MathDB

6

Part of 2015 ASDAN Math Tournament

Problems(5)

2015 Advanced #6

Source:

7/8/2022
You, your friend, and two strangers are sitting at a table. A standard 5252-card deck is randomly dealt into 44 piles of 1313 cards each, and each person at the table takes a pile. You look through your hand and see that you have one ace. Compute the probability that your friend’s hand contains the three remaining aces.
2015Advanced Topics Test
2015 Algebra #6

Source:

7/1/2022
Find all triples of integers (x,y,z)(x,y,z) which satisfy the equations \begin{align*} x^2-y-2z&=4\\ y^2-2z-3x&=-2\\ 2z^2-3x-5y&=-22.\\ \end{align*}
2015Algebra Test
2015 Guts #6

Source:

7/28/2022
A circle AA is circumscribed about a unit square and a circle BB is inscribed inside the same unit square. Compute the ratio of the area of AA to the area of BB.
2015Guts Test
2015 Geometry #6

Source:

7/1/2022
Let ABCABC be a triangle and let DD be a point on ACAC. The angle bisector of ∠BAC\angle BAC intersects BDBD at EE and BCBC at FF. Suppose that CFDE=54\tfrac{CF}{DE}=\tfrac{5}{4} and that BEBF=32\tfrac{BE}{BF}=\tfrac{3}{2}. What is CDAD\tfrac{CD}{AD}?
2015Geometry Test
2015 Team #6

Source:

8/3/2022
Let f(x)=x4−4x3−3x2−4x+1f(x)=x^4-4x^3-3x^2-4x+1. Compute the sum of the real roots of f(x)f(x).
2015team test