Intermediate Algebra for College Students

1. Basic Concepts

1.1 Study Skills for Success in Mathematics, and Using a Calculator

1.2 Sets and Other Basic Concepts

1.3 Properties of and Operations with Real Numbers

1.4 Order of Operations

1.5 Exponents

1.6 Scientific Notation

 

2. Equations and Inequalities

2.1 Solving Linear Equations

2.2 Problem Solving and Using Formulas

2.3 Applications of Algebra

2.4 Additional Application Problems

2.5 Solving Linear Inequalities

2.6 Solving Equations and Inequalities Containing Absolute Values

 

3. Graphs and Functions

3.1 Graphs

3.2 Functions

3.3 Linear Functions: Graphs and Applications

3.4 The Slope-Intercept Form of a Linear Equation

3.5 The Point-Slope Form of a Linear Equation

3.6 The Algebra of Functions

3.7 Graphing Linear Inequalities

 

4. Systems of Equations and Inequalities

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Systems of Linear Equations: Applications and Problem Solving

4.4 Solving Systems of Equations Using Matrices

4.5 Solving Systems of Equations Using Determinants and Cramer’s Rule

4.6 Solving Systems of Linear Inequalities

  

5. Polynomials and Polynomial Functions

5.1 Addition and Subtraction of Polynomials

5.2 Multiplication of Polynomials

5.3 Division of Polynomials and Synthetic Division

5.4 Factoring a Monomial from a Polynomial and Factoring by Grouping

5.5 Factoring Trinomials

5.6 Special Factoring Formulas

5.7 A General Review of Factoring

5.8 Polynomial Equations

 

6. Rational Expressions and Equations

6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions
6.2 Addition and Subtraction of Rational Expressions
6.3 Complex Fractions

6.4 Solving Rational Equations

6.5 Rational Equations: Applications and Problem Solving
6.6 Variation

7. Roots, Radicals, and Complex Numbers

7.1 Roots and Radicals

7.2 Rational Exponents

7.3 Simplifying Radicals

7.4 Adding, Subtracting, and Multiplying Radicals

7.5 Dividing Radicals

7.6 Solving Radical Equations

7.7 Complex Numbers

 

8. Quadratic Functions

8.1 Solving Quadratic Equations by Completing the Square

8.2 Solving Quadratic Equations by the Quadratic Formula

8.3 Quadratic Equations: Applications and Problem Solving

8.4 Writing Equations in Quadratic Form

8.5 Graphing Quadratic Functions

8.6 Quadratic and Other Inequalities in One Variable

 

9. Exponential and Logarithmic Functions

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Common Logarithms

9.6 Exponential and Logarithmic Equations

9.7 Natural Exponential and Natural Logarithmic Functions

  

10. Sequences, Series, and the Binomial Theorem

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 The Binomial Theorem

 

11. Conic Sections

11.1 The Parabola and the Circle

11.2 The Ellipse

11.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Their Applications