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AP Calculus: A Complete Guide

AP Calculus: A Complete Guide

10 min Read|January 29 2024
|Written by:

George Christofi


Are you ready to dive into the world of AP Calculus, but feeling a bit overwhelmed about where to start? AP Calculus, encompassing the challenging yet rewarding AB and BC courses, isn't just another high school math class. It's a critical stepping stone to advanced concepts essential in science, engineering, and beyond. This isn't just about solving equations; it's about unlocking a new way of thinking.

This complete guide is your compass through the intricacies of College Board's AP Calculus. It's packed with insights on navigating the rigorous curriculum and mastering the exams. Are you a math whiz or a curious learner aiming to stretch your abilities? Either way, AP Calculus is your arena to explore, conquer, and excel. Get ready to transform not just your math skills, but also to opening doors to endless academic and career possibilities.

Why Study AP Calculus?

Studying Calculus, particularly at the AP level, offers several key advantages that extend beyond just academic enrichment:

  • Critical Thinking and Problem-Solving Skills: Calculus enhances your ability to think logically and solve complex problems, skills highly valued in various fields.
  • Foundation for Advanced Studies: It provides a crucial foundation for further study in science, engineering, economics, and finance.
  • College Preparedness: Excelling in AP Calculus demonstrates readiness for college-level coursework, often a significant factor in college admissions.
  • Career Opportunities: A strong background in calculus opens doors to high-demand careers in technology, research, and data analysis.
  • AP Credits: Achieving a high score can lead to college credits, potentially saving time and money in your college journey.

By mastering Calculus, students not only gain substantial mathematical knowledge but also develop a skill set that benefits them in their academic and professional futures.

Here is what an expert AP Calculus tutor has to say:

"I have found that AP Calculus proved to be a strong subject that helps students develop a strong basic foundation that allows students to perform well in fields such as Science, Technology, Engineering and Mathematics (STEM)."

Understanding the Differences: AP Calculus AB vs. BC

Choosing between AP Calculus AB and BC can be pivotal in a student's academic journey, as each offers a unique scope and depth:

Curriculum Coverage: AP Calculus AB is akin to a first-semester college calculus course, focusing on introductory calculus concepts. In contrast, AP Calculus BC covers not only the complete AB curriculum but also additional topics equivalent to a second-semester college calculus course.

Additional Topics in BC:

  • Techniques of Integration
  • Euler's Method in Differential Equations
  • Arc Length
  • Parametric, Polar, and Vector Functions
  • Infinite Sequences and Series

Exam Weightage: The weightage of topics in the exam differs, of course, with BC having a broader distribution due to its additional content.

Exam weightages for AP Calculus AB and AP Calculus BC

Image showing exam weightages for AP Calculus AB and BC

Understanding these differences is crucial for students to align their class selection with their academic goals and preparation level. Both courses demand a strong foundation in mathematics but differ in their depth and breadth of calculus concepts covered.

Is AP Calculus Hard?

The perceived difficulty of AP Calculus AB and BC is best understood by examining the performance statistics:

AP Calculus-AB and AP-Calculus BC grades in 2023

Graph showing grades distribution for AP Calculus AB and BC in May 2023

AP Calculus AB

  • Total Students: 273,987
  • Mean Score: 2.99
  • Scoring 5: 22.4%
  • % Scoring 3 or Higher: 58%

This suggests a fair level of success among students, indicating that with dedication and effective study, excelling is achievable.

AP Calculus BC

  • Total Students: 135,458
  • Mean Score: 3.75
  • Scoring 5: 43.5%
  • % Scoring 3 or Higher: 78.5%

The high percentage of students scoring a 5 reflects the depth of understanding required to complete course well, yet also showcases the potential for high achievement.

Note: There is no formula sheet provided for the AP Calculus AB or BC exams.

Students are expected to know and be able to recall all the concepts and formulas covered in the AP Calculus courses. A strong understanding of the underlying mathematics is essential for success in these exams, and students are encouraged to frequently apply the formulas in practice problems to aid in memorization and comprehension. Despite the challenges, these statistics reveal that students can and do excel in AP Calculus. Success hinges on a strong foundation in mathematics, effective preparation strategies, and consistent effort throughout the course.

Dr Zhen Shao, a PhD Mathematics lecturer at the University of Oxford, says:

"Study right, manage your time, use good resources and even try out tutoring if you want to - getting a 5 in AP Calculus AB or BC is totally doable. It's not as hard as you think!"

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What is Covered in AP Calculus?

AP Calculus, encompassing both AB and BC courses, is a comprehensive exploration into the world of calculus, tailored to high school students aspiring to grasp college-level concepts.

