Volume 2, Chapter 2-1: Preparing for Math Finals

Autumn Quarter 2015 Finals Week Monday

“Yuka, please help me. I’m struggling,” I pleaded.

“Yuki, you do know that I’m not good at math either, right?” she countered, closing her book.

“No, you don’t understand, I was gone for so long! Do you know how much I missed?” I said, pointing at the math book in front of me.

“Yuki, why don’t you ask Felicity’s friend?” Yuka suggested.

”I would feel bad. She already has to deal with Felicity and I don’t want to be a burden considering we just met. It would be unfair,” I answered.

“Have you tried going to office hours? I’m sure that the TA will be more than willing to help you considering what happened,” Yuka offered an alternative.

“I did but I need more help. You don’t understand, Yuka. I took calculus in high school but this is twice as hard ,” I said.

“When’s your final again?” Yuka asked, opening up her book.

“In two days,” I replied.

“What did you do over the weekend? I know you had time,” Yuka asked.

“I saw a great fight,” I blurted out.

“You saw a fight? Where were you?” Yuka questioned.

“I saw it on TV. Reminded me of Ichizen and I got sucked in,” I lied.

“Yuki, I know things have been hard on you and there’s always the option of filing for hardship and taking it again,” Yuka suggested.

“No, I can do it. But I’ll need some help. Who else can I turn to?” I went through a list of people in my mind.

“Does Felicity know anyone that could help you?” Yuka asked.

“I know for sure she does. But I don’t really want to ask anyone in her circle,” I replied, shaking my head.

“Yuki, you gotta make a choice. Your grade or pride?” Yuka posed a serious question.

Could I swallow my pride and ask for help? I stared at Yuka who averted her eyes. Yuka, c’mon, don’t do this to me. I sighed and looked down at my math book. No reason to take this class again if I could pass now. Besides, it wouldn’t be too bad to ask Felicity.

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As I pulled out my phone, I felt regret and apprehension. Was this really the correct choice? Were there really no other possible options available? I glanced at Yuka but she only looked at her book. I placed my phone down on the table and contemplated the possible paths in front of me.

I came to a decision. I understood most of the material at a basic level. It would be a waste of time retaking the class if I obtained a decent enough grade now. Picking my phone up once again, I dialed Felicity’s number.

“Hello?” Felicity’s voice answered.

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“Felicity, I was wondering if you could help me out,” I started.

“Sure, what did you need, Yuki?” Felicity asked.

“I was wondering if Tess can help me out. I have my math final in two days and you know after what happened, I missed class for awhile. Any chance of her helping me study or at least give me pointers?” I requested.

“Hmm, I’m sure Tess can help you but she has a final right now. I think she’ll get back in a few hours. I’m sure you want to study now though. How about I give you Long or Jin’s number? If they’re free, I’m sure they’ll be willing to help you,” Felicity asked.

I pondered her offer. If Tess still was at school, I could wait. Why not? It’s not as if it would hurt to have other people help me now.

“Okay, that sounds good,” I agreed, nodding to myself.

“Alright, I’ll text you their numbers right now. Umm, Long might not answer his phone so you might want to try Jin first. He’s more likely to answer but I don’t know if he has work today. Who else could help you?” Felicity revealed.

I went through the old archives of finals but didn’t feel good about getting a decent score on the final exam. I didn’t get the base material that the harder stuff made use of. If I got to the point where it made sense then my chances of a good score increased.

“Oh, I guess there’s Shan too but I don’t know him too well. Looks like Long and Jin are your best choices until Tess can get back. Oh, there’s Long’s friend too. But I don’t know how exactly that will work out,” Felicity suggested more people.

“Do you mean Kyoi?” I asked for elaboration, recalling the insanity displayed in her eyes.

“Asking her for help comes at a price probably. Not one you want to necessarily pay,” Felicity answered, her voice trailing off at the end.

“Okay, I think I’ll avoid that then. Thanks for the contact info, Felicity. Can you send Tess’s information over too? I just realized you’re the only one that I actually have a number for,” I added.

“Of course, Yuki. Good luck studying!” she said and then hung up.

I checked my messages and then added the numbers she texted over into my contacts. I placed my phone down onto my textbook and looked over at Yuka. Yuka’s eyes met mine and she gave me an inquisitive look.

“Did you get what you wanted?” Yuka asked, her right finger on the spine of the book.

“Yes. Well, here goes nothing,” I replied and picked up my phone.

Dialing Jin’s number first, I waited and the call went to his voice mail. I hung up and attempted Long’s number. I heard Zhuyu’s voice after it rung four times. There was silence and I realized I should speak first.

“Zhuyu, it’s Tomo Yuki,” I began, my voice dropping off at the end.

“Oh, Tomo. Did something happen?” he asked, concern but also annoyance in his voice.

