Any extra-curricular or competitions that you can recommend to me?
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For math and science, the best extracurriculars are your school's science/math team (if you have one; if you don't start your own!) and going for competitions at a state/national/international level to show commitment. A really good competition to enter is the Google Science Fair. And yes, as @shriya mentioned, Olympiads (especially at the international level) are a pretty good extracurricular too. If you're looking for something less competitive, you can maybe design something of your own, like a robot or a software or try learning to code in multiple languages, or you can conduct a research study under guidance of a professor or complete a research internship.
For writing, I strongly suggest joining your school's newspaper (if you have one) and regularly contributing to it and entering writing competitions. Or you can write and publish a book (why stop at one?) . If you want to combine your math/science and writing interests, you can write a science fiction, or you can write an introductory science/math course for younger children.
I hope this helped! Remember that these are just suggestions, and these were just to give you an idea of what COULD be done, not what SHOULD be done.
Some good clubs related to those interests are Science Olympiad and Math team. As for writing look up different essay competitions in your area or nationwide. From these competitions you can earn scholarships and even awards. Tutoring in your community is also a great way to show interest.
For extracurriculars involving science, I would recommend doing activities such as olympiads and competitions, research (with a professor or independently), summer science programs (such as SSP or RSI), shadowing doctors, and volunteering in the science field. You could also form a club for any of the subjects that interest you. If you are interested in writing, make a Creative Writing Club, for math, create a Math Club, etc. If you would like to simultaneously expand your interests in both science and writing, I would recommend writing a research paper (and possibly publishing it!!)