day 54 homework ap calculus ab

AP Calculus AB Class Schedule and Homework Assignments

* Lesson recordings are from 2020-21, so they may not completely match the lessons from this year.

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AP®︎/College Calculus AB

Meet an ap®︎ teacher who uses ap®︎ calculus in his classroom, unit 1: limits and continuity, unit 2: differentiation: definition and basic derivative rules, unit 3: differentiation: composite, implicit, and inverse functions, unit 4: contextual applications of differentiation, unit 5: applying derivatives to analyze functions, unit 6: integration and accumulation of change, unit 7: differential equations, unit 8: applications of integration, unit 9: ap calculus ab solved free response questions from past exams, unit 10: ap®︎ calculus ab standards mappings.

Welcome to AP Calculus !

Welcome to AP Calculus! This site contains a lot of information I used with students when I taught AP Calculus. The syllabus I used for AP Calculus can be accessed by clicking on the following link:

AP Calculus Syllabus

Feel free to use whatever you think may help you, or teach your students. If you have any questions, or just want to drop me a line, you can contact me at [email protected] . Good luck and I hope that you have a successful experience learning and teaching this course!

Calculus AB

Precalculus Topics

Limits and Continuity

Rates of Change and Derivatives

Differentiation

Implicit Differentiation and Other Derivatives

Applications of Derivatives

L'Hopital's Rule and Related Rates

Intro to Definite Integrals

Fundamental Theorem of Calculus and Integration Methods

Differential Equations

Integrals as Net Change and Volume

Calculus AB Review

Calculus BC

Advanced Integration Methods

Parametric and Vector Functions

Polar Calculus

Sequence and Series Convergence

Power and Taylor Series

AP Exam Review

Choose Your Test

Sat / act prep online guides and tips, the expert's guide to the ap calculus ab exam.

Advanced Placement (AP)

Are you taking the AP Calculus AB exam this spring and want to be well prepared on test day? The AP Calculus AB exam in 2022 will be held on Monday, May 9, at 8 am .

Before you sit down to take the exam, though, it's critical that you know how the Calculus AB test is formatted, what topics it covers, and how you'll be scored on it. This guide will go over all of that information while also showing you official sample problems and giving you tips on the best way to prepare for AP Calculus AB.

The AP Calculus AB exam can sometimes seem overwhelming, but we're here to break it down into clear and manageable information for you. You can also check out the College Board's new AP Classroom tool for AP Calculus AB , which has additional resources and information. Let's get started!

What's the Format of the AP Calculus AB Exam?

The AP Calculus AB exam is three hours and 15 minutes long and has two sections. Both of these sections are divided into two parts (based on whether or not a calculator is allowed).

Multiple-Choice Section

Here is an overview of the format of the AP Calculus AB multiple-choice section:

• 45 questions total
• One hour 45 minutes total
• Worth 50% of your total score
• 30 questions
• No calculator allowed
• 15 questions
• Calculator required

Note that the AP Calculus AB exam has had small changes made to its format. Previously, Part A of the multiple-choice section had 28 questions, and Part B had 17 questions.

Free-Response Section

Here is a rundown of the format of the AP Calculus AB free-response section:

• Six questions total
• One hour 30 minutes total
• Two questions
• Four questions

This can all look a little complicated, but basically, the AP Calculus AB exam consists of four parts. The first two are multiple choice, and the last two are free response.

You are required to use a calculator for the middle two parts (one each for multiple choice and free response), but you may not use a calculator for the first and last parts of the exam.

What Topics Does the AP Calculus AB Exam Cover?

Content on the Calculus AB exam can be divided into three main topic areas, referred to by the College Board as Big Ideas . Within these three Big Ideas are more specific topics called Enduring Understandings (often abbreviated as "EU"). Each Enduring Understanding contains both Learning Objectives and Essential Knowledge that the student should have learned by the time of the exam.

As I mentioned, there have been some updates to the AP Calculus AB exam. Namely, the Big Ideas are now integrated within each of the eight units covered in the AP Calculus AB course.

The good news is that there haven't been any changes to the structure of the AP Calculus AB exam!

I've listed each of the Big Ideas and their Learning Objectives below, since these are the most relevant for students looking for what the exam covers.

For the sake of length and clarity, I left out the Enduring Understandings and Essential Knowledge. If you'd like to see these, as well as more detailed information on the content covered by the exam, check out the official AP Calculus AB Course Description. Still, know that the information below will give you a solid look at what you're expected to know for the exam.

Learning Objectives are listed below Big Ideas. These Learning Objectives are skills that students are expected to know how to do for the exam.

