Credential type: school examination · verified on the issuer's site September 20, 2026 issuer page
AP Calculus AB is a current, paper‑based assessment created by the College Board. It evaluates students’ mastery of limits, continuity, differentiation techniques, analytical and contextual applications, integration, differential equations and their practical uses. The exam consists of multiple‑choice and free‑response sections, lasts 195 minutes, and is scored on a 1–5 scale where a score of 3 is passing.
High‑school juniors or seniors who have completed a year‑long pre‑calculus sequence and plan to pursue college‑level mathematics, engineering, physics, economics, or related STEM fields should take AP Calculus AB in preparation for college.
Review the official Course and Exam Description, then study each domain using the OpenStax Calculus Volume 1 textbook. Practice multiple‑choice questions daily, and write timed free‑response solutions for past AP problems. Focus on the weighted domains—especially Integration (18.5 %) and Analytical Differentiation (16.5 %). Use College Board’s released practice exams to build stamina for the 195‑minute paper‑based format.
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.
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.
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.
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.
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.
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.
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.
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.
Arrive early with your admission ticket, a photo ID, and a #2 pencil. Bring a calculator that meets College Board specifications. Allocate time for both sections, double‑check free‑response answers, and stay hydrated.
The AP Calculus AB exam consists of a multiple‑choice section and a free‑response section. The exact number of questions is detailed in the official College Board exam guide and varies each year.
A score of 3 on the 1–5 AP scale is considered passing for AP Calculus AB, indicating qualified performance according to College Board standards.
The AP Calculus AB exam is administered on paper in a single session lasting 195 minutes. It consists of a multiple‑choice section followed by a free‑response section, each with its own time allocation.
The standard fee for the AP Calculus AB exam is $98 per student. Eligible students may qualify for a reduced fee of $55, and an additional $40 surcharge is added for international candidates.
Verified 2026-09-02
Content was compiled from the College Board’s official exam guide and certification pages, cross‑referenced with the OpenStax Calculus Volume 1 textbook and AP student resources to ensure accurate domain weights and exam details.