Calculus Express: A Rapid Review and Formula Guide for the AP Calculus AB Exam

Calculus Express is a concise, student-friendly study guide designed to help you quickly and effectively prepare for the AP Calculus AB exam. Its streamlined approach also makes it an excellent companion for students in any introductory calculus course, where the content closely overlaps with AP Calculus AB.

To ensure maximum relevance, every topic is modeled directly from the College Board’s official AP Calculus AB outline. The result is a focused, 110-page guide that covers all essential concepts, formulas, and examples—without the filler.

What sets Calculus Express apart is its brevity with precision. At just over 100 pages, it is specifically designed for efficient review and short-term mastery. You can actually cram with this book—memorize the key formulas and concepts, reinforce them with targeted examples, and walk into the exam confident and prepared. Other resources, often 600–900 pages long, function more like full-semester textbooks than exam-prep tools. They are valuable, but not optimized for rapid review.

Calculus Express is organized into five major sections:

• Limits
• Derivatives
• Applications of Derivatives
• Integrals
• Applications of Integrals

You’ll begin with limits, the foundation of calculus—how to evaluate them, identify asymptotes, and apply the Intermediate Value Theorem.

From there, the book moves into derivatives and their applications. You’ll learn derivative definitions, rules, rates of change, critical points, curve behavior, related rates, and more.

Next come integrals and their applications, including the Fundamental Theorem of Calculus, integration techniques, areas, accumulated change, and other AP-relevant uses.

If you want a fast, clean, no-nonsense study guide, Calculus Express delivers exactly that. No extraneous detail. No long derivations. Just the core formulas, definitions, examples, and strategies you need to succeed.

Ryan Mettling, partner and publisher of Performance Programs Company, is an accomplished online curriculum designer, author, and course developer. He is responsible for the company's strategic planning, general management, printing and production, e-pub and retail platforms, and multi-channel marketing. Ryan is a co-author of the Real Estate License Exam Prep (RELEP) Series and Real Estate Math Express. Mr. Mettling is a member of the Real Estate Educators Association (REEA), and graduated Valedictorian from the University of Central Florida's College of Business Administration.