Algebra
Geometry
Probability / Permutations
Famous Mathematicians
Famous Theorems
100
The hundreds digit of (20!−15!)
What is 0?
100
Camden constructs a square window using 8 equal-size panes of glass, as shown. The ratio of the height to width for each pane is 5:2, and the borders around and between the panes are 2 inches wide. In inches, what is the side length of the square window?
What is 26?
100
Two points are randomly placed on a number line from -1 to 1. Find the probability that the origin lies between the two points.
What is 1/2?
100
Co-inventor of calculus and founder of classical mechanics
Who was Isaac Newton?
100
a^2 + b^2 = c^2
Pythagorean Theorem
200
The sum of all real numbers x such that |x2 - 12x + 34| = 2
What is 18?
200
The two legs of a right triangle, which are altitudes, have lengths 2√3 and 6. Find the length of the third altitude of the triangle.
What is 3?
200
Chloe chooses a real number uniformly at random from the interval [0, 2016]. Independently, Laurent chooses a real number uniformly at random from the interval [0, 4032]. What is the probability that Laurent's number is greater than Chloe's number?
What is 3/4?
200
The full name of the mathematician 2.71828… is named after.
Who is Leonhard Euler?
200
A polynomial with degree n must have n roots.
What is the Fundamental Theorem of Algebra?
300
Five positive consecutive integers starting with x have average y. Express in terms of x, the average of 5 consecutive integers that start with y.
What is x + 4?
300
A regular hexagon has side length 6. Congruent arcs with radius 3 are drawn with the center at each of the vertices, creating circular sectors as shown. The region inside the hexagon but outside the sectors is shaded as shown. Find the area of the shaded region.
What is 54√3 - 18π?
300
P(A|B) = ?
(There are 2 ways to complete the formula; you only need to give one.)
What is
P(A ∧ B) / P(B), or
P(B|A)P(A) / P(B)?
300
The first person to publish the Cartesian coordinate system, or 2D plane.
Who was René Descartes?
300
Name the method used to prove sqrt(2) is irrational.
What is proof by contradiction?
400
There are two values of a for which the equation 4x2 + ax + 8x + 9 = 0 has only one solution for x. What is the sum of these values of a?
What is -16?
400
Find x.
What is 2?
400
Four fair six-sided dice are rolled. Find the probability that at least three of the four dice show the same value.
What is 7/72?
400
The mathematician who proved the Fundamental Theorem of Algebra
Who was Carl Friedrich Gauss?
400
An unsolved hypothesis about the distribution of prime numbers and zeros of the zeta function.
What is the Riemann hypothesis?
500
The sequence log12162, log12x, log12y, log12z, log121250 is an arithmetic progression. What is x?
What is 270?
500
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
What is 8?
500
Three fair six-sided dice are rolled. Find the probability that the values shown on two of the dice sum to the value shown on the remaining die.
What is 5/24?
500
Fermat’s occupation besides mathematician.
What is a lawyer?
500
An unproved conjecture that states every integer greater than 2 can be expressed as the sum of two prime numbers.
What is the Goldbach Conjecture?