AP Calculus AB Unit 1 Practice Test: Limits and Continuity

What Unit 1 Covers

Unit 1 introduces the foundational language of calculus. Before derivatives or integrals can be understood, you need a strong command of how functions behave as inputs approach a value — and what it means for a function to be continuous. This unit test covers every major concept tested in the AP Calculus AB limits and continuity section.

Key Topics in This Unit Test

• Evaluating limits from graphs, tables, and algebraic expressions
• One-sided limits (left-hand and right-hand limits)
• Infinite limits and vertical asymptotes
• Limits at infinity and horizontal asymptotes
• Continuity at a point and over an interval
• Types of discontinuities: removable, jump, and infinite
• The Intermediate Value Theorem (IVT) and its AP applications

AP Exam Skills This Unit Develops

On the AP Calculus AB exam, limits appear in both the multiple-choice and free-response sections. MCQ questions often ask you to evaluate a limit algebraically — using factoring, rationalization, or direct substitution — or to read limit behavior from a graph. FRQ questions may ask you to apply the IVT to justify that a function has a root or reaches a specific value on an interval. Justification language matters on the AP exam: you must state the conditions of a theorem, not just its conclusion.

Common Mistakes to Avoid

• Confusing the limit value with the function value: A limit describes where a function is heading, not necessarily where it is. Even if f(a) is undefined or has a different value, the limit as x approaches a can still exist.
• One-sided limit errors: When a limit does not specify a direction, both one-sided limits must agree for the two-sided limit to exist. Students frequently overlook this check.
• Misapplying the IVT: The IVT requires the function to be continuous on a closed interval. Failing to state or verify continuity is one of the most common AP justification errors.
• Infinite vs. undefined limits: A limit of infinity means the function grows without bound — it does not mean the limit exists as a number.

How to Use This Unit 1 Practice Test

Work through all questions without referencing your notes first. After completing the test, review your results question by question. For any limit you evaluated incorrectly, identify whether the error was algebraic, conceptual, or related to reading the graph or table. Revisit the specific technique — factoring, L'Hôpital (covered in Unit 4), or the squeeze theorem — before retaking the test. A strong Unit 1 score is the clearest sign your calculus foundation is solid.