Is 4 A* at A-Level the "norm" for Cambridge Maths students? Watch
Ummm... yes that is definitely a possibility. However, remember that it is an AVERAGE - pretty much everyone will have 380+ UCAS points since the minimum requirement is A*AA, but since many STEM students take Maths and Further Maths and therefore have the time for an additional subject, it is fairly common to have four A levels. Not essential, but quite common. Also, remember that UCAS points includes things like General Studies, Critical Thinking, Music Exams, etc. which Cambridge don't really look at/ base any offers on, but some applicants may have due to their schools forcing them to take silly subjects like GS or through their extracurricular interests.
To do well at STEP you would definitely need to be at least close to A* standard in Further Maths. And anyone that good at FM would do very well as Maths and Physics. So yes, it is likely that many mathmos have A*A*A* in Maths, Physics and Further Maths. I managed those grades and still would probably fail STEP though, so I guess it does require some actual maths ability beyond being able to memorise standard exam questions and markshemes (which is all A level Maths/ Further Maths really was...).