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Unit 1: Limits and Continuity (100) 0
  • How limits help us to handle change at an instant 20 0
  • Definition and properties of limits in various representations 20 0
  • Definitions of continuity of a function at a point and over a domain 20 0
  • Asymptotes and limits at infinity 20 0
  • Reasoning using the Squeeze theorem and the Intermediate Value Theorem 20 0
Unit 2: Differentiation: Definition and Fundamental Properties (80) 0
  • Defining the derivative of a function at a point and as a function 20 0
  • Connecting differentiability and continuity 20 0
  • Determining derivatives for elementary functions 20 0
  • Applying differentiation rules 20 0
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (80) 0
  • The chain rule for differentiating composite functions 20 0
  • Implicit differentiation 20 0
  • Differentiation of general and particular inverse functions 20 0
  • Determining higher-order derivatives of functions 20 0
Unit 4: Contextual Applications of Differentiation (120) 0
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change 20 0
  • Applying understandings of differentiation to problems involving motion 20 0
  • Generalizing understandings of motion problems to other situations involving rates of change 20 0
  • Solving related rates problems 20 0
  • Local linearity and approximation 20 0
  • L’Hospital’s rule 20 0
Unit 5: Analytical Applications of Differentiation (120) 0
  • Mean Value Theorem and Extreme Value Theorem 20 0
  • Derivatives and properties of functions 20 0
  • How to use the first derivative test; second derivative test and candidates test 20 0
  • Sketching graphs of functions and their derivatives 20 0
  • How to solve optimization problems 20 0
  • Behaviors of Implicit relations 20 0
Unit 6: Integration and Accumulation of Change (90) 0
  • Using definite integrals to determine accumulated change over an interval 20 0
  • Approximating integrals using Riemann Sums 10 0
  • Accumulation functions; the Fundamental Theorem of Calculus and definite integrals 20 0
  • Antiderivatives and indefinite integrals 20 0
  • Properties of integrals and integration techniques; extended 20 0
Unit 7: Differential Equations (70) 0
  • Interpreting verbal descriptions of change as separable differential equations 20 0
  • Sketching slope fields and families of solution curves 20 0
  • Solving separable differential equations to find general and particular solutions 20 0
  • Deriving and applying a model for exponential growth and decay 10 0
Unit 8: Applications of Integration (100) 0
  • Determining the average value of a function using definite integrals 20 0
  • Modeling particle motion 20 0
  • Solving accumulation problems 20 0
  • Finding the area between curves 20 0
  • Determining volume with cross-sections; the disc method and the washer method 20 0