### What's included

## Overview

Are you ready to ace calculus at the college level? With this book, you will be! Professors often say “Students don’t fail the calculus, they fail the algebra.” In other words, even if you understand calculus, your algebra and trigonometry skills can hold you back. Here’s a quick quiz—do you remember how to:

- Factor trinomials?
- Solve equations containing exponents and logs?
- Work with inverse trig functions?

If not, that’s where this book comes in handy!

**is designed to bolster the algebra and trigonometry skills you’ll need while you study calculus. As you make your way through the course,**

*Just-in-Time***is with you every step of the way, showing you the exact algebra or trigonometry topics that you’ll need and pointing out potential problem spots. The easy-to-use Table of Contents features the calculus subject listed directly across from the algebra/trigonometry skills needed to master that topic. Use this book as your study companion and put your anxiety to rest!**

*Just-in-Time*## 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 *e ^{x}*

**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.

**Appendices**

A. The Binomial Theorem

B. Derivation of The Quadratic Formula

Answers to Exercises

Index## For teachers

All the material you need to teach your courses.

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