College Board-Aligned
AP Calculus BC
This page follows the current official College Board course outline. Each unit/topic links to original local notes built for studying, practice, and review.
Course Snapshot
10
official units
54
linked topics/skills
Alignment Sources
Units & Topics
Unit 1: Limits and Continuity
On the AP exam: 4%-7% of exam score.
- Unit 1 Topic 1: How limits help us to handle change at an instant Original Notes
- Unit 1 Topic 2: Definition and properties of limits in various representations Original Notes
- Unit 1 Topic 3: Definitions of continuity of a function at a point and over a domain Original Notes
- Unit 1 Topic 4: Asymptotes and limits at infinity Original Notes
- Unit 1 Topic 5: Reasoning using the Squeeze theorem and the Intermediate Value Theorem Original Notes
Unit 2: Differentiation: Definition and Fundamental Properties
On the AP exam: 4%-7% of exam score.
- Unit 2 Topic 1: Defining the derivative of a function at a point and as a function Original Notes
- Unit 2 Topic 2: Connecting differentiability and continuity Original Notes
- Unit 2 Topic 3: Determining derivatives for elementary functions Original Notes
- Unit 2 Topic 4: Applying differentiation rules Original Notes
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
On the AP exam: 4%-7% of exam score.
- Unit 3 Topic 1: The chain rule for differentiating composite functions Original Notes
- Unit 3 Topic 2: Implicit differentiation Original Notes
- Unit 3 Topic 3: Differentiation of general and particular inverse functions Original Notes
- Unit 3 Topic 4: Determining higher-order derivatives of functions Original Notes
Unit 4: Contextual Applications of Differentiation
On the AP exam: 6%-9% of exam score.
- Unit 4 Topic 1: Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change Original Notes
- Unit 4 Topic 2: Applying understandings of differentiation to problems involving motion Original Notes
- Unit 4 Topic 3: Generalizing understandings of motion problems to other situations involving rates of change Original Notes
- Unit 4 Topic 4: Solving related rates problems Original Notes
- Unit 4 Topic 5: Local linearity and approximation Original Notes
- Unit 4 Topic 6: L’Hospital’s rule Original Notes
Unit 5: Analytical Applications of Differentiation
On the AP exam: 8%-11% of exam score.
- Unit 5 Topic 1: Mean Value Theorem and Extreme Value Theorem Original Notes
- Unit 5 Topic 2: Derivatives and properties of functions Original Notes
- Unit 5 Topic 3: How to use the first derivative test, second derivative test, and candidates test Original Notes
- Unit 5 Topic 4: Sketching graphs of functions and their derivatives Original Notes
- Unit 5 Topic 5: How to solve optimization problems Original Notes
- Unit 5 Topic 6: Behaviors of Implicit relations Original Notes
Unit 6: Integration and Accumulation of Change
On the AP exam: 17%-20% of exam score.
- Unit 6 Topic 1: Using definite integrals to determine accumulated change over an interval Original Notes
- Unit 6 Topic 2: Approximating integrals with Riemann Sums Original Notes
- Unit 6 Topic 3: Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals Original Notes
- Unit 6 Topic 4: Antiderivatives and indefinite integrals Original Notes
- Unit 6 Topic 5: Properties of integrals and integration techniques, extended Original Notes
- Unit 6 Topic 6: Determining improper integrals Original Notes
Unit 7: Differential Equations
On the AP exam: 6%-9% of exam score.
- Unit 7 Topic 1: Interpreting verbal descriptions of change as separable differential equations Original Notes
- Unit 7 Topic 2: Sketching slope fields and families of solution curves Original Notes
- Unit 7 Topic 3: Using Euler’s method to approximate values on a particular solution curve Original Notes
- Unit 7 Topic 4: Solving separable differential equations to find general and particular solutions Original Notes
- Unit 7 Topic 5: Deriving and applying exponential and logistic models Original Notes
Unit 8: Applications of Integration
On the AP exam: 6%-9% of exam score.
- Unit 8 Topic 1: Determining the average value of a function using definite integrals Original Notes
- Unit 8 Topic 2: Modeling particle motion Original Notes
- Unit 8 Topic 3: Solving accumulation problems Original Notes
- Unit 8 Topic 4: Finding the area between curves Original Notes
- Unit 8 Topic 5: Determining volume with cross-sections, the disc method, and the washer method Original Notes
- Unit 8 Topic 6: Determining the length of a planar curve using a definite integral Original Notes
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
On the AP exam: 11%-12% of exam score.
