# Course

Course Summary
Credit Type:
Exam
ACE ID:
CBAP-0021
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 8 for examinees with a score of 3 or above.
Description

## Objective:

3 hours and 15 minutes for the examination. The AP Calculus BC exam questions measure students' understanding of the concepts of calculus, their ability to apply these concepts, and their ability to make connections among graphical, numerical, analytical, and verbal representations of mathematics. Adequate preparation for the exam also includes a strong foundation in algebra, geometry, trigonometry, and elementary functions, though the course necessarily focuses on differential and integral calculus. Students may not take both the Calculus AB and Calculus BC exams within the same year. A Calculus AB sub-score is reported based on performance on the portion of the Calculus BC exam devoted to Calculus AB topics. The free-response section tests students' ability to solve problems using an extended chain of reasoning. During the second timed portion of the free-response section (Part B), students are permitted to continue work on problems in Part A, but they are not permitted to use a calculator during this time.

## Skills Measured:

Limits: students must have a solid, intuitive understanding of limits and be able to compute one-sided limits, limits at infinity, the limit of a sequence, and infinite limits; they should be able to apply limits to understand the behavior of a function near a point and understand how limits are used to determine continuity.Derivatives: students should be able to use different definitions of the derivative, estimate derivatives from tables and graphs, and apply various derivative rules and properties; students should also be able to solve separable differential equations, understand and be able to apply the Mean Value Theorem, and be familiar with a variety of real-world applications, including related rates, optimization, and growth and decay models.Integrals and the Fundamental Theorem of Calculus: students should be familiar with basic techniques of integration, including basic antiderivatives and substitution, and properties of integrals; students should also understand area, volume, and motion applications of integrals, as well as the use of the definite integral as an accumulation function. It is critical that students understand the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus.Series: students should be familiar with various methods for determining convergence and divergence of a series, Maclaurin series for common functions, general Taylor series representations, radius and interval of convergence, and operations on power series; the technique of using power series to approximate an arbitrary function near a specific value allows for an important connection back to the tangent-line problem.Mathematical Practices for AP Calculus: Mathematical Practices for AP Calculus (MPACs) capture important aspects of the work that mathematicians engage in, at the level of competence expected of AP Calculus students. These MPACs are highly interrelated tools that should be used frequently and in diverse contests to support conceptual understanding of calculus; reasoning with definitions and theorems; connecting concepts; implementing algebraic/computational processes; connecting multiple representations; building notational fluency; communicating.
Instruction & Assessment
Supplemental Materials

(CBAP-0044)
(CBAP-0045)
(CBAP-0001)
(CBAP-0003)
(CBAP-0020)
(CBAP-0020)
(CBAP-0021)
(CBAP-0004)