Algebra
Combo
Geo
NT
Formulas and Definitions
Math Trivia
100
Determine the difference of the squares of the roots of
x^2 - 17x - 19.
17sqrt(365)
100
Find the number of rectangles that can be found in a 3x4 grid of squares.
60
100
A rhombus with area 8√3 has one angle measuring 60°. Find its side length.
4
100
31^4 mod 4
1
100
This is the shape of the graphy y=1/x.
Hyperbola
100
Who's the youngest person to win IMO gold?
Terrence Tao
200
Solve in real numbers:
x^4 + 4x^3 + 6x^2 + 4x - 2 =0
sqrt(3) - 1
200
100 chickens are arranged in a circle. All at once, each chicken randomly pecks a chicken either to the left or right. What’s the expected number of unpecked chickens?
25
200
Let point X be inside regular pentagon ABCDE such that triangle AEX is equilateral. Compute the degree measure of BDX.
12°
200
For prime numbers p, q:
pq + 2p + 4q = 20.
Find p.
3
200
This function gives the number of positive integers k < n such that gcd(k, n) = 1.
Euler's Totient Function
200
Which famous mathematician said "I think, therefore I am"?
Rene Descartes(Yes, the rule of signs and the circle guy)
300
Suppose for real numbers a and b,
log_2(a), log_2(5), and log_2(b)
form an arithmetic series in that order. Compute ab.
25
300
Real numbers a, b, c are chosen from (0,1). What’s the probability a+b>c?
5/6
300
A sphere inscribed in a regular tetrahedron has volume 4. What is the volume of the tetrahedron?
(24sqrt3)/pi
300
If for positive integers a, b, ab=20lcm(a,b), find the smallest possible value of ab.
400
300
This formula gives the value of the power sum symmetric polynomials in terms of lower degree power sums and the elementary symmetric sums.
Newton Sums
300
What's the statement of the Riemann Hypothesis?
All nontrivial zeroes of the Riemann zeta function have a real part of 1/2.
400
Minimize
a^2 + b^2 + c^2
given that a + b + c = 5.
25/3
400
Compute the number of solutions to
a + b + c + d = 24
if all a, b, c, d are positive odd integers.
286
400
Three circles which are all pairwise tangent to each other have radii 1, 2, and 3. Find the radius of the circle which all of their centers lie on.
2.5
400
Find the largest of three primes which divide 27931, given 17 is one of them.
53
400
This is defined like the Fibonacci sequence but starts with 2 and 1 instead.
Lucas Numbers
400
Who's this?
Legendre
500
45/8
500
Bayus has 8 random slips of paper labeled 1, 2, 4, 8, …, 128. At random, he draws 3 slips of paper with replacement, a, b, and c. What’s the probability he can, in some order, arrange a,b, and c to be the coefficients of a quadratic with two distinct real roots?
111/128
500
In ABC points D and E lie on BC and AC, respectively. If AD and BE intersect at T so that AT/DT=3 and BT/ET=4, what is CD/BD?
4/11
500
Compute the remainder when the 100th Fibonacci number is divided by 4 (with F0=1,F1=1).
1
500
In a triangle, this point is the isogonal conjugate of the centroid.
Symmedian Point (Lemoine Point)
500
What is 1 + 1/16 + 1/81 + 1/256 + ...
(pi^4)/90