Just-in-Time Algebra and Trigonometry for Early Transcendentals Calculus

Guntram Mueller / Ronald I. Brent  
Total pages
June 2012
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This book is designed for current calculus students to review the algebra and trigonometry skills that are so crucial for success in calculus. Organized to correspond to a typical calculus course, relevant algebra and trigonometry topics are presented just as students need them, with warnings about pitfalls and exercise sets for practice. Whether used as a reference or for catching up, this text will prove invaluable for all students taking calculus.


Note: A different version of this book is available specifically for Late Transcendentals calculus courses (i.e., books with the title “Calculus”).


  • Topics are ordered to correspond to a typical calculus course, for instance, the topic “composition and decomposition of functions” is listed as a prerequisite for the Chain Rule.
  • Extensive exercise sets, especially in the sections on word problems, exponentials, and logarithms, give more opportunities for both students and instructors to tailor exercises to their specific needs.
  • Precisely written text makes the concepts clear and gives students what they need to succeed in calculus.
  • Odd-numbered exercises have answers in the back of the book. Answers to the even-numbered exercises are available to professors on Pearson's Instructor Resource Center.


New to this Edition

  • Chapter 5 now includes a new section on Graphs of Trigonometric Functions, along with exercises to go with this topic.
  • Additional exercises in chapters 14 and 15 give students more of the practice they need to master the concepts.
  • A Getting Ready for Calculus chapter is available online for students using a MyMathLab with a Pearson calculus text.
    • Hundreds of additional practice problems correspond to topics covered in Just-In-Time Algebra and Trigonometry for Early Transcendentals Calculus.
    • Use this online chapter to diagnose gaps in prerequisite skills and provide students with a review at the beginning of the course or remediation throughout the semester.
    • MyMathLab is available to qualified adopters. Learn more at www.mymathlab.com or contact your Pearson representative.


Table of Contents

Calculus Topic: Review of Basics

1. Numbers and Their Disguises

Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals


Calculus Topic: Circles, Parabolas, etc.

2. Completing the Square

Completing the square in one and two variables


Calculus Topic: Equations

3. Solving Equations

Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property


Calculus Topic: Algebraic Functions and Graphs

4. Functions and Their Graphs

Introduction, equations of lines, power functions, shifting graphs, intersection of curves


Calculus Topic: Transcendental Functions

5. Cyclic Phenomena: The Six Basic Trigonometric Functions

Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas, graphs of complex trigonometric functions


6. Exponential Functions

The family of exponentials, the function ex


7. Composition and Inverse Functions

Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression


8. Logarithmic Functions

Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm


9. Inverse Trigonometric Functions

The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities


Calculus Topic: Limits

10. Changing the Form of a Function

Factoring, canceling, long division, rationalizing, extracting a factor from under a root


Calculus Topic: Derivatives

11. Simplifying Algebraic Expressions

Working with difference quotients and rational functions, canceling common factors, rationalizing expressions


Calculus Topic: The Chain Rule

12. Decomposition of Functions

Inner, outer, and outermost functions, decomposing composite functions


Calculus Topic: Implicit Differentiation

13. Equations of Degree 1 Revisited

Solving linear equations involving derivatives


Calculus Topic: Related Rates, Applied Max-Min Problems

14. Word Problems, Algebraic and Transcendental

Applied Max-Min Problems, Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay


Calculus Topic: Integrating Trigonometric Functions

15. Trigonometric Identities

Rewriting trigonometric expressions using identities.



A. The Binomial Theorem

B. Derivation of The Quadratic Formula


Answers to Exercises



Guntram B. Mueller received his PhD in Mathematics from the University of Notre Dame. He has taught calculus many times and is very familiar with the typical strengths and weaknesses in the backgrounds of his students. That experience is what guided him, in cooperation with Dr. Ron Brent, in writing the Just-in-Time series. His advice? Buy the book! It's got just what you need, just in time.


Ronald I. Brent is a Professor of Mathematics at University of Massachusetts, Lowell, where he has taught since 1987. He earned his PhD in Mathematics from Rensselaer Polytechnic Institute. Dr. Brent is the author of many publications, including three Just-In-Time mathematics texts. His main advice to his calculus students is: “Work on your homework as if your life in this course depends upon it. Because it does!

Instructor Resources