I think part of the problem is how we are tested. I fell into the same situation in high school where I'd be able to derive complex formulas on the fly that I required to solve a problem, but it took me so long to do that compared to knowing the equation that I'd never finish exams (time would run out) and I had to resort to rote memorization in the end.

One way to level this is to allow cheat sheets or open books. This is a bold way of saying: "If you truly understand the topic, you'll be able to solve this problem even though it requires a mental step ahead from what we've seen in class." What usually happens here is that students who don't have a good grasp and get by on pattern-matching exam questions to questions done in class, complain about not having seen that type of question before.

Guess what, in real life, you almost always hit a type of question you haven't seen before! The kinds that have been known already are easily findable in any textbook. So why are schools focusing so much on the rote memorization / pattern matching rather than focusing on raw problem-solving skills? Algebra in 9th and 10th grade, precalc in 11th grade and intro calculus in 12 doesn't do anyone any good.