Unit 1
Limits & Continuity
- Introducing calculus and instantaneous change
- Defining and estimating limits
- Limit laws and algebraic techniques
- Continuity and removable discontinuities
- Intermediate Value Theorem
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AP Mathematics
AP Calculus AB
An AP Calculus AB roadmap organized around the eight College Board units, with emphasis on conceptual understanding, multiple representations, justification, and exam practice.
Course overview
An AP Calculus AB roadmap organized around the eight College Board units, with emphasis on conceptual understanding, multiple representations, justification, and exam practice.
Math Aficionado uses this structure as a tutoring roadmap: lessons can be paced around the student's current level, school sequence, assignments, and assessment goals rather than forcing every student through the same timetable.
Units & topics
Unit 2
Differentiation: Definition & Fundamental Properties
- Derivative as a limit
- Basic derivative rules
- Derivatives of elementary functions
- Differentiability and continuity
- Interpreting derivative values
Unit 3
Differentiation: Composite, Implicit & Inverse Functions
- Chain rule
- Implicit differentiation
- Derivatives of inverse functions
- Inverse trigonometric derivatives
- Higher-order derivatives
Unit 4
Contextual Applications of Differentiation
- Rates of change in context
- Motion along a line
- Related rates
- Local linearization
- L’Hôpital-style limit reasoning where appropriate
Unit 5
Analytical Applications of Differentiation
- Mean Value Theorem
- Extreme Value Theorem
- Increasing/decreasing behavior
- Concavity and inflection points
- Optimization and curve analysis
Unit 6
Integration & Accumulation of Change
- Antiderivatives
- Riemann sums
- Definite integrals
- Accumulation functions
- Fundamental Theorem of Calculus
Unit 7
Differential Equations
- Slope fields
- Separation of variables
- Initial-value problems
- Euler’s method
- Exponential and logistic models
Unit 8
Applications of Integration
- Average value
- Area between curves
- Volumes
- Accumulation and net change
- Modeling with integral expressions
Curriculum reference: College Board AP course framework. The page is an independent tutoring roadmap and is not an official course page of the source institution.
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