Questions about 8767 test
Questions about 8767 test
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 56 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, 12a, a) but I can't see why.
Thanks for the help!
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, 12a, a) but I can't see why.
Thanks for the help!
Re: Questions about 8767 test
i try to answer your questions:
17. i think it's because it's not defined for a = 1/2.
18. for the function to be differentiable, f` at x=1 must be the same for x <=1 and x>1
from there you got 2ax + b = 1 .. and then, the rest is easy..
17. i think it's because it's not defined for a = 1/2.
18. for the function to be differentiable, f` at x=1 must be the same for x <=1 and x>1
from there you got 2ax + b = 1 .. and then, the rest is easy..
Re: Questions about 8767 test
Thanks for the solutions, I see where I went wrong on each of them. Could anyone give a good comparison between the 8767 test (and other practice tests) and recent exams?

 Posts: 16
 Joined: Wed Jul 22, 2009 1:20 am
Re: Questions about 8767 test
Pardon me, but what does GRE8767 and the other similar serialnumberlike things stand for? Are they the serial numbers of the real GRE's?
Thanks!
Thanks!
Re: Questions about 8767 test
Apparently, first two numbers indicate the year.

 Posts: 16
 Joined: Wed Jul 22, 2009 1:20 am
Re: Questions about 8767 test
Thanks! So that means this particular one is from the year '87...
So it seems there are many past tests available. Where do I look for them?
So it seems there are many past tests available. Where do I look for them?
Re: Questions about 8767 test
You would better check the FAQ first before asking this.

 Posts: 16
 Joined: Wed Jul 22, 2009 1:20 am
Re: Questions about 8767 test
Thanks, lime!
The last Q&A really cracked me up!
You intended that
The last Q&A really cracked me up!
You intended that
Re: Questions about 8767 test
Best luck with preparation. Are you taking it in October or November? What programs are you going to apply for?

 Posts: 16
 Joined: Wed Jul 22, 2009 1:20 am
Re: Questions about 8767 test
Thanks!
I haven't registered for either, but most probably it will be the November one.
Applying to both math masters and PhD programs. My GPA is low... Any advice on this?
I haven't registered for either, but most probably it will be the November one.
Applying to both math masters and PhD programs. My GPA is low... Any advice on this?
Re: Questions about 8767 test
No advice. Just prepare.
Re: Questions about 8767 test
I must add that taking the 87, 93 and 97 tests is incredibly unrepresentative of the test I took in April which is much more like the current practice exam. I would say that many of the questions on those tests could easily be taken from any introductory Calculus or Algebra text while the newer tests seem to be more intentionally crafted for the limited applicability of the GRE, in fact, many of these questions are enjoyable to solve, just not in the allotted ~2 min 35 second/question pace required to finish the exam. They're not taken from any second year graduate examinations, yet they're not exactly freshman year Calc and algebra problems either.
Also, I have a question which is somewhat unrelated to this post, in fact, I could start a new topic on it if others are curious also. I was reading Fermat's Last Theorem (aka Fermat's Enigma) and it implicitly states that younger is better in Mathematical research. In fact, the Field's Metal is age limited at 40 I think. Thus, how important is age to admissions committees when evaluating students?
Also, I have a question which is somewhat unrelated to this post, in fact, I could start a new topic on it if others are curious also. I was reading Fermat's Last Theorem (aka Fermat's Enigma) and it implicitly states that younger is better in Mathematical research. In fact, the Field's Metal is age limited at 40 I think. Thus, how important is age to admissions committees when evaluating students?
Re: Questions about 8767 test
HA, it is interesting question,Also, I have a question which is somewhat unrelated to this post, in fact, I could start a new topic on it if others are curious also. I was reading Fermat's Last Theorem (aka Fermat's Enigma) and it implicitly states that younger is better in Mathematical research. In fact, the Field's Metal is age limited at 40 I think. Thus, how important is age to admissions committees when evaluating students?
from humble opinion, age is not an important factor to determine whether you will be admitted to Gradschools in Maths
Some because of many reason cannot attend classes at the age they should do, so they go to school later than some. The admission committees even give some priorities for such people, especially for women
A good examples is Smale http://en.wikipedia.org/wiki/Stephen_Smale who went to school very late and even did poorly for some first years (
when he was in Gradschool at Michigan but he wasstill awarded a Field medalHowever, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics.
So Zombie, you may be going to be a next one awarded field medal
Re: Questions about 8767 test
Haha, I don't need that type of encouragement! I might start to believe it. Then, while I try to accomplish this, I'll have that heart attack by age 35 like I've been wanting (or something like what happened to Prof. Nash...)
Another question I'll just throw out there: How impressive would a list of books read independently (ie textbooks outside of the par of the undergrad curriculum) be to an admissions board if mentioned in the statement of purpose? In fact, I think I will start a topic on this.
Another question I'll just throw out there: How impressive would a list of books read independently (ie textbooks outside of the par of the undergrad curriculum) be to an admissions board if mentioned in the statement of purpose? In fact, I think I will start a topic on this.