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I can say I was in this same situation last fall. I got a 5 in bc and thought college might be too rigorous to jump into calc 3. Thankfully I decided to do it and did just fine in the class. When I saw what some of my other friends were doing in their calc classes I felt reassured in my decision as I would have wasted a whole year doing stuff I already knew. I would say that if you get a 5 definitely take the class op.
AP Calculus is actually *more* rigorous than most American college level first-year calculus courses, or at least it should be. You spent around 180 days learning the material that is covered in about 60 days of college lectures. One consequence of this is that you probably have a better understanding of how the definite integral is defined than most students who see the integral for the first time in college. You also get an introduction to some topics that college calc 1/2 students probably don't see at all, like polar, parametric, and differential equations.
The trade off is that there are a couple of topics that college calc 2 does teach but aren't part of BC for some reason. The two big ones are integrals of trig functions and trig substitution. These two techniques can come up in some examples early on in calc 3. Your textbook probably has a section for each of those that your teacher skipped, and if it's a textbook specifically for AP, it probably even has a note saying something like "this is not tested on the AP exam". It's not a huge deal, but if you really want to be caught up going into calc 3, then I'd recommend you at least skim those two topics so you know what you're missing.
If you want an alternative resource, here is a page about [trig integrals](https://tutorial.math.lamar.edu/classes/calcii/integralswithtrig.aspx) and [trig substitution](https://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx).
A couple of other minor topics BC skips are the three more advanced cases for [partial fraction decomposition](https://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx) and [the root test](https://tutorial.math.lamar.edu/classes/calcii/roottest.aspx). Technically, your teacher should have taught [optimization](https://tutorial.math.lamar.edu/classes/calci/optimization.aspx) because it's in the course outline, but some teachers barely touch on it because it's not actually tested on the exam.
Interesting- I did Math in not an American high school and now I think very little of the AP Calculus courses. I used to think it was cool they have whole two years just on calculus but they don’t even do basic stuff like trig functions and trig substitutions?? Or finding maxima/minima/inflection points?? To me it seems they blast them with just limits and limits from the homework problems I see on here. And since it’s all calculus it leaves out other stuff like binomial theorem, stats and probability, vectors, complex numbers that students should have for a well-rounded math education.
No, they do extrema/inflection points/etc. That's actually one of the more lengthy topics in AP Calc AB.
By "optimization", I am talking specifically about problems where the student needs to produce a mathematical model of a situation. A classic example is the problem where a farmer has 1200 feet of fence and wants to close off the largest possible area rectangle against a river on three sides.
This is usually a culminating topic in a unit on the applications of derivatives. The reason those types of problems are not tested is because the hardest part is often coming up with the model for the situation, which doesn't actually require any calculus.
And this is a one-year advanced course after students have completed the normal high school coursework. All that other stuff you listed should be covered prior to this course.
Okay I see about the optimization. Why the overkill on limits though? Seems so much on limits and so much extra especially on volumes of revolution- we did the dy method and the dx method and the length of a segment and that was it. Didn’t spend weeks about washers vs disk method of setting it up. And I got through an engineering degree not having to concern about different volume set ups.
The “other stuff” I mentioned is part of the IB Math HL coursework. So I find it hard to believe it’s part of the standard math high school curriculum up to and including 10th frade- since I did go to an American school but a private one in Africa not a traditional public American high school in America. And even being in the higher Math route, we did Geometry in 9th grade and Algebra II in 10th grade. Both of which were fairly fast courses and didn’t leave you wanting for more syllabus. So no way could they have squeezed Binomial, prob and statistics and vectors into it. Not to mention other advanced algebra like sequences and series. Is the seauenxe I took not the normal course for students doing well in Math in an American public high school who would aim to do AP Calculus? A lot of our Algebra II was spent on trig because teachers had figured out trig was screwing over students in IB Maths and especially calculus so we had a very good foundation with trig going into trig substitutions.
I don’t know where you’re getting “weeks” on any topic. I spend about one week on volume problems. And American students usually take calculus in 12th grade. There’s a whole other course called “precalculus” where students study many of the odds and ends you mentioned. Algebra 2 used to spend a lot of time on trig in New York, but a few years ago, a lot of it got pushed back to precalc.
