Counting & Probability
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If you pull one marble without looking, what is the probability that it is blue?
1/2
Thursday
-4 + 4x = 10
3.5 or 3 1/2
A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
10cm
a^2 + b^2 = c^2. Who was that theorem named after?
Pythagoras
You roll 2 dice. What's the probability the sum of your rolls is 7?
1/6
Which is the greatest out of these? 3^200, 4^150, 2^300?
x^2 + 4x + 4 = 0
A circle is inscribed inside a square with a side length of 10. What is the area of the region inside the square but outside the circle (Leave in terms of pi)?
100-25pi
Which German mathematician, often called the "Prince of Mathematicians," famously discovered a quick method to sum the integers from 1 to 100 as a young child?
Carl Friedrich Gauss or just Gauss
How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 if no digit can be used more than once in a single number?
180
If the 5-digit number 483A6 is divisible by 12, where A represents a single missing digit, what is the sum of all possible values of A?
12
x^3 + 2x^2 - 3 = 0. Find the real solution.
1
An isosceles triangle has a total perimeter of 32 cm. If the unequal side is 12 cm (the base), what is the triangle's area?
48
This iconic notation for the ratio of a circle's circumference to its diameter (pi) was popularized in 1737 by which Swiss mathematician?
Leonhard Euler or just Euler
A box contains 4 defective light bulbs and 6 working light bulbs. If 3 light bulbs are chosen at random from the box, what is the probability that at least one of the chosen bulbs is defective?
5/6
How many trailing zeros are in 25!?
6 zeros
x/3 + y/4 = 2. Find the sum of the slope and y-intercepts of this line.
20/3
The side lengths of a right triangle form three consecutive terms of an arithmetic progression. If the triangle's area is 54, what is the length of its hypotenuse?
15
What is the name of the famous 17th-century formula stating that "a^n + b^n = c^n has no positive integer solutions for n > 2", which took over 350 years to finally prove?
Fermat's Last Theorem
You have 128 identical-looking coins. One of them is counterfeit and has a different weight (it is either heavier or lighter than the genuine ones). Using a two-pan balance scale, what is the minimum number of weighings needed to find the fake coin and determine whether it is heavier or lighter?
5 weighings
What is the smallest positive integer N such that N has exactly 12 positive divisors and N is divisible by 6?
60
|2x + 5| = 6x - 7. Find all solutions that work.
A sphere of radius 3 is melted down and recast into a cone with a base radius of 3. What is the height of the new cone?
12
Written around 300 BC, a 13-book mathematical series called "The Elements" serves as the foundation for modern geometry. Who wrote it?
Euclid or The Father of Geometry