Geometry
What is the hypostenuse to a right triangle with side lengths -9i and 8?
sqrt(17)*i
What is the sum of the first 3 multiples of 15 and 20?
270
What is the sum of the numerator and the denominator in the most simplified version of 20384/292?
5167
What are the odds that when 1000 is divides evenly by a random integer from 1 to 20 (inclusive)?
0.35 (7/20)
What is the maximum number of points that can be scored by all teams playing this game? (Not taking into account athletic ability)
75
What do the internal angles in any octagon add up to (in radians)?
6pi
What is the sum of all of the factors of 202 and 203?
546
For any parabola ax2+bx+c, what is the sum of the roots multiplied by the roots multiplied by each other in terms of a,b,c?
-bc/a2
A bag contains only blue balls and green balls. There are 0.1x blue balls. If the probability of drawing a blue ball at random from this bag is 1/4, then the number of green balls in the bag is (in terms of x)
0.3x
How many triangle numbers under 100?
13
In a circle inscribed in a square, how much further is it to get from the midpoint of a side of the square to the opposite midpoint when taking the circle as opposed to the fastest route? (answer in terms of the radius of the circle, x)
(pi-2)x
How many three-digit positive integers have an odd number of even digits?
450
For how many values of the constant k will the polynomial x^2+kx+36 have two distinct integer roots?
8
In the quadratic x2-8x+c
if c is a random integer between 1 and 20, what is the probability that that the quadratic has 2 real roots?
0.75
A data set consists of 6 (not distinct) positive integers: 1, 7, 5, 2, 5, and X. The average (arithmetic mean) of the 6 numbers equals a value in the data set. What is the sum of all possible values of X?
36
What is the area when 30-60-90 triangles with the 30 degree angle at the origin are arranged in a circle around the origin? (the side opposite the 30 degree angle has a length of 5)?
30sqrt(3)
The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is the sum of the digits of n?
6
How many solutions are there for the system of equations y = x2 and a circle of radius 3 centered around (0,3)
3
Chloe chooses a real number uniformly at random from the interval [0, 2017]. Independently, Laurent chooses a real number uniformly at random from the interval [0, 4034]. What is the probability that Laurent's number is greater than Chloe's number?
3/4 or .75
What is the 5th term to this sequence (assume 12 and 34 are starting values for the sequence) 12, 34, 38, 92, ___
76
In rectangle ABCD, AB = 20 and BC = 10. Let E be a point on CD such that <CBE = 15° . What is AE?
20
How many zeros are at the end of 1000!
249
if x@y represents floor((x2+y2)/xy), then what does 14@(3@(4@5) = ?
12
If you put all of the triangle numbers under 50 and all of the Fibonacci numbers under 100 in a bag, what is the probability that the number you draw is over 30?
0.25 or ¼
What's the next number in this sequence:1, 3, 6, 11, 18, 29?
42