Student Solutions Manual for 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 his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. 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, Real Numbers, and Interval Notation

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. More on Polynomial and Rational Functions

11.1 Polynomial Functions and Their Graphs

11.2 Zeros of Polynomial Functions

Mid-Chapter Check Point Section 11.1—Section 11.2

11.3 Rational Functions and Their Graphs

Chapter 11 Group Project

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Exercises (Chapters 1—11)

12. Sequences, Induction, and Probability

12.1 Sequences and Summation Notation

12.2 Arithmetic Sequences

12.3 Geometric Sequences and Series

Mid-Chapter Check Point Section 12.1—Section 12.3

12.4 The Binomial Theorem

12.5 Mathematical Induction

12.6 Counting Principles, Permutations, and Combinations

12.7 Probability

Chapter 12 Group Project

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Test

Cumulative Review Exercises (Chapters 1—12)

Appendix

Where Did That Come From? Selected Proofs