math foundations

Question 1

an integer is divisible by 3 or 9 if….

Answer 1

its digits add up to a multiple of 3 or 9

Question 2

an integer is divisible by 4 if…

Answer 2

its last two digits are a multiple of 4

Question 3

an integer is divisible by 6 if…

Answer 3

it is divisible by both 2 and 3

Question 4

odd+odd=

Answer 4

even

Question 5

odd+even=

Answer 5

odd

Question 6

even+even=

Answer 6

even

Question 7

odd*even=

Answer 7

even

Question 8

even*even=

Answer 8

even

Question 9

odd*odd=

Answer 9

odd

Question 10

How do you find the GCF?

Answer 10

1) break down integers into their prime numbers

2) multiply the prime factors they have in common

Question 11

what are the first 10 prime numbers?

Answer 11

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 12

How do you find the Least Common Multiple (LCM)?

Answer 12

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

Question 13

2^2 * 2^3 =

Answer 13

2^5

you add exponents when multiplying two numbers with the same base

Question 14

4^5 / 4^2 =

Answer 14

4^3

you subtract exponents when dividing two numbers with the same base

Question 15

(3^2)^3 =

Answer 15

3^6

exponents raised to an exponent: multiply exponents together

Question 16

5^0 =

Answer 16

1

Question 17

raising a negative number to an even exponent produces a

Answer 17

positive result

Question 18

raising a negative number to an odd exponent produces a

Answer 18

negative result

Question 19

raising an even number to any exponent produces an ___ number

Answer 19

even

Question 20

raising an odd number to any exponent produces an ___ number

Answer 20

odd

Question 21

every positive number has x number of square roots

Answer 21

x=2

one positive and one negative

Question 22

T/F: only like radicals can be added or subtracted from one another

Answer 22

True

Question 23

How do you multiply or divide one radical by the other?

Answer 23

1) multiple or divide the numbers outside the radical signs

2) multiple or divide the numbers inside the radical signs

Question 24

simplify sqrt(72)

Answer 24

sqrt(72)=sqrt(36)sqrt(2)

6sqrt(2)

Question 25

what is (2/3) / (1/6)

Answer 25

denominator gets flipped and multiplied | (2/3) * (6/1) = 4

Question 26

(3^2)*(5^2) =

Answer 26

to multiply two different bases but with the same power, multiply the bases together and raise to the power 15^2

Question 27

(6^6) / (6^5)

Answer 27

6 | when bases are the same, you subtract numerator minus denominator

Question 28

speed=

Answer 28

distance / time

Question 29

time=

Answer 29

distance / speed

Question 30

distance=

Answer 30

speed*time

Question 31

What are the all important T equations?

Answer 31

1/T= 1/a + 1/b T= ab / (a+b)

Question 32

you are reverse-FOILing (turning a polynomial back into 2 binomials). What do you do?

Answer 32

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)

Question 33

factor the difference of 9x^2 - 1

Answer 33

(3x + 1)(3x-1)

Question 34

factor the difference of a^2 + 2ab + b^2

Answer 34

(a+b)^2 or (a-b)^2

Question 35

solve this quadratic x^2- 3x + 2 = 0

Answer 35

(x-1)(x-2) | x= 1 or 2

Question 36

in a normal distribution, ____ percent of observations fall within one sd of the mean

Answer 36

68. 6 percent | 34. 3% on each side

Question 37

In a normal distribution, ____ percent of observations fall within 2 sds of the mean

Answer 37

94.6 percent | 13 more percent more on each side after 1 sd is surpassed

Question 38

In a normal distribution, ____ percent of observations fall within 2 sds of the mean

Answer 38

99. 8 percent | 2. 6 percent more on each side after 2 sds are surpassed

Question 39

What is the combination formula for groups and subgroups?

Answer 39

n! / k! (n - k)!

Question 40

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?

Answer 40

n! / k!(n - k)! 7! / 4!(3)! (7 6 5) / (3 2 1) 35

Question 41

What is the equation representing the probability of A or B occurring?

Answer 41

P(A) + P(B) - P(A and B) | this corrects for redundant inclusion of both A and B occurring

Question 42

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

Answer 42

product

Question 43

you use the combination formula n! / k! (n - k)! for (ordered / unordered) subgroups?

Answer 43

unordered! | these questions are often phrased as looking for "how many different groups"

Question 44

T/F: use the combination formula for permutation questions (aka questions where order matters)?

Answer 44

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"