Video Notebook for College Algebra with Intermediate Algebra

Description

• Instructors: As you know from your experience teaching both Intermediate Algebra and College Algebra, there is a great deal of repetition of topics in the 2 courses. In fact, over 60% of the topics covered in a College Algebra textbook are also covered in an Intermediate Algebra text.

• College Algebra with Intermediate Algebra: A Blended Course is intended to eliminate this repetition and make better use of students’ time and resources.

• Chapter R Review of Basic Algebra

Part 1: Operations

• R.1 The Set of Real Numbers
• R.2 Operations with Real Numbers
• R.3 Exponential Notation and Order of Operations

Part 2: Manipulations

• R.4 Introduction to Algebraic Expressions
• R.5 Equivalent Algebraic Expressions
• R.6 Simplifying Algebraic Expressions
• R.7 Properties of Exponents and Scientific Notation

1. Solving Linear Equations and Inequalities

• The topics in this chapter are often taught in Intermediate Algebra and then again in College Algebra. Here, the repetition is eliminated.
• 1.1 Solving Equations
• 1.2 Formulas and Applications
• 1.3 Applications and Problem Solving
• 1.4 Sets, Inequalities, and Interval Notation
• 1.5 Intersections, Unions, and Compound Inequalities
• 1.6 Absolute-Value Equations and Inequalities

2. Graphs, Functions, and Applications

• We believe that functions and graphing should be introduced early and continue as a thread that runs through the course. This allows the instructor the opportunity to use the visual element of graphing to show students how solutions of equations, zeros of functions, and x-intercepts of graphs are related. This chapter blends function topics from Intermediate Algebra and College Algebra.
• 2.1 Graphs of Equations
• 2.2 Functions and Graphs
• 2.3 Finding Domain and Range
• 2.4 The Algebra of Functions
• 2.5 Linear Functions: Graphs and Slope
• 2.6 More on Graphing Linear Equations
• 2.7 Finding Equations of Lines; Applications

3. Systems of Equations

• This chapter covers systems of equations, a topic that is often taught in both Intermediate Algebra and College Algebra. This is another instance in which repetition of topics is eliminated. In addition, it includes linear programming, a topic that is traditionally in College Algebra but not in Intermediate Algebra.
• 3.1 Systems of Equations in Two Variables
• 3.2 Solving by Substitution
• 3.3 Solving by Elimination
• 3.4 Solving Applied Problems: Two Equations
• 3.5 Systems of Equations in Three Variables
• 3.6 Solving Applied Problems: Three Equations
• 3.7 Systems of Inequalities and Linear Programming

4. Polynomials and Polynomial Functions

• 4.1 Introduction to Polynomials and Polynomial Functions
• 4.2 Multiplication of Polynomials
• 4.3 Introduction to Factoring
• 4.4 Factoring Trinomials: x² + bx + c
• 4.5 Factoring Trinomials: ax² + bx + c, a _1
• 4.6 Special Factoring
• 4.7 Factoring: A General Strategy
• 4.8 Applications of Polynomial Equations and Functions

5. Rational Expressions, Equations, and Functions

• In this chapter, the student gets a solid basic coverage of rational expressions, rational equations, and rational functions as well as coverage of the difference quotient from College Algebra. This paves the way for studying more advanced College Algebra coverage of many of these topics in Chapter 8.
• 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying
• 5.2 LCMs, LCDs, Addition, and Subtraction
• 5.3 Division of Polynomials
• 5.4 Complex Rational Expressions
• 5.5 Solving Rational Equations
• 5.6 Applications and Proportions
• 5.7 Formulas and Applications
• 5.8 Variation and Applications

