[OT] Math quiz

[David J. Braden]

One of my daughters, a ninth grader, competed in a state-wide math contest.
See how you fare on some of the problems they had (I left the really tough
ones out <g>)

(1) During one week on any night, I sleep 2 to 8 hours. If my average amount
of sleep for the week is 4.4 hours per day, what is the highest median of
hours I slept?

(2) A pirate has hidden treasure at the center of Circle Island. However,
you don't know where the center is. Using your handy meter stick and
protractor, you dray a chord of length 6 m and its perpendicular bisector
stretching to the edges of the circle of length 14 m. What is the radius of
Circle Island?

(3)What is the area of the region bounded by y = 4, y = |x-1| and y = |x +
1| ?

(4) Evaluate the infinite sum
1 + Sqrt(2)/4 + 1/4 + Sqrt(2)/16 + 1/16 + Sqrt(2)/64 + 1/64 + ...

(5) 13 houses are numbered randomly with integers drawn with replacement
from a discrete uniform distribution on the integers 1, 2, 3, ..., 15. What
is the probability that the sum of the numbers of the houses is prime?

(6) A number n is called "dual-symmetric" if it is a palindrome, and can be
expressed as a pair of factors that when placed next to each other form a
palindrome and have a product n. For example, 11 is dual-symmetric, since 11
is a palindrome, and its factors 1 and 11, placed next to each other, form
the palindrome 111. What is the smallest three-digit dual-symmetric number?

You need to get these all correct within a few minutes to have a shot at
being as good as the average child in the contest. If these are
representative of how the contest went, then you have about 10 or 11
minutes.

Good luck.

Dave Braden

 

[Don Guillett]

The lack of answers shows just how smart we really are.

 

[Harlan Grove]

(1) During one week on any night, I sleep 2 to 8 hours. If my average amount
of sleep for the week is 4.4 hours per day, what is the highest median of
hours I slept?

....

Excel's def'n of MEDIAN or the generally accepted one? Gotta get this
on-topic somehow!

I'm a bit too rusty to be able to recall how to answer #5 quickly, but I
loved #6 - standard trick question - know the trick, and it takes maybe 5
seconds to answer it; don't know the trick, and it takes more than a minute
to do real math to get the answer.

It's good that your daughter enjoys this sort of thing (or are you forcing
her into it?), but it seems cramming with some of Martin Gardner's books
would be the ideal way to prep for this exam.