STEP Advice

Age 14 to 18
Article by Yanqing Cheng

Published November 2011.

Seven pieces of advice for STEP


1. Make yourself clear.

  • Write things out neatly so both you and the examiner can follow. Every step in your solution should follow logically from the previous steps and the given conditions. If you find this difficult, write each step on a new line and leave gaps. 
  • If you number your equations, you can label any new equations with where they come from.


2. Check solutions.

  • Be wary of generating false solutions to equations. Often, you'll want to solve an equation by squaring both sides. However, fake roots will creep in when you do this. Safest bet is to check every solution, and say you've done so. 
  • Know the difference between if and only if. To prove "A if and only if B", you must show BOTH that assuming A leads to B and that assuming B leads to A. Make sure you show it both ways!


3. Read the question.

  • When you think you've finished a solution, go back to the question to make sure you've answered every part and used every condition.
  • If there's a condition you haven't used, check carefully to ensure 4.


4. Don't divide by zero.

  • Check every denominator. Enough said.
  • Check that other functions are fed numbers from their correct domains too. (No logs of negative numbers, etc)


5. Be very rigorous.

  • Check everything works for positive and negative (and complex if necessary) numbers. Check for special cases.
  • Check for plus or minus signs from square roots.
  • Check that your inductive step works on your base case (check you have a base case!).
  • Make sure that even someone who doesn't know you will be able to follow your arguments and see no flaws.


6. Know your strengths.

  • Try as many different types of question as possible in the months before your exam, so you know what kind of "feel" a question you can do has. Then, in the exam, read all the questions and identify the ones which "feel" doable.
  • Don't dismiss any category of questions before you start the exam though: even if you hate stats, there might still be a really simple question in that section!


7. Start preparing early!

  • Unless you're very confident of your own abilities, start early. Three or four questions every week from earlier papers, starting December (or earlier if you're not sure!), quickly develops your confidence.
  • Do some STEP I questions for the first few weeks if STEP II and III questions seem scary (but don't dwell too long on them).
  • If possible, get a friend or a teacher to help you check your answers for flaws or loopholes. If you're not entirely certain that you've done something right, it's worth spending the time finding the errors, rather than leaving them and starting something else.
  • Save some (recent) complete papers for May and June. You should be able to find past papers from approximately 1998 onwards online - that's more than enough to last you!


Remember, these exams are supposed to be difficult! Don't be discouraged if you find it very hard to start with. Practise lots of questions, and practise looking for loopholes: STEP examiners want to see rigorous mathematics. A watertight solution will gain you more marks than hand-waving attempts.


For further advice from past AskNRICH discussions, try here.