AP®︎ Precalculus: Topic 4.9 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 4.9 of AP Precalculus – Vector-Valued Functions.

Questions List

Topic 4.9

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Question 1 Easy

A particle moving in the xyxy-plane has position p(t)=3t i−(t2+2) jp(t) = 3t\,\mathbf{i} - (t^2 + 2)\,\mathbf{j}. Which of the following gives the particle's position in component form?

A⟨3t,t2+2⟩\langle 3t, t^2 + 2\rangle
B⟨3t,−t2+2⟩\langle 3t, -t^2 + 2\rangle
C⟨−t2−2,3t⟩\langle -t^2 - 2, 3t\rangle
D⟨3t,−t2−2⟩\langle 3t, -t^2 - 2\rangle

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus 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 4.9: Vector-Valued Functions

Learning Objective: 4.9.A

Represent planar motion in terms of vector-valued functions.

Essential Knowledge: 4.9.A.1

The position of a particle moving in a plane that is given by the parametric function f(t)=(x(t),y(t))f(t) = (x(t), y(t)) may be expressed as a vector-valued function, p(t)=x(t)i⃗+y(t)j⃗p(t) = x(t)\vec{i} + y(t)\vec{j} or p(t)=⟨x(t),y(t)⟩p(t) = \langle x(t), y(t)\rangle. The magnitude of the position vector at time tt gives the distance of the particle from the origin.

Essential Knowledge: 4.9.A.2

The vector-valued function v(t)=⟨x(t),y(t)⟩v(t) = \langle x(t), y(t)\rangle can be used to express the velocity of a particle moving in a plane at different times, tt. At time tt, the sign of x(t)x(t) indicates if the particle is moving right or left, and the sign of y(t)y(t) indicates if the particle is moving up or down. The magnitude of the velocity vector at time tt gives the speed of the particle.

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