Mixed Review: Parametric, Polar, and Vector Functions
A mixed AP Calculus BC review of parametric, polar, and vector-valued functions, with formulas, worked examples, common mistakes, and practice problems.
Introduction to Polar Coordinates
Learn how polar coordinates describe points in the plane using radius and angle, with conversion formulas, graphing, and fully worked AP Calculus examples.
Integrating Vector-Valued Functions
Learn how to integrate vector-valued functions component by component, with step-by-step examples involving position, velocity, displacement, and initial conditions for AP Calculus BC.
Graphing Polar Curves
Learn how to graph polar curves in AP Calculus BC using polar coordinates, symmetry, key angles, tables of values, and standard polar curves.
Finding the Slope of a Polar Curve
Learn how to find the slope of a polar curve using dy/dx = (dy/dθ)/(dx/dθ), with step-by-step examples for AP Calculus BC.
Finding the Slope of a Curve Defined Parametrically
Learn how to find the slope of a curve defined parametrically using dy/dx = (dy/dt)/(dx/dt), with step-by-step AP Calculus AB & BC examples.
Finding the Area of a Region Bounded by One Polar Curve
Learn how to find the area of a region bounded by one polar curve using the polar area formula, with step-by-step AP Calculus BC examples and practice problems.
Finding the Area Between Two Polar Curves
Learn how to find the area between two polar curves, including finding intersections, identifying the outer and inner curves, setting up polar area integrals, and fully worked AP Calculus examples.
Finding Points of Intersection of Polar Curves
Learn how to find points of intersection of polar curves, including checking multiple polar representations of the same point, with step-by-step AP Calculus AB & BC examples.
Differentiating Vector-Valued Functions
Learn how to differentiate vector-valued functions component by component, interpret velocity and acceleration, and solve AP Calculus BC problems involving vector-valued motion.