Algebra
Geometry
Combinatorics
Number Theory
History of Math
100
If 8x + 7 = 71, what is the value of x?
x = 8
100
What is the area of a square with side length 2?
4
100
How many ways are there to pick 2 numbers from the the range 1-6? (order doesn't matter and replications are not allowed)
15
100
How many prime numbers are there under 50?
15
100
Who is this equation named after: a^2+b^2=c^2
Pythagoras
200
The sum of three numbers is 96 The first number is 6 times the third number, and the third number is 40 less than the second number. What is the absolute value of the difference between the first and second numbers?
5
200
A right triangle has a leg of length 5 and hypotenuse 13. Find the area of this triangle.
30
200
A candy store is such that there are 100 flavors of lolipops, each with a different price from 1 to 100 cents. You have 100 nickels and 100 dimes. How many flavors of lollipops can you buy?
19
200
Find the number of ordered pairs of prime numbers (p,q) such that p+q=103.
2
200
Name a "Father of Calculus".
Newton or Leibniz
300
Suppose there exist distinct positive integers a,b,c such that ln(a)+ln(b)+ln(c)=ln(a+b+c). Find the minimum of a+b+c.
6
300
A circle is inscribed in a square with side length 2. Find the area within the square outside of the circle.
4-pi
300
In a bag of marbles, 
of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red?
4/7
300
Find the smallest prime p such that there is no integer x such that x^2+1 is divisible by p.
3
300
pi is also known as ________'s constant.
Archimedes
400
Find 2sin^4(1)+2cos^4(1)+sin^2(2)
2
400
Let A, B, C be three points on a line in that order such that AB=2 and BC=3. A circle with radius 4 is drawn through A and B. Find the distance from C to the center of that circle.
sqrt(31)
400
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)
24
400
For how many integers n, does 1+2+3...+n evenly divide 6n?
5
400
What base did the ancient Egyptians count by?
12
500
Let the roots (not necessarily real) of x^3-x^2+x-1=0 be a,b,c. Find a^2024+b^2024+c^2024
-1
500
Right triangle 
has leg lengths 
and 
. Including 
and 
, how many line segments with integer length can be drawn from vertex 
to a point on hypotenuse 
?
13
500
A box contains a red, green, and blue ball and you select a ball, record its color, and put it back, three times. What is the expected number of distinct colors you record?
19/9
500
Find the number of positive integers x less than 100 such that x^6-1 is divisible by 7
85
500
According to the Greeks, what is a perfect number?
A positive integer which it equals the sum of its proper factors.