math foundations Flashcards
an integer is divisible by 3 or 9 if….
its digits add up to a multiple of 3 or 9
an integer is divisible by 4 if…
its last two digits are a multiple of 4
an integer is divisible by 6 if…
it is divisible by both 2 and 3
odd+odd=
even
odd+even=
odd
even+even=
even
odd*even=
even
even*even=
even
odd*odd=
odd
How do you find the GCF?
1) break down integers into their prime numbers
2) multiply the prime factors they have in common
what are the first 10 prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
How do you find the Least Common Multiple (LCM)?
1) break integers into their prime numbers
2) write out each prime number the maximum number of times it appears in any of the factorizations
3) multiple those prime numbers together to get the LCM
ex: 6: (2)(3)
8: (2)(2)(2)
2: max 3 times; 3: max 1 time
so (2)(2)(2)(3)=24
2^2 * 2^3 =
2^5
you add exponents when multiplying two numbers with the same base
4^5 / 4^2 =
4^3
you subtract exponents when dividing two numbers with the same base
(3^2)^3 =
3^6
exponents raised to an exponent: multiply exponents together
5^0 =
1
raising a negative number to an even exponent produces a
positive result
raising a negative number to an odd exponent produces a
negative result
raising an even number to any exponent produces an ___ number
even
raising an odd number to any exponent produces an ___ number
odd
every positive number has x number of square roots
x=2
one positive and one negative
T/F: only like radicals can be added or subtracted from one another
True
How do you multiply or divide one radical by the other?
1) multiple or divide the numbers outside the radical signs
2) multiple or divide the numbers inside the radical signs
simplify sqrt(72)
sqrt(72)=sqrt(36)sqrt(2)
6sqrt(2)
what is (2/3) / (1/6)
denominator gets flipped and multiplied
(2/3) * (6/1) = 4
(3^2)*(5^2) =
to multiply two different bases but with the same power, multiply the bases together and raise to the power
15^2
(6^6) / (6^5)
6
when bases are the same, you subtract numerator minus denominator
speed=
distance / time
time=
distance / speed
distance=
speed*time
What are the all important T equations?
1/T= 1/a + 1/b
T= ab / (a+b)
you are reverse-FOILing (turning a polynomial back into 2 binomials). What do you do?
start by writing what you know (x)(x)
the product of the two missing terms will be the last term in the original polynomial (number without an x) ; and the sum of the two missing terms will be the coefficient of the second term of the polynomial (the one with the x)
factor the difference of 9x^2 - 1
(3x + 1)(3x-1)
factor the difference of a^2 + 2ab + b^2
(a+b)^2 or (a-b)^2
solve this quadratic x^2- 3x + 2 = 0
(x-1)(x-2)
x= 1 or 2
in a normal distribution, ____ percent of observations fall within one sd of the mean
- 6 percent
34. 3% on each side
In a normal distribution, ____ percent of observations fall within 2 sds of the mean
94.6 percent
13 more percent more on each side after 1 sd is surpassed
In a normal distribution, ____ percent of observations fall within 2 sds of the mean
- 8 percent
2. 6 percent more on each side after 2 sds are surpassed
What is the combination formula for groups and subgroups?
n! / k! (n - k)!
There are 7 kids participating in the spelling bee, and 4 get ribbons. Using the combination formula, how many different groups of finalists are there?
n! / k!(n - k)!
7! / 4!(3)!
(7 6 5) / (3 2 1)
35
What is the equation representing the probability of A or B occurring?
P(A) + P(B) - P(A and B)
this corrects for redundant inclusion of both A and B occurring
when choices or events occur one after the other and the choices are independent of one another, the total number of possibilities is the ____ of the number of options of each
product
you use the combination formula n! / k! (n - k)! for (ordered / unordered) subgroups?
unordered!
these questions are often phrased as looking for “how many different groups”
T/F: use the combination formula for permutation questions (aka questions where order matters)?
False: you multiply the number of different options by each other
ex: (7)(6)(5)..
usually phrased like “different arrangements” or “different ways of ordering”
