Cambridge offers vs acceptances for maths

Hello, I am hoping to apply for maths at Cambridge this year. Recently, after looking at the admissions statistics, I noticed that for maths the rate of offers tends to rather high (approximately 20% ish in some cases I have seen, which relative to the Cambridge courses appears a bit larger than I anticipated, a particularly anomalous one I found was 52%, but that was definitely contextual, but super interesting) but then the acceptance rate is so much lower (Around 1/3 to 1/2 people are knocked out at this process from what I have seen). I am guessing the main cause of this is STEP, however I was curious about the content of the interview, are the questions similar to the level of thinking needed for the STEP papers, and if so, is there any particular nuances I am missing as to why a person might not get in despite being viewed as having the potential to do very well by the admissions tutors? I ask so I can be careful to avoid similar mistakes if I can make it that far in the process

My perspective is as a parent of a student who has just been successful for Maths at Cambridge...
The pace, volume and complexity of the Maths course at Cambridge is extremely tough. Success at STEP is a good predictor for success on the course. So only the people who can get (or nearly get) the grades in STEP will be able to manage when they get there; STEP questions are longer and more demanding than the standard required for an A* at Further Maths even though the curriculum content is the same. Cambridge offer to around 500 but expect to take only about 250. Only about 160-170 get the STEP grades and the remaining places are given to students who narrowly miss their offer but whose STEP papers, which tutors review, look promising.
My son said that the interview wasn't like a STEP paper and that he was given problems with some familiar maths combined with unfamiliar ideas. They were interested in how he responded, with prompting and correcting of minor errors if necessary. I've read that the interview is more about seeing if you're teachable and how mathematically you can think, than about testing what you know.

My perspective is as a parent of a student who has just been successful for Maths at Cambridge...
The pace, volume and complexity of the Maths course at Cambridge is extremely tough. Success at STEP is a good predictor for success on the course. So only the people who can get (or nearly get) the grades in STEP will be able to manage when they get there; STEP questions are longer and more demanding than the standard required for an A* at Further Maths even though the curriculum content is the same. Cambridge offer to around 500 but expect to take only about 250. Only about 160-170 get the STEP grades and the remaining places are given to students who narrowly miss their offer but whose STEP papers, which tutors review, look promising.
My son said that the interview wasn't like a STEP paper and that he was given problems with some familiar maths combined with unfamiliar ideas. They were interested in how he responded, with prompting and correcting of minor errors if necessary. I've read that the interview is more about seeing if you're teachable and how mathematically you can think, than about testing what you know.

Congratulations to your child, I am sure your are super proud of them! That makes a lot of sense, given from the past Qs I have seen.

On the side of applications, I was curious how big of an impact the PS played in the application, and how your child prepped for it (Books, competitions, etc.). I was curious because all the ones I have seen go into detail about the accomplishments in competitive events, due to some personal stuff going on at the time, I only got bronze in UKMT last year (Being Y12), so I have not gone too in depth about it in my PS, but I have a lot of things I have done aside from that which stand out and I have been able to use those, but I was worried competitions are a big part of it and I may have messed up my chances because I did so bad. It is comforting to know STEP is one of the larger parts of it however, as I really love the problems and I can do well at them, so I thank you ever so much for the info!

Hello, I am hoping to apply for maths at Cambridge this year. Recently, after looking at the admissions statistics, I noticed that for maths the rate of offers tends to rather high (approximately 20% ish in some cases I have seen, which relative to the Cambridge courses appears a bit larger than I anticipated, a particularly anomalous one I found was 52%, but that was definitely contextual, but super interesting) but then the acceptance rate is so much lower (Around 1/3 to 1/2 people are knocked out at this process from what I have seen). I am guessing the main cause of this is STEP, however I was curious about the content of the interview, are the questions similar to the level of thinking needed for the STEP papers, and if so, is there any particular nuances I am missing as to why a person might not get in despite being viewed as having the potential to do very well by the admissions tutors? I ask so I can be careful to avoid similar mistakes if I can make it that far in the process

Thanks! We found these links on applying for Maths at Cambridge useful:
https://www.maths.cam.ac.uk/undergrad/admissions/what-do-we-look-for
https://www.maths.cam.ac.uk/undergrad/admissions/files/admissions/admissionsguide.pdf
https://www.maths.cam.ac.uk/undergrad/admissions/faq
https://www.undergraduate.study.cam.ac.uk/files/publications/mathematics_subject_requirements.pdf

Lots of successful applicants have done well in UKMT and BMO, but doing well in competitions isn't a requirement and they aren't the same as STEP, so it's really encouraging that you're getting on well with STEP.

Note from the second link that "All Colleges like to interview all realistic applicants." So if you are predicted the required grades (A*A*A with A*s in Maths and Further Maths), get a good reference from your school and can demonstrate that you have mathematical ability, interest and motivation in your PS, then you would surely hope to get an interview.

My son talked in his PS about studying maths outside school (STEP), books he'd read and what he liked about them, YouTube videos/channels he'd watched and how he responded to them, as well as competitions. He talked about what he enjoyed about Maths, although that can sometimes be hard to put into words. Although Cambridge Maths say they aren't interested in non-mathematical extra-curricular activities, he mentioned his briefly at the end, as other universities may want to know about that.

It's pretty much down to STEP for the most part I think. About 50% of Cambridge maths applicants fail to achieve their STEP offer if I recall correctly. I think generally offer rates are quite good, it's just that STEP is very hard and if you miss the STEP condition you are at the mercy of the college to accept you as a near miss or put you in the summer pool as I understand it.

After review of a few applications from my school that got in, I wholly agree with this, it appears as though so long as they like you at interview and you show a good level of aptitude + teachability alongside a generally god PS, you are well in the running for an offer. It is reassuring STEP is the hardest hurdle, as so far I have found it quite enjoyable! I was curious if you knew if interview Qs are similar to STEP questions (Minus the more mundane algebra of course!), as I have seen people talking about questions they had at interview, and some seem really hard and some quite reasonable and comparatively easy, so I do not have a great grasp on the level of mathematical thought the interview will operate on. Thank you ever so much for your advice!