AP®︎ Precalculus: Topic 4.4 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 4.4 of AP Precalculus – Parametrically Defined Circles and Lines.

Questions List

Topic 4.4

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Question 1 Easy

Which parametric function models one complete counterclockwise revolution around the unit circle centered at the origin, starting and ending at (1,0)(1,0)?

A(x(t),y(t))=(sin⁡t,cos⁡t),0≤t≤360(x(t),y(t))=(\sin t,\cos t),\quad 0\leq t\leq 360
B(x(t),y(t))=(sin⁡t,cos⁡t),0≤t≤2π(x(t),y(t))=(\sin t,\cos t),\quad 0\leq t\leq 2\pi
C(x(t),y(t))=(cos⁡t,sin⁡t),0≤t≤2π(x(t),y(t))=(\cos t,\sin t),\quad 0\leq t\leq 2\pi
D(x(t),y(t))=(cos⁡t,sin⁡t),0≤t≤360(x(t),y(t))=(\cos t,\sin t),\quad 0\leq t\leq 360

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 4.4: Parametrically Defined Circles and Lines

Learning Objective: 4.4.A

Express motion around a circle or along a line segment parametrically.

Essential Knowledge: 4.4.A.1

A complete counterclockwise revolution around the unit circle that starts and ends at (1,0)(1, 0) and is centered at the origin can be modeled by (x(t),y(t))=(cos⁡t,sin⁡t)(x(t), y(t)) = (\cos t, \sin t) with domain 0≤t≤2π0 \leq t \leq 2\pi.

Essential Knowledge: 4.4.A.2

Transformations of the parametric function (x(t),y(t))=(cos⁡t,sin⁡t)(x(t), y(t)) = (\cos t, \sin t) can model any circular path traversed in the plane.

Essential Knowledge: 4.4.A.3

A linear path along the line segment from the point (x1,y1)(x_1, y_1) to the point (x2,y2)(x_2, y_2) can be parametrized many ways, including using an initial position (x1,y1)(x_1, y_1) and rates of change for xx with respect to tt and yy with respect to tt.

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