Guided Notebook for College Algebra

Description

• A significantly revised, robust Review chapter is included in the new edition, including 160 new or updated exercises and 34 new videos. Also, a new section in the Review chapter discusses Operations with Radicals (section R.5)

• Chapter Summaries are organized by section and highlight important concepts and definitions with side-by-side examples and videos to make it easy for students to study key concepts. Chapter Summaries are assignable in MyLab™ Math, like a sample assignment.

• The Exercise Program has been expanded with over 1,200 new and updated exercises. Exercises help students make the most of their time spent on homework, and maximize the digital environment to increase conceptual understanding. All exercises are assignable in MyLab Math and appear in the printed eText Reference.

• Author scripted Guided Visualizations bring mathematical concepts to life, helping you visualize the concepts through directed explorations and purposeful manipulation. Guided Visualizations are integrated into the eText and can be assigned in MyLab Math to encourage active learning, critical thinking, and conceptual understanding.

• Video Assessment questions are assignable MyLab Math exercises tied to key video topics.  These questions are designed to check students’ understanding of the important math concepts covered in the video. Questions are assignable in MyLab Math.

• Enhanced Sample Assignments by Kirk Trigsted make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the author to align with this text, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.

• Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.

• Drag and Drop Exercises are a new MyLab Math exercise type that allows students to drag items containing math expressions, words, graphs, or images from a starting bin into designated target areas. Students are asked to perform a higher level of decision making in their answers with these exercise types.

BRIEF TABLE OF CONTENTS:

Review Chapter

1. Equations, Inequalities, and Applications
2. The Rectangular Coordinate System, Lines, and Circles
3. Functions
4. Polynomial and Rational Functions
5. Exponential and Logarithmic Functions and Equations
6. Conic Sections and Parametric Equations
7. Systems of Equations and Inequalities
8. Matrices
9. Sequences and Series; Counting and Probability

Appendix: Conic Section Proofs

COMPREHENSIVE TABLE OF CONTENTS:

• Review Chapter
  • R.1 Real Numbers
  • R.2 The Order of Operations and Algebraic Expressions
  • R.3 The Laws of Exponents; Radicals
  • R.4 Polynomials
  • R.5 Operations with Radicals (New Section)
  • R.6 Factoring Polynomials
  • R.7 Rational Expressions

1. Equations, Inequalities, and Applications
   • 1.1 Linear and Rational Equations
   • 1.2 Applications of Linear Equations and Rational Equation
   • 1.3 Complex Numbers
   • 1.4 Quadratic Equations
   • 1.5 Applications of Quadratic Equations
   • 1.6 Other Types of Equations
   • 1.7 Linear Inequalities in One Variable
   • 1.8 Absolute Value Equations and Inequalities
   • 1.9 Polynomial and Rational Inequalities
2. The Rectangular Coordinate System, Lines, and Circles
   • 2.1 The Rectangular Coordinate System
   • 2.2 Circles
   • 2.3 Lines
   • 2.4 Parallel and Perpendicular Lines
3. Functions
   • 3.1 Relations and Functions
   • 3.2 Properties of a Function’s Graph
   • 3.3 Graphs of Basic Functions; Piecewise Functions
   • 3.4 Transformations of Functions
   • 3.5 The Algebra of Functions; Composite Functions
   • 3.6 One-to-One Functions; Inverse Functions
4. Polynomial and Rational Functions
   • 4.1 Quadratic Functions
   • 4.2 Applications and Modeling of Quadratic Functions
   • 4.3 The Graphs of Polynomial Functions
   • 4.4 Synthetic Division; The Remainder and Factor Theorems
   • 4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
   • 4.6 Rational Functions and Their Graphs
   • 4.7 Variation
5. Exponential and Logarithmic Functions and Equations
   • 5.1 Exponential Functions
   • 5.2 Logarithmic Functions
   • 5.3 Properties of Logarithms
   • 5.4 Exponential and Logarithmic Equations
   • 5.5 Applications of Exponential and Logarithmic Functions
6. Conic Sections and Parametric Equations
   • 6.1 Introduction to Conic Sections
   • 6.2 The Parabola
   • 6.3 The Ellipse
   • 6.4 The Hyperbola
7. Systems of Equations and Inequalities
   • 7.1 Solving Systems of Linear Equations in Two Variables
   • 7.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
   • 7.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
   • 7.4 Partial Fraction Decomposition
   • 7.5 Systems of Nonlinear Equations
   • 7.6 Systems of Inequalities
8. Matrices
   • 8.1 Matrix Operations
   • 8.2 Inverses of Matrices and Matrix Equations
   • 8.3 Determinants and Cramer’s Rule
9. Sequences and Series; Counting and Probability
   • 9.1 Introduction to Sequences and Series
   • 9.2 Arithmetic Sequences and Series
   • 9.3 Geometric Sequences and Series
   • 9.4 The Binomial Theorem
   • 9.5 Mathematical Induction
   • 9.6 The Theory of Counting
   • 9.7 An Introduction to Probability

Appendix: Conic Section Proofs