<p>I know the AP Calculus BC has more topics than AP Calculus AB. I also know the AP Calculus BC provides an AB sub-score.</p>
<p>My questions are:
- Is the AP Calculus BC exam have more difficult/challenging problems than AB?
- In the AP Calculus BC exam, are the topics that are covered in AB involve more challenging problems than the problems for the same topics in the AB exam?</p>
<p>Simply,
Is AP Calculus BC = AP Calculus AB + more topics
OR
Is AP Calculus BC = AP Calculus AB + more topics + much harder problems?</p>
<p>I have no idea what the BC / AB difference is like, but judging by the BC class I am taking, there is a BIG difference. The BC covers integration techniques much more in-depth than AB: I am sure that improper integrals will appear on BC while on AB they will probably not. My teacher pulls problems from actual BC exams in practice tests, and they are definitely much more challenging than anything the AB class is getting as problems. </p>
<p>I also have a question, and I don’t feel like making a new thread, since it’s on the topic- </p>
<p>Does the BC test cover trig substitution and power reduction formulas with trig? We did not go over this in class for some reason.</p>
<p>The topics that are on both the AB and BC exam are covered in roughly comparable difficulty. Some (I don’t know how many) of the multiple-choice questions are exactly the same, as are three of the free response questions.</p>
<p>That being said, some problems “become” harder questions on the BC exam, simply because you have more techniques to look at. AB pretty much only has integration techniques for the basic functions and u-substitution, while BC also gets integration by parts, integration by partial fractions, and improper integrals. So there are more techniques to choose from in approaching a problem. A BC student might lose valuable trying to integrate a particular problem by parts, when an AB student might be more likely to get the question right because the easier u-substitution is the only technique that student thinks to try.</p>
<p>The added topics in BC include the extra integration techniques, sequences and series, and derivatives and integrals using both polar and parametric equations. Whether these topics are harder than the AB topics is a matter of personal opinion.</p>
<p>The BC test does not cover trig substitution and power reduction formulas with trig. Once (on an AB test!), I saw a multiple choice question where the substitution of x = sin (theta) (or some other trig function, can’t remember off the top of my head) was given for an integral, and the questions asked which integral was equivalent. But that’s really just a u-substitution question at that point once the substitution itself is given.</p>
<p>TheMathProf, thanks for that info. So basically you don’t need to master trig sub (the one used to integrate circular functions, etc) to pass the test? How in-depth are the solids of revolution questions (with/without cross sections)?</p>
<p>@bokannelida: (1) Nope, the trig substitution doesn’t show up at all.</p>
<p>(2) As far as the solids of revolution questions, it’s pretty much guaranteed to show up in the free response for the AB test (I think I’ve seen one year in the last ten where it hasn’t), and it’s probably better than a 50-50 shot on BC. Usually, they’ll give you one of two situations: it’ll be calculator active in which case you can graph the region in question on your calculator; or it will be non-calculator, in which case, they’ll likely give you two functions whose points of intersection are relatively trivial to find (every once in awhile, they’ll just hand you the points of intersection, but this is fairly rare). Given the trend towards more non-calculator questions this year, I would expect the latter. As far as cross-sections go, you’re really only likely to find squares, semi-circles, triangles, and rectangles; it doesn’t get too elaborate.</p>
<p>And indeed, bobtheboy’s comment is pretty accurate if you’re talking about the class. My school’s BC class is a lot harder than my school’s AB class because of the pacing (we’re one of the schools that does BC instead of AB rather than after).</p>
<p>It’s not as bad as some think they are. There’s almost always one full FR question dedicated to it, and I’d say somewhere in the neighborhood of 5-10 MC questions (I’d lean closer to 5).</p>
<p>The worst part of sequences and series for most folks is the Lagrange Error Bound. Some years, they throw that on the Free Response and a lot of students struggle with it. Some years, it’s on the multiple choice instead, and BC students around the nation are heard rejoicing.</p>
<p>While you should technically know all the tests, focusing on interval of convergence and writing Taylor series probably gets you the most bang for your buck. Ratio Test is absolutely huge for calculating the radius of convergence, and most of your endpoints to determine the interval of convergence are going to be found using an nth-term test or an Alternating Series Test. Knowing those tests, the Geometric Series Test, and the Limit Comparison Test can probably get you through 90% of the questions on series.</p>
<p>From the feedback I hear, you probably want to make sure you work through a lot of what they’ve done in previous years with sequences and series on the Free Response. A lot of students tend to freak out the first time they look at the AP format for the questions, but once you get the hang of them, they’re really not as bad as they’re made out to be.</p>
<p>BC= AB + more topics
AB corresponds to Calc 1 and BC to Calc 1 and 2, so it’s just more stuff packed in to same time period.
The way the BC test works, you get your AB subscore based on how well you did on the parts of the questions that are AB material. So yes the problems on the BC test are more difficult, but just bc they’re integrating more concepts.</p>
<p>@TheMathProf
My school recommends accelerated students take BC instead of AB. Will the BC class prepare me to take both AP tests? I assume that each will count towards National AP Scholar.</p>
<p>You can only take AB or BC in a single calendar year, not both.</p>
<p>Whether taking both tests in consecutive years (i.e. AB junior year and BC senior year) would count towards AP Scholar, I don’t know. If I had to venture a guess, I’d say no, but wouldn’t be surprised to see the answer the other way.</p>
<p>But yes, the BC class would prepare you to take the AB exam, if you decided to go that way. Although if your plan is to take the AB exam, you’d be better off in an AB class, if that were offered.</p>
<p>You either take the BC or AB test. Taking both would not only be morally ■■■■■■■■, but would demonstrate your laziness when it comes time to review your APs for adcoms.</p>
<p>There are many schools that offer AP Calculus AB one year followed by AP Calculus BC the next year as the recommended sequence in their school. Typically, schools that do this teach BC starting where AB left off, and adding in some additional advanced calculus type topics that would prepare kids for Calc III or even Diff EQ. Taking the classes recommended by your school and in the order specifically crafted by your school’s math department wouldn’t be negatively looked down upon by admissions officers.</p>
<p>I have taken both classes, and thus have relevant experience. Calc BC is Calc AB, with series (a nightmare) and a few more integrals. The difficulty level is not high for either course, so it would be best to choose whichever one has classroom policies more favorable to your disposition.</p>