AP Calculus AB

  • Understanding limits, continuity, and derivatives.
  • Exploring differentiation and its real-world applications.
  • Delving into integration, focusing on the Fundamental Theorem of Calculus.
  • Applying integration in various analytical and contextual scenarios.
AP Calculus AB course curriculum

Table showing AP Calculus AB course curriculum

AP Calculus BC

Expands on AB topics further such as:

  • Advanced techniques and applications in integration.
  • Detailed study of sequences and series.
  • Introduction to parametric, polar, and vector functions.
  • Image showing AP Calculus BC course curriculum
AP Calculus BC course curriculum

Table showing AP Calculus BC course curriculum

These courses not only deepen a student's mathematical understanding but also prepare them for advanced studies in various fields.

AP Calculus Exam Format

The AP Calculus AB and BC exams have a consistent format that includes both multiple-choice and free-response sections, accounting for equal parts of the total exam score.

AP Calculus AB Exam Format

Section I: Multiple Choice (50% of Exam Score)

  • 45 Questions in total
  • Part A: 30 questions, 60 minutes, no calculator
  • Part B: 15 questions, 45 minutes, graphing calculator required

Section II: Free Response (50% of Exam Score)

  • 6 Questions in total
  • Part A: 2 questions, 30 minutes, graphing calculator required
  • Part B: 4 questions, 60 minutes, no calculator

AP Calculus BC Exam Format

  • The format is identical to that of the AP Calculus AB exam, with the same distribution of multiple-choice and free-response sections, time allocations, and calculator policies.

In both exams, the questions encompass a range of topics and require a mix of procedural and conceptual understanding, often integrating real-world scenarios or applications.

Should I take AP Calculus AB or BC?

Choosing between AP Calculus AB and BC depends on your mathematical background, college aspirations, and comfort with complex concepts:

  • Mathematical Foundation: AB is suitable if you have a solid but basic understanding of pre-calculus. BC is better if you're more confident in your math skills and have excelled in previous calculus courses.
  • College Credits and Placement: BC might offer more college credit opportunities due to its advanced content.
  • Career and Major Considerations: If you're aiming for a STEM field, BC might give you a stronger foundation.
  • Time and Effort: BC covers all AB topics and more, requiring more study time and effort. Consider your overall academic workload.

Ultimately, choose AB if you want a thorough understanding of fundamental calculus, or opt for BC if you’re seeking a more challenging curriculum that covers a wider range of topics.

AP Calculus AB and AP Calculus BC exams taken statistics

Graph showing statistics for AP Calculus AB and BC exams taken over the years

Effective Study Strategies for AP Calculus

Mastering AP Calculus requires a strategic approach to studying. Here are some effective strategies:

  • Review Essential Concepts: Revisit foundational calculus concepts like limits, derivatives, and integrals regularly. Understanding these basics is crucial for tackling more complex problems.
  • Practice Regularly: Engage in consistent practice to reinforce conceptual understanding and develop problem-solving skills. Tackle a variety of problems to become comfortable with different question types and scenarios.
  • Time Management: Develop a study schedule and set clear goals for each session. Focus on challenging topics while maintaining strengths in areas you're confident in. Using techniques like the Pomodoro Technique can enhance focus and productivity.
  • Simulate Test Environment: Practice under exam-like conditions to adapt to time constraints and exam pressure. This helps in improving speed and accuracy.
  • Seek Feedback: Constructive feedback from teachers, AP tutors, or study groups can provide insights into areas needing improvement.

These strategies not only enhance understanding and problem-solving skills but also build confidence, crucial for excelling in AP Calculus exams.

What is a Good AP Calculus Grade?

Defining "good" AP grades in Calculus depends on several factors, including individual goals and college aspirations. Generally, AP exams are scored on a scale of 1 to 5:

  • Score 5: Extremely well qualified
  • Score 4: Well qualified
  • Score 3: Qualified

Scoring a 4 or 5 often makes students eligible for college credit or advanced placement at many universities, which can be a significant advantage. These scores demonstrate a high level of understanding and mastery of the subject matter. However, even a score of 3 is considered passing and can also be beneficial for college applications, as it shows that a student has challenged themselves with rigorous coursework. Ultimately, what constitutes a good grade will vary depending on the specific requirements and policies of each college or university.

Best AP Calculus Resources

Finding the right resources is key to succeeding in AP Calculus. Here are some of the best tools and materials to aid in your preparation:

  • Study Notes: Using study notes from a good source can certainly boost your performance in an AP Calculus exam and help you achieve a very high score.
  • Textbooks and Review Books: Books like Barron’s AP Calculus, Princeton Review AP Calculus AB Premium Prep and Princeton Review AP Calculus BC Prep offer in-depth reviews, practice tests and exercises, and exam strategies.
  • Online Platforms: Advanced Placement's YouTube playlist provides comprehensive lessons and practice exercises for both AP Calculus AB and BC.
  • Official Practice Materials: The College Board's AP Classroom offers valuable resources, including answers to past exam questions and scoring guidelines.
  • Interactive Learning Tools: Tools like Wolfram Demonstrations offer interactive classroom simulations to understand abstract concepts better.
  • Practice Tests: Regular practice tests, available on various platforms online, help familiarize you with the exam format and question types.

