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How to study for a math test in one night

One evening isn't enough to learn a whole unit, but it's plenty to fix the two or three things that would cost you the most points. The trick is spending the time on problems, not on rereading.

1. Find out what's on it (10 minutes)

Gather the review sheet, the last two homework sets and any quizzes from this unit. Make a list of the kinds of problem, not the problems: "solve a system by substitution", "find the slope from two points", "word problem with percent increase". Most tests are five to eight kinds.

2. Sort them: can, shaky, can't (15 minutes)

For each kind, do one problem on blank paper with your notes closed. Don't look anything up yet. Mark it:

• Can: got it right without hesitating. Leave it alone tonight.
• Shaky: got there, but slowly or with a guess.
• Can't: stuck or wrong.

This is the most useful 15 minutes of the night. It tells you where the points are.

3. Fix the "can't" pile first (45 minutes)

Take one kind at a time. Find a worked example in your notes or textbook and read it until you can say why each line follows. Then close it and do a different problem of the same kind. If you get stuck, look back only at the step you're stuck on, then close it again. Move on once you've done two in a row without looking.

4. Turn "shaky" into "can" (30 minutes)

Do two or three of each shaky kind, timed, no notes. Check each answer the moment you finish (plug it back in, or check the back of the book). A wrong answer you catch tonight is one you won't make tomorrow.

5. Mixed practice to finish (15 minutes)

Shuffle: pick problems from different kinds in random order. On the test nobody tells you which method to use, so practise spotting it. Write down any formula you keep forgetting on one small card and read it once before bed and once in the morning.

What not to do

• Don't just reread notes. It feels like studying because everything looks familiar, but recognising a solution isn't the same as producing one.
• Don't read worked answers to every problem. Same trap. Try first, then check.
• Don't stay up all night. Sleep is when your brain keeps what you practised. Two focused hours and a full night beats five tired hours.

In the morning

Do one problem from your weakest kind before you leave, just to warm up. In the test, start with the kinds you marked "can" to bank those points, then come back to the hard ones.