## October 9th test discussion

Forum for the GRE subject test in mathematics.
toopham
Posts: 22
Joined: Sat Apr 10, 2010 9:36 pm

### October 9th test discussion

So... how did you do?
So I am hoping to get at least 35 as raw score
That's all I am hoping for.

Question, if x^2 = x for all x, then the elements are idempotent but not necessarily commutative right?
Please tell me yes xD because that's what i picked

lpt234
Posts: 26
Joined: Sat Oct 09, 2010 4:14 pm

### Re: October 9th test discussion

In fact, it is, since (a+b)=(a+b)^2=a^2+ba+ab+b^2=a+ba+ab+b. Then, ba+ab=0. Also, 4x=4x^2=(2x)^2=2x. Then, 2x=0. So, we have 0=ab+ab=ab+ba. Then ab=ba.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

Ouch. That was significantly more difficult than I was expecting. I had been averaging around 40 for a raw score on the practice exams, but i only answered 37 today. Thirty seven! What's my raw score going to be, 30...?! What's so frustrating is that I went in feeling fairly confident, but then was blind-sided.

Do I take it again in November? I really don't want to have to pay another \$160 (how does ETS get away with this price?) and I'm debating whether or not the time spent studying for it could be put to better use elsewhere -- such as my current classes. I have an REU under my belt, three good letter writers, and strong grades: my application was decent until I got killed by the GRE! I would have been totally content with a score in 700-750, but now I'm looking at 600-650.

It is a cloudy, rainy, depressing Saturday.

PieceOfPi
Posts: 25
Joined: Mon Aug 02, 2010 3:16 pm

### Re: October 9th test discussion

I thought the most of the questions were either easy or difficult, and there weren't many "medium," "seems hard, but not that bad," or "mildly difficult." So I answered most of the easy questions first (in about 100 minutes), and then thought about tackling those mildly-difficult ones, like I did when I was taking the practice exams. But because there weren't many of those "middle-range" questions, I actually ended up skipping more than I expected (I probably answered somewhere around 50, and I feel confident about most of them). But yeah, I think I would have done better if I had more time, because there were some calculus questions that I wanted to have more time to solve.

lpt234
Posts: 26
Joined: Sat Oct 09, 2010 4:14 pm

### Re: October 9th test discussion

I don't think it's a good idea to retake it. They will mainly check your grades, REU, and letters of recommendation. You should focus on doing well in your current classes.

MattW
Posts: 47
Joined: Sat Oct 09, 2010 6:34 pm

### Re: October 9th test discussion

I was able to answer probably between 45 and 50 with confidence and then guessed on another 10 or so (58 questions answered total). I'm hoping for a score of 750 or above, so we'll have to see if that will happen. I found that time was definitely an issue during this exam. In retrospect, it would have been wise to practice timed tests.

Best of luck to all of us during this application season .

toopham
Posts: 22
Joined: Sat Apr 10, 2010 9:36 pm

### Re: October 9th test discussion

lpt234 wrote:In fact, it is, since (a+b)=(a+b)^2=a^2+ba+ab+b^2=a+ba+ab+b. Then, ba+ab=0. Also, 4x=4x^2=(2x)^2=2x. Then, 2x=0. So, we have 0=ab+ab=ab+ba. Then ab=ba.
well there goes 1/4 point.

mdornbos
Posts: 27
Joined: Sun Sep 05, 2010 11:11 am

### Re: October 9th test discussion

I was wondering about the scoring. Do they have a scaled score for each raw score already planned out? Or do they scale the scores after they see everyones results? The reason I ask is because all the different previous exams they have online have different scaled scores for each raw score.

This test was pretty difficult, it seemed a lot harder than the previous years' tests. I feel like I was too conservative because I only answered questions I was absolutely confident with, so I won't gain the "educated guess" points, but I won't lose a lot of points either.

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

### Re: October 9th test discussion

I would guess that they determine the raw score -> scaled score conversion once they have graded a sufficient number of exams, to keep the percentiles aligned. For what it's worth, the scaled scores on the April exam were much more forgiving than the scoring guidelines on the official practice exams (at least in the top-range scores).

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

I'm pretty glad to see everyone saying that this test seemed harder than most. When I did my practice exams I always finished with roughly 10 or 15 minutes left. Going over them I realized that I was losing most of my points to careless errors (for instance, taking a 1/2 out of an integral before using a uv-int(vdu) and then not putting the 1/2 back in), so I decided to be more careful on the early ones and not worry as much about the later ones. At two hours into the test I was only at 36.

