AP Precalculus — Rates of Change — Drill 1

About This Drill

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

Rates of change questions on the AP® Precalculus exam test how to compute and interpret average rates of change from tables and equations, identify function types from patterns in data, and distinguish between increasing at an increasing rate versus increasing at a decreasing rate. This drill covers average rate of change with units and context, identifying linear, quadratic, and exponential models from tables, and interpreting concavity language in real-world settings.

Questions in This Drill

1. The table below shows the height h (in feet) of a balloon at selected times t (in minutes).
   
   

   t (min)	0	2	4	6
   h (ft)	50	74	98	122

   
   What is the average rate of change of h on the interval [2, 6], and what does it represent in context?
2. The table below gives values of a function f at equally spaced values of x.
   
   

   x	0	1	2	3	4
   f(x)	3	6	12	24	48

   
   Which of the following claims and supporting statements best describes the data?
3. The table below gives values of a function g at equally spaced values of x.
   
   

   x	0	1	2	3	4
   g(x)	4	7	12	19	28

   
   Which of the following claim and explanation pairs best describes the data?
4. A cyclist begins a ride and her speed increases throughout the first 10 minutes. The table below shows her speed s (in miles per hour) at selected times t (in minutes).
   
   

   t (min)	0	2	4	6	8	10
   s (mph)	0	6	10	13	15	16

   
   Which of the following best describes the rate at which the cyclist's speed is changing over the interval [0, 10]?
5. The function f is given by f(x) = 2x² + 3x. What is the average rate of change of f on the interval [0, 3]?