William Ma - 5 Steps to a 5: AP Calculus BC 2022

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To
My wife, Mary
My daughters, Janet and Karen I could not have written this book without the help of the following people: My high school calculus teacher, Michael Cantor, who taught me calculus. To
My wife, Mary
My daughters, Janet and Karen I could not have written this book without the help of the following people: My high school calculus teacher, Michael Cantor, who taught me calculus.

Professor Leslie Beebe, who taught me how to write. David Pickman, who fixed my computer and taught me Equation Editor. Jennifer Tobin, who tirelessly edited many parts of the manuscript and with whom I look forward to coauthor a math book in the future. Robert Teseo and his calculus students who field-tested many of the problems. Allison Litvack, Rich Peck, and Liz Spiegel, who proofread sections of the Practice Tests. Mark Reynolds, who proofread part of the manuscript. Maxine Lifshitz, who offered many helpful comments and suggestions. Grace Freedson, Del Franz, Vasundhara Sawhney, and Charles Wall for all their assistance. Sam Lee and Derek Ma, who were on 24-hour call for technical support. Sam Lee and Derek Ma, who were on 24-hour call for technical support.

My older daughter, Janet, for not killing me for missing one of her concerts. My younger daughter, Karen, who helped me with many of the computer graphics. My wife, Mary, who gave me many ideas for the book and who often has more confidence in me than I have in myself.

Congratulations! You are an AP Calculus student. Not too shabby! As you know, AP Calculus is one of the most challenging subjects in high school. You are studying mathematical ideas that helped change the world.

Not that long ago, calculus was taught at the graduate level. Today, smart young people like yourself study calculus in high school. Most colleges will give you credit if you score a 3 or more on the AP Calculus BC Exam. So how do you do well on the AP Calculus BC Exam? How do you get a 5? Well, youve already taken the first step. Youre reading this book. The next thing you need to do is to make sure that you understand the materials and do the practice problems.

In recent years, the AP Calculus exams have gone through many changes. For example, today the questions no longer stress long and tedious algebraic manipulations. Instead, you are expected to be able to solve a broad range of problems including problems presented to you in the form of a graph, a chart, or a word problem. For many of the questions, you are also expected to use your calculator to find the solutions. After having taught AP Calculus for many years and having spoken to students and other calculus teachers, we understand some of the difficulties that students might encounter with the AP Calculus exams. For example, some students have complained about not being able to visualize what the question was asking and other students said that even when the solution was given, they could not follow the steps.

Under these circumstances, who wouldnt be frustrated? In this book, we have addressed these issues. Whenever possible, problems are accompanied by diagrams, and solutions are presented in a step-by-step manner. The graphing calculator is used extensively whenever it is permitted. The book also begins with a chapter on limits and continuity. These topics are normally taught in a pre-calculus course. If youre familiar with these concepts, you might skip this chapter and begin with Chapter 6.