6. Radical Expressions, Equations, and Functions

• This chapter covers traditional Intermediate Algebra topics. In addition, now that the student has studied linear functions, polynomial functions of degree two and higher, rational functions, and radical functions, we have included the College Algebra topics of increasing functions, decreasing functions, and piecewise-defined functions. We weave together topics that are covered early in College Algebra and topics from Intermediate Algebra. (Note that complex numbers are covered in Chapter 7 along with quadratic equations rather than in this chapter.)
• 6.1 Radical Expressions and Functions
• 6.2 Rational Numbers as Exponents
• 6.3 Simplifying Radical Expressions
• 6.4 Addition, Subtraction, and More Multiplication
• 6.5 More on Division of Radical Expressions
• 6.6 Solving Radical Equations
• 6.7 Applications Involving Powers and Roots
• 6.8 Increasing, Decreasing, and Piecewise Functions; Applications

7. Quadratic Functions and Equations

• This chapter blends traditional Intermediate Algebra coverage of quadratic equations with additional, more advanced topics that are traditionally associated with a College Algebra course.
• 7.1 Symmetry
• 7.2 Transformations
• 7.3 The Complex Numbers
• 7.4 Quadratic Equations, Functions, Zeros, and Models
• 7.5 Analyzing Graphs of Quadratic Functions

8. Polynomial Functions and Rational Functions

• Here, College Algebra topics regarding polynomial functions and rational functions are built on the solid foundation that was laid in Chapters 4 and 5.
• 8.1 Polynomial Functions and Models
• 8.2 Graphing Polynomials Functions
• 8.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
• 8.4 Theorems about Zeros of Polynomial Functions
• 8.5 Rational Functions
• 8.6 Polynomial Inequalities and Rational Inequalities

9. Exponential Functions and Logarithmic Functions

• Traditionally, there is little difference in the Intermediate Algebra coverage vs. College Algebra coverage of the topics in this chapter. This is an excellent opportunity to eliminate repetition and thus streamline students’ investment of time and resources. Although inverse functions are often introduced earlier in a College Algebra course, we introduce them here so that they will be fresh in the students’ minds when they are used to show the relationship between exponential functions and logarithmic functions.
• 9.1 The Composition of Functions
• 9.2 Inverse Functions
• 9.3 Exponential Functions and Graphs
• 9.4 Logarithmic Functions and Graphs
• 9.5 Properties of Logarithmic Functions
• 9.6 Solving Exponential Equations and Logarithmic Equations
• 9.7 Applications and Models: Growth and Decay; Compound Interest

10. Matrices

• These are the matrix topics that are traditionally taught in a College Algebra course, often along with systems of equations. Here they are presented in a separate chapter so that systems of equations could be covered earlier in the course with the more traditional Intermediate Algebra topics.
• 10.1 Matrices and Systems of Equations
• 10.2 Matrix Operations
• 10.3 Inverses of Matrices
• 10.4 Determinants and Cramer’s Rule

11. Conic Sections

• In the topics of conic sections and nonlinear systems of equations we find another area of considerable overlap in Intermediate Algebra and College Algebra. This is another example of how repetition is eliminated.
• 11.1 The Parabola
• 11.2 The Circle and the Ellipse
• 11.3 The Hyperbola
• 11.4 Nonlinear Systems of Equations and Inequalities

12. Sequences, Series, and Combinatorics

• These are traditional College Algebra topics.
• 12.1 Sequences and Series
• 12.2 Arithmetic Sequences and Series
• 12.3 Geometric Sequences and Series
• 12.4 Mathematical Induction
• 12.5 Combinatorics: Permutations
• 12.6 Combinatorics: Combinations
• 12.7 The Binomial Theorem
• 12.8 Probability

Appendix

• A.1 Partial Fractions

• This is a College Algebra topic that is often considered to be optional, so we have presented it in an appendix.

This author-created notebook offers fill-in-the-blank worksheets to accompany the section videos. Key vocabulary and definitions, theorems, and procedures are also included. After filling in the worksheet while watching the video, the student has an excellent study guide for review and test preparation.

