Agreed about the practice tests. The AP folks just have a certain way of presenting information that can be intimidating if you don't know both the way that the questions are going to be asked and the way that responses are going to be scored.
In preparation for Calc AB last year, I took 3 practice exams from a PR book, and also had available the 2003 and 1998 released exams. On the Multiple Choice section of the exam, there was nearly not a single question that was unfamiliar to me (with the exception of 1 or 2). They always like to ask the same things. I personally think that the most intimidating ones involve the FTC, and the derivative of inverse functions. I think these are both simple concepts, but the language used in the question used to throw me off.
Also, the FRQ likes to ask similar things too. Almost surely there will be area between curves/solid of revolution question as the first question of the FRQ. Make sure to know that formula and know how to find points of intersection on your calculator. Also, the FRQ enjoys testing on concepts in calculus like if you integrate the rate of change in position (or velocity) you'll get the change in position (or displacement) Also make sure to be able to prove your statements. If you want to say that at x = 3, f(x) has a point of inflection, you must also write the reason this is is because f''(3) = 0, or f''(3) = undef.
Always be explicit, don't use pronouns. "It is increasing" is not good. Explaining "f(x) is increasing at 3<x<5 because f'(x) > 0" would probably get you some points, though.
Make sure to read very carefully on the multiple choice. Two key differences are the difference between average rate of change and average value and finding the equation of a line given the slope (typically tangent line problem but if asking for the line with the given slope, you have to integrate).
Your best bet would be to do the FR's available online. However, questions about different series show up more on the MC so try to find some old tests. As intellec7 mentioned, you need to be able to explain your answer to the FR, which shouldn't be too hard since the calculations are rather simple. Reading the question is very important because a few words can make the difference in whether you need to integrate or differentiate in the problem.
To be perfectly accurate, a point of inflection occurs when f changes concavity, which means it is not enough for f "(x) = 0 or for f "(x) to be undefined. The key for a point of inflection is for the sign of f "(x) to change, either from positive to negative or from negative to positive.
The reason why you look for f "(x) = 0 or f "(x) to be undefined is because these give you the locations of x-values where this sign change could occur.
For instance, the function f(x) = x^4 has f "(x) = 12x^2, so f "(x) = 0 at x = 0. However, f "(x) > 0 for all x except x = 0, and so there is no inflection point at x = 0.
The rest of the advice in the last two posts is spot on.
Replies to: Best way to study for Calculus?
Also, the FRQ likes to ask similar things too. Almost surely there will be area between curves/solid of revolution question as the first question of the FRQ. Make sure to know that formula and know how to find points of intersection on your calculator. Also, the FRQ enjoys testing on concepts in calculus like if you integrate the rate of change in position (or velocity) you'll get the change in position (or displacement) Also make sure to be able to prove your statements. If you want to say that at x = 3, f(x) has a point of inflection, you must also write the reason this is is because f''(3) = 0, or f''(3) = undef.
Always be explicit, don't use pronouns. "It is increasing" is not good. Explaining "f(x) is increasing at 3<x<5 because f'(x) > 0" would probably get you some points, though.
Your best bet would be to do the FR's available online. However, questions about different series show up more on the MC so try to find some old tests. As intellec7 mentioned, you need to be able to explain your answer to the FR, which shouldn't be too hard since the calculations are rather simple. Reading the question is very important because a few words can make the difference in whether you need to integrate or differentiate in the problem.
The reason why you look for f "(x) = 0 or f "(x) to be undefined is because these give you the locations of x-values where this sign change could occur.
For instance, the function f(x) = x^4 has f "(x) = 12x^2, so f "(x) = 0 at x = 0. However, f "(x) > 0 for all x except x = 0, and so there is no inflection point at x = 0.
The rest of the advice in the last two posts is spot on.