Student Workbook for Elementary and Intermediate Algebra for College Students

Preface

• To the Student

1. Real Numbers

• 1.1 Study Skills for Success in Mathematics
• 1.2 Problem Solving
• 1.3 Fractions
• 1.4 The Real Number System
• 1.5 Inequalities
  • Mid-Chapter Test: Sections 1.1-1.5
• 1.6 Addition of Real Numbers
• 1.7 Subtraction of Real Numbers
• 1.8 Multiplication and Division of Real Numbers
• 1.9 Exponents, Parentheses, and the Order of Operations
• 1.10 Properties of the Real Number System

• Chapter 1 Summary
• Chapter 1 Review Exercises
• Chapter 1 Practice Test

2. Solving Linear Equations and Inequalities

• 2.1 Combining Like Terms
• 2.2 The Addition Property of Equality
• 2.3 The Multiplication Property of Equality
• 2.4 Solving Linear Equations with a Variable on Only One Side of the Equation
  • Mid-Chapter Test: Sections 2.1-2.4
• 2.5 Solving Linear Equations with the Variable on Both Sides of the Equation
• 2.6 Formulas
• 2.7 Ratios and Proportions
• 2.8 Inequalities in One Variable

• Chapter 2 Summary
• Chapter 2 Review Exercises
• Chapter 2 Practice Test
• Cumulative Review Test

3. Applications of Algebra

• 3.1 Changing Application Problems into Equations
• 3.2 Solving Application Problems
  • Mid-Chapter Test: Sections 3.1-3.2
• 3.3 Geometric Problems
• 3.4 Motion, Money, and Mixture Problems

• Chapter 3 Summary
• Chapter 3 Review Exercises
• Chapter 3 Practice Test
• Cumulative Review Test

4. Graphing Linear Equations

• 4.1 The Cartesian Coordinate System and Linear Equations in Two Variables
• 4.2 Graphing Linear Equations
• 4.3 Slope of a Line
  • Mid-Chapter Test: Sections 4.1-4.3
• 4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation

• Chapter 4 Summary
• Chapter 4 Review Exercises
• Chapter 4 Practice Test
• Cumulative Review Test

5. Exponents and Polynomials

• 5.1 Exponents
• 5.2 Negative Exponents
• 5.3 Scientific Notation
  • Mid-Chapter Test: Sections 5.1-5.3
• 5.4 Addition and Subtraction of Polynomials
• 5.5 Multiplication of Polynomials
• 5.6 Division of Polynomials

• Chapter 5 Summary
• Chapter 5 Review Exercises
• Chapter 5 Practice Test
• Cumulative Review Test

6. Factoring

• 6.1 Factoring a Monomial from a Polynomial
• 6.2 Factoring by Grouping
• 6.3 Factoring Trinomials of the Form ax² + bx + c, a = 1
• 6.4 Factoring Trinomials of the Form ax² + bx + c, a ≠ 1
  • Mid-Chapter Test: Sections 6.1-6.4
• 6.5 Special Factoring Formulas and a General Review of Factoring
• 6.6 Solving Quadratic Equations Using Factoring
• 6.7 Applications of Quadratic Equations

• Chapter 6 Summary
• Chapter 6 Review Exercises
• Chapter 6 Practice Test
• Cumulative Review Test

7. Rational Expressions and Equations

• 7.1 Simplifying Rational Expressions
• 7.2 Multiplication and Division of Rational Expressions
• 7.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator
• 7.4 Addition and Subtraction of Rational Expressions
  • Mid-Chapter Test: Sections 7.1-7.4
• 7.5 Complex Fractions
• 7.6 Solving Rational Equations
• 7.7 Rational Equations: Applications and Problem Solving
• 7.8 Variation

• Chapter 7 Summary
• Chapter 7 Review Exercises
• Chapter 7 Practice Test
• Cumulative Review Test

8. Functions and Their Graphs

• 8.1 More on Graphs
• 8.2 Functions
• 8.3 Linear Functions
  • Mid-Chapter Test: Sections 8.1-8.3
• 8.4 Slope, Modeling, and Linear Relationships
• 8.5 The Algebra of Functions

