MathDB

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Part of 2017 ASDAN Math Tournament

Problems(9)

2017 Algebra #1

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8/20/2022
Suppose (x+y)2=25(x+y)^2=25 and (x−y)2=1(x-y)^2=1. Compute xyxy.
2017Algebra Test
2017 Algebra Tiebreaker #1

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9/10/2022
If aa, 66, and bb, in that order, form an arithmetic sequence, compute a+ba+b.
2017Algebra Tiebreaker
2017 Calculus #1

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9/17/2022
Compute ∫013x2dx.\int_0^13x^2dx.
2017Calculus Test
2017 Calculus Tiebreaker #1

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9/17/2022
Compute ∫06x−3x2−6x−7dx.\int_0^6\frac{x-3}{x^2-6x-7}dx.
2017Calculus Tiebreaker
2017 Discrete #1

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10/12/2022
Clara and Nick each randomly and independently pick an integer between 00 and 20172017, inclusive. What is the probability that the two integers they pick sum to an even number?
2017Discrete Math Test
2017 Discrete Tiebreaker #1

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10/12/2022
Two arbitrary distinct lattice points are selected on the coordinate plane within the square marked by the points (0,0)(0,0), (3,0)(3,0), (0,3)(0,3), and (3,3)(3,3) (the lattice points may lie on a side or a corner of the square). What is the probability that the distance between the two points is at most 2\sqrt{2}?
2017Discrete Math Tiebreaker
2017 Geometry #1

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11/19/2022
What is the surface area of a cube with volume 6464?
2017Geometry Test
2017 Geometry Tiebreaker #1

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11/19/2022
In △ABC\triangle ABC, we have ∠ABC=20∘\angle ABC=20^\circ. In addition, DD is drawn on AB‾\overline{AB} such that AC=CD=BDAC=CD=BD. Compute ∠ACD\angle ACD in degrees.
2017Geometry Tiebreaker
2017 Guts #1

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11/25/2022
Alice and Bob are racing. Alice runs at a rate of 2 m/s2\text{ m/s}. Bob starts 10 m10\text{ m} ahead of Alice and runs at a rate of 1.5 m/s1.5\text{ m/s}. How many seconds after the race starts will Alice pass Bob?
2017Guts Round