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📈AP Precalculus
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📈AP Precalculus

FRQ 4 – Symbolic Manipulations (No Calculator)
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Unit 2: Exponential and Logarithmic 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
No Calculator

4. The functions f, g, p, and q are given by f(x)=log⁡4(x)+log⁡4(x−6)f(x) = \log_4(x) + \log_4(x - 6)f(x)=log4​(x)+log4​(x−6), g(x)=23x⋅8x−1g(x) = 2^{3x} ·8^{x-1}g(x)=23x⋅8x−1, p(x)=log⁡3(x2)−log⁡3(6x)p(x) = \log_3(x^2) - \log_3(6x)p(x)=log3​(x2)−log3​(6x), and q(x)=27x9x−2q(x) = \frac{27^x}{9^{x-2}}q(x)=9x−227x​.

A.
i.

Rewrite g(x)g(x)g(x) as a single power of 222 in the form 2ax+b2^{ax+b}2ax+b, where aaa and bbb are constants. Show the work that leads to your answer.

ii.

Rewrite q(x)q(x)q(x) as a single power of 333 in the form 3ax+b3^{ax+b}3ax+b, where aaa and bbb are constants. Show the work that leads to your answer.

B.
i.

Rewrite p(x)p(x)p(x) as a single logarithm base 333 without negative exponents. Show the work that leads to your answer.

ii.

Solve p(x)=−1p(x) = -1p(x)=−1 for all values of xxx in the domain of ppp. Show the work that leads to your answer.

C.

Solve f(x)=1f(x) = 1f(x)=1 for all values of xxx in the domain of fff. Show the work that leads to your answer, and verify that any solution obtained is in the domain of fff.

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FRQ Directions
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.