AP Calculus AB Practice Test
Build your understanding of AP Calculus AB Practice Test with practice questions you can work through at your own pace.
Try a sample questionExam overview and details
The AP Calculus AB Practice Test is a comprehensive assessment designed to evaluate a student's mastery of the core concepts and techniques covered in a first-semester college calculus course. This practice exam covers the full breadth of the AP Calculus AB curriculum, including Limits and Continuity, Differentiation (from its fundamental definition through composite, implicit, and inverse functions), Contextual and Analytical Applications of Differentiation, Integration and Accumulation of Change, Applications of Integration, and Differential Equations. The test consists of 36 carefully constructed questions that mirror the style, rigor, and conceptual depth of the actual AP exam. It is intended for high school students enrolled in AP Calculus AB, self-study learners preparing for the AP exam, or college students seeking a rigorous review of single-variable calculus fundamentals. By taking this practice test, students will gain a clear understanding of their strengths and weaknesses across all major topic areas, develop fluency in applying calculus concepts to both abstract problems and real-world contexts, and build the test-taking stamina and confidence necessary for success on the official exam. The questions require not only procedural fluency but also a deep conceptual understanding of why calculus works, encouraging students to think critically and connect ideas across different units.
Sample Questions
Choose an answer and explore the explanation to see how practice works.
Which familiar-function family is explicitly tied to derivative calculation by definition and rules?
One quantity changes at a known rate, and another related quantity is requested. Which source-supported method applies?
A piecewise linear rate graph encloses simple geometric regions. Which evaluation method is source-supported?
A nested function is classified as composite. Which rule selection is explicitly exemplified?
A teacher asks students to infer a likely limit from numerical data rather than from a formula. Which response matches the course framework?
Exam insights and study advice
Calculus is the mathematical language of change, and the skills tested in this practice exam have direct, tangible applications in fields ranging from physics and engineering to economics and biology. Understanding how to model rates of change, optimize systems, and accumulate quantities over time is essential for solving real-world problems such as predicting population growth, designing efficient structures, calculating the work done by a variable force, or determining the optimal price point for a product. Mastery of these concepts empowers you to analyze dynamic systems, make data-driven decisions, and communicate quantitative reasoning effectively. This practice test is not just about passing an exam; it is about building a foundational toolkit that will serve you in any STEM career and in any context where change and accumulation matter.
What this exam covers
Use the published domain weights to plan your study. Practice results do not predict your certification exam score.
01Integration and Accumulation of Change
Integration and Accumulation of Change introduces definite integrals, explains the Fundamental Theorem of Calculus linking differentiation and integration, and teaches techniques for calculating area, accumulated change, and net growth over intervals.
02Analytical Applications of Differentiation
Analytical Applications of Differentiation focuses on using first and second derivatives to sketch curves, determine concavity, locate inflection points, and apply the Mean Value Theorem for detailed analysis of function behavior.
03Applications of Integration
Applications of Integration examines practical uses of definite integrals such as calculating volumes by slicing, determining arc length of curves, and solving work or fluid‑pressure problems that require accumulation of infinitesimal contributions.
04Contextual Applications of Differentiation
Contextual Applications of Differentiation applies derivative concepts to real‑world problems, including optimization of quantities, related‑rates scenarios involving changing variables, and motion analysis where velocity and acceleration are derived from position functions.
05Differentiation: Composite, Implicit, and Inverse Functions
Differentiation: Composite, Implicit, and Inverse Functions covers techniques for differentiating composite functions using the chain rule, handling equations defined implicitly through implicit differentiation, and finding derivatives of inverse functions via reciprocal relationships.
06Differential Equations
Differential Equations covers solving basic separable first‑order equations, modeling exponential growth and decay processes, and constructing and interpreting initial‑value problems that illustrate how integration solves real‑world mathematical dynamic systems.
07Differentiation: Definition and Fundamental Properties
Differentiation: Definition and Fundamental Properties defines the derivative as a limit, presents basic differentiation rules such as power, product, quotient, and chain rules, and connects slopes to rates of change in real‑world contexts.
08Limits and Continuity
Limits and Continuity introduces the precise epsilon‑delta definition of a limit, explores limit laws, and examines continuity at individual points and across intervals, establishing the fundamental logical base for all subsequent calculus concepts.