HYPS… type colleges often have a variety of levels of the larger lower level classes to accommodate students of different academic backgrounds, abilities, and long term goals. Most also have freshman take a placement exam in multiple areas, which gives a recommendation of which course to choose. Students who want extra rigorous and challenging classes can choose them, and students who don’t want to risk taking anything much beyond AP level can also choose less rigorous options. For example, a partial list of possible math classes a freshman might choose at Stanford are below. If you want a really rigorous treatment of the material, you can take math 61DM. If you don’t want that rigorous level , you can instead choose Math 19, which sounds like it is not much above AP level.
Math 19-21 – 3 quarter version of single variable calculus
Math 41-42 – 2 quarter version of single variable calculus
Math 51-53 – differential and integral calculus in several variables, linear algebra, and ordinary differential equations
Math 61-63M – covers the material of the Math 50 series at a much more advanced level with an emphasis on rigorous proofs and conceptual arguments
Math 61-63DM – covers the same linear algebra material as the Math 60CM series and otherwise focuses on topics in discrete mathematics, algebra, and probability theory at an advanced level with an emphasis on rigorous proofs
HYPS… type colleges also generally encourage a supportive and collaborative atmosphere, rather than a competitive one. This includes things like encouraging/expecting students to work together on problem sets, having no problem with giving the vast majority of the class A’s if the vast majority do A quality work, favoring admitting students who display the desired cooperative and supporting other classmate traits, etc.
When I was a student, I generally couldn’t tell you who the top students in a particular class or my major were. For the most part, I didn’t know what their grades were or how much/little they studies for exams. I didn’t even known what the average grade was on exams within my major. I only knew how I did and a few of my friends did. Since then, I’ve seen grade surveys that suggest the vast majority of grades were A’s. I’ve seen students go so far as to risk an honor code violation to encourage classmates who appeared to be struggling and/or have given up to keep going on exams. It did not seem like a competitive beat out your classmates type atmosphere.