Guide to Self-Studying Calculus BC (while taking AB)

Test Preparation AP Test Preparation
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<p>I recently self-studied Calculus BC while in Calculus AB. I felt it was a highly worthwhile experience; my Calc AB class was moving too slow so I decided to move on to learn Calc BC by myself. It wasn't extremely difficult, but it was still pretty challenging. However, the experience was highly worth it. Not spending hundreds of hours doing Calc II in college + saving thousands of dollars = very well worthwhile experience. Plus, it made my boring / easy math class interesting. Feel free to add any other ideas to this guide if you want, by the way. </p>

<p>Self-Studying Calc BC while taking Calc AB</p>

<p>AP Calc AB vs. Calc BC
In college, there are two calculus courses: Calculus I and Calculus II. Calc AB tests on Calculus I ONLY, and Calc BC tests BOTH Calculus I and Calculus II (consider it like a big final exam in all of basic calculus!)</p>

<p>Should I do Calculus BC?
It is a very worthwhile endeavor.. anyone talented at math should definitely consider doing it. Calculus BC doesn’t have a TON of new material, and if you succeed on the BC exam instead of the AB exam, you could save thousands of dollars and skip an entire semester of calculus in college. Calculus BC isn’t impossible (especially if you’re very good at math), but it’s definitely not easy either. Taking Calc BC while doing Calc AB is like taking an additional honors-level math course during your senior year. (Think of it as taking an extra math course similar to the difficulty of honors algebra 2 or precalc) It’s not super awful, but definitely not easy either. However, generally, you should be very competent at math to independently study BC on your own. By competent, I mean having mastered the math PRIOR to calculus, and having strong analytical and problem-solving skills. I do NOT mean being innately good or possessing natural math talent. You also need to be resourceful and independent… can you trust yourself to stay caught up without a teacher forcing deadlines on you?</p>

<p>Here are the topics in Calc BC that are NOT in Calc AB: I also attached some commentary to each topic.
Unit 1 – Pre-Requisites for Calculus
Completing the Square (Know it. Helps for Integrals)
Complete Mastery of Trigonometric Identities!! (Calc BC REALLY REALLY tests your understanding of trig identities as well as trig in general. KNOW THEM!)
Polynomial Division (required for Advanced Integrals)
Partial Fractions Separation Technique (Required for Integrating using Partial Fractions… This is a very important BC topic so KNOW IT!)
Vectors in a Plane (Basically, know what a vector is.. you should learn it in physics)
Parametric and Polar Equations (This is not covered in all PreCalc Curriculums.. however, I can GUARENTEE THAT THESE WILL SHOW UP ON THE AP EXAM! THEY ARE VERY IMPORTANT!)</p>

<p>Unit 2 – Derivatives
Planar Motion based on Parametric Equations – Velocity and Acceleration Vectors (Very simple topic... it doesn't get too technical However, it WILL APPEAR ON THE AP!! Easy way to earn points)
Finding Tangent Lines to Polar and Parametric Functions (This will definitely be on the AP. It’s moderate to difficult, but you really need to know it.)
L^Hopital’s Rule (Very basic rule, yet I can promise you that this will be on the AP. MUST-KNOW!)
Finding the Derivative / Rates of Change of Polar and Parametric Functions (KNOW IT!)
Finding the Second Derivative of Parametric Functions (Most likely not on AP)
Knowing the Derivatives of ALL the functions (like arcsec(x), arccsc(x)) (This may or may not be on the AP. Still, it’s very easy. You just gotta memorize them)</p>

