AP®︎ Precalculus: Topic 3.1 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.1 of AP Precalculus – Periodic Phenomena.
Questions List
Topic 3.1
Question 1 Easy
A Ferris wheel turns at a constant rate and completes one revolution every 12 minutes. A rider's height above the ground ranges from 3 feet to 53 feet. The rider boards at the lowest point at . Let be the rider's height in feet, minutes after boarding.
What is the period of ?
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 3.1: Periodic Phenomena
Learning Objective: 3.1.A
Construct graphs of periodic relationships based on verbal representations.
Essential Knowledge: 3.1.A.1
A periodic relationship can be identified between two aspects of a context if, as the input values increase, the output values demonstrate a repeating pattern over successive equal-length intervals.
Essential Knowledge: 3.1.A.2
The graph of a periodic relationship can be constructed from the graph of a single cycle of the relationship.
Learning Objective: 3.1.B
Describe key characteristics of a periodic function based on a verbal representation.
Essential Knowledge: 3.1.B.1
The period of the function is the smallest positive value such that for all in the domain. Consequently, the behavior of a periodic function is completely determined by any interval of width .
Essential Knowledge: 3.1.B.2
The period can be estimated by investigating successive equal-length output values and finding where the pattern begins to repeat.
Essential Knowledge: 3.1.B.3
Periodic functions take on characteristics of other functions, such as intervals of increase and decrease, different concavities, and various rates of change. However, with periodic functions, all characteristics found in one period of the function will be in every period of the function.
