There are several events at the tournament, namely "The Qualifier", "25-Minus", "Group Problem Solving", "Estimation", and "THE RELAY" (caps for emphasis (if you didn't know that then leave (seriously (go)))). Let me walk you through it. First off was the State Qualifying exam. 15 questions, 1 hour. It wasn't hard at all, but due to several ridiculously stupid errors, I didn't score so hot. I got a 12 I think, they never told us, but I think it was a 12. After that was 25-minus. Basically, all the teams in a particular level sit in a room together, but you sit separately from your teammate. You are shown a problem on an overhead and a time limit. You have that amount of time to solve the problem and write it down. Times range from 45 seconds to a minute and a half. You are then shown the answers and the people that got them right raise their hands. They subtract the number of people who answered correctly from 25 and then give that many points to the teams that answered. In other words, being the only person to answer a question is good. We were all ready, psyched, ready to win it for the team, when the first problem came up. Now, what you are about to see is not the actual problem, but it will give you a rough idea. . . .
Yeah, scary. The atmosphere in the room was almost laughable. Here we were, brightest and best, and we just sat there. Some laughed. Most just sat. I tried my hardest, reducing and reducing, reducing and reducing, and ended up with some random equation with about 5 terms on top and 4 terms on the bottom. Then she showed the answer. It looked something like
There was definitely some laughter when THAT showed up on the board. Everybody that had tried sheepishly crumpled up their papers and looked around to make sure nobody had seen what they had gotten for an answer. The lady asked how many people got it right. Nobody raised their hands. Total Failure -1, Best and Brightest -0. Next problem. Imagine the last problem, but with another term added to the top and bottom. again, laughter and failure. The answer was just as stupid and the emberassment mounted. Nowe we're desparate, we want points!!! The proctor is shocked, can't believe that we haven't answered a question yet. Finally, answerable questions started appearing. My partner was smoking everybody. I answered I think 4 of them, but she definitely stole the show. So yeah, 25-minus was ok. Third event, group problem solving. This was kind of entertaining. 3 problems, 30 minutes. We looked at them and found that the las problem would be easy. We quickly knocked out the last problem and started working on the second one. The question?
Simple enough. Solve for x in terms of a, substitute it in for x in the second equation, and bingo, problem solved. Well, it got ugly. Solving for a resulted in
Ok, not so bad, quadratic equation. Until, you plug it into the second part of the equation. Then you get . Then we had a debate. Plus. . . .or minus? Such a simple question that could result in much more work than necessary if the wrong choice is chosen. We decided to do both. My partner did plus, I did minus. So, here's the equation we worked:
We just kept multiplying it out and eventually we got to, um, well, it was big. Like, really big. We decided that was the wrong route to take, so we looked at the question again. "Well, couldn't we just leave it? Use this last equation we had?" The problem didn't say to expand it all the way out, just write it in terms of A. So, we left it. On to the first problem. It said to imagine a parallelogram and gave the lengths of the sides. "Solve for the diagonals". Um, uh-oh. We couldn't, and it said that the answers were integers, so we improvised. We drew a parallelogram to scale and measured the angles. Ta-da! 9 and 15. We were done, and not confident. We knew that we had the last one right, but that was it.
The next event was the relay. Basically, teams lined up on one side of the gym, math problems on the other. One at a time members from each team would run over, solve a problem and run back. I'll avoid the gory details and suffice it to say, our school dominated. uber winning-ness. Now, lets talk about estimation. Throughout the day there was a big bowl of marshmallows (big and small). The challenge was to guess the amount of marshmallows. The winner gets a graphing calculator. Well, ha! I failed that one. I guessed 900. My partner wrote, on the little paper you write your guess one, "Let a = my guess. Define "a" such that it equals the amount of marshmallows in the bowl. QED". Personally, I think that should have won, but no.
The awards were next. I got third in the qualifying exam, enough for a ribbon but not enough for state. The first shocker was team problem solving. My partner and I had given up, but all of a sudden WHOA! We won! haha, kurazy! Either we guessed really well, or other people had no idea what was going on! w00t, that was exciting. My partner won 25-minus. Then, estimation. I was wrong, oh so wrong. The answer was 1,438. The winner, however, went to our school. Her guess? (You won't believe this. . . ) 1,444. She was off by 6! Amazing, she won a TI-84 silver. Then she won another TI-84 silver in another category! TWO CALCULATORS! She'll be selling them to wal-mart. Our school ended up winning overall, so that was good. I ended up with a bunch of ribbons and all was good. Hope you enjoyed the story! Ciao!
Wouldn't x^2 + 1/x^2 = a^2 - 2?
ReplyDeletex + 1/x = a
(x + 1/x)^2 = a^2
x^2 + x/x + x/x + 1/x^2 = a^2
x^2 + 2 + 1/x^2 = a^2
x^2 + 1/x^2 = a^2 - 2.
(Was that what you wrote down? Or am I missing something here?)
ReplyDelete