Can not taking any math honors hurt me when i reach the admission phase?

Precalc at your school sounds really unnecessary. Is it possible to test out or skip precalc?

I dont think so because precalc has just been introduced into my school. Maybe the curriculum will change. Thanks for you help

Just saying, he might mean Linear Algebra.
That’s a very different animal from Algebra I or II, and a precursor to Real Analysis. It is college level mathematics, and it doesn’t require a background in Calculus.

It’s unlikely that any high school has linear algebra as a required course. “College algebra” is a common term that usually covers Algebra II and/or pre-calculus.

Normally, a student who takes Algebra I in eighth grade is a year ahead and will be able to take calculus by the end of their senior year. Your school has an odd curriculum and I don’t think colleges would penalize you for it, but you should talk to your guidance counselor and see if there’s a way you can take calculus before you graduate.