The three digit scaled score seemed mostly random on the practice tests, but I did notice that a raw score in the thirties was usually good enough to score in the 50 to 60 percentile. I hope that holds up because I am looking at about that.

mdornbos
Posts: 27
Joined: Sun Sep 05, 2010 11:11 am

### Re: October 9th test discussion

I couldn't agree with you anymore john. I answered probably the same amount and felt blind-sided. And you're right about taking it again. It almost seems pointless to pay and spend more time studying and not on coursework just do get blind-sided again possibly. I think with the increase of people taking the test and the high scores on past tests that they feel they need to make it harder.

They say these tests are similar in difficulty. But I think we can all agree we would have gotten at least like 5 or 10 more right on a past test. That doesn't seem fair to us who took it yesterday. It seemed like they tried harder than ever to trick us and worded certain questions extremely hard. The differential equations questions were way harder than past years ones. And how about the numerical analysis question on interpolation?

ded8381
Posts: 6
Joined: Sun Oct 10, 2010 11:34 pm

### Re: October 9th test discussion

Any advice for those taking it in November?

dajohnson89
Posts: 6
Joined: Wed Aug 18, 2010 8:21 pm

### Re: October 9th test discussion

Does anyone else think the test was heavy on real analysis? I sure did.

dajohnson89
Posts: 6
Joined: Wed Aug 18, 2010 8:21 pm

### Re: October 9th test discussion

ded8381 wrote:Any advice for those taking it in November?
Practice tests are crucial. Buy the REA test book; it's available used for cheap. It has 6 practice exams. people complain that it's too difficult, and not well explained, BUT that's the point. Furthermore the practice is so helpful I can't overemphasize it.

Don't underestimate abstract algebra. Groups, rings, fields. There were several of those. Also, don't shrug off things in precalc. Learn how to do serious word problems in pre-calc; they were non-trivial on the exam.

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

mdornbos wrote:And how about the numerical analysis question on interpolation?
Oh yeah. That one seemed simple when I first looked at it but after what felt like half hour of number crunching I ended up with a number that wasn't even remotely similar to a choice. A lot of time down the drain on that question.

For those who didn't take the test or don't recall the question it was something like:
f(x) is a polynomial of power 2 that correctly approximates sin(x) at x = 0, pi/4 and pi/2. What is the value f(pi)?

Hint (not part of the question): Consider that you have 3 points and f(x) is given to be a polynomial of power 2.

MattW
Posts: 47
Joined: Sat Oct 09, 2010 6:34 pm

### Re: October 9th test discussion

ded8381 wrote:Any advice for those taking it in November?
Make sure that you're solid with your calculus and linear algebra. This makes up the vast majority of the test.
Chapel wrote:Oh yeah. That one seemed simple when I first looked at it but after what felt like half hour of number crunching I ended up with a number that wasn't even remotely similar to a choice. A lot of time down the drain on that question.
For that one you really want to use Lagrange polynomials, I can't imagine trying to do it another way. I haven't taken numerical analysis, but I've seen them creep into a couple different algebra classes.

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

### Re: October 9th test discussion

For that one you really want to use Lagrange polynomials, I can't imagine trying to do it another way. I haven't taken numerical analysis, but I've seen them creep into a couple different algebra classes.
What's wrong with plain old high school algebra?

f(x) = x*(ax+b) (since f(0)=0)

a = (8 - 8 sqrt(2))/pi^2
b = (4 sqrt(2) - 2)/pi

f(pi) = 6 - 4 sqrt(2)

If you recognize that the polynomial factors, you only need to solve two linear equations in two unknowns to find a and b. That should be doable on the exam.

P.S. Of course I don't know the answer choices. If they gave you nice choices, you might have been able to guess the answer without doing any computations whatsoever.
Last edited by owlpride on Mon Oct 11, 2010 12:28 pm, edited 2 times in total.

smartiful
Posts: 25
Joined: Mon Oct 11, 2010 12:11 pm

### Re: October 9th test discussion

A fair amount of GRE questions are "calculate as fast as you can, thinking will only cost you time". This one however was not one of them. Looking at the answer choices revealed that only one of them was fairly close to zero. Now, a degree 2 or smaller polynomial is either a straight line (but the points given were not on a straight line) or a parabola. One hump of a sin-function looks very similar to a parabola, so it is reasonable to assume that the approximation isn't too bad at least on the interval [0,pi], and thus p(pi) should be somewhat close to the true value of sin at pi. (and in fact 6 - sqrt(2) is between 0.3 - 0.4).

