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High school student here...

This coming school year I'm scheduled to start AP Calculus AB and then my school is looking into taking Multivariable Calculus at a local university. The school's calculus teacher thinks it isn't necessary for me to take BC since AB and BC are so similar. Over the summer, I did some studying and learned limits, derivatives, and am currently working on integrals. Looking over common curriculums for AB, there doesn't seem to be much beyond that and I'm worried the class may be a little boring. Do teachers really think AB is necessary or would I be better off asking to transfer to BC?

CaptainAmerica16
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    Note that the BC exam includes the material in the AB syllabus and produces an "AB subscore." In many places, a score of 4 or 5 on the AB test will get you credit for Calc I. In order to receive credit for Calc I and II, you might need both a passing BC exam score of 4 or 5 and a passing AB subscore. The BC syllabus tries to cover what's typically in a Calc II course. Chances are very good that you actually need the AB course to be adequately prepared for the AB exam. – Brian Borchers Aug 14 '18 at 03:51
  • Ok, do you think the original plan is reasonable then, learn the major basics in AB and then self-study the extra BC stuff? – CaptainAmerica16 Aug 14 '18 at 04:40
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    This question is quite an alphabet soup. Could someone edit a bit of context in? Is this jargon from USA? – Tommi Aug 14 '18 at 05:42
  • Sorry about that. Yes, this is a question from the USA. Calculus AB over here is essentially differential calculus and then BC is integral calculus. – CaptainAmerica16 Aug 14 '18 at 06:58
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    Relevant: A link to the descriptions of these courses. https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-calculus-ab-and-bc-course-and-exam-description.pdf – Adam Aug 14 '18 at 14:39
  • A related question: How can you be perfect at maths (high school)? – Jasper Aug 14 '18 at 19:00
  • Thank you for the link – CaptainAmerica16 Aug 14 '18 at 19:09
  • Progress report? – guest Oct 17 '20 at 12:21

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Stronger students should take BC, not AB. AB is basically about 0.5-0.7 of what is in the BC course. BC pretty closely matches the standard first two semesters of college calc. AB is a little bit more than a semester of college calc.

In general (i.e. in theory), BC starts at the same point as AB but just goes faster.

guest
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    My experience in high schools (substitute teaching in numerous schools, 4 years full-time teaching spread over two different schools in two different states) was every school that offered BC calculus also offered AB calculus, and stronger students almost never took AB calculus, but instead took BC calculus. In fact, the difference in student ability in these two classes was often dramatically different --- AB classes had typical college-prep level students who often struggled, and BC classes had (with a few exceptions) students who had little difficulty with its higher level material. – Dave L Renfro Aug 17 '18 at 14:29
  • @Dave L Renfro Thank you for this. For some reason, I never got the notification for your comment. I feel like everyone is making calculus out to be harder than it is. I understand the importance of having the material down, which is why I've been studying over the summer, but I haven't had much of an issue understanding the material I've encountered so far. Once you get the concepts down, it's just a bunch of rules and intuition. It makes me worried I'm approaching it wrong. – CaptainAmerica16 Aug 23 '18 at 17:20
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    @CaptainAmerica16 You should go straight into BC unless your school is doing something very VERY bizarre. AB = first semester college calculus spread through a year. BC = first and second semester calculus in one year. You get all the same content in BC as AB, but just move faster. AB is NOT a pre-req for BC. It is just a slower version, covering first half of BC. See this: https://blog.prepscholar.com/should-i-take-ap-calculus-ab-or-ap-calculus-bc [based on your remarks, go straight to BC, don't do AB] – guest Sep 26 '18 at 02:39
  • @guest That's exactly what I thought! Unfortunately, I'm stuck in AB right now as school started nearly 3 weeks ago. So, I can either make an case to switch classes or I'll have to study BC myself. – CaptainAmerica16 Sep 26 '18 at 02:46
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    @CaptainAmerica16 Just switch. What's the big deal. Worst thing that happens is you can't hack it. Big deal. Just put in a transfer slip and switch. Take control, young man! ;-) You'll be surprised how much you can get away with if you just act confident and assume people will do what you want. If they want some justification, give it then. But honestly, I would just go in with a flat transfer request. Don't even bother to justify it unless they demand one. If things get sticky, get the parental units involved...but try the direct approach first. – guest Sep 26 '18 at 02:49
  • @guest Lol, reading that just made me super nervous, but I really don't want to have to take both classes. Thank you for the advice, I'll make the request this week. – CaptainAmerica16 Sep 26 '18 at 02:52
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    If you are a strong math student, AB is a total waste of time. Just hit it hard with BC, especially in the beginning. Read the text's section ahead of lecture and work a few problems. Makes the lectures easier to follow. You may be like 1.5 weeks behind (3 weeks divided by 2), but there is a good chance some of the initial material is similar to what you learned in pre-calc anyhow. You can handle it. – guest Sep 26 '18 at 03:00
  • @guest My counselor just let me know she's looking into the switch today. I'll let you know what happens :0 – CaptainAmerica16 Sep 27 '18 at 14:17
  • @guest Good news! My counselor is allowing me a trial period where I have to still do my AB classwork, but I can attend BC lessons to see if I can handle the material. If yes, I'll officially be switched over. I'm glad I just went for it as you said. – CaptainAmerica16 Sep 28 '18 at 17:24
  • Good luck. Hit it hard. Pre-read the lessons and work all the problems (not just assigned ones). You will crush it then. – guest Sep 28 '18 at 19:33
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    @CaptainAmerica16 I understand that SO is not a forum, still I think I am not the only one wondering how you are doing in Calc BC ;) – Rusty Core Nov 14 '18 at 21:10
  • @RustyCore Thanks for asking! It took a bit to adjust to the speed of the course, but I've been doing well. Currently, have an A :D – CaptainAmerica16 Nov 15 '18 at 02:26
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Taking the AB course, and then trying to fill in the gaps independently for a BC course is risky. I do not recommend it.

