Question: Is it better to get an A in an easier course, or risk getting a lower grade in an advanced course? I've got a 4.0 now, and I'm interested in schools like Columbia and Yale. There are some math and science courses at my high school that I can probably get through but I'm not sure I can ace them.
The thing to remember about Ivy League and elite admissions in general is that the admissions people look first at how well you've done in what level of course challenge in your school. Specifically, it's better to get a high B or low A in an AP than it is to get an A+ in a lesser course.
If your school offers an array of APs, then you should take advantage of as many of them as possible. If it offers just a few, try to take as many as make sense. If your school offers no APs, then take as many advanced courses as possible. Are you getting the picture? Make your course schedule as challenging as possible.
To get an idea about what kinds of curricula Ivy admits have on their transcripts, read a review of a book I co-authored called "America's Elite Colleges: The Smart Applicant's Guide to The Ivy League and Other Top Schools." It's available through Amazon.com. My co-author is David Hawsey, also of College Confidential. See:
The book also shows the role of essays, recs, and ECs in a successful Ivy applicant's approach. You may be surprised as to how hard it is to get into schools like Columbia and Yale. All you can do now, though, is just try your best. That's all anyone could ask.