Algebra
The roots of the following equation:
15x2-x-28=0
What is (x=-4/3 or 7/5) ?
The derivative of the following function:
f(x) = 10(4x2+8x-13)13
What is
130(8x+8)(4x2+8x-13)12
The mathematical formula for standard error of the mean.
What is std. dev. / sqrt(N)?
What is 0.510
How many golf balls it would take to fill up this room?
~10^9
The solution of the following system:
-2x-3y=4
3x+y=0
What is x=4/7 and y=-12/7 ?
Calculate the derivative of the following function:
f(x) = (x2+3x-2)(sin(x))
What is
(x2+3x-2)(cos(x))+(2x+3)(sin(x))
The expected value of a fair six-sided die rolled once, where you win $5 if the result is a 6, $2 if the result is a 4 or 5, and $0 otherwise.
What is $1.50?
The expected value of a binomial distribution with parameters n and p.
What is np.
How long can you shower and still make it more environmentally friendly than taking a bath?
~10-12 mins
The product of the following matrices:
[ 2 1 7] [ 2 1 -3]
[-1 0 4] . [-2 -4 0]
[ 3 4 5] [ 6 2 1]
What is the matrix
[44 12 1]
[22 7 7]
[31 5 -4]
Calculate the integral of the following function:
f(x) = (x+4)/((x)(x2+5x+6))
What is
-ln|x+3|+2ln|x+2|+C ?
The measure of how well a regression model explains variation in a dependent variable.
What is R^2?
Bayes Theorem
What is P(A|B)=P(B|A)P(A)/P(B)
How many litres of water are on Earth?
~10^24
The rank of the following 5x5 matrix:
[1 5 -2 -1 1]
[2 1 -1 -2 -1]
[0 2 3 0 8]
[-1 0 3 1 6]
[-1 3 -2 1 -1]
3
Calculate the double integral of the following on the intervals x=[0,2] and y=[-1,1]
9x2y2+4xy+2
What is 24?
Type of correlation:
n=20
y=B+Cx+E
H:C=0
t-statistic: t=50
What is a linear correlation between y and C?
What is P(x=k) = e-lambda*lambdak/k!.
If all the humans in the world were crammed together, how much area would we require?
~10^3 km^2
In Abstract Algebra, this structure contains a binary operation that is associative, has an identity, and has inverses.
What is a group?
In Multivariable Calculus, this method allows you to convert a function in any dimension to a single variable?
What is parameterizing by t?
Let A be an estimator of a population with mean M with A=(2a+b+c+...+z)/10. This is the kind of estimator A is.
On a game show, you pick one of three doors. A car is behind one, and goats are behind the other two. The host, who knows where the car is, opens one of the two doors you didn't pick, revealing a goat. He then asks if you want to stick with your original choice or switch to the other unopened door. This is the probability you win the car if you switch.
What is 2/3?
How many trees would need to be planted to lower the average global temperature by one degree?
~10^12