AP®︎ Calculus BC: Topic 9.3 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 9.3 of AP Calculus BC – Finding Arc Lengths of Curves Given by Parametric Equations.

Questions List

Topic 9.3

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Question 1 Easy

A curve is defined by the parametric equations x=t2x=t^2 and y=t3y=t^3 for 0≤t≤10\leq t\leq 1.

Which of the following gives the length of the curve?

A∫01(2t+3t2)2 dt\displaystyle\int_0^1 \sqrt{(2t+3t^2)^2}\,dt
B∫01(t2)2+(t3)2 dt\displaystyle\int_0^1 \sqrt{(t^2)^2+(t^3)^2}\,dt
C∫01(2t)2+(3t2)2 dt\displaystyle\int_0^1 \sqrt{(2t)^2+(3t^2)^2}\,dt
D∫01[(2t)2+(3t2)2] dt\displaystyle\int_0^1 \left[(2t)^2+(3t^2)^2\right]\,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 9.3: Finding Arc Lengths of Curves Given by Parametric Equations

Learning Objective: CHA-6.B

Determine the length of a curve in the plane defined by parametric functions, using a definite integral.

Essential Knowledge: CHA-6.B.1

The length of a parametrically defined curve can be calculated using a definite integral.

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