| |

| |

| |

Review of Basic Algebraic Concepts | |

| |

| |

| |

Sets of Number and Interval Notation | |

| |

| |

| |

Operation on Real Numbers | |

| |

| |

| |

Simplifying Expressions | |

| |

| |

| |

Linear Equations in One Variable -- Problem Recognition Exercises: Expressions and Equations | |

| |

| |

| |

Applications of Linear Equations in One Variable | |

| |

| |

| |

Literal Equations and Applications to Geometry | |

| |

| |

| |

Linear Inequalities in One Variable | |

| |

| |

| |

Properties of Integer Exponents and Scientific Notation | |

| |

| |

| |

Graphing Linear Equations and Functions | |

| |

| |

| |

Linear Equations in Two Variables | |

| |

| |

| |

Slope of a Line -- Problem Recognition Exercises: Intercepts and Slope | |

| |

| |

| |

Equations of a Line | |

| |

| |

| |

Application of Linear Equations and Modeling | |

| |

| |

| |

Introduction to Relations | |

| |

| |

| |

Introduction to Functions | |

| |

| |

| |

Graphs of Basic Functions | |

| |

| |

| |

Systems of Linear Equations | |

| |

| |

| |

Solving Systems of Linear Equations by Graphing | |

| |

| |

| |

Solving Systems of Linear Equations by Using the Substitution Method | |

| |

| |

| |

Solving Systems of Linear Equations by Using the Addition Method -- Problem Recognition Exercises: Method of Solving Systems of Equations | |

| |

| |

| |

Applications of Systems of Linear Equations in Two Variables | |

| |

| |

| |

Systems of Linear Equations in Three Variables and Applications | |

| |

| |

| |

Solving Systems of Linear Equations by Using Matrices | |

| |

| |

| |

Polynomials | |

| |

| |

| |

Addition and Subtraction of Polynomials and Polynomial Functions. | |

| |

| |

| |

Multiplication of Polynomials | |

| |

| |

| |

Division of Polynomials -- Problem Recognition Exercises: Operations on Polynomials | |

| |

| |

| |

Greatest Common Factor and Factoring by Grouping | |

| |

| |

| |

Factoring Trinomials | |

| |

| |

| |

Factoring Binomials | |

| |

| |

| |

Additional Factoring Strategies | |

| |

| |

| |

Solving Equations by Using the Zero Product Rule | |

| |

| |

| |

Rational Expressions and Rational Equations | |

| |

| |

| |

Rational Expressions and Rational Functions | |

| |

| |

| |

Multiplication and Division of Rational Expressions | |

| |

| |

| |

Addition and Subtraction of Rational Expressions | |

| |

| |

| |

Complex Fractions -- Problem Recognition Exercises: Simplifying Rational Expressions | |

| |

| |

| |

Solving Rational Equations -- Problem Recognition Exercises: Rational Expressions and Equations | |

| |

| |

| |

Applications of Rational Equations and Proportions | |

| |

| |

| |

Variation | |

| |

| |

| |

Radicals and Complex Numbers | |

| |

| |

| |

Definition of an nth-Root | |

| |

| |

| |

Rational Exponents | |

| |

| |

| |

Simplifying Radical Expressions | |

| |

| |

| |

Addition and Subtraction of Radicals | |

| |

| |

| |

Multiplication of Radicals -- Problem Recognition Exercises: Operations on Radical Expressions | |

| |

| |

| |

Rationalization | |

| |

| |

| |

Solving Radical Equations | |

| |

| |

| |

Complex Numbers | |

| |

| |

| |

Quadratic Equations and Functions | |

| |

| |

| |

Square Root Property and Completing the Square | |

| |

| |

| |

Quadratic Formula | |

| |

| |

| |

Equations in Quadratic Form -- Problem Recognition Exercises: Recognizing Equation Types | |

| |

| |

| |

Graphs of Quadratic Functions | |

| |

| |

| |

Applications of Quadratic Functions and Modeling | |

| |

| |

| |

More Equations and Inequalities | |

| |

| |

| |

Compound Inequalities | |

| |

| |

| |

Polynomial and Rational Inequalities | |

| |

| |

| |

Absolute Value Equations | |

| |

| |

| |

Absolute Value Inequalities -- Problem Recognition Exercises: Equations and Inequalities | |

| |

| |

| |

Linear Inequalities in Two Variables | |

| |

| |

| |

Exponential and Logarithmic Functions | |

| |

| |

| |

Algebra and Composition of Functions | |

| |

| |

| |

Inverse Functions | |

| |

| |

| |

Exponential Functions | |

| |

| |

| |

Logarithmic Functions | |

| |

| |

| |

Properties of Logarithms | |

| |

| |

| |

The Irrational Number e -- Problem Recognition Exercises: Logarithmic and Exponential Forms | |

| |

| |

| |

Exponential and Logarithmic Equations | |

| |

| |

| |

Conic Sections | |

| |

| |

| |

Distance Formula, Midpoint, and Circles | |

| |

| |

| |

More of the Parabola | |

| |

| |

| |

The Ellipse and Hyperbola -- Problem Recognition Exercises: Identifying and Graphing Conic Sections | |

| |

| |

| |

Nonlinear Systems of Equations in Two Variables | |

| |

| |

| |

Nonlinear Inequalities and System if Inequalities | |

| |

| |

Additional Topics Appendix | |

| |

| |

| |

Binomial Expansions | |

| |

| |

| |

Determinants and Cramer's Rule | |

| |

| |

| |

Sequences and Series | |

| |

| |

| |

Arithmetic and Geometric Sequences and Series | |