Calculus
int_0^infty e^(-x^2)dx
sqrt pi / 2
James tosses 6 identical dice, the outcome of each die will be from 1 to 6. What is the total number of outcomes of the resulting roll? (order of the dice does not matter)
((11),(6)) = 462
Name the 5 platonic solids.
Tetrahedron, cube, octahedron, dodecahedron, icosahedron
NO CALCULATOR!
Which is greater:
2.7^e or e^2.7
e^2.7
Who proved Fermat's Last Theorem?
Andrew Wiles
d/dx ln(xln(xln(x...)))
1/(x-x/ln(xln(xln(x...)))
James flips five coins, exactly three of which lands heads. What is the probability that the first two are both heads?
3/10
What is the tangent double angle identity? (What is tan(2x))
tan(2x) = (2tanx)/(1-tan^2x)
Alice and Bob are playing a game. A coin is put in the top left square of an 8x8 chessboard. They alternate turns and each player can move one square either down, right, or diagonally down and right. Whoever moves the coin to the bottom right square wins. Alice plays first. Is there a winning strategy and if so, which player will win?
Alice has a winning strategy
What is the smallest number that can be expressed as the sum of two positive cube numbers in two different ways? Famously called Ramanujan's number.
10^3 + 9^3 = 12^3 + 1^3 = 1729
int_-infty^infty sin(pix)/(pix) - sin^2(pix)/(pix)^2 dx
0
1/e
A circle of radius 6 is drawn centered at the origin. How many squares of side length 1 and integer coordinate vertices intersect the interior of this circle?
132
Consider the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... obtained by writing one 1, two 2s, etc. What is the 2023rd term of this sequence?
64
John Urschel received a doctorate in mathematics from MIT. He was also a professional football player in the NFL. What team did he play for?
Baltimore Ravens
What is the integer part of sum_{i=2}^9999 1/sqrti
197
Hannah has two coins, one of which is fair and the other of which always comes up heads. She takes one of them at random and flips it twice. Given that it came up heads both times, what is the probability that it is the coin that always comes up heads?
4/5
What is the radius of the largest circle centered at the origin under the curve
e^(-x^2)?
sqrt(1/2(1+ln(2))
How many zeroes are there at the end of the number 125!
Which mathematician famously died from a gunshot wound to the stomach at the age of 20?
Galois
int_2^4 sqrt(ln(9-x))/(sqrt(ln(9-x)) + sqrt(ln(x+3))) dx
1
How many 8 x 8 matrices are there in which every entry is a 0 or 1 and each row and each column contains an odd number of 1s?
2^49
Given n random points on a circle, what is the probability that the convex polygon formed by these points does not contain the center of the circle?
n (1/2)^(n-1)
What is the smallest possible value of positive integer n > 1, such that there exists positive integers a, b, c where
a^2 + b^2 = c^2 and abc+n
is a square number?
4
Which US president published a proof of the Pythagorean Theorem in the New-England Journal of Education on April 1, 1876? (This was 5 years before he became president)
James Garfield