AP Calculus BCExam information
What it is, what's tested, and how it's scored.
AP Calculus BC exam details
The Advanced Placement (AP) Calculus BC exam serves as the final examination for AP Calculus BC, an advanced, college-level course offered to high school students.
The AP Calculus BC course provides students the opportunity to engage in high-level instruction that extends beyond the scope of what's taught in standard high school math classes. The course covers topics such as derivatives, integrals, differential equations, parametric functions, and infinite sequences. AP Calc BC serves as a more advanced version of AP Calculus AB, diving deeper into the material covered in AB and introducing additional concepts.
The exams are administered by the College Board, a nonprofit organization that promotes college readiness through standardized testing and curriculum development.
The AP Calculus BC 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
AP Calculus BC exams are 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 BC 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 Calc BC 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
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Unit 10: Infinite Sequences and Series
The AP Calculus BC course framework emphasizes the following Mathematical Practices, or skill areas that train 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 BC 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.
- Part A — 2 questionsTime allotted: 30 minutesGraphing calculator required
- Part B — 4 questionsTime allotted: 60 minutesCalculator not permitted
Achievable AP Calculus BC content outline
1
Limits and Continuity
Introduces the foundational concept of limits and how they describe the behavior of functions near specific points. Covers one-sided limits, limits at infinity, continuity, and the Intermediate Value Theorem. Emphasizes graphical, numerical, and analytical understanding as the basis for all of calculus.
2
Differentiation: Definition and Fundamental Properties
Explores the derivative as a limit and its geometric interpretation as the slope of a tangent line. Covers rules for differentiating basic functions, including power, exponential, and trigonometric functions. Introduces higher-order derivatives and connects derivatives to motion and rates of change.
3
Differentiation: Composite, Implicit, and Inverse Functions
Extends differentiation to more complex scenarios, including the chain rule, implicit differentiation, and derivatives of inverse functions. Covers derivatives of logarithmic, exponential, and inverse trigonometric functions, emphasizing problem-solving and algebraic fluency.
4
Contextual Applications of Differentiation
Applies derivatives to real-world and physical contexts. Includes related rates, linearization, and local linear approximations. Focuses on using derivatives to model dynamic change in motion, growth, and other applied situations.
5
Analytical Applications of Differentiation
Develops analytical tools for curve sketching and optimization. Covers identifying extrema, concavity, inflection points, and asymptotes using the first and second derivative tests. Includes optimization problems, the mean value theorem, and interpreting derivative graphs to understand function behavior.
6
Integration and Accumulation of Change
Introduces integration as the reverse process of differentiation. Covers the Fundamental Theorem of Calculus, antiderivatives, and definite integrals. Explains Riemann sums, accumulation functions, and using integrals to represent total change in various contexts.
7
Differential Equations
Focuses on basic first-order differential equations and their applications. Includes slope fields, separable equations, and modeling exponential growth and decay. Introduces logistic growth models and how differential equations describe dynamic systems.
8
Applications of Integration
Explores how integrals are used to find physical quantities and geometric measures. Includes finding areas between curves, volumes of solids of revolution, arc length, and the average value of a function. Emphasizes interpreting integrals in applied, geometric, and physical settings.
9
Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Extends calculus concepts to alternative coordinate systems and representations of motion. Covers derivatives, areas, and arc lengths for parametric and polar functions, as well as vector-valued functions in motion problems.
10
Infinite Sequences and Series
Introduces sequences and the idea of convergence. Covers series tests, including geometric, p-series, ratio, and alternating series. Explores Taylor and Maclaurin series, power series, and how functions can be represented as infinite sums for approximation and analysis.