FutureDr08

Hi, I am a C student in AP Calc AB, and I find the material pretty challenging, but need some help to do well. I really want to score a 4 and get college credit.

Any advice on how to study for multiple choice and free response?

dchow08

Hi,

I got a 5 on the test last year, and I really knew the material well, so I think I'm qualified to give you some tips:

- You've got to learn the material. There is just no way around it. So if you want that 4 or 5, you've got to get one-to-one with the Calculus textbook you're using. Get serious. It's there to help you.
- Make sure you know the very important stuff (all the stuff is important, really):

- derivatives, position, velocity, acceleration, the difference between velocity and speed
- power rule, other rules for finding the derivatives, product rule, chain rule, quotient rule
- related rates (the trick is to find a relationship between the derivatives. There's always something like dV/ds x ds/dt = dV/dt (since the ds's cross out)).
- understanding of integration (for example, if I have a chart of how much oil is depleted over time, what would the area under the curve mean? Stuff like that. There are examples on old AP tests, on the CollegeBoard website).
- memorize formulas for integration (do power rule backwards, substitution)
- Mean Value Theorem, FUNDAMENTAL THEOREM OF CALCULUS, Intermediate Value Theorem (?)
- LRAM, RRAM, MRAM techniques of estimating area by hand.
- Geometric, 3-d solids, 2-d areas (find area under curve, slice method, washer method, disk method, shell method).
- things you've just got to memorize (derivative of sin, cos, tan, inverse sin, inverse cos, inverse tan, e, ln)
- Extra stuff if you have time that might be asked on multiple-choice just to stump people: partial fractions, trigonometric substitution
- Other stuff I didn't mention, such as slope fields

The point is: there is no way around it. You've got to know what you're doing. Understand the concepts! I'm concerned that, since you do have a C, you're not understanding the concepts. It's easy to fall behind. You've got to catch up!

I recommend Calculus Made Easy by Thompson, Gardner (helps with understanding of derivatives and integrals). This should have been read a long time ago, when you were just learning about derivatives. It gives a very good explanation of the concepts of the derivative and integral.

Make sure you really know for free response
- integrating to find volume of solid rotated around axis/area under curve
- chart problems concerning integration (what does it mean in this context)
- related rates
- position, velocity, acceleration (look at old FRQ's, they ask this all the time)
- slope fields. This might be big this year. They haven't asked a slope fields FRQ in quite a long time, and this year might be it. Last year when I took the class my teacher was like, make sure you know slope fields! There's a good chance they'll show up this year! But, on last year's test, slope fields only showed up on one multiple-choice question. So expect it this year!

If you need help, feel free to send me a private message. Don't ask me for specific homework questions, but if you don't understand a concept (e.g. Washer method), feel free to ask.

TheMathProf

Slope fields showed up in 2006, which is not that long ago. If you see slope fields, it has so far always been paired with a separable differential equation that is worth 5-6 points. The trick here, however, is that separating, integrating, including the +C, and solving for C from the initial condition gives you all but one of these points, unless they ask you for the domain, which is usually an additional point on top of this.

Partial fractions and trig substitution are not AB topics.

If you're cramped for time, related rates is a difficult topics for most students that usually comprises just one question on the multiple choice if you're lucky. If you're unlucky, it's one of the six free response questions, though. It hasn't been lately, and I'm not sure what this means.

I would make sure you know the concept of calculating average value. That topic comes up far more often than it deserves to given its relative importance to the idea of calculus.

In addition to the above free response question topics, I would make sure you're familiar with the Fundamental Theorem of Calculus. They almost always give a graph of some function. Sometimes that function is directly labeled f ', but other times, it's just called g(x), and they define f as the integral from some constant to x of g(x) dx. These questions are pretty regularly on the exam, and if you understand the concepts well, it's a pretty manageable 9 points.

FutureDr08

thanks for the suggestions, i have a month before the test, which I think is enough time to "master" the material meaning I have learned all the things you all mentioned but not mastered it because I make errors in the process or have goofy math mistakes, but I will def. study everything you mentioned

keep the advice coming, thanks

TheMathProf

The thing that I see a lot when it comes to goofy mistakes has to do with the chain rule. Some people always forget it (a sure ticket to a 1), while other people only sometimes forget it.

The other thing I would do is take your time through the review process. You can work on getting faster later, but if it takes you fifteen minutes to get through part (a) and make sure you make no mistakes, then you should take fifteen minutes now. Work on getting things right at the moment would be my advice.

FutureDr08

ok we are doing good practice in class, but I am afraid of the noncalc. free reponse questions as in 07 they were TOUGH...

also is the Princeton Review book a good review of major topics and prepare me well?

dchow08

TheMathProf: I think when I was taking the test last year there was a multiple-choice question that asked about partial fractions. It's possible that they ask one super-hard question that few people will get.

There was a related rates question last year.

One of my friends really liked the Princeton Review book, claiming that it was the only reason he got a 5 on the test. It's a little hard for me to believe, though. Anyway, if you want to find out about test prep books, go to Amazon and look at the reviews. There are lots of reviews on that book.

