1. Mathematics never hurt anyone, except when it did. It is incomparably powerful when trying to understand the modern world, but mathematical ideas need to exist alongside thinking from other disciplines.
The world is complex and interconnected. Reject bubbles of specialism.
2. Miss Buss made NLCS so that young women would be able to play the same games as their brothers, and with the same advantages.
Though today's society is fairer than ever before, it has been a man's world since the beginning of time and women are still woefully under-represented in public life and leadership roles. Society teaches women to underestimate their powers. You have the opportunity to lead the way.
By winning in whatever field you enter, you can change the rules of the game for the better.
3. Don't play life as though it is a game of Monopoly. Monopoly makes you a bad person. Furthermore, Mathematics tells us that cooperation is better for individuals as well as for the collective. Why not think of upcoming exams as an opportunity to work together?
Individual lives are full of struggle: "success is going from failure to failure with no loss of enthusiasm." So you should learn to rejoice - to really rejoice - in the success of other people.
Because that way, you get to win all the time.