"I'm Lemma Pumping, Nice to meet you." Lemma, having learned a lot from her father's stories and books he brought from public libraries enabled her to accelerate into this grade for her first day at school.

"Lemma Pumping? What a weird name! Why does she look like 9?!" Everyone in the classroom laughed. 

"Sit there on the corner next to the window." As she walked towards her seat, everyone just stared at her in silence until she sat down. Being from the slums, it was her first time feeling the cold air from an air conditioner, making her sneeze. Looking at her surroundings gets her an idea of what her class is, where most of them look far older than she is. There were 12 students.

"Ackchie!" She, then, mumbled to herself, "Why would Dad put a sneeze function on me?" 

"She's so cute!!!" The girls in the classroom ran to her and hugged her tightly. 

"We will protect you!"

"Cute! You're so cute! Your skin is amazing!"

"Wowww! What's with your eyes?! Why are they blue?! White hair? Are you a foreigner?" 

"Hmph. Why are you people hugging that slumrat?" One of the guys in the classroom, tall and drab, told off the girls. "Her scent would stick into your clothes."

"Don't listen to him, Lemma. Lawrence is just scum." Lawrence Zy, 4th son of the Zy dynasty who owns the unstoppable ZM malls. Their family collectively has an estimated asset of about a trillion USD. Needless to say, his family owns this country. But Lemma didn't care about that, simply because she didn't know.

"What did you say to me, you fat punk?"

"Huh? Do you know who you're talking to?"

"Yeah. A fat punk."

They were butting heads immediately. Surprisingly, Yuuta, their classroom adviser, just watched with amusement. 

"I'm Lawrence Zy! Zy! I'm sure you know my name! My father will hear about this!"

"I have no idea what you're talking about, but my father will also hear about this!"

"UGH!" Both of them simultaneously uttered.

"Why do I have to sit next to this guy?" ,wondered Lemma, "Is this what school is supposed to be..." She gazed outside the window and saw children playing basketball, races on the track, and just a stream of people walking along the large roads of the campus.

"As you all might know, it is the duty of the Star Section to be the symbols of our society." In this academy, there are 5 regular sections and a Star Section per grade, where the best students are placed. To be in a Star Section means to be in the top 0.1% of the grade. This was the first instance a first-time student transferred to 4th grade.

"Just to repeat for Lemma, the top 3 students in Star Sections can jump 3 grades above. Oh, yeah. Pop Exam timeeeeeeeeeeeeeeeeee..." Yuuta pulls a lever behind him and test papers fell from the ceiling to each student's tables.

Given sin(A ± B) = sin A cos B ± cos A sin B and cos(A ± B) = cos A cos B ∓ sin A sin B, show that cos A sin B = 1/2 [sin(A + B) − sin(A − B)] and sin2 A = 1/2[1 − cos 2A].

It was a surprise math test.