<p>Unit 3 – Integrals
This is where it gets tough. Calc BC not only expects you to know these topics, but also expects you to be able to have semi-strong problem-solving skills / thinking skills in this unit.
Improper Integrals (Not too important… maybe 1-2 questions on it at most)
Integrating by Partial Fractions (DEFINITELY will be on the AP.. know it!!)
Integration by Parts (EXTREMELY Important!!! You’d better know it!)
Knowing Inverse Trig / Normal Trig Integrals (memorization here.. just do it)
Adv. Trig Integrals (ex. integrate (sin(x))^3 )(Probably not on AP.. skip if short on time)
Arc Length of Parametric Functions (Might be on AP.. skip if short on time)
Arc Length of Regular Functions (WILL be on AP. This is a must-know topic.)
Areas of Polar Function Graphs (Ehh… try your best to know how to do this..)</p>

<p>Unit 4 – Differential Equations
Euler’s Method – (I can promise you this will be on the AP. This is also a very very simple topic, so learn it! Easy way to earn points here!)
Logistic Differential Equations (Very easy topic. Just know dy/dt = (ky)(L-y) and y = L / (1 + ce^(-Lkt)) easy way to earn points here!)</p>

<p>Unit 5 – Sequences / Series
Basically, for this unit, the most important things to know are the ratio test, power series, and taylor / maclaurin series, as well as lagrange error bounds. Also, be sure to know how to test power series for convergence / divergence using the ratio test, and also be sure to know how to test convergence of power series at END POINTS!! You also need to be able to differentiate and integrate power series.</p>

<p>See collegeboard AP Calculus BC Course Description for the entire listing of topics
Actual link: <a href="http://apcentral.collegeboard.com/apc/public/repository/ap-calculus-course-description.pdf%5B/url%5D"&gt;http://apcentral.collegeboard.com/apc/public/repository/ap-calculus-course-description.pdf&lt;/a&gt;&lt;/p>

<p>Tips / Advice for Preparing
Unfortunately, there are a few complications. You really can’t begin to self-study most of Calc BC until you are proficient with integral calculus. And integral calculus isn’t taught for quite a while in Calc AB, so you have to cram a lot of Calc BC into a very limited timespan. </p>

<p>So, in September / October, gather the equipment you need to make such the journey:
1) Find other students who are also studying Calc BC on their own to work with you.
2) Get a review book. The two best books are by Princeton Review and Peterson’s. The Peterson book is a little advanced, but is pretty clear and also helps you prepare for college calculus. The Princeton Review is extremely clear but a little too basic at times. Get both books if you want. When you get your review book, get it off amazon.com to save money, NOT Barnes and Noble. Also, get an old version (2004-2005 is fine, but 1999 is NOT). The new versions are basically the same as the old versions.
3) Find some useful websites. Here are a few useful ones:
Just</a> Math Tutoring
<a href="http://www1.rcas.org/shs/RConway%20Math/documents/BC%20Calculus%20PRACTICE%20Test%2008.pdf%5B/url%5D"&gt;http://www1.rcas.org/shs/RConway%20Math/documents/BC%20Calculus%20PRACTICE%20Test%2008.pdf&lt;/a>
AP</a> Central - AP Calculus BC Course Home Page
AP</a> Central - The AP Calculus BC Exam
Math</a> Study Guides - SparkNotes
Pauls</a> Online Math Notes
AP</a> Calculus BC Notes
AP</a> Calculus BC Notes and Handouts
Karl's</a> Calculus Tutor: Table of Contents
Elementary</a> Calculus
Practice Test: <a href="http://asmsa.org/math/marizza/Calculus/APTEST/ap04_calcmc_collection_final_4_12_05.pdf%5B/url%5D"&gt;http://asmsa.org/math/marizza/Calculus/APTEST/ap04_calcmc_collection_final_4_12_05.pdf&lt;/a&gt;&lt;/p>

<p>In addition, be sure to use your PreCalc notes as well as your review book and textbook!
4) Plan your study schedule. Make a general idea of when you’ll do what. Basically, you will have to learn the concepts, do practice problems, then try some old AP problems, and review concepts. </p>

