4

Part of 2017 ASDAN Math Tournament

Problems(5)

2017 Algebra #4

Source:

What is the maximum possible value for the sum of the squares of the roots of

x^4+ax^3+bx^2+cx+d

a

b

c

d

2

0

1

7

2017Algebra Test

2017 Calculus #4

Source:

10\text{ m}

long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of

1\text{ m/s}

, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is

6\text{ m}

2017Calculus Test

2017 Discrete #4

Source:

6

-digit positive integers have their digits in nondecreasing order from left to right? Note that

0

cannot be a leading digit.

2017Discrete Math Test

2017 Geometry #4

Source:

An ant starts at corner

A

of a square room

ABCD

with side length

2\sqrt{2}

. In the middle of the room, there is a circular pillar of radius

1

centered at the center of

ABCD

. What is the minimum distance it has to travel to get to corner

C

2017Geometry Test

Source:

Alice and Bob are painting a house. Alice can paint a house in

20

hours by herself. Bob can paint a house in

40

hours by himself. Both people start at the same time, paint at their own constant rate, and work together to paint one house. When the house is fully painted, what fraction of the house was painted by Alice?