MathDB

2

Part of 2015 ASDAN Math Tournament

Problems(8)

2015 Advanced #2

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7/8/2022
Nick is taking a 1010 question test where each answer is either true or false with equal probability. Nick forgot to study, so he guesses randomly on each of the 1010 problems. What is the probability that Nick answers exactly half of the questions correctly?
2015Advanced Topics Test
2015 Advanced Tiebreaker #2

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7/8/2022
Heesu plays a game where he starts with 11 piece of candy. Every turn, he flips a fair coin. On heads, he gains another piece of candy, unless he already has 55 pieces of candy, in which case he loses 44 pieces of candy and goes back to having 11 piece of candy. On tails, the game ends. What is the expected number of pieces of candy that Heesu will have when the game ends?
2015Advanced Topics Tiebreaker
2015 Algebra #2

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7/1/2022
Find the sum of the squares of the roots of x2−5x−7x^2-5x-7.
2015Algebra Test
2015 Algebra Tiebreaker #2

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7/1/2022
Compute ∑n=0∞n+12n.\sum_{n=0}^\infty\frac{n+1}{2^n}.
2015Algebra Tiebreaker
2015 Guts #2

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7/28/2022
Meena owns a bottle cap collection. While on a vacation, she finds a large number of bottle caps, increasing her collection size by 40%40\%. Later on her same vacation, she decides that she does not like some of the bottle caps, so she gives away 20%20\% of her current collection. Suppose that Meena owns 2121 more bottle caps after her vacation than before her vacation. How many bottle caps did Meena have before her vacation?
2015Guts Test
2015 Geometry #2

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7/1/2022
There is a rectangular field that measures 20m20\text{m} by 15m15\text{m}. Xiaoyu the butterfly is sitting at the perimeter of the field on one of the 20m20\text{m} sides such that he is 6m6\text{m} from a corner. He flies in a straight line to another point on the perimeter. His flying path splits the field into two parts with equal area. How far in meters did Xiaoyu fly?
2015Geometry Test
2015 Geometry Tiebreaker #2

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7/20/2022
Let ABCDABCD be a square with side length 55, and let EE be the midpoint of CDCD. Let FF be the point on AEAE such that CF=5CF=5. Compute AFAF.
2015Geometry Tiebreaker
2015 Team #2

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8/3/2022
Jonah recently harvested a large number of lychees and wants to split them into groups. Unfortunately, for all nn where 3≤n≤83\leq n\leq8, when the lychees are distributed evenly into nn groups, n−1n-1 lychees remain. What is the smallest possible number of lychees that Jonah could have?
2015team test