AP Calculus AB
College-level differential and integral calculus aligned to the College Board AP Calculus AB curriculum. Covers limits, differentiation, integration, and differential equations at the depth required to score a 5.
8 units and 42 lessons, for Grade 11 to Grade 12. Free on Slate.
Unit 1: Limits and Continuity
The rigorous foundation of calculus, with AP-level precision and exam-style problems.
Unit 2: Differentiation: Definition and Fundamental Properties
Derive the derivative from first principles and master the rules for every elementary function.
- The Derivative: Definition and Interpretations (10 min)
- Differentiability and Non-Differentiable Points (10 min)
- Power, Constant Multiple, Sum, and Difference Rules (10 min)
- Product and Quotient Rules (10 min)
- Derivatives of All Six Trigonometric Functions (10 min)
- Derivatives of Exponential and Logarithmic Functions (10 min)
Unit 3: Differentiation: Composite, Implicit, and Inverse
Master the three most powerful differentiation tools beyond the basic rules.
- The Chain Rule (10 min)
- Implicit Differentiation (10 min)
- Derivatives of Inverse Functions (10 min)
- Derivatives of Inverse Trigonometric Functions (10 min)
- Higher-Order Derivatives and Related Rates (10 min)
Unit 4: Contextual Applications of Differentiation
Apply derivatives to motion, approximation, and limits, with AP exam context throughout.
Unit 5: Analytical Applications of Differentiation
Use calculus to fully analyze function behavior and solve optimization problems.
- Mean Value Theorem and Extreme Value Theorem (10 min)
- Critical Points and the First Derivative Test (10 min)
- Concavity, Inflection Points, and the Second Derivative Test (10 min)
- Absolute Extrema on Closed and Open Intervals (10 min)
- Optimization Problems (10 min)
- Connecting f, f', and f'' in Graph Analysis (10 min)
Unit 6: Integration and the Fundamental Theorem of Calculus
Build integration from area estimation to the FTC, the deepest connection in all of calculus.
Unit 7: Differential Equations
Solve and interpret differential equations at AP Calculus AB depth.
- Introduction to Differential Equations and Verification (10 min)
- Slope Fields (10 min)
- Euler's Method (10 min)
- Solving Separable Differential Equations (10 min)
- Exponential Growth and Decay (10 min)
Unit 8: Applications of Integration
Apply integration to area, volume, motion, and accumulation: all high-frequency AP exam topics.
- Area Between Curves (10 min)
- Volumes of Solids of Revolution (10 min)
- Volumes by Known Cross-Sections (10 min)
- Accumulation Functions and Net Change Theorem (10 min)
- Particle Motion Using Integration (10 min)
- Average Value of a Function (10 min)