American Undergraduate Programs focus upon the holistic development of personality of a student. They do not have a single point focus on academics alone. Moreover the learning is not only teacher and book knowledge driven but also focuses on peer-learning and developing intellectual abilities in a student.
So admission to the best colleges and universities in the U.S. is based on the complete profile of a prospective student. This profile is a function of numerical and subjective parameters. Numerical parameters include academic grades (GPA), scores on SAT-Reasoning Test, and sometimes scores on SAT-IIs and APs. Subjective parameters are more complex and include quality and participation in extra-curricular activities, work experience, unique perspective a candidate may have, cross cultural experience, leadership and team skills, the diversity a candidate may add to his peer-group at the college, etc. Most of the subjective parameters are indicated in essays that a student needs to write. Letters of Recommendation provide a neutral third person assessment of the subjective parameters by the teachers.
As students applying to colleges come from diverse countries, backgrounds, academic-subjects and systems of education, so SAT provides a common objective numerical yardstick to compare all candidates.
Good colleges are also concerned whether an admitted student would be capable of handling the academically rigorous programs offered by them. High GPA and SAT scores take care of this concern, so they are important parameters for selection.
Moreover, as top Ivy League colleges receive a huge number of admission applications, so an easy way to weed out/reject a bulk of candidates is to use a minimal score on the SAT as a qualifier. This cut-off value of SAT score is higher for more competitive top Ivy League colleges and changes every year.
Apart from the SAT, some programs may require you to prove your academic excellence by submitting scores on, SAT-II tests(upto three subjects) and at times even Advanced Placements. We will look at this specific requirement later.