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~Guide to Self-Studying AP Calculus BC~

EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
edited November 2013 in AP Tests Preparation
Two years ago, I self-studied Calc BC while doing Calc AB. Although the course wasn’t overly difficult, it definitely wasn’t easy either. However, the experience (in general) is highly worthwhile, and I’d highly recommend it to anyone strongly considering a career in math/science/engineering. The following is a mini-guide to self-studying the BC curriculum, as many schools don’t yet offer the BC course. If you have any questions, please make a post on the thread AND send me a message. I hope this info helps! :)

1. Calculus AB vs Calculus BC
Calculus AB focuses on first-semester calculus material, such as limits, derivatives, integrals, and basic differential equations. Calculus BC tests all the material from Calculus AB and also material from a second-semester calculus course, such as derivatives/integrals in polar/parametric coordinates, advanced integration techniques, and power series. The BC test is approximately ~60% Calculus AB and ~40% Calculus 2 topics and you typically need a high 50 to low-mid 60 percent for a 5. If you take BC, you will also receive an “AB Subscore,” which is basically a score that describes how well you did on the Calc AB portion of the BC exam.

2. Should I do Calculus BC?
It is a very worthwhile endeavor.. anyone talented at math should definitely consider doing it. If you like math and can spend approximately 6-8 hours/week during January-May self-studying, then you’re all set! Calculus BC doesn’t have a TON of new material, and you could also save thousands of dollars and skip an entire semester of calculus in college. Calc BC also isn’t too tough – think of it as like taking an additional honors-level math course during your senior year. You also need to be resourceful and independent… can you trust yourself to stay caught up without a teacher forcing deadlines on you?

Of course, if you're still unsure, wait and try out Calc AB - if it's tough, then don’t try BC. If you're coasting through Calc AB, however, then consider doing BC! Lastly, some other factors to consider could be your college’s AP policies, as well as your future career plans (if you plan on becoming a history major, I highly doubt calculus BC will be useful to you).

3. The Process in-a-nutshell
First, I definitely recommend getting a review book. The best ones in my opinion are either Princeton Review or Peterson’s. Any old edition is fine, and both Princeton Review and Peterson’s are GREAT. You could also get a textbook if you want, but a review book should be more than sufficient for the exam itself. You should only get a textbook if you truly want to learn and master the BC material - It may help slightly for the actual test, but with a good review book + lots of old AP problems + internet video tutorials, you will be fine for the exam. If you really want a textbook, however, any old edition by either Larson, Stewart, Finney and Thomas should be fine.

Some other good books include the following.
Amazon.com: Calculus Made Easy (9780312185480): Silvanus P. Thompson, Martin Gardner: Books
Amazon.com: Cracking the AP Calculus AB & BC Exams, 2009 Edition (College Test Preparation) (9780375428852): David S. Kahn: Books

Once you have your materials, start learning the concepts ASAP. I typically recommend reading the review book first and/or watching a video (see links below), and then go through a lot of practice problems from your review book/textbook/old AP problems. Once you’ve done a fairly large amount of problems and feel confident with the topic, then move on the next one.

As long as you master the material from the review book (either Princeton Review or Peterson's, either is OK) and you do LOTS of old FRQ and multiple-choice problems, you should do very well on the AP exam. Also, if you have the time, I recommend going through some of the websites mentioned below and/or reading a textbook (see above for suggestions), but this isn't necessary if you have mastered the material from the review book / practice problems.

4. Some Advice
(1) Start early! - Ideally in early Fall if possible! Although some people have succeeded in “cramming” for the test, you’ll have a much more enjoyable experience with Calc BC if you pace yourself and start early!
(2) Take advantage of your school’s resources - I’m sure many of your math teachers would be more than happy to help you in this independent study. Also, try to convince some of your friends to join you in self-studying. Two heads are much better than one!
(3) Plan your study schedule..I highly recommend creating a calendar, and sticking to it. For each new concept, schedule a time to learn it, and also time to do a lot of practice problems that contain the concept.
(4) Old AP questions are crucial - be sure to work through as many as you can!
(5) Don’t forget to work hard in Calc AB. After all, the material from Calculus AB is ~60% of the AP Calculus BC Exam!
(6) Whenever you are confused on something, or see a problem that you’re struggling with, make note of that so you don’t forget. FOCUS on the topics that you struggle with. Don’t waste your time with topics that you already understand.
(7) In total, you should expect to put 60-100 hours into this independent study (depending on your math background / whether or not you’re focused when you’re studying)
(8) If you find that your review book/textbooks aren’t making much sense, there are also some amazing video tutorials on the Internet which can be found here:

Online video tutorials
PatrickJMT (amazing website.. very clear and helpful tutorials)
Khan Academy (different instructor but very clear explanations also)

