Precalculus – Three Distinct Series

Students have different goals, learning styles, and levels of preparation. Instructors have different teaching philosophies, styles, and techniques. Rather than write one series to fit all, the Sullivans have written three distinct series. All share the same goal—to develop a high level of mathematical understanding and an appreciation for the way mathematics can describe the world around us. The manner of reaching that goal, however, differs from series to series.

Contemporary Series 11e

The Contemporary Series is the most traditional in approach yet modern in its treatment of precalculus mathematics. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor.

Enhanced with Graphing Utilities Series 8e

This series provides a thorough integration of graphing utilities into topics, allowing students to explore mathematical concepts and encounter ideas usually studied in later courses. Using technology, the approach to solving certain problems differs from the Contemporary Series, while the emphasis on understanding concepts and building strong skills does not.

Concepts through Functions Series 5e (New Edition!)

This series differs from the others, utilizing a functions approach that serves as the organizing principle tying concepts together. Functions are introduced early in various formats. This approach supports the Rule of Four, which states that functions are represented symbolically, numerically, graphically, and verbally. Each chapter introduces a new type of function and then develops all concepts pertaining to that particular function. The solutions of equations and inequalities, instead of being developed as stand-alone topics, are developed in the context of the underlying functions. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor.

New to this Edition

Instructional Videos—Every instructional video is new, created exclusively for this product! The videos have the following features:
• Author-driven—The authors reviewed every script and every video to ensure the approach used in presenting material and solving problems reflects that in the text. In addition, the videos were reviewed by the authors for accuracy. Author Michael Sullivan III appears in many videos.
• Objective-based—one video for each objective in the book
• Segmented—videos divided into shorter parts for ease of navigation (Introductions, Examples, and Summary)

Interactive Figures (formerly titled Guided Visualizations)—The suite of Interactive Figures has been expanded
to support teaching and learning. The figures (created in GeoGebra, many by author Michael Sullivan III) illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently.

MyLab Exercises—Author Michael Sullivan III reviewed all MyLab exercises for this revision and edited them to
better match the language and approach of the text and to make the solutions (within View an Example and Help
Me Solve This) more student-friendly.

CoRequisite Support for College Algebra/Precalculus

The Sullivan CoRequisite solution is currently available in all Concepts 5e titles.

All three titles corequisite support material is based on the Sullivan/Struve Intermediate Algebra 4e title.

The CoRequisite support provides students with the material necessary to be successful in the corresponding material in the college course.

The learning path for students in a corequisite course is something that each individual instructor must decide upon.  However, the course downloaded from Pearson has been developed by Michael Sullivan, III and comes with the following learning path:

  1. For Chapter R, Elementary Algebra Review.
    1. Student takes a diagnostic quiz on Sections R1.2 through R1.5. The material in these sections qualifies as an arithmetic quiz.  If the student passes, the student then moves to taking a diagnostic quiz on Sections R1.6, R2.1, R4.1 through R4.3, and Section A.2 (from Appendix A in the college text), which represents an Elementary Algebra quiz.
    2. If the student does not pass the arithmetic diagnostic quiz, then the student takes a quiz corresponding to each section. For each section, if the student passes the quiz, the student moves to the next section.  If the student does not pass, the student works a personalized homework which focuses on those objectives for which the student did not demonstrate mastery.  Upon completion of the personalized homework, the student retakes the section-level quiz until mastery is achieved.
    3. Once the student completes the arithmetic sections, the student takes a diagnostic quiz on Elementary Algebra. If the student passes the quiz, the student may move to Preparing for Chapter F.  If the student does not pass the Elementary Algebra diagnostic quiz, then the student takes a quiz corresponding to each section.  For each section, if the student passes the quiz, the student moves to the next section.  If the student does not pass, the student works a personalized homework which focuses on those objectives for which the student did not demonstrate mastery.  Upon completion of the personalized homework, the student retakes the section-level quiz until mastery is achieved.
  2. Student works through a multimedia assignment for each section of Preparing for Chapter F.
  3. Student works through a multimedia assignment for each section of Preparing for Chapter 1.
  4. And so on.

Each assignment in the Preparing for chapters has two MyLabMath assignments.

