Hey, I just the GRE8767 test posted online. I found the test fairly easy, aside from the parts on probability/diff eq since I havent had a course in either of them. I got a raw score of 49 which is supposedly around the 80th percentile, and this was with 5-6 really stupid mistakes (e.g. not thinking hard about induction and thinking sin^2(x) + cos^2(x) = x instead of 1, forgetting Green's Theorem, etc). The only thing I have to compare this to is my score on one of the REA book practice tests which was somewhere in the 30s for raw score and maybe near the 50th percentile, although those tests are supposed to be harder than the actual exam.

I guess I'm wondering if the 8767 test is similar to recent exams. Are the extra questions still mostly on probability/diff eq? I guess diff eq is probably more of a standard topic, I just don't know it. Are the other online practices (the 2 left on the UCSB site and the practice book) harder than the 8767? Are they more like the actual test? I'm trying to figure out a study plan for the summer. Should I take the time to learn probability/diff eq or should I forfeit those questions and just make sure I know the other stuff perfectly? The anwer is probably some of both since I have a lotof time until October, but I'd like to hear thoughts from people who've taken the exam.

Also I was a bit confused by 2 questions on the 8767 test that I got wrong.

17. Define a binary operation on the rationals by a*b = a + b + 2ab. Is it commutative? Is there an identity? Are there inverses?

Commutativity is obvious, the identity is 0, and the test claims that there are no inverses. But a * (-a/(1+2a)) = 0, unless I've made an addition error. And (-a/(1+2a)) will be rational if a is. So it seems like there are inverses. Any ideas on that one?

27. Define f(x) = x if x less than or equal to 1, and f(x) = ax^2+bx+c otherwise. For what values of a, b, and c will this function be differentiable? It will be continuous if a+b+c=1, but that isn't good enough. The answer is triples of the form (a, 1-2a, a) but I can't see why.

Thanks for the help!