MathDB

10

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Advanced #10

Source:

7/1/2022
Find the remainder when (12+1)(22+1)(32+1)…(422+1)(1^2+1)(2^2+1)(3^2+1)\dots(42^2+1) is divided by 4343. Your answer should be an integer between 00 and 4242.
2014Advanced Topics Test
2014 Algebra #10

Source:

7/8/2022
Let p(x)=c1+c2⋅2x+c3⋅3x+c4⋅5x+c5⋅8xp(x)=c_1+c_2\cdot2^x+c_3\cdot3^x+c_4\cdot5^x+c_5\cdot8^x. Given that p(k)=kp(k)=k for k=1,2,3,4,5k=1,2,3,4,5, compute p(6)p(6).
2014Algebra Test
2014 General #10

Source:

7/4/2022
Find the area of the smallest possible square that contains the points (2,−1)(2,-1) and (4,4)(4,4).
2014General Test
2014 Geometry #10

Source:

7/12/2022
In a convex quadrilateral ABCDABCD we are given that ∠CAD=10∘\angle CAD=10^\circ, ∠DBC=20∘\angle DBC=20^\circ, ∠BAD=40∘\angle BAD=40^\circ, ∠ABC=50∘\angle ABC=50^\circ. Compute angle BDCBDC.
2014Geometry Test
2014 Team #10

Source:

7/1/2022
Three real numbers xx, yy, and zz are chosen independently and uniformly at random from the interval [0,1][0,1]. Compute the probability that xx, yy, and zz can be the side lengths of a triangle.
2014team test