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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.