Big Idea 1: Change

• Understand how and when change occurs
• Determine the rate of change
• Interpret how different equations are structurally similar
• Determine change over an interval of time
• Analyze functions for intervals of continuity or points of discontinuity
• Determine the applicability of important calculus theorems using continuity
• Find the rate of change based on the area of a region between a curve and the x-axis
• Model motion not constrained to a linear path

Big Idea 2: Limits

• Understand limits, and making sense of features of functions and their graphs
• Mathematical properties and rules for simplifying and evaluating limits applies to differentiation
• Prove a limit exists
• Recognize the connection between differentiability and continuity
• Interpret the meaning of a derivative within a problem
• Solve problems involving the slope of a tangent line
• Solve problems involving related rates, optimization, and rectilinear motion
• Solve problems involving rates of change in applied contexts
• Solve how the sum if infinitely discrete terms can be a finite value represented in a continuous function.

Big Idea 3: Analysis of Function

• Close loopholes so a conclusion about a function is always true
• Understand how the change of two units of measurement relate to one another, and the rate at which they change.
• Interpret what numbers might tell you about other rates of change
• Apply the Mean Value Theorem to to justify a conclusion
• Include additional information in a sound mathematical argument that optimizes a simple equation
• Integrate to find areas related to differentiating to find slopes
• Calculate derivatives and antiderivatives
• Evaluate definite integrals
• Analyze graphs defined using parametric equations or polar functions using chain rules.
• Apply definite integrals to problems involving the average value of a function, motion, and area and volume.
• Analyze differential equations to obtain general and specific solutions
• Interpret, create, and solve differential equations from problems in context

AP Calculus AB Units

Since the Big Ideas of AP Calc AB are covered throughout the course, it's also useful to know what each unit covers.

In the table below, you'll find each of the course's units, along with a brief description of the topics covered in that unit. We've also included the weighted breakdown of questions on the AP Calc AB exam that come from each unit. So for example, 10-12% of your exam grade will come from questions about Limits and Continuity, while 17-20% of your exam grade will come from questions about Integration and Accumulation of Change.

Knowing the topics covered in AP Calc AB, along with how they factor into your AP exam score, will help guide your studying and make it more productive!

Also, keep in mind there's a lot more to know about these units and unit topics . For more information, be sure to check out the official AP Calculus AB Course Guide provided by the College Board.

AP Calculus AB Sample Questions

Looking at sample questions is one of the best ways to get a feel for what the AP Calculus AB exam will be like. Here are four sample questions, one from each part of the AP exam. Each of these questions was taken from the official AP Calculus AB Course Description , which you can look at for more complete answer explanations and additional sample problems.

Multiple Choice (No Calculator)

This question tests your ability to calculate derivatives. You'll need to use the chain rule to differentiate composite functions. The correct answer to this problem is B.

Multiple Choice (Calculator Allowed)

This question tests your ability to solve problems with rapid rates of change. You'll have to find the derivative in order to find the rate of change of the temperature of the water. The correct answer is B.

Free Response (Calculator Allowed)

This question tests your knowledge of integrals. Parts A, B, and C are each worth 3 points.

Free Response (No Calculator)

This question tests your knowledge of multiple topics, including derivatives and integrals. You can receive up to 1 point for part A, 2 points for part B, and 3 points each for parts C and D.

How Is the AP Calculus AB Exam Scored?

As mentioned, the multiple-choice section and the free-response section are each worth 50% of your total exam score.

For the multiple-choice section, you earn 1 point for each question you answer correctly. No points are deducted for incorrect answers, so you should answer every question! You can earn up to 45 points for this section.

For the free-response section, each of the six questions is worth 9 points, so you can earn up to 54 points. Different parts of each question can be worth a different amount of points (for example, on one question you may be able to earn up to 1 point for part A, 3 points for part B, 3 points for part C, and 2 points for part D).

After your points are added up for each of your sections, your AP Calculus AB score is converted to the standard AP scoring scale of 1-5 . The exact formula for doing this can change slightly from year to year.

However, in 2008, the process for converting raw AP scores to scaled scores involved multiplying the number of multiple-choice questions you answered correctly by 1.2272, and then adding that number to the points you received on the free-response section. This value is rounded to the nearest whole number and becomes your composite score.

Each AP score (from 1-5) corresponds to a range of composite scores. Below, you can see the conversion chart and score distributions for test takers from the 2020 Calculus AB exam :

Source: The College Board

3 Tips for Preparing for the AP Calculus AB Exam

Studying for the AP Calculus AB exam can be tough. Use these three tips to make your studying more effective and increase your chances of getting a great score.

Tip 1: Memorize Important Formulas

There are certain formulas for AP Calculus AB that you should have down pat. There's no formula sheet given on the AP exam, so you'll have to memorize the formulas you'll need. Many teachers give out formula sheets for students to memorize.

There are also various formula cheat sheets you can use to review before the exam. To find these, simply Google "AP Calculus AB formula sheet" and look at your options.

