AP Calculus Help by Topic: Practice Problems & Videos

The following help materials contain practice problems, worked-out solutions, and video lessons for topics from Calculus I and II. The video lessons referenced in the help files are from the Video Calculus series.

September 2024 update: The video links within these materials have been updated to work on all browsers.

Limits and Continuity

• Calculating limits intuitively
• Definition of a limit
• The arithmetic of limits; limits of sums, differences, products and quotients
• Trigonometric limits
• Continuity, including the Intermediate and Extreme Value Theorems

Differentiation

• Definition of the derivative; calculating derivatives using the definition; interpreting the derivative as the slope of the tangent line
• Differentiation formulas; the power, product, reciprocal, and quotient rules
• The chain rule
• Differentiating trigonometric functions
• Higher Order Derivatives
• Implicit differentiation
• Rates of change per unit time; related rates
• Velocity and Acceleration
• Differentials and Newton's method

Applications of Derivatives

• Rolle's Theorem and the Mean Value Theorem
• Critical numbers and the first derivative test
• Concavity and the second derivative test
• Curve sketching
• Extreme values on intervals
• Optimization problems.

Integration

• The definite integral; Riemann sums, area, and properties of the definite integral
• The fundamental theorem of calculus
• Antidifferentiation and indefinite integrals
• Integration by substitution
• Mean Value Theorem for integrals; average value

Logarithmic, Exponential and other Transcendental Functions

• Logarithms
• Exponential Functions
• Inverse Trig Functions

Differential Equations

• Differential Equations
• Other Bases and Exponential Growth

Applications of Integration

• Area; area under a curve, area between two curves
• Volume; volumes by slicing
• Volumes of solids of revolutions; disks and washers, cylindrical shells
• Center of mass of a rod and centroid of a planar region

Integration Techniques, L'Hopital's Rule, and Improper Integrals

• Integration by Parts
• Trig Powers and Trig Substitution
• Partial Fractions
• L'Hopital's Rule
• Improper Integrals

Sequences and Series

• Sequences
• Series
• Alternating Series, Ratio and Root Tests
• Taylor Polynomials
• Power Series
• Taylor and Maclaurin Series

Parametric Equations and Polar Coordinates

• Plane Curves and Parametrics
• Polar Coordinates and Graphs
• Area in Polar Coordinates

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