According to Collegeboard, AP Calculus BC is a rough equivalent of first and second semester college Calculus courses; it extends the content learned in AP Calculus AB.

#### Prequisites to learn AP Calculus BC

- Algebra
- Geometry
- Trigonometry
- Analytical Geometry
- Elementtary Functions
- Sequence and Series
- Polar Equations

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### AP Calculus BC Course Content

The course is organized around the foundational concepts of calculus: I. 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.

II. 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.

III. 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.

IV. 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.

Format of Assessment

Section I: Multiple Choice | 45 Questions | 1 Hour, 45 Minutes |

50% of Exam Score

• Part A: 30 questions; 60 minutes (calculator not permitted)

• Part B: 15 questions; 45 minutes (graphing calculator required)

Section II: Free Response | 6 Questions | 1 Hour, 30 Minutes |

50% of Exam Score

• Part A: 2 questions; 30 minutes (graphing calculator required)

• Part B: 4 questions; 60 minutes (calculator not permitted)