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Preparing for the GRE c General Test - Math Review - MyGRETutor.com

Integers

Positive and Negative whole num-bers, including zero. For example,−3,−2,−1, 0, 1, 2, 3, 4, are integers.

Rational Numbers

Any number that can be expressed as aratio. For example, 3.5 or 22

6.

Order of Operations

In an expression, always perform thecalculations inside the parentheses first,then exponents, then multiplication, di-vision, addition, and finally subtraction.Thus, (2× (3 + 1)) + 2 × 3 = 14

Factorization

The factors of a number are all of the in-tegers that divide evenly into that num-

ber. For example, the factors of 27 are1, 3, 9 and 27.

Multiples

The multiples of a number x are all of those numbers that can be divided by x

without a remainder. For example, themultiples of 14 are 14, 28, 42, ...

Odd, Even, and Primes

Odd numbers are not divisible by 2.

Even numbers are multiples of 2. Primenumbers have only two factors, 1 andthemselves. Example odd are 3,5,7; ex-ample even numbers are 2,4,6; exampleprime numbers are 2,3,5,7,11, ...

Percentages

“Percent” means “out of 100”. For ex-ample, 25 percent means 1

4, so 25% of 

12 apples is 3 because 12 ×1

4= 3.

AverageAverage is the sum of all terms dividedby the number of terms. For 3, 4, and8, the average is 15

3= 5.

Median and Mode

The median is the middle value of alist of numbers ordered by size. Themode is the number in a list that ap-pears most often. For a set of numbers{3, 4, 6, 6, 6, 8, 9}, the mean is 6, becausethe sum is 42 and so 42

7= 6, and the

mode is 6.

Counting and Probability

If an event x occurs with probability p,and event y occurs with a probability q,then the probability of events x and y

happening together is p× q, or pq.

Bases and Exponents

The base of an expression is the num-

ber that is being manipulated, and theexponent is the value to which a num-ber is raised. In xa, x is the base and a

is the exponent.

Zero Power and x−y

Any number raised to the zero power is1. A number with a negative exponent isequivalent to 1 divided by that number;so x−y = 1

xy

Exponents & MultiplicationIf two numbers of the same base but dif-ferent exponents are multiplied, you addthe exponents. So na × nb = na+b.

Exponents & Division

If dividing two numbers of the samebase, subtract the exponent of the de-nominator from the exponent of the nu-merator. So na

nb= na−b.

Exponents, PowersAn exponent raised to some power is thesame as the product of the power andthe raise: (na)b = nab.

Exponents, Products

The product of two numbers raisedto some exponent can be rewritten asthe product of the individual numbers:(nm)a = na ×ma

Variables, equationsA variable is a symbolic representationused to denote a quantity or expression.In 4x = 12, the variable is x, and in thiscase x is equal to 3. In order to solve forn variables, you need n equations.

Substitution

Substitution is used to solve equations.If there are two equations with two vari-ables between them, then solve for oneof the variables, and then use the result

to solve for the second variable.

Factoring

Rules for factoring equations:a2 + 2ab + b2 = (a + b)(a + b)a2 − 2ab + b2 = (a− b)(a− b)

a2 − b2 = (a− b)(a + b)

Intersecting Lines

Opposite angles of intersecting lines

equal.

Triangles

The area of a triangle is one-half btimes the height: A = 1

2bh. The t

angles of a triangle sum to 180 degr

Equilateral, Isosceles

An equilateral triangle has 3 equal sand 3 equal angles. The angles of a elateral triangle are each 60 degrees.

isosceles triangle has 2 equal sides 2 equal angles. For an isosceles trianthe sides opposite the two equal anhave equal lengths.

Rectangles

The area of a rectangle is length tiwidth: A = lw. The perimeter of a rangle is 2l+ 2w. A square is a rectanwhere all of the sides are of equal lenEach angle in a rectangle is 90 degre

Parallelograms

The area of a parallelogram is lentimes height: A = lh.

Area, Radius, Diamet

Perimeter of a Circle

The radius, r, of a circle is the distafrom the center of the circle to its edIt’s area is π times radius squared:πr2. The diameter is twice the radD = 2r, and the circumference C = 2

Arcs

An arc of a circle is a segment of perimeter. The length of an arc is times the intersecting angle, x.

Solid Geometry

The volume of a rectangular solilength times width times height: V

lwh. The volume of a right cylindebase times height, where the base circle, and so V  = πr2h.