The effectiveness of competition rewards to Oxbridge application

If you have a good STEP score, the only college that would care would be Peterhouse. Even then, they only ask for it after you get an interview and pass the interview. If you can get a 1 in STEP II a year early (applying with it), I can't imagine you being rejected for poor math skills. The biggest obstacle would be getting and passing an interview, which has more to do with your supercurriculars and interview performance.

Thank you very much! Do you think an additional STEP3 I score would make me more competitive? I am considering whether to prepare for STEP2 only or STEP3 all together. BTW, what conditions shall I meet if applying for Jardine scholarship? Would I be rejected to read in Cambridge if not considered so competitive for a scholarship? Thank you!

I do not think Cambridge will reject you if you do not qualify for the Jardinie scholarship

I am an AS student from a Chinese international school.
I heard from fellow students that Cambridge would reject some of the applicants since they do not have competition rewards like AIME 8 or BMO Distinction (Chinese student, really competitive area). My aim is Engineering major in Cambridge. I wonder if I would be rejected since I did not have enough rewards. If I had good ESAT scores like 8.1+ for each paper and BPhO gold or top gold, would I be invited for interviews? Or I need more rewards like Physics BOWL gold or AIME 8.
I personally prefer to try STEP rather than BMO after viewing the papers. Would STEP II 1 only be as effective as BMO/AMC rewards? Which role do competition experience and competition rewards play in your application?
Thank you very much!

You don't require STEP papers for Engineering at Cambridge. But A-Level Further Maths is highly recommended for Engineering, especially at the top-end universities.

Academic Requirements | Engineering Applicant Information