How important are the math II scores at Caltech? I know an 800 is the 90 percentile, so do they expect you to score an 800, or is any score in the high 700s good? Will it hurt to have a score in the high 700s?
The Math 2 test is a bit different than the other subject tests. Check this out: https://secure-media.collegeboard.org/digitalServices/pdf/sat/sat-percentile-ranks-subject-tests-2016.pdf. With a 780, you’re already down to the 72 percentile. My D also told me you can get several questions wrong on the math 2 and yet still get an 800, so there is wiggle room to make some mistakes and still get an 800.
The majority of their class of 2020 scored an 800 on the math 2: http://www.admissions.caltech.edu/content/class-profile. They just have so many people applying and limited seats. If you have some special hook, they may be more flexible. But Caltech has some of the hardest academics in the country, so I would think they would want all of their accepted students to be top math students in order to have a greater chance of success there.