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📈AP Precalculus
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📈AP Precalculus

FRQ 2 – Modeling a Non-Periodic Context (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 81/8

2. A wetland restoration project tracks cumulative area restored. The table gives cumulative area restored, in acres, at selected times t, in weeks. The quantity is modeled by G(t) = at^2 + bt + c. Project leaders determine that the model is appropriate until its prediction reaches 63 acres, the available restoration area.

cumulative area restored at t = 0, 2, and 4 weeks

  • G(t) = at^2 + bt + c

t (weeks)

G(t) (acres)

0

15

2

39

4

55

A.
i.

Use the three data pairs to write three equations that can be used to find a, b, and c in G(t).

ii.

Find the values of a, b, and c as decimal approximations.

B.
i.

Find the average rate of change of cumulative area restored from t = 0 to t = 4. Express the result in acres per week, and show the computations that lead to your answer.

ii.

Interpret the meaning of the average rate of change from part B(i) in the context of the wetland restoration project.

C.
i.

Write and solve an equation whose solution gives the first time t when the model predicts 63 acres. Express t as a decimal approximation.

ii.

Explain how the value from part C(i) can be used with the available restoration area to determine an appropriate domain restriction for G. Refer to the context in your explanation.

Timed

00:00

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Free Response Question Practice

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

  • Read each question carefully before responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.