The AP Test Thread

**this1neguy** · Joined: 19 Aug 2007 Posts: 5444 Location: Flint, MI

When I took AP Psych a couple of years back my teacher didn't do a great job of preparing us and silly me didn't study enough outside of class, so I ended up getting a 3 despite thinking the test felt pretty easy. Shrug. If you make sure to study well or you have a better teacher than mine, it shouldn't pose a problem.
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**yksi-kaksi-kolme** · Joined: 22 Jun 2008 Posts: 2803 Location: philly skramzzzz

OK so my teacher cleared me to take Calc BC instead of AB, and now I'm asking scorehero the best way to self-teach this stuff. I already know integration by trig substitution, trig power-reducing, partial fraction decomps, and improper integrals, so I have integration pretty well covered (need to review Shell method). Plus I know how to turn every indeterminate form into a L'Hopital-able one. Basically, this is what I plan to learn inside and out:

-Differential equations
-Parametric/Polar Functions (seem pretty easy)
-Series and Sequences

I do need to know a few more odds and ends outside of those main things, though. Arc length is still sketchy since half the time I can't even integrate the function... any other tiny things above AB that I need to know?

I've already started learning each concept... diff eq is kinda sketchy so I need to look at that more (except seperables those are easy), parametric functions are insanely easy, polar ehh gotta look at those more in-depth, and I started off series and sequences by proving Euler's formula with the Maclaurin series expansions of e^x, sinx, and cosx so that helped make them a little more intuitive, but I still have to learn the polynomial stuff.

Can anyone recommend a good review book to self-teach BC materials? I have Larson, Hostetler, and Edwards but I'm looking for more practice outside of that book; something more AP-like.
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**bclare** · Joined: 21 Jun 2008 Posts: 6048 Location: Boston

If you know the AB stuff well enough, you can get a 4 on BC without even knowing any of the BC stuff. If I understand correctly that you're taking the test this year, in a little over a month, then it may be best to focus on being really good at AB problems and learning sequences and series.

As for a book, I've generally been quite pleased with Schaum's guides. They aren't AP specific, so you'd just be looking at a Calculus outline. It's on amazon for $11 here but you should be able to find it in a Barnes and Noble or whatever bookstore. One thing about Schaum's outlines is that they aren't big on theory, it's just a very mechanical overview with practice problems. Good if you're just hoping to beef up for a test though.
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**ready2rock** · Posted: Fri Mar 30, 2012 8:10 am Post subject:

I didn't take the BC test in high school, but when I was in calc 2 last semester, I found this youtube user pretty helpful.

On another note, I'm in calc 3 right now and really enjoying it. i feel like my professor really has a passion for mathematics, and the material is really interesting (we're doing double and triple integrals).
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**JosephL** · Posted: Fri Mar 30, 2012 10:52 am Post subject:

**yksi-kaksi-kolme** · Joined: 22 Jun 2008 Posts: 2803 Location: philly skramzzzz

Oh yeah I've heard of Schaum's outline. The other calc teacher at my school uses it, though much to the disdain of his students because he's a very old-fashioned guy who's brilliant with math but has such an advanced understanding that he can't convey the concepts to students in a way they can understand...

BUT ANYWAY I'm hoping that means I can snag a spare copy from him. Not to sound cocky but I'm pretty damn confident that I can get a very safe 5 on AB so I just figured it wouldn't be too tough to learn the extra stuff. And really bclare, a 4 on BC? That's actually pretty cool... if anything it makes me feel less worried about sucking at differential equations

I'll be sure to go hard on series. I already know the definitions of Taylor and Maclaurin, I just have to learn applications (if those are even covered on BC) and the T/M polynomials.
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**bclare** · Joined: 21 Jun 2008 Posts: 6048 Location: Boston

There could be some applications. Really though, if you ace the AB parts then that already puts your score at a 3, almost a 4, so if you know anything about BC then a 4 is entirely doable. Sequences and series is definitely the major BC topic. If you have any questions, feel free to ask (maybe the calculus thread would be a better place than here)
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**yksi-kaksi-kolme** · Joined: 22 Jun 2008 Posts: 2803 Location: philly skramzzzz

OK, if I have any questions I'll ask them there as I get further learning this stuff. The idea of Taylor series makes a lot of sense though, especially with the pictures on Wikipedia showing the idea behind them (approximating a function by increasing the degree of a polynomial to infinity).

I feel pretty cool though, apparently I'm the first person at my school who's decided to take BC and I'm not going to waste the opportunity to prove myself provided how much negotiating it took to even be allowed to take it.
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**yksi-kaksi-kolme** · Joined: 22 Jun 2008 Posts: 2803 Location: philly skramzzzz

So it's been over 48 hours and the Calc BC FRQs have been released. I wasn't sure whether to discuss them here or in calc thread, but I settled on here.

I think I did very well. #1 was pretty easy AB-level stuff, and I knew how to do every part correctly, so hopefully I'll get full credit if not for some technicality.

#2 was a little tougher for me; I ran out of time unfortunately. I got part b and d easily, but a and c tripped me up. I knew the first part of a, hopefully (moving to the right because the change in x with respect to change in t is positive?) but the second part I only scribbled down dy/dx = (dy/dt)/(dx/dt) and wasn't able to do the calculation in time, unfortunately. c I had no clue, I just plugged numbers into the derivative since derivative of position is EDIT: velocity... probably not right. I think velocity is the integrand of the arc length integral. Whatever, I know I got at least half of this one right.

#3 was simple fundamental theorem stuff.

#4 was a VERY interesting question, imo. I really like how comprehensive it was, having you approximate the integral four different ways. I confidently knew all 4 ways and my answers were very reasonable... this was a cool question.

#5 was balls because the variables kept tripping me up - part a was at least obvious, but in B I forgot to add my dB/dt when I derived B. Oops. C I was only able to solve it in terms of t, not B. Whatever this question was dumb

#6 was a gimme - simple Maclaurin series and Taylor Remainder stuff. Very confident with this one especially since I checked it with WolframAlpha

So yeah that was my experience with the FRQs. I'm very confident in 4 of the 6 free responses, and with the other two, I know I got one half right and the other like maybe a third right. How did all you other guys who took it do?
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**sorasgoof** · Joined: 09 Mar 2008 Posts: 2314

So, IB exams.

...more stressful than any AP exam I've ever taken. >_>
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**bclare** · Joined: 21 Jun 2008 Posts: 6048 Location: Boston

**yksi-kaksi-kolme** · Joined: 22 Jun 2008 Posts: 2803 Location: philly skramzzzz

Hm, so what I got for 5c on the exam was:

dB = dt/5 (100-B)
dB/(100-B) = dt/5

-ln|100-B| + C = t/5
t = -5ln|100-B| + C

0 = -5ln|100-20| + C
C = 5ln|80|

t = -5ln|100-B| + 5ln|80|
t = 5ln|80/(100-B)|

Is that correct? I thought I had to get it in terms of B = something. Differential equation notation greatly confuses me for some reason...

EDIT oh wait you have to exponentiate to solve for B don't you
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**bclare** · Joined: 21 Jun 2008 Posts: 6048 Location: Boston