PiRIT

Algebra

100

The roots of the following equation:

15x²-x-28=0

What is (x=-4/3 or 7/5) ?

200

The solution of the following system:

-2x-3y=4

3x+y=0

What is x=4/7 and y=-12/7 ?

300

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] 

400

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

500

In Abstract Algebra, this structure contains a binary operation that is associative, has an identity, and has inverses.

What is a group?

Calculus

100

The derivative of the following function: 

f(x) = 10(4x²+8x-13)¹³

What is 

130(8x+8)(4x²+8x-13)¹²

200

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))

300

Calculate the integral of the following function:

f(x) = (x+4)/((x)(x²+5x+6))

What is 

-ln|x+3|+2ln|x+2|+C ?

400

Calculate the double integral of the following on the intervals x=[0,2] and y=[-1,1]

9x²y²+4xy+2

What is 24?

500

In Multivariable Calculus, this method allows you to convert a function in any dimension to a single variable? 

What is parameterizing by t?

Statistics

100

The mathematical formula for standard error of the mean.

What is std. dev. / sqrt(N)?

200

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?

300

The measure of how well a regression model explains variation in a dependent variable.

What is R^2?

400

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?

500

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.

What is an unbiased estimator?

Probability

100

The probability of you flipping a fair coin 10 times in a row and you get all heads.

What is 0.5¹⁰

200

The expected value of a binomial distribution with parameters n and p.

What is np.

300

Bayes Theorem

What is P(A|B)=P(B|A)P(A)/P(B)

400

The pmf of the Poisson distribution with parameter lambda and k.

What is P(x=k) = e^-lambda*lambda^k/k!.

500

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?

Fermi

100

How many golf balls it would take to fill up this room?

~10^9

200

How long can you shower and still make it more environmentally friendly than taking a bath?

~10-12 mins

300

How many litres of water are on Earth?

~10^24

400

If all the humans in the world were crammed together, how much area would we require?

~10^3 km^2

500

How many trees would need to be planted to lower the average global temperature by one degree?

~10^12