Elementary and Intermediate Algebra Book

Chapter 1 — Operations on Real Numbers and Algebraic Expressions

1.1 Success in Mathematics

1.2 The Number Systems and the Real Number Line

1.3 Adding, Subtracting, Multiplying, and Dividing Integers

1.4 Adding, Subtracting, Multiplying, and Dividing Rational Numbers Expressed as Fractions and Decimals

Putting the Concepts Together (Sections 1.1 — 1.4)

1.5 Properties of Real Numbers

1.6 Exponents and the Order of Operations

1.7 Simplifying Algebraic Expressions

Chapter 1 Activity

Chapter 1 Review

Chapter 1 Test

Chapter 2-Equations and Inequalities in One Variable

2.1 Linear Equations: The Addition and Multiplication Properties of Equality

2.2 Linear Equations: Using the Properties Together

2.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

2.4 Evaluating Formulas and Solving Formulas for a Variable

Putting the Concepts Together (Sections 2.1 — 2.4)

2.5 Introduction to Problem Solving: Direct Translation Problems

2.6 Problem Solving: Direct Translation Problems Involving Percent

2.7 Problem Solving: Geometry and Uniform Motion

2.8 Solving Inequalities in One Variable

Chapter 2 Activity

Chapter 2 Review

Chapter 2 Test

Chapter 3 — Introduction to Graphing and Equations of Lines

3.1 The Rectangular Coordinate System and Equations in Two Variables

3.2 Graphing Equations in Two Variables

3.3 Slope

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Form of a Line

3.6 Parallel and Perpendicular Lines

Putting the Concepts Together (Sections 3.1 — 3.6)

3.7 Variation

3.8 Linear Inequalities in Two Variables

Chapter 3 Activity

Chapter 3 Review

Chapter 3 Test

Cumulative Review Chapters 1-3

Chapter 4 — Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations in Two Variables by Graphing

4.2 Solving Systems of Linear Equations in Two Variables Using Substitution

4.3 Solving Systems of Linear Equations in Two Variables Using Elimination

Putting the Concepts Together (Sections 4.1 — 4.3)

4.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations

4.5 Solving Mixture Problems Using Systems of Linear Equations

4.6 Systems of Linear Inequalities

Chapter 4 Activity

Chapter 4 Review

Chapter 4 Test

Chapter 5 — Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Monomials: The Product and Power Rules

5.3 Multiplying Polynomials

5.4 Dividing Monomials: The Quotient Rule and Integer Exponents

Putting the Concepts Together (Sections 5.1 — 5.4)

5.5 Dividing Polynomials

5.6 Applying Exponent Rules: Scientific Notation

Chapter 5Activity

Chapter 5 Review

Chapter 5 Test

Cumulative Review Chapters 1-5

Chapter 6 - Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c, a ¿ 1

6.4 Factoring Special Products

6.5 Summary of Factoring Techniques

Putting the Concepts Together (Sections 6.1 — 6.5)

6.6 Solving Polynomial Equations by Factoring

6.7 Modeling and Solving Problems with Quadratic Equations

Chapter 6 Activity

Chapter 6 Review

Chapter 6 Test

Getting Ready for Intermediate Algebra: A Cumulative Review of Chapters 1-6

Chapter 7 — Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with a Common Denominators

7.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

7.5 Adding and Subtracting Rational Expressions with Unlike Denominators

7.6 Complex Rational Expressions

Putting the Concepts Together (Sections 7.1 — 7.6)

7.7 Rational Equations

7.8 Models Involving Rational Expressions

Chapter 7 Activity

Chapter 7 Review

Chapter 7 Test

Getting Ready for Intermediate Algebra: A Cumulative Review of Chapters 1-7

Chapter 8— Graphs, Relations, and Functions

8.1 Graphs of Equations

8.2 Relations

Putting the Concepts Together (Section 8.1 — 8.2)

8.3 An Introduction to Functions

8.4 Functions and Their Graphs

8.5 Linear Functions

8.6 Compound Inequalities

8.7 Absolute Value Equations and Inequalities

Chapter 8 Activity

Chapter 8 Review

Chapter 8 Test

Chapter 9- Radicals and Rational Exponents

9.1 Square Roots

9.2 nth Roots andRational Exponents

9.3 Simplify Expressions Using the Laws of Exponents

9.4 Simplifying Radical Expressions

9.5 Adding, Subtracting, and Multiplying Radical Expressions

9.6 Rationalizing Radical Expressions

Putting the Concepts Together (Sections 9.1 — 9.6)

9.7 Functions Involving Radicals

9.8 Radical Equations and Their Applications

9.9 The Complex Number System

Chapter 9 Activity

Chapter 9 Review

Chapter 9 Test

Chapter 10- Quadratic Equations and Functions

10.1 Solving Quadratic Equations by Completing the Square

10.2 Solving Quadratic Equations by the Quadratic Formula

10.3 Solving Equations Quadratic in Form

Putting the Concepts Together (Sections 10.1 — 10.3)

10.4 Graphing Quadratic Functions Using Transformations

10.5 Graphing Quadratic Functions Using Properties

10.6 Quadratic Inequalities

10.7 Rational Inequalities

Chapter 10 Activity

Chapter 10 Review

Chapter 10 Test

Cumulative Review Chapters 1-10

Chapter 11- Exponential and Logarithmic Functions

11.1 Composite Functions and Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

Putting the Concepts Together (Sections 11.1 — 11.3)

11.4 Properties of Logarithms

11.5 Exponential and Logarithmic Equations

Chapter 11 Activity

Chapter 11 Review

Chapter 11 Test

Chapter 12- Conics

12.1 Distance and Midpoint Formulas

12.2 Circles

12.3 Parabolas

Putting the Concepts Together (Sections 12.1 — 12.3)

12.4 Ellipses

12.5 Hyperbolas

12.6 Nonlinear Systems of Equations

Chapter 12 Activity

Chapter 12 Review

Chapter 12 Test

Cumulative Review Chapters 1-12

Chapter 13- Sequences, Series, and The Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences and Series

Putting the Concepts Together (Section 13.1 — 13.3)

13.4 The Binomial Theorem

Chapter 13 Activity

Chapter 13 Review

Chapter 13 Test

Appendix A: Review of Fractions, Decimals, and Percents

A.1 Fractions

A.2 Decimals and Percents

Appendix B: Division of Polynomials; Synthetic Division

Appendix C: The Library of Functions

Appendix D: Geometry

Appendix E: More on Systems of Equations

E.1 Systems of Linear Equations in Three Variables

E.2 Using Matrices to Solve Systems

E.3 Determinants and Cramer’s Rule