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I am studying for GRE Math. I am looking for specific tips. What types of questions usually come up? Does anyone know any tricks (e.g. integration tricks) that might be helpful? Which theorems are absolutely essential? Apparently, most of the test is calculus and probability theory. What types of calculus and probability questions come up? Overall, how to score high on the GRE Math? Please be specific.

Edit: Please do not state the obvious. I know I need to study and take the practice tests. I am looking for specific tips and tricks that might help answer some types of questions faster.

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    $\begingroup$ A specific tip: take as many practice tests as you can get your hands on. Pay attention to the time. If you don't work efficiently you will not answer all the questions. I've known some good students who went into the exam without taking practice tests and they did poorly because they weren't ready to work as quickly as they needed to answer all the questions. $\endgroup$
    – KCd
    Commented Oct 20, 2012 at 23:55
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    $\begingroup$ So, did you downvote our answers? I know, for example, that you downvote a lot more than upvote, and that you have 2 downvotes today, which as far as this site is concerned, just started 40 minutes ago. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 0:39
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    $\begingroup$ @Graphth Just to let you know -- voting is a feature of StackExchange. So what is your concern? $\endgroup$
    – glebovg
    Commented Oct 21, 2012 at 0:49
  • $\begingroup$ I voted to close this question because it overly broad, which falls under "not a real question". Essentially, his question is, "What are tricks in any subject of undergraduate mathematics that could possibly make some GRE problem simpler?" It's too broad to even answer. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 0:54
  • $\begingroup$ math.stackexchange.com/questions/1922417 $\endgroup$
    – BCLC
    Commented Oct 21, 2016 at 3:25

3 Answers 3

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The Math Subject GRE is 50% Calc 1, 2, 3, and Differential Equations. High school algebra and linear algebra are another 15-20% probably. If you do well on just those questions, you will be in the 70th or 80th percentile. Note, this is compared to students wanting to study math at graduate school, so this is very good. So, concentrate on those. But, also learn as much other stuff as you can.

Here is a link to a previous test, including the breakdown of subjects.

http://www.ets.org/Media/Tests/GRE/pdf/Math.pdf

Note 25% is "Additional Topics". You'd need to learn several semester courses worth of material to get this stuff. Don't worry about that too much unless you are already pretty good at it. Notice that probability is a subcategory of a subcategory in this category. So, I think you are not quite right on how much probability is on the exam. The point here is concentrate on your strengths. Learning an entire new subject may get you 1 extra question. You're much better off mastering Calc 1-3, Differential Equations, and Linear Algebra. If you are already good at other subjects, then good, practice problems on those too but your time on those should be less.

When I studied for it, I used a test prep guide and I studied a lot of calculus from my calculus text book, for the most part.

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    $\begingroup$ I never memorized such tables, but the two examples you give can easily be rederived from scratch. (1) y = arcsin(x) ==> sin(y) = x ==> cos(y)dy/dx = 1 ==> dy/dx = 1/cos(y). Then use cos(y) = cos(arcsin x) = sqrt(1-x^2). To get that last one you need to draw a little right triangle diagram with angle y and sides x and sqrt(1-x^2). (2) cot = cos/sin = sin'/sin, so an antiderivative is log|sin| + C, more or less. $\endgroup$
    – KCd
    Commented Oct 21, 2012 at 0:05
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    $\begingroup$ @glebovg I want to reiterate what I said earlier in the comments, and what Neal said in his answer, you have to study. It will be hard work if you want to do well. If you can't work hard, there's no reason to go to grad school. And, in grad school, you will want to know all this basic calculus stuff when you're teaching. So, you can figure out a few tricks here and there to make it easier to memorize. But, just memorize them. Take the time, put in the work, do it. There are no magic tricks to eliminate hard work. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 0:08
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    $\begingroup$ @glebovg Just go to the chat room and ask this question there if you have a bunch of follow up questions. The comments are not meant for this. Math isn't about memorizing formulas, but doing a bunch of problems as quickly as possible is going to work out faster the more you have memorized, and try to do math without memorizing formulas. I got 81% on this test and I'm an average grad student at an average school. I know what I'm talking about. You said you want to do well on the test, memorize the stuff. It's not like it's hard. You can memorize all integral formulas in an hour. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 0:13
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    $\begingroup$ @glebovg: math is indeed not about memorizing formulas, but it's not about filling in answers to a multiple-choice test either. The GRE math subject test is largely not a test about math, then. Whether you like it or not, you ought to memorize a few basic derivatives and integrals, and practice computing double integrals and finding eigenvectors from the exercises in a calculus and linear algebra book. As I said elsewhere, sitting down and taking past practice tests (real ones, released by ETS) will give the best sense of what the actual test is like. $\endgroup$
    – KCd
    Commented Oct 21, 2012 at 1:38
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    $\begingroup$ @glebovg: Yes, math encompasses many interesting concepts and ideas, but there are also formulas and methods that prove helpful. They keep one from having to reprove things over and over. So although I agree that there is more to math than memorizing formulas, remembering some useful formulas and methods makes the utilization of the concepts and ideas much more productive. Especially on a multiple choice test, remembering some key formulas and methods helps to move the test along. $\endgroup$
    – robjohn
    Commented Oct 26, 2012 at 22:32
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Be sure to study, especially if you are several years past the calculus sequence. This examination is not like easier examinations, where you can get a reasonably high score with little effort. You can't cram for it either - this is like a qualifying exam, where you need to put in consistent effort over several months. (As a bonus, the extra study will also help in your graduate classes when it is assumed knowledge.)

