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 freeresponse section
, which requires you to write out your answers to multistep 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.
2021 AP Test Changes Due to COVID19
Due to the ongoing COVID19 coronavirus pandemic, AP tests will now be held over three different sessions between May and June.
Your test dates, and whether or not your tests will be online or on paper, will depend on your school. To learn more about how all of this is going to work and get the latest information on test dates, AP online review, and what these changes means for you, be sure to check out
our 2021 AP COVID19 FAQ article
.
What to Expect on the AP Calculus AB 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 highlevel 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
.
Formatwise, the AP Calculus AB test is divided into two sections—a multiplechoice section and a freeresponse 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:
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 
— 
Both the multiplechoice and freeresponse 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.
AP Calculus AB Free Response Section Overview
As explained above, the freeresponse section is the second section on the AP Calculus AB exam, after the multiplechoice 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
realworld 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 freeresponse section:
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 
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:
Mathematical Practice 
Description 
% of FreeResponse Section 
Practice 1: Implementing Mathematical Processes  Determine expressions and values using mathematical procedures and rules  3755% 
Practice 2: Connecting Representations  Translate mathematical information from a single representation or across multiple representations  916% 
Practice 3: Justification  Justify reasoning and solutions  3755% 
Practice 4: Communication and Notation  Use correct notation, language, and mathematical conventions to communicate results or solutions  1324% 
Each AP Calc AB FRQ is graded on a scale of 09 points.
Questions have multiple parts to them, labeled AC or AD, and you’ll get a certain number of raw points (typically 13) 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 multiplechoice score and converted into a
final AP score on a scale of 15
.
AP Calculus AB FRQ Samples and Solutions
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
.
Part A Sample Question (Calculator Required)
In this problem, parts AC 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.
(A) Model Solution
Here, you will get a point for approximating using values from the table and another for correctly interpreting with units.
(B) Model Solution
You’ll get a point for doing the midpoint sum setup correctly and another point for approximating using values from the table with units.
(C) Model Solution
Here, you will get a point for using the definite integral and another for finding the correct answer with supporting work.
(D) Model Solution
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.
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Wave goodbye to your calculator for this next question!
Part B Sample Question (No Calculator)
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.
(A) Model Solution
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.
Here, you will get a point for providing the correct answer and another point for explaining your reasoning.
(B) Model Solution
You will get a point for proposing
x
= 2 as a candidate and another point for justifying your answer with the math.
(C) Model Solution
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).
(D) Model Solution
Here, you’ll get a point for using the product rule and another for finding the correct answer (60).
AP Calculus AB Free Response Section: 6 Essential Tips
Here are some tips to keep in mind as you prepare for the AP Calc AB Free Response section.
#1: Know How to Use Your Calculator
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, multistep 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
:
 Zooming to reveal local linearity
 Constructing a table of values to conjecture a limit
 Developing a visual representation of Riemann sums approaching a definite integral
 Graphing Taylor polynomials to understand intervals of convergence for Taylor series
 Drawing a slope field and investigating how the choice of initial condition affects the solution to a differential equation
Make sure you can do
all
these major functions (and more!) well before you take the AP Calculus AB exam.
#2: Memorize Key Formulas
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 nocalculator part) of the freeresponse 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
.
#3: Learn What the Task Verbs Mean
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
:

Approximate:
Use rounded decimal values or other estimates in calculations, which require writing an expression to show work. 
Calculate/Write an expression:
Write an appropriate expression or equation to answer a question. Unless otherwise directed, calculations also require evaluating an expression or solving an equation, but the expression or equation must also be presented to show work. “Calculate” tasks might also be formulated as “How many?” or “What is the value?” 
Determine:
Apply an appropriate definition, theorem, or test to identify values, intervals, or solutions whose existence or uniqueness can be established. “Determine” tasks may also be phrased as “Find.” 
Estimate:
Use models or representations to find approximate values for functions. 
Evaluate:
Apply mathematical processes, including the use of appropriate rounding procedures, to find the value of an expression at a given point or over a given interval. 
Explain:
Use appropriate definitions or theorems to provide reasons or rationales for solutions and conclusions. “Explain” tasks may also be phrased as “Give a reason for…” 
Identify/Indicate:
Indicate or provide information about a specified topic, without elaboration or explanation. 
Interpret:
Describe the connection between a mathematical expression or solution and its meaning within the realistic context of a problem, often including consideration of units. 
Interpret (when given a representation):
Identify mathematical information represented graphically, symbolically, verbally, and/or numerically, with and without technology. 
Justify:
Identify a logical sequence of mathematical definitions, theorems, or tests to support an argument or conclusion, explain why these apply, and then apply them. 
Represent:
Use appropriate graphs, symbols, words, and/or tables of numerical values to describe mathematical concepts, characteristics, and/ or relationships. 
Verify:
Confirm that the conditions of a mathematical definition, theorem, or test are met in order to explain why it applies in a given situation. Alternately, confirm that solutions are accurate and appropriate.
#4: Use Realistic Practice Questions
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 freeresponse section and the test as a whole.
It’s best to begin your prep by taking an official fulllength 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 freeresponse 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.
#5: Get Used to Showing Your Work
To earn full points on freeresponse 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!
#6: Practice Pacing Yourself
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 freeresponse question
, so try your best not to go over this “limit” in your studying—especially when you take fulllength 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.
Recap: Acing the AP Calculus AB Free Response Section
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 freeresponse section is split into two parts:
 Part A: 2 questions, 30 minutes, graphing calculator required
 Part B: 4 questions, 60 minutes, calculator not permitted
Altogether,
this section counts for 50% of your AP Calc AB score
(the other half is your multiplechoice section score). FRQs are divided into three or four parts (labeled AC/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:
 Know how to use your calculator
 Memorize key formulas
 Learn what the task verbs mean
 Use realistic practice questions
 Get used to showing your work
 Practice pacing yourself
Heed these six tips and you’re sure to ace the AP Calculus AB FRQ section in no time!
What’s Next?
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 freeresponse questions
!