<p>Yes, AP tests are important for admissions, especially for Ivies (I asked a Princeton adcom for confirmation) Here is why they are important:</p>
<p>1.) If you have a "B," you can still redeem yourself with a score of "5."
2.) AP scores gives a good indication of your work ethic.
3.) If you get a "B" in a couse but a 5 on the exam, the college will get a better idea about the rigor of your courses.
4.) A poor GPA (about 3.6) with 5s on a number of AP exams still keeps you in the running. A 3.6 with no AP scores reported gives an idea that you are not competent enough for that particular college.
5.) A student with a 3.6 with over 80% AP courses in the transcript is much more impressive than a student with a 4.0 with few APs (2 or three). This is even the case with the context of the school.
6.) A student who self studies a number of APs is highly regarded by adcoms because of initiation, especially with a good score. I learned this from Chuck Hugh's book.</p>