In general, any formula you use regularly in class is a good one to memorize. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems.

Tip 2: Know How to Use Your Calculator

You're allowed to use your calculator for two of the four exam parts, and most of the questions in these two sections will be difficult, if not impossible, to solve without a graphing calculator.

While it might seem obvious that you should know how to work your calculator, knowing exactly how and when to use its different functions can save you a lot of time on the exam and increase your chances of getting the correct answer.

According to the College Board, the four calculator capabilities you'll use the most during the AP Calculus AB exam and should easily be able to do with your calculator are as follows:

• Plot the graph of a function within an arbitrary viewing window
• Find the zeros of functions (solve equations numerically)
• Numerically calculate the derivative of a function
• Numerically calculate the value of a definite integral

When you're preparing for the exam, be sure that you know how to do each of these (completing practice problems can help!).

Tip 3: Get Used to Showing All Your Work

For most free-response questions on the AP Calculus AB test, the final answer to a problem is only worth 1-2 points out of a possible 9. This means that the majority of points are earned through intermediate steps of the problem —and if you don't show how you reached those intermediate steps, you won't get a high score on this section.

Even if you get a correct answer by using your calculator, you have to write the setup (such as the equation being solved or the derivative being evaluated) as well as the answer in order to get credit for your work.

You might be used to not writing down certain work that seems particularly obvious on homework and class tests. However, even if your teacher doesn't mind, AP graders will.

Remember that AP graders are more interested in how you reached your final answer than they are in what that final answer is, so get yourself in the habit of showing each step of your work well before exam time.

Conclusion: What to Know About the AP Calculus AB Exam

The AP Calculus AB exam can be intimidating if you don't know what to expect. Knowing how the exam will be formatted and what types of questions it will ask can go a long way toward helping you feel more prepared and confident on test day.

The exam has two sections, multiple-choice and free-response, which are each divided into two parts, based on whether or not you may use a calculator. Each of these sections is worth 50% of your total AP score.

The exam itself covers three main topics:

• Derivatives
• Integrals and the Fundamental Theorem of Calculus

In order to prepare for the AP Calculus AB exam in the best way, keep these three tips in mind during your review:

• Memorize important formulas
• Know how to use your calculator
• Get used to showing all your work

What's Next?

Now that you know what the AP Calculus AB exam covers, the next step is to practice! Read our guide to get links to every Calculus AB practice test available online .

Wondering how challenging other AP classes are? Learn what the easiest AP classes are and what the hardest AP classes are so that you know exactly what to expect!

Not sure which other math classes you should take? Math is often the trickiest school subject to choose classes for, but our guide will help you figure out exactly which math classes to take for each year of high school .

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.

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AB Calculus Manual (Revised 12/2019)

In addition to the Essentials section of the manual that provide complete coverage of all topics for the AB exam, there is a Non-Essentials section as well that givers topics that are relevant to AB calculus but not on the actual AP ® exam. There is also a Review section that goes over the most common algebraic concepts that give students trouble.

This manual can easily replace an expensive textbook. Teachers teach right from it and students write in it.

The Solution Manual is exactly the same as the student manual except that the solutions with all important steps are shown. There is a one-to-one relationship between the pages of the student manual and the solution manual. So, for example, page 73 will have a series of problems and blank space for the students to write in the solutions. The solution manual's page 73 will have the same problems but with the solutions shown.

In addition, a set of answer pages (no shown work, just the answer) comes with the solution manual for the homework problems.  It is also available in download form as a stand-alone product.

New!  A new student section has been written called Calculus from 30,000 feet . Borrowed from Steven Strogatz's book Infinite Powers , this addendum is meant to be used after the AP exam and gives students a greater insight into how the Infinity Guideline breaks down comples probems into simper ones and then reassembles them. No homework or problems - just an attempy to see the Calculus forest from the trees.

School administrations are increasingly concerned with standards. This material in this manual is aligned to the AP ® standards as defined in the their 2019 document: AP ® Calculus AB and BC Course and Exam Description available on the website: www.apcentral.collegeboard.org. Although this is included with purchase of the AB Solutions in any format, you can download information about the standards at: AB Standards :

LET ME HELP YOU TEACH YOUR CLASS!

Because of the devastating impact to our way of life because of COVID-19, schools are in a particularly difficult position. It is still up in the air how safe they can be for the students but, no matter what,  classes have to be taught be adults. And those who teach courses like AP calculus are more likely to have years of experience, may be older and simply have to take fewer risks. For a number of schools and communities, the virtual classroom is the safest for everyone.

