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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. Variables, Real Numbers, and Mathematical Models
1.1 Introduction to Algebra: Variables and Mathematical Models
1.2 Fractions in Algebra
1.3 The Real Numbers
1.4 Basic Rules of Algebra
Mid-Chapter Check Point Section 1.1–Section 1.4
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponents and Order of Operations
Chapter 1 Group Project
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
2. Linear Equations and Inequalities in One Variable
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Solving Linear Equations
2.4 Formulas and Percents
Mid-Chapter Check Point Section 2.1–Section 2.4
2.5 An Introduction to Problem Solving
2.6 Problem Solving in Geometry
2.7 Solving Linear Inequalities
Chapter 2 Group Project
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises (Chapters 1–2)
3. Linear Equations in Two Variables
3.1 Graphing Linear Equations in Two Variables
3.2 Graphing Linear Equations Using Intercepts
3.3 Slope
3.4 The Slope-Intercept Form of the Equation of a Line
Mid-Chapter Check Point Section 3.1–Section 3.4
3.5 The Point-Slope Form of the Equation of a Line
Chapter 3 Group Project
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises (Chapters 1–3)
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by the Substitution Method
4.3 Solving Systems of Linear Equations by the Addition Method
Mid-Chapter Check Point Section 4.1–Section 4.3
4.4 Problem Solving Using Systems of Equations
4.5 Systems of Linear Equations in Three Variables
Chapter 4 Group Project
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Exercises (Chapters 1–4)
5. Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 Multiplying Polynomials
5.3 Special Products
5.4 Polynomials in Several Variables
Mid-Chapter Check Point Section 5.1–Section 5.4
5.5 Dividing Polynomials
5.6 Long Division of Polynomials; Synthetic Division
5.7 Negative Exponents and Scientific Notation
Chapter 5 Group Project
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises (Chapters 1–5)
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring By Grouping
6.2 Factoring Trinomials Whose Leading Coefficient Is 1
6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1
Mid-Chapter Check Point Section 6.1–Section 6.3
6.4 Factoring Special Forms
6.5 A General Factoring Strategy
6.6 Solving Quadratic Equations By Factoring
Chapter 6 Group Project
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises (Chapters 1–6)
7. Rational Expressions
7.1 Rational Expressions and Their Simplification
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with the Same Denominator
7.4 Adding and Subtracting Rational Expressions with Different Denominators
Mid-Chapter Check Point Section 7.1–Section 7.4
7.5 Complex Rational Expressions
7.6 Solving Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Modeling Using Variation
Chapter 7 Group Project
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
8. Basics of Functions
8.1 Introduction to Functions
8.2 Graphs of Functions
8.3 The Algebra of Functions
Mid-Chapter Check Point Section 8.1–Section 8.3
8.4 Composite and Inverse Functions
Chapter 8 Group Project
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
9. Inequalities and Problem Solving
9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications
9.2 Compound Inequalities
9.3 Equations and Inequalities Involving Absolute Value
Mid-Chapter Check Point Section 9.1–Section 9.3
9.4 Linear Inequalities in Two Variables
Chapter 9 Group Project
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises (Chapters 1–9)
10. Radicals, Radical Functions, and Rational Exponents
10.1 Radical Expressions and Functions
10.2 Rational Exponents
10.3 Multiplying and Simplifying Radical Expressions
10.4 Adding, Subtracting, and Dividing Radical Expressions
Mid-Chapter Check Point Section 10.1–Section 10.4
10.5 Multiplying with More Than One Term and Rationalizing Denominators
10.6 Radical Equations
10.7 Complex Numbers
Chapter 10 Group Project
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises (Chapters 1–10)
11. Quadratic Equations and Functions
11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formulas
11.2 The Quadratic Formula
11.3 Quadratic Functions and Their Graphs
Mid-Chapter Check Point Section 11.1–Section 11.3
11.4 Equations Quadratic in Form
11.5 Polynomial and Rational Inequalities
Chapter 11 Group Project
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Test
Cumulative Review Exercises (Chapters 1–11)
12. Exponential and Logarithmic Functions
12.1 Exponential Functions
12.2 Logarithmic Functions
12.3 Properties of Logarithms
Mid-Chapter Check Point Section 12.1–Section 12.3
12.4 Exponential and Logarithmic Equations
12.5 Exponential Growth and Decay; Modeling Data
Chapter 12 Group Project
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Test
Cumulative Review Exercises (Chapters 1–12)
13. Conic Sections and Systems of Nonlinear Equations
13.1 The Circle
13.2 The Ellipse
13.3 The Hyperbola
Mid-Chapter Check Point Section 13.1–Section 13.3
13.4 The Parabola; Identifying Conic Sections
13.5 Systems of Nonlinear Equations in Two Variables
Chapter 13 Group Project
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Test
Cumulative Review Exercises (Chapters 1–13)
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Summation Notation
14.2 Arithmetic Sequences
14.3 Geometric Sequences and Series
Mid-Chapter Check Point Section 14.1–Section 14.3
14.4 The Binomial Theorem
Chapter 14 Group Project
Chapter 14 Summary
Chapter 14 Review Exercises
Chapter 14 Test
Cumulative Review Exercises (Chapters 1–14)
Appendices
A. Mean, Median, and Mode
B. Matrix Solutions to Linear Systems
C. Determinants and Cramer's Rule
D. Where Did That Come From? Selected Proofs