AP Calculus (AB & BC)

What This Unit Covers Unit 1 establishes the mathematical foundation for calculus by introducing limits as the primary tool for analyzing functions near specific points. You will explore how limits allow us to define instantaneous change and continuity, providing the conceptual bridge necessary to understand derivatives and integrals later in the course.

Why It Matters on the Exam Limits and continuity typically account for 10–12% of the AP Calculus exam. You should expect a mix of conceptual multiple-choice questions regarding graph analysis and algebraic free-response questions that require you to evaluate limits, identify types of discontinuities, or apply the Intermediate Value Theorem.

How to Study It

• Master algebraic manipulation: Practice factoring, conjugate multiplication, and common denominators to resolve indeterminate forms (0/0), as these are the most common algebraic hurdles in the unit.
• Visualize the behavior: Don’t just rely on equations; practice sketching functions and using tables of values to identify vertical and horizontal asymptotes.
• Learn the "Vocabulary of Continuity": Be prepared to write formal justifications for continuity using the three-part definition (the limit exists, the function is defined, and they are equal) to secure full points on free-response questions.
• Know your theorems: Memorize the formal conditions for the Squeeze Theorem and the Intermediate Value Theorem (IVT), as these are frequently tested in "justify your answer" problems.