Parametric Equations

AP Calculus AB/BC - 9.1 Defining and Differentiating Parametric Equations

AP Calculus AB/BC - 9.3 Finding Arc Lengths of Curves Given by Parametric Equations

AP Calculus AB/BC - AP Calculus Multiple Choice Questions

AP Calculus AB/BC - AP Calculus AB/BC Multiple Choice Help (MCQ)

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

Henry draws a heart defined by the parametric equations x(t) = sin(t) and y(t) = 1 + cos(t) - cos^2(t). What is the slope dy/dx of the curve at the point (sqrt(3)/2, 5/4)?

Which of the following are a pair of parametric equations with the parameter t?

The motion of a rolling ball on the coordinate plane is given by the set of parametric equations x(t) = 12sin(t) and y(t) = 6t^2. Which of the following derivatives is incorrect?

Liam's height in inches, h(t), and weight in pounds, w(t), as a child at t years old can be modeled by the parametric equations h(t) = 3t+25 and w(t) = t^2/2+20. When Liam weighed 70 pounds, how tall was he in inches?

Henry draws a heart defined by the parametric equations x(t) = sin(t) and y(t) = 1 + cos(t) - cos^2(t). What is the concavity of the curve at the point (sqrt(3)/2, 5/4)?

Which of the following pairs of parametric equations are concave down at t = 1?

The motion of a rolling ball on the coordinate plane is given by the set of parametric equations y(t) = 12cos(t) and x(t) = 6e^t. Which of the following derivatives is incorrect?

The path of a lost cow on the xy-plane is given in parametric equations by x(t) = t^2 + t and y(t) = t^2-t. Is the path of the cow concave up or down at t=0?

A video game character's attack and defense increase over time (t > 0) is given by the parametric equations A(t) = 3t^2+5t and D(t) = 2t^2+8t. James the gamer plots these values on a plot with attack as the x-axis and defense as the y-axis. Is the resulting curve concave up or concave down?

Consider the parametric equations: x(t) = t^2 y(t) = 3t What is the arc length of the curve between t = 0 and t = 2?

The parametric equations of a curve are: x(t) = 2cos(t) y(t) = 2sin(t) What is the arc length of the curve between t = 0 and t = π/2?

Consider the parametric equations: x(t) = e^t + e^(-t) y(t) = e^t - e^(-t) What is the arc length of the curve between t = 0 and t = ln(2)?

Consider the parametric equations: x(t) = t^2 - 1 y(t) = t^3 + 2t What is the arc length of the curve between t = -1 and t = 1?

When dealing with parametric equations, what do we need to take the integral of in order to find the distance traveled?

A particle moves along a curve defined by the parametric equations x = 2cos(t) and y = 3sin(t). What is the magnitude of the acceleration vector of the particle at time t = π/6?

A particle moves along a curve defined by the parametric equations x = 3t^2 and y = 2t^3. What is the approximate distance traveled by the particle from time t = 0 to t = 2?

A particle moves along a curve defined by the parametric equations x = t^3 and y = t^2. What is the acceleration vector of the particle at time t = 2?

Consider a particle moving along a curve in the plane defined by the parametric equations x = 2t and y = t^2. What is the velocity vector of the particle at t = 3?

A particle moves along a curve defined by the parametric equations x = t^2 and y = t^3. What is the velocity vector of the particle at time t = 2?