Math Workout for the GRE, 3rd Edition (2013)

GLOSSARY

Here is a list of mathematical terms that every GRE student should know well. Terms in italics have been cross-referenced from other definitions within this list.

A

Absolute Value

The absolute value of a number is defined as the distance of that number from zero. For the GRE, the important parts of absolute value are that the absolute value of a positive number is positive, the absolute value of a negative number is positive, and if a variable has an absolute value sign around it then that variable has two solutions: If |x| = 5 then x = 5 or −5.

Acute Angle

An angle that measures less than 90°.

All That Apply

A GRE question format that has square answer boxes. You must select every answer choice (out of anywhere between 3 and 8 answer choices) that applies. There is no partial credit; if any correct answer choices are not selected, or any incorrect answer choices are selected, the entire response is considered incorrect.

Arc

Any measurement around the circumference of a circle.

Area

The amount of space within a two-dimensional figure. The important formulas for area are: Triangle Area = bh; Parallelogram or Rectangle Area = bh; Square Area = s²; and Circle Area = πr²

Arrangement

A possible arrangement of a certain number of terms when the order in which those items are selected does not matter. (See also Combination.)

B

Ballparking

Approximating what the right answer might be and eliminating all impossible answer choices.

Base (of an exponent)

The bottom, larger number in an exponential expression. In the expression 3⁴, the base is 3.

Base (of a triangle)

The bottom side of a triangle; used to find a triangle’s area.

Binomial

An algebraic expression that contains two terms, such as (x + 2).

Bisect

To cut into two equal parts.

C

Chord

A line segment that connects two points on a circle’s circumference. The longest possible chord, the diameter, goes through the center of the circle.

Circumference

The perimeter of a circle. C = 2πr

Coefficient

A number that appears next to a variable and should be multiplied by that variable. In the expression 5a, which is shorthand for “5 × a,” the coefficient is 5.

Combination

A possible arrangement of a certain number of terms when the order in which those items are selected does not matter. (See also Arrangement.)

Concentric

Having the same center. (Most often used in terms of circles.)

Constant

Any number that is not a variable.

D

Denominator

The bottom number in a fraction. If a denominator equals zero, the fraction is undefined.

Diameter

A line segment that connects two points on a circle’s circumference and goes through the center. The diameter is the circle’s largest chord, and it is twice as long as the radius.

Difference

The result of subtraction. The difference of 5 and 3 is 2.

Distributive Property

A mathematical property whereby any number multiplied by a sum or difference of two or more numbers must be multiplied by all the numbers therein. The expression 3(2x + 5) can be rewritten, or distributed, to (3 × 2x) + (3 × 5), or 6x + 15.

Divisible

A number a is divisible by another number b if b divides into a evenly, with no remainder. In other words, is an integer.

Divisor

A number that can be divided into another number.

E

Equilateral Triangle

A triangle with three sides of the same length and three angles of the same measure (60°).

Exponent

The small number in the upper-right corner of an exponential expression. In the expression 3⁴, the exponent is 4. This means the base 3 must be multiplied by itself 4 times (3 × 3 × 3 × 3).

Extra Information

Information in a math problem that doesn’t actually help solve the problem. In the GRE, questions rarely have extra information. If you are ever stuck on a GRE problem, reread the question to see if there’s any information you haven’t used yet.

Even

Divisible by 2.

F

Factor

Any number that can be divided evenly into another number. 3 divides evenly into 12 so 3 is a factor of 12.

Factorial

A process whereby an integer is multiplied by each of the positive integers less than itself exactly once. “Eight factorial” is denoted as 8! and can be found by multiplying 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals 40,320.

F.O.I.L.

Acronym for First, Outside, Inside, Last that indicates how two binomials can be multiplied together.

FROZEN

An acronym to help you remember the weird numbers that can be helpful to Plug In on Must Be or Quant Comp Plug In questions. Try normal, easy numbers first, but then try some of the FROZEN numbers on the remaining answers. FROZEN stands for Fractions, Repeats, One, Zero, Extremes, Negative.

Function

A method of showing a relationship between two or more variables. On the GRE, function questions may involve symbols that are not typically in math questions, and will require following the directions given for that particular function.

I

Improper Fraction

A fraction in which the numerator is greater than the denominator. These fractions can be converted to mixed fractions.

Integer

Any number that has no fraction or decimal associated with it. Think of integers as the counting numbers on the number line including 0. Integers can be positive or negative.

Irrational Number

Any number that cannot be denoted as a fraction. Most irrational numbers you’ll come in contact with on the GRE will be square roots and π.

Isosceles Triangle

A triangle with two sides of the same length and two angles of the same measure.

L

Like Terms

Any algebraic terms that contain the exact same configuration of variables and therefore can be combined. For example, 3a²b and 6a²b are like terms, so they can be added to make 9a²b. The variables in 5xy³ and 10x³y are similar but not identical, so these are not like terms.

M

MADSPM

A mnemonic device to remember the rules for combining exponents for quantities with the same base: When Multiplying terms with the same base, Add the exponents. When Dividing terms with the same base, Subtract the exponents. When raising a term with an exponent to another Power, then Multiply the exponents.

Mark

A button at the top of the screen during the GRE test. Clicking the Mark button will put a check mark next to that question on the Review screen.

Mean

The average value of a list of numbers.

Median

The middle value in a list of numbers. Among an odd number of elements, the median is the middle number; among an even number of elements, the median is the average of the two middle numbers.

