MathDB

5

Part of 2016 ASDAN Math Tournament

Problems(6)

2016 Algebra #5

Source:

8/6/2022
Let f(x)f(x) be a real valued function. Recall that if the inverse function f−1(x)f^{-1}(x) exists, then f−1(x)f^{-1}(x) satisfies f(f−1(x))=f−1(f(x))=xf(f^{-1}(x))=f^{-1}(f(x))=x. Given that the inverse of the function f(x)=x3−12x2+48x−60f(x)=x^3-12x^2+48x-60 exists, find all real aa that satisfy f(a)=f−1(a)f(a)=f^{-1}(a).
2016Algebra Test
2016 Calculus #5

Source:

8/8/2022
Find lim⁡x→0sin⁡(x)−xxcos⁡(x)−x.\lim_{x\rightarrow0}\frac{\sin(x)-x}{x\cos(x)-x}.
2016Calculus Test
2016 Discrete #5

Source:

8/10/2022
ABCDABCD is a four digit number (A≠0A\neq0) such that both ABCABC and BCDBCD are divisible by 99 (ABCDABCD is not necessarily divisible by 99, and B,C,DB,C,D may be 00). Compute the number of four digit numbers satisfying this property.
2016Discrete Math Test
2016 Guts #5

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8/14/2022
In the following diagram, the square and pentagon are both regular and share segment ABAB as designated. What is the measure of ∠CBD\angle CBD in degrees?
2016Guts Round
2016 Geometry #5

Source:

8/11/2022
Let Γ1\Gamma_1 be a circle of radius 66, and let Γ2\Gamma_2 be a circle of radius 11. Next, let the circles be internally tangent at point PP, and let APAP be a diameter of circle Γ1\Gamma_1. Finally, let YY be a point on Γ2\Gamma_2 such that AYAY is tangent to it. Compute the length of PYPY.
2016Geometry Test
2016 Team #5

Source:

8/17/2022
Given that xx and yy are real numbers, compute the minimum value of x4+4x3+8x2+4xy+6x+4y2+10.x^4+4x^3+8x^2+4xy+6x+4y^2+10.
2016team test