Many students opt to take a math AP exam, and Calculus AB is a popular choice since it's slightly easier than Calculus BC. But to get a high score on it, you'll need to do very well on the free-response section, which requires you to write out your answers to multi-step problems. In this complete guide, we go over the AP Calculus AB Free Response section structure, provide examples to show you how it's graded and what a correct answer looks like, and give you some tips for acing this tricky section of the exam. The AP Calculus AB exam is one of two Calculus tests you can take. (The other is AP Calculus BC, which covers a slightly bigger and harder array of high-level math concepts.) Calculus AB tests your knowledge of various calculus concepts, including derivatives, limits, and differential equations. You can learn more about what it tests by referring to the AP Calculus AB and BC Course and Exam Description. Format-wise, the AP Calculus AB test is divided into two sections—a multiple-choice section and a free-response section—each of which makes up 50% of your score. You'll have three hours and 15 minutes for the exam. Here's a brief overview of the format of the AP Calculus AB test: Both the multiple-choice and free-response sections are divided up into a Part A and a Part B. Note too that you'll have questions on which you may not use a calculator and some on which you are required to use a graphing calculator (required on Part B in Section 1, Part A in Section 2). Now then, let's take an even closer look at the AP Calculus AB Free Response section. As explained above, the free-response section is the second section on the AP Calculus AB exam, after the multiple-choice section. You'll have a total of 90 minutes to complete this section, which consists of six questions divided into two parts: Part A and Part B. According to the College Board, these questions "include various types of functions and function representations and a roughly equal mix of procedural and conceptual tasks." There will also be "at least 2 questions that incorporate a real-world context or scenario into the question" (bold emphasis mine). Here's a quick recap of what you can expect on Parts A and B in the free-response section: The AP Calculus AB FRQ section requires you to use four "Mathematical Practices," or skills, as defined by the College Board. Here's how these practices are weighted on this section of the test: Each AP Calc AB FRQ is graded on a scale of 0-9 points. Questions have multiple parts to them, labeled A-C or A-D, and you'll get a certain number of raw points (typically 1-3) for each part. The maximum number of points you can get on one FRQ is 9 points, meaning you've correctly and fully answered every part of the question. The points you earn for the six FRQs are combined with your multiple-choice score and converted into a final AP score on a scale of 1-5. Here, we show you two examples of real Calculus AB Free Response questions taken from the 2020 Course and Exam Description. We'll go over how to solve each question to earn full credit. All answers come from the official scoring guidelines. In this problem, parts A-C are each worth 2 points, while part D is worth 3 points. You'll need to understand differential functions to be able to solve this correctly. You will also need to show your work clearly at each step in order to earn full points. Here are model answers for each part of this AP Calc AB FRQ. Here, you will get a point for approximating using values from the table and another for correctly interpreting with units. You'll get a point for doing the midpoint sum setup correctly and another point for approximating using values from the table with units. Here, you will get a point for using the definite integral and another for finding the correct answer with supporting work. You'll earn a point for using the slope, another point for finding that L(t) = 2,000, and a final point for getting the right answer (14.759) and showing your work. Wave goodbye to your calculator for this next question! For this AP Calculus AB FRQ, you are not allowed to use a calculator, so be prepared to solve everything by hand and show your work! You can earn up to 2 points for parts, A, B, and D, and up to 3 points for part C. You must be able to understand differential functions and derivatives, as well as what intervals are, to get this right. Below are model answers to each of the four parts of this question. The graph of f is decreasing and concave down on the intervals (1, 1.6) and (3, 3.5) because f′ is negative and decreasing on these intervals. You will get a point for proposing x = 2 as a candidate and another point for justifying your answer with the math. You will get a point for finding the antiderivative of the form a[f(x)]2, another point for showing that a = 1/2, and a third point for finding the right answer (-40). Here, you'll get a point for using the product rule and another for finding the correct answer (60). Here are some tips to keep in mind as you prepare for the AP Calc AB Free Response section. As you know, there are two parts on the AP Calculus AB Free Response section. With Part A, you get two questions, which together count for 16.7% of your total AP test score. A graphing calculator is required for this section—not merely permitted!