Higher Algebra

Also known equally "High School Algebra"

OK. So what are yous going to learn here?

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

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

With your new skills y'all will be able to put together mathematical models then you can notice skilful quality solutions to many tricky real earth situations.

Near the end of about pages is a "Your Turn" department ... do these! You demand to balance your reading with doing. Answering questions helps yous sort things out in your mind. And don't estimate the answer: apply pen and paper and attempt your best before seeing the solution.

Language

And then what is this thing called Mathematics? And how exercise you lot go most learning it?

Reading Math

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

Sets

Side by side, we need to think almost mathematics in terms of sets.

set

  • Introduction to Sets

Numbers

Now we know what a set is, let us await at dissimilar sets of numbers that are useful:

  • The Evolution of Numbers
  • Prime and Composite Numbers
  • Primal Theorem of Arithmetics
  • Whole Numbers and Integers

pi symbol

  • Rational Numbers
  • Using Rational Numbers
  • Irrational Numbers
  • 0.999... = 1
  • Existent Numbers

square root of minus one

  • Imaginary Numbers
  • Complex Numbers
  • Multiplying Circuitous Numbers
  • The Circuitous Plane

  • Common Number Sets

Inequalities

"Equal To" is overnice but not e'er available. Mayhap we merely know that something is less than, or greater than. So permit'due south larn about inequalities.

a≥b

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

Exponents

Nosotros volition be using exponents a lot, so permit's get to know them well.

8 to the Power 2

  • 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 beginning things e'er studied in Algebra. They are simple, yet powerful in their ability to model real world situations.

polynomial example

  • What is a Polynomial?
  • Calculation And Subtracting Polynomials
  • Multiplying Polynomials
  • Polynomials - Long Multiplication
  • Dividing Polynomials
  • Polynomials - Long Partition

  • 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

  • Primal Theorem of Algebra
  • Residual Theorem and Factor Theorem
  • General Course of a Polynomial

Graphing Polynomials

  • How Polynomials Behave
  • Polynomials: The Rule of Signs
  • Polynomials: Premises on Zeros

Equations

And, of course, we need to know nigh 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 u.s.! They are a great way to see what is going on and can assistance us solve many things. Merely nosotros need to be careful, as they sometimes don't requite the total story.

Intercepts

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

Linear Equations

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

Slope-Intercept Form

  • Equation of a Straight Line
  • Linear Equations
  • Point-Gradient 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 relates an input to an output. But from that uncomplicated foundation many useful things tin can exist built.

doman and range

  • What is a Function?
  • Domain, Range and Codomain

  • Evaluating Functions

  • Increasing and Decreasing Functions
  • Maxima and Minima of Functions
  • Fifty-fifty and Odd Functions
  • Set up-Architect Notation

  • Common Functions Reference:

    • Square Function
    • Square Root Role
    • Cube Function
    • Reciprocal Function
    • Absolute Value Office
    • Floor and Ceiling Part

  • Part Transformations
  • Equation Grapher
  • Operations with Functions
  • Composition of Functions
  • Changed Functions

Equations of 2d Degree

"2nd degree" but ways the variable has an exponent of 2, similar ten2. Information technology is the side by side major step after linear equations (where the exponent is 1, similar x).

Quadratic Graph

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

Solving

We already have experience in solving, but at present we can learn more!

3d Box

  • Mathematical Models and Mathematical Models 2
  • Judge Solutions
  • Intermediate Value Theorem
  • Solving Radical Equations
  • Change of Variables
  • Algebra Mistakes

Solving Inequalities

We learned about inequalities above, at present let'south 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

We already know about exponents ... well logarithms only get the other manner. And together they can exist very powerful.

Exponent vs Logarithm

  • 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 we have two or more linear equations that work together? They can often exist solved! It isn't very hard merely can take a lot of calculations.

A Matrix

  • Systems of Linear Equations

  • Matrices
  • Types of Matrix
  • How to Multiply Matrices
  • Determinant of a Matrix
  • Changed of a Matrix:
    • Using Uncomplicated Row Operations (Gauss-Hashemite kingdom of jordan)
    • Using Minors, Cofactors and Adjugate
  • Scalar, Vector, Matrixand Vectors
  • Matrix Calculator
  • More at Matrix Index

  • Solving Systems of Linear Equations Using Matrices

  • Systems of Linear and Quadratic Equations

Probability

lock

Is it probable? Y'all exist the approximate!

  • Probability
  • The Basic Counting Principle
  • Combinations and Permutations

Sequences, Series and Fractional Sums

A Sequence is a set of things (usually numbers) that are in social club. We can also sum upward a series, where Sigma Annotation is very useful.

sequence term

  • Sequences
  • Sequences - Finding A Rule
  • Sigma Notation
  • Fractional Sums
  • Arithmetic Sequences and Sums
  • Geometric Sequences and Sums

Finally

These last few subjects use what we have learned in a higher place.

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

And that is all!

But at that place are many other interesting algebra topics such as:

  • Euler's Formula for Circuitous Numbers
  • Taylor Series (needs a basic agreement of derivatives)