AP Calculus BC Tuition

Content Description: Explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.

Prior Knowledge Required: Familiar with the behavior and graphing of functions, along with basic algebraic manipulation and the concept of approaching a value.

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

Prior Knowledge Required: Understand limits and slopes as rates of change, with a solid grasp of basic function operations and continuity.

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

Prior Knowledge Required: Comfortable with the chain rule and have a good understanding of differentiating simple functions, as well as the concepts of function composition and inverse functions.

Content Description: You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine the limits of certain indeterminate forms.

Prior Knowledge Required: Prior experience in applying derivatives to solve real-world problems, including setting up equations based on word problems.

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

Prior Knowledge Required: Skilled in using derivatives to analyze function behavior and interpret graphs, including the first and second derivative tests.

Content Description: 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.

Prior Knowledge Required: Understand limits, basic differentiation, and the concept of the area under a curve, as well as the relationship between a function and its derivative.

Content Description: 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.

Prior Knowledge Required: A solid foundation in integration techniques and a basic understanding of exponential growth and decay models.

Content Description: 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.

Prior Knowledge Required: Be proficient with definite and indefinite integrals, and understand how to apply integration to compute areas, volumes, and solve net change

Content Description: 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.

Prior Knowledge Required: Comfortable with differentiation and integration of standard functions. Prior knowledge of analyzing motion along a straight line and basic coordinate geometry is also necessary.

Content Description: You’ll explore the 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.

Prior Knowledge Required: Strong understanding of limits and convergence, as well as familiarity with basic series and sequences. Prior knowledge should include working with functions, summation notation, and the concept of approximation errors in mathematical analysis.