Pythagorean Theorem
The hypotenuse of a triangle with legs 15 and 36
What is 39?
The area of one part of a circle with radius 6 when a diameter is drawn
What is 18pi?
A = The area of a square with side length sqrt(71)
B = The sum of the roots of x2 - 1 = 0
C = The sum of the coefficients of (x + y)2
The value A + 2B - C
What is 67?
The sum 1 + 1/2 + 1/4 + ...
What is 2?
The expansion (x + y)3
What is x3 + 3x2y + 3xy2 + y3?
The square of the last side of a right triangle if the hypotenuse is 34 and one leg is 33
What is 67?
The fraction of area that a quarter-circle can cover in a square
A = The number of ways to order A, A, B, C
B = The number of sides in a dodecagon
The larger of A and B
What is 12?
The sum 1 + 2 + 3 + ... + 102
What is 5253?
The third term of the expansion (x + y)8
What is 28x6y2?
The equation of the circle with radius 5, centered at (2, -1)
What is (x - 2)2 + (y + 1)2 = 25?
The area of a circle with a right triangle of legs 10 and 24 inscribed
B = the largest integer satisfying x2 < 2025
C = The maximal value of xy if x + y = 2
The value A * B * C
What is 528?
The sum 2/3 + 4/9 + 8/27 + 16/81 + ...
What is 2?
The fifth coefficient in the expansion of (x - y)9
The length of the altitude to the hypotenuse in a right triangle, if that altitude splits the hypotenuse into lengths 4 and 6
What is 2sqrt(6)?
When drawing two circles of radius 6 so that each circle passes through the other circle's center,
The area of their intersection
What is 24pi - 18sqrt3?
A = the area of an ellipse with major axis 9 and minor axis 8
B = the volume of a cylinder with radius 3 and height 8
C = the period of sin(2x)
D = the sum of the coefficients of pi(x + y)3
The value A + B + C + D
What is 99pi?
The sum 1/1 + 2/3 + 3/9 + 4/27 + 5/81 + ...
What is 9/4?
The coefficient of xy2z in (x + y + z)4
What is 12?
The side length of a square that fits inside a 3-4-5 triangle and shares a right angle with the 3-4-5 triangle
What is 12/7?
The distance between the centers of two circles if the external tangent has length 12 and the radii of the circles are 2 and 7
What is 13?
A = the radius of a circle of area 9pi
B = the perimeter of a triangle with sides 123, 234, 441
C = the area of a triangle with side length 6
D = the value x2 + 1/x2 when x + 1/x = 5
E = the number of ways to order 5 people A, B, C, D, E
F = the value 6 + sqrt(6 + sqrt(6 + sqrt(6 + ...)))
G = the coefficient of the second term in (2x + 3)5
The value A + B + C + D + E + F + 2G
What is 1433 + 9sqrt3?
The sum 10/4 + 20/8 + 30/16 + 40/32 + 80/64 + ...
What is 10?
The second coefficient of the expansion (3x + 2y)1/2
What is sqrt(3) / 3?