With that in mind, I have put together YouTube Videos that will teach your class the basic concepts of AP calculus. What is most exciting is that these will follow the classwork section of the AP Calculus manual. Students can download (for free) and print the AB manual student pages. They can download the video for each section and have thorough explanations of just about all the problems in the classwork section.  They can stop the video and write in solutions in their printed student manual. They can replay any section to better understand the steps. If they have questions, they can write them down and when you "meet" with them, you can help clear up their confusion.

They are narrated by me and the style is the same as if I were teaching a class. I show the thought process involved in solving calculus problems. The solutions are the same that appear in the solution manual, but these are explained audibly as well.  Unlike other math videos, you will not see me taking time to write solutions. They appear on the screen instantly and are legible and professional.   Videos will range from 10 minutes to 45 minutes depending on their complexity. Some of the more involved concepts are split into two videos, similar to what you would do when teaching - take several days to cover a topic.  When you "meet" with the students, you can then concentrate on the homework problems.

This is a huge but very exciting undertaking. These videos took time to construct, usually one every two days.  All the videos in the AB Essentials and Non-Essentials sections are complete, as well as the Precalculus Review . There is close to 24 hours of instruction.

I suggest that you first view the introduction video to understand how the YouTube videos coordinate with the manual. Then view several of the videos to get a feel for them. Feel free to direct students to this page so that they can download them directly. Have them feel free to make comments (keeping them clean!) for each video. And of course if there is a mistake or I didn't make something clear enough or if they have a question, they can mention that in the comment or, ask you or me directly.

Here is my YouTube channel:

https://www.youtube.com/channel/UC-y4_ldufRdVd5r_CuCzDCQ

• AB Multiple Choice Exam Prep
• AB Free Response Exam Prep
• BC Multiple Choice Exam Prep
• BC Free Response Exam Prep
• Diving In to AP ® Calculus
• AB Step by Step
• BC Step by Step
• AB Calculus Exams & Quizzes
• BC Calculus Exams & Quizzes
• Calc AB Manual
• Calc BC Manual
• Combined AB/BC Calc Manual
• AB Calculus Powerpoints
• BC Calculus Powerpoints
• Calculus OnTheWall Intro Video
• Calculus Jeopardy
• Calculus Across & Down
• Word Search Poster
• Test Your Strength: AB Version
• Test Your Strength: BC Version
• Test Your Strength: Precalc
• Math Wars AB
• Math Wars BC

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Ultimate Guide to the AP Calculus AB Exam

What’s covered:, what does the ap calculus ab exam cover, sample ap calculus ab exam questions, ap calculus ab exam score distribution, average score, and passing rate, tips for preparing for the exam, how will your ap scores affect your college chances.

AP Calculus is a popular course for high schoolers, particularly those planning to pursue a college education. Hundreds of thousands of high schoolers each year study to obtain a passing/high score on the AP Calculus AB Exam so that they can “test out” of math distribution requirements in the early university years, saving them time and money.

In 2022, over 250,000 of the 1.2 million students taking AP exams took the AP Calculus AB exam. This places it among the top 4 most popular AP exams. If you are interested in taking the AP Calculus AB exam, whether you have taken the class or are planning to self-study, read on for a breakdown of the test and advice on how to best prepare for it.

The purpose of the AP Calculus AB exam is to test your knowledge of specific “big concepts” that you have learned either through taking the AP Calculus AB course or through self-study.

The “big concepts” of AB Calculus, as defined by College Board, are:

• Derivatives
• Integrals and the Fundamental Theorem of Calculus

With regard to limits, students should be comfortable with computing limits, including one-sided limits, limits at infinity, the limit of a sequence, and infinite limits. The exam will also test each student’s ability to estimate the limit of a function at a point and apply limits to understand the behavior of a function near a point.

With regard to derivatives, students should be comfortable with finding the slope of a tangent line to a graph at a point and using a graph to determine whether a function is increasing or decreasing. Students should also be able to find concavity and find extreme values. Additionally, the exam will require students to solve problems involving rectilinear motion.

Finally, with regard to integrals, students should be able to use various techniques and methods to approximate an integral. Students should also be familiar with area, volume, and motion applications of integrals, as well as with the use of the definite integral as an accumulation function.

How Long Is the AP Calculus AB Exam? What Is the Format?

The AP Calculus AB exam is one of the longest AP exams, clocking in at three hours and 15 minutes. It has two sections. The first section contains 45 multiple choice questions, spans one hour and 45 minutes, and accounts for 50% of your total score. The second section consists of six free response questions, spans one hour and 30 minutes, and accounts for the remaining 50% of your score.

Each section is divided into two parts, Part A and Part B. Students are permitted to use calculators during one part and not allowed to use them during the other.

Can I Use a Calculator?

