Can I use short excerpts from online materials to prepare college test questions?

Online materials is too vague a term. What are you planning to excerpt? Since this is for a commercial venture, you would probably have to get permission as it would most likely not be considered fair use

Length of material has no bearing. The answer is no for publishing for a price. The book is for sale for a profit and the questions and answers the book have to be treated as part of the book. I have seen math questions used in textbooks and study guides give a credit to the source and the words to a say use authorized / approved by copyright holder.

My opinion: The publisher of the textbook you are writing for will not want to be exposed to such a legal risk. This is why so many educational materials use constructed passages—written to order by hired writers. Fair use is for things like quotations in book reviews and not for commercial products whose profits will accrue to someone else with no benefit to the original author.

Short answer:

It probably does not count as fair use.

Long Answer:

Fair use is actually a lot more expansive than many people think while simultaneously being a lot narrower than many people think. It is more expansive in that commercial ventures can actually make fair use of copyrighted material under certain circumstances. It is narrower in that those with proper standing to make a fair use claim to copyright material have fewer protections than they often think.

The US Supreme Court has found that the following four factors must be taken into account when determining whether or not something qualifies as fair use:

1. the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
2. the nature of the copyrighted work;
3. the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
4. the effect of the use upon the potential market for or value of the copyrighted work.

As determined in Campbell v. Acuff-Rose Music (1994), however, none of these factors is dispositive. That is to say, all four are supposed to be balanced. That a work is reused for commercial purposes does not immediately mean it is not a fair use. In the Campbell case, for instance, it was noted that to say otherwise is to outlaw virtually all commercial parodies. Similarly, you can often use the entirety of a work if it’s nature is such that you can only use all or nothing (e.g., Marcel Duchamp’s L.H.O.O.Q. uses all of Leonardo da Vinci’s Mona Lisa and the former couldn’t have existed without using all—or at least the vast majority—of the latter).

It is a delicate balance, though, which is why the notion of transformativity weighs so heavily in most decisions. Transformation requires personal creative work—something typically avoided by people who are just trying to get away with something. In your case, that the tests are themselves free would probably be considered irrelevant given that they only come with the purchase of a textbook. You would also be lifting whole examples, which affects the value of the original (each non-unique example it contains lowers its value). Moreover, there would be no transformation: the examples would neither be changed nor repurposed (the latter being more important).

While I cannot say for certain what a court would decide, it seems to me that this is unlikely to count as fair use and simply isn’t worth the risk. It is not unreasonably difficult to come up with original examples—another factor a court would probably take into consideration—so you really might as well do so. This is especially true if the publisher does not realize you are lifting examples from copyrighted sources. I doubt they would look kindly on opening them up to that kind of risk, especially if they include a note in their text that no such thing has been done.

Standard disclaimer: I am not a lawyer. The above is based on seminars I’ve taken on copyright law and discussions with colleagues who have studied and/or practiced copyright law. The information may be out of date or based on a misunderstanding. It is always advisable to speak to a practicing attorney.