AP Calculus BC Notes

These notes are adapted from Mr. Chad Gilliland's AP Calculus BC Playlist

Note: This will not follow the normal AP curriculum, but it will cover the same content, just in a different order. Also I don't intend on this being very comprehensive, more of just a example and brief definition and formula kind of guide.

Notes by Unit

This page was last updated 8/15/2025.

Unit 1 - Limits and Continuity	Limits and Their Properties Continuity Intermediate Value Theorem	Notes
Unit 2 - Differentiation	Derivatives More on Derivatives Derivatives Using Data Basic Differentiation Rules Product and Quotient Rules Chain Rule Implicit Differentiation	Notes
Unit 3 - Applications of Differentiation	Definition of the Derivative Meets Derivative Rules Related Rates Extrema on an Interval Mean Value Theorem and Rolle's Theorem Increasing and Decreasing Functions and the First Derivative Test Concavity and the Second Derivative Second Derivative Test Graphs of f, f', and f'''	Notes
Unit 4 - Particle Motion and Integration	Particle Motion Optimization Antiderivatives and Indefinite Integrals Integration Using U-Substitution Integration and Area Under a Curve Riemann Sums and the Definite Integral Fundamental Theorem of Calculus U-Substitution with Definite Integrals Another Kind of U-Substitution Fundamental Theorem of Calculus Average Value of a Continuous Function	Notes
Unit 5 - Integration with Data, functions defined by integrals, and natural logs	Integration Using Data Second Fundamental Theorem of Calculus Natural Logs and Differentiation The Natural Log Function and Integration Derivatives of Inverse Functions Exponential Functions Bases other than e Inverse Trig Functions and Differentiation Inverse Trig Integration	Notes
Unit 6 - Differential Equations	Differential Equations Euler's Method Exponential Growth and Decay	Notes
Unit 7 - Area between curves, volume, and arc length	Area Between Two Curves Volume with Known Cross Sections Volume: The Disc Method Arc Length	Notes
Unit 8 - Techniques of Integration	Integration by Parts Integration by Partial Fractions Logistic Growth	Notes
Unit 9 - Improper Integrals, Sequences and Series, Taylor Polynomials, and Taylor Series	Improper Integrals nth Term Test Geometric Series and Telescopic Integral Test and p-Series Comparison of Series Alternating Series Ratio Test Taylor Polynomials Radius and Interval of Convergence Taylor Series Lagrange Error Bound More on Error	Notes
Unit 10 - Parametrics, Vectors, and Polar	Parametric Equations: The Basics Vectors and Motion along a Curve Polar Coordinates and Polar Graphs Area Bounded by a polar curve Notes on Polar More on Polar Graphs	Notes

Extra Notes

Integration

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