While taking the AP Calculus AB exam, you may use a scientific calculator on Part B of the multiple choice section and on Part A of the free response section. Your calculator should be able to plot the graph of a function within an arbitrary viewing window, find the zeros of functions, numerically calculate the derivative of a function, and numerically calculate the value of a definite integral. More information and a list of acceptable calculator models can be found in the official Calculator Policy .

Multiple Choice: Section I, Part A

Note: A calculator may not be used on questions on this part of the exam.

(D) nonexistent

Multiple Choice: Section I, Part B

Note: A graphing calculator is required for some questions on this part of the exam.

At what values of x does f have a relative minimum on the interval 0 < x < 3?

(A) 1.094 and 2.608

For -5 < x < 5, on what open intervals is the graph of g concave up?

(A) -5 < x < -1.016 only

(B) -1.016 < x < 5 only

(C) 0.463 < x < 2.100 only

(D) -5 < x < 0.463 and 2.100 < x < 5

Free Response: Section II, Part A

Note: A graphing calculator is required for problems on this part of the exam.

(A) Find the area of S .

(B) A solid is generated when S is revolved about the horizontal line y = 5. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid.

(C) Region R is the base of an art sculpture. At all points in R at a distance x from the y -axis, the height of the sculpture is given by h(x) = 4 – x . Find the volume of the art sculpture.

Free Response: Section II, Part B

Rochelle rode a stationary bicycle. The number of rotations per minute of the wheel of the stationary bicycle at time t minutes during Rochelle’s ride is modeled by a differentiable function r for 0 ≤ t ≤ 9 minutes. Values of r(t) for selected values of t are shown in the table above.

(A) Estimate r’ (4). Show the computations that lead to your answer. Indicate units of measure.

(B) Is there a time t , for 3 ≤ t ≤ 5 at which r(t) is 106 rotations per minute? Justify your answer.

While many exam distributions fall along a bell curve, with the majority of students receiving a score of 3, the AP Calculus AB exam shows a flatter distribution. Simply put, many students do well and many students do poorly. In 2022:

• 20.4% of test-takers received a 5
• 16.1% of test-takers received a 4
• 19.1% of test-takers received a 3
• 22.6% of test-takers received a 2
• 21.7% of test-takers received a 1

This means that 55.6% of students who took the exam received a 3 or higher (typically considered passing).

Note: The credit you will receive for AP exam scores varies widely from school to school. For example, prestigious schools (and even prestigious programs at schools) might accept only a 4 or a 5 to receive course credit. Though a score of 3 is typically considered passing, it’s not always enough. You can use this search tool to see what scores will allow you to receive credit at a specific college or university.

Step 1: Assess Your Skills

Take a practice test to assess your initial knowledge of the material. It’s important to know where you are, so that you know how far you need to go.

Keep in mind that Calculus is an age-old study, so you can use practice tests from before you were even born and you’ll be assessing/learning just the same!

There are a couple of options for taking practice tests:

• Print a practice exam and self-proctor
• Use a diagnostic test offered through a commercial study guide
• Talk to your teacher about proctoring a practice exam after school or over the span of a few lunch periods

The 2012 exam has been openly published by the College Board and might be a good place to start. The College Board also has free response questions from the last few decades published online, though you should note that these are not complete assessments.

Once you have taken your formative assessment, score it to identify the areas you already understand and those in need of improvement.

Note: When grading the free response portion of the exam, make sure you grade yourself based on the rubric! Act like you are an AP scorer, scrutinizing and nitpicking every portion of your answer. The little points add up, and your area of improvement could very well be “needing to show my work.”

Step 2: Study the Material

After taking your assessment, you should be able to identify areas that need improvement. These areas could be related to content—not knowing which technique should be used to approximate which type of integral or not understanding the relationship between concavity and limits on a graph. Alternatively, the areas you struggle with might have more to do with form—like struggling to read graphs or conceptualize tables.

Identify your areas for improvement, write them down, and focus on one area during each study session. Look over your mistakes and put in the work to understand them. Watch videos online about specific concepts, read sections in books about them, and talk to your friends and classmates about them.

Then do it again and again and again until the areas you struggle with become areas you excel in.

Some students choose to use commercial study guides when studying. This can be extremely beneficial, depending on your learning style. That said, if you choose to use a commercial study guide, use it in conjunction with your initial assessment. Study books are divided into sections organized around both big and small concepts. Don’t get stuck reading a guide front to back and don’t waste time on content that you have already mastered!

Lastly, you might consider looking into the free resources that are available online! For decades, AP teachers have been publicly posting complete study guides, review sheets, and test questions. Use these for your benefit.

Step 3: Practice Multiple Choice Questions

Once you feel like you’ve mastered the concepts you initially struggled with, put them into action by answering some multiple choice practice questions.

