Introductory Algebra Book

Chapter R  Prealgebra Review

R.1  Factors and the Least Common Multiple

R.2  Fractions

R.3  Decimals and Percents

Chapter 1 Real Numbers and Introduction to Algebra

1.1  Tips for Success in Mathematics

1.2  Symbols and Sets of Numbers

1.3  Exponents, Order of Operations, and Variable Expressions

1.4  Adding Real Numbers

1.5  Subtracting Real Numbers

Integrated Review–Operations on Real Numbers

1.6  Multiplying and Dividing Real Numbers

1.7  Properties of Real Numbers

1.8  Simplifying Expressions

Chapter 2 Equations, Inequalities, and Problem Solving

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Further 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 Solving Linear Inequalities

Chapter 3  Exponents and Polynomials

3.1 Exponents

3.2 Negative Exponents and Scientific Notation

3.3 Introduction to Polynomials

3.4 Adding and Subtracting Polynomials

3.5 Multiplying Polynomials

3.6 Special Products

Integrated Review–Exponents and Operations on Polynomials

3.7 Dividing Polynomials

Chapter 4 Factoring Polynomials

4.1 The Greatest Common Factor

4.2 Factoring Trinomials of the Form x² + bx + c

4.3 Factoring Trinomials of the Form ax² + bx + c

4.4 Factoring Trinomials of the Form ax² + bx + c, by Grouping

4.5 Factoring Perfect Square Trinomials and the Difference of Two Squares

IntegratedReview–Choosing a Factoring Strategy

4.6 Solving Quadratic Equations by Factoring

4.7 Quadratic Equations and Problem Solving

Chapter 5  Rational Expressions

5.1 Simplifying Rational Expressions

5.2 Multiplying and Dividing Rational Expressions

5.3 Adding and Subtracting Rational Expressions with the Same Denominator and least Common Denominator

5.4 Adding and Subtracting Rational Expressions with Different Denominators

5.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

5.6 Proportion and Problem Solving

5.7 Simplifying Complex Fractions

Chapter 6 Graphing Equations and Inequalities

6.1 Reading Graphs and the Rectangular Coordinate System

6.2 Graphing Linear Equations

6.3 Intercepts

6.4 Slope and Rate of change

6.5 Equations of Lines

Integrated Review–Summary on Linear Equations

6.6 Introduction to Functions

6.7 Graphing Linear Inequalities in Two Variables

6.8 Direct and Inverse Variation

Chapter 7 Systems of Equations

7.1 Solving Systems of Linear Equations by Graphing

7.2 Solving Systems of Linear Equations by Substitution

7.3 Solving Systems of Linear Equations by Addition

Integrated Review–Summary on Solving Systems of Equations

7.4 Systems of Linear Equations and Problem Solving

Chapter 8 Roots and Radicals

8.1 Introduction to Radicals

8.2 Simplifying Radicals

8.3 Adding and Subtracting Radicals

8.4 Multiplying and Dividing Radicals

Integrated Review–Simplifying Radicals

8.5 Solving Equations Containing Radicals

8.6 Radical Equations and Problem Solving

Chapter 9 Quadratic Equations

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations by the Quadratic Formula

Integrated Review–Summary on Quadratic Equations

9.4 Graphing Quadratic Equations in Two Variables

Appendices

A The Bigger Picture

B Factoring Sums and Differences of Cubes

C Mean, Median, Mode

D Sets

E Review of Angles, Lines, and special Triangles

F Tables

Answers To Selected Exercises

Solutions to Selected Exercises