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AP® Calculus BC Practice Test

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Unit 1: Limits and Continuity (114) 0
  • How limits help us to handle change at an instant 21 0
  • Definition and properties of limits in various representations 26 0
  • Definitions of continuity of a function at a point and over a domain 24 0
  • Asymptotes and limits at infinity 23 0
  • Reasoning using the Squeeze theorem and the Intermediate Value Theorem 20 0
Unit 2: Differentiation: Definition and Fundamental Properties (100) 0
  • Defining the derivative of a function at a point and as a function 33 0
  • Connecting differentiability and continuity 20 0
  • Determining derivatives for elementary functions 24 0
  • Applying differentiation rules 23 0
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (103) 0
  • The chain rule for differentiating composite functions 30 0
  • Implicit differentiation 25 0
  • Differentiation of general and particular inverse functions 28 0
  • Determining higher-order derivatives of functions 20 0
Unit 4: Contextual Applications of Differentiation (143) 0
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change 23 0
  • Applying understandings of differentiation to problems involving motion 32 0
  • Generalizing understandings of motion problems to other situations involving rates of change 21 0
  • Solving related rates problems 24 0
  • Local linearity and approximation 22 0
  • L’Hospital’s rule 21 0
Unit 5: Analytical Applications of Differentiation (152) 0
  • Mean Value Theorem and Extreme Value Theorem 24 0
  • Derivatives and properties of functions 33 0
  • How to use the first derivative test; second derivative test and candidates test 32 0
  • Sketching graphs of functions and their derivatives 20 0
  • How to solve optimization problems 22 0
  • Behaviors of Implicit relations 21 0
Unit 6: Integration and Accumulation of Change (126) 0
  • Using definite integrals to determine accumulated change over an interval 28 0
  • Approximating integrals with Riemann Sums 10 0
  • Accumulation functions; the Fundamental Theorem of Calculus and definite integrals 25 0
  • Antiderivatives and indefinite integrals 27 0
  • Properties of integrals and integration techniques; extended 26 0
  • Determining improper integrals 10 0
Unit 7: Differential Equations (84) 0
  • Interpreting verbal descriptions of change as separable differential equations 21 0
  • Sketching slope fields and families of solution curves 20 0
  • Using Euler’s method to approximate values on a particular solution curve 10 0
  • Solving separable differential equations to find general and particular solutions 23 0
  • Deriving and applying exponential and logistic models 10 0
Unit 8: Applications of Integration (123) 0
  • Determining the average value of a function using definite integrals 25 0
  • Modeling particle motion 20 0
  • Solving accumulation problems 20 0
  • Finding the area between curves 28 0
  • Determining volume with cross-sections; the disc method and the washer method 20 0
  • Determining the length of a planar curve using a definite integral 10 0
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (60) 0
  • Finding derivatives of parametric functions and vector-valued functions 10 0
  • Calculating the accumulation of change in length over an interval using a definite integral 10 0
  • Determining the position of a particle moving in a plane 10 0
  • Calculating velocity; speed and acceleration of a particle moving along a curve 10 0
  • Finding derivatives of functions written in polar coordinates 10 0
  • Finding the area of regions bounded by polar curves 10 0
Unit 10: Infinite Sequences and Series (60) 0
  • Applying limits to understand convergence of infinite series 10 0
  • Types of series: Geometric; harmonic and p-series 10 0
  • A test for divergence and several tests for convergence 10 0
  • Approximating sums of convergent infinite series and associated error bounds 10 0
  • Determining the radius and interval of convergence for a series 10 0
  • Representing a function as a Taylor series or a Maclaurin series on an appropriate interval 10 0
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Previous Year Free Response Questions (0) 15
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  • AP Calculus BC 2019 (0) 3