Originally Answered: Does failing one class in high school prevent me from entering Ivy league?
See if you can retake the course over the summer, depending on how/if the new grade would appear on your transcript and in your GPA. Some schools will let you retake a course and will replace your old grade with your new grade, but some schools will average the two grades together, and some will not replace the old grade, but will show on your transcript that you retook the class and that grade, but it doesn't go into your GPA.
Just so you know, 85% of Ivy applicants are qualified, not sorta qualified, but ultra-qualified. But only 6 - 11% are admitted. If you don't have a 4.0 (or extremely close if you attend an extremely rigorous private school) and a 2100+ SAT, you probably don't have much of a chance of admission unless you've done something really wow or have endured extreme hardship, like being homeless for years but still getting good grades in high school. Seriously.
To be admitted to an Ivy, you need to stand out. The only great students with not much more who get in are those that just happen to be the type the Ivy is looking for that year, in an area they're looking for a student at. (The Ivies like to take from all over the country.) But other than that, you really need to have an impressive resume. (My dh participates in the admissions process for his Ivy alma mater, and I have a sophomore, so I know how it works.)
Are you sure the Ivies are a good fit, colleges you'd really enjoy attending? Have you visited and spent time at them? They really are for kids who are way into school and academics. Keep your mind open and think outside of the box.
CollegeBoard http://www.collegeboard.com/ College Search > Find your match
It's not good if you're failing Algebra II. Study more or get tutoring. What are you going to do in pre-Calc and AP Calculus AB? They are much more difficult. Be sure to look at the suggested high school classes that the Ivies want to see, not the requirements, but the preferred path.