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📈AP Pre-Calculus
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📈AP Pre-Calculus

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 ManipulationsAllTests algebraic manipulation skills that span all units

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

Practice FRQ 1 of 21/2
1. The following functions are defined for this question:
p(t)=120t+240t2+4p(t) = \frac{120t + 240}{t^2 + 4}p(t)=t2+4120t+240​
A marine biologist is studying the population of a certain species of fish in a lake. The population, in thousands of fish, can be modeled by the function P(t)=120t+240t2+4P(t) = \frac{120t + 240}{t^2 + 4}P(t)=t2+4120t+240​, where ttt is the number of years since the study began, for 0≤t≤100 ≤ t ≤ 100≤t≤10. The rate of change of the population is given by P′(t)P'(t)P′(t).
  • p(t)=120t+240t2+4p(t) = \frac{120t + 240}{t^2 + 4}p(t)=t2+4120t+240​
A. Find P(3)P(3)P(3). Using correct units, explain the meaning of your answer in the context of the problem.
B. Find the average rate of change of P(t)P(t)P(t) over the interval 2≤t≤62 ≤ t ≤ 62≤t≤6. Using correct units, interpret the meaning of your answer in the context of the problem.
C. Determine the end behavior of P(t)P(t)P(t) as ttt increases without bound. Express your answer using the mathematical notation of a limit, and explain what this means in the context of the fish population.
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FRQ Directions
Free Response Question Practice

This practice environment simulates the AP AP Pre-Calculus 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."
  • Use the timer to practice time management. You can pause, restart, or hide the timer as needed.
  • Mark for Review if you want to come back to a question later.
  • Your responses are saved automatically as you type. You can also use the drawing tool for questions that require diagrams or graphs.
  • Use the toolbar for formatting options like bold, italic, subscript, and superscript.
  • Navigate between questions using the Previous and Next buttons at the bottom of the screen.

Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.