Wish I had realised that before wasting some minutes on solving the 2 equations.

MattW
Posts: 47
Joined: Sat Oct 09, 2010 6:34 pm

### Re: October 9th test discussion

That wasn't nearly as bad as I had imagined it being, now I feel a bit foolish. On the test, the thought of solving three equations with three unknowns didn't appeal to me very much, especially with all the irrational numbers involved.
Lagrange polynomials made the question pretty quick though .

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

I'm just going to let it go. I'm not going to take it again in November. It's going to be really embarrassing on my applications though. A math major getting that bad of a score? That's like saying that you're a professional baseball player, then getting up to the plate and holding the bat by the wrong end...

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

Well, it isn't that strange to see math majors do poorly on the test. Bear in mind that it is almost exclusively math majors that take the test to begin with. Now... if you score poorly on the Quant section of the general GRE, that would be a very bad thing.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

The general GRE quant score is pretty mediocre. Didn't do poorly by any means, but didn't blow it out of the water like a good math major should have. Now that the subject GRE score is low, it'll look worse.

Eh, the more I think about it, the less worried I am. I have an otherwise pretty decent application besides the GRE scores, so I just need to focus on the positive and maintain a good, enthusiastic attitude. I'm still excited about applying.

I just realized that I will be in a higher percentile on the Putnam than both the general and subject GRE. How did THAT happen?!

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

A good Putnam score will go a long way towards making up for GRE scores, especially if you have some good letters behind you. I really wish my undergrad had offered the Putnam exam.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

It's only the 70th percentile on the Putnam, but given the exam's reputation, I would hope that it would offset my GRE scores somewhat.

Your school didn't offer the Putnam? Do you attend a really small school or something? That's weird!

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

### Re: October 9th test discussion

What's the consensus on mentioning Putnam scores on grad school applications? Waaay back in the days I decided that anything below the top 200 wasn't worth mentioning, and I barely missed that mark twice in a row.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

I would think it depends on the school. For instance, I'm not going to go bragging to MIT that I scored in the 70th percentile, but on an application to, say, University of Iowa or Missouri, maybe (I'm hoping) it'll carry a little bit more weight. If you're right around 200 (that'd be around the 98th percentile...?) then I think you should mention it on pretty much any application, although it might not mean as much on an application to Harvard where you're likely competing with the Putnam Fellows themselves. Putting it on a Harvard app may make you look a bit silly, but I highly doubt it would actually hurt your application. That high of a score is nothing to blink at; it's very impressive.

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

### Re: October 9th test discussion

I think the top 200 corresponds roughly to the 90th percentile, but that's not really the point. (Personally, I like to exclude zero scores from consideration because the Putnam people include students who leave after 5 minutes in the statistics. Let's only compare ourselves to students who gave the test a fair shot.)

I figure that in order to score in the top 200, I would need complete solutions to at least 4 problems. That doesn't give me bragging rights at MIT, but it's a good start.

In contrast, one can usually make the top 1000 with partial solutions to two problems. Solving two problems is a much lesser accomplishment because A1 and B1 are kept easy on purpose. The test makers want to have problems on the exam that "everyone" can solve. Personally, I am hesitant to advertise scores that only show that I can solve homework-style problems on the Putnam.

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

john wrote:It's only the 70th percentile on the Putnam, but given the exam's reputation, I would hope that it would offset my GRE scores somewhat.

Your school didn't offer the Putnam? Do you attend a really small school or something? That's weird!
The math department at NYIT is really lazy and by the time I got there mostly regarded themselves as nothing more than a support role for the engineering schools. I had taken a bunch of math classes to fill general electives (because I liked math) so when I left the Architecture program a math major was a perfect fit. I probably should have transfered, but I wasn't inclined to do that to finish my last 20 credits at the time.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

You're correct, it'd be around the 90th percentile of people with nonzero scores. But you'd still be in the top 10 percent of the best math majors in the country. But again, if you're aiming for schools where you have to compete with the top 1 percent, then perhaps it's sort of pointless. So, I guess if you decide to apply to schools outside of the top 25, I'd say include it. But I get the feeling you're aiming pretty high.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

Chapel wrote:
john wrote:It's only the 70th percentile on the Putnam, but given the exam's reputation, I would hope that it would offset my GRE scores somewhat.

