AP Precalculus – Rates of Change in Sinusoidal Functions – Drill 1

About This Drill

AP Precalculus – Rates of Change in Sinusoidal Functions – Drill 1 is a Math practice drill covering Rates of Change in Sinusoidal Functions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice interpreting increasing and decreasing intervals, concavity, and average rate of change for sinusoidal functions in both abstract and real-world contexts. These AP® Precalculus questions cover Topic 3.15.

Questions in This Drill

1. The function \( f(x) = \sin(x) \) is defined on \( [0, 2\pi] \). On which of the following intervals is \( f \) decreasing?
2. The function \( f(x) = \sin(x) \) is decreasing on the interval \( \left(\dfrac{\pi}{2}, \pi\right) \). Which of the following best describes the behavior of \( f \) on this interval?
3. The table below shows selected values of \( f(x) = 3\sin\!\left(\dfrac{\pi}{6}x\right) \).
   
   

   x	0	3	6	9	12
   f(x)	0	3	0	−3	0

   
   Which of the following correctly compares the average rate of change of \( f \) on \( [0, 3] \) to the average rate of change of \( f \) on \( [3, 6] \)?
4. The distance (in miles) from a satellite to a ground station is modeled by \( d(t) = 500 + 200\sin\!\left(\dfrac{\pi}{6}t\right) \), where \( t \) is time in hours. On which of the following intervals is the distance decreasing at a decreasing rate?
5. A student claims: “Because \( h(t) = \sin(t) \) is positive on \( (0, \pi) \), the function is increasing on that entire interval.” Which of the following identifies the error in the student’s reasoning?