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: 
Repeating a bit other remarks: in the U.S., exams in upper-division courses are usually designed by the individual instructor, and vary widely.

There *is* a tradition in top-tier places in the U.S. to "challenge" students on exams, and students seem to expect this, while, yes, in some local cultures students expect/demand exams that contain no surprises. 

For that matter, it is not clear to me that "testing cleverness" is necessarily an important goal for timed exams. I am well aware that there is a huge tradition in which quickness and cleverness are construed as fundamental skills/talents. Certainly these are important for math contests, and occasionally useful in the practice of mathematics, but I don't think our classes *teach* these things, in any case. Thus, testing for quickness and cleverness is testing for something outside the course content. Thus, in many regards it is an irrelevant challenge to the students.

That is, substantial mathematics often has *genuine* complications and difficulties that exist despite examples and forthrightness, and it is sometimes (often?) counterproductive to create "challenging (surprise) problems" from material that should be straightforward.

But, yes, people on admissions committees are well aware of such traditions and their variations, don't worry.

For me, the letters of recommendation from math faculty are far more important than grades on the transcript, in any case. Similarly, the statement of purpose of the applicant tells much more than the transcript. And, one more time, the skill set relevant to surprise questions on timed exams becomes ever less relevant throughout grad school.
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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.