“How should I prepare for the GRE Math Subject Test?” This is a common question asked by students embarking on the math graduate school application process, yet many professors don’t have a great answer. A common part of one’s graduate school application portfolio, the GRE Math Subject Test is notorious as a standardized test that covers fundamentals from courses throughout undergraduate mathematics. Despite being an integral part of one’s application, there aren’t many relevant resources for preparing for this exam. Only a handful of practice exams are available, many of them outdated and irrelevant to the current exams. GRE practice books published by the ETS help with math content review, but do not develop strategies for tackling the seemingly esoteric style of problems on the subject test. In this post, we suggest strategies for helping students prepare specifically for this test.

**Creating Content Flow Charts:** You might have seen students prepare for the subject test by reviewing specific content and working on practice problems on the chosen content. One of the potential issues with this approach is that problems on the GRE Math Subject test tend to require recall of many different aspects of a subject instead of focus on an isolated topic. An example is the following sample problem I created for a GRE prep program at Harvey Mudd College:

If f(x) is the real-valued function f(x)=x|x|, then which of the following must be true:

I) f is continuous on all of the reals

II) f is differentiable at x=0

III) f is odd

a) II only b) II and III only c) I and II and III d) III only e) I only

Approaching this problem requires quick recall of different concepts on single variable functions. In order to practice having recall at their fingertips, I highly suggest students make a **content flow chart** for a subject area. This involves placing definitions, theorems, and implications from a particular subject area all on one large poster. For instance, if a student is reviewing single variable calculus, they might create small boxes with the definitions for continuity, differentiability, and integrability. Then, they can place an arrow from the differentiability box to the continuity box because the former implies the latter. Furthermore, they can write or draw examples of what could go wrong in the other direction. This could include specific counterexamples, and also general properties of functions that are continuous but not differentiable. Content flow charts allow students to see a topic holistically, which is extremely advantageous for quick recall.

**Prepare Specifically for the Test Itself:** As mathematicians and educators it is our natural tendency to want to teach the inner workings of a subject area, and spend time motivating the concepts at hand. However, the goal with the GRE Math Subject Test is to answer problems as quickly and accurately as possible, rather than lament over depth. This is one of the biggest struggles I had while holding prep sessions, but it’s a key one to address. To see an example of this, consider the following problem:

Suppose x and y are integers, and 8x-5y is divisible by 7. Which of the following must also be divisible by 7?

a) -6x+2y b) -6x+3y c) -5x+3y d) -5x+3y e) -5x-2y

As mathematicians, our natural tendency is to explain phenomena that divisibility captures. However, it can be much quicker, as in this problem, to focus on strategies inherent to the test. A quick way to address this problem is to pick a nontrivial pair (x,y) of integers, say for example x=3,y=2, for which 8x-5y is divisible by 7, then check which of the given answers also satisfies the same divisibility property.

**Patterns in Old Exams:** Past GRE exams tend to have problems types that are repeated over and over. Knowing how to do such problems quickly saves time on the exam itself. For instance, an analysis of past GRE data shows that multivariable calculus is the subject area with the poorest results, however almost every practice exam has a question on applying Green’s Theorem directly, where doing so simplifies a problem to multiplying the area of a region by some constant. Knowing this one concept gets students ahead on the exam.

**Create a GRE Community:** Along with Dr. Ivan Ventura (now at Cal Poly Pomona), I held GRE practice sessions early fall once a week for 6 weeks, with pizza served. Having practice sessions over food set the tone for a casual study environment. I think this was essential in relieving the stress and anxiety students had.

These are just a few tips that can be very helpful for students studying for the subject test. I hope you can use them at your institution!

For more practice problems, visit my GRE Math Subject Test YouTube page here:

These information is very helping. please up to date this on daily basis.

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Feel free to check out videos on this on YouTube:

https://www.youtube.com/channel/UCSoVyBb75Mf9o_eZGuKa2HQ

It’s interesting the way we each approach problems differently.

For your divisibility problem, I would naturally reduce all of the coefficients modulo 7 (choosing equivalent coefficients between 0 and +6), which immediately gives me the answer. While, for me, finding non-trivial values for x and y so that the given expression is divisible by 7 and then substituting those numbers into each expression takes a lot more time.

But the fact that different methods will work is one of the beauties of mathematics!

Thank you for the post!

Yes definitely! I adapted the problem from one that will be in a forthcoming book, where when reducing coefficients it’s not as straightforward to see the result. However, I really like your idea for this one, thanks for sharing!

This is so useful. I love the video since it has clear explanation and helps me recap the things learned years ago without having to go through all my previous notes. Thank you so much!

For calculus, is Apostol’s book enough or should I refer Stewart’s book for exercises?

First time visiting your website, I really like your blog!