Two days after this exam marked by a cheating scheme that, according to some in the group, was absolutely perfect for security, Geneviève received a message by mail about the final of the tournament.
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Square Root of the Answer
Dear Geneviève,
On behalf of the organizing committee, the news to announce you are bittersweet. There were too many teams tied for first for us to designate a winner, so it's impossible for us to grant the grand prize promised to all deserving teams. It happens that the Louisiana team is one of them and is therefore the South-Central regional champion, ex aequo with a Texan team.
As the sole eleventh grade representative from a South-Central state to have obtained a perfect score, you earned the prize awarded to the best performance of a non-senior student from the South-Central region. You will thus be able to participate in a summer mathematical camp of your choice, all expenses paid.
In addition, you won the Mirzakhani prize awarded to the best performance from a non-senior female student, all regions combined, which comes with a $9500 scholarship.
As for what happens to the original first prize, each winning school will receive a sum equivalent to the borrowing limit in the form of direct loans for an undergraduate student, or $57,500.
The organizing committee
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The regions as defined by the contest originate from the A-105 Circular of the federal Office of Management and Budget, and the contest's South-Central region corresponds to region 6, containing New Mexico, Texas, Oklahoma, Louisiana, and Arkansas.
The organizers awarded auxiliary prizes to non-seniors? I hope there will be another one that will take part in the SRA next year, and the fruits of an entire year of hard work are finally rewarded! she thinks, reading the letter, happy of what just happened, and explains everything to her parents, check in hand:
"Victory! We are in a multiple-way tie for first with several other teams! And I won the prize of the best female performance from a non-senior!" Gen announces in front of her parents.
"That's our daughter! Congratulations!" her father then howls.
"It's an ending as happy as I could possibly have wished for it, a highlight of this Cinderella season. We have $9500 that we can save up for college. I also won the prize of the best performance by a non-senior of the South-Central region, so I can attend a summer mathematical camp of my choice for free. I would like to attend the Young Scholars Program at the University of Chicago. For as long as my teachers were talking about this university..."
A Cinderella season for the mathletics team of the school, a happy ending but the booster club is unaware of. If it was a happy ending for Gen and the other three people on the team, it was happening otherwise for Sam who, despite his pivotal role in Monday's cheating scheme, has visibly slept poorly and comes over to her, trying to understand what happened during this chemistry test. However, she didn't check her own chemistry grade before Sam's arrival.
"Gen, I don't understand! Help me resolve this chemical nightmare before it's too late!" a distraught Sam asks her.
"Sam, did you lose confidence in Marcia? You always trusted her on a chemical level"
"Marcia was very busy studying for other courses, and you too as well for the past two days. She and you both seemed to know the material well" Sam retorts to her.
"Is this nightmare a long answer question?" Gen asks Sam.
"Yes"
"What happened, happened, we can't change anything. But what makes the resolution of this chemical nightmare so important to you?" Gen asks another question.
"If I don't understand anything to the material now, it does not bode well for college! My success is seriously compromised, it would not be worth attending! I may have followed the instructions of the cheating scheme to the letter, it's no use!" Sam keeps ruminating.
"The question being: what made you lose sleep over that? Was there a particular long answer question on this exam that gives you nightmares?"
"These nightmares makes me believe that it's useless for me to do anything related to chemistry! I wonder if it would not induce a domino effect!"
"What are you afraid of exactly?"
"That my very own academic talent is about to vanish! I got exposed!"
"Your role in this cheating scheme was to take in the multiple-choice answers from Dylan and communicate them to your section. Where were you in the classroom?"
"At the back. Easier to use a laser pointer on particular tiles, and Marcia enthusiastically accepted to be seated at the front; having known I would not have accepted to take the laser pointer. But my point stands; I don't have what it takes to succeed in college and if I succeed neither here nor in college, I am an academic failure!"
