Detailed Course Information

Prerequisites

• The Top Ten List of Mistakes
• Concepts of Inequality
• Inequalities and Interval Notation
• Properties of Absolute Value
• Evaluating Absolute Value Expressions
• An Introduction to Exponents
• Evaluating Exponential Expressions
• Applying the Rules of Exponents
• Evaluating Expressions with Negative Exponents
• Converting between Decimal and Scientific Notation
• Converting Rational Exponents and Radicals
• Simplifying Radical Expressions
• Simplifying Radical Expressions with Variables
• Rationalizing Denominators
• Determining Components and Degree
• Adding, Subtracting, and Multiplying Polynomials
• Multiplying Big Products
• Using Special Products
• Factoring Using the Greatest Common Factor
• Factoring by Grouping
• Factoring Trinomials
• Factoring Perfect Square Trinomials
• Factoring the Difference of Two Squares
• Factoring Sums and Differences of Cubes
• Factoring by Any Method
• Rational Expressions and Domain
• Working with Fractions
• Writing Rational Expressions in Lowest Terms
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions
• Rewriting Complex Fractions
• Introducing and Writing Complex Numbers
• Rewriting powers of i
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers

• An Introduction to Solving Equations
• Solving a Linear Equation
• Solving a Linear Equation with Rationals
• Solving a Linear Equation That Has Restrictions
• An Introduction to Solving Word Problems
• Solving for Perimeter
• Solving a Linear Geometry Problem
• Solving for Consecutive Numbers
• Solving to Find the Average
• Solving for Constant Velocity
• Solving a Problem about Work
• Solving a Mixture Problem
• Solving an Investment Problem
• Solving Business Problems
• Solving Quadratics by Factoring
• Solving Quadratics by Completing the Square
• Completing the Square: Another Example
• Proving the Quadratic Formula
• Using the Quadratic Formula
• Predicting the Type of Solutions Using the Discriminant
• Solving for a Squared Variable
• Finding Real Number Restrictions
• Solving Fancy Quadratics
• An Introduction to Word Problems with Quadratics
• Solving a Quadratic Geometry Problem
• Solving with the Pythagorean Theorem
• Solving a Motion Problem
• Solving a Projectile Problem
• Solving Other Problems
• Determining Extraneous Roots
• Solving an Equation Containing a Radical
• Solving an Equation with Two Radicals
• Solving an Equation with Rational Exponents
• An Introduction to Variation
• Direct Proportion
• Inverse Proportion
• An Introduction to Solving Inequalities
• Solving Compound Inequalities
• More on Compound Inequalities
• Solving Word Problems Involving Inequalities
• Solving Quadratic Inequalities
• Solving Quadratic Inequalities: Another Example
• Solving Rational Inequalities
• Solving Rational Inequalities: Another Example
• Determining the Domains of Expressions with Radicals
• Matching Number Lines with Absolute Values
• Solving Absolute Value Equations
• Solving Equations with Two Absolute Value Expressions
• Solving Absolute Value Inequalities
• Solving Absolute Value Inequalities: More Examples

• Functions and the Vertical Line Test
• Identifying Functions
• Function Notation and Finding Function Values
• Determining Intervals Over Which a Function Is Increasing
• Evaluating Piecewise-Defined Functions for Given Values
• Solving Word Problems Involving Functions
• Finding the Domain and Range of a Function
• Domain and Range: One Explicit Example
• Satisfying the Domain of a Function
• An Introduction to Slope
• Finding the Slope of a Line Given Two Points
• Interpreting Slope from a Graph
• Graphing a Line Using Point and Slope
• Finding the Distance between Two Points
• Finding the Second Endpoint of a Segment
• Collinearity and Distance
• Triangles
• Finding the Center-Radius Form of the Equation of a Circle
• Finding the Center and Radius of a Circle
• Decoding the Circle Formula
• Solving Word Problems Involving Circles
• Graphing Equations by Locating Points
• Finding the x- and y-Intercepts of an Equation
• Writing an Equation in Slope-Intercept Form
• Writing an Equation Given Two Points
• Writing an Equation in Point-Slope Form
• Matching a Slope-Intercept Equation with Its Graph
• Slope with Parallel and Perpendicular Lines
• Constructing Linear Function Models of a Set of Data
• Linear Cost and Revenue Functions
• Graphing Some Important Functions
• Graphing Piecewise-Defined Functions
• Matching Equations with Their Graphs
• The Greatest Integer Function
• Graphing the Greatest Integer Function
• Using Operations on Functions
• Composite Functions
• Components of Composite Functions
• Finding Functions That Form a Given Composite
• Finding the Difference Quotient of a Function
• Deconstructing the Graph of a Quadratic Function
• Nice-Looking Parabolas
• Using Discriminants to Graph Parabolas
• Maximum Height in the Real World
• Finding the Vertex by Completing the Square
• Using the Vertex to Write the Quadratic Equation
• Finding the Maximum or Minimum of a Quadratic
• Graphing Parabolas
• Shifting Curves along Axes
• Shifting or Translating Curves along Axes
• Stretching a Graph
• Graphing Quadratics Using Patterns
• Determining Symmetry
• Reflections
• Reflecting Specific Functions

