MathDB

8

Part of 2017 ASDAN Math Tournament

Problems(5)

2017 Algebra #8

Source:

8/20/2022
Consider the sequence of real numbers ana_n satisfying the recurrence anan+2−an+12−(n+1)anan+1=0.a_na_{n+2}-a_{n+1}^2-(n+1)a_na_{n+1}=0. Given that a1=1a_1=1 and a2=2018a_2=2018, compute a2018⋅a2016a20172.\frac{a_{2018}\cdot a_{2016}}{a_{2017}^2}.
2017Algebra Test
2017 Calculus #8

Source:

9/17/2022
Compute ∫012xex−12x2ex+2dx.\int_0^1\frac{2xe^x-1}{2x^2e^x+2}dx.
2017Calculus Test
2017 Discrete #8

Source:

10/12/2022
Let S={1,2,3,4,5,6}S=\{1,2,3,4,5,6\}. Compute the number of functions f:S→Sf:S\rightarrow S such that f(f(f(s)))=2f(f(f(s)))=2 if ss is odd and f(f(f(s)))=1f(f(f(s)))=1 if ss is even.
2017Discrete Math Test
2017 Geometry #8

Source:

11/19/2022
Let △ABC\triangle ABC be a right triangle with right angle ∠ACB\angle ACB. Square DEFGDEFG is contained inside triangle ABCABC such that DD lies on ABAB, EE lies on BCBC, FF lies on ACAC, AD=AFAD=AF, and GA=GD=GFGA=GD=GF. Suppose that CE=2CE=2. If MM is the area of triangle ABCABC and NN is the area of square DEFGDEFG, compute M−NM-N.
2017Geometry Test
2017 Guts #8

Source:

11/25/2022
How many integer solutions are there to y2=x2−2017y^2=x^2-2017?
2017Guts Round