“Nothing dangerous happened. I’m sure Tess would have called you if that happened. I actually wanted to ask you for a favor,” I replied.

“What is it? I’ll try to help you if I can that is,” he agreed.

“My math final is in two days. Could you give me tips or at least tell me what to expect?” I requested.

Silence followed my question. The rustling of papers then followed. Zhuyu spoke again as I heard the sound of typing in the background.

“Sorry about that. Yeah, I’ll see what I can do. It’s kind of hard to say everything over the phone. Do you have G-Chat installed? Give me call on there and I’ll see what exactly you need help on,” he asked.

“Yes, I have that. Thank you,” I said.

“It’s fine, I don’t have my final today. I’m about done studying anyways. Let’s see here..,” he said.

After he gave me his user name, I walked over to my backpack. Pulling out my laptop, I logged into G-Chat and added Zhuyu as a contact. After a minute, Zhuyu’s status changed from offline to online.

“I think I’ll head home now. I wouldn’t want to bother you with your math study. Have fun!” Yuka said as she left.

“So soon? You can stay if you want. You might learn something, you know?” I asked, plugging in my earphones.

“No, I think it’s better if you study without any distractions. I’m feeling hungry anyways so I’m going home to make lunch,” Yuka answered and then waved goodbye.

I gave Zhuyu a call and adjusted my settings while waiting for him. The familiar melody of a connecting call played. Finally, I heard static and then Zhuyu’s voice.

“Sorry about the slight delay, I needed to set up my microphone. Tomo, let’s get started. It’ll help if you can tell me where exactly you feel like you need help,” he suggested.

“Well, I’m pretty confident about the first half of the material. The second half, mainly the last two weeks, are what’s causing me trouble,” I replied, flipping open the textbook.

“Okay. So from what I remember, I believe you covered circles, derivatives, derivative rules, chain rule, and stuff like that. That’s good to know you’re solid on that. The rest of it just builds on it so if you know that well then it should help you with the material covered in the last few weeks,” Zhuyu analyzed.

“How do you remember that?” I asked, genuine surprise at the fact he recalled the material covered in Calculus I.

“I have some friends who are taking that class right now too. I’ve been helping them over the quarter. So I’m assuming you need some help on related rates and optimization,” he surmised.

“Yeah, that’s where I’m struggling for the most part. Anything you think can help?” I asked, checking the homework assignments involving those subjects.

“Hmm, I think this might help. Here you go, these are general things you should look over,” Zhuyu said.

Zhuyu sent over five files. I opened them up, recognizing some of the problems as ones I did for homework already. The solutions were written out by hand in good detail, each step clear and precise. A few stray pencil marks were on the sides but everything else was clean. How did he do this?

“Thanks for the stuff. Uh, any other advice you have for me?” I asked.

“Know your trig, general stuff like that. Usually related rates, at least at this university, rely on manipulating trig identities. Optimization can get pretty hard so focus on the homework problems which have the more conceptual ideas involved,” Zhuyu answered.

Zhuyu continued on, listing off things I should be aware of. I jotted down his advice in my math notebook, amazed by it. This was good stuff and it could really help. We talked for about fifteen minutes and Zhuyu reminded me I could contact him later if I had any further questions.

I ended the call and flipped through the five pages of notes I took during the call. Wow, five pages. He gave me that much information. I was now glad I made the decision to contact Felicity.

I heard my cellphone ping while looking through my book. A text from Tess. Tess was outside my house apparently. I peered through the window blinds and saw Tess’ car outside. Opening the door, I expected Tess but saw no one. Tess’ car was there so where was the driver?

“Tomo, you should be more careful about your surroundings,” I heard Tess’ voice.

I spun around and saw Tess walking out of my driveway. She wore a golden colored jacket with zippers on both sleeves. This time, her hairpins formed a triangle. Wait, this was not the time to admire her hairpins.

“Did you just come from my backyard?” I asked, peering at my back door.

“Yes. Everything is fine though. I have to get some stuff from the back of my car,” she directed.

I only nodded, still unsure how I missed her entering my backyard. I should have heard something. I sat on my sofa, thinking about how she evaded detection. Three minutes later, I heard knocking and opened the door for the second time. Tess, a bag slung over her left shoulder, entered and looked at me.

“I think we should go up to my room. It’s a lot easier for me to work there,” I said, pointing at the stairs.

Tess nodded, following me. I glanced back at Tess. She had her normal stoic expression on, not even the slightest hint of a smile. Maybe I should ask Felicity about Tess’ personality.

“Here we are,” I said, letting Tess enter first.

Tess walked in and placed her bag near my bed. I realized I had no extra chair and told Tess she could sit on my bed. Tess nodded and opened her bag, revealing the contents. I saw three notebooks and a pile of papers held together by a thick binder clip.

“So..that’s a lot of stuff there, Tess. Wait, actually before we start, how did your finals go?” I asked.

