Beginning & Intermediate Algebra Book

1. Review of Real Numbers

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Fractions and Mixed Numbers

1.4 Exponents, Order of Operations, Variable Expressions and Equations

1.5 Adding Real Numbers

1.6 Subtracting Real Numbers

Integrated Review–Operations on Real Numbers

1.7 Multiplying and Dividing Real Numbers

1.8 Properties of Real Numbers

2. Equations, Inequalities, and Problem Solving

2.1 Simplifying Algebraic Expressions

2.2 The Addition and Multiplication Properties of Equality

2.3 Solving Linear Equations

Integrated Review–Solving Linear Equations

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Further Problem Solving

2.8 Solving Linear Inequalities

3. Graphing

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

Integrated Review–Summary on Slope and Graphing Linear Equations

3.5 Equation of Lines

3.6 Functions

4. Solving Systems of Linear Equations

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

Integrated Review–Solving Systems of Equations

4.4 Solving Systems of Linear Equations in Three Variables

4.5 Systems of Linear Equations and Problem Solving

5. Exponents and Polynomials

5.1 Exponents

5.2 Polynomial Functions and Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Special Products

Integrated Review–Exponents and Operations on Polynomials

5.5 Negative Exponents and Scientific Notation

5.6 Dividing Polynomials

5.7 Synthetic Division and the Remainder Theorem

6. Factoring Polynomials

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x ² + bx + c

6.3 Factoring Trinomials of the Form ax ² + bx + c by Perfect Square Trinomials

6.4 Factoring Trinomials of the Form ax ² + bx + c by Grouping

6.5 Factoring Binomials

Integrated Review–Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

7. Rational Expressions

7.1 Rational Functions and Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator

7.4 Adding and Subtracting Rational Expressions with Unlike Denominators

7.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Equations

7.7 Simplifying Complex Fractions

8. More on Functions and Graphs

8.1 Graphing and Writing Linear Functions

8.2 Reviewing Function Notation and Graphing Nonlinear Functions

Integrated Review–Summary on Functions and Equations of Lines

8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

8.4 Variation and Problem Solving

9. Inequalities and Absolute Value

9.1 Compound Inequalities

9.2 Absolute Value Equations

9.3 Absolute Value Inequalities

Integrated Review–Solving Compound Inequalities and Absolute Value Equations and Inequalities

9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities

10. Rational Exponents, Radicals, and Complex Numbers

10.1 Radicals and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Denominators and Numerators of Radical Expressions

Integrated Review–Radicals and Rational Exponents

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

11. Quadratic Equations and Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods

Integrated Review–Summary on Solving Quadratic Equations

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

12. Exponential and Logarithmic Functions

12.1 The Algebra of Functions; Composite Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Exponential Growth and Decay Functions

12.5 Logarithmic Functions

12.6 Properties of Logarithms

Integrated Review–Functions and Properties of Logarithms

12.7 Common Logarithms, Natural Logarithms, and Change of Base

12.8 Exponential and Logarithmic Equations and Problem Solving

13. Conic Sections

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

Integrated Review–Graphing Conic Sections

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities

14. Sequences, Series, and the Binomial Theorem

14.1 Sequences

14.2 Arithmetic and Geometric Sequences

14.3 Series

Integrated Review–Sequences and Series

14.4 Partial Sums of Arithmetic and Geometric Sequences

14.5 The Binomial Theorem

Appendix A. Operations on Decimals/Percent, Decimal, and Fraction Table

Appendix B. Review of Algebra Topics

Appendix C. An Introduction to Using a Graphic Utility

Appendix D. Solving Systems of Equations by Matrices

Appendix E. Solving Systems of Equations by Determinants

Appendix F. Mean, Median, and Mode

Appendix G. Review of Angles, Lines, and Special Triangles