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AP® Precalculus – Sinusoidal Functions: Amplitude, Period, Midline – Drill 1

Drill 23 · Math · Sinusoidal Functions: Amplitude, Period, Midline

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About This Drill

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

Test your understanding of the core properties of sinusoidal functions — amplitude, period, and midline — the most heavily tested topic on the AP® Precalculus exam. Practice identifying these features from graphs, equations, and context, and master the LCM method for finding the period of sums of sinusoidal functions.

Questions in This Drill

  1. A sinusoidal function f has a minimum value of −3 and a maximum value of 11. What are the amplitude and midline of f?
  2. The function \( g(x) = 3\sin(2x) + 5\cos(4x) \) is the sum of two sinusoidal functions. What is the period of \( g(x) \)?
  3. A sinusoidal function f is shown in the graph below. Each grid square represents 1 unit.

    Graph of a sinusoidal function with peaks at x=2 and x=10 and a trough at x=6

    What is the period of f?
  4. Which of the following equations represents a sinusoidal function with amplitude 4, period \( \pi \), and midline \( y = -2 \)?
  5. A buoy bobs up and down in the ocean. Its height h (in feet above the ocean floor) is modeled by a sinusoidal function of time t in seconds. The buoy reaches a maximum height of 14 feet at t = 2 and the next minimum height of 6 feet at t = 8. What is the period of the function?