Contains Math!

How Royalty get their Education

Three years later (Frozen Universe)-Elsa's POV

"So if I have here a number n, say n= 7, and my function is 6(n+9), then what is the new value function at n=7?"

"Let's see. Order of operations says I do what's inside the parenthesis first," I said.

"Good, good," Gwen said encouragingly.

"So 7+9 is 16 and 6*16 is 96!" I said confidently

"Excellent! Now let's try another more challenging problem."

*knock knock*

"Must be your sister. She probably wants to build a snowman again." As if on cue, my sister opened up with that annoying song again.

Do you wanna build a snowman?

Or ride our bikes around the halls

I think some company is overdue

I've started talking to

the pictures on the walls-

(Hang in there, Joan!)

It gets a little lonely

All these empty rooms,

Just watching the hours tick by-

(Tick-Tock, Tick-Tock, Tick-Tock, Tick-Tock, Tick-Tock)

"Just ignore it. I'll handle this," Gwen said as she open the door and confronted Anna.

"Sorry, Anna. You sister's quite busy right now. Maybe some other time?"

"But it's been three years!"

"Yeah, but education is more important than playtime, you know. I'm sure you'll figure it out someday. Now run along now." Gwen shut the door in my sister's face. I could hear her footsteps on the other side of the door. Suddenly, I felt ashamed. I finally realized what my years of solitude had done. Anna was being deprived of her one friend. Me. And I didn't even qualify as a friend anymore. Heck, what kind of friend are you if you shut people out for three years?! I tried to talk to Gwen about it. Of course she wasn't much of a big help, though she tried.

"You sure you can control those powers now?" she asked.

"Yeah. I've been practicing, and I can control it for several hours at a time now."

"Ok. I'll get your parents, and then they'll see if your ready or not." But when my parents came, my nervousness took over. For some reason, they backed me into a corner.

"Hey, I'm claustrophobic, you know!" I tried to warn them.

"That's the true test. We need to see if you can control your powers without the gloves on when you're in difficult situations," my dad said. He continued to get even closer. I suddenly lost control and fired off several ice crystals.

"We'll have to give it a few more years," father said.

"Can I at least talk to Anna at a distance?" I asked.

"We'll see what we can do," my mom said. A few days later on Anna's birthday, my wish was granted. I received a laptop. Apparently Anna got one too for as soon as I logged on to Facebook, I received a friend request from her. I practically screamed in joy.

"Thank you, thank you! You're the best parents a child could ever wish for!" I gushed.

"Oh if only all children were this easy to please," my dad sighed.

"Remember now, use it wisely," my mom warned.

"Oh I will," I said happily as I clicked on 'Accept Friend Request'.

"Hey sis. I see you got one too," Anna messaged me.

"Yup. Now we can talk even though we can't see each other. Haha, kinda like pen-pals," I wrote.

"Pen-pals who haven't written in like three years. Why didn't you come out of your room for all those years?"

"I'm not allowed to say. Anyways, happy birthday!"

"Huh? It's my birthday today?"

"Yeah. Did isolation mess up your brain or something?"

"Oh, I remember now! I'm ten today!" And just like that, we talked our way through the next three years.

Middle of the third year-Ben's POV

"Anna, time for today's geometry lesson. Stop chatting with your sister and come over here!" I called.

"Coming!"Anna replied as she ran towards the classroom. When she got there, she found me already on the lesson for today.

"So, today we're going to be focusing on special right triangles. Now what makes these triangles special? Well, there are certain properties that these triangles process that are unique."

"No duh! I could've guessed that when you told me they were special."

I decided to ignore that comment. "One of the triangles is the 30-60-90 triangle, and the other is the 45-45-90 triangle. The ratios of the lengths of the sides of a 45-45-90 triangle are x, x, and x2. That of the 30-60-90 triangle are-"

"x, x3, and 2x. If you know the ratios, you do not need to use the Pythagorean Theorem to find missing side lengths."

"How do you know all of this? I never taught you any of this!" I said in amazement.

"When I first met you, you didn't come across as someone who took their education seriously, to be honest."

"Yeah, that's true. I could get good grades if I only wanted to, but I don't feel like trying," I admitted.

"Under the fairly appropriate assumption that you would probably not be able to teach well, I took it upon myself to master subjects way beyond my years. Hit me with what you're doing in your math class. I bet I could get you an answer."

"Nah. I'm taking calculus. It's probably way too advanced for you."

"Calc? That was like last year for me!"

"Oh really? Then tell me, what is the definition of a derivative?"

"The derivative of a function of a real variable measures the sensitivity to change of a quantity, the dependent variable, which is determined by another quantity, the independent variable. Graphically, it is the slope of the tangent line of any point."

"Great! You can help me with my calculus homework then!"

"Sure, I guess. What do you need help with?"

"Well, we're on integration by parts. I have no idea how to even begin," I said.

"Oh, that's easy. First, you have to know what integration of parts states."

"I'm sorry, what?"

"Let's say that u=u(x) and v=v(x). Then du=u'(x) and dv=v'(x), right?"

"Ok, I can see the derivatives of the two functions now. So what this thing does for us is find the integral of a function u with respect to a function v by multiplying the two functions together and subtracting the integral of v with respect to u?"

"Exactly! You've got it!"

"Ok, let me try an example."

"Hmm. Try the integral of x cos(x)."

"I have no idea where to begin. This looks like a bunch of baloney."

"Concentrate, Ben! What other integration techniques have you learned? Surely integration by substitution?"

"Oh, right! I set u=x. And therefore du=dx. dv=cos(x), so v=sin(x). Following from the rule, uv is just x sin(x). The integral of v is-cos(x), so the integral of x cos(x) is x sin(x) +cos(x)."

"Well, you forgot the integration constant, C, but other than that, you did well."

"Yes! I knew I wasn't a loser in math!"

"I never said you were. I only said you lacked effort."

"Um, why are we having this conversation anyway?" I asked.

"I have no idea. I just had to prove my intelligence to someone."

"Hmm. With such an IQ, shouldn't you go study at AIT?"

"Yeah. My parents already know about my genius, so they expect me to get into AIT quite easily."

"I'm sure you can get in just by applying."

"Perhaps, or perhaps not. We'll have to see."

Someone, anyone, please review!