"You didn't forget about the clause of the better among two? Cross your fingers that the better among two be the AP exam then. In fact, what's the question that troubles you?"
"I don't remember all details clearly, but it alluded to an insoluble gas. And I also remember having answered this question by invoking an equilibrium constant"
If only I had as much intelligence as either Marcia or Geneviève! They both seemed to understand the material very easily! Sam thinks, while the question to which he alludes is the following:
Using the « méthode champenoise » grape juice is fermented in a closed bottle, following the reaction
Using the « méthode champenoise » grape juice is fermented in a closed bottle, following the reaction [https://img.wattpad.com/b846bd54dff058901d53b5375dd6a694d40ef710/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f6c5767344f304e367a6b5a755f673d3d2d313239303338393238302e313732626132626137386264386635393135373935363739353230362e706e67?s=fit&w=1280&h=1280]
In an 825 ml bottle, we insert 750 ml of grape juice (density: 1.00 g/ml) and the juice is left to ferment to obtain wine at 12.0% alcohol concentration in volume once closed.
A) By supposing that the resulting gas is insoluble in water (hypothesis that will be relaxed later) at 25.0 degrees Celsius, what is the pressure of carbon dioxide in the bottle?
B) With the quantity of gas calculated in A), calculate the quantity of CO2 dissolved in the wine, with K_H = 0.0310 M/atm.
"Here I must admit that this question is highly susceptible to confuse people. You are off base because you decided to go with an equilibrium constant while finding n was the core of the problem. In addition, we had to solve backwards; if there is twelve percent of alcohol in the wine, then there was twelve percent sugar in the initial grape juice. Hence ninety ml of alcohol and thus the same volume of sugar" Gen explains to him.
"But we know the molar mass of sugar?"
"Effectively very easy to calculate. And V is equal to the remaining space in the bottle"
We then have 90g of sugar, and the molar mass of sugar is 180g. One half-mole of sugar, and, by stoichiometry, we have a mole of carbon dioxide. Then it becomes a problem of PV=nRT. But we know R and n; V = 0.825 - 0.750 =0.075 L, T = 25+273 = 298 K and, since we can express V in liters, then P will be in kilopascals. Hence, P = 8.3145*298/0.075 = 33036 kPa = 33.0 MPa.
"Now that we know that we have a mole of gas, what will be the actual pressure of the gas in the bottle?" Sam asks, partially relieved, and he left the question completely blank on the actual exam.
This story originates from a different website. Ensure the author gets the support they deserve by reading it there.
"We simply know that the quantity of gas in the wine plus that in the bottle must be equal to a mole total, by conservation of mass"
We then know that, by Henry's law, that the wine dissolves 0.75L x 0.031M/atm = 0.02325 mol/atm. But the quantity of gas in the wine depends on the pressure in the bottle such that we have, noting that R is worth 0.0821 if the pressure is expressed in atmospheres, 0.02325 x 0.0821 x 298 / 0.075 times the quantity of gas in the bottle as a fraction of the quantity of gas in the wine. Or 7.5844 times. The dissolved quantity of gas is therefore equal 7.5844/8.5844 ~0.883 moles.
"We needed to tie the quantity of gas in the wine to that in the bottle? I'm not surprised to have lost an entire problem! I didn't understand anything!" Sam keeps panicking.
"Don't panic then; I am sure that most people will have had trouble on it! Maybe curvature will save us all!" Gen tries to calm him down.
Curvature. Used very widely when grades are very bad section-wide; either everyone's grades are raised, or an entire question is canceled. For some it could tip the scale towards the regular final, but in other schools all across the country, which are badly hurting for students to enroll in advanced placement courses, they will even award an A by default on an advanced placement course upon receipt of a 4 or 5 on the corresponding AP Exam, or even a 3 sometimes.
