How should I study for a math exam?

Start with worked examples in the textbook, walking through each line on your own paper before moving on. Then do problem sets without looking at the solutions until you've finished. Finally, do at least one timed mixed problem set close to the exam.

Why doesn't doing more practice problems help?

It can, but only if you do them properly. Solving 50 problems while peeking at hints produces less learning than solving 10 with no peeking. The act of being stuck and working through it is most of the learning.

What should I do when I get stuck on a math problem?

Sit with it for at least five minutes before looking at hints. Try to identify what you don't know: is it the concept, the method, or the arithmetic? Each has a different fix. Only after that, look up the relevant worked example, not the answer.

Are worked examples better than practice problems?

Both have a place. Worked examples teach the pattern; practice problems test whether you've learned it. Beginners get more from worked examples; advanced students get more from problems. Most students under-use worked examples and over-rely on volume.

How do I memorize formulas for a math exam?

Don't try to memorize them in isolation. Use them in problems repeatedly. Formulas you derive a few times stick better than formulas you read a hundred times. For a small number of unavoidable rote formulas, spaced repetition flashcards work.

How to Study Math Without Doing 100 Problems a Night

Most students who struggle with math don't lack effort; they apply effort the wrong way. The volume-first approach (do as many problems as possible, peek when stuck) feels productive and produces less learning than a slower, more deliberate routine.

Start with worked examples

For any new topic, read the worked examples in the textbook before you try problems on your own. Don't just read; work them on your own paper line by line. Cover the next step, predict it, then uncover and check.

Worked examples teach you the pattern of how problems are solved. Beginners don't yet have the patterns to invent solutions from scratch. Trying to invent them from cold (no examples, just the problem) is how students get stuck and conclude they're bad at math when they're actually just under-supplied with patterns.

A reasonable ratio for a new topic: one to two worked examples studied carefully for every five problems you try. Once the topic feels familiar, drop the ratio.

The no-peeking rule

The single biggest difference between students who improve at math and students who don't is whether they peek mid-problem.

Solving a problem with no help, including the moments of feeling stuck, is what builds skill. Looking at the solution after one minute of struggle short-circuits the learning and creates an illusion of competence.

The rule: once you've started a problem, no peeking until you've either solved it or sat with it for at least five minutes of real effort. If you're still stuck after five minutes, go look at the relevant worked example, not the solution to the problem in front of you. Then come back and try again.

Mix the problem types

Once you have the patterns, mix problem types within a session. Don't drill 20 problems of one kind, then 20 of another. Alternate. This is the principle of interleaving, and it's especially powerful in math, where the real skill is recognizing which method to use, not executing one you've already loaded.

Most textbooks are blocked by chapter, which makes interleaving harder. The fix: pick 5 problems each from three different chapters and shuffle them. Solve them in random order. Yes, it's harder. That's the point.

Wrong answers are the material

When you get a problem wrong, the wrong answer is more valuable than the right ones, if you analyze it properly. For each wrong answer, write one sentence about what went wrong:

Misread the problem.
Forgot to apply the chain rule.
Algebra error in line 4.
Didn't know the method existed.

Each of those is a different fix. Misreads need slower reading. Forgotten methods need flashcard review. Algebra errors need timed arithmetic drills. Method gaps need worked examples on that topic.

A page of wrong answers, properly analyzed, is a study plan.

Before the exam

A week out, do one timed mixed problem set covering all topics, in the time limit the exam will use. Don't grade harshly; this is for pacing and gap-finding. Patch the gaps. Two days before the exam, do a second timed set on the patched material. That's the whole prep loop.

Questions

How should I study for a math exam?: Start with worked examples in the textbook, walking through each line on your own paper before moving on. Then do problem sets without looking at the solutions until you've finished. Finally, do at least one timed mixed problem set close to the exam.
Why doesn't doing more practice problems help?: It can, but only if you do them properly. Solving 50 problems while peeking at hints produces less learning than solving 10 with no peeking. The act of being stuck and working through it is most of the learning.
What should I do when I get stuck on a math problem?: Sit with it for at least five minutes before looking at hints. Try to identify what you don't know: is it the concept, the method, or the arithmetic? Each has a different fix. Only after that, look up the relevant worked example, not the answer.
Are worked examples better than practice problems?: Both have a place. Worked examples teach the pattern; practice problems test whether you've learned it. Beginners get more from worked examples; advanced students get more from problems. Most students under-use worked examples and over-rely on volume.
How do I memorize formulas for a math exam?: Don't try to memorize them in isolation. Use them in problems repeatedly. Formulas you derive a few times stick better than formulas you read a hundred times. For a small number of unavoidable rote formulas, spaced repetition flashcards work.