Introductory and Intermediate Algebra

1.1a The Real Number Line and Inequalities

1.1b Introduction to Absolute Values

1.2 Addition with Real Numbers

1.3 Subtraction with Real Numbers

1.4 Multiplication and Division with Real Numbers

1.5 Exponents, Prime Numbers, and LCM

1.6a Reducing Fractions

1.6b Multiplication and Division with Fractions

1.7 Addition and Subtraction with Fractions

1.8 Order of Operations

1.9 Properties of Real Numbers

2.1a Variables and Algebraic Expressions

2.1b Simplifying Expressions

2.1c Evaluating Algebraic Expressions

2.2 Translating Phrases into Algebraic Expressions

2.3a Solving Linear Equations Using Addition and Subtraction

2.3b Solving Linear Equations Using Multiplication and Division

2.4 Solving Linear Equations

2.5 More Linear Equations: ax + b = cx + d

2.6a Applications: Number Problems and Consecutive Integers

2.6b Applications of Linear Equations: Addition and Subtraction

2.6c Applications of Linear Equations: Multiplication and Division

2.7 Applications with Percent

4.1 Introduction to the Cartesian Coordinate System

4.2 Graphing Linear Equations by Plotting Points

4.3 Graphing Linear Equations in Slope-Intercept Form

4.4a Finding the Equation of a Line

4.4b Graphing Linear Equations in Point-Slope Form

4.5 Introduction to Functions and Function Notation

4.6 Graphing Linear Inequalities

5.1 Simplifying Integer Exponents I

5.2a Simplifying Integer Exponents II

5.2b Scientific Notation

5.3 Identifying and Evaluating Polynomials

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6a The FOIL Method

5.6b Special Products

5.7a Division by a Monomial

5.7b The Division Algorithm

6.1a Greatest Common Factor of Two or More Terms

6.1b Greatest Common Factor of a Polynomial

6.1c Factoring Expressions by Grouping

6.2 Factoring Trinomials: Leading Coefficient 1

6.3a Factoring Trinomials by Trial and Error

6.3b Factoring Trinomials by Grouping

6.4a Special Factorizations - Squares

6.4b Special Factorizations - Cubes

6.5 Additional Factoring Practice

6.6 Solving Quadratic Equations by Factoring

6.7 Applications of Quadratic Equations

7.1a Defining Rational Expressions

7.1b Multiplication and Division with Rational Expressions

7.2 Addition and Subtraction with Rational Expressions

7.3 Complex Fractions

7.4a Solving Equations: Ratios and Proportions

7.4b Solving Equations with Rational Expressions

7.5 Applications Involving Rational Expressions

7.6 Applications: Variation

8.1 Solving Systems of Linear Equations by Graphing

8.2 Solving Systems of Linear Equations by Substitution

8.3 Solving Systems of Linear Equations by Addition

8.4 Applications: Distance - Rate - Time, Number Problems, Amounts and Costs

8.5 Applications: Interest and Mixture

8.6 Solving Systems of Linear Equations with Three Variables

8.7 Matrices and Gaussian Elimination

8.8 Systems of Linear Inequalities

9.1 Evaluating Radicals

9.2 Simplifying Radicals

9.3 Rational Exponents

9.4a Addition and Subtraction with Radicals

9.4b Multiplication with Radicals

9.4c Rationalizing Denominators

9.5 Equations with Radicals

9.6 Functions with Radicals

9.7 Complex Numbers

9.8 Multiplication and Division with Complex Numbers

10.1a Quadratic Equations: The Square Root Method

10.1b Quadratic Equations: Completing the Square

10.2 Quadratic Equations: The Quadratic Formula

10.3 Applications: Quadratic Equations

10.4 Equations in Quadratic Form

10.5 Graphing Parabolas

10.6a Solving Quadratic Inequalities

10.6b Solving Inequalities with Rational Expressions

11.1 Algebra of Functions

11.2 Composition of Functions and Inverse Functions

11.3 Exponential Functions

11.4 Logarithmic Functions

11.5 Properties of Logarithms

11.6 Common Logarithms and Natural Logarithms

11.7 Exponential and Logarithmic Equations

11.8 Applications: Exponential and Logarithmic Functions

A.1a Decimals and Percents

A.1b More with Decimals

A.2 Synthetic Division

A.3 Using a Graphing Calculator to Solve Equations

A.4 Determinants

A.5 Determinants and Systems of Linear Equations: Cramer's Rule

A.6 Permutations

A.7 Combinations

A.8 Review: Solving Systems of Linear Equations - Two Variables