<p>There’s also the question of opportunity. Taking upper-level courses can cost (a lot) of money. Competitions such as the AMC and AIME may be easier to do for a good number of applicants.</p>
<p>I took Calc 3 first semester my sophomore year and could have gone a lot further had my parents been able to afford the cost of the local university (the local community college later offered Differential Equations my junior year, at a much lower cost, and I took Linear Algebra online after that).</p>