• Using Long Division with Polynomials
• Long Division: Another Example
• Using Synthetic Division with Polynomials
• More Synthetic Division
• The Remainder Theorem
• More on the Remainder Theorem
• The Factor Theorem and Its Uses
• Factoring a Polynomial Given a Zero
• Presenting the Rational Zero Theorem
• Considering Possible Solutions
• Finding Polynomials Given Zeros, Degree, and One Point
• Finding all Zeros and Multiplicities of a Polynomial
• Finding the Real Zeros for a Polynomial
• Using Descartes' Rule of Signs
• Finding the Zeros of a Polynomial from Start to Finish
• Matching Graphs to Polynomial Functions
• Sketching the Graphs of Basic Polynomial Functions
• Understanding Rational Functions
• Basic Rational Functions
• Vertical Asymptotes
• Horizontal Asymptotes
• Graphing Rational Functions
• Graphing Rational Functions: More Examples

• Understanding Inverse Functions
• The Horizontal Line Test
• Are Two Functions Inverses of Each Other?
• Graphing the Inverse
• Finding the Inverse of a Function
• Finding the Inverse of a Function with Higher Powers
• An Introduction to Exponential Functions
• Graphing Exponential Functions: Useful Patterns
• Graphing Exponential Functions: More Examples
• Using Properties of Exponents to Solve Exponential Equations
• Finding Present Value and Future Value
• Finding an Interest Rate to Match Given Goals
• e
• Applying Exponential Functions
• An Introduction to Logarithmic Functions
• Converting between Exponential and Logarithmic Functions
• Finding the Value of a Logarithmic Function
• Solving for x in Logarithmic Equations
• Graphing Logarithmic Functions
• Matching Logarithmic Functions with Their Graphs
• Properties of Logarithms
• Expanding a Logarithmic Expression Using Properties
• Combining Logarithmic Expressions
• Evaluating Logarithmic Functions Using a Calculator
• Using the Change of Base Formula
• The Richter Scale
• The Distance Modulus Formula
• Solving Exponential Equations
• Solving Logarithmic Equations
• Solving Equations with Logarithmic Exponents
• Compound Interest
• Predicting Change
• An Introduction to Exponential Growth and Decay
• Half-Life
• Newton 's Law of Cooling
• Continuously Compounded Interest

• An Introduction to Linear Systems
• Solving Systems with Substitution
• Solving Systems by Elimination
• An Introduction to Linear Systems in Three Variables
• Solving Linear Systems in Three Variables
• Solving Inconsistent Systems
• Solving Dependent Systems
• Solving Systems with Two Equations
• Investments
• Solving with Partial Fractions
• Solving Nonlinear Systems Using Elimination
• Solving Nonlinear Systems with Substitution
• An Introduction to Systems of Inequalities
• Graphing Systems of Inequalities
• Graphing the Solution Set of a System of Inequalities
• Solving for Maxima-Minima
• Applying Linear Programming

• An Introduction to Matrices
• The Arithmetic of Matrices
• Multiplying Matrices by a Scalar
• Multiplying Matrices
• Multiplying Matrices: Can They Multiply?
• Using the Gauss-Jordan Method
• Using Gauss-Jordan: Another Example
• Evaluating 2x2 Determinants
• Evaluating 3x3 Determinants
• Applying Determinants
• Using Cramer's Rule
• Using Cramer's Rule in a 3x3 Matrix
• An Introduction to Inverses
• Inverses: 2x2 Matrices
• Another Look at 2x2 Inverses
• Inverses: 3x3 Matrices
• Solving a System of Equations with Inverses

• An Introduction to Conic Sections
• An Introduction to Parabolas
• Determining Information about a Parabola from Its Equation
• Writing an Equation for a Parabola
• An Introduction to Ellipses
• Finding the Equation for an Ellipse
• Applying Ellipses: Satellites
• An Introduction to Hyperbolas
• Finding the Equation for a Hyperbola
• Applying Hyperbolas: Navigation
• Identifying a Conic
• Name That Conic

• Using the Binomial Theorem
• Binomial Coefficients
• Understanding Sequence Problems
• Solving Problems Involving Arithmetic Sequences
• Solving Problems Involving Geometric Sequences
• Proving Formulas Using Mathematical Induction
• Examples of Induction
• Solving Problems Involving Permutations
• Solving Problems Involving Combinations
• Solving for Probability and Odds: Dice Rolls
• Solving for Probability and Odds: Decks of Cards