<p>Unfortunately, there is very little you can do for self-studying Calc BC until you are at least halfway through Calc AB. However, to start, learn parametric, vector, and polar functions ASAP. Those functions are very important for AP Calc BC so know them well. In addition, review all the PreCalc concepts I mentioned earlier. You should be doing this until you reach the END of the basic derivatives unit.
As soon as you finish the basic derivatives unit, start learning how to differentiate parametric / polar functions, as well as velocity / acceleration vectors. (velocity / acc. Vectors are used when a parametric equation is used to represent motion in a plane) Also, start learning L^Hopital’s Rule, and memorizing all the derivatives you’ve learned. In addition, you need to know to the arcsec(x) and arccsc(x) derivatives. Try to finish this in 2-3 weeks. It should not take too terribly long. </p>

<p>In addition, while you’re doing all of this, try to learn sequences and series at the same time. I recommend starting to learn series / sequences AFTER finishing the basic derivatives unit. Again, just START TO do it. </p>

<p>*Note: as you learn these topics, be sure to try practice problems and look over your mistakes on those practice problems. In addition, if you’re struggling to understand one guide’s particular explanation, then use another resource to learn the topic. For example, if the review book’s explanation on Polar Derivatives isn’t making any sense, then try the textbook’s explanation, or maybe a website’s explanation. </p>

<p>There’s gonna be quite a long while until you can actually start learning the other Calc BC topics, so as you wait, you should either review, relax, catch up (if you’ve been slacking), or doing practice problems. </p>

<p>AS SOON AS YOU manage to finish integrals (in calc AB), start learning integration by parts, integration with partial fractions, and improper integrals, and all the other integrals stuff. (refer back to topic listing earlier to understand what I mean) This is why I told you to start early and learn all that Polar / parametric stuff earlier. You’ve got a ton of integration stuff to learn and a lot of practice problems to do. </p>

<p>And on yeah, now you have to learn the Calc BC topics on differential equations, as well as an entire unit on sequences and series. (this is why you should start series / sequences early!) When you’re at this stage, it’s going to be a little rough. I’m not going to tell you what to do here. Come up with your own schedule, and work on your own pace to learn all those concepts ASAP. And once again, allow me to stress the EXTREME importance of going through examples and practicing problems. You can’t just memorize the mathematical formula or learn the concept and expect to be able to do the problems!! </p>

<p>A few more final tips / pieces of advice:
1) Try to get as much as you can done early, so the few months before the AP don’t become too crazy!
2) Do AP Free-response questions. They are very very important / helpful. You can find them at:
AP</a> Central - The AP Calculus BC Exam
4) Don’t forget to work hard in Calc AB. After all, the material from Calculus AB is 60-65% of the AP Calculus BC Exam!!
5) If you plan on skipping Calculus II in college using AP credit, be careful. The AP Calc BC exam really is easy compared to most Calculus II courses in college. Try to do some additional studying on your own if you plan on doing that.
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. Basically, keep track of what areas you struggle in, so you can actually focus on those areas.
7) For a 5, you usually need a 60-65% correct on the exam. A 4 is approximately 49-60% correct.</p>

<p>For those of you who really want to skip Calc II in college, I recommend learning these topics after doing Calc BC:
Work
Fluid Pressure
Moments of Inertia
Center of Mass, Centroids
Hyperbolic Trig
Trig Substitutions
Trig Integrals
Integration by Tables
Simpson's Rule
The Binomial Series?</p>

<p>Ooh, another cool link: Study</a> Hacks Blog Archive How to Ace Calculus: The Art of Doing Well in Technical Courses</p>

<p>Hope this helps! :)</p>

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<p>tl;dr thats ridiculous</p>

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<p>THANKS!!! I was looking for something like this for next year</p>

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<p>Wow thank you so much. So this is what I’ll be expecting for BC next year. :)</p>

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<p>thanks! this was very helpful</p>

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<p>Thank you so much for breaking it down into topics like this! <3</p>

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<p>should be stickied nice guide</p>

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<p>My experiences with BC:</p>

