GRE Math

Permutation questions ask for... Combination questions ask for..

"arrangements," "orders," "schedules," or "lists" "ways" order doesn't matter in sets "{}," but does matter with lists

How do you set up rate equation for multiple workers working at the same rate?

# of workers X Rate X Time = Work

If you flip a coin 3 times, what's the probability you get exactly 2 heads? If you flip it five times, what's the probability you get exactly 3 heads?

(3! / 2!1!) / 2 X 2 X 2 (5! / 3!2!) / 2 X 2 X 2 X 2 X 2)

Equation for the sum of the measure of interior angles in any polygon with n sides

(n-2) X 180° = 1080°

In functions, for any positive number r:

- The graph of y=f(x) + r is obtained from the graph of y=f(x) by shifting the graph up r units. - The graph of y=f(x) - r is obtained from the graph of y=f(x) by shifting the graph down r units. - The graph of y=f(x+r) is obtained from the graph of y=f(x) by shifting the graph left r units. - The graph of y=f(x-r) is obtained from the graph of y=f(x) by shifting the graph right r units.

When is a function undefined?

- When a zero is the denominator - When there's a negative number under a square root sign

Common quadratics: - (x+y)^2 - (x-y)^2

- x^2 + 2xy + y^2 - x^2 - 2xy + y^2

In order to increase a set's standard deviation, you must...

...add a value that is more than one standard deviation away from the mean of the set.

When a transversal (a line that intersect two lines at two distinct points) cuts a pair of parallel lines, the angles are always...

...supplementary.

4 triangle midpoint rules

1) A line from one angle to the midpoint of the opposite side creates two triangles of equal area. 2) A line created by the midpoints of two sides creates a parallel line with the third side of the triangle 3) That line is ½ of the third side 4) The area of the new triangle is ¼ of the original triangle

Steps for finding a combination of things from different sources

1. Draw a bracket for each source 2. Write into each bracket the number of choices that can be made from that source or calculate 3. Multiply

Steps for finding a combination of things from the same source, where uniqueness/placement/order does matter

1. Draw dashes on your scratch paper equal to the number of items you need to select 2. Write into the first dash the number of items you can choose from 3. (Generally) count down the numbers in the dashes until you run out of dashes 4. Multiply

Steps for finding a combination of things from the same source, where uniqueness/placement/order doesn't matter

1. Draw dashes on your scratch paper equal to the number of items you need to select 2. Write into the first dash the number of items you can choose from 3. (Generally) count down the numbers in the dashes until you run out of dashes 4. Underneath last dash write the number 1, and count up from 1 until you run out of dashes 5. Solve

Steps for calculating standard deviation

1. Find the mean of the data points 2. Find the difference between the mean and each data point 3. square each of the differences 4. Find average of the squared differences 5. Take the square root of the average

An inscribed angle is always...

1/2 of the measure of the arc it forms

2^10

1024

How many edges to cubes have?

12

2^7 =

128

One last common right triangle length ratio

1x : 2x : x√5

First 25 prime numbers

2 (only even prime), 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

What are the increments that are used in a standard deviation?

2%, 14%, 34%, 34%, 14%, 2%

2^11 =

2048

2^8 =

256

Pythagorean triplets

3 : 4 : 5 (6 : 8 : 10) 5 : 12 : 13 7 : 24 : 25 8 : 15 : 17

2^9 =

512

Surface area of a cube

6(e^2)

2^6 =

64

Equilateral triangle area formula

A = (s^2) X (√3) / 4

Compound interest rate

A = P(1 + r/n) ^nt n = number of times it is compounded in the interest period

Area of parallelogram from the diagonal

A = d^2 / 2

What does normal distribution mean?

A bell curve when the middle number is the mean

Composite number

A positive integer greater than 1 that is not prime

If a triangle's angles have the ratio 1:1:2, the triangle must be...

A right isosceles triangle.

Quartiles

A set divided into four equal sections; "Q1" represents the greatest number i the first 25%, etc. Q1 = 25th percentile Q4 = 100th percentile

Rhombus

All sides are equal. Opposite angles are equal.

Simple interest equation

Amount at end of investment = P + PRT P = principle r = interest rate (APR) t = time (# of years)

Prime factorization

Any non-prime number greater than 1, can be expressed as the product of prime factors

Being in the 80th percentile means...

