Number Properties Flashcards
First Prime Numbers to 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Divisibility Test for 3
Sum of all digits is divisible by 3, then divisible by 3
Divisibility Test for 4
if last two digits are divisible by 4, then divisible by 4
Divisibility Test for 5
Last digit is 0 or 5, divisible by 5
Divisibility Test for 6
If both divisibilty tests for 2 and 3 apply, then this does
Divisibility Test for 7
Long Division
Divisibility Test for 8
If last three digits are divisible by 8, then divisible by 8
Divisibility Test for 9
If sum of all the digits in the given number is divisible by 9, that number is divisible by 9
Divisibility Test for 2
last digit is a multiple of 2 or is 0
Divisibility Test for 10
last two digits are an integer multiple of 10
x^2
0
xy>0 means, xy
both positive, both negative (xy>0)
one positive, one negative (xy
Critical rule for inequality manipulation - divide or multiply by negative number…
flip the sign
Do not multiply or divide by variable in inequality unless…
you know the sign for sure
Square root of variable in inequality leads to…
absolute value
use conjugate to (example: x + sqrt5)
simplify denominator (x-sqrt5)/(x-sqrt5)
Direct Proportionality
y=kx or y/x = k
Indirect proportionality
y = k/x or yx = k
Inequalities and Reciprocals, if x
1) If both x and y are positive, flip sign with reciprocal (1/x>1/y)
2) If both x and y are negative, flip sign with reciprocal (1/x>1/y)
3) If x is negative and y is positive, do not flip sign (1/x
Inequalities and squaring
1) If both are positive, don’t flip sign
2) if both are negative, flip sign
3) if one is negative, one positive, can’t square
4) if don’t know signs, can’t square
Combining inequalities (do and do not)
Do multiply and add
Do not subtract and divide
Quadratic Formula
x = -b +- sqrt(b^2 - 4ac)
all over 2a
Discriminant and what it tells us
b^2 - 4ac
tells us how many solutions - positive, 2 solutions,0, 1 solution, negative, no solutions
Quadratics, 3 special products
x^2-y^2 = (x+y) (x-y)
(x+y)^2 = (x+y) (x+y) = x^2 + 2xy + y^2
(x-y)^2 = (x-y) (x-y) = x^2 - 2xy + y^2
Divisibility & Addition/Subtraction (Multiples of Integer)
Add or subtract multiples of an integer, get a different multiple of that integer
Divisibility & Addition/Subtraction (Non-Multiples of Integer)
Multiple + or - Non-Multiple = Non-Multiple
Non Multiple + or - Non-Multiple = Sometimes Yes, Sometimes no, except when integer is 2 (always yes)
Advanced GCF & LCM
GCF - find by multiplying the shared primes (take the smallest count, including 0) in any of the columns
LCM - find by multiplying the largest count in any column - LCM is formed out of all the primes, less shared primes
of Factors in a Perfect Square, Cube
Odd # of factors in perfect square
An even # of factors can never be a perfect square
Perfect squares’ prime factorization contains only even powers of primes!
Perfect cubes’ prime factorization contains only powers of primes that are multiples of 3
