Elementary and Intermediate Algebra

Note: every chapter concludes with a Chapter Summary and Review and a Chapter Test. Chapters 3, 6, 9, 12, and 14 also have a Cumulative Review.




1. Introduction to Algebraic Expressions

1.1 Introduction to Algebra

1.2 The Commutative, Associative, and Distributive Laws

1.3 Fraction Notation

1.4 Positive and Negative Real Numbers

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponential Notation and Order of Operations



2. Equations, Inequalities, and Problem Solving

2.1 Solving Equations

2.2 Using the Principles Together

2.3 Formulas

2.4 Applications with Percent

2.5 Problem Solving

2.6 Solving Inequalities

2.7 Solving Applications with Inequalities



3. Introduction to Graphing and Functions

3.1 Reading Graphs, Plotting Points, and Scaling Graphs

3.2 Graphing Equations

3.3 Linear Equations and Intercepts

3.4 Rates

3.5 Slope

3.6 Slope-Intercept Form

3.7 Point-Slope Form; Introduction to Curve Fitting

3.8 Functions



4. Systems of Equations in Two Variables

4.1 Systems of Equations and Graphing

4.2 Systems of Equations and Substitution

4.3 Systems of Equations and Elimination

4.4 More Applications Using Systems

4.5 Solving Equations by Graphing



5. Polynomials

5.1 Exponents and Their Properties

5.2 Negative Exponents and Scientific Notation

5.3 Polynomials and Polynomial Functions

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Special Products

5.7 Polynomials in Several Variables

5.8 Division of Polynomials

5.9 The Algebra of Functions



6. Polynomial Factorizations and Equations

6.1 Introduction to Polynomial Factorizations and Equations

6.2 Equations Containing Trinomials of the Type x2 + bx + c

6.3 Equations Containing Trinomials of the Type ax2 + bx + c

6.4 Equations Containing Perfect-Square Trinomials and Differences of Squares

6.5 Equations Containing Sums or Differences of Cubes

6.6 Factoring: A General Strategy

6.7 Applications of Polynomial Equations



7. Rational Expressions, Equations, and Functions

7.1 Rational Expressions and Functions

7.2 Multiplication and Division

7.3 Addition, Subtraction, and Least Common Denominators

7.4 Addition and Subtraction with Unlike Denominators

7.5 Complex Rational Expressions

7.6 Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Formulas, Applications, and Variation



8. Inequalities

8.1 Graphical Solutions and Compound Inequalities

8.2 Absolute-Value Equations and Inequalities

8.3 Inequalities in Two Variables

8.4 Polynomial and Rational Inequalities



9. More on Systems

9.1 Systems of Equations in Three Variables

9.2 Solving Applications: Systems of Three Equations

9.3 Elimination Using Matrices

9.4 Determinants and Cramer's Rule

9.5 Business and Economics Applications



10. Exponents and Radical Functions

10.1 Radical Expressions, Functions, and Models

10.2 Rational Numbers as Exponents

10.3 Multiplying Radical Expressions

10.4 Dividing Radical Expressions

10.5 Expressions Containing Several Radical Terms

10.6 Solving Radical Equations

10.7 Geometric Applications

10.8 The Complex Numbers



11. Quadratic Functions and Equations

11.1 Quadratic Equations

11.2 The Quadratic Formula

11.3 Applications Involving Quadratic Equations

11.4 Studying Solutions of Quadratic Equations

11.5 Equations Reducible to Quadratic

11.6 Quadratic Functions and Their Graphs

11.7 More About Graphing Quadratic Functions

11.8 Problem Solving and Quadratic Functions



12. Exponential and Logarithmic Functions

12.1 Composite and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

12.5 Natural Logarithms and Changing Bases

12.6 Solving Exponential and Logarithmic Equations

12.7 Applications of Exponential and Logarithmic Functions



13. Conic Sections*

13.1 Conic Sections: Parabolas and Circles

13.2 Conic Sections: Ellipses

13.3 Conic Sections: Hyperbolas

13.4 Nonlinear Systems of Equations



14. Sequences, Series, and the Binomial Theorem*

14.1 Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem



R. Elementary Algebra Review

R.1 Introduction to Algebraic Expressions

R.2 Equations, Inequalities, and Problem Solving

R.3 Introduction to Graphing and Functions

R.4 Systems of Equations in Two Variables

R.5 Polynomials

R.6 Polynomial Factorizations and Equations



Appendix A: Working with Units

Appendix B: Distance, Midpoints, and Circles



*Available on included CD-ROM