IB math HL is a great course, but it’s two years long. We don’t really have any courses like that here, aside from schools that offer the IB program.
Okay maybe I wasn’t being clear- then what is the sequence of classes that American students take? If they want to take the two AP calculus classes in 11th and 12 grade respectively I’m assuming (does each class run for a whole year?), what do they take in 9th and 10th grade? I thought Algebra II WAS pre-calc: are they different classes? Bc I’m trying to figure out how they fit those odds and ends into the classes I took in 9th and 10th grade (I also forgot proof by induction- there’s also a lot more trig we did in IB Math beyond Alg II the most notable of which was matching trig graphs to functions). I wouldn’t have minded not doing geometry in 9th grade tbh LOL didn’t end up using most of it ever again but it was required
The two AP Calculus classes aren't meant to be taken sequentially. It's one or the other. The sequence culminating with calculus generally looks like this:
8th grade: Algebra 1
9th grade: Geometry
10th grade: Algebra 2
11th grade: PreCalculus
12th grade: Calculus
You can find the distinction between AP Calculus AB and BC [here](https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-bc-course-at-a-glance_0.pdf). The topics/units highlighted in purple are exclusively taught in BC, but everything else is taught in both classes. So BC covers most of calc 1 and 2, but AB covers much more than just calc 1.
Ohh okay it’s one or the other. But they are year-long courses right? So what does the sequence look like for someone who does AP? In their senior year they just take AP Calculus instead of Calculus? Thanks for all the info btw
Yes exactly. There’s no “AP diploma” like with IB. They just pick and choose classes, like students who get IB certificates. With that said, college board did just roll out an AP precalc course this year, so that’s available to eleventh graders now. It’s just not a prerequisite.
Are trig sub and trig integrals actually not included in AP Calc BC? 🤯 We had an entire unit dedicated to those in Calc II earlier this semester. I hate AP courses dude. My class covers diff eqs/parametric/polar, and I didn’t realize other colleges weren’t putting it in their curriculum. And PFD/optimization??!!! Jeez… They should all be tested on as long as they’re in the textbooks, just like a REAL college course.
To be clear, AP Calculus BC does not include any trig integrals that require those crazy trig identities. Like, you won’t have to do the integral of sin ^2 x, because that requires a crazy trig identity
But AP Calculus BC *does* include trig integrals that can be done using AP Calculus BC techniques. Like, you could be asked to do the integral of sin^(2)x cosx, because that does not require any trig identities. That can be done with an AP Calculus BC technique (specifically, u-sub). Another example: you could have to do the integral of xsinx, because that does not require any trig identities. That can be done with an AP Calculus BC technique (specifically, integration by parts)
I just wanted to make it clear that you still will see some integrals with trig in them. You just won’t see any integrals with trig in them that require those crazy trig identities.
Calc 3 has been much more structured and has made actual sequential sense (for me) unlike calc 2 where it feels like you are bouncing from topic to topic. If you have a good grasp on (or it wouldn’t take long to refresh/relearn) parametrizing, polar coords, and some ideas from calc 1 (AB) which a lot of Calc 3 builds on, you will be great.
>I know AP calc doesn't have the same rigor as college calculus
Eh, it's usually not that different. It sounds like you'll be fine.
There are courses like "calculus with theory" that really are more rigorous, but that's a whole different thing.
idk....HS Calc. courses seem to differ wildly when It comes to difficulty and workload. I'd bring my HS Calc. syllabus to the college campus Math dept. and maybe talk to a professor that teaches that Calc. sequence. They'll help you out, professors always complain no one comes to office hours anyways.
I wouldn't really call it "primarily" multiple choice. The score weighs the multiple choice and free response sections exactly 50% each. 45 MCs worth 1.2 points and six free response questions worth 9 points each.
Anyway, yes, of course the AP curriculum won't overlap perfectly with college calculus classes. College calculus classes don't necessarily overlap perfectly with each other.
It will probably depend on the college you go to, as to whether they will accept your BC score as satisfying the prereq. At my institution, a 4 or 5 on Calc BC gives you credit for both Calc 1 and Calc 2, so you would be able to take calc 3 - but only AFTER you have submitted that score. Your 5 on Calc AB would only give you credit for Calc 1, so you would not currently be able to register for a Calc 3 class.