<ol>
<li>Very, very, very, very easy test. I completely finished the multiple choice sections(no skipped, no mistakes barring stupid arithmetic mistakes) in 13-15 minutes, got a perfect on FRQs.</li>
<li>Most multiple choice questions don’t say evaluate this integral or something else straightforward; instead, they test concepts. So make sure you understand the actual concepts behind integration, differentiation, and linearization.</li>
<li>For essays, READ THE QUESTION. If it says average, check if it’s asking for average rate or average value.</li>
</ol>

<p>Do not worry about integration too much. Although you should know basics of partial fractions, integration by parts, etc., you don’t really need to worry about integration on FRQs. Just know how to integrate polynomials and how to do integrals on calculator.</p>

<p>Learn to do series questions (expressing trig as Mclaurin series), it shows up almost every year.</p>

<p>Skip polar. It is usually only one question, this year it did not show up at all.</p>

<p>Learn parametrics. Rectangular is just parametric with y(t) = y(x) and x(t) = t.<br>
This makes arc length formula really easy.</p>

<p>That’s about it. I’m pretty sure I will get 97% + on this exam, it is honestly very easy and straightforward.</p>

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<p>I did BC Calculus online this year. Last year I took AB Calculus as a class, and got a 5. I believe that my college next year offers the same credit for BC as they do for AB. Check out what credit you can get for calc at the colleges you’re looking at before you decide.</p>

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<p>tl;dr</p>

<p>What’s the point of self-studying BC while taking AB if you can’t take both exams in the same year? If you learn both at the same time, you’re going to have to go through a year of stagnation before you can take the BC exam.</p>

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<p>BC gives you a sub-score for AB and gives you credit for both of them.</p>

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<p>So you just take the BC exam and not the AB exam? That makes sense I guess. :cool:</p>

<p>Thanks.</p>

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<p>Is BC really that easy, or are you all just super smart? I talked to some kids–who are one of the smartest kids in the school-- who are in BC, and they practically groan about it. So now I’m kind of worried. :(</p>

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<p>Thanks for your post “theboydave” :)</p>

<p>@post #13
You never know. Calc BC varies in difficulty from school to school. Calculus BC may be easy for some, and may be hell for others. Reflect upon your high school math experience. Calc BC is absolutely not easy (only 2-4% of seniors actually take it). If math has been easy, then do BC. If math has been challenging, reconsider. If you’re not sure, initially sign up for Calc BC and see how it goes. If Calc BC is too tough for you, it’s fine. You SHOULD be able to switch to the AP calc ab test (see your teacher on this though)</p>

<p>I see Calc BC as a very worthwhile endeavor. However, please remember that it’s not a worthwhile endeavor for all.</p>

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<p>Thanks, Equilibrium! and thanks for the advice :D</p>

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<p>Thanks Equilibrium for the guide and advice. It should definitely be stickied, and I know I’m bookmarking it along with the links for next year when I self-study Calc BC. Thanks a lot man, I feel like I’m a lot more prepared now and actually know what I have to do for Calc BC.</p>

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<p>Sweet, great guide. I think I’ll try this next year.</p>

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<p>Really 60% for a 5?</p>

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<p>@lemone, yes really!</p>

<p>I also self-studied BC. Here’s my two cents. Cal I and AB is cookie-cutter calculus. It is FORMULAS and relations like geometry. You establish a rule, maybe twist it a little, and apply it.
BC, however, is like Algebra II. At least at my school, Algebra II involved CONCEPTS rather than FORMULAS.</p>

<p>So AB Calculus is cutting cookies, just a simple change of shape of the dough, while BC is baking cookies, taking the same ideas and actually doing something interesting and tasty!</p>

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<p>@post #8</p>

<p>I agree with most of what you’re saying. However, Polar Curves SOMETIMES appear as an entire FRQ question on the AP exam. You definitely shouldn’t skip them. After all, the only really tough thing about them is finding areas of polar curves. The rest of polar curve calc is pretty simple</p>