  • The first assignment is a multimedia assignment that incorporates the Author in Action lecture videos, the new applet discovery exercises, “How To” guided exercises, and the Quick Check exercises from the text. Recall, the Quick Check exercises follow many of the examples in the text. To assist students in utilizing the text, the Textbook learning aid for each Quick Check exercise will link directly to the corresponding example in the text. All learning aids, with the exception of “View an Example”, will be available for this portion of the homework. Our experience as instructors has been that too many students rely on this learning aid while doing homework, thereby reducing the effect of homework as students simply mimic the View an Example content.
  • The second assignment is based on the Skill Building and Mixed Practice exercises from the text. Skill building exercises are tied to objectives within the text, so the Textbook learning aid will link directly to the objective within the section. The idea is to reduce the amount of guidance provided to the student (compared with Quick Check exercises) so they are more responsible for identifying the problem type. The Mixed Practice exercises are based on multiple concepts learned within the section or text, so the Textbook learning aid is linked to the section. The student must determine the problem type based on Quick Check and Skill Building exercise experience. The “View an Example” learning aid is disabled for this exercise set as well. Because this text has Skill Builder available in MyLabMath, you may consider reducing the number of exercises in the second assignment. By checking the Skill Builder box, the assignments will adapt to provide support exercises personalized to each student’s needs.

Note:  If you are using a mastery-based learning model, you will need to build quizzes (at either the chapter or section level to assess mastery of skills for each Preparing for chapter).

Study Skills

In our experience as corequisite instructors, one of the main impediments to success for our students has been their lack of study skills.  In fact, data based on Tennessee corequisite students compiled by the Tennessee Board of Regents showed that students who failed both their corequisite course and college-level course also only earned roughly 20% of all attempted college credits for all their courses, while students who passed both courses also earned roughly 85% of all attempted credits for all their courses.  What does this suggest?  It suggests that students who are not successful in corequisite courses tend not to be successful in any of their courses.  These students can be described as not being college-ready (as opposed to academically ready). Therefore, corequisite courses must develop quality study skills in students.  To address this, we offer the following study skills videos.

  1. Mindset
  2. College Transition
  3. Online Learning
  4. Reading to Learn
  5. Stress Management
  6. Time Management
  7. Financial Literacy

Course Dependencies

Teaching a corequisite course is a delicate balancing act. The instructor must be  sure the students have mastery of the corequisite content while also making sure the  integrity of the corresponding college algebra course is maintained (and the course  content is completed). Therefore, it is likely necessary for an instructor to begin  some college algebra material even though the corresponding corequisite content  is not complete. The table below lists sections in the corequisite course that should  be mastered prior to introducing the corresponding college algebra material. A  detailed table of contents for both the college algebra text and corequisite support text follows below.

CoRequisite Section Completed before……College Algebra Section
Arithmetic Review (Sections R1.1, R1.2, R1.3, R1.4, R1.5) Elementary Algebra Review (Sections R1.6, R2.1, R4.1, R4.2, R4.3 from CoRequisite Text and Section A.2 from Appendix A in College Text) 
R2.1 Algebraic Expressions R2.2 Linear Equations in One VariableSection F.1 The Distance and Midpoint Formula
R4.5 Greatest Common Factor; Factoring by Grouping R4.6 Factoring Trinomials (only trinomials where the leading coefficient is 1) R4.7 Factoring Special Products (only the difference of two squares)Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
R5.2 Solving Quadratic Equations by Completing the Square (only real roots)Section F.4 Circles
  
R2.6 Linear Inequalities in One VariableSection 1.1 Functions
R7.1 nth Roots and Rational Exponents (nth roots only)Section 1.3 Properties of Functions
R2.3 An Introduction to Problem SolvingSection 1.6 Mathematical Models: Building Functions
  
R4.6 Factoring Trinomials (leading coefficient different from 1) R5.3 Solving Quadratic Equations by the Quadratic Formula (only real roots) R5.4 Solving Equations Quadratic in FormSection 2.3 Quadratic Functions and Their Zeros
R5.1 The Complex Number System R5.3 Solving Quadratic Equations by the Quadratic Formula (complex roots)Section 2.7 Complex Zeros of a Quadratic Function
R2.7 Compound InequalitiesSection 2.8 Equations and Inequalities Involving the Absolute Value Function
  
R4.7 Factoring Special Products (sum and difference of two cubes) R4.4 Dividing Polynomials; Synthetic DivisionSection 3.2 The Real Zeros of a Polynomial Function
R6.1 Multiplying and Dividing Rational ExpressionsSection 3.4 Properties of Rational Functions
R6.2 Adding and Subtracting Rational Expressions R6.3 Complex Rational Expressions R6.4 Rational EquationsSection 3.5 The Graph of a Rational Function
  
R7.1 nth Roots and Rational Exponents R7.2 Simplifying Expressions Using the Laws of ExponentsSection 4.3 Exponential Functions
R7.3 Simplifying Radical Expressions Using Properties of RadicalsSection 4.6 Logarithmic and Exponential Equations