FRQs

This guide organizes advice from past students who got 4s and 5s on their exams. We hope it gives you some new ideas and tools for your study sessions. But remember, everyone's different—what works for one student might not work for you. If you've got a study method that's doing the trick, stick with it. Think of this as extra help, not a must-do overhaul.

📌 Overview

• Students answer 6 questions mixing various function representations, real world scenarios, and both procedural and conceptual tasks
• 50% of Exam Score
• 90 min or 15 min per question
• 2 questions require a graphing calculator
• 2 questions do not allow a graphing calculator

💭 General Advice

Tips on mindset, strategy, structure, time management, and any other high level things to know

• The exam has consistently asked for a graph of a derivative, differential equations, separation of variables, and rates (on a graph or table) throughout the years. Practice these concepts frequently!
• Practice as many released FRQs from the College Board as you can! Become familiar with how they ask questions and observe a pattern in the types of questions they ask throughout the years.
• Some questions are memory checks and ask you to recall pieces of information that you must memorize, like limit rules, basic function graphs, derivatives, anti-derivatives, and others (see Equations to Memorize for helpful hints in this area!).
• For time management, be sure to skip any longer problems, and instead complete shorter, more simple questions. Answering simple questions could also help activate forgotten knowledge that could help solve bigger problems.
• Practice, practice, practice! The FRQs tend to follow general patterns regardless of how different they are. Learning how they are typically written will help you prepare for the exam.
  • There are six problems on the FRQ, and they all follow approximately the same pattern - this means cover the same units for the corresponding problems from unit to unit - so get familiar with what units are generally tested on each FRQ!
  • For example, the first part of an FRQ of AB and BC Calculus is always on Riemann Integration (working with tables, right/left/midpoint Riemann/trapezoid and whether they are an underestimate or an overestimate, and simply interpretation) and on approximating differentiation (which is just the rise/run for the two tangent points). Even if it’s not the first problem, it will be there, so fully master this skill.
    • AB: one FRQ usually requires proper set up of L’Hopital’s Rule
    • BC: there will always be one FRQ related to Taylor series—usually FRQ 6
  • Apart from just practicing answering released FRQs, analyze the evaluation criteria and examples of answers to help you understand exactly what the questions are asking and avoid silly mistakes on exam day!
• Always make sure you understand why you got a problem wrong on your homework, quiz, test, etc. Tracking your mistakes in a notebook or document can also help you understand what types of mistakes you often make, or what units/topics are the hardest for you, which can guide your review!
• Try to stick to the recommended 15 min time limit per FRQ question. This is especially important when practicing FRQs before the test - try to stick as close to this timing as possible!

🕐 Before You Write

What should a student do in the first few minutes, before they start writing?

• Make sure your interpretation of the question is correct
• Figure out what they are testing, in other words what would the rubric look like for this question, what key elements would a grader look for
• Fully understand the given graphs, given functions, etc. For example, sometimes FRQs could provide derivative functions/graphs instead of the original function. Be sure to recognize these differences.
• Try to quickly go over the solution in your head involving key steps in the problem solving process ( This does not require any numerical solutions ). This could help you spot logical flaws in your argument before you have already written half of the FRQ. Sometimes the correct solution isn’t worth more than 1 mark but just a logical progression through the entire solution, every step you have written - and the cohesion between them.
  • notes such as definitions of constants (integrating from something to ‘a’, which you may have stored in your calculator) can be the difference between almost zero credit on one part of an FRQ and a perfect score on that question— the reader should be able to tell exactly what you did without making any assumptions

✏️ Writing the FRQ

• Evaluate the problem carefully. How will you approach it and what formulas will you use? Write your solution process on scratch paper (the question paper, not the answer sheet) and double check. But have a sense of time as well - don’t fall behind on the clock too much.
• Use the theorems that you have memorized to prove questions whenever you can. Sometimes this is the difference between earning or not earning the point.
• Sufficiently prove your answer with work, explanations, and use correct units in your final solution.
• Always show all your work and attempt all parts of an FRQ. Remember, even if you don’t get the correct answer for a previous part, you can still get some points on the next part if you use the correct formula/process.
• Write everything down, no matter how obvious it may seem. For example, if a problem requires you to find the point where the tangent to a curve is horizontal, always begin with $\frac{\text{d}y}{\text{d}x}=0$.
  • Always set up the integral on paper, even if it's a fairly simple one in the calculator section—simply writing it down can be up to two points at a time.
  • Similarly, always show separation of variables in problems when you use it—the rubric may contain a note that without the setup, no other points can be achieved in that part of the question.
• If there is a word problem associated with the FRQ, make sure you write all your solutions in the context of the problem. This means adding correct units and interpreting results in plain language. AP scorers could take points if context is not mentioned.
  • Ex: For a function describing the rate of fish dying in the pond, the integral tells us the actual number of fish that died in the pond (over the time interval a to b). Your unit in this case would be “$x$ dead fish” or something similar.
  • On the flip side, if they don’t tell you to write units (i.e. if the associated problem isn’t a word problem), don’t write units unless you’re absolutely positive that you’re correct. They can take points off it’s wrong (even if the question didn’t ask for units).
• If you’re unsure how to approach the problem, just write down whatever you can that is related to the problem. You can get points for just having the formula written down, or writing down the condition—basically, info dump any related information that you can think of. This can also stimulate your memory and help you answer the question later on if you have time to return to it!
• Always write the formula or theorem, you may get a point for it. Even if you can’t solve the problem, setting it up can get you a point or two. Make sure unless it’s something like IVT or MVT, you spell out the entire theorem.
• You don’t have to simplify anything for it to be marked correct. If you get a Riemann sum approximation FRQ with a table, $(2)(3)+(4)(6)+(8)(3)$ will be marked correct. This not only saves time, but prevents you from losing points you would otherwise earn because of algebra.

🧮 Graphing Calculator Tips

• The graphing calculator required questions actually require a calculator - know your calculator skills! This is unlike the calculator MCQ, which may not really require a calculator, and where using one might actually slow you down.
  • Become familiar with the specific calculator you’ll be using before exam day. The first two FRQs may be impossible if you need to spend ten minutes figuring out a brand new of calculator in the middle of the test.
• Be sure to know how to calculate derivatives on the calculator, how to find intersection points/zeros on the calculators, how to put your calculator into parametric/polar mode, and other calculus functions that are able to be done within your calculator
• If you’ll be using an equation a lot in a problem, it may be worth the time to save it as Y1 in your calculator.
  • Most common graphing calculators also contain a button where these saved equations can be used in integrals— for BC, remember that this often applies to polar mode, too.
• In Y3, prior to the exam, put in “d/dx(Y1).” Since you often use the derivative, it’ll get one step out of the way. You can also do this with integrals, or second derivative if you think you’ll need it.

ƒ Equations to Memorize

• All derivatives and antiderivatives formulas
  • e.g. the power rule
    • $\frac{\text{d}}{\text{d}x}\ x^n=nx^{n-1}$
• Limit rules
  • General rules for evaluating
  • L’Hopital’s
  • Indeterminate forms
• Arc Length for General/Parametric
• Derivative main/alternative definition
• Exponential Model General Solution
• Conditions for all formulas

BC Only

• Logistic Model General Solution
• Geometric Series
• Taylor Polynomial
  • Know the series for $\text{sin}(x)$, $\text{cos}(x)$, $\text{ln}(x)$, and $e^x$
• Lagrange Error Bound
• Polar Integral
• First and second derivatives of parametric equations
• Euler's Methods Formula
• Convergence tests
  • Ratio test
  • Root test
  • Limit comparison test
  • Direct comparison test
  • Integral test