Calculus Practice Problems - by Patrick
Introduction
This book is intended for a variety of calculus students. Perhaps you want a supplement to your current calculus class or you’re looking to brush up on a course you took long ago. Or maybe you’re teaching yourself and need a comprehensive book of extra practice problems.
The 1,001 questions in this book cover calculus concepts that a high school student would encounter in a calculus course in preparation for the AP exam. It also covers most of the concepts that a calculus student could expect to see in the first two semesters of a three- semester calculus course. The types of questions are questions that I regularly assigned when teaching both as homework questions or are questions that a student could’ve expected to see on a quiz or test.
Jump around the book as you like. You can find a robust algebra and trigonometry review at the beginning of the book to make sure that you’re prepared for calculus. The number-one reason students have difficulty in calculus is not calculus itself but having a weak back- ground in algebra and trigonometry. If you’re rusty on the fundamentals, spend time on those first two chapters before jumping into the rest of the text!
As with many things worth doing in life, there’s no shortcut to becoming proficient in mathematics. However, by practicing the problems in this book, you’ll be on your way to becoming a much stronger calculus student.
What You’ll Find
The 1,001 calculus practice problems in the book are divided into 15 chapters, with each chapter providing practice of the mechanical side of calculus or of applications of calcu- lus. Some of the questions have a diagram or graph that you need in order to answer the question.
The end of the book provides thorough and detailed solutions to all the problems. If you get an answer wrong, try again before reading the solution! Knowing what not to do is often a great starting point in discovering the correct approach, so don’t worry if you don’t immediately solve each question; some problems can be quite challenging.
Beyond the Book
This book provides a lot of calculus practice. If you’d also like to track your progress online, you’re in luck! Your book purchase comes with a free one-year subscription to all 1,001 practice questions online. You can access the content whenever you want. Create your own question sets and view personalized reports that show what you need to study most.
Contents at a Glance:
- Introduction
- Part I: The Questions
- Chapter 1: Algebra Review
- Chapter 2: Trigonometry Review
- Chapter 3: Limits and Rates of Change
- Chapter 4: Derivative Basics
- Chapter 5: The Product, Quotient, and Chain Rules
- Chapter 6: Exponential and Logarithmic Functions and Tangent Lines
- Chapter 7: Implicit Differentiation
- Chapter 8: Applications of Derivatives
- Chapter 9: Areas and Riemann Sums
- Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem
- Chapter 11: Applications of Integration
- Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions,and L’Hôpital’s Rule
- Chapter 13: U-Substitution and Integration by Parts
- Chapter 14: Trigonometric Integrals, Trigonometric Substitution,
- and Partial Fractions
- Chapter 15: Improper Integrals and More Approximating Techniques
- Part II: The Answers
- Chapter 16: Answers and Explanations
- Index
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