## GRE-Math

##### Created by:

vweagle  on July 13, 2008

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# GRE-Math

 In FRACTIONS with the SAME NUMERATOR...the smaller denominator is the larger fraction
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#### Definitions

In FRACTIONS with the SAME NUMERATOR... the smaller denominator is the larger fraction
in FRACTIONS with the SAME DENOMINATOR... the larger numerator is the larger fraction
to solve for larger fractions with unlike parts... cross multiply keeping numerators of the same side OR find a common numerator or denominator
Positive# * Positive Fraction = a smaller #
Negative# * Positve Fraction= a larger #
# is divisible by 2 if... the number is even
# is divisible by 3 if... the sum of its digits are divisible by 3
# is divisible by 4 if... the last two digits are divisible by 4
# is divisible by 5 if... it ends in 5 or 0
# is divisible by 6 if... it is divisible by 2 and 3
# is divisible by 9 if... the sum of its digits are divisible by 9
The PROBABILITY of an event = (# of desired outcomes)/ (# of possible outcomes)
MULTI-STEP PROBABILITY problem= (Prob of E#1)*(Prob of E#2)
When MULTIPLYING same numbers with different powers... add the exponents
When DIVIDING same numbers with different powers... subtract the exponents
When you have a number with a power raised to a power... multiply the exponents
A number to the power "0" = 1 (except if the number is "0")
A number to a NEGATIVE POWER = 1 / (number to positive power)
A number to a FRACTION POWER = a ROOT
3 steps to solve an ALGEBRAIC INEQUALITY: 1) multiply to get rid of fractions 2) isolate "x" by adding or subtracting to each side 3) multiply by -1 to get positive "x" which will change direction of inequality ( < to >)
6 steps to solve for VARIABLE IN TERMS OF ANOTHER: goal to isolate variable alone on one side 1) clear donominators by corss-multiplying 2) remove parentheses by distributing 3) put all terms containing the variable on one side and all others on the other side by adding and subtracting 4) factor out the variable 5) divide to get the variable alone 6) if necessary multiply by -1 to get rid of negative terms
3 steps to solve QUADRATIC EQUATION: always has TWO answers 1) set it equal to "0" 2) factor it out 3) find values that make each factor equal to "0"
"pi" is approximately equal to ... 3.14
square root of 2 is approximately equal to... 1.4
the square root of 3 is approximately equal to... 1.7
sum of angles of a straight line = 180
sum of angles around a point = 360
SUPPLEMENTARY angles make a straight line and =180
COMPLIMENTARY angles make a right angle and = 90
To get the slope from 2 points (change in Y) / (change in X)
To get slope from an equation put it into "y = mx + b" format
the sum of the interior angles of a triangle = 180
the length of any side of a triangle is... less than the sum of the other 2 sides AND greater than the difference of the other 2 sides
The greatest angle in a traingle... lies opposite the longest side
Triangle Area = (1/2)base * height
ISOSCELES triangles... have two sides of equal length ( and therefore two equal angles)
EQUILATERAL triangle... has three sides of equal length and three equal angles
the ratio of the area of similar triangles... is the square of the ratio of their sides
3 traingles that fit neatly in the PYTHAGOREAN theorem are... (3, 4, 5) (6, 8, 10) and (5, 12, 13)
ratio of sides in a 45-45-90 right triangle are 1:1: √2
ratio of sides in a 30-60-90 triangle is 1: √3:2
sum of interior angles of a POLYGON = (#sides-2) *180
sum of interior angles of a QUADRILATERAL = 360
CIRCUMFERENCE of a CIRCLE = C = 2πr OR πd
AREA of a CIRCLE A = π(r)squared
Finding ARC length ARC/Circumference = central angle / 360
CHORD a straight line connecting two points on a circle... can never be longer than the diameter
VOLUME of a RECTANGULAR SOLID = lengthwidthheight
SURFACE AREA of a RECTANGULAR SOLID = sum of area of faces = 2lw + 2lh + 2wh
VOLUME of a CYLINDER = area of base height = π(r)sq h
LATERAL SURFACE AREA of a CYLINDER = circumference of base * height

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