You may use a calculator if and only if you know how you would do it without a calculator, so perhaps it would be helpful to learn how you would do things without a calculator.
You may look up the definitions of words, phrases, or symbols. If you don't know what something in the question means, you should look it up.
You may look up the definition of theorems, formulas, or algorithms if the question asks you to use them or prove them, but otherwise you may not look them up.
You may not look up proofs.
Don't help your friends break the rules. You may collaborate with your friends to solve the problems.
You may write stuff down to help you solve the problems. You may write down notes as you solve a problem, but referring to your notes on later problems is the same as looking stuff up.
You may not guess the answer.
If you cheated on a certain problem, but you still don't know the solution to the problem, then you may still attempt to solve the problem, but you still cheated.
If you are not working on a problem, you may study by looking things up.
You may look something up if it is not related to math. For example, you may look up a song to listen to.