- Unit 9 Topic 1: Finding derivatives of parametric functions and vector-valued functions Original Notes
- Unit 9 Topic 2: Calculating the accumulation of change in length over an interval using a definite integral Original Notes
- Unit 9 Topic 3: Determining the position of a particle moving in a plane Original Notes
- Unit 9 Topic 4: Calculating velocity, speed, and acceleration of a particle moving along a curve Original Notes
- Unit 9 Topic 5: Finding derivatives of functions written in polar coordinates Original Notes
- Unit 9 Topic 6: Finding the area of regions bounded by polar curves Original Notes
Unit 10: Infinite Sequences and Series
On the AP exam: 17%-18% of exam score.
- Unit 10 Topic 1: Applying limits to understand convergence of infinite series Original Notes
- Unit 10 Topic 2: Types of series: Geometric, harmonic, and p-series Original Notes
- Unit 10 Topic 3: A test for divergence and several tests for convergence Original Notes
- Unit 10 Topic 4: Approximating sums of convergent infinite series and associated error bounds Original Notes
- Unit 10 Topic 5: Determining the radius and interval of convergence for a series Original Notes
- Unit 10 Topic 6: Representing a function as a Taylor series or a Maclaurin series on an appropriate interval Original Notes
Notes
Original EduCompanion Notes
These local notes follow the current College Board AP Calculus BC unit/topic list.
Unit 1: Limits and Continuity
Unit 1 Topic 1: How limits help us to handle change at an instant
Open College Board-aligned original notes
Unit 1 Topic 2: Definition and properties of limits in various representations
Open College Board-aligned original notes
Unit 1 Topic 3: Definitions of continuity of a function at a point and over a domain
Open College Board-aligned original notes
Unit 1 Topic 4: Asymptotes and limits at infinity
Open College Board-aligned original notes
Unit 1 Topic 5: Reasoning using the Squeeze theorem and the Intermediate Value Theorem
Open College Board-aligned original notes
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 2 Topic 1: Defining the derivative of a function at a point and as a function
Open College Board-aligned original notes
Unit 2 Topic 2: Connecting differentiability and continuity
Open College Board-aligned original notes
Unit 2 Topic 3: Determining derivatives for elementary functions
Open College Board-aligned original notes
Unit 2 Topic 4: Applying differentiation rules
Open College Board-aligned original notes
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 3 Topic 1: The chain rule for differentiating composite functions
Open College Board-aligned original notes
Unit 3 Topic 2: Implicit differentiation
Open College Board-aligned original notes
Unit 3 Topic 3: Differentiation of general and particular inverse functions
Open College Board-aligned original notes
Unit 3 Topic 4: Determining higher-order derivatives of functions
Open College Board-aligned original notes
Unit 4: Contextual Applications of Differentiation
Unit 4 Topic 1: Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
Open College Board-aligned original notes
Unit 4 Topic 2: Applying understandings of differentiation to problems involving motion
Open College Board-aligned original notes
Unit 4 Topic 3: Generalizing understandings of motion problems to other situations involving rates of change
Open College Board-aligned original notes
Unit 4 Topic 4: Solving related rates problems
Open College Board-aligned original notes
Unit 4 Topic 5: Local linearity and approximation
Open College Board-aligned original notes
Unit 4 Topic 6: L’Hospital’s rule
Open College Board-aligned original notes
Unit 5: Analytical Applications of Differentiation
Unit 5 Topic 1: Mean Value Theorem and Extreme Value Theorem
Open College Board-aligned original notes
Unit 5 Topic 2: Derivatives and properties of functions
Open College Board-aligned original notes
Unit 5 Topic 3: How to use the first derivative test, second derivative test, and candidates test
Open College Board-aligned original notes
Unit 5 Topic 4: Sketching graphs of functions and their derivatives
Open College Board-aligned original notes
Unit 5 Topic 5: How to solve optimization problems
Open College Board-aligned original notes
Unit 5 Topic 6: Behaviors of Implicit relations
Open College Board-aligned original notes
Unit 6: Integration and Accumulation of Change
Unit 6 Topic 1: Using definite integrals to determine accumulated change over an interval
Open College Board-aligned original notes
Unit 6 Topic 2: Approximating integrals with Riemann Sums
Open College Board-aligned original notes
Unit 6 Topic 3: Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
Open College Board-aligned original notes
Unit 6 Topic 4: Antiderivatives and indefinite integrals
Open College Board-aligned original notes
Unit 6 Topic 5: Properties of integrals and integration techniques, extended
Open College Board-aligned original notes
Unit 6 Topic 6: Determining improper integrals
Open College Board-aligned original notes
Unit 7: Differential Equations
Unit 7 Topic 1: Interpreting verbal descriptions of change as separable differential equations
Open College Board-aligned original notes
Unit 7 Topic 2: Sketching slope fields and families of solution curves
Open College Board-aligned original notes
Unit 7 Topic 3: Using Euler’s method to approximate values on a particular solution curve
