Math Cards Flashcards
what branch of math is used to determine the likely hood of something happening
statistics
How do you represent repeated addition of the same number
multiplication
How do you represent repeated multiplication of the same number
exponentiation
What is the opposite of addition?
subtraction
What is the opposite of multiplication?
division
What are the two opposite of exponentiation
Logarithms and radicals
What is a set of numbers in a particular order?
a sequence
What is the sum of every number in a sequence?
a series
What is the name for a equation for the sum of a variable is raised to a different constant power. Ex. 7x^4 + 6x^2 - 4x - 2
a polynomial
What is the name for an equation where a constant is raised to variable power
exponential
What is PI in terms of a circle?
the ratio of a circles circumference to its diameter
What is the common decimal approximation of PI?
3.14
What is the common decimal approximation of e?
2.718
What is the common decimal approximation of root(2)?
1.41
What is In?
the natural log, aka log base e
What is In(e^a)?
a
What is a coefficient of a term in the polynomial
the number in front of that term. Ex: in 7x^5 the coefficient is 7
Simplify log( n ^ k )
k • log(n)
How do you simplify (n ^ k) ^ m
n ^ (k * m)
How do you simplify n ^ k * n ^ m
n ^ (k + m)
For n>m which one is bigger
n
What is the real value for root(-1)
undefined
What is a ^ 3 - b ^ 3 factored
(a - b) * (a ^ 2 + a * b + b ^ 2 )
What is a ^ 2 - b ^ 2 factored
(a + b) * ( a - b)
What is a ^ 3 + b ^ 3 factored
(a + b) * (a ^ 2 - a * b + b ^ 2 )
how many ways are to arrange a set of n objects
n! ways
What dose nCk stand for
n chose k
What is the formula for n!
n * (n - 1) * (n - 2)…. (3) * (2) * (1)
What is the formula for nCk
n! / [(n - k)! * k!]
What is the formula for nPk
n! / (n - k)!
What is the difference between permutations and combinations
combinations don’t care about order, while permutations do
What is (x - 1)! * x
x!
What is x / (x - 1)!
x!
What is 0!
1
How do you chose n objects from a group of k if order doesn’t matters
nCk
How do you chose and arrange n objects from a group of k, without replacements
nPk
How do you chose and arrange n objects from a group of k, with replacements
n^k
How do you chose n objects from a group of k if order matters
nPk
How do you find the chance of two independent events both happening
Multiply the chances of them happening separately
Given two independent events. How do you find the chance of that either one event and or the other will happen
Take the chance of either one not happening and multiply it by the chance of the other not happening. Then take the complement of that
What is an events complement
The chance of the event not ocurring
How do you find an events complement
you take one hundred percent minus the probability of the event
What is an arithmetic series
A series where each subsequent number has a common difference
What is an geometric series
A series where each subsequent number has a common ratio
What is an arithmetic sequence
the order of numbers with a common difference
What is an geometric sequence
the order of numbers with a common ratio
What is a recursive formula
A formula where each term is defined by its previous term, with an initial value defined
What is a direct formula
A formula where the nth term can be found without finding the previous terms
What is this formula used for. f(1) = a, f(x) = f(x - 1) + d
A recursive arithmetic sequence
What is this formula used for. f(x) = a + d * (k - 1)
A direct arithmetic sequence
What is this formula used for. f(1) = a, f(x) = r * f(x - 1)
A recursive geometric sequence
What is this formula used for. f(x) = a * r ^ (k - 1)
A direct geometric sequence
What is this formula used for. f(n) = k*[2a+d * (n - 1)] / 2
A arithmetic series
What is this formula used for. a * (r ^ k - 1) / (r - 1)
A finite geometric series
What is this formula used for. a / (1 - r )
A infinite geometric series
What is the formula for 1+2+3+4…..n
(n ^ 2 + n) / 2
When is a infinite geometric series defined
When the ratio is between -1 and 1
What is the binomial explanation theorem
For a given binomial (x + y) raised to the nth power (x + y) ^ n the coefficient of a ^ k is nCk * b ^ (n - k)
What is a probability distribution with an expected value of 0
A fair game
What is the mean of a set
the Average
What is the median of a set?
The middle number
OR the average of the middle numbers if the set has an even number of elements
What is the mode of a set
the most common number
What is the variance?
a measure of how data points differ from the mean
What is the expected value of a set
the mean
What is IQR?
IQ3 - IQ1, the difference between the third and first quartile
What is IQ1?
the average of the group of numbers that are below the mean of a set
What is IQ3?
the average of the group of numbers that are above the mean of a set
What is the range of a set?
the difference between the biggest and smallest numbers in the set
How to calculate the variance
For each number in the set you take difference from the mean than square it than divide by total number.
What is the standard deviation
the square root of the variance
What is a Z score of a number?
the difference between the number and the Mean over the standard deviation
What dose the symbol for standard deviation look like
an “o” with a line off the top of it going left
What dose the symbol for mean look like
A “u” with lines coming down from both ends
How do you find the mean earnings of a game
Chance of each outcome multiplied by their payout
What is (1+1/n)^n as n gets bigger and bigger
e
What is 1/0!+1/1!+1/2!+1/3!+1/4!+1/5!…..
e
What is the name for 1,1,2,3,5,8,13,21,34,55….
fibinatchi sequence
What are natural numbers
every real number starting from 1 that can be written as the sum of 1 and a previous natural number. AKA [1,2,3,4,5…..]
What are integers
every real number starting from 0 that can be written as the sum of 1 and a previous natural number. AKA [0,1,2,3,4,5…..]
What are rational numbers
every real number that can be written as a ratio of two integers. Ex. 5/7, 9/2, 12.24, 92.333…. , 7, 2
What are irrational numbers
every real number that can not be written as a ratio of two integers. Ex. pi, ln(7), root(8), e/5, -e
What is a real number
A number that has no imaginary part Ex. ln(7), e, 5, pi+e, 9, 0, -8
What is a prime number
A number that has only two distinct whole factors
What is the standard simple interest formula
I=PRT
What is the compounded interest formula
P(1+R/n)^nT
in all interest formulas what is P
the starting amount
in all interest formulas what is T
the time
in all interest formulas what is R
interest rate
in compound interest formulas, what is n
the amount of times it is compounded per unit of time
What’s the formula for compounded interest with a continues contribution after the compounding
P * n * [ ( 1 + r / n ) ^ nt - 1 ) / r ] [where P is the starting amount, r is intrest rate. n is number of times compounding per unit of time, and t is time]
About how much falls within 1 standard deviation of the mean
67%
About how much falls within 2 standard deviation of the mean
96%
About how much falls within 3 standard deviation of the mean
99.7%
