Unit 1
Limits & Continuity
- Introducing calculus and instantaneous change
- Defining and estimating limits
- Continuity
- Intermediate Value Theorem
- Asymptotic behavior
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AP Mathematics
AP Calculus BC
The full AP Calculus BC pathway, extending the AB curriculum with parametric and polar functions, vector-valued functions, and infinite sequences and series.
Course overview
The full AP Calculus BC pathway, extending the AB curriculum with parametric and polar functions, vector-valued functions, and infinite sequences and series.
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 definition
- Derivative rules
- Derivatives of elementary functions
- Differentiability
- Interpreting derivative values
Unit 3
Composite, Implicit & Inverse Differentiation
- Chain rule
- Implicit differentiation
- Inverse functions
- Inverse trigonometric derivatives
- Higher-order derivatives
Unit 4
Contextual Applications of Differentiation
- Rates of change
- Motion
- Related rates
- Local linearization
- Differential approximation
Unit 5
Analytical Applications of Differentiation
- Mean Value Theorem
- Extreme Value Theorem
- Function analysis
- Optimization
- Curve sketching and reasoning
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
- Area and volume
- Average value
- Accumulation models
- Arc-length-style applications where appropriate
- Interpreting integral results
Unit 9
Parametric, Polar & Vector-Valued Functions
- Parametric equations
- Calculus with parametric curves
- Polar coordinates and polar area
- Polar derivatives
- Vector-valued functions, velocity, and acceleration
Unit 10
Infinite Sequences & Series
- Sequences and convergence
- Series tests
- Power series
- Taylor and Maclaurin series
- Radius/interval of convergence and error
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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