“It was fine. Tomo, I think you should be much more concerned about yourself than me. This was the final I took during my summer quarter there and I rewrote the steps for you. That notebook has some review material and..,” Tess explained, holding up each item as she spoke.

I was speechless, not sure how to respond. Tess really went the extra step for me and I would have to thank her somehow for this. As I thought about how to respond, Tess continued speaking.

“Tomo, it seems that you’re thinking about something irrelevant. If it’s about thanking me then stop. Just get a good score and I’ll be fine with that. Well, I may request a favor here or there,” Tess saw right through me.

I nodded and started going through the material with Tess. When I came to a difficult problem, she looked over at my initial work and directed me to the correct answer. Tess’ explanations were clear but lacked something. As I went through practice problems, I realized what Tess lacked.

There was no personality involved in her explanations. Comparing her notes to Zhuyu’s, the difference between them was clear. Tess’ solutions were more mechanical, mirroring a solution manual. Zhuyu’s solutions contained personal comments and small mistakes crossed out. His solutions were much rougher while Tess’ contained a certain polish.

I wasn’t going to be picky about help and the combination of their notes really helped me comprehend the last two weeks of material. After three hours of discussing math with Tess, I checked the alarm clock on my desk. It flashed 8:00 and I checked on Tess. She appeared fine, no signs of fatigue. Tess continued her explanations without any signs of slowing down.

“Hey, Tess, are you tired at all?” I asked, pausing her in mid-explanation.

“No, I’m fine. Anyways, apply the law of cosines here and then apply the initial condition here and here. You’ll need to use some trigonometry to calculate the length and I suggest either this or this,” she explained, circling the two equations I needed.

I clicked my lead pencil and followed her instructions. Tess pulled out her phone, glancing down at the screen. I peeked over, hoping for a glance of the display. However, Tess tilted her phone and I missed my chance. Finishing the problem, I checked Tess’ solutions and nodded.

“Good job. Keep in mind you’ll want to use that equation in this specific case. It is possible to use the other one but it’ll take more steps. Let’s move onto something else now. I think you have enough practice for these related rates. Tomorrow, you should also go over some non-triangle related rate problems,” Tess suggested, looking down at her phone again.

“Do you need to get home? If you do, you should go. I think I feel pretty good after talking to you,” I asked.

“Not yet. Tomo, is Long online right now?” she asked, looking at my computer screen.

“I don’t know. Did you need talk to him?” I responded, opening up my laptop.

“I wanted to address a specific problem I noticed,” she nodded.

I traded places with Tess and she typed with rapid speed on the keyboard. She added Kisai to my contacts list and then started a group call. I saw lines of text flow down the screen along with alternating screen shares from Zhuyu and Kisai. I would leave Tess to her own devices and focus on solving problems.

Ten minutes later, Tess stood up from my office chair and grabbed one of the notebooks in her bag. She pulled out a pen and started writing down numbers. She checked the screen once in awhile and finally looked back at me again.

“So is everything good then?” I asked, peering over at the notebook.

“It should be now. Something seemed off about my work and I just resolved it,” Tess answered, closing the notebook.

When it was nine, I stretched and decided that was enough for today. Tess noticed me placing my pencil down. She glanced at her cellphone and I heard the jingle of her keys.

“Tess, I think it’s about time that we’re done. You want to get home soon, right?” I asked, looking over at her.

“Not really. I could go on for three more hours at least. I don’t have midterms tomorrow so I can stay up late,” Tess answered.

“Uh, I think we’re done. I’m sure you’re hungry since you haven’t eaten dinner yet. So, it’s probably a good idea that we just finish up here for today,” I declined.

“But..,” Tess declined.

“No, I really think that you should get home now. Don’t you feel hungry?” I asked, checking her expression.

“I can last until lunch tomorrow. You don’t have to worry about that,” Tess explained.

“Wait, are you serious? I think that’s not normal,” I commented, surprised by Tess’ revelation about her eating habits.

“Is it? I don’t really think much about it. But if you really want me to leave then I’ll do it. I’ll come back tomorrow around five. That’s okay, right?” she asked, standing up.

“Five sounds good. I’ll eat dinner early tomorrow,” I agreed.

“You misunderstand, I meant five in the morning. Your midterm is the day after tomorrow so I’m sure you want to start early,” Tess clarified.

“Wait, I don’t think I’ll be ready that early. How about nine? I think I should be ready by then?” I asked.

“Nine, huh? Okay, that sounds good. I’ll see you tomorrow, Tomo,” she nodded at my suggestion.

I returned to my room with the dinner that my mom saved after Tess left. As I scooped up food into my mouth, I looked over at what Tess scribbled down. That wasn’t calculus or at least not the one I was learning. I saw theorems and an outlined proof. Yeah, not going to touch that for awhile.

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