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.