The College Board provides a set of sample questions with scoring explanations . Additionally, the College Board Course Description includes many practice multiple choice questions along with explanations of their answers. As you go through these, try to keep track of which areas are still tripping you up, and go over those concepts again until you have a better grasp on them. Focus on understanding what each question is asking and keep a running list of any vocabulary that is still unfamiliar to you.

Step 4: Practice Free Response Questions

When you score your own formative assessment, you will notice that every step you take to arrive at a solution to a free response question must be clearly notated for the exam reader. Even if you use your calculator to solve an equation, compute a numerical derivative, or find a definite integral, write the equation, derivative, or integral first. Otherwise, you can lose little points—and little points add up!

The free response portion of the AP Calculus AB exam tests your ability to solve problems using an extended chain of reasoning. In most cases, an answer without supporting work will receive no credit. This means that, as you answer practice free response questions, you are not just practicing getting the right answer, but getting the right answer in the right way!

You can get a better understanding of the free response section’s scoring by reading scoring commentary from the Development Committee and authentic examples of student responses and their scoring explanations from previous exam administrations.

Step 5: Take Another Practice Test

Every couple of weeks, when you are feeling confident or when you just want to see your progress, we recommend that you take another complete practice test. This will allow you to see which areas have improved the most and which areas still need improvement. Taking new practice tests at some interval will serve as a progress report of sorts.

Step 6: Exam Day Specifics

In 2023, the AP Calculus AB Exam will be administered on Monday, May 8 at 8 AM local time.

For complete registration instructions, check out CollegeVine’s guide: How to Register for AP Exams (Even If You Didn’t Take the Class) .

For information about what to bring to the exam, see CollegeVine’s post: What Should I Bring to My AP Exam (And What Should I Definitely Leave at Home)?

While AP scores are not required when applying for college, they can be a way for high-performing students to set themselves apart, particularly when applying to prestigious universities. Through the process of self-reporting scores , you can show your hard work and intelligence to admissions counselors.

That said, the main benefit of scoring high on AP exams comes once you land at your dream school, as high scores can allow you to “test out” of entry-level requirements, often called GE requirements or distribution requirements. This will save you time and money.

If you’re starting to think about what schools you should apply to, we recommend that you use CollegeVine’s free chancing engine . This tool will consider your test scores, GPA, extracurriculars, and more, to calculate your chances of acceptance at various schools and to help you decide where to apply.

Once you know which schools you are applying to, you can use the  College Board’s search tool to see what score you should strive for on the AP Calculus AB exam.

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Advanced Placement

The Complete Guide to AP Calculus AB Exam [Updated for 2024]

Written by Apoorvaa Agarwal

• The AP Calculus AB course is organized into 4 topics : Limits and Derivatives, Applications of Differentiation, Integration, and Applications of Integration. 
• The AP Calculus AB exam is divided into two sections: multiple-choice (45 questions, 1 hour 45 minutes) and free-response (6 questions, 90 minutes).
• The mean score for the AP Calculus AB exam in 2021 was 2.91 out of 5 . This is slightly lower than the mean score for AP Calculus BC in 2021, but it is still higher than the mean score for all AP subjects in 2021. 
• The pass rate of the AP Calculus AB Exam for 2021 was 55.7% . This is slightly lower than the pass rate for AP Calculus BC in 2021, but it is still higher than the pass rate for AP overall. 
• With AP Calculus AB, some majors that you could choose from include mathematics, engineering, and economics . Some career pathways you could pursue include mathematician, engineer, economist, and data scientist .

Struggling with your AP Calculus AB exam preparation? Finding concepts such as limits, derivatives, and integrals challenging? Don’t worry, you’re not alone. The AP Calculus AB exam is known for its rigorous content.

The pass rate for the AP Calculus AB exam was 55% and the mean score for the same in 2022 was 2.91 out of 5 . The subject was given a difficulty rating of 5.5 out of 10 by class alumnae on a reddit survey.

This comprehensive guide is designed to provide you with the tools, strategies, and practice materials necessary to navigate through the exam confidently.

The blog aims to equip learners with the necessary tools and knowledge to succeed in the AP Calculus AB exam .

Need help learning AP Calculus AB? Find an expert 1-on-1 online  AP Calculus AB tutor  from Wiingy and give your grades a boost!

What is the AP Calculus AB exam?

AP Calculus AB is an introductory-level calculus course that prepares students for further study in mathematics, science, engineering, and other quantitative fields.

The exam is designed to give students a chance to showcase their proficiency in calculus and earn college credit or advanced placement in related courses.

AP Calculus AB exam format

How long is the ap calculus ab exam.

The AP Calculus AB Exam lasts for a total of 3 hours and 15 minutes and is split into two sections: multiple-choice and free-response.

The multiple-choice section , which is worth 50% of the total score , lasts for 1 hour and 45 minutes and includes 45 questions .

