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Year 12 stuck on whether to consider applying for Maths or NatSci (Physics)

I'm doing Maths, Further Maths, Physics and Russian for A Level and am aiming for 4 A*s (school recommends all FM candidates to take their fourth subject too to prove candidates didn't have a light workload in Year 13).

I know that I want to do something to do with maths or physics. This includes finance, engineering, and maths or physics itself.

I also have not decided what I would like to pursue the most out of these, and considering how hard I found it to choose these A Levels (despite them being my strongest subjects), I doubt I will be able to choose anytime soon.

I've looked at many courses at universities such as Oxbridge and Imperial (where I'm aiming for) and currently the prospect of doing something like the following appeals to me.

At Cambridge, assuming you take the Maths Tripos, you can do the first year as a joint Maths + Physics course (75%/25% split). You can then change your second year course to NatSci (Physics) which would still have about 25% Maths in it (I believe, not too sure) and third year would be full NatSci. After this, I will have a BA or BSc in NatSci and can therefore apply for a Masters in whichever type of Engineering I'd like to, if I wish. However, if I get a BA in Maths (up to third year of the Tripos) then I cannot do that.

My concern is that, if I follow this route and decide not to pursue Engineering, a BA/BSc in NatSci is much more limited than a BA in Maths. Ideally I'd like to study Maths and Physics equally and be open to Engineering if I so decide, but that's not possible as far as I can see. What's my best option?
Why limit yourself to Cambridge or Imperial? They are not the only half decent universities. If you open your horizons a little you will find many course options that allow you to mix and match as you seem to want. When it comes to getting jobs, having the right skills usually comes before the prestige of your university... unless of course you want to operate in an old-boys network where the colour of your tie is much more important than your ability to do the job.

That said, in engineering, ability is everything. There is little room for incompetence, unlike in politics.

Good luck with your decision making!

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