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