AP Precalculus FRQ Practice

📈AP Precalculus

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

FRQ	Focus	Units	Why
FRQ 1	Function Concepts (Calculator)	1-2	Tests function analysis with graphing calculator - Units 1-2 polynomial/rational functions
FRQ 2	Modeling a Non-Periodic Context	1-2	Tests modeling with polynomial, rational, exponential, or logarithmic functions
FRQ 3	Modeling a Periodic Context	3 only	Tests modeling with trigonometric functions - all Unit 3 content
FRQ 4	Symbolic Manipulations	2-3	Tests exponential, logarithmic, and trigonometric equation solving and rewriting

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 101/10

1. A wildlife biologist models the population of a deer herd in a forest preserve. The function $p$ is defined by $p(t) = -2t^3 + 15t^2 + 10t + 80$ , where $p(t)$ is the number of deer and $t$ is the number of years since the study began, for $0 ≤ t ≤ 7$ . The table gives values of $p(t)$ at selected values of $t$ .

$t$ (years)	$p(t)$ (deer)
0	80
1	103
2	144
3	191
4	232
5	255
6	248
7	199

Use the data in the table to find the average rate of change of $p$ over the interval $1 ≤ t ≤ 4$ and the average rate of change of $p$ over the interval $4 ≤ t ≤ 7$ . Using these values, describe how the deer population is changing over the interval $1 ≤ t ≤ 7$ . Include units in your response.

Use the function $p(t) = -2t^3 + 15t^2 + 10t + 80$ to determine the average rate of change of $p$ over the interval $2 ≤ t ≤ 2.001$ and the average rate of change of $p$ over the interval $5 ≤ t ≤ 5.001$ . Based on your results, compare the rate at which the deer population is changing at $t = 2$ with the rate at which it is changing at $t = 5$ . Include units in your response.

Based on the function $p(t) = -2t^3 + 15t^2 + 10t + 80$ , describe the end behavior of $p$ as $t$ increases without bound. Explain what this end behavior suggests about the appropriateness of using $p(t)$ as a model for the deer population for large values of $t$ , and identify a restriction on the domain that would make the model more reasonable.

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