Detailed Course Description

The Real Numbers

• Properties, Identities, & Inverses
• An Introduction to Exponents
• Evaluating Exponential Expressions
• Working with Fractions
• Concepts of Inequality
• Inequalities and Interval Notation
• Properties of Absolute Value
• Evaluating Absolute Value Expressions
• Operations Considering Signs
• Prime and Composite Numbers and Their Roots
• Order of Operations
• Forms of Conditional Statements
• Inductive Reasoning

• An Introduction to Solving Equations
• Equality or Identity?
• Equivalent Equations and Equations with No Solution
• Solving Linear Equations
• An Introduction to Solving Word Problems
• Finding Perimeter
• Solving a Linear Geometry Problem
• Solving for Constant Velocity
• Solving a Business Problem
• Solving a Mixture Problem
• Solving an Investment Problem
• Solving for Consecutive Numbers
• Finding an Average
• An Introduction to Solving Inequalities
• Solving Inequalities
• Solving Word Problems with Inequalities
• Sets, Intersections, and Unions
• Solving Compound Inequalities
• More on Compound Inequalities
• Matching Number Lines with Absolute Value
• Solving Absolute Value Equations
• Solving Equations with Two Absolute Value Expressions
• Solving Absolute Value Inequalities
• Solving Absolute Value Inequalities: More Examples

• Using the Cartesian System
• Thinking Visually
• An Introduction to Slope
• Finding the Slope Given Two Points
• Finding the Distance and Midpoint between Two Points
• The Center-Radius Equation of a Circle
• Decoding the Circle Formula

• Using Intercepts to Graph Lines
• Working with Specific Lines
• Interpreting Slope from a Graph
• Graphing with a Point and the Slope
• Writing an Equation in Slope-Intercept Form
• Writing an Equation Given Two Points
• Writing an Equation in Point-Slope Form
• Matching a Point-Slope Equation with its Graph
• Slope for Parallel and Perpendicular Lines
• Constructing a Linear Model from a Set of Data
• Scatterplots and Predictions
• Interpreting Line Graphs
• Linear Cost and Revenue

• An Introduction to Linear Systems
• Solving a System by Graphing
• Solving a System by Substitution
• Solving a System by Elimination
• An Introduction to Systems in Three Variables
• Solving Systems with Three Variables
• Solving Inconsistent Systems
• Solving Dependent Systems
• Solving Systems with Two Equations
• Investments
• An Introduction to Graphing Linear Inequalities
• Graphing Inequalities with Two Variables
• Graphing the Solution Set of a System of Inequalities

• Applying the Rules of Exponents
• Evaluating Expressions with Negative Exponents
• Converting between Decimal and Scientific Notation
• Determining Components and Degree
• Adding and Subtracting Polynomials
• Multiplying Polynomials
• The FOIL Method
• Multiplying Big Products
• Using Special Products
• Factoring Using the Greatest Common Factor
• Factoring by Grouping
• Factoring Trinomials
• Factoring Trinomials: More Examples
• Factoring Perfect Square Trinomials
• Factoring the Difference of Two Squares
• Factoring Sums and Differences of Cubes
• Factoring by Any Method
• The Zero Factor Property
• Using Long Division with Polynomials
• Long Division: Another Example

• An Introduction to Rational Expressions
• Writing Rational Expressions in Lowest Terms
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions
• Rewriting Complex Fractions
• Solving a Linear Equation with Rationals
• Solving a Linear Equation with Restrictions
• Solving Rational Inequalities
• Solving Rational Inequalities: Another Example
• Determining Domain
• Solving a Problem About Work
• Resistors in Parallel
• An Introduction to Variation
• Direct Proportion
• Inverse Proportion
• Joint and Combined Proportion

• Radical Notation and Properties of Roots
• Variables and Negative Values under a Radical
• Converting Rational Exponents and Radicals
• Simplifying Radicals
• Simplifying Radical Expressions with Variables
• Adding and Subtracting Radical Expressions
• Rationalizing Denominators
• Solving an Equation Containing a Radical
• Solving Equations with Two Radical Expressions
• Extraneous Roots
• Solving Equations with Rational Exponents
• Introducing and Writing Complex Numbers
• Rewriting Powers of i
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Finding the Length of the Diagonal of a Cube
• Applications in Meteorology

• Introducing Relations and Functions
• Function Notation and Values
• Functions and the Vertical Line Test
• Finding Domain and Range
• Domain and Range: An Explicit Example
• Satisfying the Domain of a Function
• Graphing Important Functions
• An Introduction to Quadratics
• Solving Quadratics by Factoring
• Finding x- and y-Intercepts
• Nice-Looking Parabolas
• Graphing Parabolas
• Solving by Completing the Square
• Completing the Square: Another Example
• Finding the Vertex by Completing the Square
• Using the Vertex to Write the Equation
• Building a Polynomial Equation from Its Solutions
• Using the Vertex to Write the Equation
• Building a Polynomial Equation from Its Solutions
• Proving the Quadratic Formula
• Using the Quadratic Formula
• Predicting Types of Solution from the Discriminant
• Using the Discriminant to Graph Parabolas
• Solving for a Squared Variable
• Finding Real Number Restrictions
• Solving a Quadratic Geometry Problem
• Solving with the Pythagorean Theorem
• Solving a Motion Problem
• Solving a Projectile Problem
• Solving Other Problems