#sign of quadratic expression

[9nid]

🧠 Master Graphical Applications of Quadratic Equations – Part 2 | JEE Series Part-15 | By 9nid

🎯 Introduction Quadratic Equations are one of the most tested and important topics in JEE Mathematics, and understanding their graphical behavior can make even the toughest questions feel easy! In Part-15 of the JEE Series by @9nid, we dive deeper into the Graphical Application of Quadratic Equations (Part-2) — focused on visualizing inequalities and interpreting expressions using…

[edusquaremaths]

🧠 Master Graphical Applications of Quadratic Equations – Part 2 | JEE Series Part-15 | By 9nid

🎯 Introduction Quadratic Equations are one of the most tested and important topics in JEE Mathematics, and understanding their graphical behavior can make even the toughest questions feel easy! In Part-15 of the JEE Series by @9nid, we dive deeper into the Graphical Application of Quadratic Equations (Part-2) — focused on visualizing inequalities and interpreting expressions using…

[chiharuhashibira]

What about a shorts featuring your fave Kimetsu No Yaiba teacher?

But make it Professor X Student 👀

Whew~ Here we go with the final part of Special Classes >////<

Have you enjoyed your History, Art, and PE classes? Yes? Oh that's good cause you'll also love your Math class 🤭

You are 22yo here, and a graduating student. Sanemi is 27.

Let's start now! 🌸

𝓜𝓪𝓼𝓽𝓮𝓻𝓵𝓲𝓼𝓽

𝑺𝒑𝒆𝒄𝒊𝒂𝒍 𝑪𝒍𝒂𝒔𝒔𝒆𝒔: 𝑴𝒂𝒕𝒉𝒆𝒎𝒂𝒕𝒊𝒄𝒔

𝐊𝐲𝐨𝐣𝐮𝐫𝐨 𝐑𝐞𝐧𝐠𝐨𝐤𝐮 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐓𝐞𝐧𝐠𝐞𝐧 𝐔𝐳𝐮𝐢 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐆𝐢𝐲𝐮 𝐓𝐨𝐦𝐢𝐨𝐤𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐒𝐚𝐧𝐞𝐦𝐢 𝐒𝐡𝐢𝐧𝐚𝐳𝐮𝐠𝐚𝐰𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐎𝐛𝐚𝐧𝐚𝐢 𝐈𝐠𝐮𝐫𝐨 𝐕𝐞𝐫𝐬𝐢𝐨𝐧

Content Warnings: ProfessorXStudent/Suggestive/Curse Words/Dom Sanemi/Degredation/Blow job/Matured Content/18+/Sexually Explicit/Blood/Violence

Minors DNI.

(Image is not mine, credits to the rightful owner)

🌸𝑺𝒂𝒏𝒆𝒎𝒊 𝑺𝒉𝒊𝒏𝒂𝒛𝒖𝒈𝒂𝒘𝒂🌸

"Oi! That's not the answer! Have you listened to anything that I taught earlier?! Go back to your seat!"

You sat there and watched as Sanemi, your math professor, cast a critical eye over the room. You started to feel anxious because he might ask you to solve the problem in front of the class. And unfortunately, as if fate were conspiring against you, his purple eyes eventually landed on you.

Sanemi sat on your desk while maintaining an expression of irritation. "And what do you say, Y/L/N-san? Why don't you solve that math problem for me?" He asked the question sarcastically. You gave a small nod before rising from your seat, at which point you noticed that your chest felt heavy. You are aware that Sanemi is still glancing in your direction.

After a minute of solving, you turned to face the class and your professor, who was still sitting on your desk, looking amused, which surprised you. You took a deep breath and mustered up all of your courage before you spoke.

"f(x) is a quadratic function, and its graph is a parabola. As a result, it is not a one-to-one function because the parabola can be interrupted by horizontal lines at two different locations. The correct answer is a D."

Sanemi got to his feet and started walking towards you while softly clapping his hands. Your expression remained expressionless, and you experienced shyness despite the fact that you were aware that many eyes were staring at you at this very moment. You felt an arm stretched across your shoulder, and when you looked up, you noticed that Sanemi's face had finally stopped showing signs of annoyance.

"Woah! I thought this class was full of dumb brats! You surprised me, Y/L/N-san!"

You bowed your head respectfully and then proceeded to return to your seat. You no longer feel the same level of anxiety in your chest.

Because you are so accustomed to the harsh methods of teaching that Sanemi uses, these compliments seemed like a miracle that you would only hear once in your entire life.

--

"Sensei is so intimidating! Even if I do know the answer, I often forget it."

"So true! He's so harsh, and he is so anno—"

"Sssh, Aoi-san, if sensei hears you, he'll definitely make your life hell."

You couldn't help but overhear the conversations of the other students when your math class ended. What they are saying is true. Sanemi Shinazugawa isn't the nicest professor at the university. Oh well, he isn't soft at all, and he makes sure that you all know it.

Compared to the angel and most loved history teacher, Kyojuro, Sanemi's class is definitely an embodiment of hell. Especially if you're not studying well.

And as for you, you cannot fail any of your subjects. You are not the friendly type and you prefer to be alone than socialise. If you fail, you'll have no choice but to repeat the same subject with different people, and that would be so tiring.

Also, you already work outside your class hours aside from maintaining your scholarship. You can't lose all of that just because the professor teaching your math subject is the infamous Sanemi Shinazugawa.

--

After that day, on which you had successfully astonished Sanemi, a few days passed. It's well past midnight, yet you're still at the convenience store, where you are conducting an inventory check. The next thing you know, a man with a beard is grabbing your hand.

"Hey missy~ It looks like you're so busy. Need help?"

You pulled your hand away from him and took a step back. You felt a shiver when you managed to see that the man looked wasted. "No sir. Thank you." Despite the fear that started to bubble up in your stomach, you still tried to be as respectful as you are.

You were about to go when suddenly the man grabbed your hand again, tighter this time. You yelled but realised that the other employees were inside the stock room. You didn't want to shout, as you didn't want to scare the other customers, so you tried to squirm from his hold.

"Sir, let go of me."

"Come with me. I'll give you a better time counting how many times I can make you cum."

You were astounded by what he said and felt the tears almost fall from your eyes. But then, before they could fall, you suddenly heard a familiar voice that astounded you. You looked up, and there Sanemi was standing behind the man. His nails dug into the man's shoulder as he stared at him with fury in his eyes.

"One, I hate perverts. And two, I hate perverts who use numbers to rizz a poor kid. Let go of her before I make you rethink all of your life choices, you fucker."

And after only hearing his voice, the bearded man stumbled on his way out of the convenience store. And the good thing is, no commotion happened.

"You okay?" Sanemi said, pointing at your reddened arm. You looked back at him and noticed that he wasn't wearing his professor's outfit. The man looked so cool with his messy hair. He even looked cooler with that black leather jacket over his white shirt.

So, my professor looks like a normal person outside class...

You immediately recalled how tough he was earlier when he tried to save you from that pervert, and this sprang to mind before you could even think of anything else. You had no idea that he was capable of acting in such a way. And with that, you felt your heart racing as you felt heat coming up your cheeks when your eyes met.

"Hello?" He waved in front of your dumbfounded face and raised an eyebrow. It seems like Sanemi doesn't recognise you. So you shook your head and bowed in front of him.

"Sensei, thank you for saving me!"

"Hmm? Sensei?"

"I'm Y/L/N, Y/N, from the university. You're my math prof—"

"Oh, okay?"

You looked up once again and saw Sanemi looking away. He seemed preoccupied with the can of beer in front of him. Awkwardness filled the air. I think I shouldn't have told him I was his student! I hate how awkward I am when my mouth opens. You sighed and decided to thank him once again.

"Shinazugawa-sensei, thank you again. I'll get back to work."

Before you could head back to the storage room, Sanemi spoke up in a monotone.

"Uh, what time does your shift end?"

You were astounded by his question. Why would he ask that? You turned to look at him, but then you bumped your head on his chest. Apologising, you stepped back and stared into his lilac eyes as you spoke up.

"My shift's done in 30 minutes, sensei."

"It's late. Do you have someone to pick you up?"

You looked at Sanemi as if he were doing something unusual. Oh well, he does. Usually his mouth is full of curses, and his tone is always angry. But now it's different. Despite being monotone, it has a hint of... care?

"No sensei. I take the bus home."

"Okay. I'll just wait for you then."

"Uh why?"

"It's dangerous going home this late. And you're my student, so you're my responsibility. I'll drive you home."

Your heart started to toss and turn inside your chest, which almost made you want to throw up because of too much fluster. Sanemi is your saviour, and now he suddenly looks so cool that you can't take your eyes off him.

You didn't protest, as he is right. It's dangerous out there, especially since there was a man who tried to abduct you earlier.

A part of you felt a bit happy, as no one had shown you this care before, not even your parents. And with that last thought, you managed to end your shift.

You changed into a skirt and a shirt. As you walked out of the convenience store, you saw your math professor leaning against his car. "Three minutes late." He said this, checking his wristwatch before looking back at you.

You swear you could see the astonishment on his face when his eyes landed on you. But of course, that quickly faded away as he stood in front of you. "Sensei, I'm sorry if I made you wait."

"Just a favor. Don't call me sensei outside the university. People might think something's wrong if they heard you and saw you enter my car this late at night."

"Oh, sorry, Shinazugawa-san."

"Much better."

He opened the door for you, and his gestures shocked you. Last week, you saw how he almost threw a book at one of the students, and now here he is, being a gentleman. It's so not him.

You entered his car and were greeted with a minty, manly scent. Wow, this is Shinazugawa-san's vibe, for sure. You looked around and managed to settle down comfortably on the seat beside him. You tied your hair back and stared at Sanemi as he started the car. His hands looked so big. If that bearded pervert ever attempted to harm you, he wouldn't be able to withstand a punch from this man.

"Do you have a hand fetish or something?"

