Score Higher on AP Pre-Calculus 2024: FRQ Tips from Students

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 are given 4 free response questions on a variety of skills throughout the course such as applying tests, collecting data, and using probability
• 37% of Exam Score
• 60 Minutes for 4 questions, about 15 minutes per question
  • FRQ 1 – Function Concepts (Calculator)
  • FRQ 2 – Modeling a Non-Periodic Context (Calculator)
  • FRQ 3 – Modeling a Periodic Context (No Calculator)
  • FRQ 4 – Symbolic Manipulations (No Calculator)

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💭 General Advice

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

• Skip the questions you think might take more time or you don’t remember how to solve. It’s better that you have some points rather than no points because you were stuck on a problem.
• Write down any formulas and show all your work, because sometimes you get partial credit for having the right formula or part of the work right, even if you don’t end up at the right answer.
• If you have a calculator, make sure to stay in radian mode and never round answers (always round to 3 decimal places unless the test says otherwise) until the very end, so store decimals in your calculator or know the exact answer.
• Practice, Practice, Practice!!! My teacher always says practice makes permanent, especially in math. Have your teacher assign AP questions through AP Classroom that reflect what is actually going to be tested on the exam.
• Identify what the FRQ is asking you to do. If you are unfamiliar with the topic at that given moment, skip it and look at what you CAN do. You can always come back, and the questions that are shown after the one you are struck with can possibly help bring back some key information your teachers have previously taught you!
• When you have your calculator, it is a useful tool, but make sure you can do the calculations (most of the way through) without it. Essentially, practice doing as much as you can without a calculator.
  • Obviously, go to it for exact decimals and for checking your work, but the more practice you have with doing the calculations by hand, the less you will rely on your calculator and the more prepared you will be for the no-calculator questions.
  • It will help you develop “number sense” or mathematical intuition. It’s very easy to make a mistake with a calculator, and because it’s a computer, we tend to trust the answer it spits out. If you develop good intuition by practicing without a calculator, you’re more likely to spot mistakes.
• Don’t limit your practice to a single type of problem!! You should explore different sources, books, websites, and previous homework/assignments. By doing so, you can get to know the range of approaches to solve the problems.
• Think about starting or joining study groups with friends who are also taking AP Precalc. You will definitely improve your knowledge and can gain a deeper understanding of concepts by studying and communicating with others.
• Take the course at a glance, highlight the skills that you don’t know and you know, and study in chunks, emphasizing the skills you don’t know.

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✍️Before you Write

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

• Before you start, divide the time into sections so that you don’t run out of time.
• Know what task verb is being used in the question and how to approach it. For example, if the question says “solve,” then find the solutions to the given equation or if it tells you to “interpret,” you need to describe the connection between the expression and its meaning within the context of the problem.
• Identify what concepts are being used or that are related to a problem. It will be easier to figure out which ones you can do quickly and which ones you’ll want to take more time on before you start. Also, this may help if you get stuck on how to approach a problem.
• Take a few minutes to briefly outline how you will answer each question. Write down any important formulas or tactics you want to use. This can help you stay focused while actually solving the problem.
• Before the test begins, quickly go over your notes or completed assignments. This can help you brush up on relevant concepts and methods.

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💈Question Types

FRQ #1 – Function Concepts

• Understand how composite and inverse functions work as well as limits.
• Think about end behavior and know the difference between the different functions like linear, quadratic, exponential, and logarithmic.
• Present functions that have been expressed analytically, numerically, and graphically. This three-part question will test your knowledge of concepts such as function composition, inverse functions, input-output values, zeros in a function, end behavior in a function, and choosing the right function type to build a function model.
• Graphing calc allowed!!
• As simple as it sounds, make sure you understand functions conceptually. Understanding the concept underlying the function will make understanding composite and inverse functions a lot easier!

FRQ #2 – Modeling a Non-Periodic Context

• This question will present a real-life context and will ask you to construct functions types seen in Unit 1 & 2: polynomial, piecewise-defined, exponential, and logarithmic. Make sure to brush up on these topics and be experts on function manipulation, and a graphing calc is allowed.
• Provides a context from real life.
• Part A, you will build a system of equations and use a method of choice to find the parameters in order to construct a function model using the provided information.
• In part B, you will use average rates of change and their units to compute, apply, and reason.
• You will defend a conclusion regarding the model's assumptions or limits in part C.
• As long as you review the four function types, modeling should be a breeze! What might present a bigger challenge is the conclusion you’ll have to support based on your model. Make sure you practice this a lot leading up to the exam and understand how graphs relate to real world contexts.

FRQ #3 – Modeling a Periodic Context

• This question will again present a real-life context and always be related to sinusoidal functions (Unit 3), so make sure you know how to construct a sinusoidal model based on points and know your periods and phase shifts like the back of your hand. No graphing calc allowed.
• Shows a sinusoidal function model of a real-life context.
• You will utilize the provided information in part A to locate the coordinates of five labeled points on the sinusoidal function graph, as well as the function's midline, over the course of two complete cycles.
• You will determine the parameters of the sinusoidal function's analytical presentation in part B.
• You must construct the sinusoidal model in Parts (A) and (B) by applying the context to determine the horizontal dilation and translation of the sine or cosine function (period and phase shift) and the vertical dilation and translation of the sine or cosine function (amplitude and vertical shift).
• You will respond to questions regarding the function's behavior and explain how the rate changed in Part (C).
• This is definitely a tough question, but easy to master with a little attention in your studying! Make sure you understand the guts of sinusoidal functions, understanding what to manipulate to change their frequency, amplitude, etc.

FRQ #4 – Symbolic Manipulations

• There are several functions available in this question, including trigonometric, logarithmic, exponential, and/or inverse trigonometric. You must use provided functions to solve equations in two sections of the question. You must rewrite the provided function expressions in equivalent forms for the third section of the question.
• In order to answer each section of the question, you will have to determine the exact values of the expressions that can be obtained, combine terms using algebraic techniques and exponents and logarithms, and demonstrate the work that goes into the answers.
• No graphing calc!!
• Memorize the trig identities and understand how to use and apply them to verify trig identities
• Know your properties! Mainly logarithmic and exponential.
• Make sure you can reproduce the unit circle. Practice drawing it—drawing it onto the exam will help you with computing the exact value for trig expressions.

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😕 Commonly Made Mistakes

• #1: Don’t get cocky! ALWAYS check your work. There might have been a single process or negative sign you missed that could lead to a completely wrong answer.
• Don’t rush! Even when your time is running out, take your time to solve the question to the best of your ability. The more focus you put into solving the problem, the faster and more accurately you will solve it.
• Go over each question and the guidelines carefully. Even if you think it’s right, following directions incorrectly or skipping them altogether can lead to incomplete solutions.