MathDB

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Part of 2016 ASDAN Math Tournament

Problems(10)

2016 Algebra #1

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8/6/2022
If x=14x=14 and y=6y=6, then compute x2−y2x−y\tfrac{x^2-y^2}{x-y}.
2016Algebra Test
2016 Algebra Tiebreaker #1

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8/8/2022
Let xx and yy be positive real numbers such that x+y=1x+1y=5x+y=\tfrac{1}{x}+\tfrac{1}{y}=5. Compute x2+y2x^2+y^2.
2016Algebra Tiebreaker
2016 Calculus #1

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8/8/2022
Let f(x)=(x−1)3f(x)=(x-1)^3. Find f′(0)f'(0).
2016Calculus Test
2016 Discrete #1

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8/10/2022
Moor owns 33 shirts, one each of black, red, and green. Moor also owns 33 pairs of pants, one each of white, red, and green. Being stylish, he decides to wear an outfit consisting of one shirt and one pair of pants that are different colors. How many combinations of shirts and pants can Moor choose?
2016Discrete Math Test
2016 Calculus Tiebreaker #1

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8/8/2022
Compute lim⁡x→1x3−1x−1.\lim_{x\rightarrow1}\frac{x^3-1}{x-1}.
2016Calculus Tiebreaker
2016 Geometry #1

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8/11/2022
Compute the area of the trapezoid ABCDABCD with right angles BADBAD and ADCADC and side lengths of AB=3AB=3, BC=5BC=5, and CD=7CD=7.
2016Geometry Test
2016 Discrete Tiebreaker #1

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8/10/2022
You own two cats, Chocolate and Tea. Chocolate and Tea sleep for CC and TT hours a day respectively, where CC and TT are chosen independently and uniformly at random from the interval [5,10][5,10]. In a given day, what is the probability that Chocolate and Tea will together sleep for a total of at least 1414 hours?
2016Discrete Math Tiebreaker
2016 Geometry Tiebreaker #1

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8/11/2022
ABCDEABCDE is a pentagon where AB=12AB=12, BC=20BC=20, CD=7CD=7, DE=24DE=24, EA=9EA=9, and ∠EAB=∠CDE=90∘\angle EAB=\angle CDE=90^\circ. Compute the area of the pentagon.
2016Geometry Tiebreaker
2016 Guts #1

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8/14/2022
Bill is buying cans of soup. Cans come in 22 shapes. Can AA is a rectangular prism shaped can with dimensions 20×16×1020\times16\times10, and can BB is a cylinder shaped can with radius 1010 and height 1010. Let α\alpha be the volume of the larger can, and β\beta be the volume of the smaller can. What is α−β\alpha-\beta?
2016Guts Round
2016 Team #1

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8/17/2022
Pooh has an unlimited supply of 1×11\times1, 2×22\times2, 3×33\times3, and 4×44\times4 squares. What is the minimum number of squares he needs to use in order to fully cover a 5×55\times5 with no 22 squares overlapping?
2016team test