AP Calculus BC
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Explore the concepts, methods, and applications of differential and integral calculus, including topics such as parametric, polar, and vector functions, and series. You’ll perform experiments and investigations and solve problems by applying your knowledge and skills.
Determining expressions and values using mathematical procedures and rules
Connecting representations
Justifying reasoning and solutions
Using correct notation, language, and mathematical conventions to communicate results or solutions
A first-semester college calculus course and the subsequent single-variable calculus course
You should have successfully completed courses in which you studied algebra, geometry, trigonometry, analytic geometry, and elementary functions. In particular, you should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions, as well as sequences, series, and polar equations. You should know how to graph these functions and solve equations involving them. You should also be familiar with algebraic transformations, combinations, compositions, and inverses for general functions.
Mon, May 8, 2023,
8 AM Local
This is the regularly scheduled date for the AP Calculus BC Exam.
The course content outlined below is organized into commonly taught units of study that provide one possible sequence for the course. Your teacher may choose to organize the course content differently based on local priorities and preferences.
You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.
Topics may include:
4%–7% of exam score
You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
Topics may include:
4%–7% of exam score
You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
Topics may include:
4%–7% of exam score
You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
Topics may include:
6%–9% of exam score
After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems.
Topics may include:
8%–11% of exam score
You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques.
Topics may include:
17%–20% of exam score
You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay and logistic models.
Topics may include:
6%–9% of exam score
You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find lengths of curves, areas of regions, or volumes of solids defined using functions.
Topics may include:
6%–9% of exam score
You’ll solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. You’ll also deepen your understanding of straight-line motion to solve problems involving curves.
Topics may include:
11%–12% of exam score
You’ll explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. You’ll also learn how to determine the largest possible error associated with certain approximations involving series.
Topics may include:
17%–18% of exam score
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AP Calculus AB and BC Course and Exam Description
This is the core document for the course. It clearly lays out the course content and describes the exam and AP Program in general.
AP Calculus BC can lead to a wide range of careers and college majors