Hallmark features of this title

• Eliminating the repetition of topics across the 2-course sequence makes better use of students’ time and resources.
  • Chapter R (Review of Basic Algebra) covers the prerequisites skills and concepts needed for the intermediate and college algebra material. Instructors can assign the chapter in an individualized instruction format (since students enter the course at various levels of math background), cover some or all of the chapter with the entire class at the beginning of the course, or refer students to it on a just-in-time basis as each topic is needed.
  • With Chapter 2 (Graphs, Functions, and Applications), graphs and functions are introduced early and continue as a thread that runs through the course. This gives the instructor the opportunity to use the visual element of graphing to show students how solutions of equations, zeros of functions, and x-intercepts of graphs are related.
  • Chapters 1 (Solving Linear Equations and Inequalities), 3 (Systems of Equations), 9 (Exponential Functions and Logarithmic Functions), and 11 (Conic Sections) deal with topics that are traditionally covered in both intermediate and college algebra. Here, this repetition is eliminated.
  • Chapters 4 (Polynomials and Polynomial Functions) and 5 (Rational Expressions, Equations, and Functions) provide thorough coverage of these topics, thus laying a solid foundation for the more advanced College Algebra coverage of these topics in Chapter 8.
  • Chapters 6 (Radical Expressions, Equations, and Functions) and 7 (Quadratic Functions and Equations) blend topics from intermediate algebra with those traditionally taught in college algebra.
  • Chapters 10 (Matrices) and 12 (Sequences, Series, and Combinatorics) end the course with topics traditionally covered in college algebra.
• Visualizing concepts and making connections:
• Because the concept of a function can be challenging for students, the authors consistently use the language and notation of functions, visually relate functions to equations and graphs, and show how we use functions to model real data throughout the course.
• By introducing functions and graphs early (in Chapter 2), the authors are able to show both algebraic and graphical solutions to examples. Adding this element of visualization helps students quickly develop an understanding of the concepts.
• Integrated review and reinforcement: Frequent opportunities for practice and review help students develop a solid understanding of algebra skills and concepts.
• Now Try Exercises, following most Examples, direct students to work a similar problem in the section exercises for immediate reinforcement of the material just covered.
• Mid-Chapter Reviews offer mixed review exercise sets to help students reinforce their understanding of the concepts. Also included are Collaborative Discussion and Writing exercises for small group or class discussion of concepts.
• Section exercises cover concepts just presented and offer ongoing review of topics presented earlier in the course.
• Vocabulary exercises check students’ understanding of the language of mathematics and can serve as reading quizzes.
• Skill Maintenance Exercises allow students to review and reinforce previously learned material. Synthesis Exercises encourage critical thinking by asking students to apply multiple skills or concepts within a single exercise. Selected exercise sets start with a set of Reading Check exercises designed to check students’ grasp of the concepts and skills in the section.
• Chapter Summary and Review offers comprehensive in-text practice and review. The Study Guide, with key concepts, terms, and examples, provides students with a concise and effective review of the chapter for test prep.
• Chapter Test gives students the opportunity to test themselves and target areas for further study before the class test.

About our authors

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University – Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children’s camp.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University – Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children and grandchildren.

Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and is currently pursuing a PhD in Educational Studies at Ball State University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.

Marvin Bittinger has taught math at the university level for more than 38 years, and he is now professor emeritus of mathematics education at Indiana University – Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” In addition, he also has an interest in philosophy and theology, particularly apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 3 granddaughters.

This author-created notebook offers fill-in-the-blank worksheets to accompany the section videos. Key vocabulary and definitions, theorems, and procedures are also included. After filling in the worksheet while watching the video, the student has an excellent study guide for review and test preparation.

Additional information

Dimensions	1.40 × 8.50 × 10.80 in
Imprint	Pearson
Format	gen
ISBN-13	09780134555904
ISBN-10	0134555902
Author	Judith A. Beecher, Judith A. Penna, Barbara L. Johnson, Marvin L. Bittinger
BISAC	MAT023000
Subjects	mathematics, higher education, MAT023000, Precalculus, College Algebra