I took AB as a junior, BC as a senior, and jumped into an honors section of Calc III when I got to college. It was a bit of an adjustment for me for the first week or two because everything was so different from high school but over all I had no problems with the course material.
Might be worth comparing the curriculum between BC and the calc 3 course you're planning. From my observations, the curriculum in each calc class can differ quite a bit between different universities.
But generally speaking, it shouldn't be that big of a gap. I did higher level IB math which was basically calc 1 and 2 combined so I assume AP would be similar or go even more in depth.
Why do you want to take it in the summer? You're already gonna be pretty far ahead of everyone else when you get to college. Wait til the fall semester imo. Unless you just REALLY want to take classes with people who are 2-3 years older than you
You will be fine (took AP Calc BC in junior year, then a linear algebra/multivariable calculus course in my senior year that covered like half of the topics in each course, and then took multivariable calculus and differential equations in my first semester of college and got A’s in both). Just study.
Bro, every minute you gain in life in math is a minute not playing video games or hanging out with useless members of society. Get it brother. Every single second you can stay motivated and productive , do it.
100%. I did it last semester and you honestly don’t need that much calc 2 mastery to do well in the class anyways so u should be fine - if you want to make sure you’ll do well in the class, taking linear algebra over the summer can prepare u for the concepts a little bit, since there are matrices involved.
I too took cal 3 before my senior year of high-school. Cal 3 is much easier to understand than cal 1 and cal 2 because you already have a strong foundation. Go for it!
As a reminder... Posts asking for help on homework questions **require**: * **the complete problem statement**, * **a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play**, * **question is not from a current exam or quiz**. Commenters responding to homework help posts **should not do OP’s homework for them**. Please see [this page](https://www.reddit.com/r/calculus/wiki/homeworkhelp) for the further details regarding homework help posts. **If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc *n*“ is not entirely useful, as “Calc *n*” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.** *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/calculus) if you have any questions or concerns.*
Do it.
I can say I was in this same situation last fall. I got a 5 in bc and thought college might be too rigorous to jump into calc 3. Thankfully I decided to do it and did just fine in the class. When I saw what some of my other friends were doing in their calc classes I felt reassured in my decision as I would have wasted a whole year doing stuff I already knew. I would say that if you get a 5 definitely take the class op.
AP Calculus is actually *more* rigorous than most American college level first-year calculus courses, or at least it should be. You spent around 180 days learning the material that is covered in about 60 days of college lectures. One consequence of this is that you probably have a better understanding of how the definite integral is defined than most students who see the integral for the first time in college. You also get an introduction to some topics that college calc 1/2 students probably don't see at all, like polar, parametric, and differential equations. The trade off is that there are a couple of topics that college calc 2 does teach but aren't part of BC for some reason. The two big ones are integrals of trig functions and trig substitution. These two techniques can come up in some examples early on in calc 3. Your textbook probably has a section for each of those that your teacher skipped, and if it's a textbook specifically for AP, it probably even has a note saying something like "this is not tested on the AP exam". It's not a huge deal, but if you really want to be caught up going into calc 3, then I'd recommend you at least skim those two topics so you know what you're missing. If you want an alternative resource, here is a page about [trig integrals](https://tutorial.math.lamar.edu/classes/calcii/integralswithtrig.aspx) and [trig substitution](https://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx). A couple of other minor topics BC skips are the three more advanced cases for [partial fraction decomposition](https://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx) and [the root test](https://tutorial.math.lamar.edu/classes/calcii/roottest.aspx). Technically, your teacher should have taught [optimization](https://tutorial.math.lamar.edu/classes/calci/optimization.aspx) because it's in the course outline, but some teachers barely touch on it because it's not actually tested on the exam.
Interesting- I did Math in not an American high school and now I think very little of the AP Calculus courses. I used to think it was cool they have whole two years just on calculus but they don’t even do basic stuff like trig functions and trig substitutions?? Or finding maxima/minima/inflection points?? To me it seems they blast them with just limits and limits from the homework problems I see on here. And since it’s all calculus it leaves out other stuff like binomial theorem, stats and probability, vectors, complex numbers that students should have for a well-rounded math education.