He asked that you cut off your thoughts. You looked away and apologised once again. Sanemi brushed it off and started driving.

"So where do you live?" He asked as his eyes peeled off the road. You told him your address, and he went on to ask you why you decided to work in a place too far from where you live.

"Oh, I have no choice. I need to grind for my future."

You felt like Sanemi wanted to say something, but he eventually stopped himself. And of course, you didn't say anything further. You don't want to make the travel more awkward than it already is. And when we say awkward, it's because you only answer when asked as if you're reading a script.

"So, what can you say about our classes? Don't tell me that I'm rude, 'cause I'm sure well aware of that."

Sanemi was the one who decided to break the silence. You played with the hem of your skirt and looked at your lap. You actually don't want to answer him, as you never wanted to offend him in any way. You sighed, and finally,

"You're cool."

"Oh. That's new." A small smile broke on Sanemi's lips, and that made you blush. Before you could say anything, Sanemi spoke up in a low tone. "I know that you're just saying that because of earlier, though. But thanks."

"Mmm..."

"Are you scared of me at class?"

"No."

"Why?"

"Because I study well. Why would I be afraid of you?"

"Good answer. You know, I'm tired of fucktard students who think my subject's not important."

And there, the curse words began. "I see."

"Are you really this silent? LOL"

You almost laughed when Sanemi verbally said LOL as it sounded funny. You tried to stop yourself from giggling, and you looked away. But yeah, back to his question. You just shrugged your shoulders and leaned back.

"Eh? You'll make our travels feel longer if you stay like that."

"Travels?"

"Your shift ends at the same time every day?"

"Yes. But what do you mean by trav—"

"Now we're talking." He chuckled and continued, "Whether you like it or not, I'll be here after your shifts as I also go home to the same town. I have a friend who's dorm is beside the convenience store, so don't fucking tell me that it'll be a bother, cause nope."

"But sen—"

"Sanemi. Call me by my first or last name when we're out of the university. You weren't paying attention earlier! Tsk!"

"Sorry..."

"And stop apologising too much."

You felt your heart go fast as Sanemi smiled at you. "I told you, you're my student, so you're my responsibility. And I don't want what happened earlier to repeat."

"Thank you, Sanemi-san."

--

That first time Sanemi drove you home became your math professor's task every time that you were at that convenient store.

You still acted a bit awkwardly towards him, but after a few days of those moments recurring, Sanemi slowly brought you out of your shell. And also, he managed to start making you feel more flushed than before. You started liking him and the times when he was there for you.

At the university, he's still like the chaos incarnate with his harsh antics. He even made one student cry because he became mad at them for being too loud in the hallway while he was teaching. And of course, at class, he didn't show you any special treatment. He even started to call you airhead at the uni.

But yeah, you didn't have any grudges against him, as all you wanted to do at the university was learn and pass. And you're clearly aware that Sanemi's just doing his job in his own way.

It just also seems like Sanemi has this facade at school. But you won't dive deep into that, as you never wanted to pry.

"Hey airhead."

The sound of Sanemi's voice reverberating through the hallway shook you out of your stupor. You turned your head to look at him and noticed that the math professor was approaching you from behind. There are no math classes today, so you were astounded to see Sanemi.

It is impossible not to fall in love with the charming way in which the sun's rays fall on him. Because of the way that his piercing eyes were fixed on you and the way that his hands were crossed, almost exposing his bare chest, you can't help but feel as though your breath is being slowly sucked out of you.

You bit your lip, still staring at him, when he finally stopped in front of you.

"Airhead, I'm going to fucking melt if you keep staring at me like that."

You blushed and looked away. But then, before you could give an excuse, Sanemi spoke first. "Your classes are done?"

"Yes sensei."

"Come with me. Help me check your papers."

You immediately nodded and followed him to the classroom of the Math Club. The members were out early today, so Sanemi got the entire room for himself. And yes, the man likes solitude sometimes.

Sanemi closed the door behind him and sat on his desk. "Just pull a chair from somewhere there." He pointed at the empty seats, and you complied.

Sanemi has been a nice guy to look out for you after work, and you really appreciate that. You wanted to pay him back sometimes, but he declined it, so one night you told him that you'd be his apprentice at the university, and you'd even help him with his tasks if needed. There, he agreed.

It wasn't the first time that the two of you shared this room to indulge yourselves in numbers. It was a win-win for you. First, you are definitely learning. If there are mistakes, Sanemi teaches you the formula, so that's an instant special class for you. Second, you kind of want to spend time with him, so these moments make your dreams come true.

Your work is just 4 hours as you are just a student, and the owner of the convenience store is too kind to make you work for 8 hours after your 6 hours of school. So, you won't be late even if you stay here at the university, as your work starts around 9 p.m.

Sanemi cleared his throat, which made you look at him. He was staring at you intensely, and when your eyes met, it was him who averted it this time. "Uh, so, how's the day? Any homeworks?" He asked with an awkward tone, which definitely surprised you, as he was usually sounding either cocky, angry, or caring.

"Yes sensei. On Iguro-san's chemistry classes."

"Hah! I hope my friend doesn't give you a hard time." Sanemi chuckled.

"He doesn't. He's less harsh than you are."

It was late when you realised what you said. You covered your mouth and stared at Sanemi, who had the veins on his forehead popping in irritation. "You brat. Math is important! If I weren't harsh, would you all fucking listen to me?"

"I will. I like it when you're gentle."

What you said surprised Sanemi. His cheeks suddenly turned pink, but he tried his best to hide it. You noticed it but didn't say a word. But inside you, you felt hot. You like it when Sanemi blushes. You bit your lip again and crossed your leg as you felt something weird down there.

His breathing has changed, and you watched his exposed chest as he did so. Your eyes landed on his scars, and a part of you wondered how they would feel if you touched them.

On the other hand, lots of crazy thoughts suddenly filled Sanemi's head.

She likes me when I'm gentle. What does this little fuck mean?

Your words almost caused his mind to shut down. He always looks forward to when you speak, as you're always so quiet, but times like this really astound him. He's flustered around you, and that's because he likes to have his own damsel in distress.

Your math professor's attracted to you, and you have no idea.

Sanemi straightened his collar and cleared his throat before continuing to check the papers. You watched as he moved in his seat, but you couldn't help but be perplexed as to why he responded in such an unexpected manner. You stepped up, bent towards him, and reached for some additional paperwork that had been placed in front of him so that you could also check those.

But then, instead of reaching the test papers, it was Sanemi's hand that you accidentally touched. "Oh sorry... I was just trying to get some papers." You said this and proceeded to take some papers, not knowing what your actions were doing to the professor.

His eyes watched you as you gently sat back, and without you noticing, those lavender orbs fell on your breast. He was observing you the whole time. As you breathed in and out, Sanemi watched your chest rise and fall.

You finally finished checking and smiled at your professor. But he was too taken with the sight in front of him. You tucked your hair back behind your ear and stood up from your seat.

"I'm done, Shinazugawa-sensei."

"Hey airhead, can you stop doing that?"

"Huh? Doing what?"

"Oh, for fuck's sake!" Sanemi stood up from his seat, and in just a blink of an eye, he pinned you on the wall, Kabedon style.

You blushed at what he was doing, as you didn't know why he was doing this in the first place. "S-sensei?" You asked, blinking in shock as you felt his hot breath touch your neck.

Sanemi stared at your eyes, and there you saw how they were painted with passion and... hunger? A part of you wanted to leave, but then the bigger part wanted whatever this was. He leaned in until your foreheads touched, then spoke to you in a deep, husky voice.

"The fuck are you doing with me, airhead? You don't know how much you make me want to do this."

"I don't know what you're saying..."

"You want me to be gentle, huh? What makes you think that I'll be gentle to a bitch like you?"

"Sensei..."

Before you could say any words, Sanemi smashed his lip over yours. You were stunned for a few moments before you realised that your math professor, your saviour, and your crush are pinning you on the wall and kissing you right now.

With that in mind, you slowly wrapped your hands around his neck and finally kissed him back, letting his tongue explore your mouth as you moaned.

But then...

"Oh fuck..."

Sanemi pulled out and walked far from you, his hand massaging his forehead. You stood up and watched him, feeling a bit anxious while doing so. He suddenly looks mad.

"Sensei..."

"What the hell, Y/N-san!" He suddenly said it in a roaring voice that made you shiver and almost tear up. He noticed that, so he went near you and held your shoulders. The lust in his eyes faded, and what you saw now was regret as he looked at you.

"Hey, I-I didn't want to take advantage of you. Believe me, Y/L/N-san. It's just that I didn't know what happened to me."

"I like you, sensei."

Those words just escaped your lips and left both of you stunned. You didn't want to tell him that, but you wanted him to calm down. You bit your lower lip, and with that, Sanemi finally took a step back.

"No. You can't. I'll just make you cry."

"Why?"

"Just follow what I'm saying."

You felt angry with what he was saying. Yes, he is older than you, but you hate the fact that he is mansplaining you now. You closed your fist in anger, with nails digging into your palm. And while glaring at him. You finally spoke up.

"Then why the fuck would you kiss me, Sanemi?"

Sanemi rubbed his face in frustration, and finally...

"Because you're fucking easy. I can fuck you if I want to. But you see, I'm doing you a favour here. If all this time you had liked me, then you might as well bend over on that table—"

SLAP!

You didn't care if you were inside his den or if he was your professor. What he told you hurt you, and all you wanted to do now was leave. Tears rolled down your cheeks as you watched Sanemi massage the cheek that you just slapped.

"I hate you! You're just like anybody else."

You said that and finally went out of the room, leaving the man with his guilt.

Yes, Sanemi chose to hurt your feelings instead, as he didn't want you to like a man like him. He's harsh; he even hurts the feelings of his younger brother.

He had hurt a lot of women because of that attitude, and now he didn't want to hurt you too.

So, even if he hated it, he said those words to push you away.

I like you too. But even if I wanted to give you my love, you're my student. I can't hurt you that way.