Utilizing a combination of these resources can significantly enhance your understanding and performance in AP Calculus.

How to Get a 5 in AP Calculus?

Scoring a 5 on the AP Calculus exam requires a combination of thorough understanding, strategic preparation, and consistent practice. Here are some key steps to achieve this top score:

  • Understand the Fundamentals: Master the core concepts of calculus. Solid understanding of limits, derivatives, integrals, and their applications is essential.
  • Practice Regularly: Solve a variety of problems regularly. This not only reinforces concepts but also improves problem-solving speed and accuracy.
  • Use High-Quality Study Notes: Utilize reputable textbooks and online resources for in-depth study and practice.
  • Take Practice Exams: Regularly taking full-length practice exams helps familiarize you with the exam format and time constraints.
  • Focus on Weak Areas: Identify and spend extra time strengthening your weaker topics.
  • Learn Time Management: Practice completing questions and sections within the allotted time to improve your time management skills during the exam.
  • Consider AP Tutoring: Expert AP Calculus tutors can help you achieve a perfect score of 5. They have abundant experience and can teach you every step of the way on how to achieve your goals.

Getting a score of 5 is about understanding calculus deeply and being able to apply it effectively under exam conditions. Remember, consistent effort and a well-planned study strategy are key to excelling in AP Calculus.

University and Career Opportunities with AP Calculus

Excelling in AP Calculus opens a plethora of opportunities in both university admissions and future career paths:

  • College Admissions: A strong performance in AP Calculus is highly regarded in college admissions, showcasing your ability to excel in rigorous academic subjects.
  • Advanced Placement and Credits: Scoring well may earn you college credits or the ability to skip introductory courses, giving you a head start in your college education.
  • STEM Fields: AP Calculus is fundamental for STEM (Science, Technology, Engineering, Mathematics) majors, providing a strong foundation for advanced studies in these areas.
  • Problem-Solving Skills: The analytical and problem-solving skills developed are highly valued in various fields, including finance, economics, engineering, and technology.
  • Career Opportunities: Proficiency in calculus is crucial for careers in research, data analysis, actuarial science, and more, where mathematical modeling and analysis are key.

Thus, success in AP Calculus not only enhances your academic profile but also equips you with critical skills for a wide range of high-demand careers.

Common Mistakes to Avoid in AP Calculus

Succeeding in AP Calculus involves not only understanding the material but also avoiding common pitfalls:

  • Overlooking the Basics: A strong grasp of fundamental concepts is crucial. Neglecting them can lead to difficulties in understanding more complex topics.
  • Poor Time Management: Not allocating enough time for practice or struggling with time during the exam are common issues. Regular timed practice can help.
  • Calculator Dependency: Over-reliance on calculators can be detrimental. Ensure proficiency in solving problems manually, especially for sections where calculators are not allowed.
  • Neglecting to Practice Free-Response Questions: Many students focus solely on multiple-choice questions. However, practicing free-response questions is essential for understanding how to structure and present your answers.
  • Ignoring Exam Format and Instructions: Familiarize yourself with the exam's structure and follow instructions carefully to avoid losing easy marks.

By being aware of and actively working to avoid these mistakes, students can enhance their preparation and performance in AP Calculus.

Conclusion on AP Calculus

AP Calculus, whether AB or BC, stands as a rigorous but immensely rewarding course that lays the foundation for numerous academic and career paths. Excelling in this course not only enhances college applications but also prepares students for a diverse range of STEM fields. The skills developed in AP Calculus, such as problem-solving and analytical thinking, are invaluable in various professional sectors. Remember, the journey through AP Calculus is as enriching as it is demanding, offering students the chance to develop skills that will benefit them far beyond their high school years.


Is AP Calculus harder than regular calculus?

Yes, AP Calculus AB or BC are generally considered more challenging than regular high school calculus. The difference lies in the pace and depth of the material covered. AP Calculus moves faster and delves deeper into calculus concepts, providing a more rigorous and comprehensive understanding of the subject. This makes it more demanding than a regular high school calculus course, which tends to cover the basics at a slower pace. The decision to choose AP Calculus AB or BC over regular calculus often depends on a student's readiness for a faster-paced and more in-depth study of calculus.

What grade is a 5 on AP Calc?

A score of 5 on the AP Calculus exam is considered equivalent to an A+ or A grade in a corresponding college course. This score represents an "Extremely well qualified" level of performance, indicating a high level of understanding and mastery of the subject matter. It's the highest score on the AP scale and reflects exceptional proficiency in calculus.

