I've had a similar experience, but it was with another Asian girl.
My parents are Chinese, and I was born and raised in Canada. In about the 11th grade, a girl who was born and raised in China moved to my town and joined our grade. She is two years older than me, but is in the same grade because she came to Canada only a couple years ago and needed time to learn English.
I can only understand and speak conversational Chinese; can't read or write it. I admire immigrant students because they become quite fluent in several languages and this girl could speak Cantonese, Mandarin and English (her English wasn't that bad when I met her). But she just made it her goal to compete with me. I had really good grades in High School in all my subjects (she was in every class I was), and she would without fail, ask me how I did on all of my exams. I would show her and she would snicker if mine was higher, or say she got the same. My school was small, and a lot of people did not do very well, so I never went to ask how they did, because I know they would ask how I did. But this girl, she would always come up to me and ask about my grades. She would always be shy about her age too. NOBODY found it a big deal that she was older than us, but she made it into a big deal. She even said, "I'm older, so I should be smarter".
Well anyway, I think I just made my own rant... but point being: there will be people competing with you, but you are not competing with them. If asked, I will reply and then go on with my day. Don't let things bother you too much.
I think the stereotype for Asians arises from the high expectations of immigrant parents for their children. In a lot of cases, the immigrant parents were doctors, engineers etc in their home country, but their license and degrees mean nothing when they come to the West. They came to the West for better conditions for their children and hope for them to be doctors, lawyers etc while they take on a new job of perhaps restaurant owner, or doing labour-intense jobs. The math thing is probably because math is taught earlier, faster, and more intense than it is here in North America. I remember my Malaysian friend saying he did algebra in elementary school.
And grades are important in High school. It can determine what scholarships you can receive when you graduate. I'm in Canada, and getting into most Universities is pretty easy and they basically only consider your high school grades (other exceptions), but I'm not sure about the U.S since you have to take the SATs.
Edit: Yeah, just do what Jare said.