--

Days passed, and you still went to his classes with a heavy heart. You didn't answer his classes like before; you didn't even react if he taunted the other students. And yes, he did that; you know he avoided you like the plague. He never called your name. He didn't even try to look at you. Suddenly, you're invisible again.

The night after that encounter, all you did was cry. You didn't even go to work. You lied through your teeth when you told your manager that you were sick.

And yes, Sanemi stopped driving you home. Perhaps what he said was true. I'm fucking easy? You thought about it for the hundredth time as you finished your shift. You stepped out of the convenience store, wishing you would see him parked by the—

"Sanemi..."

"Oi, Y/N. How are you?"

The sight of Sanemi again was like a blow to the chest. He had his back against the car, arms folded. You decided to ignore him, walking away, but then he caught your arm.

"Hey, please listen to me."

"What the fuck do you want? If you want to fuck someone, go to a strip club or something."

"No."

"Then what?!"

You pulled your hands away from him, glaring as if you wanted him to just disappear. His sight reminds you of all the hurtful things he said at that time.

"I'm sorry. I messed up."

"Go tell your sorry to some other easy kid. I won't buy that. You are free to fucking fail me if you so choose. I'll just transfer."

"Hey! No!"

You walked away, leaving Sanemi again, but he chased you and blocked your way. He isn't wearing any of those facades as he faces you right now. He looks distressed and sad, and a part of you wanted to give in, but men are like this. They do things like this if they need something from you, and you hate him anyway.

"I love you, Y/N."

"And now you suddenly love me? Oh, please, perhaps you're just horny again."

You tried to escape from him, but Sanemi didn't let you. He held your shoulders and stared into your eyes, begging for you to listen to him.

But then, before he could speak, a person suddenly appeared behind you.

"I hate to disturb this love quarrel, but you need to pay for messing up with me."

And suddenly, all your strength seemed to be sipped out of your body as you saw how Sanemi pushed you away as the perverted man from before tried to stab you. Sanemi received the attack on his side, which made the culprit run away.

The man who stabbed Sanemi was then unintentionally run over by a truck and sent flying, as if fate were on your side to avenge you.

Your eyes widened as everything went red. Your professor coughed blood and fell on your shoulder.

"No... No... No Sanemi! Don't die on me!"

"I love you, Y/N."

"I love you too. Please don't leave me."

"I love... you... Sorry..."

He said that, and then he passed out.

--

"What happened to Nii-chan?"

You were astounded when you met his little brother. He entered Sanemi's room with worry on his face. You always see this guy at school, and Sanemi seems to hate him so much. You're a year ahead of Genya and you didn't even think that Sanemi was his brother.

"Sanemi-san saved me earlier. I'm sorry if this happened to him, Shinazugawa-kun."

"No! Don't say that! It's not your fault at all. My Nii-san's really great. He would save people a thousand times if he only could."

You watched as Sanemi's brother sat on the couch beside you, looking at his unconscious brother. It's the first time that you've really looked at him, so it's also the first time that you've seen that he also had scars like Sanemi had.

"Sorry Shina—"

"I'm Genya. Are you my brother's girlfriend? He always speaks about a girl who seems to fit your description."

"Oh?"

You blushed at Genya's words. So, Sanemi's thinking of you? For real? He even went all the way to telling those feelings to his little brother. You weren't able to speak as if he knew that you were a student at the same university where his brother teaches. He'll surely freak out.

"Do you think your brother will be okay?"

"Yes. He had endured this kind of injury a lot of times. I'm sure that his wound now won't be the one that kills him."

A lot of times? Questions filled your head as you stared at Genya. He seems a bit relaxed. Perhaps he trusts his brother so much.

"What do you mean, though?"

"Oh, Nii-chan saved my life when I was younger from an accident. See these scars? He also has this, but it's a lot worse. He endured all the pain just to save me. Nii-san would do anything for the people he loves. Even if it means hurting himself."

Your heart started beating fast once again as you remembered that, before he passed out, Sanemi had told you that he loved you. Perhaps that's why he took that stab at you. But why would he hurt your feelings back then in the classroom if he really did? You're confused as much as you are happy to know that the professor loves you. There were a lot of things that you wanted to hear from him.

"The fuck are you doing here, Genya?"

Both you and Genya were astounded as Sanemi's faint voice was heard. Both of you stood up and ran to his side. Sanemi groaned and tried to sit, but you stopped him.

"Hey no... Just lay down. Please."

He complied without any complaints, but then he looked at Genya. Sanemi caressed his brother's arm. "Hey, you won't get rid of Nii-san that easy." He grinned, which made Genya smile too. "I know Nii-san."

That's the first time that you've seen the innocence and peace on Sanemi's face. He looked like an angel. You smiled at them and were about to leave the siblings, but then Sanemi caught your arm and looked at you with loving eyes.

"Are you okay? What happened to the fucktard?"

"Sanemi-san, I'm good. You should relax first."

"But I want to know."

"The man died. After stabbing you, he ran onto the street and got hit."

"Oh, he got what he deserved!"

Genya spoke in a loud tone that made Sanemi chuckle. You held Sanemi's hand, caressing it as your eyes locked with each other. Then suddenly...

"Genya, I see that you've met my star student, Y/N."

"Oh? Student?!"

Genya was astounded by what Sanemi said. But no one could beat the surprise on your face. Yes, you'll always be his student, and that shit hurts.

But before you can say anything...

"And Genya, I'll punch you if you ever try hitting on her. She's not just my star student. I also love her."

"Nii-san..."

"Sanemi..."

"Your secret's safe with me, Nii-chan. It's nice meeting you finally, Y/N-san."

"Thank you. Genya, can you leave us alone for a while? I'll talk with you later."

After a nod, Genya walked out of the room. Sanemi held your hand tightly and smiled at you. "I'm glad you are okay, Y/N." His voice was soft as he said those words. He had a smile, as if he had just won the lottery. Perhaps saving you is really important to him.

"Yes. It's because of you, sensei— I mean, Sanemi."

He chuckled and caressed your hand with his fingers. "I'm so sorry if I told you lots of hurtful words back then. I didn't mean to tell you those. I was just scared to hurt you. I always hurt the people who become close to me."

"No. I think you're wrong. Why don't you try giving yourself credit? Like with Genya-kun. He adores you so much."

"But... I wasn't able to save our whole family."

"Don't blame yourself for everything, Sanemi. You did your best. And I think your family is proud of you. And I'm not saying that you shouldn't be harsh or whatever; I'm just saying that you shouldn't push people away because you're not saving them. You're hurting them."

"Like what I did to you. God, I hate myself for saying those things. I'm sorry."

"I've already forgiven you. Don't think about that too much."

You leaned in to kiss his lips, which surprised the man when you pulled out.

You smiled at him and caressed his face. "I don't want to lose you again, Y/N." He said this as he caressed your hand.

"You won't lose me anymore, Sanemi. I love you."

"I love you too. Will you be my girlfriend?"

"Yes."

--

"Hey airhead!"

You were surprised when Sanemi's voice echoed in the hallway. You looked up at him, and there, you were astounded by how stunning he is. With the sun setting the spotlight on him, you saw his littlest details. The way his grin lights up his face, his arms swing gracefully at his sides, and his gaze follows yours.

You weren't able to look away even before he finally spoke up, teasing you. "I'm going to fucking melt if you keep staring at me like that."

This is deja vu. Sanemi crossed his arms and,

"Come with me. Help me check the papers again."

"Okay sensei."

You walked behind Sanemi, and when you reached the classroom, he locked it. You were about to pull up a chair to sit and check the papers when Sanemi sat on his chair and patted his lap. "Nope. Sit here."

"Sensei..."

"You don't want to obey me?" He asked with a challenging voice, which definitely turned you on. So, of course, you slowly sat on his lap while blushing madly.

"So, I want you to solve this for me."

Sanemi said while caressing your thighs under the table. With his touch, you felt your body tingle. You spread your legs and thanked yourself for choosing to wear a skirt today. You felt yourself becoming wetter, so you slowly rubbed yourself against Sanemi's groin, causing him to moan.

"I thought we'd check papers, sensei?" You said it innocently, teasing him.

Sanemi rested his head on the crook of your neck and used his right hand to cup your breast under your shirt. "I love it when you play innocent, baby." He said, obviously turned on by your actions.

"What am you saying, sensei? You said I need to solve something, so I'm just patiently waiting." You said this, continuously feigning innocence as you felt Sanemi's cock get harder with the friction.

"Oh, I'm going to fuck you so hard, Y/N."

He said, making you giggle. But suddenly, Sanemi stood up, making you stand up too. He pointed to the table and smirked at you. "Bend over."

You felt your titties become harder as arousal took over your body. Heat crept up to your face as you heard the change in Sanemi's breathing. Also, the fact that you're both at the university right now turned you on. You loved that it was risky.

So, with no doubt in mind, you bend over the table, exposing your wet underwear to him. Sanemi loved the view. After unbuckling his belt and removing his pants, he approached you, and you felt his hard cock rubbing against your clothed cunt.

You wanted to see how big it was, as this is your first time with him. Days before this, you had your first foreplay with him, but that was over the phone. He made you cum thrice just by his voice.

"What is two times two?"

"Four."

"Yes, I will make you cum four times in this room."

You felt excited. And what made you more aroused was when Sanemi went down on you and started licking your cunt as you were bent down like a slut for him. He removed your underwear and began running his tongue through your slit.

Sanemi chuckled as you squirmed because of the pleasure. His chuckle reverberated on your skin, sending your tingles.

Then, to your astonishment, Sanemi spanked your ass, making you yelp.

Sanemi stood up and caressed your ass. "Mmm, you don't know how much you're turning me on right now. Face me and kneel down." He said, which you happily obeyed.

You faced him with your eyes trailing from his lustful expression down to his unbuttoned shirt, then down to his big and hard cock.

