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Choosing extended essay subject

Hi
I am doing IB-Diploma and I want to become an engineer(not sure about the exact type but mechanical, civil or chemical are the ones I have been thinking about) in the future.

Which subject should I choose for Extended essay? Obviously, Physics is the first choice, I love it and it is the most relevant to Engineering. However, we also have to give in our second and third choices. In this case, I am really confused. Should I give Maths as the second choice and Chemistry as the third or Chemistry as the second choice and Maths as third.

Before you say that I should choose the one I am more interested in, I am equally interested in both. I love the application and thought process in Chemistry, and equally much I love to explore solutions using geometry and algebra. I would love any of the two. But which one is the subject that will be better to put in as second choice thinking from engineering point of view.

In case you want to know where I want to apply, I am going to apply to Cambridge and London Imperial College, but highly unlikely I will get there. Most likely, it will be University of Edinburgh.

Thanks

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