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<p>This seems appropriate, however. Regardless of how good you are at math, if you don’t know trig, placement into calculus is a mistake, like placement into Multivariable Calculus without an understanding of integrals is silly. From that standpoint, they can’t place you with disregard for what you know. On the other hand, some schools offer different levels (including different rates of acceleration) based on how good you are at math (I took geometry, algebra 2, precalc with trig, and BC calculus in 2 years through such an arrangement of courses). This would probably be preferable as a system, but the cost is inhibitive, especially if there aren’t enough students with the ability, background, or motivation.</p>
<p>Not skipping will not show a lack of motivation. It’s not expected that students skip classes. Doing so, assuming you get a solid background (particularly in trig, logs, and polar coordinates), would prepare you for further coursework, but doing so for college is not a good idea, especially due to the risk of dooming yourself to a less-than-stellar understanding of precalc. I don’t necessarily recommend against it, but I would ask guidance counselors and math teachers for advice specific to you.</p>