AP Calculus AB/BC

Note: If you are only looking for AP Calculus AB prep, do NOT look at the files/sections labeled “BC-only”.

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Course roadmap

AP Calculus is built around three connected ideas:

• Limits describe what functions approach.
• Derivatives describe instantaneous change.
• Integrals describe accumulation.

AB focuses on limits, derivatives, integrals, differential equations, and applications. BC includes all of AB plus additional techniques with parametric, polar, and vector-valued functions, and infinite series.

When studying, try to connect each unit to at least two representations:

• formulas,
• graphs,
• tables,
• verbal/contextual descriptions.

Most AP questions are not just asking whether you can compute. They are asking whether you can justify why a theorem applies, interpret a derivative or integral in context, and apply different systems of thinking to problems.

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Units

Unit 1: Limits and Continuityreview85%Unit 2: Differentiation: Definition and Fundamental Propertiesreview85%Unit 3: Differentiation: Composite, Implicit, and Inverse Differentiationdeveloping70%Unit 4: Contextual Applications of Differentiationdeveloping70%Unit 5: Analytical Applications of Differentiationdeveloping70%Unit 6: Integration and Accumulation of Changedeveloping70%Unit 7: Differential Equationsdeveloping70%Unit 8: Applications of Integrationdeveloping70%Unit 9: Parametric, Polar, and Vector-Valued Functions (BC-only)developing70%Unit 10: Infinite Sums and Series (BC-only)developing70%

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Resources

• Resources — general AP prep links, College Board, and books.