<p>I'm no expert. However, I have seen through my children how 3 private schools, all of which consider themselves academically superior, handle math placement. Some things that may be relevant:</p>
<p>1) All three use placement exams ALMOST EXCLUSIVELY to determine math placement. My daughter transferred after 10th grade from a stronger to a not-quite-as strong school (we moved). She had 2 years worth of excellent grades, detailed teacher comments, and 10th grade PSAT scores -- they still insisted on a placement exam. I think you should definitely go with having a placement exam if it is offered. I'm suspicious that the school doesn't insist on it.</p>
<p>2) All three have at least 2 levels of any one course, and one (the best one, academically speaking) has 3 levels, as in, Geometry, Honors Geometry, Enriched Geometry. </p>
<p>3) The exact contents of 'Pre-Calc' are like the recipe for mystery meat. Depends on the teacher, book, school, etc. One of my kids did 'pre-calc' as a self-study concurrently with Alg. II, w/a weekly 20-min mtng with his Alg. II teacher. Worked for him. (As in, he got a 5 on AP Calc AB, got an A in the class, got A's the following year in 'Multivariable Calculus' and was admitted to excellent and selective math/science schools.)</p>
<p>4) For my kids, pushing (where necessary) to get into the highest math levels possible was the right thing to do. They worked up to expectations and classmates' levels, and were very happy with their successes. The one time we insisted that 9th grade (therefore, new to the school) D (who did not see herself as talented in math) take regular Geometry instead of Honors, she went on to ace the class and was invited into the honors track for 10th grade. She still holds that decision against us and thinks it proves that we think she's dumb. Kids, ya gotta love 'em, cause nobody else would put up with their crap.</p>
<p>5) In our family, we are very strong proponents of high-school kids learning as much math as they possibly can, <em>especially</em> if they don't think they'll go on to do math/science in college. a) you never know - your interests may change and then you'll be sorry you don't have the basics down since math/science is so hierarchically structured. b) our culture excels at producing educated people who think they understand all about human nature, policy issues, good decision-making, etc. but are essentially innumerate. As in, can't tell you what 20% of 100 is. There's something very wrong with that, and I'm doing my best to fix this problem, starting with encouraging all my kids to do as much math as they can in high school, regardless of talents and future plans. I didn't want to write a long post (oops) but I hope you will reconsider strategizing about your daughter's strengths/weaknesses and 12-th grade schedule, etc. and just go for the best math sequence that she can succeed in with hard work.</p>
<p>Good luck!</p>