Math Flashcards
integers
counting numbers including negative numbers (but not fractions/irrational numbers)
factor
a number that will divide evenly into the number in question
multiple
a number that is itself a factor of the number in question
prime number
integer whose only factors are itself and 1 (0 and 1 are NOT prime, no such thing as a negative prime)
prime numbers under 30
2,3,5,7,11,13,17,19,23,29
divisibility rules
1) divisible by 2 if its units digit is divisible by 2
2) divisible by 3 if the SUM of all its digits is divisible by 3
3) divisible by 4 if its last two digits form a number that is divisible by 4
4) divisible by 6 if the its divisible by both 2 and 3
5) divisible by 8 if the last 3 digits form a number divisible by 8
6) divisible by 9 if the SUM of its digits is divisible by 9
order of operations
P/E/MD/AS- parenthesis exponents multiplication/division addition/subtraction
associative law
when adding/multiplying a series of numbers you can regroup them however you want
distributive law
a(b+c)- = ab + ac and a(b-c) = ab- ac
Rules for exponents
1) a^2 = a * a
2) a^2 * a^3 = (aa)(aaa) = a^(2+3) = a^5
3) (a^2)^3 = (aa)(aa)(aa) = a^(23) = a^6
4) a^2/a^3 = aa/aaa = 1/a = a^(2-3) = a^(-1)
5) 15^12 - 15^11 = 15^11(15-1) = 15^11(14) CANT JUST SUBTRACT, FACTOR
more rules for exponents
1) raising a fraction between 0 and 1 to a power greater than 1 results in a SMALLER fraction
2) a negative number raised to an EVEN power because POSITIVE, a negative number raised to an ODD power remains NEGATIVE
3) a number raised to a negative power = 1 over the number to the positive power (ie. 2^-2 = 1/2^2)
4) a number raised to the 0 power = 1 0^0 = undefined
5) a number to the 1 power = the number itself
square root rule
1) when ETS asks for square root of 16 they want 4, not -4
2) multiply/divide like normal; multiply/divide the bases, then deal with the square root sign
3) can’t add/subtract unless the bases are the same, if the bases are different estimate their values and then add
square roots to know
square root 1 = 1
square root 2 = 1.4
square root 3 = 1.7
square root 4 = 2
Quadratic equations- 3 types
1) (x+y)(x-y) = x^2 - y^2
2) x^2 + 2xy +y^2 = (x+y)^2
3) x^2 - 2xy + y^2 = (x-y)^2
how to solve quadratic equations
F- first
I- inside
O- outside
L- last
steps to solve quadratic equations
1) separate the x^2 into (x )(x )
2) find the factors of the 3rd term that when added/subtracted give the 2nd term
3) figure out the +/- for the terms, they have to yield the middle term when added/subtracted and the last term when multiplied
4) if a number answer is required, set whole equation = 0; solve; set each ( ) = 0 and solve for x
reducing fractions
factor top and bottom and then cancel, or divide by factors that are common to both
* you can ONLY reduce across a multiplication sign
adding/subtracting
must have same denominator
bowtie method:
1) multiply the denominators together to get a common denominator
2) multiply the denominator of each fraction by the numerator of the other one
3) add/subtract those numbers
4) reduce if necessary
decimals–> %, %–> decimal
.01 = 1/100 = 1% .1 = 1/10 = 10% .2 = 1/5 = 20% .25 = 1/4 = 25% .333 = 1/3 = 33 1/3% .4 = 2/5 = 40% .5 = 1/2 = 50% .6 = 3/5 = 60% .66 = 2/3 = 66 2/3% .75 = 3/4 = 75% .8 = 4/5 = 80% 1.0 = 1/1 = 100% 2.0 = 2/1 = 200%
percentage change
percentage change = (difference/original) * 100
average
average = total/# of things
*as long as you have 2 out of 3 you can solve
standard deviation rule
68-96-100 - percentages of data points that fall 1, 2 and 3 standard deviations from the mean
rate
distance amount/(time*rate)
*as long as you have 2 out of 3 you can solve
the 3 angles inside a triangle add up to
180 degrees