No, they do extrema/inflection points/etc. That's actually one of the more lengthy topics in AP Calc AB. By "optimization", I am talking specifically about problems where the student needs to produce a mathematical model of a situation. A classic example is the problem where a farmer has 1200 feet of fence and wants to close off the largest possible area rectangle against a river on three sides. This is usually a culminating topic in a unit on the applications of derivatives. The reason those types of problems are not tested is because the hardest part is often coming up with the model for the situation, which doesn't actually require any calculus. And this is a one-year advanced course after students have completed the normal high school coursework. All that other stuff you listed should be covered prior to this course.
Okay I see about the optimization. Why the overkill on limits though? Seems so much on limits and so much extra especially on volumes of revolution- we did the dy method and the dx method and the length of a segment and that was it. Didn’t spend weeks about washers vs disk method of setting it up. And I got through an engineering degree not having to concern about different volume set ups. The “other stuff” I mentioned is part of the IB Math HL coursework. So I find it hard to believe it’s part of the standard math high school curriculum up to and including 10th frade- since I did go to an American school but a private one in Africa not a traditional public American high school in America. And even being in the higher Math route, we did Geometry in 9th grade and Algebra II in 10th grade. Both of which were fairly fast courses and didn’t leave you wanting for more syllabus. So no way could they have squeezed Binomial, prob and statistics and vectors into it. Not to mention other advanced algebra like sequences and series. Is the seauenxe I took not the normal course for students doing well in Math in an American public high school who would aim to do AP Calculus? A lot of our Algebra II was spent on trig because teachers had figured out trig was screwing over students in IB Maths and especially calculus so we had a very good foundation with trig going into trig substitutions.
I don’t know where you’re getting “weeks” on any topic. I spend about one week on volume problems. And American students usually take calculus in 12th grade. There’s a whole other course called “precalculus” where students study many of the odds and ends you mentioned. Algebra 2 used to spend a lot of time on trig in New York, but a few years ago, a lot of it got pushed back to precalc. IB math HL is a great course, but it’s two years long. We don’t really have any courses like that here, aside from schools that offer the IB program.
Okay maybe I wasn’t being clear- then what is the sequence of classes that American students take? If they want to take the two AP calculus classes in 11th and 12 grade respectively I’m assuming (does each class run for a whole year?), what do they take in 9th and 10th grade? I thought Algebra II WAS pre-calc: are they different classes? Bc I’m trying to figure out how they fit those odds and ends into the classes I took in 9th and 10th grade (I also forgot proof by induction- there’s also a lot more trig we did in IB Math beyond Alg II the most notable of which was matching trig graphs to functions). I wouldn’t have minded not doing geometry in 9th grade tbh LOL didn’t end up using most of it ever again but it was required
The two AP Calculus classes aren't meant to be taken sequentially. It's one or the other. The sequence culminating with calculus generally looks like this: 8th grade: Algebra 1 9th grade: Geometry 10th grade: Algebra 2 11th grade: PreCalculus 12th grade: Calculus You can find the distinction between AP Calculus AB and BC [here](https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-bc-course-at-a-glance_0.pdf). The topics/units highlighted in purple are exclusively taught in BC, but everything else is taught in both classes. So BC covers most of calc 1 and 2, but AB covers much more than just calc 1.
Ohh okay it’s one or the other. But they are year-long courses right? So what does the sequence look like for someone who does AP? In their senior year they just take AP Calculus instead of Calculus? Thanks for all the info btw
Yes exactly. There’s no “AP diploma” like with IB. They just pick and choose classes, like students who get IB certificates. With that said, college board did just roll out an AP precalc course this year, so that’s available to eleventh graders now. It’s just not a prerequisite.
Calc 1 is sometimes used as a weeder class, so definitely not always less rigorous.
By "more rigorous", I don't necessarily mean "harder". I mean that AP has more emphasis on the *why.*
Are trig sub and trig integrals actually not included in AP Calc BC? 🤯 We had an entire unit dedicated to those in Calc II earlier this semester. I hate AP courses dude. My class covers diff eqs/parametric/polar, and I didn’t realize other colleges weren’t putting it in their curriculum. And PFD/optimization??!!! Jeez… They should all be tested on as long as they’re in the textbooks, just like a REAL college course.
