AP Precalculus FRQ practice

Write AP Precalculus free-response answers in an exam-style editor.

📈AP Precalculus

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

FRQ	Focus	Units	Why
FRQ 1	Function Concepts (Calculator)	1-2	Tests function analysis with graphing calculator - Units 1-2 polynomial/rational functions
FRQ 2	Modeling a Non-Periodic Context	1-2	Tests modeling with polynomial, rational, exponential, or logarithmic functions
FRQ 3	Modeling a Periodic Context	3 only	Tests modeling with trigonometric functions - all Unit 3 content
FRQ 4	Symbolic Manipulations	2-3	Tests 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 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 $R(x) = \frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}$ , where R(x) represents the revenue in thousands of dollars from selling x hundred units, for appropriate values of x.

$x$	$C(x)$
0	12.0
1	10.5
2	11.0
3	13.5
4	18.0
5	24.5

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

Rewrite $R(x) = \frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}$ 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.

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 $\frac{2x^3 - 3x^2 - 11x + 6}{x^2 - x - 6}$ and using the result to describe what value, if any, R approaches.

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