Sunday, April 20, 2014

ALGEBRA 2 ------ BY. MWL. JAPHET MASATU.

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 Reading Math
Learning Mathematics
The Language of Mathematics
Symbols in Algebra

Sets

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

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 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

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 inequalities.

Introduction to Inequalities a≥b
Properties of Inequalities
Intervals


Exponents

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

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


Equations

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

Equations and Formulas
Solving Equations
Simplify
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 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


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? 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

Solving

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
Matrices
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

Probability

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


Finally

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:

No comments:

Post a Comment