—so it is extremely important that you know how to use it effectively to solve those tricky, multi-step problems, which typically require you to graph complicated functions. If you are not that comfortable with your calculator, you'll likely struggle with figuring out how to even start a problem! Below are some examples of how you might be required to use your graphing calculator on the AP Calc exam, according to the College Board: Aside from knowing how to use your calculator, you should take care to really get down critical formulas you'll need to know, especially for Part B (the no-calculator part) of the free-response section. Unfortunately, the College Board does not give out any formula sheets for the exam, but your AP Calculus teacher will probably give you a list of some to study for the test. As a general rule, any formula you learn in class will likely be an important one to know for test day. Every part of each AP Calculus AB FRQ contains a task verb that tells you what to do. It's a good idea to familiarize yourself with these different task verbs so that you can know right away what the question wants to see and how you can earn full credit for your answer. Here are the most commonly used task verbs on AP Calc, according to the College Board: By far the best way to prepare for the AP Calc AB exam—any AP exam, really!—is to use official questions and practice tests. Doing this will help you quickly get used to the difficulty, content, and pacing of both the free-response section and the test as a whole. It's best to begin your prep by taking an official full-length practice test so you can see what areas you struggle with the most and then zero in on those in your study sessions. Make sure that you time yourself accordingly and tweak any older tests you use for practice so that they reflect the current format of the test. You can get started with our collection of AP Calculus AB practice tests. For free-response questions specifically, the College Board offers tons of sample questions in its Exam Description and on its Calculus AB exam page, which has an impressive collection of student sample responses as well. To earn full points on free-response questions, you'll need to show all your work, from the very first step all the way to the last. As you saw above with the sample FRQs, you'll often earn a point or two simply for justifying your response and showing how you got your answer. As you practice with official questions, make sure that you're writing out everything it takes to get to the right answer. Note that showing your work doesn't just mean finding the correct answer, but also indicating the setup and intermediate steps needed to get there. Even if the steps for solving a problem seem really obvious to you, remember that this is the stuff AP graders want to see! Our final tip is to focus on pacing yourself in your prep so you're not spending too much time on any one AP Calc AB FRQ. As a reminder, you'll have about 15 minutes to spend on each free-response question, so try your best not to go over this "limit" in your studying—especially when you take full-length practice tests. If you find that certain FRQs are taking you longer than 15 minutes, that's a sign that you need to target those question types in your prep and review their content more. The AP Calc AB Free Response section might sound intimidating, but as long as you know what to expect on test day and how to prep effectively, you're more than capable of walking away with an amazing (or even perfect!) AP score. The Calculus AB free-response section is split into two parts: Altogether, this section counts for 50% of your AP Calc AB score (the other half is your multiple-choice section score). FRQs are divided into three or four parts (labeled A-C/D) and are worth up to 9 raw points each. To prepare for this tricky section of the AP Calc exam, be sure to do the following: Heed these six tips and you're sure to ace the AP Calculus AB FRQ section in no time! Got more questions about the AP Calculus AB exam as a whole? Then read our expert guide to the AP Calculus AB exam. Want resources you can use for your AP Calculus AB test prep? We've got you covered with our collection of Calculus AB practice tests and questions. Not sure whether to take Calculus AB or BC? Let us help you figure out which AP test is the ideal choice for you. And if you decide to opt for Calc BC instead of AB, you'll definitely want to check out our comprehensive guide to the Calculus BC free-response questions! What to Expect on the AP Calculus AB Exam
AP Calc AB Section % of Score Time # of Questions Calculator? 1. Multiple Choice Part A: 33.3% Part A: 60 mins Part A: 30 Part A: No Part B: 16.7% Part B: 45 mins Part B: 15 Part B: Yes Total: 50% Total: 1 hr 45 mins Total: 45 — 2. Free Response Part A: 16.7% Part A: 30 mins Part A: 2 Part A: Yes Part B: 33.3% Part B: 60 mins Part B: 4 Part B: No Total: 50% Total: 1 hr 30 mins Total: 6 — TOTAL 100% 3 hrs 15 mins 51 — AP Calculus AB Free Response Section Overview
AP Calc AB Free Response Time # of Questions Time per Question % of Total Score Calculator Policy Part A 30 mins 2 15 mins 16.7% Required Part B 60 mins 4 15 mins 33.3% Not permitted Mathematical Practice Description % of Free-Response Section Practice 1: Implementing Mathematical Processes Determine expressions and values using mathematical procedures and rules 37-55% Practice 2: Connecting Representations Translate mathematical information from a single representation or across multiple representations 9-16% Practice 3: Justification Justify reasoning and solutions 37-55% Practice 4: Communication and Notation Use correct notation, language, and mathematical conventions to communicate results or solutions 13-24% AP Calculus AB FRQ Samples and Solutions
Part A Sample Question (Calculator Required)
(A) Model Solution
(B) Model Solution
(C) Model Solution
(D) Model Solution
Part B Sample Question (No Calculator)
(A) Model Solution
Here, you will get a point for providing the correct answer and another point for explaining your reasoning.(B) Model Solution
(C) Model Solution
(D) Model Solution
AP Calculus AB Free Response Section: 6 Essential Tips
#1: Know How to Use Your Calculator
Make sure you can do all these major functions (and more!) well before you take the AP Calculus AB exam.#2: Memorize Key Formulas
#3: Learn What the Task Verbs Mean
#4: Use Realistic Practice Questions
#5: Get Used to Showing Your Work
#6: Practice Pacing Yourself
Recap: Acing the AP Calculus AB Free Response Section
What's Next?