Notes & Explanations
tutorial.math.lamar.edu (No videos, just notes. Slightly more advanced introduction, but notes are extremely clear)
An online textbook: Free Online Course Materials | Textbook | MIT OpenCourseWare
Advice in studying math: Study Hacks Blog Archive How to Ace Calculus: The Art of Doing Well in Technical Courses

Practice Questions
Old AP FRQs: AP Central - AP Calculus BC Course Home Page
Old AP Multiple-Choice (1969 to 1998): http://staff.4j.lane.edu/~windom/AP/ap%20multiple%20choice.pdf
Some More Recent Practice Multiple-Choice:

5. The Most/Least Important Topics for the BC Exam
While I do believe you should try to learn all the BC topics as well as you can, the following are by far the most crucial topics for the BC exam.

MOST IMPORTANT (must know!)
- Polar and Parametric Functions (many schools don’t cover this, but it is absolutely crucial for the BC exam)
- Be able to apply derivatives to polar and parametric functions (a semi-challenging topic, but this shows up very frequently on the BC exam)
- L^Hopital’s Rule (very simple topic, but ALWAYS shows up somewhere on the exam!)
- Integrating by Partial Fractions (Very important)
- Integration by Parts (EXTREMELY important!)
- Arc Length of Parametric and Regular functions (important! fairly straightforward topic)
- Euler’s Method
- Integrating Polar and Parametric Functions (this is definitely a very challenging topic - if you have the time, try your best to know it, but if you can’t, you should be okay. However, these questions have been known to show up on FRQs and definitely will be on the MC section)
- Logistic Differential equations

Series: Yes, series (despite their unpopularity) are very important for the AP exam. However, the BC exam practically always focuses on power series, taylor/maclaurin series, the ratio test, integrating & differentiating power series, and lagrange error bounds. These topics pretty much dominate all the power series stuff that will actually show up on the exam.

- Integrals via Trig Substitutions
- Integrals involving complicated trig functions (i.e. integrate sin^3(x))
- Series convergence tests other than the ratio test

For a full list of Calc BC topics (also can be found in your review book): http://apcentral.collegeboard.com/apc/public/repository/ap-calculus-course-description.pdf

6. A Brief Timeline of the Course
a. If you’ve already taken Calc AB:
Spend a 1-2 months reviewing the AB material (ideally before January), and then work on the BC material at your pace. Plan to finish the BC topics by late-March, and spend most of April reviewing and running through old AP FRQs and practice questions (from your review book/textbook).

b. If you are taking BC and AB at the same time.
This is going to be tougher, as many BC topics require knowledge of AB topics. However, it’s definitely still very doable. Basically, after you cover the pre-requisite topic in Calc AB, IMMEDIATELY start working on the BC topics that are related to the AB topics. So, for example, once you have finished the unit on derivatives, IMMEDIATELY start working on differentiating polar and parametric functions.

If you’re taking BC along with AB, your schedule should look like this:
August-October: Make sure you understand all the course pre-requisites, especially parametric/polar equations. Start working on learning to apply derivatives to polar/parametric equations.

October-December: Start working on power series NOW. Also, make sure you completely master the Calc BC topics on derivatives!!

January- March: I really hope you’ve covered integrals by now. If you haven’t, then make sure you completely understand the BC topics in derivatives + you have some basic understanding of power series. If you have some basic knowledge of integrals, start working on all the integration topics mentioned above. If you’re pressed for time, skip the less-tested topics (i.e integrating trigonometric power functions, such as sin^3(x).) You should also FINISH COMPLETELY THE UNIT ON POWER SERIES during this time period!!

March-May: Make sure you understand the rest of the BC topics, and do a quick review. Then start doing lots and lots of old AP questions – I recommend working at least 5 years of old AP FRQs and at least two MC practice tests.

7. Post-AP Situation
Yay! Congrats on making it through Calculus BC! :D However, for those of you who really want to skip Calc II in college, and are strongly considering an engineering/science/math major, I *highly* recommend learning these topics after doing Calc BC using the websites I listed above:

- Work, and how to compute it using calculus
- Conics (i.e. hyperbolas, ellipses)
- Computing Moments of Inertia/Center of Mass using integrals
- Hyperbolic Trigonometry (the sinh and cosh functions)
- Simpson's Rule (another way to numerically estimate areas under curves)
- The Binomial Series
- Vector dot product, Vector cross product, and Planes in 3-d (very very useful for multivariable calculus)

Also, if you understand the majority of the BC topics (especially polar/parametric), then you can definitely move on to Calc III (multivariable/vector calc). If you're unsure, try taking Calc III for a few days, and if you feel overwhelmed, then feel free to drop back to Calc II in college.

