AP®︎ Calculus BC: Topic 9.2 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 9.2 of AP Calculus BC – Second Derivatives of Parametric Equations.

Questions List

Topic 9.2

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Question 1 Easy

A curve is defined by x=x(t)x=x(t) and y=y(t)y=y(t), where both functions are twice differentiable and dxdt≠0\frac{dx}{dt}\ne 0.

Which of the following equals d2ydx2\frac{d^2y}{dx^2}?

Ad2ydt2d2xdt2\dfrac{\frac{d^2y}{dt^2}}{\frac{d^2x}{dt^2}}
Bddt(dydx)d2xdt2\dfrac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{d^2x}{dt^2}}
Cddt(dydx)dxdt\dfrac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dx}{dt}}
Dddt(dydx)⋅dxdt\frac{d}{dt}\left(\frac{dy}{dx}\right)\cdot\frac{dx}{dt}

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 9.2: Second Derivatives of Parametric Equations

Learning Objective: CHA-3.G

Calculate derivatives of parametric functions.

Essential Knowledge: CHA-3.G.3

d^2y/dx^2 can be calculated by dividing d/dt(dy/dx) by dx/dt.

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