MathDB

2

Part of 2016 ASDAN Math Tournament

Problems(10)

2016 Algebra #2

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8/6/2022
A pet shop sells cats and two types of birds: ducks and parrots. In the shop, 112\tfrac{1}{12} of animals are ducks, and 14\tfrac{1}{4} of birds are ducks. Given that there are 5656 cats in the pet shop, how many ducks are there in the pet shop?
2016Algebra Test
2016 Calculus #2

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8/8/2022
Suppose aa and bb are two variables that satisfy ∫02(−ax2+b)dx=0\textstyle\int_0^2(-ax^2+b)dx=0. What is ab\tfrac{a}{b}?
2016Calculus Test
2016 Algebra Tiebreaker #2

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8/8/2022
Simplify the expression 20+1423+20−1423.\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}.
2016Algebra Tiebreaker
2016 Calculus Tiebreaker #2

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8/8/2022
Consider the curves with equations xn+yn=1x^n+y^n=1 for n=2,4,6,8,…n=2,4,6,8,\dots. Denote L2kL_{2k} the length of the curve with n=2kn=2k. Find lim⁡k→∞L2k\lim_{k\rightarrow\infty}L_{2k}.
2016Calculus Tiebreaker
2016 Discrete #2

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8/10/2022
The largest factor of nn not equal to nn is 3535. Compute the largest possible value of nn.
2016Discrete Math Test
2016 Geometry #2

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8/11/2022
Two concentric circles have differing radii such that a chord of the outer circle which is tangent to the inner circle has length 1818. Compute the area inside the bigger circle which lies outside of the smaller circle.
2016Geometry Test
2016 Discrete Tiebreaker #2

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8/10/2022
Define a <spanclass=′latex−italic′>subsequence</span><span class='latex-italic'>subsequence</span> of a string S\mathcal{S} of letters to be a positive-lenght string using any number of the letters in S\mathcal{S} in order. For example, a subsequence of HARRISONHARRISON is ARRONARRON. Compute the number of subsequences in HARRISONHARRISON.
2016Discrete Math Tiebreaker
2016 Geometry Tiebreaker #2

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8/11/2022
A four-pointed star is formed by placing for equilateral triangles of side length 44 in a coordinate grid. The triangles are placed such that their bases lie along one of the coordinate axes, with the midpoint of the bases lying at the origin, and such that the vertices opposite the bases lie at four distinct points. Compute the area contained within the star.
2016Geometry Tiebreaker
2016 Guts #2

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8/14/2022
Let f(x)=ax3+bx2+cx+df(x)=ax^3+bx^2+cx+d be some cubic polynomial. Given that f(1)=20f(1)=20 and f(−1)=16f(-1)=16, what is b+db+d?
2016Guts Round
2016 Team #2

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8/17/2022
Three unit circles are inscribed inside an equilateral triangle such that each circle is tangent to each of the other 22 circles and to 22 sides of the triangle. Compute the area of the triangle.
2016team test