Math Concepts Flashcards
Consecutive integers
At least one is even and one odd
Combinations
When selecting a set of items from a group, when the order of the set does not matter.
Dividend
Numerator
Divisor
Denominator
Prime factorization of a perfect square
Includes an even number of each prime number.
Perfect square divisors
Has an odd number of divisors.
Divisibility rule for 2
One’s digit is 0, 2, 4, 6, 8
Divisibility rule for 3
Sum of digits is divisible by 3
Divisibility rule for 4
Last two digits are divisible by 4
Divisibility rule for 5
One’s digit is 0 or 5
Divisibility rule for 6
Divisible by 2 and 3
Divisibility rule for 9
Sum of digits is divisible by 9
Divisibility rule for 10
One’s digit is 0
Number of positive divisors
Get prime factorization:
p^a • q^b • r^c …
# = (a+1)(b+1)(c+1)…
GCD by prime factorization
Find all matching prime factors and multiply them out
LCM by prime factorization
Multiple common prime factors once by all uncommon prime factors.
composite number
not a prime number
a”-n
1/a^n
sqrt(a)*sqrt(b)
sqrt(ab)
sqrt(a)/(sqrt(b))
sqrt(a/b)
irrational number
cannot be represented by decimal that terminates or repeats
real numbers
irrational + rational numbers
|x|
distance from x to 0
|a + b|
< or = |a| + |b|
|a| |b|
|ab|
solving for inequality
sign is reversed if multiply or divide by negative number
compound interest with interest rate of r percent compounded annually
P(1+r)^t where r is percent (like 10% = .1) and t is time in years
compound interest with interest rate of r percent compounded n times per year
P(1+r/n)^nt where r is percent (like 10% = .1) and t is time in years
simple annual interest rate of r percent
P(1 + rt) where r is percent (like 10% = .1) and t is time in years
calculate distance between two points
sqrt((x1-x2)^2+(y1-y2)^2) [Create a right triangle and use pythagorean theorem to determine hypotenuse distance]
slope for y=mx + b
m
y intercept for y=mx + b
b
slope for two points
(y2 - y1) / (x2 - x1)
word form of slope
“rise over run”
slope for perpendicular lines
slopes are negative reciprocals
slope for parallel lines
slopes are equal
determining y intercept when given two points
calculate slope and then create formula y = mx + b and solve b for either point (x, y)
equation for parabola
y = ax^2 + bx + c
graph for a quadratic equation
parabola where the x intercepts are solutions to the quadratic equation
equation for a circle
(x - a)^2 + (y - b)^2 = r^2 with center at (a, b) and radius r
graph for x^2 + y^2 = z
circle with center at origin and radius z
sum of all angles in a triangle
180 degrees
sum of all angles in an n-sided polygon
(n-2) * 180 degrees
relationship between sides of triangles
length of each side must be less than the sum of the lengths of the other two sides
relationship of sides in 30-60-90 triangle
30 angle side is 1/2 hypotenuse and the other leg is the 30-angle side times sqrt(3)
1:sqrt(3):2
relationship of sides in isoscoles right triangle
the two 45 degree sides are equal and the hypotenuse is that side times sqrt(2)
1:1:sqrt(2)
area of a trapezoid
1/2(b1 + b2)(h)
circumference of a circle
2(pr)r
length of arc for circle with radius r and interior angle a
length/2(pi)r = a/360
i.e. ratio of length to circumference is equal to the ratio of the interior angle to 360
area of circle
(pi)r^2
volume of a rectangular solid
lwh
volume if a right circular cylinder
(pi)r^2*h
normal distribution
mean = median = mode (approx.)
normal distribution 1 st. dev.
68% of data
normal distribution 2 st dev
95% of data
normal distribution 3 st. dev
99% of data
variance
standard deviation squared
range
top - bottom
standard deviation
average distance from mean
calculate standardization for x with std dev S and mean M
(x - M)/S units away from the S
permutations for n items
n!
0!
1
select r items from n in a given order
n! /(n - r)!
select r items from n in no particular order
n!/(r! *(n-r)!)
probability of an event
number of outcomes included / total number of possible outcmes
P(E or F or both)
P(E) + P(F) - P(both E and F)
P(E and F) where E and F are independent
P(E)*P(F)
expected value
the mean of a random variable
a^2 - b^2
( a - b )( a + b )
a^2 + 2ab + b^2
(a + b)(a + b)
a^2 - 2ab + b^2
(a - b)(a - b)
