Course Introduction

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 Focus

AP Calculus BC is designed to be the equivalent to both first and second semester college calculus courses. AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.

AP Calculus BC

$1,100.00

20节课, $55/1hr

Course Content

Unit 1: Limits and Continuity

You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.

Unit 2: Differentiation: Definition and Fundamental Properties

You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.

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

You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.

Unit 4: Contextual Applications of Differentiation

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.

Unit 5: Analytical Applications of Differentiation

After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems.

Unit 6: Integration and Accumulation of Change

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.

Unit 7: Differential Equations

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.

Unit 8: Applications of Integration

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.

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

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.

Unit 10: Infinite Sequences and Series

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.

AP Calculus BC

Grade: G9-12