The free-response section also makes up 50% of the total score and lasts for 1 hour and 30 minutes , consisting of 6 questions .

There is a 10-minute break provided after the multiple-choice section for students to use the restroom, eat a snack, or take a break before starting the free-response section.

Topic for AP Calculus AB exam review

The AP Calculus AB exam consists of several critical units, each with a specific weightage assigned to them.

What’s the 2024 AP Calculus AB exam date and time?

The 2024 AP Calculus AB Exam will take place on May 13th, 2024 , which is a Monday , at 8:00 A.M. local time.

When it comes to managing time on the test day, a few pointers should be kept in mind:

• Familiarize yourself with the exam structure and the time allotted for each section beforehand.
• Make a plan for how you will use your time during the exam. This could include setting specific time limits for each question or section.
• Don’t spend too much time on any one question. If you get stuck, move on and come back to it later if you have time.
• Use your breaks wisely to rest, recharge, and refocus for the next section.
• Bring a watch or use the clock in the exam room to keep track of time.
• Stay calm and focused, and trust in your preparation and abilities.

Remember, time management is a crucial part of doing well on the AP Calculus AB Exam. With these tips, you can approach test day feeling confident and prepared.

What is AP Calculus AB equivalent to and who can take it?

AP Calculus AB course is equivalent to a first-semester college calculus course, and students who take the AP Calculus AB exam and score well may receive college credit or advanced placement in calculus courses.

AP Calculus AB is typically taken by high school students who have completed precalculus or an equivalent course and are interested in pursuing a STEM-related major or career.

While there are no specific prerequisites for the course, students should have a solid foundation in algebra, geometry, and trigonometry. 

It’s also important to note that the course requires a significant amount of time and effort, so students should be prepared to dedicate themselves to the material.

Is AP Calculus AB hard?

Is AP Calculus AB hard? According to a survey of former AP Calculus AB students, the course is generally considered to have a moderate level of difficulty , with a rating of 5.5 out of 10.

In 2022, only 55.7% of students who took the AP Calculus AB exam received a score of 3 or higher, which is lower than the pass rates for many other AP exams. 

Despite its level of difficulty, AP Calculus AB remains a popular choice among high school students, with 268,352 students opting to take the course in 2022 . This is likely because it is highly regarded by many selective colleges and universities.

This suggests that the course is quite challenging, but with determination and hard work, students can still succeed on the exam.

According to a survey of over 2,900 students who took various AP exams , AP Calculus AB is considered the 12th most challenging AP course , with 11 other courses being deemed more difficult based on student feedback.

*Source: ExamStudyExpert

Even though other AP courses are perceived as more challenging than AP Calculus AB, it’s important to recognize that these courses are not as commonly taken. For instance, in 2022, only 46,301 students took the AP Physics C – Mechanics exam compared to over 260,000 students who took the AP Calculus AB exam.

So, even if AP Calculus AB is considered to be moderately difficult, it remains a highly popular and well-respected AP course.

How to prepare for the AP Calculus AB exam?

• Feed your brain, ace the exam: Just like our bodies, our brains need fuel to function at their best. Make sure to eat brain-boosting foods such as nuts, fish, and fruits to optimize your study sessions.
• Dress for success: Wearing comfortable clothes can help you feel relaxed and confident during the exam. Avoid tight or uncomfortable clothing that can distract you from your focus.
• Study smart, not hard: Don’t just cram information into your brain without understanding it. Use study techniques such as practice problems, flashcards, and quizzes to reinforce your knowledge and make the most of your study time.
• Take a break, and clear your mind: Taking regular breaks during study sessions can help improve focus and retention. Take a walk, do some stretching, or meditate to refresh your mind and recharge your energy.
• Get a study buddy, conquer the test: Studying with a friend or group can make studying more enjoyable and effective. Quiz each other, work through problems together, and share helpful resources to ace the exam as a team.
• Visualize your success, and achieve your goals: Positive visualization can be a powerful tool for achieving success. Take a few moments each day to visualize yourself acing the exam and achieving your goals. This can help boost confidence and motivation, leading to better performance on test day.

Preparing for the AP Calculus AB exam can be a challenging and demanding process, but there are a variety of resources available to help students prepare for the test.

• Official College Board website with course outlines, practice questions, and past exams
• Textbooks and study guides like “Calculus: Graphical, Numerical, Algebraic” by Finney, Demana, Waits, and Kennedy
• Online resources such as Khan Academy, YouTube videos, and online practice tests.
• Wiingy is a platform that provides personalized one-on-one tutoring with expert tutors who have experience teaching AP Calculus AB and can create a customized study plan for you.
• Study groups and tutoring sessions with classmates or teachers

Remember that every student is different, so finding the right combination of resources that works for you is crucial for exam success. Make use of these resources and develop a study plan that fits your learning style and pace to prepare effectively for the AP Calculus AB exam.

