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VIDEO: Tackling FRQ 4 – Symbolic Manipulations

Updated: Apr 25

We've now come to the final question on the AP Precalculus Exam. FRQ 4 is all about symbolic manipulations, and most resembles what you would probably expect on a typical Precalculus exam. Here students will work on solving equations and rewriting expressions, making use of logarithmic, exponential, and trigonometric properties and identities. This FRQ is non-calculator (like FRQ 3), but does not feature a real-world context.

In this video, we share the structure of FRQ 4, including what students can expect in each part and subpart. We also identify the specific content that students should be familiar with for this question.

Download the handout for students to complete while watching the video.

This video is part of the official Calc Medic AP Precalculus Review Course. To receive access to more videos, practice problems, and full length practice exams, get a quote.

Important Take-aways:

  • FRQ 4 will always be about "Symbolic Manipulations".

  • FRQ 4 does not allow students to use a calculator.

  • FRQ 4 only addresses two skills: solving an equation and rewriting a function in an analytically equivalent form.

  • FRQ 4 has a special set of directions explaining what is considered a “simplified” solution.

  • FRQ 4 will require students to flexibly manipulate logarithmic, exponential, and trigonometric expressions. Students must know their properties and identities, including the Pythagorean identities and sum and difference identities for sine and cosine.

  • Part (C) will require students to carefully consider the number of solutions and in some cases write a general expression for all the solutions to a given equation.

  • Only content from CED Units 2 and 3 is included in this FRQ.

Time to Practice

Now that your students are comfortable with what FRQ 4 is all about, it's time to put this knowledge to the test! We've created a sample question in the style of FRQ 4 you can use to help your students practice their new skills.

Practice FRQ


Note: this practice FRQ was created by Calc Medic and is not an officially released question from the College Board.

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Mr. Kwong
Mr. Kwong
Apr 24

Do you need to include the domain in the rewriting of the function in equivalent form? In the practice exams on AP Classroom, they include the domain.

Sarah Stecher
Sarah Stecher
Apr 25
Replying to

I agree with your suggestion! I just updated the key to include the domain of x>0 in A (ii).

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