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 is a more advanced version of AP Calculus AB, delving deeper into AB material 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
AP Calculus AB and AP Calculus BC share the same foundational curriculum (Units 1 through 8), though BC adds more advanced content in Units 9 and 10: Parametric Equations and 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
Introduces limits graphically, numerically, and analytically as the foundation of calculus. Covers continuity, limits at infinity, asymptotic behavior, and special limit forms.
2
Derivative basics
Develops the idea of a derivative from its limit definition and interprets derivatives as rates of change and slopes of tangent lines. Covers fundamental differentiation rules and the relationship between continuity and differentiability.
3
Advanced differentiation
Expands differentiation techniques to more complex functions and relationships. Covers the chain rule, implicit differentiation, inverse functions, and higher-order derivatives.
4
Contextual uses
Applies derivatives to real-world and mathematical situations. Covers motion, related rates, linear approximation, and evaluating indeterminate forms with L'Hôpital's rule.
5
Analytical uses
Uses derivatives to analyze function behavior and solve optimization problems. Covers extrema, concavity, inflection points, curve sketching, and important calculus theorems.
6
Integration
Introduces integration as accumulation and the reverse process of differentiation. Covers Riemann sums, the Fundamental Theorem of Calculus, integration techniques, and improper integrals.
7
Differential equations
Explores differential equations as models for changing quantities. Covers slope fields, separation of variables, exponential growth and decay, Euler's method, and logistic models.
8
Applications of integrals
Applies integration to solve geometric and physical problems. Covers average value, motion, area between curves, volumes of solids, and arc length.
9
Parametric, polar, and vectors
Extends calculus to alternative coordinate systems and vector-valued functions. Covers motion along curves, parametric equations, polar coordinates, and areas in polar form.
10
Infinite sequences and series
Introduces infinite sequences and series and methods for determining convergence. Covers convergence tests, alternating series, absolute convergence, and error estimation.
11
Series representations of functions
Explores representing functions with power series and polynomial approximations. Covers Taylor and Maclaurin series, convergence intervals, and approximation techniques.