Work experience application- how should I answer this question?

Those are really math intesive courses. I wish you luck next year; try to stick with it if you can.

'Why are you interested in getting work experience and what do you hope to gain?'
Don't take my interpretation of it without speaking to others, but the question sounds like it more or less focuses on what the company would be able to get out of you.
I would answer it along the lines of:
1) See if you would be a fit for the job and career in X
2) Fit for the company
3) Explore my passion for ABC/to do 123
4) Gain an insight of what working for an established (or suitable flattering adjectives for the size of the company) DEF company would be like and whether I would be able to continue contributing to the company after university/A Levels

What I would try to avoid doing is say what you want to get out of it, and focus more on what the company can get out of you during the course in time (partly because I think that's what things look like from their perspective).

Hope this helps