"You feeling scared now, Y/N?" He said this, smirking at you. But then, without any words, you knelt down and slowly caressed his cock as you adored it. It was so big that you might actually cum more than four times because of it.

Slowly, you swiped the tip on your lip and licked the cum that was already oozing out of it because of being turned on. You held it with your right hand and trailed the bottom of the shaft up to the top before putting it all inside your mouth.

"Oh fuck. Your mouth feels so good, Y/N."

Sanemi held your head and thrust on you as you bobbed your head on his cock. You felt almost gagging as it reached your throat, but you stopped it and decided to look at Sanemi in the eyes as he enjoyed your blowout. "Mmm, baby, I'll fucking make you scream in pleasure if we just weren't at uni this time." He said, patting your head like a good girl.

You were about to give him a hand when suddenly Sanemi yanked your hair and spread you out on the floor. Taking off the rest of your clothes, he started kissing you. Slowly, you felt his hands on your clit as he started rubbing them in circles.

You moaned in his mouth as you bucked your hips up in pleasure. "Shhh, the students might hear us, baby," he whispered as he pressed his lips to yours once more.

With how he stimulates your clit, you can't help but feel overwhelmed. "Mmm near baby!" You said this as you squirmed underneath him. "Yes, baby, cum for me like a good girl."

With that, Sanemi rubbed your pussy faster than before, which almost made you scream, but thankfully, he managed to cover your mouth. And there, after a few seconds, you felt the tingly sensation all over your body. Your eyes rolled with pure lust as your hips bucked up to match the pace of his fingers.

You felt the high subside, and yet Sanemi isn't done with you. Even if you're still intoxicated from your first orgasm, Sanemi lifted you onto the table once more and sucked your titties.

"That's the first one, baby. Now, let's go with the rest."

Sanemi pulled your hair, which made you moan as he kissed your neck, leaving a trail of love bites. As he did so, your hands worked to remove his remaining clothing as well. And when his clothes fell on the floor, you ran your nails on his back.

"Fuck me." You whispered that made him smile.

"Of course I will."

Slowly, Sanemi aligned his cock on your pussy, and with one swift thrust, he finally succeeded in penetrating you, compelling you to cling to him as your pleasure began to return. You bit his neck, which made him groan in your ear.

"Oh fuck. Do that again, and I'll fucking punish you, airhead."

You looked into his eyes and saw him looking at you intensely as he continued to thrust into you slowly. You caressed his face and kissed his cheek. "I love you."

That seemed to fuel him, as suddenly Sanemi's thrusts became harder and faster, making your breast jiggle beneath him. He sucked on one of your nipples and continued to fuck your brains out.

You wrapped your legs around his waist to let him go deeper. With that, Sanemi managed to repeatedly strike the perfect spot within you, and you felt your orgasm building up once more. "Ahhh, Sanemi, I'm cumming."

"Good girl."

He rubbed your clit again while continuously fucking you so hard. And there, after just three seconds, you squirted on his cock, making him smirk.

He pulled out of you and watched as you panted underneath him. "That's two for you and still zero for me." Just looking at him right now, you can really say that this man has stamina.

"But we're not done yet, babe... That was so hot when you squirted on my cock. Do it again."

He said and with that, Sanemi finally bent you over the table. You used the poor table as a support, as you felt that your strength had already escaped from your body.

Without hesitation, while holding your waist, Sanemi thrust deeply into your dripping pussy and fucked you.

With every thrust, you managed to whimper in pleasure. "Fuck Sanemi, you're so good." You muttered between your pants, and that made your math professor more aroused. You felt his thrusts become faster again as his nails dug into your waist. You whimpered in pain and pleasure, with tears already welling in your eyes.

He cupped your breasts and left love marks on your neck. "Fuck so tight for me, love." And with that, you matched his pace, also moving your hips with his rhythm. Then, for the third time, you felt your pussy increasing in temperature as his cock continued to strike your gspot.

And there, you finally squirted once again, letting out an audible moan as you did so. Sanemi covered your mouth and continued to fuck you as the tingles subsided.

Without pulling out, Sanemi turned you towards him and lifted you. "Third. I'm so done edging. I'm going to make you cum for the fourth time. And yes, baby, I will fill you with my seed. I know you want that, right?" He asked gently as he playfully squeezed your ass.

You didn't answer, as you felt weak with pleasure. Sanemi smirked and gave you a passionate kiss, biting your lip while inserting his cock into you. You held on to him tightly and wrapped your legs around his waist so that you wouldn't fall.

"Don't worry. I won't let you fall."

"Are you sure you can... your wound..."

"I can. I'm all healed, remember?"

You sobbed on his shoulder as he abruptly inserted his cock into you, preventing you from speaking. It felt so good! Sanemi moaned in your ear as he slowly let the pleasure build. He won't hold back this time.

As Sanemi lifted you up and down his cock, you couldn't help but be impressed by his strength. His thrusts were deeper this time, so to tease him, you clenched your pussy around his manhood, which made him moan loudly. "Fuck! Fuck!"

He couldn't take it anymore, so he placed you down on the table again and lifted your legs on his shoulders. He desperately desired to cum inside you, so he fucked you faster, nearly causing you to scream with pleasure. He didn't cover your mouth this time; he couldn't as he was too focused on how beautiful you are beneath him.

With the lascivious sound of your moaning and skin slapping, he can't help but feel his orgasm inside of him. You, on the other hand, are already feeling the tingles as you feel like cumming.

Sanemi smashed his lips on yours, and there, both of you cummed in unison. You squirmed as your cunt squirted on his cock while he released his seed inside of you. You felt like passing out as the high subsided. Sanemi finally pulled out, making his cum drip on the floor. But who would care? You're drunk on passion.

He lifted you and placed you on his lap as you embraced him tightly. You love this man so much, and you can't help but be happy that he is finally yours.

Sanemi ran his hand through your hair and kissed your forehead. "You're such a good girl. Came four times for... sensei." He teased you, which made you blush.

"Y/N... when I saw you in trouble back then, I told myself that I wanted to protect you. And here we are now."

"Thank you, Sanemi." You said this as your eyes locked with each other. The wind blew over your naked bodies, making you feel the shivers, but then Sanemi embraced you and let you rest on his chest.

"You're just like me when I was younger, babe. I used to do everything for myself and Genya. I even worked back in college too, like you."

"So, you saw yourself in me?"

"Kind of. But you're better. So, I am trying to protect you from bad things. Even from myself... Because a part of me knows that it's wrong to like your student."

"But do you regret loving me now?" You asked, anxious as you watched Sanemi sigh.

"No. The thing that I regret most is trying to hurt you. You're not an easy girl, Y/N. Don't ever believe any of the shitty words I said before."

You smiled at him and kissed his lips. Feeling your strength once again, you slowly sat on his lap, facing him this time. "What I regret is hating you... I love you, Sanemi. Thank you for always saving me." You said it with tears falling from your eyes. You embraced him and buried your face in the crook of his neck.

"Shhh... Don't cry, babe. Please."

Sanemi lifted your head and wiped away your tears. He kissed your forehead and caressed your cheek.

Eyes locked with each other again, you realised how your life would change today. And it'll change for the better with Sanemi by your side. Yes, the infamous Sanemi Shinazugawa fell in love with you, and you're happy with it.

"I love you, Sanemi."

"We're in school, baby." He teased, and that made you chuckle. So then,

"I love you, Shinazugawa-sensei."

"I'm just kidding! But I love you too, Y/N."

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

𝓣𝓱𝓪𝓷𝓴 𝔂𝓸𝓾 𝓯𝓸𝓻 𝓻𝓮𝓪𝓭𝓲𝓷𝓰 𝓽𝓱𝓮 𝓢𝓹𝓮𝓬𝓲𝓪𝓵 𝓒𝓵𝓪𝓼𝓼𝓮𝓼 𝓢𝓮𝓻𝓲𝓮𝓼~

You won't know how happy I am that I finally completed this~

Originally, it was supposed to be just headcanons but you know me, I can't write short fics that easy HAHA So, when I was writing 𝑺𝒑𝒆𝒄𝒊𝒂𝒍 𝑪𝒍𝒂𝒔𝒔𝒆𝒔: 𝑯𝒊𝒔𝒕𝒐𝒓𝒚 for Kyojuro, I revised it tonnes of times XD

But there, the series flowed until here we are with Sanemi's part! I hope you loved it🤭 As promised, I made it long as it was delayed already HAHA!

Reblogs, Comments, and Requests are highly appreciated! Love you!

THANK YOU SO MUCH FOR THE SUPPORT~ I'll see you on my other stories UwU

MDNI!

Ja ne~

~𝓒𝓱𝓲𝓱𝓪𝓻𝓾-𝓬𝓱𝓪𝓷🌸

𝐊𝐲𝐨𝐣𝐮𝐫𝐨 𝐑𝐞𝐧𝐠𝐨𝐤𝐮 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐓𝐞𝐧𝐠𝐞𝐧 𝐔𝐳𝐮𝐢 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐆𝐢𝐲𝐮 𝐓𝐨𝐦𝐢𝐨𝐤𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐒𝐚𝐧𝐞𝐦𝐢 𝐒𝐡𝐢𝐧𝐚𝐳𝐮𝐠𝐚𝐰𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐎𝐛𝐚𝐧𝐚𝐢 𝐈𝐠𝐮𝐫𝐨 𝐕𝐞𝐫𝐬𝐢𝐨𝐧

[rlyehtaxidermist]

how to construct the geometry where this is a rhombus:

consider points in terms of polar coordinates (theta, r)

define distance analogously to taxicab geometry, as the sum of the radial distance between two points and the arc distance (taken along the circle of smaller radius)

further constrain that arc distance may only be measured clockwise - i.e., for points of equal r, AB + BA = 2pi r. this is necessary in order to allow major arcs and minor arcs to both properly serve as line segments (i.e., be uniquely determined by their endpoints), but it breaks the usual commutativity of the endpoints of a line segment

then we have our four points (0, r1), (0, r2), (theta, r2), (theta, r1). the lengths of our segments are then

which allows us to solve for theta (given that r2 is nonzero):

The quadratic formula gives two possible values of theta,

We can discard the root with the positive sign as theta must be between 0 and 2pi, so the allowed angle must be

While the image can be scaled arbitrarily, the ratio of the radii is fixed; returning to our expression for r1 gives

From here, it is straightforward to set r2 to 1, which will show that the lengths of the arcs and the radius segments are all equal.