How can Wiingy help with AP Calculus AB exam prep?

In 2022, only 20.4% of the 268,852 students who took the AP AP Calculus AB  exam scored a 5. While 3 is considered the unofficial passing rate, most elite universities, such as Harvard or Princeton, offer AP credit only if you score 5 or higher. 

Getting a 5 is possible if you have the right support in your high school, but that’s rarely the case.

Here at Wiingy, we work with vetted AP AP Calculus AB  tutors with demonstrated expertise and experience in helping students score a 5 on AP exams . 

Unlike tutor marketplaces, every Wiingy tutor is screened individually and undergoes a comprehensive assessment. Less than 3% of applicants are selected to become tutors on Wiingy’s platform, ensuring tutors are highly qualified and experienced in teaching AP courses.

Our tutors will work with you 1-on-1 to master the content and skills you need to succeed. Experienced tutors can provide you with curriculum-specific guides and practice questions and familiarize you with the exam format to help you ace the test.

We know that sometimes you don’t want to pay for private tutoring because it is too expensive. It’s common to see tutoring costs between $100 to $150 per hour. Wiingy’s rates are very affordable, starting from just $28 per hour , much lower than the average AP tutoring offered by other platforms.

One more advantage of studying with us is that we don’t require you to sign up for any packages or yearly subscriptions . You can sign up for as little as a single lesson and add more lessons as per your requirements.

While we try to match you with the perfect tutor as per your needs, we know that sometimes even the best tutors might not be the right fit for you. That’s why we offer you the Perfect Match Guarantee , which means that if you are not satisfied with your tutor for any reason, you can request a free replacement at any time . 

Sign up with Wiingy AP AP Calculus AB  Tutoring today and achieve your goal of scoring a 5 on your AP Test ! 

In conclusion, the AP Calculus AB exam, encompassing various units such as limits, derivatives, integrals, and applications of calculus, presents a significant challenge.

While the pass rates and mean scores of the AP Calculus AB exam have shown a slight decline over the years, with the pass rate being 61.4% in 2020 and 55.7% in 2022 , and the mean scores being 3.07 and 2.91 respectively , its important to approach the exam with dedication and focused preparation.

With a difficulty rating of 5.5 out of 10 , allocating sufficient time to study each unit thoroughly and practicing with a variety of problems is essential.

The 2024 AP Calculus AB Exam will take place on May 13, 202 4, which is a Monday , at 8:00 A.M. local time. And will comprise of both multiple choice and free response questions of 1 hour 30 minutes each.

Frequently asked questions (FAQs)

How many questions are on the ap calculus ab exam.

The AP Calculus AB exam has 51 questions in total. The exam is divided into two sections: Section I contains 45 multiple-choice questions, and Section II contains 6 free-response questions. The entire exam is 3 hours and 15 minutes long.

Can I self-study AP Calculus AB?

If you are confident about it then yes it is possible to self-study for the AP Calculus AB exam. However, it is important to note that the course covers a lot of material and requires a strong foundation in algebra and precalculus. Therefore, self-studying for the exam may require a significant amount of time and effort.

The AP Calculus AB exam is approximately 3 hours and 15 minutes long. The exam is divided into two sections: Section I contains 45 multiple-choice questions that must be answered within 1 hour and 45 minutes, while Section II contains 6 free-response questions that must be completed in the remaining 1 hour and 30 minutes.

Should I take AP Calc AB or BC?

The decision to take AP Calculus AB or BC depends on your math background, future academic plans, and personal goals. AP Calculus AB covers the basics of calculus, including limits, derivatives, integrals, and applications of calculus. AP Calculus BC builds on these concepts, adding topics such as sequences and series, parametric equations, and polar coordinates.

Which is more difficult, AP Calculus AB or BC?

AP Calculus BC is generally considered to be more difficult than AP Calculus AB because it covers more advanced topics such as infinite series, parametric equations, and polar functions. AP Calculus AB is a bit more straightforward and focuses on basic concepts such as limits, derivatives, and integrals. However, this does not mean that AP Calculus AB is easy. It is still a challenging course that requires a strong foundation in algebra and trigonometry.

 References

• https://apcentral.collegeboard.org/courses/ap-calculus-ab/exam
• https://www.princetonreview.com/college-advice/ap-calculus-ab-exam
• https://www.bestcolleges.com/resources/ap-calculus-ab/
• https://collegeprep.uworld.com/ap-calculus-ab/exam-information/
• https://reports.collegeboard.org/media/pdf/2021-ap-student-score-distributions_1.pdf
• https://apcentral.collegeboard.org/media/pdf/ap-score-distributions-by-subject-2022.pdf

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