One way to think about this is what if another kid from your school applied to Columbia? How can you make your application stand apart from theirs? This is not meant to compete with them, but to highlight who YOU are in your class choices, your extra curriculars, etc. Let it all tell a story about your strengths. Make it hard for them to turn you down.
You also have plenty of time to research other schools which realistically even the the best kid, at the best high school, who got the A in Math Analysis will need to do.
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