Open College Board-aligned original notes
Unit 7 Topic 4: Solving separable differential equations to find general and particular solutions
Open College Board-aligned original notes
Unit 7 Topic 5: Deriving and applying exponential and logistic models
Open College Board-aligned original notes
Unit 8: Applications of Integration
Unit 8 Topic 1: Determining the average value of a function using definite integrals
Open College Board-aligned original notes
Unit 8 Topic 2: Modeling particle motion
Open College Board-aligned original notes
Unit 8 Topic 3: Solving accumulation problems
Open College Board-aligned original notes
Unit 8 Topic 4: Finding the area between curves
Open College Board-aligned original notes
Unit 8 Topic 5: Determining volume with cross-sections, the disc method, and the washer method
Open College Board-aligned original notes
Unit 8 Topic 6: Determining the length of a planar curve using a definite integral
Open College Board-aligned original notes
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Unit 9 Topic 1: Finding derivatives of parametric functions and vector-valued functions
Open College Board-aligned original notes
Unit 9 Topic 2: Calculating the accumulation of change in length over an interval using a definite integral
Open College Board-aligned original notes
Unit 9 Topic 3: Determining the position of a particle moving in a plane
Open College Board-aligned original notes
Unit 9 Topic 4: Calculating velocity, speed, and acceleration of a particle moving along a curve
Open College Board-aligned original notes
Unit 9 Topic 5: Finding derivatives of functions written in polar coordinates
Open College Board-aligned original notes
Unit 9 Topic 6: Finding the area of regions bounded by polar curves
Open College Board-aligned original notes
Unit 10: Infinite Sequences and Series
Unit 10 Topic 1: Applying limits to understand convergence of infinite series
Open College Board-aligned original notes
Unit 10 Topic 2: Types of series: Geometric, harmonic, and p-series
Open College Board-aligned original notes
Unit 10 Topic 3: A test for divergence and several tests for convergence
Open College Board-aligned original notes
Unit 10 Topic 4: Approximating sums of convergent infinite series and associated error bounds
Open College Board-aligned original notes
Unit 10 Topic 5: Determining the radius and interval of convergence for a series
Open College Board-aligned original notes
Unit 10 Topic 6: Representing a function as a Taylor series or a Maclaurin series on an appropriate interval
Open College Board-aligned original notes
Shared Google Drive Notes
No shared Google Drive notes are currently mapped for this course. Local original notes are still available above.
Practice Questions
Each note page includes a quick practice prompt. Use these unit practice cards to review the same way AP questions ask you to apply ideas, evidence, and reasoning.
Unit 1 Practice
Use the linked notes for Limits and Continuity to answer AP-style prompts, then check your explanation against the official topic list.
- Define the most important concept from this unit.
- Apply it to a scenario, graph, source, passage, or data table.
- Explain the reasoning that connects evidence to the answer.
Unit 2 Practice
Use the linked notes for Differentiation: Definition and Fundamental Properties to answer AP-style prompts, then check your explanation against the official topic list.
- Define the most important concept from this unit.
- Apply it to a scenario, graph, source, passage, or data table.
- Explain the reasoning that connects evidence to the answer.
Unit 3 Practice
Use the linked notes for Differentiation: Composite, Implicit, and Inverse Functions to answer AP-style prompts, then check your explanation against the official topic list.
- Define the most important concept from this unit.
- Apply it to a scenario, graph, source, passage, or data table.
- Explain the reasoning that connects evidence to the answer.
Unit 4 Practice
Use the linked notes for Contextual Applications of Differentiation to answer AP-style prompts, then check your explanation against the official topic list.
- Define the most important concept from this unit.
- Apply it to a scenario, graph, source, passage, or data table.
- Explain the reasoning that connects evidence to the answer.
Study Guides
Use this as a unit review index. Open each unit, work through the topic notes, then return here to move to the next unit.
Unit 1: Limits and Continuity
5 topics to review, 4%-7% of exam score
Unit 2: Differentiation: Definition and Fundamental Properties
4 topics to review, 4%-7% of exam score
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
4 topics to review, 4%-7% of exam score
Unit 4: Contextual Applications of Differentiation
6 topics to review, 6%-9% of exam score
Unit 5: Analytical Applications of Differentiation
6 topics to review, 8%-11% of exam score
Unit 6: Integration and Accumulation of Change
6 topics to review, 17%-20% of exam score
Unit 7: Differential Equations
5 topics to review, 6%-9% of exam score
Unit 8: Applications of Integration
6 topics to review, 6%-9% of exam score
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
6 topics to review, 11%-12% of exam score
Unit 10: Infinite Sequences and Series
6 topics to review, 17%-18% of exam score