Arithmetic
Geometry
Algebra
Advanced
Challenge if you dare
101
1011101110 (binary) to base 8 is
What is 1356?
101
If an equilateral triangle has the same area as a regular hexagon, what is the ratio of their side lengths (triangle:hexagon)?
What is sqrt(6)?
101
If 10^x = a, express 10^(x-1) in terms of a.
What is a/10?
101
The mean number of calories in a burger is 900, and the standard deviation is 24. The z-score of Kenny's Burger if Kenny made a 1020 calorie burger is:
What is 5
101
A smaller sphere of radius 5m is entrapped within a larger sphere of radius 20m. The radii of both spheres grow at constant rates. The smaller sphere's radius increases by 2m per second while the larger sphere increases with a rate of r meters per second. If the probability of a random point within the smaller sphere given that the point is inside the larger sphere remains constant at any given time, find that probability.
What is 1/64?
102
In a set of 6 positive integers, the mode is 12 and the median is 20. The mean is 22. The largest possible number in this set is:
What is 50?
102
There exists a kite with a right angle. The length of the diagonal that connects the right angle is 8. This diagonal cuts the other diagonal into two segments of lengths 3 and 7.5. Find the perimeter of the kite.
What is 27?
102
How many solutions are in
||x-a|-b| = c (if a,b,c are all real nonzero numbers and c>0)
What is 4?
102
The function f(x) is linear and has a slope of 3/2, and it passes the point (3,-4). The inverse of f(x) is:
What is (2/3)(x + 4) + 3?
102
If z^6 = 1, the maximum imaginary part of z is:
What is sqrt(3)/2?
103
Get rid of the parametric
x = tan(t)
y = sec (t)
What is y = +/- sqrt(x^2 +1)
103
If the radii of one sphere is 2 times bigger than the other, what is the ratio of the smaller volume to the larger?
What is 1/8?
103
(NO CALCULATORS) If there are 4 sophomores and 5 juniors, how many ways can we make a team if there must be one more junior than a sophomore? (There must be at least one person on the team.)
What is 126?
103
(NO CALCULATORS) Find cos(15) + sin(15) in the simplest form. Those are degrees btw.
What is sqrt(6)/2?
103
Two identical cones with radii 6 and height 12 are lined up so that the vertex of each cone is touching the center of the base of the other cone. The volume of the resulting shape is:
What is 252pi?
104
10! mod 11
What is 10?
104
What is the interior angle of a 30 sided shape?
What is 168 degrees?
104
(NO CALCULATORS) Find the sum:
1^3 + 2^3 + 3^3 ---+ 19^3 + 20^3
What is 44100?
104
Given that log(2) = 5, log (3) = 2, and log (7) = 25, find log263. (Don't even try using a calculator.)
What is 29/5?
104
A quadrilateral is inscribed in a circle and has side lengths (consecutively) 27, 13, 9, 22. The diameter is:
What is 23?
105
If 7^77 was represented in base 4, what would be its units digit?
What is 3?
105
A 8x8x8 cube is painted divided to a bunch of 2x2x2 cubes. How many of these 2x2x2 cubes have no paint?
What is 8?
105
Solve for x + y + z
2x + 3y +2z = 6
5x + y + 2z = 10
x + 2y + 2z = 8
What is 4?
105
What is n?
What is 256?
105
What is the coefficient of x^3 for (x+1)^2n in terms of n?
What is 2n choose 3?