Math Concepts

Question 0

Consecutive integers

Answer 0

At least one is even and one odd

Question 1

Combinations

Answer 1

When selecting a set of items from a group, when the order of the set does not matter.

Question 2

Dividend

Answer 2

Numerator

Question 3

Divisor

Answer 3

Denominator

Question 4

Prime factorization of a perfect square

Answer 4

Includes an even number of each prime number.

Question 5

Perfect square divisors

Answer 5

Has an odd number of divisors.

Question 6

Divisibility rule for 2

Answer 6

One’s digit is 0, 2, 4, 6, 8

Question 7

Divisibility rule for 3

Answer 7

Sum of digits is divisible by 3

Question 8

Divisibility rule for 4

Answer 8

Last two digits are divisible by 4

Question 9

Divisibility rule for 5

Answer 9

One’s digit is 0 or 5

Question 10

Divisibility rule for 6

Answer 10

Divisible by 2 and 3

Question 11

Divisibility rule for 9

Answer 11

Sum of digits is divisible by 9

Question 12

Divisibility rule for 10

Answer 12

One’s digit is 0

Question 13

Number of positive divisors

Answer 13

Get prime factorization:
p^a • q^b • r^c …
# = (a+1)(b+1)(c+1)…

Question 14

GCD by prime factorization

Answer 14

Find all matching prime factors and multiply them out

Question 15

LCM by prime factorization

Answer 15

Multiple common prime factors once by all uncommon prime factors.

Question 16

composite number

Answer 16

not a prime number

Question 17

a”-n

Answer 17

1/a^n

Question 18

sqrt(a)*sqrt(b)

Answer 18

sqrt(ab)

Question 19

sqrt(a)/(sqrt(b))

Answer 19

sqrt(a/b)

Question 20

irrational number

Answer 20

cannot be represented by decimal that terminates or repeats

Question 21

real numbers

Answer 21

irrational + rational numbers

Question 22

|x|

Answer 22

distance from x to 0

Question 23

|a + b|

Answer 23

< or = |a| + |b|

Question 24

|a| |b|

Answer 24

|ab|

Question 25

solving for inequality

Answer 25

sign is reversed if multiply or divide by negative number

Question 26

compound interest with interest rate of r percent compounded annually

Answer 26

P(1+r)^t where r is percent (like 10% = .1) and t is time in years

Question 27

compound interest with interest rate of r percent compounded n times per year

Answer 27

P(1+r/n)^nt where r is percent (like 10% = .1) and t is time in years

Question 28

simple annual interest rate of r percent

Answer 28

P(1 + rt) where r is percent (like 10% = .1) and t is time in years

Question 29

calculate distance between two points

Answer 29

sqrt((x1-x2)^2+(y1-y2)^2) [Create a right triangle and use pythagorean theorem to determine hypotenuse distance]

Question 30

slope for y=mx + b

Answer 30

m

Question 31

y intercept for y=mx + b

Answer 31

b

Question 32

slope for two points

Answer 32

(y2 - y1) / (x2 - x1)

Question 33

word form of slope

Answer 33

"rise over run"

Question 34

slope for perpendicular lines

Answer 34

slopes are negative reciprocals

Question 35

slope for parallel lines

Answer 35

slopes are equal

Question 36

determining y intercept when given two points

Answer 36

calculate slope and then create formula y = mx + b and solve b for either point (x, y)

Question 37

equation for parabola

Answer 37

y = ax^2 + bx + c

Question 38

graph for a quadratic equation

Answer 38

parabola where the x intercepts are solutions to the quadratic equation

Question 39

equation for a circle

Answer 39

(x - a)^2 + (y - b)^2 = r^2 with center at (a, b) and radius r

Question 40

graph for x^2 + y^2 = z

Answer 40

circle with center at origin and radius z

Question 41

sum of all angles in a triangle

Answer 41

180 degrees

Question 42

sum of all angles in an n-sided polygon

Answer 42

(n-2) * 180 degrees

Question 43

relationship between sides of triangles

Answer 43

length of each side must be less than the sum of the lengths of the other two sides

Question 44

relationship of sides in 30-60-90 triangle

Answer 44

30 angle side is 1/2 hypotenuse and the other leg is the 30-angle side times sqrt(3) 1:sqrt(3):2

Question 45

relationship of sides in isoscoles right triangle

Answer 45

the two 45 degree sides are equal and the hypotenuse is that side times sqrt(2) 1:1:sqrt(2)

Question 46

area of a trapezoid

Answer 46

1/2(b1 + b2)(h)

Question 47

circumference of a circle

Answer 47

2(pr)r

Question 48

length of arc for circle with radius r and interior angle a

Answer 48

length/2(pi)r = a/360 i.e. ratio of length to circumference is equal to the ratio of the interior angle to 360

Question 49

area of circle

Answer 49

(pi)r^2

Question 50

volume of a rectangular solid

Answer 50

l*w*h

Question 51

volume if a right circular cylinder

Answer 51

(pi)r^2*h

Question 52

normal distribution

Answer 52

mean = median = mode (approx.)

Question 53

normal distribution 1 st. dev.

Answer 53

68% of data

Question 54

normal distribution 2 st dev

Answer 54

95% of data

Question 55

normal distribution 3 st. dev

Answer 55

99% of data

Question 56

variance

Answer 56

standard deviation squared

Question 57

range

Answer 57

top - bottom

Question 58

standard deviation

Answer 58

average distance from mean

Question 59

calculate standardization for x with std dev S and mean M

Answer 59

(x - M)/S units away from the S

Question 60

permutations for n items

Answer 60

n!

Question 61

0!

Answer 61

1

Question 62

select r items from n in a given order

Answer 62

n! /(n - r)!

Question 63

select r items from n in no particular order

Answer 63

n!/(r! *(n-r)!)

Question 64

probability of an event

Answer 64

number of outcomes included / total number of possible outcmes

Question 65

P(E or F or both)

Answer 65

P(E) + P(F) - P(both E and F)

Question 66

P(E and F) where E and F are independent

Answer 66

P(E)*P(F)

Question 67

expected value

Answer 67

the mean of a random variable

Question 68

a^2 - b^2

Answer 68

( a - b )( a + b )

Question 69

a^2 + 2ab + b^2

Answer 69

(a + b)(a + b)

Question 70

a^2 - 2ab + b^2

Answer 70

(a - b)(a - b)