### The Devil is in the Definition: How to learn math definitions for the GRE

I know that for people who’ve been away from math for a while, the GRE requires a lot of refreshment on topics and skills. Even for those of us who’ve been around math all along, there may be topics we haven’t seen since high school on the exam.

Most of getting good at GRE math is practicing your skills, learning to recognize clues and patterns on the exam, and knowing what material is being tested and how it is tested. One key step is knowing the definition of math words, because those definitions often come with important restrictions.

For example, when a question starts by specifying that x is an integer, that restriction will probably be a key to the problem. There is an infinite amount of numbers that are not integers, including fractions and radicals. It’s also important to remember that integers don’t have to be positive – there are negative integers, and zero is in integer as well.

My suggestion is that you clarify the definitions, but not simply memorize them. Let’s say that I realize knowing the definition of “integer” is important, so I decide to make a flashcard that says “integer” on one side and “a member of the set of whole numbers” on the other.

Great. That’s true, and if the test were going to ask me to define the word “integer”, that would be a great thing to know. But remember: for the most part, the quant section of the GRE is a skill test, not a knowledge test. It tests your ability to notice patterns and details, perform math tasks, plan an efficient road to a solution, and reason with numbers. So the definition of “integer” that I want to know is something that will help me.

I am not the biggest fan of flashcards for the quant portion of the GRE, but if I were going to make one for “integer”, I’d want to make sure the back of the card included:

• My own definition in my own words,

• Key trouble issues to watch out for, and

• How the concept tends to show up on the exam.

As I did additional problems, I might add information to the back of the card, so that eventually it would look something like this:

• not decimals or fractions

• Includes zero and negatives!

• When they say “non-negative integer”, think “positive OR zero”

• When they say “number,” think about fractions

• When the exponent is a positive integer, the value usually gets bigger. UNLESS that positive integer is one – value stays the same.

The key is that your definition should include all the things that tripped you up, written in your own language, and written in a way that tells you what to do, not what not to do. (Notice my card doesn’t say anything like, “don’t test only positive numbers”, because generally it’s much harder for us to remember directions given in the negative.) It’s less of a definition and more of a collection of key points that help you clarify how this topic is applied on the exam. In this way, you become a better issue-spotter and avoid common mistakes.

Thinking of definitions in this way can help you to realize their importance while also learning them in a way that’s directly applicable to the exam. The next paragraph is a big, long list of terms for which you might find a definition card useful. All these terms are covered in ETS’s math review for the GRE. You certainly don’t need to make definition cards for each of these words, but if you think it would help you, go for it!

You might find it helpful to make definition cards for the following terms: integer, even, odd, positive, negative, divisible, factor, multiple, greatest common factor, least common multiple, remainder, prime number, prime factor, composite number, zero, one, rational number, reciprocal, square root, terminating decimal, real number, less than, greater than, absolute value, ratio, proportion, percent, percent increase, percent decrease, domain, compound interest, slope, y-intercept, reflection, symmetric, x-intercept, parallel, perpendicular, line of symmetry, parabola, vertex, circle, stretched, shrunk, shifted, line segment, congruent, midpoint, bisect, perpendicular bisector, opposite angles, verticle angles, right angle, acute, obtuse, polygon, triangle, quadrilateral, pentagon, hexagon, octagon, regular polygon, perimeter, area, equilateral triangle, right triangle, hypotenuse, legs, square, rectangle, parallelogram, trapezoid, chord, circumference, radius, diameter, arc, measure of an arc, length of an arc, sector, tangent, point of tangency, inscribed, circumscribed, rectangular solid, face, cube, volume, surface area, circular cylinder, lateral surface, axis, right circular cylinder, frequency, count, frequency distribution, relative frequency, relative frequency distribution, univariate, bivariate, central tendency, mean, median, mode, weighted mean, quartiles, percentiles, dispersion, range, outliers, interquartile range, standard deviation, sample standard deviation, population standard deviation, standardization, finite set, infinite set, nonempty set, empty set, subset, list, intersection, union, disjoint, mutually exclusive, universal set, factorial, probability, permutation, combination, and normal distribution.

### GRE Vocab: Holiday Hangover

Yes, the holidays have come and gone. Welcome to 2014! But having spent the last month listening to Christmas music non-stop, I have lots of these songs still stuck in my head. Whether or not you celebrate Christmas, these songs are around this time of year and tend to plant themselves in our minds. So if they’re stuck in your head too, there’s a good chance to learn a little vocab!

Here are seven examples of GRE words in holiday songs. If you find others, share them in the comments!

(1) Terrific. Here’s one of those words that the GRE likes to use for its less-conventional meaning. We usually think of terrific as “great”, but it really means “awesome” in the literal sense: big and awe-inducing, often in a bad or scary way. Like the word “terror”. To be honest, I can only think of one popular culture use of “terrific” in this way, and that’s in “Home for the Holidays,” which tells us, “…from Atlantic to Pacific, gee the traffic is terrific!”

(2) Conspire. In “Winter Wonderland,” the singer says, “Later on, we’ll conspire as we dream by the fire.” So picture the couple in the song, chatting away and planning for the new year. To conspire is to make secret plans together, although those plans are to do something bad… maybe that song is a bit naughtier than the sing-song tone would have us believe.

(3) Incarnate. “Incarnate” means given a body or shape, and it’s usually easiest to remember by thinking of the more-frequently-used “incarnation”. But you could also think of the lyrics to “Hark! The Herald Angels Sing”, which implore the listener to “hail the incarnate deity” when telling the story of the first Christmas.

(4) Cloven. The song “It Came upon a Midnight Clear” is full of great vocab, but one of the best words in “cloven”, which means “cut in two”. We mostly hear this word describing “cloven hooves” – or hooves that are split in the middle, such as those of a cow. The song speaks of angels coming to earth and says, “through the cloven skies they come”, describing the sky breaking in two.

(5) Traverse. “Traverse” means to move to travel across something. “We Three Kings” begins, “We three kinds of Orient are bearing gifts we traverse afar.” And if you’ve always sung that as “travel afar”, you’re already all set on this one.

(6) Lament. To lament is to grieve or be sorrowful, often in a way that involves crying or wailing. In “Good Kind Wenceslas”, the king and his page are traveling “though the rude wind’s wild lament and the bitter weather.” That wailing of the winter wind is a great way to remember the word “lament”.

(7) Laud. We mostly hear “laud” used as a verb meaning “to praise or glorify,” but it is also a noun for the praise or glory that is given. It’s used in this way in “What Child is This,” which says, “Haste, haste to bring Him laud, the Babe, the son of Mary.”

There’s a point here far beyond these seven words: GRE vocab is everywhere. When you hear or read a word that you don’t know, look it up! You might find that you start noticing GRE vocab everywhere. And who knows – learning it might be, dare we say it, sort of fun.