AP Calculus ABExam information
What it is, what's tested, and how it's scored.
AP Calculus AB exam details
The Advanced Placement (AP) Calculus AB exam serves as the final examination for AP Calculus AB, an advanced, college-level course offered to high school students.
AP Calculus AB provides students the opportunity to engage in high-level instruction that extends beyond the scope of what's taught in standard high school classes. AP Calc AB provides an introduction to college-level calculus, covering topics such as derivatives, integrals, and differential equations in depth. The final exam evaluates students' understanding of the material covered throughout the course.
Both the exam and class curriculum are administered by the College Board, a nonprofit organization that promotes college readiness through standardized testing and curriculum development.
The AP Calculus AB exam is hosted by College Board and costs $99 to register. Participants have 3 hours 15 minutes to answer 45 multiple-choice questions, 6 free-response questions. The passing score is 3 (on scale of 1-5).
Time
3 hours 15 minutes
Format
45 multiple-choice questions
6 free-response questions
Exam fee
$99
Passing score
3 (on scale of 1-5)
Details
The AP Calculus AB exam is taken in school or at designated testing centers. The test is typically distributed in a hybrid format: multiple-choice questions are administered digitally using the Bluebook testing app, while free-response questions are answered on paper. The AB exam is divided into two sections, each taking 1 hour and 45 minutes and 1 hour and 30 minutes to complete. A 10-minute scheduled break is included between the two sections.
The AP Calculus AB course and exam will cover the following topics:
Unit 1: Limits and Continuity
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 6: Integration and Accumulation of Change
Unit 7: Differential Equations
Unit 8: Applications of Integration
The AP Calculus AB course framework emphasizes the following Mathematical Practices, or skill areas that allow students to solve complex problems and apply mathematical concepts to real-world scenarios:
Implementing Mathematical Processes: Using mathematical processes to determine expressions and values.
Connecting Representations: Translating mathematical information from a single representation.
Justification: Justifying solutions through accurate computation and step-by-step reasoning.
Communication and Notation: Utilizing correct notation, language, and standard math conventions.
The College Board is responsible for creating a standardized curriculum guide for all AP classes and exams. Individual instructors will determine the order, depth, and focus of units taught.
College Board's AP Calculus AB exam summary
Multiple choice questions
50%
45 total questions
Questions cover algebraic, exponential, logarithmic, trigonometric, and general functions, and may be presented in analytical, graphical, tabular, or verbal form.
- Part A — 30 questionsTime allotted: 60 minutesCalculator not permitted
- Part B — 15 questionsTime allotted: 45 minutesGraphing calculator required
Free response questions
50%
6 total questions
Questions include various types of functions and function representations with a balanced mix of both procedural and conceptual tasks. At least two problems incorporate a real-world context or scenario in the question wording.
- Part A — 2 questionsTime allotted: 30 minutesGraphing calculator required
- Part B — 4 questionsTime allotted: 60 minutesCalculator not permitted
Achievable AP Calculus AB content outline
1
Limits
Limits are the foundation of calculus. Topics in this section include limits from graphs, numerical tables, and algebraic expressions. The unit also covers infinite limits, limits at infinity, asymptotes, and continuity, including the Intermediate Value Theorem.
2
Derivative basics
Formal definition of the derivative as the limit of a difference quotient and interpretation as both slope and rate of change. Learn basic rules for finding derivatives: power, product, and quotient rules for polynomials and rational functions. The unit also covers derivatives of exponential, logarithmic, and trigonometric functions.
3
Advanced differentiation
This chapter focuses on more challenging techniques of differentiation, such as the chain rule, implicit differentiation, and finding derivatives of inverse functions, including inverse trigonometric functions.
4
Contextual uses
Apply derivatives to problems involving motion, position, velocity, and acceleration. Use related rates to connect changing quantities and apply linear approximations to estimate function values. Limits will be revisited using L'Hopital's rule.
5
Analytical uses
Learn how to use the first and second derivatives to analyze, describe, and graph different functions by finding extrema and studying concavity. The chapter also covers the Mean Value Theorem and Rolle's Theorem, as well as solving optimization problems in various contexts.
6
Integration
Approximate areas with Riemann sums and trapezoidal sums. Evaluate definite integrals and apply the Fundamental Theorem of calculus, which connects differentiation and integration. Learn other basic integration techniques, such as the U-substitution method and integration by partial fractions.
7
Differential equations
Introduction to differential equations and slope fields. Solve separable differential equations and explore real-world applications of exponential growth and decay models.
8
Applications of integrals
Apply integration to geometric and real-world problems. Topics include computing the average value of a function, finding the area between curves, and calculating volumes of solids of revolution and solids with known sections.