I hope this info helps - best of luck! :)
- Equilibrium

PS - Thanks to everyone for helping me revise the previous versions of this guide! Hopefully, this will be my last revision!...
edited November 2013
57 replies
Post edited by Equilibrium on
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Replies to: ~Guide to Self-Studying AP Calculus BC~

  • smorgasbordsmorgasbord 1790 replies13 discussionsRegistered User Posts: 1,803 Senior Member
    This is an excellent guide. Well done, Equilibrium!
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  • atheosatheos 48 replies1 discussionsRegistered User Posts: 49 Junior Member
    This is a solid guide, I would include the Arco AP Calculus book. I just ordered a copy, it gets great reviews.

    I should be getting a lot of use out of this, I need to get most of the way through BC this summer, because I'm either taking or self-studying all 9 STEM AP exams plus US History for my junior year. Thanks bro.
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    Thanks! Good luck with studying.
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  • WiseGuyWiseGuy 343 replies6 discussionsRegistered User Posts: 349 Member
    Great timeline and explanation! Definitely will be helpful for those looking to learn BC.
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  • TechhexiumTechhexium 595 replies29 discussionsRegistered User Posts: 624 Member
    Hey Equilibrium, I used one of your old guides and I took the BC exam in May. I'm really hoping for a 4 or 5!

    Anyway for future self-studiers, here is a PDF that tells you what you should do in the FRQs. Hope this helps!

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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    That's great to hear! :) Also, thanks for the link!
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  • yodeloyodelo 948 replies126 discussionsRegistered User Posts: 1,074 Senior Member
    haha this thread is awesome!
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    ^ Thanks a lot! :D
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  • stressedoutttstressedouttt 3980 replies131 discussionsRegistered User Posts: 4,111 Senior Member
    subscribed to thread :) this should be really helpful.
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
  • Twiggy22Twiggy22 336 replies93 discussionsRegistered User Posts: 429 Member
    Ok lets say you want to self study Calc BC at the same time as you are taking AB in an actual class .. And you find Calc AB to be pretty good .. not to hard but not to easy .. but like a little bit more towards the easy side.. should you self study calc BC ? ..
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  • moose97moose97 119 replies12 discussionsRegistered User Posts: 131 Junior Member
    It depends on your previous math ability. If you have a solid grasp of Algebra II, trig, and to some extent vectors, you should be more than fine.
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    That's honestly more of a personal decision. It sounds like BC should be very doable for you, but I'd consider other factors, such as your class schedule, any other commitments you have, and how much interest you have in calculus. If you can fit BC into your schedule without overstressing yourself *and* you definitely plan to pursue a science/math/engineering major in college, then I'd highly encourage it. If you're still unsure, I'd recommend to just try out some of the easier BC topics at the beginning of AB, and see how you like it. If you find the BC topics to be reasonable, then definitely go for it! I hope this info helps - Best of luck.
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  • elf4EVAelf4EVA 1559 replies33 discussionsRegistered User Posts: 1,592 Senior Member
    Would it be possible to self-study BC without taking AB? I am planning on it this year because I already know almost all of what is being taught in Honors Precalc right now, and I consider myself to be one of the stronger math students at my school. I'm not asking if it will be easy, because I know it won't be. I actually want to learn the material and not just get a 5 on the AP exam. Thoughts? By the way, this guide is so helpful! I will definitely follow it, even if I'm not taking AB. :)
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    Well, anything is doable, as long as you set your mind on it :)

    Of course, it will be very challenging. To give you an estimate, BC usually takes 100 hours total (depending on your background), and I estimate AB to take 150+ hours total.

    The total is about 250 hours, and possibly more if you truly wish to master the material. Can you put in this time commitment w/o overwhelming yourself? How important for you is it to finish Calc BC this year? Do you have any other commitments that may interfere with this goal? Self-studying BC and AB will be challenging, but is definitely doable. At the end, however, do you think it will be worth it?

    Good luck with your decision - let me know if you have any other questions.
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    Another possibly helpful link:
    Math 1106 Home page (try the old exams)

    Also, if any of you have questions, please make a post AND message me (I don't check my account regularly anymore, but a message shows up on my email)
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  • AngelJessAngelJess 1 replies0 discussionsRegistered User Posts: 1 New Member
    Hey can I self study calculas BC even without talking Calculas AB at school?
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    Of course it is doable. However, you will not only have to learn all of the BC material but also the AB material at the same time, which will require a massive effort. I'd only recommend doing it if it's your only option (ie your school doesn't offer AB or BC) - otherwise, I'd consider any possible alternatives, such as doing AB only this year or doing BC next year. Doing both AB and BC by yourself will take a massive amount of work, so you should only do it if you have enough free time.
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  • EquilibriumEquilibrium 1157 replies60 discussionsRegistered User Posts: 1,217 Senior Member
    Bump - hope you self-studiers are doing well so far! If you're interested, it's still not too late!
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