Calculus
A rigorous, full-year introduction to differential and integral calculus. Builds complete understanding of limits, derivatives, and integrals with applications, preparing students for AP Calculus or college math.
8 units and 43 lessons, for Grade 11 to Grade 12. Free on Slate.
Unit 1: Limits and Continuity
Build the rigorous foundation that makes calculus possible.
- Introduction to Limits (10 min)
- Limit Laws and Algebraic Evaluation (10 min)
- One-Sided Limits (10 min)
- Limits at Infinity and Horizontal Asymptotes (10 min)
- Continuity at a Point and on an Interval (10 min)
- Special Trigonometric Limits (10 min)
Unit 2: The Derivative: Definition and Basic Rules
Develop the derivative from first principles and master the fundamental differentiation rules.
Unit 3: The Chain Rule and Advanced Differentiation
Master the chain rule and implicit differentiation, the most widely used tools in differential calculus.
- The Chain Rule (10 min)
- Implicit Differentiation (10 min)
- Derivatives of Inverse Trigonometric Functions (10 min)
- Higher-Order Derivatives (10 min)
- Related Rates (10 min)
Unit 4: Applications of Derivatives
Use derivatives to analyze functions and solve optimization problems: the heart of differential calculus.
- The Mean Value Theorem (10 min)
- Increasing, Decreasing, and Critical Points (10 min)
- Concavity and the Second Derivative Test (10 min)
- Comprehensive Curve Sketching (10 min)
- Optimization Problems (10 min)
- L'Hôpital's Rule (10 min)
- Linear Approximation and Differentials (10 min)
Unit 5: Integration and the Fundamental Theorem
Develop integration from Riemann sums to the Fundamental Theorem, the deepest result in calculus.
Unit 6: Applications of Integration
Use integrals to compute areas, volumes, and accumulation quantities.
- Area Between Curves (10 min)
- Volumes of Revolution: Disk and Washer Methods (10 min)
- Volumes by the Shell Method (10 min)
- Average Value of a Function (10 min)
- Accumulation Functions and Particle Motion (10 min)
Unit 7: Differential Equations
Solve and interpret the simplest class of differential equations that model real-world change.
- Introduction to Differential Equations (10 min)
- Slope Fields (10 min)
- Separable Differential Equations (10 min)
- Exponential Growth and Decay Models (10 min)
Unit 8: Advanced Integration Techniques
Expand the integration toolkit beyond u-substitution.
- Integration by Parts (10 min)
- Trigonometric Integrals (10 min)
- Integration by Partial Fractions (10 min)
- Improper Integrals (10 min)