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Summary: Alas, to get that perfect score, you have to reconsider everything you have been taught at school.   My system of preparation for the standardized tests in mathematics (ACT, SAT, SAT2, GRE, etc.) is somewhat unique and unconventional. In fact, it goes against the grain of most of what you have been taught in school... and likely even in a test-prep class, if you have taken one. Sound a bit unnerving? Perhaps. But consider this: those same math teachers who tell you what to do, had most certainly not scored well themselves when they were your age. What is more, chances are good that they cannot score that well now, either. That's because their ways are... well, unduly complicated. What is a better approach? First of all, I will teach you how to solve 95% of all questions mentally, without writing a thing. Why bother, you may ask. Several reasons. One, it will teach you—anew—what you once knew but have since forgotten: the mathematical imagination... read more

Standardized test math doesn't behave like normal math. On a normal math test, your knowledge of the concepts and material is being tested, using (hopefully) fair test questions. On a standardized test, though, they're looking for you to think outside the box, to apply math concepts and algorithms to unusual situations, and to really understand what they're looking for and find the quickest way to go about it. Let's take a question from a recent GRE student's lesson: If 4x – 5y = 10 and 6y – 3x = 22, then what is x + y? Now, this is a set of two equations with two variables each, so it looks to me like a perfect candidate for solving as a system. If I were solving this one on a regular math test, I'd start off trying the substitution method, since I'm more comfortable with that one. So let's explore that one first: I'll start by solving the first equation for y: 4x – 5y = 10 - 5y = 10 – 4x y = (-10/5) – (4/-5)x y = -2 + (4/5)x Then... read more

Alas! You have to take the GRE in order to get into the program of your choice. Keep in mind that if you do not prepare well, you may have to take the test again, which will cost you probably around $200 or more. If you do not prepare well and it sets your studies back a year, that could cost you a year of earning potential in your lifetime. That's not a fun math problem. Maybe you need that extra year to prepare, but if you are ready, why go at the GRE in a less than 100% manner?   Let's say you already have your fall date set and you have two months or less to prepare for the exam. Here is what I recommend. Research the GRE stats of the university you are considering. Contact your POI (person of interest) and find out how well you need to perform on the GRE. If you need to score in the 90th percentile in the quantitative portion, that's something you need to know. Your POI may say that you need to score in the 60th, but if everyone who was admitted in the previous... read more

Normally, an equation has a single solution when it contains only one undefined variable.  For example, take the equation 3x + 7 = 19.   3x + 7 = 19     [original equation] 3x = 12     [subtracted 7 from both sides] x = 4     [divided both sides by 3]   This is one case of a larger trend in algebra.  As I've already said, you can solve an equation for one answer when it contains a single variable.  However, this is derived from the larger rule that you can solve a set of equations where there are as many distinct equations as there are variables.  These are called simultaneous equations, and occur any time that two equations are both true over a certain domain.  In the more practical sense, this is what you should do if an exam asks you to solve for a value and gives you two different equations to use.   To solve simultaneous equations, we can use three strategies. Addition... read more

The general form for a box-and-whisker plot is really easy. Let's take a simple data set.   8.2, 15.9, 12.8, 7.4, 24.7, 23.2, 9.6, 7.9, 8.3, 10.2   First, we need to take those data and put them in numerical order.  When we do that, this is what the data set looks like: 7.4, 7.9, 8.2, 8.3, 9.6, 10.2, 12.8, 15.9, 23.2, 24.7   [Note: Any computer program that runs spreadsheets or statistical analysis will probably accept the data in any sequence.  Ordering the data is only necessary when doing this process by hand.] Once ordered, we need to find the median of the set. The median means the "middle" value. In this case, the set has 10 values, so there's no singular "middle" value of the set when ordered least to greatest. To create one, we'll take the two middle values and average them. (9.6 + 10.2)/2 = 9.9 [The only reason we took an average is because there is not "middle"... read more

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