"You know exactly what I envy in you and your friend"
"Sam, you know in which context what you envy in me yields a benefit. But know, however, that life is not always rosy even at the intellectual level you envy in Marcia or me. Oh, you believe that because we seem to have it easy in class, that we shouldn't have to fear anything in the academic or intellectual arenas? Even I harbor doubts and it's not just when a major math tournament soon approaches. On that point, however, I might be tempted to think about all the implications of a situation, a problem, sometimes it confuses me. It does not happen to me very often, but it's when things go wrong that I question myself as you do right now"
"There's no reason for you not to succeed. I, however, am not on your level" Sam keeps ruminating.
"Honestly, how much do you think you will get on the AP Chemistry exam?" Gen asks Sam.
"I know that, because of this problem, I will not get more than eighty percent on the regular final. Therefore, I do not expect to have more than a four on it"
"These two exams are independent, and you look like you are panicking because you have completely failed a question! You know that some people among us have struggled more on math, especially those who didn't take the calculus BC course! I am sure that you're not the only one to have lost points over stupidities! As much people would have made use of the pyramid to cheat on long answer questions, there's a danger that we may have lost information on each pyramid tier!"
"Just knowing that I am not alone to have lost points on stupidities gives me no comfort! I fell into a trap, and you said it so yourself that it's easy to fall in it! There's not just Marcia and you that could have avoided it, I am certain of it!"
I avoided the worst in chemistry but cheating in a pyramid is so inefficient that the teachers let that pass! One may be wondering if Dylan's accomplice could actually have helped anyone on short and long answer questions; the cheating scheme is not considered a success, she thinks, while maybe Sam relied too much on his "supplier" as the laser pointer carrier that day. Dylan never appeared exceptional to me, good or bad, as a student, and same thing with his teammate Randy, at least in pre-calculus. Yet it appears people are less tempted to cheat in less advanced courses: no one asked him for help to cheat in a regular course.
Since she feels that it might help appease tensions, she simply posts the solution on Facebook, while considering Facebook's limitations about mathematical notation.
"Enough talk about chemistry. I took the time to resolve this nightmare with you, thinking that it would help you get past it, to calm your nerves for your other exams, and everyone else in the course as well"
Meanwhile, Shane, while reading the solution, seems to have more questions surfacing in his mind. I partially forgive her for now. I'm eagerly waiting to see how both sections reacted to the cheating scheme before I can forgive her in full. I think I'm in good position to reach my goal, because I did well on that problem, too, at least assuming both Marcia and Geneviève both solved this problem correctly – all year I assumed that, in class, if one of the two got it, the other would also. In French, in chemistry or in calculus. But could I have done more, especially with Marcia that held the hidden camera? Shane thinks, while having the impression the imperfection of his cheating scheme would cost him, or the other beneficiaries, precious points.
He can only blame himself for having focused too much on multiple-choice questions but with five of the best six in the class that are off-limits for the calculus final exam, he must ask himself other questions and not only logistics. Schemes of this type have a lot of variables and seem to have a greater chance of success if their « suppliers » are good. Yet, he really played the safety card in chemistry. Speaking of chemistry, the grades have been released, and a few minutes before lunchtime.
"Shane, I hope that you're happy because your cheating scheme didn't serve me!" the long snapper screams at him.
"OK, long snapper, what could the tight end have done more?" Shane asks the long snapper.
"It's the tight end who sold me on this cheating scheme; oh, you will get all the answers that you need, but he gave me nothing on short and long answers! I'm getting a B+ on the course, despite my B- on the final, and frankly a three on the AP exam would already be a great victory for me"
Dylan and the long snapper are far from being the only ones among the 53 players on the football team to take advanced placement courses, but decidedly the long snapper was the football player that placed the most hopes on the cheating plan, far more than his teammate that played a much bigger role in the plan without actually taking the course. Clearly the cheating scheme yielded mixed results, enough for the plan to cause tensions among certain beneficiaries that seemed to harbor anger towards its organizer or others who, on the other hand, seemed to like him.
