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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 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 models the cost of producing x hundred units of a product using the function C, where C(x) represents the total cost in thousands of dollars. Selected values of C(x) are given in the table below. The function R is given by R(x)=2x3−3x2−11x+6x2−x−6R(x) = \frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}R(x)=x2−x−62x3−3x2−11x+6​, where R(x) represents the revenue in thousands of dollars from selling x hundred units, for appropriate values of x.

xxx

C(x)C(x)C(x)

0

12.0

1

10.5

2

11.0

3

13.5

4

18.0

5

24.5

A.

Use the data in the table to find the average rate of change of C over the interval 1≤x≤41 ≤ x ≤ 41≤x≤4. Using correct units, interpret the meaning of your answer in the context of the problem. Then, using the average rates of change over [0,2][0, 2][0,2] and [3,5][3, 5][3,5], determine whether C is concave up or concave down over the interval 0≤x≤50 ≤ x ≤ 50≤x≤5. Justify your answer.

B.

Rewrite R(x)=2x3−3x2−11x+6x2−x−6R(x) = \frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}R(x)=x2−x−62x3−3x2−11x+6​ by factoring the numerator and denominator completely. Use the result to identify all zeros, vertical asymptotes, and holes of R. For each feature, give the x-value and explain how you determined it from the factored form.

C.

Determine the end behavior of R as x increases without bound and as x decreases without bound. Express each answer using the mathematical notation of a limit. Justify your answers by performing polynomial long division on 2x3−3x2−11x+6x2−x−6\frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}x2−x−62x3−3x2−11x+6​ and using the result to describe what value, if any, R approaches.

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Free Response Question Practice

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

  • Read each question carefullybefore 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.
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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.