I love seeing a meme and being like oh, tumblrs going to love this one

[mysticprofessorstudentgarde-blog]

𝐄𝐯𝐞𝐫 𝐰𝐨𝐧𝐝𝐞𝐫 𝐰𝐡𝐚𝐭 𝐰𝐨𝐫𝐝𝐬 𝐬𝐜𝐢𝐞𝐧𝐭𝐢𝐬𝐭𝐬 𝐚𝐧𝐝 𝐞𝐧𝐠𝐢𝐧𝐞𝐞𝐫𝐬 𝐮𝐬𝐞 𝐭𝐡𝐞 𝐦𝐨𝐬𝐭 𝐞𝐯𝐞𝐫𝐲𝐝𝐚𝐲? 🤔 Well, your questions are about to be answered now! 𝐂𝐡𝐞𝐜𝐤 𝐭𝐡𝐞 𝐯𝐢𝐝𝐞𝐨 𝐛𝐞𝐥𝐨𝐰 and experience a full discussion of the 10 most used words in the Science, Technology, Engineering, and Mathematics strand! 🔬📏 𝗘𝗾����𝗮𝘁𝗶𝗼𝗻 – A mathematical statement that shows the equality of two expressions using an equal sign 😊) 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The equation E = mc² explains the relationship between energy and mass in physics. 𝗩𝗲𝗰𝘁𝗼𝗿 – A quantity in physics and mathematics that has both magnitude and direction, such as force or velocity 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The velocity of a moving car is represented as a vector because it has both speed and direction. 𝗖𝗼𝗺𝗽𝗼𝘂𝗻𝗱 – A substance made of two or more different elements chemically bonded together 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: Water (H₂O) is a compound made of hydrogen and oxygen. 𝗗𝗲𝗿𝗶𝘃𝗮𝘁𝗶𝗼𝗻 – The process of obtaining a formula or result from fundamental principles or existing equations 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The derivation of the quadratic formula involves completing the square. 𝗥𝗲𝗮𝗰𝘁𝗶𝗼𝗻 – A process in which substances interact to form new substances with different properties 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The reaction between vinegar and baking soda produces carbon dioxide gas.

𝗛𝘆𝗽𝗼𝘁𝗵𝗲𝘀𝗶𝘀 – A testable prediction or educated guess based on prior knowledge and observations 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The scientist proposed a hypothesis that increasing sunlight would boost plant growth. 𝗠𝗮𝘀𝘀 – The amount of matter in an object, usually measured in kilograms or grams 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The mass of an object remains the same regardless of its location in the universe. 𝗖𝗲𝗹𝗹 – The basic unit of life in all living organisms 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: Red blood cells transport oxygen throughout the human body. 𝗧𝗵𝗲𝗼𝗿𝘆 – A well-substantiated explanation of an aspect of the natural world, supported by evidence and experimentation 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: The theory of evolution explains how species change over time due to natural selection. 𝗚𝗿𝗮𝘃𝗶𝘁𝘆 – A force that attracts objects with mass toward one another, such as the Earth pulling objects downward 𝙎𝙖𝙢𝙥𝙡𝙚 𝙎𝙚𝙣𝙩𝙚𝙣𝙘𝙚: Gravity keeps planets in orbit around the sun. 𝑼𝒏𝒕𝒊𝒍 𝒐𝒖𝒓 𝒏𝒆𝒙𝒕 𝒘𝒐𝒏𝒅𝒆𝒓! 😉

[vaasuki1359]

Best Website for Digital SAT Math Questions

Preparing for the SAT is a significant step in a student’s academic journey. The math section, in particular, can be a challenging hurdle, but with the right resources, it becomes much more manageable. In the digital age, having access to quality digital SAT math questions is crucial. This blog will guide you through the best website for finding digital SAT math practice questions, with a focus on LearnQ.ai, and provide detailed insights into the types of questions you can expect on the SAT. We'll also share tips and strategies to help you master the math section.

What Are the SAT Math Topics?

The SAT math section covers a range of topics, organized into four major categories by the College Board. Understanding these topics is essential for effective preparation.

1. Algebra

This category includes 13-15 questions on:

Linear equations

Systems of linear equations

Linear functions

Linear inequalities

2. Advanced Math

Also comprising 13-15 questions, this section covers:

Quadratic and polynomial functions

Exponents and roots

Rational expressions and equations

3. Problem-Solving and Data Analysis

With 5-7 questions, this area includes:

Ratios, rates, and proportions

Percentages

Probability

Scatterplots

Statistical inference

4. Geometry and Trigonometry

This category, with 5-7 questions, includes:

Area and volume

Lines, angles, and triangles

Right triangles and trigonometry

Circles

The Question Types in SAT Math

The SAT math section features two main types of questions:

Multiple-Choice Questions

There are 33 multiple-choice math questions on the digital SAT. These questions present four answer choices, differing from the traditional five-choice format seen in many academic tests. Despite this difference, the fundamental approach to solving them remains the same: identify the correct answer from the provided options.

Student-Produced Response Questions

Student-produced response questions, also known as grid-ins, account for 11 out of the 44 math questions. In the digital SAT, you’ll enter your answers into a box on the computer screen. These responses can be negative numbers, a change from the paper version of the SAT.

Important Rules for Entering Responses:

Enter only one answer, even if multiple solutions are possible.

A positive answer can be up to 5 digits in the exam; a negative answer can be up to 6 digits, including the negative sign.

Reduce fractional answers or express them as decimals if they exceed the available space.

Truncate or round decimal answers at the fourth digit if necessary.

Enter the mixed numbers as improper fractions.

Avoid using symbols like commas, percent signs, or dollar signs.

Approaching Algebra SAT Math Questions

Algebra questions can be mastered with the right approach. Here’s a step-by-step guide to tackle them with confidence:

Breaking Down the Problem Statement

Read and understand the problem statement thoroughly. Identify what is being asked and note down the relevant information provided.

Identifying Knowns and Unknowns

Distinguish between known quantities and unknown variables. This clarity helps in setting up the equations correctly.

Applying Algebraic Operations to Solve Equations

Use digital SAT algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable and solve the equation.

Checking Solutions for Accuracy

Always check your solutions by substituting the value back into the original equation to ensure it satisfies all conditions.

Comprehensive Suite Of AI Tools To Boost Digital SAT Score

#1 AI Tools For Guranteed SAT Score Boost. 24/7 AI Tutor For Personalized Help, 10,000+ Fresh SAT Questions To Practice. Get Free Personalized SAT Study Plan!

Keywords: #digitalsat, #satexamscore, #digitalsatinUSA, #satonline, #satscore, #satclassesonline, #digitalsattraining

[techtrends-today]

How to Sign Up for the Maths Olympiad - Enrolling Made Easy

The Indian National Mathematical Olympiad (INMO) is a top-notch math competition for high schoolers in India, running since 1989. Hosted by the Homi Bhabha Centre for Science Education, it's a big deal for students after the tenth grade. Starting with the Regional Mathematical Olympiad (RMO) and leading up to the International Mathematical Olympiad (IMO), each stage gets students one step closer to global fame. Ready to flex those brain muscles of your child?

Steps of the Maths Olympiad

Want to ace the Maths Olympiad? Here's the scoop:

Process 1: IOQM (Indian Olympiad Qualifier in Mathematics)

Kick-off with a 3-hour quiz featuring 30 multiple-choice questions. Just fill in your answers on an OMR sheet—easy, right?

Process 2: INMO (Indian National Mathematics Olympiad)

This stage features six challenging questions over a four-hour period. Solutions must be written on a response script and submitted with rough sheets at the end of the test.

Process 3: OCSC (Orientation Cum Selection Camp)

Top performers from the INMO, approximately 35 students, are invited to the International Mathematical Olympiad Training Camp (IMOTC). This camp prepares students for the IMO.

Process 4: PDT (Pre-Departure Training Camp)

Six top-performing students from IMOTC receive intense training for 8-10 days. Top-notch gurus from all corners of the country whip these students into shape for the IMO showdown.

Step 5: The Big Math Showdown (International Mathematics Olympiad)

In this last stage, teams from more than 100 countries face off. Each team has up to six brainy students, plus their leaders and mentors.

Eligibility

To take the INMO exam, students need to ace the first level. Simple as that!

Typically, around 30 students from classes 8 through 12, including five female candidates fulfilling the girls’ quota, are shortlisted. Special provisions exist for students from KV schools outside India who can bypass the selection process, although 12th-grade girls in KVs are not eligible for the girls' quota.

Syllabus

The INMO syllabus includes advanced topics such as:

Arithmetic of Integers

Geometry

Quadratic Equations & Expressions

Trigonometry

Coordinate Geometry

Systems of Linear Equations

Permutations & Combinations

Inequalities

Elementary Combinatorics

Probability Theory

Number Theory

Finite Series & Complex Numbers

Elementary Graph Theory

Polynomial Factorization

How to Enroll in the Maths Olympiad

Through Schools

Students can access the IMO Registration Form via their schools. Registered schools receive a prospectus and registration paperwork. Schools not registered can request a prospectus via the SOF website.

Through Mentorship Programs

Enrolling through a mentorship program like Sri Chaitanya’s Early Champions Advantage can provide significant benefits. Their carefully crafted curriculum, built on years of research, tackles the unique hurdles students face in Olympiads like a pro.

Conclusion

Joining the Maths Olympiad isn’t just about winning trophies; it’s about getting really good at math and solving tricky problems. Taking that first step can be scary, but with the right help, students can shine. Need a boost? Check out programs that give students a leg up in every part of the Maths Olympiad journey. Start your journey today and take your mathematical skills to new heights!

