What math course should I take in my senior year in order to have a great chance of earning acceptance to an Ivy League school if I am currently a sophomore enrolled in Precalculus?
The Ivy League colleges expect that the majority of their admitted students will have taken the “Most Demanding” course load available at their high schools. The applications will actually ask school guidance counselors to indicate whether each student's course load is "Most Demanding," "Very Demanding," "Demanding," "Average" or "Below Average" in the context of what the high school offers.
But I don’t know what options are available at your school so I can’t advise you about which specific courses to choose. Many Ivy League aspirants take Calculus AB in grade 11 and Calc BC in grade 12, but not all high schools offer a calculus sequence like this. Some students take AP Calculus as juniors and then have the option of taking college-level math as seniors.
So you should talk to your school’s college counselor to find out what path will allow him or her to designate your curriculum choices as “Most Demanding” when it comes time to apply to college.
Note, however, that course selection alone will not give anyone a “great chance” of earning a spot at the most-sought after colleges. At these places, the majority of applicants have top grades in top classes and outstanding test scores, too. Such successes will only get applicants to the outer gates. Then the admission folks ask, “What is special?”
So, certainly taking a rigorous math program will help transport you to those outer gates, but you’ll need a lot more to get you through them.
Good luck as you continue that journey.