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Memo #1 from the keen-grasp-of-the-obvious department:
Give them an /algebra/ test. A poor algebra score is a strong
predictor of a poor showing in the algebra-based physics course.
The converse is not necessarily true, but one-sided information
is better than none.
Students who are weak in algebra should be strongly discouraged from
enrolling in the physics course to begin with. This is waaaay better
than enrolling and then dropping after it is too late to sign up for
something else.