Hi there! I am transferring to a private school next year as a sophomore, and I want to take Algebra 2 over the summer so I may take Precalculus honors. However, I would like to major in Computer Science and Algebra 2 is required in order for me to be eligible. But how would colleges know I completed this class? Especially my top-choice elite universities.
When you apply to colleges, you include records for all high schools and colleges attended up to then (whether or not the courses at each are included in the records at your main high school).
But it looks like you are already a year ahead (geometry in 9th grade, algebra 2 in 10th grade if you do not take a summer math course, leading to precalculus in 11th grade and calculus in 12th grade), so is it really necessary to try to get even further ahead? Only a few US universities require or recommend calculus for frosh admission, and none require or recommend math beyond calculus for frosh admission.
If you are taking a summer class through your high school it will likely appear on your transcript. If you are taking through some other program such as online through BYU, you will receive a document that verifies that you took the course and what your grade is. You can turn that in to your guidance counselor.
To add to what @ucbalumnus said, CS is not as math intensive as say ME. Being ahead really doesn’t offer much advantage, especially if it comes at the expense of compromise in a foundational math course. Summer terms are typically accelerated.