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AP® Calculus BC
AP Calculus BC is the second part of AP Calculus, which focuses on students’ understanding of calculus concepts and provide experience with methods and applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), each course becomes a cohesive whole, rather than a collection of unrelated topics. Both courses require students to use definitions and theorems to build arguments and justify conclusions. The courses feature a multirepresentational approach to calculus, with concepts, results, and problems expressed graphically, numerically, analytically, and verbally. Exploring connections among these representations builds understanding of how calculus applies limits to develop important ideas, definitions, formulas, and theorems. A sustained emphasis on clear communication of methods, reasoning, justifications, and conclusions is essential. Teachers and students should regularly use technology to reinforce relationships among functions, to confirm written work, to implement experimentation, and to assist in interpreting results.
What is included
10 units and 111 lessons of AP® Calculus BC, free to start in Stellar at your own pace.
Units
10 units in AP® Calculus BC
- 01Limits and ContinuityThis unit introduces limits as the foundation for understanding change, continuity, and the behavior of functions near specific input values. Students learn to evaluate limits using graphs, tables, algebraic methods, and theorems while connecting these ideas to discontinuities and asymptotes.16 lessonsPreview unit
- 02Differentiation: Definition and Basic Derivative RulesThis unit introduces the derivative as an instantaneous rate of change and the slope of a tangent line. Students develop derivative notation, estimate derivatives, connect differentiability to continuity, and learn foundational derivative rules.10 lessonsPreview unit
- 03Differentiation: Composite, Implicit, and Inverse FunctionsThis unit extends differentiation to more complex function types. Students learn the chain rule, implicit differentiation, inverse function derivatives, inverse trigonometric derivatives, and higher-order derivatives.6 lessonsPreview unit
- 04Contextual Applications of DifferentiationThis unit focuses on interpreting derivatives in real-world and applied contexts. Students connect derivatives to motion, related rates, linear approximation, and indeterminate limits using L’Hospital’s Rule.7 lessonsPreview unit
- 05Analytical Applications of DifferentiationThis unit uses derivatives to analyze the shape and behavior of functions. Students study extrema, monotonicity, concavity, graph relationships, optimization, and implicit relations.12 lessonsPreview unit
- 06Integration and Accumulation of ChangeThis unit introduces integration as accumulation and as the reverse process of differentiation. Students learn Riemann sums, definite integrals, the Fundamental Theorem of Calculus, antiderivatives, and major integration techniques.14 lessonsPreview unit
- 07Differential EquationsThis unit introduces equations involving derivatives and shows how they can model real-world change. Students work with slope fields, Euler’s Method, separable equations, initial conditions, and exponential and logistic models.9 lessonsPreview unit
- 08Applications of IntegrationThis unit applies definite integrals to real-world and geometric problems. Students find average values, accumulated change, areas, volumes, arc length, and distance traveled.13 lessonsPreview unit
- 09Parametric Equations, Polar Coordinates, and Vector-Valued FunctionsThis unit expands calculus beyond standard y = f(x) functions. Students study parametric equations, vector-valued functions, polar coordinates, two-dimensional motion, arc length, and polar area.9 lessonsPreview unit
- 10Infinite Sequences and SeriesThis unit introduces infinite series and methods for determining convergence or divergence. Students study geometric series, convergence tests, alternating series, Taylor polynomials, error bounds, and power series representations.15 lessonsPreview unit
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