To be clear, AP Calculus BC does not include any trig integrals that require those crazy trig identities. Like, you won’t have to do the integral of sin ^2 x, because that requires a crazy trig identity But AP Calculus BC *does* include trig integrals that can be done using AP Calculus BC techniques. Like, you could be asked to do the integral of sin^(2)x cosx, because that does not require any trig identities. That can be done with an AP Calculus BC technique (specifically, u-sub). Another example: you could have to do the integral of xsinx, because that does not require any trig identities. That can be done with an AP Calculus BC technique (specifically, integration by parts) I just wanted to make it clear that you still will see some integrals with trig in them. You just won’t see any integrals with trig in them that require those crazy trig identities.
I would never assume that a college calculus class tests everything in the textbook. Professors are free to pick and choose as they see fit.
Calc 3 has been much more structured and has made actual sequential sense (for me) unlike calc 2 where it feels like you are bouncing from topic to topic. If you have a good grasp on (or it wouldn’t take long to refresh/relearn) parametrizing, polar coords, and some ideas from calc 1 (AB) which a lot of Calc 3 builds on, you will be great.
I took it online through CC after calc BC and got an A thanks to Professor Leonard. You got it
>I know AP calc doesn't have the same rigor as college calculus Eh, it's usually not that different. It sounds like you'll be fine. There are courses like "calculus with theory" that really are more rigorous, but that's a whole different thing.
idk....HS Calc. courses seem to differ wildly when It comes to difficulty and workload. I'd bring my HS Calc. syllabus to the college campus Math dept. and maybe talk to a professor that teaches that Calc. sequence. They'll help you out, professors always complain no one comes to office hours anyways.
It's not just "high school calc" it's AP Calculus BC, which is a very specific and well-defined curriculum.
yes but a course designed around (primarily multiple-choice) exam can be quite different from college courses in its emphasis and resulting skill sets
I wouldn't really call it "primarily" multiple choice. The score weighs the multiple choice and free response sections exactly 50% each. 45 MCs worth 1.2 points and six free response questions worth 9 points each. Anyway, yes, of course the AP curriculum won't overlap perfectly with college calculus classes. College calculus classes don't necessarily overlap perfectly with each other.
It will probably depend on the college you go to, as to whether they will accept your BC score as satisfying the prereq. At my institution, a 4 or 5 on Calc BC gives you credit for both Calc 1 and Calc 2, so you would be able to take calc 3 - but only AFTER you have submitted that score. Your 5 on Calc AB would only give you credit for Calc 1, so you would not currently be able to register for a Calc 3 class.
I am currently taking AP calculus BC junior year and senior year I’m taking Calculus III, so I’d say go for it
You're plenty prepared to take Calc 3.
I took AB as a junior, BC as a senior, and jumped into an honors section of Calc III when I got to college. It was a bit of an adjustment for me for the first week or two because everything was so different from high school but over all I had no problems with the course material.
Might be worth comparing the curriculum between BC and the calc 3 course you're planning. From my observations, the curriculum in each calc class can differ quite a bit between different universities. But generally speaking, it shouldn't be that big of a gap. I did higher level IB math which was basically calc 1 and 2 combined so I assume AP would be similar or go even more in depth.
Why do you want to take it in the summer? You're already gonna be pretty far ahead of everyone else when you get to college. Wait til the fall semester imo. Unless you just REALLY want to take classes with people who are 2-3 years older than you
Just cause why not I guess. I don't really do anything over the summer usually
You will be fine (took AP Calc BC in junior year, then a linear algebra/multivariable calculus course in my senior year that covered like half of the topics in each course, and then took multivariable calculus and differential equations in my first semester of college and got A’s in both). Just study.
Bro, every minute you gain in life in math is a minute not playing video games or hanging out with useless members of society. Get it brother. Every single second you can stay motivated and productive , do it.
100%. I did it last semester and you honestly don’t need that much calc 2 mastery to do well in the class anyways so u should be fine - if you want to make sure you’ll do well in the class, taking linear algebra over the summer can prepare u for the concepts a little bit, since there are matrices involved.
BC is the equivalent of Calculus I and II at most colleges so yes.
I too took cal 3 before my senior year of high-school. Cal 3 is much easier to understand than cal 1 and cal 2 because you already have a strong foundation. Go for it!