Math Notes Essay

Submitted By bkingxd
Words: 1108
Pages: 5

Preliminaries

Integer Exponents In this section we will start looking at exponents and their properties.

Rational Exponents We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Real Exponents This is a short acknowledgment that the exponent properties from the previous two sections will hold for any real exponent.

Radicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals.

Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials This is the most important section of all the preliminaries. Factoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

Complex Numbers Here is a very quick primer on complex numbers and how to manipulate them.

Solving Equations and Inequalities

Solutions and Solution Sets We introduce some of the basic notation and ideas involved in solving in this section.

Linear Equations In this section we will solve linear equations, including equations with rational expressions.

Applications of Linear Equations We will take a quick look at applications of linear equations in this section.

Equations With More Than One Variable Here we will look at solving equations with more than one variable in them.

Quadratic Equations, Part I In this section we will start looking at solving quadratic equations. We will look at factoring and the square root property in this section.

Quadratic Equations, Part II We will finish up solving quadratic equations in this section. We will look at completing the square and quadratic formula in this section.

Quadratic Equations : A Summary We’ll give a procedure for determining which method to use in solving quadratic equations in this section. We will also take a quick look at the discriminant.

Applications of Quadratic Equations Here we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation.

Equations Reducible to Quadratic Form In this section we will solve equations that can be reduced to quadratic in form.

Equations with Radicals Here we will solve equations with square roots in them.

Linear Inequalities We will start solving inequalities in this section by looking at linear inequalities.

Polynomial Inequalities In this section we will look at solving inequalities that contain polynomials.

Rational Inequalities Here we will solve inequalities involving rational expressions.

Absolute Value Equations We will officially define absolute value in this section and solve equations that contain absolute value.

Absolute Value Inequalities We will solve inequalities that involve absolute value in this section.

Graphing and Functions

Graphing In this section we will introduce the Cartesian coordinate system and most of the basics of graphing equations.

Lines Here we will review the main ideas from the study of lines including slope and the special forms of the equation of a line.

Circles We will look at the equation of a circle and graphing circles in this section.

The Definition of a Function We will discuss the definition of a function in this section. We will also introduce the idea of function evaluation.

Graphing Functions In this section we will look at the basics of graphing functions. We will also graph some piecewise functions in this section.

Combining functions Here we will look at basic arithmetic involving functions as well as function composition.

Inverse Functions We will…