I don't recommend learning your school syllabus ahead of time because that could mean you get very bored in class. I know from personal experience because I learned to read before I went to school and my first year was terrible because I had nothing to do. It's not something I would recommend to anyone.
Rather than doing something like that, I would recommend using a more advanced book like Spivak at the same time as you learn calculus. That way, you won't get ahead of time. Regarding linear algebra, you could do the same thing if you ever do it in college, using a book like Axler. But that all depends how you like abstract math. You may not like it.
Luckily, linear algebra has little overlap with calculus so it shouldn't affect it very much.
This is the book I will be given next year. Is this a quality book?