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AP Calculus AB
Limits, derivatives and integrals with animated tangent lines and area-under-the-curve sweeps.
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Scored lab investigations
Unit 1 · 10–15%
Limits & Continuity
- One-Sided & Two-Sided Limits13 min · 3 objectives
- Algebraic Limits & the Squeeze Theorem14 min · 3 objectives
- Infinite Limits & Asymptotes14 min · 3 objectives
- Continuity & the Intermediate Value Theorem13 min · 3 objectives
- Limits from Graphs and Tables14 min · 3 objectives
- Classifying Discontinuities, and Removing the Removable14 min · 3 objectives
Unit 2 · 10–15%
Differentiation: Definition & Rules
- The Derivative as a Limit14 min · 3 objectives
- The Power Rule & Basic Rules13 min · 3 objectives
- The Product & Quotient Rules14 min · 3 objectives
- The Chain Rule & Trig Derivatives15 min · 3 objectives
- Differentiability and Where Derivatives Fail14 min · 3 objectives
- Derivatives from Graphs and Tables14 min · 3 objectives
Unit 3 · 5–10%
Composite & Implicit Differentiation
- Implicit Differentiation14 min · 3 objectives
- Derivatives of Inverse Functions15 min · 3 objectives
- Higher-Order Derivatives12 min · 3 objectives
- Exponential, Logarithmic & Combined Derivatives14 min · 3 objectives
- Tangents to Implicit Curves, Horizontal and Vertical15 min · 3 objectives
- Chains Inside Chains, and Inverse Derivatives14 min · 3 objectives
Unit 4 · 10–15%
Contextual Applications
- Related Rates15 min · 3 objectives
- Linearization & Local Approximation13 min · 3 objectives
- L’Hôpital’s Rule13 min · 3 objectives
- Motion Along a Line14 min · 3 objectives
- Interpreting Derivatives in Context, with Units14 min · 3 objectives
- Particle Motion: Speed, Acceleration, and Direction15 min · 3 objectives
Unit 5 · 15–20%
Analytical Applications
- The Mean Value Theorem13 min · 3 objectives
- Critical Points & the First Derivative Test14 min · 3 objectives
- Concavity & the Second Derivative Test14 min · 3 objectives
- Optimization15 min · 3 objectives
- Absolute Extrema and the Candidates Test14 min · 3 objectives
- Reconstructing f from f′ and f″15 min · 3 objectives
- Justification: Writing the Sentence That Scores15 min · 3 objectives
Unit 6 · 15–20%
Integration & Accumulation
- Riemann Sums & the Definite Integral14 min · 3 objectives
- Antiderivatives & the Fundamental Theorem15 min · 3 objectives
- U-Substitution14 min · 3 objectives
- Accumulation Functions14 min · 3 objectives
- Riemann Sum Variants, and Which Way They Err15 min · 3 objectives
- The Two Fundamental Theorems, Kept Straight15 min · 3 objectives
- Definite Integrals from Graphs and Properties14 min · 3 objectives
Unit 7 · 5–10%
Differential Equations
Unit 8 · 10–15%
Applications of Integration
- Area Between Curves14 min · 3 objectives
- Volumes: Disks, Washers & Cross Sections15 min · 3 objectives
- Average Value of a Function12 min · 3 objectives
- Motion Revisited: Accumulating Velocity14 min · 3 objectives
- Choosing dx or dy, and Splitting When You Must15 min · 3 objectives
- Net Change: What an Integral of a Rate Means14 min · 3 objectives
- Volumes with Known Cross Sections15 min · 3 objectives