number theory
Is 67 divisible by 6, 7, both, or neither?
Neither
How many ways to choose 2 items from a set of 12?
66
25
what mathematical constant is used to calculate the area of a circle?
pi (π)
Who came up with the Reimann hypothesis?
A number is divisible by 6 and 10. What is the smallest positive integer greater than 1 that it must also be divisible by?
30 (LCM)
5 people are sitting in a circle. If rotations and reflections are not considered distinct, then how many configurations are there?
12
Three consecutive integers add up to 72. What is the largest of these integers?
25
How many faces does a dodecahedron have?
12
who is known as the "father of geometry"?
Euclid
If n is a single digit integer and n mod 9 is congruent to 17 mod 9, then what is n?
8
A flag has 3 vertical stripes. Each stripe can be red, white, or blue, but no two adjacent stripes can be the same color. How many different flags are possible?
12
A number is increased by 20%, then decreased by 20%; what is the ratio between the value of the new and original number?
24/25 (96/100)
A regular pentagon and regular hexagon are both inscribed in the same circle. What's the maximum number of intersection points between them?
10
this Greek mathematician ran through the streets yelling “Eureka!” after discovering how to measure volume using water displacement
Archimedes
How many factors does 2025 have?
15
The word BALLOON has 7 letters (B, A, L, L, O, O, N). How many distinct arrangements of these letters are possible if the two L’s are not next to each other?
900
Find the sum of the distinct roots of (x^3)+(2x^2)+(3x)=-(x^2)-1
-1
Assume the circumference of the earth is 25,000 miles. Jason runs 6,250 miles north, turns 90 degrees to his right, runs 6,250 more miles, turns 90 degrees, and runs 6,250 more miles. How many miles is he from his starting point?
0
who came up with the Cartesian coordinate system?
René Descartes
How many different remainders can result when the 294th power of an integer is divided by 343?(Inspired by AMC 10, so worth 700 points)
2
If I toss 7 dice, the probability that that the numbers on the faces sum to 10 is (84/(6^7)). For what other sum will the probability be (84/(6^7))?
39
If (a)+(1/a)=3, then what is (a^4)+(1/a^4)?
(Worth 600 points)
47
What shapes can be formed by slicing a cone at an angle not parallel to the base?(name all)
ellipse, parabola
Who first published a general solution to the cubic? (worth 600 points)
Cardano