Intermediate Algebra

Note: every chapter concludes with a Chapter Summary and Review and a Chapter Test. Chapters 3, 6, 9, and 11 also have a Cumulative Review.


 

1. Basics of Algebra and Graphing

1.1 Some Basics of Algebra

1.2 Operations with Real Numbers

1.3 Equivalent Algebraic Expressions

1.4 Exponential and Scientific Notation

1.5 Graphs

1.6 Solving Equations and Formulas

1.7 Introduction to Problem Solving and Models

 

2. Functions, Linear Equations, and Models

2.1 Functions

2.2 Linear Functions:  Slope, Graphs, and Models

2.3 Another Look at Linear Graphs

2.4 Introduction to Curve Fitting:  Point-Slope Form

2.5 Domains and the Algebra of Functions

 

3. Systems of Linear Equations and Problem Solving

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution or Elimination

3.3 Solving Applications:  Systems of Two Equations

3.4 Systems of Equations in Three Variables

3.5 Solving Applications:  Systems of Three Equations

3.6 Elimination Using Matrices

3.7 Determinants and Cramer's Rule

3.8 Business and Economics Applications

 

4. Inequalities and Problem Solving

4.1 Inequalities and Applications

4.2 Solving Equations and Inequalities by Graphing

4.3 Intersections, Unions, and Compound Inequalities

4.4 Absolute-Value Equations and Inequalities

4.5 Inequalities in Two Variables

 

5. Polynomials and Polynomials Functions

5.1 Introduction to Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Polynomial Equations and Factoring

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

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

5.6 Equations Containing Perfect-Square Trinomials and Differences of Squares

5.7 Equations Containing Sums or Differences of Cubes

5.8 Applications of Polynomial Equations

 

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions:  Multiplying and Dividing

6.2 Rational Expressions and Functions:  Adding and Subtracting

6.3 Complex Rational Expressions

6.4 Rational Equations

6.5 Solving Applications Using Rational Equations

6.6 Division of Polynomials

6.7 Synthetic Division

6.8 Formulas, Applications, and Variation

 

7.  Exponents and Radical Functions

7.1 Radical Expressions, Functions, and Models

7.2 Rational Numbers as Exponents

7.3 Multiplying Radical Expressions

7.4 Dividing Radical Expressions

7.5 Expressions Containing Several Radical Terms

7.6 Solving Radical Equations

7.7 Geometric Applications

7.8 The Complex Numbers

 

8. Quadratic Functions and Equations

8.1 Quadratic Equations

8.2 The Quadratic Formula

8.3 Applications Involving Quadratic Equations

8.4 Studying Solutions of Quadratic Equations

8.5 Equations Reducible to Quadratic

8.6 Quadratic Functions and Their Graphs

8.7 More About Graphing Quadratic Functions

8.8 Problem Solving and Quadratic Functions

8.9 Polynomial and Rational Inequalities

 

9. Exponential and Logarithmic Functions

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithmic Functions

9.5 Natural Logarithms and Changing Bases

9.6 Solving Exponential and Logarithmic Equations

9.7 Applications of Exponential and Logarithmic Functions

 

10. Conic Sections

10.1 Conic Sections: Parabolas and Circles

10.2 Conic Sections: Ellipses

10.3 Conic Sections: Hyperbolas

10.4 Nonlinear Systems of Equations

 

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

 

Appendix Unit Conversion and Dimensional Analysis

 

Answers

Photo Credits

Index

Index of Applications

Index of Calculator References