Yes, the 2007 FRQ's for non-calculator section were tough; I took a lot of past FRQ's for practice and the 2007 ones were more difficult than the rest. But the test is graded on a curve, so as long as you did relatively well you should be fine. Don't worry about that. If you suffer, everyone else will too!

intellec7

I agree with TheMathProf that Partial Fractions is a BC topic. Perhaps they expected you to integrate numerically, or by another method.

FutureDr08

I hate integrals, I hate related rates, I hate volume by cross-sections....lol I do not like calculus very much, but not many people do....

I am more of a Bio person myself.

back to PR book review!

FutureDr08

any topics on FR that may appear this year based on teacher, students, and class predictions? (ironically, they are somewhat true and sometimes very true)

so if related rates was last year, there will be none this year?

TheMathProf

I don't know that the pattern holds from year-to-year of what's going to be on it or not. My understanding is that it takes two years to actually make a test, so this year's test was already in the making while the 2007 test was being administered.

I would predict a calculator-active question based on areas and volumes of solids of revolution. Sometimes there is a volumes with known-cross-sections problem here, and sometimes there isn't.

I would predict a Fundamental Theorem of Calculus question of some sort.

I would predict some kind of function that test your knowledge of how functions accumulate over time. Since you've seen the 2007 test, this is question #2 on that test, which indicates something to do with water in a tank.

I would predict some kind of position, velocity, acceleration question.

I'd expect some kind of question where some constant (usually k) indicates something to do with some kind of function at some moment in time. Sometimes they stick this one in the area/volumes question, sometimes they stick this in the accumulation question, sometimes they stick this elsewhere.

I would expect a slope fields and separable differential equations question. I know they didn't have one last year. Just a hunch on this one, as I have no inside information.

I'd also expect some question that has discrete data points given in a table rather than in an easily identifiable function form, where you'll have to do average rate of change, approximations using rectangles/trapezoidal rule, and the like. This may be combined with one of the earlier questions.

Also, and again, this is just a hunch, but I found it really interesting that they got really particular about the conditions needed for the Mean Value Theorem and the Intermediate Value Theorem on Question #3 of last year's FRQ's. I strongly suspect this will be back sometime in the near future, although I don't know if I'd be so bold as to predict that it will be in place for this year. (Interestingly enough, this is the first FR question in quite awhile where the nationwide average was under 1.00 in a long time.)

* * * * *

I don't personally recommend any particular prep book simply because of my inexperience with them. I would personally use the ones whose explanations of topics make the most sense.

* * * * *

I forgot about the related rates question last year. Luckily, and this is unlike past precedent with these problems, you only lost 3 points maximum if you didn't know how to do it.

As far as the partial fractions, it won't be on the AB test. It will either be a problem that you know how to do using some other method (u-substitution perhaps?) or it will be on the calculator section, and they will expect you to use your calculator to get it done.

* * * * *

Two last pieces of advice that I forgot about the last time through:

(1) Don't give up on a question just because you can't answer one part of it. Many times, questions have re-entry points. For instance, last year's related rates question (#5) had a re-entry point at part (c) if you couldn't do the related rates question in part (b). Sometimes, you can start from a later point and earn a few valuable points where other students had already given up.

(2) You really only need about 70 points (out of 108) in order to make a 5. You only really need about 55 points in order to make a 4. Now some of the questions are harder on the AP Test than they may be in the class, but I know that a lot of the folks I know freak out about these test because they're used to everything being scored according to a 90-80-70-60 type of system. That kind of thinking will really freak you out and could really mess with you on the actual exam.

asc3nd

Are there any calculator tricks/programs when taking the AB test?

TheMathProf

Honestly, there really shouldn't need to be any.

There are really only four things that you can do on your graphing calculator without showing supporting work anyway:

(1) After writing out a definite integral, you can evaluate it.
(2) After writing out or being given a function, you can evaluate the derivative at a point.
(3) Given a function, you can graph the function on a given window.
(4) You can use the calculator to find the zeroes of a function, or the intersection point of two functions.

Since you need to show work for everything else anyway, there's really little benefit to any programs.

FutureDr08

"Also, and again, this is just a hunch, but I found it really interesting that they got really particular about the conditions needed for the Mean Value Theorem and the Intermediate Value Theorem on Question #3 of last year's FRQ's. I strongly suspect this will be back sometime in the near future, although I don't know if I'd be so bold as to predict that it will be in place for this year. (Interestingly enough, this is the first FR question in quite awhile where the nationwide average was under 1.00 in a long time.)"

Funny you say that, my teacher was showing us the 2007 question yesterday and she said last year was really bizarre and tough because the AP test makers tried to put in every topic onto the FR, and the theorems were crazy she thought, many AP calc teachers complained but I guess there was a big CURVE? and yeah that sucks if this year's test was made 1-2 years ago, because then it might be as hard as last year AHHH NOW YOU ARE SCARING ME....

anyways yeah THANKS SO MUCH for your predictions, because I do appreciate them and will make sure I get those as well as other topics, moreover, are you a math teacher?

asc3nd

How can you do:
(1) After writing out a definite integral, you can evaluate it.
(2) After writing out or being given a function, you can evaluate the derivative at a point.
(4) You can use the calculator to find the zeroes of a function, or the intersection point of two functions.