'09 District

[nsguy1350]

I received a 296, getting 51 correct, missing 5, skipped 4.
I should've gotten at least a 304, but the last problem I was attempting I did not answer because I put the integral wrong into my calculator and I wasn't receiving an answer choice: I didn't see, after checking several times, that I put in [unparseable or potentially dangerous latex formula] instead of [unparseable or potentially dangerous latex formula]. That ANGERED ME. lol, I was disappointed. I wanted to break 300 at least.

Questions:

I can't draw it, but how do you do:
42. Two chords, PS and QR intersect in the interior of a circle at point C such that mARC_QS = 40 degrees and mANGLE_PCR = 60 degrees. If points R and S are not on ARC_PQ then mARC_PR is?

45. Which of the following is a focus for [unparseable or potentially dangerous latex formula].
Do I have to find it the long way, by completing the square, then finding a, b, and c, then using the fact that [unparseable or potentially dangerous latex formula] for hyperbolas? I skipped because I thought it would take to long, after messing with it for a few seconds.

50. I got this one correct, but I did it through intuition, not through work. How would you set it up? I tried harmonic mean, but I failed at something.
Harry Green can mow the #1 fairway in 1.5 hours. If Harry hires Sandy Trappe to help him they can mow it in 1 hour working together. How long would it take Sandy to mow it herself?

And then 56, which I cannot draw. I think you can just look on TCM here.

I missed #60 because I didn't see "lateral surface area", instead I went for total. I missed #49, being stupid with the reference angle. On #39, I used the identity [unparseable or potentially dangerous latex formula], but I found the 12th Lucas number instead of the 11th! A miscount! I missed #6 because I didn't see that it said "isosceles triangle", so I put bisector, thinking of angle bisector, and then I missed 23, because I found the fifth time instead of the fourth (9 + 2sum from 1 to 3, NOT 1 to 4 :'( ).
See, I could do all of those problems, along with one that I skipped (+ another if I had time), but I decided to have the reading comprehension skills of a 3rd grader. That's a good 52 points right there! Could've been a 348....
Oh, that would've been great, if only I could read :p

EDIT: typo fixed

[redhawk2015]

#42: If two chords intersect inside a circle, then the angle they intersect to create is the average of the angles created by the chords...so this should be C. 80.

#50: Since Harry can mow the fairway in 1.5 hours, in 1 hour he can mow 2/3 of the fairway. Together, they can mow one fairway in one hour. Therefore, Sandy can mow (1-(2/3))=1/3 of the fairway in one hour, or the whole fairway in E. 3 hours.

#56: AE+BE = diameter = 16.4, so CD = radius = 8.2; CB (another radius)-BE = CE = 1.8; Using the Pythagorean Theorem, DE=D. 8

[nsguy1350]

Thanks, I'll keep all of this in mind next time.