Question: Recently two friends of mine have come back to Australia after having done 2 semesters of 3rd and 4th year subjects (about half mathematics) at different branches of the University of California.

They said that the tests would only ask questions directly from or similar to material covered in lectures and example sheets. If questions deviated from the lectures or example sheets very much students would complain to the lecturer. Thus, if one studied the example sheets enough they got an A relatively easily. They returned with A or A+ in all of their maths subjects, but they average about 75-80 for their maths subjects here.
In Australia, about 70% of the exam is usually like that. The rest are questions that we learned enough theory to feasibly do, but we hadn't seen that type of question before so it requires some level of cleverness to get it within the time limits of the exam.

My questions are

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> Can anyone corroborate that the maths tests at american universities are actually like this?
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> If so, is this well known and accounted for by the people who look at grad school applications from international students?
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> How do they fairly evaluate the performance of international applications? How are Australian applicants generally viewed by them?
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Edit: Chris's answer below seems to answer the first question by "not quite", which is what I expected I suppose. The other questions still stand.

Answer: 
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> Can anyone corroborate that the maths tests at american universities are actually like this?
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Some are, some aren't. Grading standards are heavily influenced by national and departmental culture, but ultimately they're entirely up to the instructor, **just as they are in Australia.**

But I expect that most upper-division exams in *strong* departments require enough mastery of the material (as opposed to memorization of examples) to answer a completely novel question that requires the same techniques. The key word here is *mastery*, not *cleverness*.

(I go further than Paul Garrett. Cleverness is not only inappropriate to test on exams; it's actually a *dangerous* habit to cultivate. My most frequent advice to students in my classes is "You're trying to be clever. Stop it. Just solve the problem, one step at a time.")

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> If so, is this well known and accounted for by the people who look at grad school applications from international students?
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Yes, admissions committees are well aware of significant differences between universities, both within the US and internationally.

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> How do they fairly evaluate the performance of international applications?
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Generally, by comparing them with other international applicants, preferably from the same country, if not the same university. In other words, exactly the same way we judge American applicants.

In my department, if we get an otherwise strong application from a university we've never heard of, we try to judge by the recommendation letters. But sometimes we just have to gamble, so we admit one or two of the very best students from an unknown university just to *find out* how good it is. If they do well, we admit more from that university later; if they do badly, we don't.

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> How are Australian applicants generally viewed by them?
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Well, that depends on the individual applicant, doesn't it?
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> The rest are questions that we learned enough theory to feasibly do, but we hadn't seen that type of question before so it requires some level of cleverness to get it within the time limits of the exam.
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The math and science classes I have taken at top tier universities in the U.S. have had these types of problems as a significant part of exams. As a caveat, those were also classes designed for math and science students. I have tutored students in non-math fields who have taken math and science classes that were less rigorous in that regard (e.g., "Calculus for Business majors").

Suffice it to say that as undergraduates progress deeper into their respective field, they will generally experience more challenging material on the exams.