As far as tricks, I don't recall any that aren't standard. What I remember is a straightforward examination that touches on most everything in an undergraduate math curriculum. It didn't seem to be an exam that requires cleverness, just reasonable thorough ability with undergraduate mathematics.

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    $\begingroup$ @Neal The downvoter is glebovg, who changed his question to add in smugly "Do not state the obvious" and then downvoted both of our answers because we don't give him magical formulas to make this test magically easy. I'm never answering a question for him again, not that I'm so full of myself to think that will really hurt him. But, hopefully others will do the same and that might. Note 80% of his votes are downvotes. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 0:51
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    $\begingroup$ @glebovg And, note that a downvote signifies "This answer is not useful". So, yes, these votes aren't hugely important, but I am not an amazing genius, I did very well on the test, beating 81% of all students interested in math grad school that took the same test, and I took the test 4 years after I finished undergrad. So, I know what it takes to do well on the test. So, at least I feel that my answer answered your question and was useful. If you want to know cool tricks that can help you solve calculus problems, then ask that specific question, and give your example in the question. $\endgroup$
    – GeoffDS
    Commented Oct 21, 2012 at 2:32
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    $\begingroup$ How is Gauss-Jordan elimination a 'trick'? It's the core computational concept in any linear algebra course. $\endgroup$ Commented Oct 21, 2012 at 3:30
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    $\begingroup$ @glebovg: Dear glebovg, I don't think that Feynmann integration tricks and so on are necessary, or even relevant. If you know them and they help you with calculus, great; but if you don't, they are not what you should be trying to learn in order to prepare for the GRE --- they will just be (a possibly pleasant, but that's not the point) diversion. You just need to be able to do calculus and linear algebra accurately and quickly, and you don't need any particular tricks for that. (Just so you know where I'm coming from: I took this exam almost 20 years ago, and ... $\endgroup$
    – Matt E
    Commented Oct 21, 2012 at 3:47
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    $\begingroup$ @glebovg: The Feynman integration trick is more commonly called differentiation under the integral sign. I would be surprised if there is a GRE math subject test question on integrals whose solution is sped up by knowing that. In my experience differentiation under the integral sign as a method of computing integrals is not going to be relevant to the math subject test. That you can get the series for $\cos(x^2)$ from the series for $\cos(x)$ by replacing $x$ with $x^2$ might be good to know (faster than finding the $x^6$ term painfully by differentiating $\cos(x^2)$ several times). $\endgroup$
    – KCd
    Commented Oct 22, 2012 at 3:12
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Consensus from people I know is that the current tests are generally a bit harder than the practice tests which are available. If you want to score about the 85th percentile on test day, you should be able to finish a practice test to about the 90th percentile in a little over 2 hours having never seen that particular exam before.

Another thing is that it helps to have a familiarity with the sort of calculus questions that are asked on the test, and a good strategy can be the following: grade for advanced calculus or beginning real analysis classes at your undergraduate institution. I found that having been a grader for my university's honors calculus class and a first quarter real analysis course helped because I had kept the knowledge in my head and I could quickly go through and do these sorts of problems. Other friends of mine who took the test who had graded calculus and analysis before reported similar statements.

Finally, it helps to keep in mind that doing well on this test does not correlate strongly with going to good graduate programs. Most reasonable places look at the math subject GRE and expect you to not fail it- it is not so important except as a basic hurdle to get over. What I've heard from admissions committees is that most important things are good letters of recommendation from professors.

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  • $\begingroup$ I agree about the letters. $\endgroup$
    – glebovg
    Commented Oct 21, 2012 at 0:57
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    $\begingroup$ @glebovg: While letters are the most important thing, some schools (including good ones) make a first cut of the applications whose subject test score is below a certain level (schools generally don't release that information, so don't ask for it here, but it's probably safe to say if you are in the 90+ percentile you'll be fine at most top places). You won't get into any math grad program in the US by excelling at the math subject test, but you could easily cut yourself out of contention if you do badly. Also, keep in mind that schools in Canada and Europe don't require this test at all. $\endgroup$
    – KCd
    Commented Oct 21, 2012 at 1:31
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    $\begingroup$ What would you say is the bar for "failing" the MATH GRE? $\endgroup$
    – user74261
    Commented Oct 23, 2015 at 1:54
  • $\begingroup$ @KCd, What about my GPA? How important is it? is it of the same importance of recommendation letters? more important? less? I have a gpa of 3.6 point (of 5) which corresponds to 86%. Is that good enough for my application being considered in good schools? $\endgroup$
    – FNH
    Commented Apr 16, 2017 at 19:52
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    $\begingroup$ If the letters are strong than that GPA won't knock you out. But I suspect the top schools get more than enough applications from people who received mostly A's in their undergraduate coursework. Talk with faculty in your own department about this. $\endgroup$
    – KCd
    Commented Apr 16, 2017 at 22:02

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