# Theorems allowed

Hello everyone !

I create this topic to ask which theorems we are allowed to use when answering STEP, STEPII and STEPIII questions.

Can we use any theorem we know ?
(For instance, for the STEPI Assignment 5 Warm down, I first thought of using the pigeonhole principle. In fact, this was not fit - however, had it been useful, could I have used it albeit we did not see it in class ?
Another example could be a basic use of geometric similarities, like homotheties. )

Or are we bound to use the theorems seen at school ?

In which case, being French and studying in France, we have no Y13 which means I'll study at a "Classe PrĂ©paratoire" next year. Contrary to our high schools, these "Classe prĂ©paratoire" focus on Maths and Physics, and I don't know if the syllabus is similar to the one of Y13 in England.
Does anyone know if the syllabuses are equivalent ?

Thank you for your help !

### A general rule of thumb is

A general rule of thumb is that you shouldn't use any results that make the question trivial. If you use an alternative method that is "in the spirit of the question" (in the sense that it doesn't reduce the amount of work massively) that is fully correct, you will receive full marks.

To find out what's on the syllabus, see the STEP specification. Bear in mind that I believe this will be updated for 2018 to reflect the new UK A-Level specification (if it hasn't been already) so there may be a few changes to come.

With regards to your specific queries, the pigeonhole principle is definitely fine. In the UK, students will have met similar triangles at GCSE (or Standard Levels in Scotland) and I don't think any question would require knowledge of geometric similarity beyond that.

### Thanks

Thank you for your answer. The STEP specification is quite what I needed to check what was required and what was not. And the rule of thumb should be enough to feel whether an answer is correct or not !

Thanks !

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP