MathDB

4

Part of 2016 ASDAN Math Tournament

Problems(6)

2016 Algebra #4

Source:

8/6/2022
Suppose that f(x)=x2−10x+21f(x)=x^2-10x+21. Find all distinct real roots of f(f(x)+7)f(f(x)+7).
2016Algebra Test
2016 Calculus #4

Source:

8/8/2022
The radius rr of a circle is increasing at a rate of 22 meters per minute. Find the rate of change, in meters2/minute\text{meters}^2/\text{minute}, of the area when rr is 66 meters.
2016Calculus Test
2016 Discrete #4

Source:

8/10/2022
At a festival, Jing Jing plays a game where she must knock down ten targets with as few balls as possible. Every time Jing Jing knocks down a target, she can reuse the ball she just threw and does not have to pick up a new ball. Suppose that Jing Jing knocks down each target with a probability of 34\tfrac{3}{4}. Compute the expected number of balls that Jing Jing needs to knock down all ten targets.
2016Discrete Math Test
2016 Guts #4

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8/14/2022
Eddy is traveling to England and needs to exchange USD to GBP (US dollars to British pounds). The current exchange rate is 1.31.3 USD for 11 GBP. He exchanges xx USD to GBP and while in England, uses x2\tfrac{x}{2} GBP. When he returns, the value of the British pound has changed so that 11 GBP equals α\alpha USD. After exchanging all his remaining GBP, he notes that he has x2\tfrac{x}{2} USD left. What is α\alpha?
2016Guts Round
2016 Geometry #4

Source:

8/11/2022
Let ABCDABCD be a rectangle with AB=9AB=9 and BC=3BC=3. Suppose that DD is reflected across ACAC to a point EE. Compute the area of trapezoid AEBCAEBC.
2016Geometry Test
2016 Team #4

Source:

8/17/2022
Three roots of the quartic polynomial f(x)=x4+ax3+bx+cf(x)=x^4+ax^3+bx+c are −1-1, 33, and 55. What is a+b−ca+b-c?
2016team test