Learning paths
- Lessons
- 124
- Topics
- 123
Free, no account neededA tour of AP Calculus14 short steps.
Start lessonThe course, in test order
Before calculus
6 lessons
Unit 1: Limits and Continuity
17 lessons
- 2 lessonsFreeInstantaneous change
- Limit notation
- Reading limits from graphs
- Reading limits from tables
- Limit laws
- Rewrite before taking a limit
- Choose a limit method
- Squeeze arguments
- Translate limit representations
- Classify discontinuities
- Test point continuity
- Continuity intervals
- Repair a discontinuity
- Vertical asymptotes
- End behavior and horizontal asymptotes
- Intermediate Value Theorem
Unit 2: Differentiation: Definition and Fundamental Properties
10 lessons
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
6 lessons
Unit 4: Contextual Applications of Differentiation
7 lessons
Unit 5: Analytical Applications of Differentiation
12 lessons
- Mean Value Theorem
- Extreme Value Theorem and critical points
- Increasing and decreasing intervals
- First-derivative extrema test
- Global extrema and endpoints
- Concavity and inflection
- Second-derivative extrema test
- Sketch from derivative evidence
- Connect f and derivative graphs
- Build an optimization model
- Solve and interpret optimization
- Analyze implicit curves
Unit 6: Integration and Accumulation of Change
14 lessons
- Signed accumulation
- Riemann and trapezoidal approximations
- Integral as a limiting sum
- Differentiate accumulation
- Analyze accumulation graphs
- Integral properties and geometry
- FTC endpoint evaluation
- Antiderivatives and constant families
- Substitution
- Long division and completed squares
- Integration by parts (BC only)
- Linear partial fractions (BC only)
- Improper integrals (BC only)
- Choose integration methods
Unit 7: Differential Equations
9 lessons
Unit 8: Applications of Integration
13 lessons
- Average value
- Displacement and distance
- Net change in context
- Area using vertical slices
- Area using horizontal slices
- Regions requiring multiple integrals
- Square and rectangular cross sections
- Triangular and semicircular cross sections
- Disks about coordinate axes
- Disks about shifted axes
- Washers about coordinate axes
- Washers about shifted axes
- Cartesian arc length (BC only)
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9 lessons
Unit 10: Infinite Sequences and Series
15 lessons
- Partial sums and series convergence
- Geometric series
- Term test for divergence
- Integral test
- Harmonic and p-series
- Direct and limit comparison
- Alternating series
- Ratio test
- Absolute and conditional convergence
- Alternating remainder
- Taylor polynomial and approximation
- Lagrange remainder
- Radius and endpoint tests
- Taylor and Maclaurin series
- Transform power series
Exam review
6 lessons