Math portion- GRE

41^2

40^2= 1600 +40 +41= 1681 if we know value of n^2 (multiple of 10 or 5) we can get the next square up, (n+1)^2, by adding n and (n+1)

which angle of triangles mean that sides are equal?

60

Surface area of a cube formula

6s^2 (s=side)

what is an integer

A WHOLE number (not a fraction or decimal!) that can be positive or negative

rise over run

A quick way to find the slope of a line if given the graph

formula for compound interest annually

A= P(r^y) A= 1000(1.05)^8 1000 5% for 8 years

area of a circle

A=πr²

integer

All whole numbers (both positive and negative) and zero.

what is a real number

Any number on a number line as a rational and irrational number.

prime factorization

Breaking down a composite number until all of the factors are prime

distance formulla

D=RT

multiplying even and odds

E*O=E O*O=O E*E=E

formula for compound interest quarterly

Interest 5% quarterly 5/4= 1.25 1.0125 interest quarterly for 6 years 1000(1.0125)^6(4)

simple interest

Interest earned only on the original principal amount invested 1000 in bank account with 5% compound interest get 50 each year no matter if change in amount of money in bank account

volume of a box equation

LxWxH

inequality rule with changing direction

Multiplying or dividing by a negative number, needs to reverse the direction of the inequality. -3x < -30 x > 10

remainder

The amount left over when one number is divided by another.

percent increase formula

[(new value-original value)/original value] x 100

The sum of a series of integers formula

[n(n+1)] / 2:

standard deviation

a computed measure of how much scores vary around the mean score

prime numbers

a number which can only be divided by itself and 1

(a+b)- (c-d)

a+b-c+d have to distribute negative sign to whole parentheses

(a^n)+ (a^m)=

a^m+n

a^m/a^n

a^m-n

adding and subtracting even and odd number rules

add or subtract "likes"= even add or subtract "unlikes"= odd

multiplying exponents

add the exponents

divisibility rule for 3 and 9

add up all number is integer 234 2+3+4=9 divisible by 3 or 9

what is an undefined number?

anything divided by 0

How to find circumference of part of a circle with arclength?

arclength/ 2 pi R= angle /360 find full circumference of circle then divide by part of circle

triangles with same base and lie between same parallels

area is equal

How to find area of part of a circle with a sector?

area of sector/ pi R^2= angle /360

Parallel Lines angles

big angles are equal and small angles are equal. The sum of 1 small and 1 big angle should be 180 degrees.

what is the associative property

when adding or multiplying you can group numbers in any order. Example, (3+5) + 7 = 3 + (5+7)

Extraneous Solutions/Roots

when plugged back into the original, they make it undefined

Standard deviation graph

within one S of M = percentage from M - S to M + S = 68% (within two S of M = percentage from M - 2S to M + 2S = 95%

slope formula

y2-y1/x2-x1

Finding factors of number by finding primer factors first

by finding prime factors of a number you can find other factors in that number 4680= 2^3 *3^2*5*13 45: 3^2*5 (yes a factor of 4680)

how to figure out if which fraction is greater?

cross multiply number sense (449/150) (20/7) (450/150)= 1/150 less (21/7)= 1/7 less 449/150 greater

Rebuilding the Dividend Equation

d= q*s + r

how to find third side of a triangle with variables

differences of side A and B< length of 3rd side < sum of A and B

Square root of an exponent

divide by the root

angles of two triangles with the same chord

equal eachother

adjacent angles in trapezoids

equal to 180

how to find LCM

find gcf with prime factorization then multiply all factors 32 and 24 24: 2^3 3 32: 2^5 gcf: 2^3= 8 24= 8*3 32= 8*4 lcm= 8*3*4= 96 m/gcf= a n/gcf= b lcm= gcf*a*b

how to know if number below 100 is prime

if divisible by prime number below 10--- not prime

GCM and LCM rule

if x=GCD of A &B and y=LCM of A&B then AB= xy

how to multiply percentage increase?

increased by 17% multiply 1.17

compound interest

interest earned on both the principal amount and any interest already earned

the remainder is always --- than the divisor

less

the remainder is always ----- than the divisor

less

How to find range

max-min

exterior angle theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

divisor

The number by which another number is divided.

volume of a cube

V=s³

How to solve complex algebra questions with fration

multiply sides with LCM

when an exponent is raised to a power

multiply the powers

waht does getting the product mean?

multiplying

numbers of m to n inclusive

n-m+1

7 choose 3

n=7 r=3 n!/r! (n-r)!

equation for finding "k "different objects that can be selected from a group of "n" objects

nCk= n! / k! (n-k)!

what is a factor

numbers you multiply together to get another number

how to find y intercept of equation?

plug in 0 for x

result of division?

quotient

square root of a fraction

square root of (1/36)= 1/6

The combined work rate of people or machines working together is

the sum of the individual work rates

FOIL method

to multiply two binomials, find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms

average velocity formula

total displacement/total time

what can be cancelled in a proportion?

vertically and horizontally but never diagonal

distributive law with same base fractions

(a+c)/ b= a/b + c/b

power of a product rule

(ab)^m=a^m*b^m

how to distribute exponent across addition or subtraction

(p+q)^2= p^2+2pq+q^2

how to find GCF

1) Prime factorization 2) Find common powers and terms, choose the highest power in common 3) Multiply 360 and 800 360= 2^3 3^2 5 800= 2^5 5^2 2^3 and5=40

Shrinking and expanding gaps

1) Two travelers in opposite directions: add the speeds 2)Two travelers in same direction: subtract (bigger-smaller) the speeds *sometimes it makes the most sense to set up a D=RT equation for the gap itself instead of each traveler/leg

When we need to divide N by 5, instead we can:

1. double N (Nx2) 2. divide this by 10 or divide by 10 first then multiply by 2

area of a triangle

1/2 bh

how to multiply numbers mentally

16 x 35 we can divide by two, and multiply by two 16/2 = 8 35 x2= 70 8 x 70= 560 ** can use this when one factor ends in 5 or 50 ** do it double if ends in 25 or 75

30-60-90 triangle

1:√3:2

if slope is -3/2 then perpendicular slope is

2/3 (opposite)

circumference of a circle

2πr

multiply what for percentage decrease

30% decrease 1-0.3= 0.7 multiply number by 0.7

squaring shortcuts

35^2 has to be in between 30^2 and 40^2 end in 25 multiply the first digit by (digit +1) : 3 x 4=12 put 25 behind it 1225