Your school didn't offer the Putnam? Do you attend a really small school or something? That's weird!
The math department at NYIT is really lazy and by the time I got there mostly regarded themselves as nothing more than a support role for the engineering schools. I had taken a bunch of math classes to fill general electives (because I liked math) so when I left the Architecture program a math major was a perfect fit. I probably should have transfered, but I wasn't inclined to do that to finish my last 20 credits at the time.
Oh boy, do I feel your pain. I am in a math department at a small engineering school as well. All through my math classes I've had to listen to whiny engineering majors.

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

### Re: October 9th test discussion

john, I see your point. Putnam scores may or may not help depending on how our performance compares to the students at the places we apply to - just as with any other piece of our application
You're correct, it'd be around the 90th percentile of people with nonzero scores. But you'd still be in the top 10 percent of the best math majors in the country.
Actually, demographic data on who is taking the Putnam would be really interesting. For example, how many students who are taking the Putnam go on to graduate school, and how many graduate students in math took the Putnam as an undergraduate? How representative are the students taking the Putnam of all undergraduate math majors in the US? Or how does the set of students taking the Putnam compare to the set of students taking the math subject GRE?

The most brilliant math majors I know personally do not bother to take the Putnam, but that's a very limited sample size. On the other hand, given how popular the Putnam is at Harvard and MIT, there are bound to be some very high achieving students in the exam pool.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

To be honest, I never thought about the zero scores including the walk-outs. My percentile looks pretty dismal when I'm compared to only the nonzero scores. Ouch. I'm going to keep the walk-outs in, they're helping my score!

Yeah, the Putnam won't represent all of the math majors. There are a few really smart math majors left out, as you've noted, and there are many weaker ones left out too. I know that quite a few math majors at my school won't take the Putnam because they're afraid of the humiliation of getting a zero. Also, there have been quite a few computer science majors at my school taking the Putnam, and if I remember correctly, the best score at my school that anybody can remember was from a chemical engineer.

I'd say the top of the Putnam crowd is still a fair representation of the best in the country though, even if a few are left out.

Are the really smart ones at your school blowing off the Putnam because they feel they have better things to do with their time, or for some other reason? Perhaps because they like to sleep in on Saturday mornings...?

ded8381
Posts: 6
Joined: Sun Oct 10, 2010 11:34 pm

### Re: October 9th test discussion

I scored a 20 on the last putnam -- don't remember want percentile that was.

The schools I'm currently considering: North Carolina State, Purdue, University of Washington, University of Oregon, Oregon State University, and University of Idaho

Is my score worth reporting to any of these schools? Thanks!

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

john wrote:I'd say the top of the Putnam crowd is still a fair representation of the best in the country though, even if a few are left out.
So is it more fair to say sufficient but not necessary.

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

Chapel wrote:
john wrote:I'd say the top of the Putnam crowd is still a fair representation of the best in the country though, even if a few are left out.
So is it more fair to say sufficient but not necessary.
I'm afraid I don't understand. Are you asking me a question or are you dis/agreeing with something I said?

Chapel
Posts: 59
Joined: Mon Sep 13, 2010 11:25 pm

### Re: October 9th test discussion

Sorry, that should have a question mark at the end of it.

Basically I was just saying that being at the top of Putnam means you probably are one of the best math undergrads, but not being at the top of Putnam does not mean that you are not one of the best math undergrads. Is that true in your opinion?

john
Posts: 22
Joined: Sat Oct 09, 2010 4:41 pm

### Re: October 9th test discussion

It's always hard to try and defend broad, sweeping generalizations, but I think it's true more often than not.

jplusip
Posts: 22
Joined: Mon Jun 21, 2010 12:40 pm

### Re: October 9th test discussion

So for those of you who took it:
How helpful was the ole' Cracking the GRE 3rd/4th edition? If it wasn't very helpful, I may just discard it and focus solely on Courant and Birkhoff/Mac Lane's books.

alex
Posts: 37
Joined: Wed Oct 20, 2010 12:54 am

### Re: October 9th test discussion

yes, i would like to know how helpful that cracking book is too. i'm taking the test in a few weeks and i'm a good chunk of the way through the book so hopefully it's good. i know that there are a ton of typos which can be pretty frustrating when you spend 30 minutes on an impossible-seeming problem only to learn that the way it was written, it actually was impossible, but other than those moments, i like the problems pretty well.

plus, it seems from the question at the top of this thread that it might be pretty helpful because that idempotent, commutative thing is explicitly worked out in the book.