How can I study for a math exam to maximize my ability to solve problems?

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So I have a linear algebra final in a little over a week. I have already started to study, this consists of going through notes and rewriting the important definitions, proofs, theorems, etc. After I have worked my way through all the chapters we were taught I will practice problems from previous exams and in homework sections in our class notes.

However, whenever I study for exams like this I find that I constantly have to look back at examples to start solving the problem. I can generally continue the problem once seeing how it is started, but I struggle to come up with methods of solving on my own. For this course's midterm, I felt confident and knew my stuff but blanked on a couple of problems which really brought down my mark.

So what should I be doing in order to maximize my likelihood of success? Or rather, is there a unique that math (or linear algebra) should be studied to benefit the student?