College Board AP® Calculus BC Exam Questions By Topic

Definition of a Limit, Infinite Limits & Limits at Infinity, Properties of Limits, Evaluating Limits Analytically, Evaluating Limits Numerically & Graphically, Asymptotes, Squeeze Theorem & Trigonometric Limits, Selecting Procedures for Determining Limits

Continuity, Removable Discontinuities, Non-removable Discontinuities, Intermediate Value Theorem

Average Rate of Change, Instantaneous Rate of Change, Derivatives & Tangents, Estimating the Derivative at a Point, Differentiability & Continuity

Derivative Rules, Derivatives of Exponentials and Logarithms, Derivatives of Sine and Cosine Functions, The Product Rule, The Quotient Rule, Derivatives of Tangent and Reciprocal Trig Functions, Finding Limits using Derivatives

The Chain Rule, The Inverse Function Theorem, Derivatives of Inverse Trigonometric Functions, Higher-Order Derivatives

Implicit Differentiation, Selecting Procedures for Calculating Derivatives

Unit 4 Topics, Unit 4 Summary

Meaning of a Derivative in Context, Motion in a Straight Line, Related Rates

Approximating Values of a Function

L'Hospital's Rule

Unit 5 Topics, Unit 5 Summary

Mean Value Theorem, Extreme Value Theorem, Critical Points, Increasing & Decreasing Functions, First Derivative Test for Local Extrema, Candidates Test for Global Extrema, Concavity of Functions, Second Derivative Test for Local Extrema, Graphs of f, f' & f'', Optimization Problems

Second Derivatives of Implicit Functions, Critical Points of Implicit Relations

Unit 6 Topics, Unit 6 Summary

Indefinite Integrals, Derivatives & Antiderivatives, Indefinite Integral Rules, Constant of Integration

Accumulation of Change, Riemann Sums, Trapezoidal sums, Accumulation Functions, Fundamental Theorem of Calculus, Properties of Definite Integrals, Evaluating Definite Integrals

Integrals of Composite Functions, Integration Using Substitution, Integration Using Completing the Square, Integration Using Long Division, Integration by Parts, Integration Using Partial Fractions, Improper Integrals, Selecting Techniques for Integration

Unit 7 Topics, Unit 7 Summary

Introduction to Differential Equations, Slope Fields, Separation of Variables, Finding Particular Solutions, Approximating Solutions Using Euler's Method, Exponential Models, Logistic Models

Unit 8 Topics, Unit 8 Summary

Average Value of a Function, Definite Integrals as Accumulated Change, Position, Velocity & Acceleration, Distance & Speed

Area Between a Curve & x-Axis, Area Between a Curve & y-Axis, Area Between Two Curves, Multiple Areas, Arc Length

Volumes from Areas of Known Cross Sections, Squares as Cross Sections, Rectangles as Cross Sections, Triangles as Cross Sections, Semicircles as Cross Sections

Disc Method Around the x-Axis, Disc Method Around the y-Axis, Disc Method Around Other Axes, Washer Method Around the x-Axis, Washer Method Around the y-Axis, Washer Method Around Other Axes

Unit 9 Topics, Unit 9 Summary

Defining Parametric Equations, Derivatives of Parametric Equations, Second Derivatives of Parametric Equations, Arc Lengths of Parametric Equations, Motion with Parametric Equations

Defining Vector-Valued Functions, Derivatives of Vector-Valued Functions, Integrating Vector-Valued Functions, Motion with Vector-Valued Functions

Defining Polar Coordinates, Derivatives of Polar Curves, Areas from a Single Polar Curve, Areas between Two Polar Curves

Unit 10 Topics, Unit 10 Summary

Convergent & Divergent Infinite Series, Geometric Series, Harmonic Series & p-series

nth Term Test for Divergence, Integral Test for Convergence, Comparison Tests for Convergence, Ratio Test for Convergence, Alternating Series Test for Convergence, Absolute & Conditional Convergence, Alternating Series Error Bound

Taylor Polynomial Approximation of a Function, Radius & Interval of Convergence of Power Series, Taylor or Maclaurin Series for a Function, Representing Functions as Power Series, Error Bounds for Power Series