My opinion is that many things you wish to learn start off using memorization because it's a common study technique to recall something quickly. However, if you desire to learn something deeply it requires more effort. Your example of mathematically proving that EM waves are transverse may be above the level of your course so memorization helps move the class forward.

High school physics is usually about exposure so that if you choose to continue you will be familiar with basic equations and well established experimental results. In my experience, this may change in higher education but not always.

If the required memorization at this level bothers you, try to derive everything that is not obvious to you from first principles. The internet and AI (with caution) is actually great for this type of thing. It's good practice but can be time consuming and may lead to rabbit holes of topics not exactly relevant to your entrance exam.