how important are high school math and science?

If we want more scientifically competent students, they're pretty important. Biologist PZ Myers, regarding a recent study, notes:

High school physics was as effective at prepping students for college physics as high school biology was at prepping students for college biology.

Success in one area of science doesn't transfer across areas, unfortunately; a physics whiz is not a guaranteed biology nerd. What really helps, though:

Math is the #1 most effective preparation for doing well in all sciences, across the board; the more math you can get in high school, the better you're going to do in any science class you might want to take. Look at those giant gray bars — it makes almost a 2-grade point difference to be all caught up in math before you start college. Parents, if you want your kids to be doctors or rocket scientists, the best thing you can do is make sure they take calculus in high school. Please. Failing to do so doesn't mean your kid is doomed, but I can see it in the classroom, that students who don't have the math background have to work twice as hard to keep up as the students who sail in with calculus already under their belt.