Some kind of maths or science is very helpful but it doesn’t have to be physics.
Road engineering will require knowledge of how things deal with weight and how materials behave over a long time, so you will need to study some Mechanics, which is the maths of how physical objects behave. But I didn’t study Physics at A level at all, and during my degree I got taught Mechanics as a separate topic. I had learned enough “science thinking” doing Maths and Chemistry, so it wasn’t a problem not doing Physics.
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Hayley commented on :
I know a few engineers who come from a mathematics background.