Intermediate Algebra for College Students

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Intermediate Algebra for College Students, Bob has written textbooks covering introductory algebra, college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Prentice Hall. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

1. Algebra, Mathematical Models, and Problem Solving

1.1 Algebraic Expressions and Real Numbers

1.2 Operations with Real Numbers and Simplifying Algebraic Expressions

1.3 Graphing Equations

1.4 Solving Linear Equations

            Mid-Chapter Check Point Section 1.1—Section 1.4

1.5 Problem Solving and Using Formulas

1.6 Properties of Integral Exponents

1.7 Scientific Notation

            Chapter 1 Group Project

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Test


2. Functions and Linear Functions

2.1 Introduction to Functions

2.2 Graphs of Functions

2.3 The Algebra of Functions

            Mid-Chapter Check Point Section 2.1—Section 2.3

2.4 Linear Functions and Slope

2.5 The Point-Slope Form of the Equation of a Line

            Chapter 2 Group Project

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Test

            Cumulative Review Exercises (Chapters 1—2)


3. Systems of Linear Equations

3.1 Systems of Linear Equations in Two Variables

3.2 Problem Solving and Business Applications Using Systems of Equations

3.3 Systems of Linear Equations in Three Variables

            Mid-Chapter Check Point Section 3.1—Section 3.3

3.4 Matrix Solutions to Linear Systems

3.5 Determinants and Cramer's Rule

            Chapter 3 Group Project

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Test

            Cumulative Review Exercises (Chapters 1—3)

 

4. Inequalities and Problem Solving

4.1 Solving Linear Inequalities

4.2 Compound Inequalities

4.3 Equations and Inequalities Involving Absolute Value

            Mid-Chapter Check Point Section 4.1—Section 4.3

4.4 Linear Inequalities in Two Variables

4.5 Linear Programming

            Chapter 4 Group Project

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Test

            Cumulative Review Exercises (Chapters 1—4)


5. Polynomials, Polynomial Functions, and Factoring

5.1 Introduction to Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Greatest Common Factors and Factoring By Grouping

5.4 Factoring Trinomials

            Mid-Chapter Check Point Section 5.1—Section 5.4

5.5 Factoring Special Forms

5.6 A General Factoring Strategy

5.7 Polynomial Equations and Their Applications

            Chapter 5 Group Project

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Test

            Cumulative Review Exercises (Chapters 1—5)


6. Rational Expressions, Functions, and Equations

6.1 Rational Expressions and Functions: Multiplying and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Rational Expressions

6.4 Division of Polynomials

            Mid-Chapter Check Point Section 6.1—Section 6.4

6.5 Synthetic Division and the Remainder Theorem

6.6 Rational Equations

6.7 Formulas and Applications of Rational Equations

6.8 Modeling Using Variation

            Chapter 6 Group Project

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Test

            Cumulative Review Exercises (Chapters 1—6)


7. Radicals, Radical Functions, and Rational Exponents

7.1 Radical Expressions and Functions

7.2 Rational Exponents

7.3 Multiplying and Simplifying Radical Expressions

7.4 Adding, Subtracting, and Dividing Radical Expressions

            Mid-Chapter Check Point Section 7.1—Section 7.4

7.5 Multiplying with More Than One Term and Rationalizing Denominators

7.6 Radical Equations

7.7 Complex Numbers

            Chapter 7 Group Project

            Chapter 7 Summary

            Chapter 7 Review Exercises

            Chapter 7 Test

            Cumulative Review Exercises (Chapters 1—7)


8. Quadratic Equations and Functions

8.1 The Square Root Property and Completing the Square

8.2 The Quadratic Formula

8.3 Quadratic Functions and Their Graphs

            Mid-Chapter Check Point Section 8.1—Section 8.3

8.4 Equations Quadratic in Form

8.5 Polynomial and Rational Inequalities

            Chapter 8 Group Project

            Chapter 8 Summary

            Chapter 8 Review Exercises

            Chapter 8 Test

            Cumulative Review Exercises (Chapters 1—8)


9. Exponential and Logarithmic Functions

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

            Mid-Chapter Check Point Section 9.1—Section 9.4

9.5 Exponential and Logarithmic Equations

9.6 Exponential Growth and Decay; Modeling Data

            Chapter 9 Group Project

            Chapter 9 Summary

            Chapter 9 Review Exercises

            Chapter 9 Test

            Cumulative Review Exercises (Chapters 1—9)


10. Conic Sections and Systems of Nonlinear Equations

10.1 Distance and Midpoint Formulas; Circles

10.2 The Ellipse

10.3 The Hyperbola

            Mid-Chapter Check Point Section 10.1—Section 10.3

10.4 The Parabola; Identifying Conic Sections

10.5 Systems of Nonlinear Equations in Two Variables

            Chapter 10 Group Project

            Chapter 10 Summary

            Chapter 10 Review Exercises

            Chapter 10 Test

            Cumulative Review Exercises (Chapters 1—10)

 

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Summation Notation

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

            Mid-Chapter Check Point Section 11.1—Section 11.3

11.4 The Binomial Theorem

            Chapter 11 Group Project

            Chapter 11 Summary

            Chapter 11 Review Exercises

            Chapter 11 Test

            Cumulative Review Exercises (Chapters 1—11)

 

Appendix

Where Did That Come From? Selected Proofs