AP®︎ Precalculus: Topic 3.15 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.15 of AP Precalculus – Rates of Change in Polar Functions.

Questions List

Topic 3.15

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Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12

Question 1 Easy

Let r=f(θ)=1+3cos⁡θr=f(\theta)=1+3\cos\theta.

What is the distance between the point (f(2π3),2π3)\left(f\left(\frac{2\pi}{3}\right),\frac{2\pi}{3}\right) and the origin?

A332−1\frac{3\sqrt{3}}{2}-1
B52\frac{5}{2}
C−12-\frac{1}{2}
D12\frac{1}{2}

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 3.15: Rates of Change in Polar Functions

Learning Objective: 3.15.A

Describe characteristics of the graph of a polar function.

Essential Knowledge: 3.15.A.1

If a polar function, r=f(θ)r=f(\theta), is positive and increasing or negative and decreasing, then the distance between the point with polar coordinates (f(θ),θ)(f(\theta),\theta) and the origin is increasing.

Essential Knowledge: 3.15.A.2

If a polar function, r=f(θ)r=f(\theta), is positive and decreasing or negative and increasing, then the distance between the point with polar coordinates (f(θ),θ)(f(\theta),\theta) and the origin is decreasing.

Essential Knowledge: 3.15.A.3

For a polar function, r=f(θ)r=f(\theta), if the function changes from increasing to decreasing or decreasing to increasing on an interval, then the function has a relative extremum on the interval corresponding to a point relatively closest to or farthest from the origin.

Essential Knowledge: 3.15.A.4

The average rate of change of rr with respect to θ\theta over an interval of θ\theta is the ratio of the change in the signed radius values to the change in θ\theta over an interval of θ\theta. Graphically, the average rate of change indicates the rate at which the signed radius is changing per radian.

Essential Knowledge: 3.15.A.5

The average rate of change of rr with respect to θ\theta over an interval of θ\theta can be used to estimate values of the function within the interval.

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