[pillow-anime-talk]

two tiny notes.

request: i’m back~ finished saiki k recently, so could i have one where top student reader has a crush on kaidou but since she sees yumehara get close to him, she believes she has no chance and starts acting weird... ofc, no one notices except her childhood friend saiki! which is why kusu-chin (idk i feel like reader would call him that) helps her w/o her knowing (because ���it’s troublesome if y/n acts weird”) even though he’s aware that kaidou already likes her back -- cherry anon

# tags: scenario; friendship & crush culture; fluff; some kind of angst, i guess; mild romance; sfw

includes: female reader ft. kaidou shun & kusuo saiki {saiki k. no psi nan}

author’s note: aaa, hello cherry, i missed you! hope you like it :( 

You sighed softly, looking at Kaidou who was just solving (or rather trying to solve) a math and quadratic equations problems. Obviously, you wanted to offer your help during the next break, but as soon as the bell announced to all students about lunchtime, Yumehara overtook you and offered the boy to solve the calculations together. You muttered something incomprehensible under your breath and went back to reading your thick, brown book, which you always carried with you to keep your mind occupied with something interesting between classes.

“Eat something. Your mom made your favorite omelettes and steamed vegetables.” Your best friend’s composed voice reached your mind, and you just shrugged without even looking in his direction.

“I don’t feel like it right now, Kusu-chin. I will eat them at home after lessons.” You answered him in your head and then you went back to your crime novel written by your favorite author. Naturally, from time to time your gaze landed on the figure of a blue-haired boy and a girl with flushed cheeks, which made you feel a strange, even stupid heaviness and sadness on your stomach. But you shook your head quickly as you read the next sentence.

Meanwhile, your dearest friend rolled his both eyes, looking at you, then at a young boy slightly shorter than him, whose likeability meter towards Chiyo didn’t exceed even half the full number.

Not that Saiki had any interest in helping you... he just didn’t want to hear you grumble on the way home and your sad voice on the phone call. It’s not like he was worried or anything... Yeah, he just wanted to spend the next few days in peace without worrying that something would snatch him out of his comfort bubble or interrupt him when he will play on the console.

{ ･ﾟ✧ }

The days passed very quietly and you made a decision to slowly step back from your relation with Kaidou; when the boy asked what time it was, you said that you didn’t have a watch with you, even though you were holding the smartphone in your left hand, when the teenager invited you for ramen or to a cafe for your favorite sweets, you excused yourself that you had to help your mother make dinner, and at moments when the red-eyed young man offered to walk you home, you announced that you had to go to grandma, to clean her bathroom or kitchen. Of course, you meant your grandmother, who didn’t even live in Japan... Well.

Kusuo looked at it with a blank expression on his face, not knowing whether to laugh or cry at the fact that the person you liked was reciprocating these feelings, but you considered them as only friendly gestures. The image of Yumehara and smiling Shun kept appearing in your head, making your heart clench painfully and literally bleeding ‘cause that sweet smile wasn’t directed at you, but at another, really cute girl. Your pink-haired friend didn’t like to help others, but he always did everything in his power to make people around him a better life; no matter if it was his grandfather, Amp, Reita or you. All relatives were important to Saiki, and you, as his best female friend, have been practically at the top of this ‘hierarchy’ for years.

Therefore, he swallowed his saliva and counterfeited your pretty handwriting without much problem by writing a small note to Kaidou with the place and time of the meeting. He did the same the other way around, changing his handwriting to that of Shun’s. Then two smol envelopes landed in your school lockers between your books and spare pencils.

It was a very good plan; a plan that couldn’t go wrong. Kusuo even made sure that in the event of an accident, the envelope fell out in front of your shoes so you could pick it up and read its contents. Of course, you went to the meeting place, because firstly, you were curious about what was important, and secondly, it was signed by someone you still cared about damn much, even if you avoided a sixteen-year-old boy like fire.

Your heart was beating so fast and your cheeks looked more ruddy than normal when you saw Kaidou under the cherry tree which was covered with fluffy, white snow.

“Y/N-chan...! Here!”

“Hello, Kaidou-kun.”

The likeability meters next to your heads were equal to one hundred percent.

‘... The hearts at the ends of the notes were enough?’ A high school student with green glasses thought, but then nodded a little. ‘Sometimes I don’t understand the idea of ​​love and all my friends.’

The boy smirked, happy to leave the two of you alone. As the gentleman he was, he didn’t want to disturb your confessions... and he knew perfectly well that you would come to his house shortly after that to tell him about what happened under the big tree. He just had to wait, prepare two cups of hot tea and your favorite snacks. 

Even if your Kusu-chan didn’t show it, he wanted the best for you (and others besties) because you were the most important person for him.

[perfectlytinyworkspace]

motion in two dimensions

independent orthogonal forces

forces that drive motion can only act in a single direction

one occurrence of 2-D motion = 2 single-direction, orthogonal/perpendicular forces x and y 

allows break down of 2-D motion into x and y when solving problems

vectors

describe x, v, a and other physical quantities with magnitude + direction, allowing for calculations in which these quantities are 2-D

magnitude: expressed with a scalar value u

direction: expressed with a unit vector u-hat, scalar value = 1

transform/translate vectors to solve problems without affecting core properties

multiplying by constant c keeps direction, stretches magnitude

shifting vector in parallel along x- and y-axes keeps direction and magnitude, changes position

-u keeps magnitude, changes direction to opposite

vector components and addition

use descriptions of physical quantities provided by vector definitions to perform 2-D calculations

1. transform vectors to operate on them

add vectors by moving in parallel until tip of one vector term meets tail of the other

subtract vectors by translating subtracted vector to its negative opposite and adding

2. to find the sum of 2-D vectors, break down arguments into their x- and y-components and add them independently:

(A+B)x = Ax + Bx 

(A+B)y = Ay + By

and to find the x- and y-component values, use trigonometry with vector angles from the origin and x-axis:

Ax = A • cos(angle A) | Ay = A • sin(angle A)

Bx = B • cos(angle B) | By = B • sin(angle B)

3. to find the scalar magnitude of a vector A, find its x- and y-components and utilize Pythagorean Theorem

projectile motion

freefall - motion that is influenced only by constant gravitational acceleration

projectile motion - the trajectory followed by an object in freefall after it has been launched with a 2-D initial velocity

2-D velocity vector can be broken down into x- and y-components

velocity relates displacement and time; thus displacement is also broken down into x-displacement and y-displacement

to solve for various quantities of an object’s projectile motion, break fundamental constant acceleration equations  down by x and y to utilize the fundamental projectile motion equations

finding x- and y-components using angles may necessitate trigonometric identities and the quadratic formula

solve for shared x- and y-terms and substitute variable equivalences from one equation into the other to eliminate unknowns

uniform circular motion 

1. any change in velocity results in a nonzero acceleration

velocity is direction + magnitude, hence change in v direction results in nonzero a even if magnitude remains the same

in circular rotational motion, velocity has constant magnitude but ever-changing direction

rotational motion has nonzero acceleration even when velocity remains constant throughout time interval

2. velocity is 2-D and can be broken down into x- and y-components, which are then derived to find x- and y-acceleration

v = vx + vy 

apply product rule of derivation: v’ = a = dvx/dt + dvy/dt

angle θ made between v and rotational displacement x remains constant

3. for rotational motion x-acceleration = 0, but y-acceleration’s sign changes. Taking the derivative of v(y) with limit as t → 0 takes sin and cos out of equation and gives us a nonzero rotational acceleration expression 

4. in the circle, the radius vector r points outward towards the circumference. The nonzero rotational acceleration expression equates acceleration to v/r • - (r-hat) and thus acceleration points in the opposite direction of the radius vector, -r, which points inward towards the circle’s center

[astrognossienne]

the four quadrants of a natal chart

Building on the concept of hemispheres, is the lesser-known astrological concept of quadrants, which essentially, are four segments of an astrological chart. The quadrant encompasses three houses/signs. Looking at a natal chart through the quadrant method can also be an alternative to using common house systems. Personally, I favour the Placidus system, but regardless of what house system you use, honestly, no one house system will be totally accurate on its own. Anyway, as detailed in the hemispheres post, the chart is divided into two sets of hemispheres; the northern/southern, and the eastern/western. Quadratic emphasis is achieved when six or more planets are concentrated in a certain quadrant. This emphasis can either be northeastern, northwestern, southeastern, or southwestern. Here is an explanation of the quadrants’ significance on a person’s disposition:

I-III: is the quadrant of the awareness of self; this quadrant is comprised of houses one through three. It is also known as the spring quadrant, or the northeastern hemisphere. It’s led by the ascendant (ASC), or the first house, the house of Aries.

1st house: me and my identity

2nd house: my values and self-worth

3rd house: my thoughts and communication

This individual is predisposed to being more distrustful, self-reliant, and autonomous. The individual is expected to integrate personality with self-worth, value systems and communication. This is a person who built themselves from the ground up. They look inward. Emphasis is put on self-awareness and focusing on what the individual needs with lots of time being alone doing what they want. They can have trouble seeing others’ points of view and have a subjective outlook on life.

IV-VI: the quadrant of merging with your immediate environment; this quadrant is comprised of houses four through six. It is also known as the summer quadrant, or the northwestern hemisphere. It’s led by the imum coeli (IC), or the fourth house, the house of Cancer.

4th house: concern is given to the family and domestic situation

5th house: concern is given to creativity

6th house: concern is given to cooperation and working with others

This individual is predisposed to being more self-expressive, creative, thoughtful, and innovative. They have a developed awareness of people outside themselves, manly those in their inner circle and work environment. This individual defines themselves through their relationships with others and they’re strongly influenced by the people in their life, particularly children, their family and co-workers. These individuals are the most complex out of all the quadrants and can be emotionally taxing on their loved ones. They’re paradoxical because they want to take risks without rocking the boat. Tends to be very well-liked and popular.

