College Board-Aligned
AP Calculus AB
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
8
official units
39
linked topics/skills
Alignment Sources
Units & Topics
Unit 1: Limits and Continuity
On the AP exam: 10%-12% 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: 10%-12% 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: 9%-13% 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: 10%-15% 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: 15%-18% 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 using 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 Original Notes
Unit 7: Differential Equations
On the AP exam: 6%-12% 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: Solving separable differential equations to find general and particular solutions Original Notes
- Unit 7 Topic 4: Deriving and applying a model for exponential growth and decay Original Notes
Unit 8: Applications of Integration
On the AP exam: 10%-15% 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
Notes
Original EduCompanion Notes
These local notes follow the current College Board AP Calculus AB 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 using 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
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: Solving separable differential equations to find general and particular solutions
Open College Board-aligned original notes
Unit 7 Topic 4: Deriving and applying a model for exponential growth and decay
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
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, 10%-12% of exam score
Unit 2: Differentiation: Definition and Fundamental Properties
4 topics to review, 10%-12% of exam score
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
4 topics to review, 9%-13% of exam score
Unit 4: Contextual Applications of Differentiation
6 topics to review, 10%-15% of exam score
Unit 5: Analytical Applications of Differentiation
6 topics to review, 15%-18% of exam score
Unit 6: Integration and Accumulation of Change
5 topics to review, 17%-20% of exam score
Unit 7: Differential Equations
4 topics to review, 6%-12% of exam score
Unit 8: Applications of Integration
5 topics to review, 10%-15% of exam score