials
* Polynomials - Long Multiplication
* Dividing Polynomials
* Polynomials - Long Division

* Degree (of an Expression)
* Special Binomial Products
* Difference of Two Cubes

* 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

## Equations

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

* Equations and Formulas
* Solving Equations
* Simplify
* Solving Word Questions
* Zero Product Property
* Implication and Iff
* Theorems, Corollaries, Lemmas

## Graphs

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
* 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
* 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

## Functions

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

* What is a Function?
* 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:
	+ Square Function
	+ Square Root Function
	+ Cube Function
	+ Reciprocal Function
	+ Absolute Value Function
	+ Floor and Ceiling Function

* 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
* Factoring Quadratics
* Completing the Square
* Derivation of Quadratic Formula
* Graphing Quadratic Equations
* Quadratic Equations in the Real World
* Circle Equations

## Solving

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

* Mathematical Models and Mathematical Models 2
* 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
* Inequality Graphing Tool
* 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.

* Introduction to Logarithms
* Exponents, Roots and Logarithms
* Working with Exponents and Logarithms
* 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

* Matrices
* Scalar, Vector, Matrixand Vectors
* How to Multiply Matrices
* Determinant of a Matrix
* Inverse of a Matrix:
	+ Using Elementary Row Operations (Gauss-Jordan)
	+ Using Minors, Cofactors and Adjugate
* Matrix Calculator

* Solving Systems of Linear Equations Using Matrices

* Systems of Linear and Quadratic Equations

## Probability

Is it likely? You be the judge!

* Probability
* 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
* Sequences - Finding A Rule
* Sigma Notation
* Partial Sums
* Arithmetic Sequences and Sums
* Geometric Sequences and Sums

## Finally

These last few subjects use what you have learned above.

* Partial Fractions
* Mathematical Induction
* Pascal's Triangle
* Binomial Theorem

*And that is all!*