VII-IX: the quadrant of the awareness of others; this quadrant is comprised of houses seven through nine. It is also known as the autumn quadrant, or the southeastern hemisphere. It’s led by the descendant (DSC), or the seventh house, the house of Libra.

7th house: the individual needs to connect with others in order to establish partnerships/relationships

8th house: the individual needs to connect with others intimately in order to experience the totality of human emotions

9th house: the individual needs to connect with others in order to explore ways of thinking and relating to others different from themselves

This individual is predisposed to being social yet highly self-contained and in control of their destiny. They’re interested in putting aside the self in order for meaningful interactions with others, whether it be an exchange of ideas, bodily fluids, or cultures. Relationships, partnerships, intimacy, life and death, psychology, world philosophy and discovering what they lust for and desire the most are areas of importance. They look outward. Sharing, merging and balancing themselves with others gives them fulfillment and keeps them vital. Their energy is such that they’re rarely alone, whether they like it or not.

X-XII: the quadrant of merging with society at large; this quadrant is comprised of houses ten through twelve. It is also known as the winter quadrant, or the southwestern hemisphere. It’s led by the midheaven (MC), or the tenth house, the house of Capricorn.

10th house: the person needs to be a part of society in order to achieve, succeed, and have others see them as an authority

11th house: the person needs to be a part of society in order to espouse ideas that will help humanity and promote friendship

12th house: the person needs to be a part of society in order to give help and compassion to others

This individual is predisposed to contribute to society in some way, shape or form. With them, it's about everyone, not just themselves. Theirs is a public life and they naturally attract the spotlight, whether they like it or not. Focus is put on their reputation, altruism, and the realization of their dreams. They see themselves in relation to others, whether it be groups in general, their friends, or the world at large. They long to project their achievements, ideas, and/or creativity in order to simultaneously serve the greater good and ensure that they leave a legacy. Others tend to drain them of their energy and resources; nonetheless, success comes to them when they give of themselves.  

[bravebatgirl]

NEW CHAPTER OF AWAE POST S3 FIC UP -- Chapter 6: Marigold

Summary:  The girls are busy preparing for upcoming assessments, when a surprise visitor comes a'knocking on the door. However, things are not all that they appear, and tensions rise amongst the fervent feelings of passion.

preview below:

Heaving a contented sigh, she’d just begun to sit when a knock upon the front door stopped her in her tracks. Her brows furrowed and she glanced around at the others, even more so perplexed as to see their own confused expressions. It was a Saturday, very nearly two p.m. but none of them had arranged to meet with any of their suitors.

At that moment, Lily came swiftly through the kitchen and passed the girls, signing to Anne that she’d answer the door and the rest of them could continue studying. The redhead in smiled in response, sitting down and pulling out her fountain pen once more, tapping the end of it against her bottom lip as she glared at the a’s and b’s and c’s that refused to be coherent to her. Damned quadratic equations, she thought with a growl, drowning out all distractions as she put her entire energy into trying to make sense of the questions before her.

Not a minute later, Lily came bustling through again, and Anne glanced up to see a quiet, knowing smile on her face. To what she knew, Anne hadn’t the first clue. The brunette’s gaze flickered to the door once more, brows quirking up at whoever was beyond the mahogany frame, before glancing back at the young redhead with a smirk. Anne wondered if she’d ever seen the lovely young servant-girl smirk so mischievously. She shook her head in confusion at her, raising her hands up in a ‘what’ gesture. Then, finally, she watched as the girl began to sign, ‘it’s for you. I’d suggest going quickly before the others catch on or Mrs Blackmore sees you’. Anne suddenly became very pleased that she was the sole person of her friendship circle who knew how to decipher the silent language.

Clearing her throat surreptitiously, she rose from her chair and made a show of stretching. “Excuse me a moment, ladies; just going to relieve myself. I’ll be back shortly.”

“Okay”, Josie casually muttered back, eyes glued to the pages. “Let us know who’s at the front when you go past.”

“I, uh… sure”, she said, walking backwards toward the hallway. Diana’s eye came up to meet hers, gaze narrowed suspiciously. Anne shook her head unknowing back at her, mouthing ‘I don’t know. Honest’. She gave one last uneasy smile before wheeling around the corner, coming to face the opened front door, and pulling up short, completely and utterly frozen. Her eyes widened impossibly large, drinking in the person before her; her mouth working, scrabbling for words but to no avail. It felt like time had stopped in a wonderful moment of starstruck, disbelieving reverence.

“Anne”, the man breathed out, like a silent prayer to the wind. Like her name was the most sacred thing in existence. If she heard him say it like that every time, she might very well just start believing it.

“You’re…”, she choked out, swallowing thickly as she dared to take a step forward, “You’re here.”

[lovemesomesurveys]

A How artistic are you? I’m not at all. Do you want to go to Africa? I’d love to stay at Giraffe Manor! AC/DC or Aerosmith? Aerosmith. 
Do you know what Armenia is?
  Yes.

B
 What’s your beer of choice (if any)?  Blech, none. Do you know the title of Buffalo Springfield’s one-hit wonder?  Okay, I didn’t recognize the name so I Googled it and yes, I am familiar with their one hit wonder. I actually wasn’t familiar with the song title either, but after reading the lyrics I quickly realized what song it was. Do you have a brother? (Do you like it that way?) I have two brothers, and yes I love them. Which bank do you use?  Not sharing that. C
 Which comedian do you most enjoy?  I think Kevin Hart is funny. Would you ever live in California?  I have all my life. Is it possible/likely that you’ll become a cat lady?  *Dog lady, but yes. How many different countries have visited? Just one. D
 Do you believe there’s a devil? Yes. But demons maybe?  Yes. Does eating dessert often make you feel guilty?  Nope. Can you legally drive?  I’m definitely old enough to have my license, but I don’t.  What have you been diagnosed with (if you don’t mind sharing)? Depression, anxiety, and other physical health stuff. E
 How often do you drink energy drinks?  I like to drink Starbucks Doubleshot energy drinks often. 
Where did you live when you were 11 years old? The house next door to where I live now, ha. We had our big move to the house next door to us haha about 10 years ago because our landlords wanted to install new flooring and stuff to our house, but since they had just finished this one they offered for us to just move in here lol. Do you like the actor who played Edward Scissorhands in that movie?
 Why not just say Johnny Depp? Anyway, yes, I think he’s a very talented actor. Have you ever felt an earthquake?  No, just aftershocks from one. F
 When was the last time you saw your father one-on-one? Yesterday. Do you think French is the most beautiful language?  I don’t know what I’d say is the most beautiful language. Is Friday your favorite day of the week?  No. All the days are the same for me, so meh. Have you listened to Jimi’s song ‘Fire?’  Doesn’t sound familiar. G
 Do you have real gold jewelry?  No. How often do you watch ‘Gossip Girl’?  I never have. Is Google your homepage?  Yeah. 
Do you like Geico’s commercials? Most of them are annoying. The gecko character is cute, though. H
 When did you last feel happy? Uhhh. Do you prefer Hollister, Hot Topic, or H&M?  Hot Topic is the only one I shop at now, but I used to shop at the other 2 as well. Did you dress up last Halloween?  Nope. I stopped doing that a few years ago. Would you voluntarily watch the History Channel?  Yeah and I do if there’s something of interest on. I
 Have you ever been on an island?  No. I live on one in Animal Crossing, though. ha. Would you be able to locate Indonesia on a globe?  I think so. Do you know if Iceland or Greenland has more ice?  Greenland. I remember it’s the opposite of their name for some reason. 
Did you watch the last presidential inauguration?  No. J
 Do you enjoy jogging?  No. On which instrument could you most easily play ‘Jingle Bells’?  I’ve played it on the piano. How much do you know about John Lennon? *shrug* I know some stuff. Do you know how Jell-O is made?  I know how to make Jell-O with the mix, but no I don’t know how the mix itself is made. K
 Have you tried Krispy Kreme doughnuts? (Was it love at first bite?) Yeah, but no they’re definitely not my favorite. They’re not real donuts to me, they’re just pure sugar.  
How many pairs of khaki pants do you own? “Uh, khakis?” ha, if you know, you know. Anyway, I don’t own any. 
Have you ever been a fan of the Killers?  Yeah. L
 Does it bother you when couples are lovey-dovey in public? No, unless they’re having like full on makeout sessions, straddling each other and feeling each other up and whatnot lol. Hand holding/locked arms/arm around each other, hugging, little pecks, and just being playful with each other is cute.  
Do you have your own lighter (why or why not)?  No. I don’t have a need for one. In how many languages (besides English) can you count to 100?  I can in Spanish. What’s your favorite lollipop flavor? Not a lollipop fan. M
 Do you believe in miracles (why or why not)? I do because I'm a woman of faith. What do you think of shows like Maury and Jerry Springer? I used to like watching Maury, Jerry Springer was just for laughs.  
Do you care that Mars (the candy co.) uses deadly animal testing? I haven’t heard that... I’d have to fact check. How did you form your opinion of marijuana? Based off the research supporting that it has a lot of benefits. I was especially swayed when I saw how it helped cancer patients.

