Vector-Valued Functions: An Introduction
An introduction to vector-valued functions, including position, velocity, acceleration, and motion in the plane for AP Calculus BC.
Total Distance Traveled by a Particle in the Plane
Learn how to calculate the total distance traveled by a particle moving in the plane using speed, velocity vectors, and definite integrals. Includes worked examples and AP Calculus practice problems.
The Area of a Polar Region: An Introduction
Learn how to find the area of a region bounded by a polar curve, with the polar area formula, step-by-step methods, fully worked examples, and AP Calculus practice problems.
Speed as the Magnitude of a Velocity Vector
Learn how to find speed from a velocity vector by taking its magnitude, with step-by-step examples for AP Calculus BC.
Setting Up Arc Length Integrals: A Step-by-Step Method
Learn how to set up arc length integrals for curves in AP Calculus, with a step-by-step method and fully worked examples for AP Calculus BC.
Second Derivatives of Parametric Equations
Learn how to find the second derivative of parametric equations, with a step-by-step method and fully worked AP Calculus AB & BC examples.
Practice Problem Set: Vector-Valued Functions
Practice vector-valued functions for AP Calculus BC with problems covering position, velocity, acceleration, speed, derivatives, and motion in the plane.
Practice Problem Set: Polar Curves and Area
Practice problems covering polar curves, polar area, intersections, symmetry, and area between polar curves for AP Calculus BC.
Practice Problem Set: Parametric Equations
A focused AP Calculus practice problem set covering parametric equations, derivatives, second derivatives, tangent lines, motion, and interpreting parametric curves.
Position, Velocity, and Acceleration of a Particle in the Plane
Learn how position, velocity, and acceleration describe the motion of a particle in the plane, with vector-valued functions and fully worked AP Calculus BC examples.