Being greater than 80% (in the top 20%)

Interquartile range

Difference between the greatest value of one quartile and the greater value of another (Q3 - Q1 = interquartile range of the 3rd and first quartile)

What are a triangles "altitudes?"

Distance of a perpendicular to a specific vertex. A triangle has three altitudes.

How to solve mutually exclusive group problems

Draw a chart

Remote angle theorem (triangle)

Exterior angle equals the sum of the opposite interior angles

How to find average (mean and median) of arithmetic set?

Find average of first and last term

Rules of divisibility: 8

If the last three digits is divisible by 8

Rules of divisibility: 4

If the last two digits its divisible by 4

Rules of divisibility: 6

If the number is divisible by 2 and 3 (i.e., the units digit is 0, 2, 4, 6, or 8 and the sum of the digits is divisible by 3)

Rules of divisibility: 3

If the sum of the digits is divisible by 3

Rules of divisibility: 9

If the sum of the digits is divisible by 9

Ratio of similitude in similar triangles

If this ratio is k, then their respective areas are k^2. For example, if a triangle has sides that are 3 times longer, than its area is 9 times greater.

If a triangle inside a circle has two sides that are also radii, then the triangle is a...

Isosceles or an equilateral

What are the "roots" of an equation?

It's solutions

Divisor/factor

Leaves no remainder when divided

P (A or B) formula (independent but not mutually exclusive events?)

P(A or B) = P(A) + P(B) - P(A and B)

P(at least 1) equals?

P(at least 1) = 1 - P(none)

How many sides do different polygons have?

Pentagon - 5 Hexagon - 6 Septagon/Heptagon - 7 Octagon - 8 Nonagon - 9 Decagon - 10

How do you set up rate equation for multiple workers working at different rates?

Rate 1 +/- Rate 2 = Rate together and (Work 1 / Time 1) +/- (Work 2 / Time 2) = (Work together / Time together) Use addition equation when workers are working together and use subtraction when they are working against one another.

Basic rate equation

Rate X Time = Work

Surface area of rectangular prism

SA = 2(l X h + l X w + h X w)

How do you know for sure a triangle is a special kind?

SAS, ASA, or SSS

To find out how many times two lines intersect

Set then equal to each other and find how many solutions for x there are

What is the sum of all integers 1 to 100 inclusive?

Sum = Avg X (# of #'s) Sum = 50.5 X 100

Arc measure is equal to...

The central angle that forms it

What are diagonals in any 3D shape?

The longest distance between any two corners.

Relative frequency

The number of values with the characteristic of interest expressed as a percent of the total number of values

Group formula for three overlapping groups

Total = G1 + G2 + G3 - (# in two groups) - 2(# in 3 groups) + uncounted

Solving percent problems

Use the proportion (is/of) = (percent/100)

When do you set up rate equation as a direct proportion?

When there problem involves only one worker Rate = work/time or, work/time = work'/time' Rate X time = work (distance)

Midpoint formula of any two points

[ (x1 + x2) / 2)], [ (y1 + y2) / 2]

Equation for the diagonal in a rectangular box, where a, b, and c are the dimenions of the figure

a^2 + b^2 + c^2 = d^2

Distance formula of any two points

d = √ [ (x2 - x1 )^2 + (y2 - y1)^2]

Combination formula

n! / k!(n-k)!

Length of arc of a circle, where x is the arc's central angle

x / 360(C) = x / 360(2Πr)

Area of an arc's sector, where x is the sector's central angle

x / 360(Πr^2)

30-60-90 triangle side length ratio

x : x√3 : 2x

X and Y are directly proportional

x/y = constant x/y = x'/y'

X and Y are inversely proportional

xy=constant xy=x'y'

Square root of 2

~1.4

Square root of 3

~1.7

Square root of 5

~2.2

Square root of 6

~2.4

Square root of 7

~2.6

Square root of 8

~2.8

Finding percent increase/decrease (the percent by which something has increased or decreased)

•Formula: % change = difference/original x 100 •For percent increase questions, the denominator should always be greater

Repeating sequence problems

•When a group of k numbers repeats itself, to find the nth number, divide n by k and take the remainder r. The rth term and the nth term are always the same •If the repeating sequence 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7,...in which six digits keep repeating, what is the 500th term in the sequence? Since six numbers repeat, divide 500/6=83.3, ignore the decimal portion—the quotient is 83—and 83 X 6= 498, the remainder is 500-498=2. The 500th term is the same as the 2nd term, which is 4.