This is the conclusion of my article on collected tips and tricks to help you pass a school or university exam. They are called exam techniques and they helped me and they can help you.

Part C) The Exam Itself  (ii)

14) One thing to try if you can’t quite get a derivation to work out (not entirely serious 🙂
What you could consider doing in questions of the form “derive the result shown below” where you’re not sure of all the steps:  start at the top of the page, state the assumptions clearly, and write down the equations where you’re going to start.  About a page and a half later, write the result, and start working backwards from there.  Where the two halves meet, write “Clearly,”

This gives the examiner a problem.  Provided you’ve got the steps right, and the two halves almost meet up, it’s hard for him to know whether the missing step is clear to you or not.  It might be.  You could get the benefit of the doubt.

Of course, there is some risk here, if you have made a mistake, and your “clearly” connects two lines that can not possible agree.  While the strict marking schemes we use these days make it hard to penalise students directly for this sort of thing, it will tend to put the examiner in a poor frame of mind, and he might start being less generous in marking other sections of the paper where he has some discretion.

15) Don’t get stuck.  Move on.
Avoid writer’s block, you haven’t got time for it.  If you get stuck on a question, move on.  Start doing another one.  Staring at a question you don’t know how to answer is a waste of time, and you’d be amazed how often, when coming back to a question after half-an-hour, it suddenly becomes clear.

16) Take a bottle of water in with you.  Sip it slowly throughout.
It’s a good way of remaining calm.  Also, you can get through a lot of nervous sweat during a hard exam.  Your body will work better if you replace it.

17) Use common sense.
If the answer to “how high is the radio tower” is 217 miles, or to “what is the free electron density in the semiconductor” is 0.003 electrons per cubic metre, then you’re probably wrong.  Even if you don’t have time to go back and find the mistake, at least write something to indicate that you know it’s wrong.  You might get some credit for that.

18) Always explain what you are doing.
Too many times I find an exam script where the student has written an equation with variables in it, and not told me what the variables represent.  If the answer is right, then I can usually figure out what the variables must be, and the student gets the marks.  But if the answer is wrong, then sometimes it’s impossible to work out what they were supposed to be.  In this case the students gets zero for an incomprehensible answer.

Don’t just write long lines of mathematics.  Explain what you’re trying to do with the derivation before you set off, and add comments as you go.  It’s easy, and can gain a lot of marks for method, even when the answer is wrong.

19) If you’re running out of time.
Suppose you’ve got time left to do one question, but two questions left to do.  Which one do you choose?  The way to maximise your marks is to do the first half of both of them.  You gain marks faster at the start of a question than at the end.

If you don’t have time to write sentences, but you do know what to do, then just write bullet points.  If you don’t have time to do the calculations, write and explain what calculations you would do.  You can get marks for method.

20) Never leave an exam early.
The only possible excuse for this is when you are absolutely sure that you have got 100%, and that should never happen.  There is always something you can do to improve your paper.  Check, and check again.  When you’ve finished, start back at the beginning, and try to do the questions in different ways, and check they agree.  Add more explanations.

If you’ve got time left at the end, try remembering the mnemonic: ACUTE.

Assumptions (have you explained them all, even when not explicity asked.)
Calculations (have you checked them all – doing things different ways if possible and time permits.  Did you press those calculator buttons right?  Do the answers to different parts of the question agree?  Check, and check again.)
Units (have you written the units you’re using?  Do the units for all formulas make sense and agree – this is a very powerful technique for checking that your derivations are right and you’re using the right formula.)
Truth (have you done all the parts of all the sections in the questions?  If asked to make a list and explain why, don’t just make a list.  This is probably the biggest cause of unnecessary lost marks – read the question and answer the question, the whole question, and nothing but the question.  Just like the truth in a court of law.)
Explanations (have I explained what I’m doing at all stages – good explanations will get marks for method even if the answer is wrong; miss out the explanation and you’re throwing away easy method marks.)

I have never left an exam early in my life.