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Unit 1: Limits and Continuity (100)
  • How limits help us to handle change at an instant (20)
  • Definition and properties of limits in various representations (20)
  • Definitions of continuity of a function at a point and over a domain (20)
  • Asymptotes and limits at infinity (20)
  • Reasoning using the Squeeze theorem and the Intermediate Value Theorem (20)
Unit 2: Differentiation: Definition and Fundamental Properties (80)
  • Defining the derivative of a function at a point and as a function (20)
  • Connecting differentiability and continuity (20)
  • Determining derivatives for elementary functions (20)
  • Applying differentiation rules (20)
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (80)
  • The chain rule for differentiating composite functions (20)
  • Implicit differentiation (20)
  • Differentiation of general and particular inverse functions (20)
  • Determining higher-order derivatives of functions (20)
Unit 4: Contextual Applications of Differentiation (120)
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change (20)
  • Applying understandings of differentiation to problems involving motion (20)
  • Generalizing understandings of motion problems to other situations involving rates of change (20)
  • Solving related rates problems (20)
  • Local linearity and approximation (20)
  • L’Hospital’s rule (20)
Unit 5: Analytical Applications of Differentiation (120)
  • Mean Value Theorem and Extreme Value Theorem (20)
  • Derivatives and properties of functions (20)
  • How to use the first derivative test; second derivative test and candidates test (20)
  • Sketching graphs of functions and their derivatives (20)
  • How to solve optimization problems (20)
  • Behaviors of Implicit relations (20)
Unit 6: Integration and Accumulation of Change (90)
  • Using definite integrals to determine accumulated change over an interval (20)
  • Approximating integrals using Riemann Sums (10)
  • Accumulation functions; the Fundamental Theorem of Calculus and definite integrals (20)
  • Antiderivatives and indefinite integrals (20)
  • Properties of integrals and integration techniques; extended (20)
Unit 7: Differential Equations (70)
  • Interpreting verbal descriptions of change as separable differential equations (20)
  • Sketching slope fields and families of solution curves (20)
  • Solving separable differential equations to find general and particular solutions (20)
  • Deriving and applying a model for exponential growth and decay (10)
Unit 8: Applications of Integration (100)
  • Determining the average value of a function using definite integrals (20)
  • Modeling particle motion (20)
  • Solving accumulation problems (20)
  • Finding the area between curves (20)
  • Determining volume with cross-sections; the disc method and the washer method (20)