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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 111/11

1. A company manufactures and sells custom printed t-shirts. The company's weekly revenue, in hundreds of dollars, from selling x t-shirts is modeled by the function R, where R(x)=−x3+50x2+600xx+20R(x) = \frac{-x^3 + 50x^2 + 600x}{x + 20}R(x)=x+20−x3+50x2+600x​ for 0≤x≤2000 ≤ x ≤ 2000≤x≤200. The table below gives values of R at selected values of x.

  • q(x)=−x2+70x−800q(x) = -x^2 + 70x - 800q(x)=−x2+70x−800

x (t-shirts)

R(x) (hundreds of dollars)

0

0

20

480

40

746.67

60

900

80

977.78

100

1000

120

989.09

160

913.33

200

800

A.

Use the data in the table to find the average rate of change of R over the interval 20≤x≤10020 ≤ x ≤ 10020≤x≤100. Indicate units of measure, and interpret the meaning of your answer in the context of the problem.

B.

Use a decimal approximation to find the average rate of change of R over the intervals 60≤x≤8060 ≤ x ≤ 8060≤x≤80 and 80≤x≤10080 ≤ x ≤ 10080≤x≤100. Use these two values to describe how the rate of change of R is changing near x=80x = 80x=80, and explain what this means about the company's weekly revenue near a production level of 80 t-shirts.

C.

Perform polynomial long division to rewrite R(x)=−x3+50x2+600xx+20R(x) = \frac{-x^3 + 50x^2 + 600x}{x + 20}R(x)=x+20−x3+50x2+600x​ in the form R(x)=q(x)+rx+20R(x) = q(x) + \frac{r}{x+20}R(x)=q(x)+x+20r​, where q(x)q(x)q(x) is a polynomial and rrr is a constant. Use your result to determine the end behavior of R as x increases without bound within the context of the model, and explain whether the end behavior is meaningful given the restrictions on the domain.

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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."
  • 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.