In the county I grew up in, there was a student who took the first semester of a one-year high school AP calculus course, and then tried to take second semester calculus at the local junior college. He was woefully underprepared, and did not succeed. This was despite his being very bright and a very good student. (He had the second-highest Academic Decathlon scores in the county.) This was also despite having excellent instructors for both his high school calculus course, and for his junior college calculus course.

A solid understanding of calculus through the Reynolds Transport Theorem is key to doing well in many science and engineering subjects. If you have holes in your understanding of calculus -- especially holes that you do not realize you have -- you will suddenly find yourself in a difficult position in later classes.

Jasper
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  • What kind of things are taught in BC? Everyone makes it seem like it's basically the same as AB, but with like 3 extra units – CaptainAmerica16 Aug 14 '18 at 18:39
  • I'll be sure to research the theorem, but now you're making me worried. I haven't had difficulty in math before. Do you think I would still struggle with strong self-study habits? I've managed to skip two years of math this way. – CaptainAmerica16 Aug 14 '18 at 18:50
  • @CaptainAmerica16 -- You need a way to confirm that you understand all of the prerequisite material for the classes you plan to take subsequently. Unfortunately, (based on my observations of other students -- not personal experience) the AP Calculus tests are not a good way to confirm this. – Jasper Aug 14 '18 at 18:57
  • I have a semi math mentor who works in the math tutoring department at my school. I'll ask him his opinion on good ways to retain material. I'm wondering if I would have been better off taking standard calculus. I wouldn't get college credit, but at least the curriculum wouldn't be focused on a passing a test. – CaptainAmerica16 Aug 14 '18 at 19:00
  • Also, is it just me or is Math Educators SE a little buggy? – CaptainAmerica16 Aug 14 '18 at 19:10
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    Reynolds Transport Theorem --- FYI, this seems to be well beyond anything in BC level calculus, and most probably anything in the typical 3-4 semester elementary calculus sequence in U.S. universities. Instead, it would be more appropriate for the standard (at least when I was an undergraduate) 3rd/4th year 2-semester advanced calculus sequence. – Dave L Renfro Aug 17 '18 at 14:24
  • @DaveLRenfro -- If a calculus sequence does not get to the Reynolds Transport Theorem until the student is in their junior or senior year of college, then it is not designed to support science and engineering students. Science and engineering students need the Reynolds Transport Theorem for their sophomore year courses. – Jasper Aug 17 '18 at 15:55
  • @DaveLRenfro -- Green's Theorem and Stokes' Theorem are special cases of the Reynolds Transport Theorem. Green's Theorem and Stokes' Theorem are often taught in third-semester calculus. That is, they immediately follow the content taught in BC-level calculus. (BC-level calculus is supposed to include some vector calculus, according to the College Board course description that Adam linked to.) – Jasper Aug 17 '18 at 16:03
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    "BC-level calculus is supposed to include some vector calculus, according to the College Board course description that Adam linked to." What you said in your comment before where this quoted sentence appears might be true for strong science and engineering sophomores at selective universities, but vector calculus is definitely not included in BC calculus, at least nothing that involves partial differentiation. What is involved are some basic concepts involving vector valued functions of ONE real variable (i.e. curves in the plane and sometimes curves in space). – Dave L Renfro Aug 17 '18 at 20:56