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Library AP Calculus AB/BC Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
⁂   AP Calculus AB/BC · Unit 9

9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

11–12% of the AP exam. Key topics: Derivatives of parametric equations: dy/dx and d²y/dx², Arc length of a parametric curve, Vector-valued functions: position, velocity, and acceleration vectors, Motion along a curve in the plane using vectors, Speed as the magnitude of the velocity vector, Polar coordinates and the relationship to rectangular coordinates, Area enclosed by a polar curve, Arc length of a polar curve.

11–12% exam weight BC track

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Study guide content for this unit is being prepared. Check back soon for complete lesson notes, formula sheets, and worked examples.

Topics in this unit

  • Derivatives of parametric equations: dy/dx and d²y/dx²
  • Arc length of a parametric curve
  • Vector-valued functions: position, velocity, and acceleration vectors
  • Motion along a curve in the plane using vectors
  • Speed as the magnitude of the velocity vector
  • Polar coordinates and the relationship to rectangular coordinates
  • Area enclosed by a polar curve
  • Arc length of a polar curve

Worked FRQ Solutions

Free-response questions from past AP exams that test this unit's concepts.