GRE Math

The percent increase of a quantity

(Actual increase/original amount)100%

The percent decrease of a quantity

(actual decrease/Original amount)100%

Time

(distance)/(rate) d/r

Surface area of a rectangular solid

2(lw+lh+wh)

Area of a Trapezoid:

A=½(base₁+base₂)(height)

THE DENOMINATOR CAN NEVER

BE ZERO! 1/∅=null

For any number x

Can be negative, zero, or positive

In a rectangle, all angles are

Right

Average

Sum/n

Ratios: If a set of objects is divided into 2 groups in the ratio of a:b, then the first group contains

a/a+b and the second group contains b/a+b of the objects. 4:6 becomes 4/4+6=4/10=2/5 6/4+6=6/10=3/5

a% of b

b% of a

Rate

d/t (distance)/(time)

Distance Formula

d=Square root of (x₂-x₁)²+(y₂-y₁)²

If a number is the result of increasing another number by k%, to find the original number

divide by 1+k% 125=100+25% 125÷1.25=100

If a number is the result of decreasing another number by k%, to find the original number

divide it by 1-k% 75=100-25% 75÷(1-25)=75÷.75=100

Volume of a cube

edge³

Formula for a diagonal

l²+w²+h²=d²

Area of a circle

(pi)r²

Pi

Circumference/diameter c/d

It is the number in the set that occurs most often

Mode

For any given Area, the rectangle with the smallest perimeter is a

Square (versus a rectangle)

An Angle that's 180°

Straight Angle

An increase (or decrease) of a% (50%) followed by another increase (or decrease) of a% (50%) is NEVER the same as a single increase/decrease of 2a% (100%)

True

If a lamp decreases to $80, from $100, what is the decrease in price?

(actual decrease/Original amount)100% 20/100x100% is 20%

Volume of a rectangular solid

(length)(width)(height)

The sum of the measures of the n angles in a polygon with n sides

(n-2) x 180

In any Regular Polygon, the measure of each interior angle

(n-2)x180/n

Volume of a Cylinder

(pi)r²h

Distance

(rate)(time) d=rt

3 is the opposite of

-3

X is the opposite of

-X

If a>b then

-a<-b

A decrease of a% followed by a decrease of b% always results in a smaller decrease than a single decrease of (a+b)%

...

To calculate the weighted average: Multiply each number in the set by the number of times it appears, add all the products, and divide by the total number of numbers in the set.

...

Assume that the average of a set of numbers is A. If a number x is added to the set and a new average is calculated, then the new average will be less than, equal to, or greater than A, depending on whether x is less than, equal to , or greater than A, respectfully.

1+2+3/3=2 1+2+3+4/4=10/4=2.5

Probability of E not occurring:

1-P(E)

The reciprocal of any non-zero number

1/x

If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is

180

The consecutive angles in a parallelogram equal

180°

If two numbers are in the ratio of a:b (2:4), then for some number x (3), the first number is ax (2x3) and the second number is bx (4x3). If the ratio is in the lowest terms, and if the quantities must be integers, then x(3) is also an integer.

2(3)+4(3)=6(3)

Circumference of a circle

2(pi)r

Surface area of a cylinder

2(pi)rh

The surface area of a cynlinder plus top and bottom

2(pi)rh+2(pi)r²

To divide any number by a fraction, multiply number by the reciprocal of the fraction

20÷2/3=20/1x3/2=30

If a lamp increases from $80 to $100, what is the percent increase?

25%. (actual increase/original amount)100% 20/80x100%=1/4x100%=25%

If a set of objects is divided into 3 groups in the radio a:b:c, then the first group contains a/a+b+c, second group contains b/a+b+c, etc.

2:3:4

In a Regular Polygon, the measure of each exterior angle

360/n

If you measure all exterior angles in a polygon, they all equal

360°

In any polygon, all external angles equal up to

360°

The sum of all angles around a point

360°

The sum of the angles in a quadrilateral is

360°

Volume of a Sphere

4/3(pi)r³

Each diagonal divides a square into 2

45 45 90 Right triangles (x, x, x*square root of 2)

Formula for the surface area of a cube

6e²

In a Rectangle, each angles measures

90°

Area of a Parallelogram:

A=(base)(height)

Area of a Rectangle:

A=(side)² or A=½(diagonal)²

How do you solve proportions?

Cross multiplication a/b=c/d ad=cb 4/6=10/15 4(15)=6(10) 60=60

Vertical lines

Do not have slopes!

If an experiment is done 2 or more times, the probability that first one event (heads) will occur and then a second event (heads) will occur is a product of the probabilities.

Heads 1/2x1/2x1/2=1/8

What kind of trapezoid has equal parallel sides?

Isosceles Trapezoid

In a set of n numbers that are arranged in increasing order, it is the middle number, if n is odd or the average of the middle two if it is even.

Median

Slope of any line that goes down as you move from left to right is

Negative

7 divided by ∅

Null

If E is certain

P(E)=1/1=1

Probability of an Event

P(E)=number of favorable outcomes/total number of possible outcomes

If Event is impossible

P(E)=ø

The Perimeter of a rectangle

P=2(l+w)

The Perimeter of a Square

P=4s (s=side)

A quadrilateral where two diagonals bisect each other

Parallelogram

Slope of any line that goes up from left to right

Positive

An equation that states that two ratios are equivalent i.e. 4/6=10/15=2/3

Proportion

A fraction that compares two quantities measures in different units

Rate. "Miles per hour" "Dollars per week" "cents per ounce" "students per classroom"

To simplify a complex fraction, multiply every term in the numerator and denominator by the least common multiple of all the denominators that appear in the fraction.

Simplify numerators and denominators and divide

For any given perimeter, the rectangle with the largest AREA is a

Square (versus a rectangle)

If "n" is even, the average of the numbers is the average of what?

The middle two terms (10, 20, 30, 40, 50, 60) 30+40/2=35

An increase of k% followed by a decrease of k% is equal to a decrease of k% followed by an increase of the k% and is always less than the original value.

The original value is never re-gained. 100+50=150 150-75=75 versus 100-50=50+25=75

The total deviation below the average is equal to

The total deviation above the average (80, 90, 90, 90, 100)

An increase of a% followed by an increase of b% <i>always</i> results in a larger increase than a single increase of (a+b)%

True

If one of the angles formed by an intersection is right, they're all right

True

To increase a number by k%

multiply by 1+k% i.e. 100 x (1+50%)=100x1.5=150

To decrease a number by k%

multiply by 1-k% i.e. 100 x (1-50%)=100x.5=50

Formula if two jobs need to be completed and there are m ways to do the first job and n ways to do the second job.

mxn

Any n-sided polygon can be divided into how many triangles? (by drawing diagonals from one vertical)

n-2

Sum of numbers in an average

n/Average

If a<b, the percent increase in going from a to b is always greater than the

percent decrease in going from b to a

Circumference of a circle

pi(diameter)

The area of a sector formed by an arc and 2 radii

x/360 x (pi)r² or x/360 x A

If an arc measures x, the length of the arc is

x/360 x 2(pi)r or x/360 x C

(x+y)²

x²+2xy+y²

(x-y)²

x²-2xy+y²

(x-y)(x+y)

x²-y²

Slope

y₂-y₁/x₂-x₁

Any Horizontal line slope

zero

½% of 100 is

½

If a product of two numbers is ∅, one number must be

∅

Product of any number and ∅ is

∅

∅ divided by 7

∅

The only number that is equal to its opposite

∅ ∅=∅

Probability of Event all cases

∅≤P(E)≤1