Is AP Calc worth it?

Yes, taking AP Calculus is generally considered worthwhile, especially for students interested in STEM fields like chemistry, mathematics, physics, and biology. AP Calculus introduces essential concepts such as limits, derivatives, rates of change, integrals, and accumulation, which are crucial in various scientific and mathematical studies. Beyond the academic benefits, AP Calculus can enhance problem-solving skills and critical thinking, useful in many situations, not just in math problems. Additionally, excelling in AP Calculus can look impressive on college applications and may even lead to college credits, depending on the exam score and the college's policy. Overall, AP Calculus can provide both academic and personal benefits, helping build confidence and fostering a sense of accomplishment.

Is AP Calc better than IB math?

Choosing between AP Calculus and IB Math depends on individual goals and preferences. IB vs AP: AP focuses on teaching specific content and testing knowledge via exams, with a significant emphasis on meeting certain content goals. IB, on the other hand, emphasizes writing, developing critical-thinking skills, and not just the exams themselves. IB also requires an extended essay and extracurricular requirements. Each program has different philosophies and goals, and one is not inherently better than the other. Your choice should be based on which program aligns better with your learning style, academic interests, and college aspirations.

What is the hardest unit in AP calculus?

Determining the hardest unit in AP Calculus AB can vary among students based on individual strengths and weaknesses. However, some of the units that are generally found to be challenging include Limits and Continuity, Differentiation, especially involving Composite, Implicit, and Inverse Functions, and Contextual Applications of Differentiation. The difficulty often arises from the abstract nature of these topics and the need for a strong foundational understanding to solve complex problems. Students typically find units that require high levels of analytical thinking and application of multiple concepts simultaneously to be more challenging.

Can you take AP Calculus without precalculus?

Yes, you can. Taking AP Calculus without precalculus can be challenging. Precalculus lays the groundwork for understanding calculus, introducing essential concepts like limits and series, as well as algebraic techniques crucial for solving calculus problems. While it's not impossible to jump into AP Calculus AB or BC without this background, doing so requires a strong foundation in mathematics and may demand extra effort to get up to speed with the course's rigorous demands. It's generally recommended to complete precalculus first to ensure a smoother transition and better success in AP Calculus.

Can I skip AP Calc AB?

Yes, it's possible for students with strong math skills to skip AP Calculus AB and go straight to AP Calculus BC. However, this decision should be made after considering certain factors such as your school's policy and math department guidelines. Some schools may have specific prerequisites that need to be met before enrolling in AP Calculus BC. It's important to evaluate your own mathematical background and readiness for the accelerated pace and advanced topics covered in AP Calculus BC before making this decision.

Is AP Calculus AB a full-year course?

Yes, AP Calculus AB is indeed a full-year course. It's structured to provide a comprehensive exploration of differential and integral calculus over an academic year. This format allows students to thoroughly understand and engage with the material, ensuring a solid foundation in calculus concepts, which is essential for success in the course and on the AP exam. The full-year structure is designed to align with the complexity and depth of college-level calculus courses.

Can AP Calculus help in non-STEM college majors?

AP Calculus can be beneficial for students pursuing non-STEM majors. It provides a strong foundation in mathematical thinking and problem-solving skills, which are valuable in a wide range of fields. For example, students interested in economics, finance, or business can benefit from the analytical skills developed in AP Calculus. Additionally, achieving a qualifying score in AP Calculus can fulfill college math requirements, allowing students to focus on courses more central to their major.

Are graphing calculators necessary for AP Calculus?

Yes, graphing calculators are an integral part of the AP Calculus course and exams. They are essential for plotting functions, finding zeros, calculating derivatives, and determining the value of definite integrals. While their use is critical, AP Calculus exams are designed to be fair to all students, regardless of the calculator's advanced capabilities. It's important to become adept at using a graphing calculator, as it's a powerful tool for both exploration and solving mathematical problems.

Can I self-study for the AP Calculus exam?

Yes, you can self-study for the AP Calculus exam. This approach requires a significant amount of discipline and self-motivation. You'll need to be proactive in learning the material, which includes understanding complex concepts, solving a variety of problems, and preparing for the exam format. Resources like textbooks, online courses, and practice exams are essential. It's also important to develop a structured study plan and regularly assess your understanding and progress. Self-studying for AP Calculus can be challenging, but with dedication and the right resources, it is achievable.

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Professional tutor and Cambridge University researcher

George Christofi

Written by: George Christofi

Oxford University - Masters Philosophy

George studied undergraduate and masters degrees in Classics and Philosophy at Oxford, as well as spending time at Yale. He specialises in helping students with UK and US university applications, including Oxbridge and the Ivy League. He writes extensively on education including on schools, universities, and pedagogy.

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