Mixed Fraction

A number that contains both an integer and a fraction, like 3.

Mode

The value that occurs most often in a list of numbers.

Multiple

The product of two integers.

N

Next

A button at the top of the screen during the GRE test. Clicking on the Next button will move you on to the next question. Simply clicking on an answer alone will not advance you to the next question; you must also hit Next.

Numerator

The top number of a fraction. If the numerator of a fraction equals zero (and the denominator does not), the fraction equals zero.

Numeric Entry

A question format on the GRE. Numeric entry questions have an empty box rather than answer choices. Some questions require fractions to be entered: These will have two empty boxes, one on top of another. Fractions don’t need to be reduced to lowest terms (e.g. , , and are all considered equivalent), and decimals do not need to be truncated (3.6 is the same as 3.600). Do not round decimals unless explicitly told to do so.

O

Obtuse Angle

An angle that measures between 90° and 180°.

Odd

Not divisible by 2.

P

π (pi)

The result when the circumference of a circle is divided by the diameter of that same circle. Roughly equal to 3.1415926535897932384626…, but think of it as 3.14.

Parallel Lines

Lines within the same plane that will never intersect. On the coordinate axes, parallel lines have the same slope.

Parallelogram

A quadrilateral with two pairs of parallel sides.

PEMDAS

Acronym for Parentheses, Exponents, Multiply/Divide, Add/Subtract that describes the proper order of operations.

Perimeter

The sum of the lengths of all the sides of a polygon. The perimeter of a circle is called the “circumference.”

Perfect Square

A number whose square root is an integer. The first five perfect squares are 1, 4, 9, 16, and 25.

Perpendicular

Intersecting at a right angle.

PITA (Plugging In the Answers)

Technique for answering multiple-choice questions without doing any algebra (see Chapter 4).

Plug In

A mathematical technique that changes an algebra problem into an arithmetic problem. Can be done whenever there are variables in the answers or the problem contains an unknown quantity that cannot be directly solved for. For more information see Chapter 4: Algebra, and How to Get Rid of It.

Prime Number

Any number whose only factors are itself and 1. The first twenty prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and 71.

Product

The result of multiplication; the product of 12 and 4 is 12 × 4, or 48.

Pythagorean theorem

The formula you can use to find the length of the third side of a right angle (a² + b² = c²), where a and b are the lengths of the legs and c is the length of the hypotenuse.

Pythagorean triplet

Any set of three integers that works in the Pythagorean theorem. The four most common Pythagorean triplets are 3 : 4 : 5, 5 : 12 : 15, 7 : 24 : 25, and 8 : 15 : 17.

Q

Quadrilateral

A polygon with four sides.

Quantitative Comparison

A question type on the GRE in which two quantities are given and you need to determine which is larger (or if the answer is impossible to determine). Often abbreviated in this book as “Quant Comp” or “QC.”

Quotient

The result of division; the quotient of 12 and 4 is 12 ÷ 4, or 3.

R

Radical

Another name for a root; one might refer to as “radical 2.”

Radicand

The number inside the square root symbol.

Radius

The distance from the center of a circle to any point on the circumference of that circle.

Range

The difference between the greatest value and the least value in a set of numbers.

Rational Number

Any number that can be represented as the quotient of two integers.

Reciprocal

The product of any number and its reciprocal is 1: = 1 The result when the numerator and denominator are “flipped.” The reciprocal of is .

Remainder

The result when a number does not divide evenly into another. When 7 is divided by 3, the remainder is 1.

Review

A button at the top of the screen during the GRE test. Clicking on the Review button will show a list of all questions, indicating which questions have been answered, remain unanswered, or have been marked to return to later. Make sure to click on Review before clicking on Exit Section, to make sure you have answered (or at least guessed on) every single question within a section.

Right Angle

An angle that measures 90°.

Right Triangle

A triangle in which one angle measures 90°.

Rhombus

A quadrilateral with four equal sides. (If all four angles are the same measure, then the rhombus is also a square.)

S

Scratch Paper

Your saving grace on the GRE. Your favorite math buddy, more helpful than the calculator, more understanding than the computer screen. All work should be done on the scratch paper provided. In some testing centers, this may be normal paper, in others it may be a series of laminated boards. No matter what, the testing center will always provide scratch paper of some sort and necessary writing utensils. The first step in any GRE problem is to start setting the problem up on the scratch paper. Ask for more during the 10-minute break.

Set

A collection of distinct values

Square

A quadrilateral with four equal sides and four equal angles (each of which measures 90°).

Square Root ()

The square root of x is the number that, when squared, results in x. For example, = 4, because 4² = 16.

Slope

The rate at which a line is rising or falling within a coordinate plane. To find the slope of a line, use the formula , which represents the “rise” over the “run.”

Sum

The result of addition; the sum of 12 and 4 is 12 + 4, or 16.

Surface Area

The sum of the areas of each face of a three-dimensional figure.

T

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Trigger

A word or phrase within a GRE math problem that indicates exactly how you will answer that question. For instance, if a problem contains variables within the answers, then it is a Plug In question.

V

Variable

An element in an algebraic term or equation that is unknown or can vary. Variables are represented as letters.

Y

y-intercept

The point where a line intersects with the y-axis. Represented by b in the equation y = mx + b.

Z

Zero

A number that has no value and therefore can’t be used as a divisor on the GRE. Zero is not positive or negative, but it is even. It is also the additive identity, because any number plus zero equals that number (m + 0 = m).