FAQs
6 Expert Tips to Ace the AP Calculus AB Free Response? ›
Since you only need to get about 60% of available points to score a 5 on either AP Calculus exam, and since you have ample time on all sections, you can strategize the exam differently than you would almost any classroom test.
How to ace AP Calculus AB Frq? ›- Keep an eye on your time. ...
- Show your work, even when you're using a calculator. ...
- Try to solve each part of the question. ...
- Be sure to fully answer the question being asked.
Since you only need to get about 60% of available points to score a 5 on either AP Calculus exam, and since you have ample time on all sections, you can strategize the exam differently than you would almost any classroom test.
Is it easy to get a 5 in AP Calculus AB? ›This common question has no easy answer. To achieve a 5 on the AP® Calculus AB exam, you will need a combination of tenacity, commitment to learning the material, and a dedicated study plan.
How to guess on AP Calc? ›A good strategy is to eliminate as many incorrect answers as you can, and then guess from the remaining options. Over time, studies have shown no consistent bias towards any letter, so guessing randomly among the remaining options after elimination is your best bet.
How rare is a 5 in AP Calc? ›In the 2023 AP Calculus AB score distributions, you'll find that 22.39% of students scored a 5. Additionally, 16.18% of students scored a 4, and 19.4% of students scored a 3.
What is the hardest AP to get a 5 on? ›TOP 10 Toughest AP Subject to Score a 5
AP 3-D Art and Design tops this list with the 5-score rate of 6.4% but has a passing rate of 73.5%. So while it is the hardest AP subject to achieve a perfect 5, the second on this list, AP Physics 1, is actually the hardest.
How many people get a perfect 5 in AP Calculus AB? Only one test taker achieved a perfect score on the 2022 AP Calculus AB exam. However, for the 2023 AP Calc AB exam, 22.4% of test-takers scored a 5.
Which AP calculus is the hardest? ›Finally, AP Calculus BC is the toughest AP math exam, if not one of the hardest AP exams period. AP Calculus AB is also challenging, but covers less material and moves more slowly.
Are AP exams curved? ›AP test scores are indeed "curved," but it's more accurate to call it a "scaling process." Instead of a traditional curve that compares your performance to other students' performance, the AP exam scaling process converts your raw score (the number of points you earned through multiple-choice questions and free- ...
What calculator is best for AP Calc? ›
For the AP Calc BC exam, students commonly use either a Texas Instruments calculator (typically the TI-84 Plus or TI-84 Plus CE) or the Casio fx-9750GII. Each of these options has its own set of advantages and disadvantages, so ultimately it will come down to personal preference and budget.
How many questions do you need to get right on the AP Calc exam? ›Exam Weighting (Multiple-Choice Section)
Albert's AP® Calculus AB score calculator shows that you would need to answer at least 23 of the multiple-choice questions correctly and receive at least 27 points in the free-response portion of the exam in order to achieve a score of 3 or better.
Albert's AP® Calculus AB score calculator shows that you would need to answer at least 23 of the multiple-choice questions correctly and receive at least 27 points in the free-response portion of the exam in order to achieve a score of 3 or better.
How much time for each FrQ AP Calc AB? ›Section | Question Types | Time Per Section |
---|---|---|
Section I | Multiple-Choice Questions (MCQs) | 1 hour 45 mins |
Section II | Free-Response Questions (FRQs) | 1 hour 30 mins |
- Practice. Answering essay questions generally requires a good deal of training and practice. ...
- Examine the question. ...
- Determine what's required to answer the question. ...
- Choose your evidence. ...
- Develop a thesis. ...
- Support your thesis. ...
- Get examples from past exams.
In summary, AP Calculus AB is considered to have a moderate level of difficulty, with a rating of 5.5 out of 10 based on a survey of class alumni. It ranks as the 12th most difficult AP course out of the 28 large AP classes surveyed.