N
 How often do you sleep naked?  Never. I wouldn’t find that comfortable at all, I very much like being clothed.  Do you actually check the Nutrition Facts before eating something?  Not usually, but I sometimes will just out of curiosity. 
Who is your favorite musical artist/band beginning with ‘N’? Nirvana. 
How nerdy are you (in what ways)? I’m socially awkward, for one. I also cared about school and did well, which is often considered nerdy. Also, a book nerd, Star Wars nerd, Marvel and DC movies nerd...  I enjoy those things so I don’t care, but they’re deemed “nerdy.” What do you think about olives?  Black olives are good, green olives are gross. Are you much of an outdoorsy person? Not at all. The only time I enjoy being outside is when I’m sitting out at the beach. How big of an Oprah fan are you?  I don’t really consider myself a fan. How often do you shop online?
  Quite often. P
 Are you looking forward to your prom? If you already went, how was it? My prom was over a decade ago D: Anyway,  I danced with the guy I had a huge crush on at the time, so hey it wasn’t too bad. How are your local policemen? I think they do a pretty good job overall.  What is your ideal PB&J sandwich like? Just peanut butter and grape jelly, pretty simple. What do you think of the movie ‘Pineapple Express’? I could not get into that movie at all.  Q
 How true is the saying, ‘quitters never win and winners never quit’?  I mean, can’t say “never”, but the main point from the saying makes sense. Do you prefer Quiznos or Subway and why?  I’ve gone to Subway many times, but I think I’ve only been to a Quiznos once or twice. Have you learned the quadratic formula yet? (Do you remember it?) I think I actually remember it. What is the one question you most want to ask someone and who?
  I don’t know. R
 How many rooms are in your home?  2 bedrooms. 
Do you like raspberries?
  Nah. What’s one of your best memories from during a rain storm? Hmm. I don’t know, but I just really love that kind of weather. 
Have you actually read Shakespeare’s ‘Romeo & Juliet’?  Yeah, my freshman year in high school. S
 Do you know any Sign Language?  I know the alphabet and a few sayings. What is your sleeping schedule generally like?  Oh, my sleeping schedule is an absolute joke. How well do you sing? I can’t sing well at all. How often do you listen to 60-70’s music? Now and then. I actually have several songs on my main Spotify playlist from those decades. T What do you think of Twitter?  I like being able to post my random thoughts and following certain celebrities and just interesting people for funny and interesting stuff. How much do you value the Ten Commandments?  I value them a lot. Are there many trees where you live?  Not really. 
How much taller/shorter do you wish to be? “I wish I was a little bit taller.” 🎶

U
 Where do you usually buy your underwear?  Various places. How do you define ‘ugly’?  It goes a lot deeper than just the outer appearance. Do you like to shop at Urban Outfitters?  I’ve only been to an actual store a couple times and I’ve checked out their website a few times, but I just think they’re ridiculously overpriced. V
 Would you like being described as ‘voluptuous’? No one would use that word to describe me. 
For listening to music, do you like to crank up the volume or keep it calm? I like it at a reasonable level, I don’t need it blaring.  Do you ever watch the annual Victoria’s Secret fashion show? They cancelled that a few years ago, but I never had any interest in watching that. 
Would you agree that ‘variety is the spice of life’?  Yeah. W
 Are you currently on wireless Internet?  Yeah, that’s all I have. I haven’t had to connect to a wifi router or whatever with a cord in a very long time. Can you recall memories of learning how to whistle? I still can’t do it. Do you go to White Castle or just vicariously through ‘Harold & Kumar'? I’ve never actually been to one cause they don’t have one anywhere near me (they’re on the east coast, I’m a west coast gal). I’ve only had the the White Castle burgers from the store that you cook in the microwave. I actually like them, but I’m sure the real deal is even better. X
 Why did you need your most recent x-ray and what were the results? I had to get a CT Scan a couple years ago. When it comes to ‘xoxo’, do you interpret ‘x’ as the hug or the kiss?  It’s hugs and kisses, so the X’s are hugs. What does X stand for in Roman numerals? Can you write the previous number?  X is 10, IX is 9. Why do you think xylophones are only popular with young children? That’s true, that is a pretty common baby toy. At least it was when I was little. Also, I played the xylophone in music class in elementary school. I don’t know why that’s a thing with kids. Y
 Can you explain the meaning of the yin-yang symbol? Opposite, but complimentary principles. Like, you can’t have good without bad, lightness without darkness, etc. It’s about balance. Do people more often mistake you as being younger or older than you are? Younger. Did you know that yawning is contagious?  Yeah.  Would you like a bottle of Yoo-Hoo or it’s not really your thing?  I actually like Yoo-Hoo, but I prefer it in the little carton or whatever with the straw (kinda like a Capri Sun, but it’s a box carton). It’s the perfect size, not too much. The strawberry one is my favorite. I haven’t had one in a long time, though. Z
 How many places’ zip codes do you know by heart?  Uhh, not many. What comes to mind when I say ‘Zero to Hero’? Disney’s Hercules movie.

[vamsi2020]

QUADRATIC EQUATIONS / VIDEO - 3 / SIGN CHANGE OF QUADRATIC EXPRESSION / ...

[emilyelizabethfowl]

the father of this house is an emotional vampire.

it's not easy to notice, but once you do, it becomes incredibly obvious whenever it happens.

one of the major signs is the boredly confused expression on his victim's face.

for example: today, little sister brought quadratic sequences as her homework.

free fact: i have never seen those before, and she's only 11. either it's something new, or Poland's curricullum just omits them completely.

she explained what you're meant to do to me: find the differences between the numbers in the sequence, and when you've got a second sequence of those, find the difference between them as well. then plug the numbers into corresponding formulas - 2a equals first bottom row number, 3a plus b equals first middle row number, a plus b plus c equals first front row number - and compile those values into a standart T(n)=an^2+bn+c formula.

all fun and giggles, i do the examples alongside her, but then she stumbles upon a problem born of stuborness and tiredom - she does not understand she has to plug the numbers - 1 and 2 at least - into the formula to check if she's got it right (despite her claims, she hadn't. 3rn and 7th example had a descending sequence.).

at this point, father of the house steps in. he starts lecturing her - i missed the first half, but when i came back in, he was somehow on how she had to check a bunch of random numbers - like 0, negative 1 or 6.7 - against the formula.

why, i ask? why does she need to do that right now? it's not necessary.

i don't care, foth says. she has to do that.

he caries on with his lecture.

i glance at little sister. she's got her chin on her hand, and an expression of bored confusion on her face.

i realize i hold exactly the same stance and face.

i no longer feel as excited about quadratic sequences as i had just moments ago. little sister probably doesn't either.

great job, foth. that's exactly what you meant to do, i'm certain. nothing going wrong around here.

[myheartsbeenachingbut]

If I am having a brain fart over forgetting a negative sign on a quadratic expression then these people are having diarrhea over not knowing that Spain exists

And he goes, “What are you?”     Which is fucking rude.

[mademains]

Quadratic inequalities

#QUADRATIC INEQUALITIES HOW TO#

To be neat, the smaller number should be on the left, and the larger on the right. The distance we want is from 10 m to 15 m: (Note: if you are curious about the formula, it is simplified from d = d 0 + v 0t + ½a 0t 2, where d 0=20 , We can use this formula for distance and time: We also know the endpoints are excluded since 3 creates a denominator of zero and we have a strict inequality.A stuntman will jump off a 20 m building.Ī high-speed camera is ready to film him between 15 m and 10 m above the ground. $$(-2)^2 - 5(-2) - 6 > 0$$ $$4 + 10 - 6 > 0$$ $$ equire$$ Since the test of the number 4 produces a false statement, we know values that are greater than 4 will not satisfy the inequality. Let's choose -2, we will plug this in for x in the original inequality. We can solve quadratic inequalities to give a range of. Let's begin with interval A, we can choose any value that is less than -1. Quadratic inequalities are similar to quadratic equations and when plotted they display a parabola. Step 3) Substitute a test number from each interval into the original inequality. This interval is labeled with the letter "C". The solution to a quadratic inequality in one variable can have no values, one value or. Let us consider the quadratic inequality x2 5x Lastly, we have an interval that consists of any number that is greater than 6. The standard quadratic equation becomes an inequality if it is represented as ax2 + bx + c 0).

This interval is labeled with the letter "B". One interval contains any number less than -1 and is labeled with the letter "A". Quadratic Inequalities Given 3 x 2 > -x + 4 Rewrite the inequality with one side equal to zero. On the horizontal number line, we can set up three intervals: We have split the number line up into three intervals. It shows the data which is not equal in graph form. Introduces a conceptual basis for solving quadratic inequalities, looking at linear inequalities and using a knowledge of what quadratic graphs look like. An equation is a statement that asserts the equality of two expressions and a linear inequality is an inequality which involves a linear function. These endpoints will allow us to set up intervals on the number line. In quadratic inequalities worksheets, we learn that a quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Therefore, set the function equal to zero and solve. For a quadratic inequality in standard form, the critical numbers are the roots. $$x^2 - 5x - 6 > 0$$ Step 1) We will change this inequality into an equality and solve for x. It is important to note that this quadratic inequality is in standard form, with zero on one side of the inequality.

The endpoints are included for a non-strict inequality and excluded for a strict inequalityĮxample 1: Solve each inequality.

If a test number makes the inequality false, the region that includes that test number is not in the solution set.

If the test number makes the inequality true, the region that includes that test number is in the solution set.

If it is less than or greater than some number or any other polynomial. Consider a quadratic polynomial ax2+bx+c.

Substitute a test number from each interval into the original inequality Graphing a quadratic inequality is easier than you might think You just need to know the steps involved This tutorial takes you through those steps to. What do you mean by Quadratic inequalities.

For example, to solve a quadratic inequality -x2+x+2>0, we can find the values of x where the parabola.

Use the endpoints to set up intervals on the number line Students will solve quadratic inequalities and match each inequality with its solution set. Quadratic inequalities are best visualized in the plane.

These endpoints separate the solution regions from the non-solution regions.

If the quadratic inequality is not in one of the. is an example of a quadratic inequality, as it contains a single variable raised to the second power at maximum.

The solutions will give us the boundary points or endpoints Hence, we obtain four possible general forms of quadratic inequalities: ax 2 + bx + c > 0.

Replace the inequality symbol with an equality symbol and solve the equation.

Quadratic Inequalities A quadratic inequality is of the form: $$ax^2 + bx + c > 0$$ Where a ≠ 0, and our ">" can be replaced with any inequality symbol.

#QUADRATIC INEQUALITIES HOW TO#

In this lesson, we will learn how to solve quadratic and rational inequalities.