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Course Overview

AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.

Course Content

Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. The framework specifies what students must know, be able to do, and understand, with a focus on big ideas that encompass core principles, theories, and processes of the discipline. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world.

The AP Calculus BC framework is organized into 10 commonly taught units of study that provide one possible sequence for the course. As always, you have the flexibility to organize the course content as you like.

Unit

Exam Weighting (Multiple-Choice Section)

Unit 1: Limits and Continuity

4%–7%

Unit 2: Differentiation: Definition and Fundamental Properties

4%–7%

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

4%–7%

Unit 4: Contextual Applications of Differentiation

6%–9%

Unit 5: Analytical Applications of Differentiation

8%–11%

Unit 6: Integration and Accumulation of Change

17%–20%

Unit 7: Differential Equations

6%–9%

Unit 8: Applications of Integration

6%–9%

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

11%–12%

Unit 10: Infinite Sequences and Series

17%–18%

Mathematical Practices

The AP Calculus BC framework included in the course and exam description outlines distinct skills, called mathematical practices, that students should practice throughout the year—skills that will help them learn to think and act like mathematicians.

Skill

Description

Exam Weighting (Multiple-Choice Section)

Exam Weighting (Free-Response Section)

1. Implementing Mathematical Processes

Determine expressions and values using mathematical procedures and rules.

53%–66%

37%–59%

2. Connecting Representations

Translate mathematical information from a single representation or across multiple representations.

18%–28%

9%–16%

3. Justification

Justify reasoning and solutions.

11%–18%

37%–59%

4. Communication and Notation

Use correct notation, language, and mathematical conventions to communicate results or solutions.

Only assessed in the free-response section.

9%–20%

AP and Higher Education

Higher education professionals play a key role developing AP courses and exams, setting credit and placement policies, and scoring student work. The AP Higher Education site features information on recruitment and admission, advising and placement, and more.

This chart shows recommended scores for granting credit, and how much credit should be awarded, for each AP course. Your students can look up credit and placement policies for colleges and universities on the AP Credit Policy Search.

Meet the Development Committee for AP Calculus BC.