• Chapter 8 Summary
• Chapter 8 Review Exercises
• Chapter 8 Practice Test
• Cumulative Review Test

9. Systems of Linear Equations

• 9.1 Solving Systems of Equations Graphically
• 9.2 Solving Systems of Equations by Substitution
• 9.3 Solving Systems of Equations by the Addition Method
• 9.4 Solving Systems of Linear Equations in Three Variables
  • Mid-Chapter Test: Sections 9.1-9.4
• 9.5 Systems of Linear Equations: Applications and Problem Solving
• 9.6 Solving Systems of Equations Using Matrices
• 9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule

• Chapter 9 Summary
• Chapter 9 Review Exercises
• Chapter 9 Practice Test
• Cumulative Review Test

10. Inequalities in One and Two Variables

• 10.1 Solving Linear Inequalities in One Variable
• 10.2 Solving Equations and Inequalities Containing Absolute Values
  • Mid-Chapter Test: Sections 10.1-10.2
• 10.3 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities

• Chapter 10 Summary
• Chapter 10 Review Exercises
• Chapter 10 Practice Test
• Cumulative Review Test

11. Roots, Radicals, and Complex Numbers

• 11.1 Roots and Radicals
• 11.2 Rational Exponents
• 11.3 Simplifying Radicals
• 11.4 Adding, Subtracting, and Multiplying Radicals
  • Mid-Chapter Test: Sections 11.1-11.4
• 11.5 Dividing Radicals
• 11.6 Solving Radical Equations
• 11.7 Complex Numbers

• Chapter 11 Summary
• Chapter 11 Review Exercises
• Chapter 11 Practice Test
• Cumulative Review Test

12. Quadratic Functions

• 12.1 Solving Quadratic Equations by Completing the Square
• 12.2 Solving Quadratic Equations by the Quadratic Formula
• 12.3 Quadratic Equations: Applications and Problem Solving
  • Mid-Chapter Test: Sections 12.1-12.3
• 12.4 Factoring Expressions and Solving Equations That Are Quadratic in Form
• 12.5 Graphing Quadratic Functions
• 12.6 Quadratic, Polynomial, and Rational Inequalities in One Variable

• Chapter 12 Summary
• Chapter 12 Review Exercises
• Chapter 12 Practice Test
• Cumulative Review Test

13. Exponential and Logarithmic Functions

• 13.1 Composite and Inverse Functions
• 13.2 Exponential Functions
• 13.3 Logarithmic Functions
• 13.4 Properties of Logarithms
  • Mid-Chapter Test: Sections 13.1-13.4
• 13.5 Common Logarithms
• 13.6 Exponential and Logarithmic Equations
• 13.7 Natural Exponential and Natural Logarithmic Functions

• Chapter 13 Summary
• Chapter 13 Review Exercises
• Chapter 13 Practice Test
• Cumulative Review Test

14. Conic Sections

• 14.1 The Parabola and the Circle
• 14.2 The Ellipse
  • Mid-Chapter Test: Sections 14.1-14.2
• 14.3 The Hyperbola
• 14.4 Nonlinear Systems of Equations and Their Applications

• Chapter 14 Summary
• Chapter 14 Review Exercises
• Chapter 14 Practice Test
• Cumulative Review Test

15. Sequences, Series, and the Binomial Theorem

• 15.1 Sequences and Series
• 15.2 Arithmetic Sequences and Series
• 15.3 Geometric Sequences and Series
  • Mid-Chapter Test: Sections 15.1-15.3
• 15.4 The Binomial Theorem

• Chapter 15 Summary
• Chapter 15 Review Exercises
• Chapter 15 Practice Test
• Cumulative Review Test

APPENDICES

• A. Review of Decimals and Percent
• B. Finding the Greatest Common Factor and Least Common Denominator
• C. Geometry
• D. Review of Exponents, Polynomials, and Factoring

Answers

Applications Index

Subject Index