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📈AP Precalculus
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📈AP Precalculus

FRQ 1 – Function Concepts (Calculator)
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Unit 1: Polynomial and Rational Functions
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AP Precalculus FRQ Types & Units

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

FRQFocusUnitsWhy
FRQ 1Function Concepts (Calculator)1-2Tests function analysis with graphing calculator - Units 1-2 polynomial/rational functions
FRQ 2Modeling a Non-Periodic Context1-2Tests modeling with polynomial, rational, exponential, or logarithmic functions
FRQ 3Modeling a Periodic Context3 onlyTests modeling with trigonometric functions - all Unit 3 content
FRQ 4Symbolic Manipulations2-3Tests 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 51/5

1. A marine biologist models the population of a coral reef fish species using the polynomial function ppp, where p(t)p(t)p(t) gives the estimated number of fish (in hundreds) ttt years after the reef was established. Selected values of p(t)p(t)p(t) are given in the table below. The rational function qqq is given by q(t)=2t2−8t−3q(t) = \frac{2t^2 - 8}{t - 3}q(t)=t−32t2−8​, which models the rate of change of available reef resources (in suitable units) at time ttt years, where t≠3t ≠ 3t=3.

ttt (years)

p(t)p(t)p(t) (hundreds of fish)

0

1.2

1

3.5

2

6.8

3

9.1

4

9.6

5

8.3

6

5.4

A.

Use the data in the table to find the average rate of change of ppp over the interval 1≤t≤41 ≤ t ≤ 41≤t≤4 and over the interval 4≤t≤64 ≤ t ≤ 64≤t≤6. Based on these values, describe how the fish population is changing over the interval 1≤t≤61 ≤ t ≤ 61≤t≤6, and explain what this suggests about the behavior of ppp on this interval.

B.

Determine all zeros, vertical asymptotes, and holes of q(t)=2t2−8t−3q(t) = \frac{2t^2 - 8}{t - 3}q(t)=t−32t2−8​, if any exist. For each feature identified, state its value and provide a mathematical justification.

C.

Describe the end behavior of q(t)=2t2−8t−3q(t) = \frac{2t^2 - 8}{t - 3}q(t)=t−32t2−8​ as ttt increases without bound and as ttt decreases without bound. Use polynomial long division to rewrite q(t)q(t)q(t) in an equivalent form, and use that form to explain the end behavior of qqq. Express each end behavior using the mathematical notation of a limit.

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Free Response Question Practice

This practice environment simulates the AP AP Precalculus Free Response Questions section. Here are some guidelines:

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