"I scored an A on this final test and in the course!" Shane shouts.
"You see now that the cheating scheme was not completely useless!" Dylan comments to the long snapper. "There is someone that fully benefitted from it! Just not necessarily those who needed it the most"
"I earned the same grade as the long snapper, and I did it with a question that I completely missed!" Sam exclaims. "Did the long snapper also miss an insoluble gas question?"
"The insoluble gas question was not completely failed, I just started out with PV = NRT, to put the formula for the pressure as well as the other known values, but N was left blank on my copy" the long snapper answers Sam.
"So a player on the football team complains about an academic issue caused by a bad cheating plan?" a student not taking the course is asking.
"Where were you during this exam?" Marcia asks, thinking that positioning mattered.
"The forward left corner" the long snapper answers.
Even months after the end of the football season, as execrable as it has been, people still recognize the ex-players that must be replaced in two months? I see that the cheating scheme has worked a little better in the other section; I may have been a little too harsh on Geneviève. She wasn't very enthusiastic to the idea of cheating, but she always preferred to give some help before the exams start than when they are underway, Shane thinks, while he realizes the impact of his scheme's flaws.
"If we need to cheat, I hope someone else has a better plan!" Sam announces. "A plan that covers long answer questions better than a pyramid!"
"It shouldn't be necessary for a regular class" Shane answers him, before leaving the scene.
During finals season, punctuated with cheating as exciting as the others, it was out of question for Geneviève to talk about the Square Root of the Answer results, not thinking it's good to distract the rest of the student body with extracurricular news, even though she knows that the entire town awaits an announcement about it with impatience.
The town will have its chance at commencement, which is covered by the community media, like the parish newspaper.
"Before the commencement ceremony begins, we would like to underscore the exceptional end of the mathematics season, which ends with a thirteen-way tie for first at the national final of the Square Root of the Answer, and we have one of the thirteen teams in the tie. An we also won the prize of the best female performance by a non-senior" the principal starts.
"How do you see the next season?" the journalist asks Trent in the acclaim of the new graduates and their families.
"First, three of the four players that made our victory on the Square Root of the Answer possible will receive their diplomas today. It will be a considerable challenge for us to return to the national final, but one must remember that we started from far away. Pre-COVID Venomous Agendas fans only cared about their football team and the pandemic has ruined everything about sports in this parish! This season we only took part in the AMC10/12 and the Square Root of the Answer, for the next season, we will take part in extra competitions, such as the Math Madness, the Purple Comet and maybe even the ARML if there is an interest, but the ARML is subject to negotiations with the neighboring parishes. Of course, since the SRA put us on the national mathletics map, we will continue to compete. From this point forward, for all those taking the calculus BC in future years, so long as we will take part in the SRA, extra credit will be granted each week for questions of multi-variable calculus as well as for integral calculus questions for the first half of the year and, if we qualify for the national final again, we will allow everyone who wish to do so to participate in the final unofficially for extra credit. Since Geneviève performed exceptionally during the season, she will be the team captain for the next season" Trent answers as thoroughly as possible.
"The Square Root of the Answer is fine and dandy, but is there a reason why we would need to negotiate with the neighboring parishes to participate in the ARML?" the journalist asks him.
"The teams of the ARML are significantly larger than teams on the Purple Comet, the Math Madness or the SRA. We may not have the required depth to field fifteen players, even by searching everywhere among the best students of the entire parish; after all, we are not a magnet school, and even magnet schools of Bâton-Rouge or New Orleans must seek reinforcements elsewhere in their parishes to compete" Trent answers the follow-up question.
The crowd might be cheering now, but are we becoming the Permian of mathletics? Will the town keep following us beyond the sole SRA? Or is it because, to the eyes of the public, just hearing about calculus, even single-variable, seems to have a mystical aura that the rest of the material does not inspire in the public? Geneviève thinks, while her future on the mathletics team is now assured for her final year in high school.