You will most likely need both; math probably being a bit more important. But don't worry; you can practice the skills that you are currently not good at. Why don't you publish a blog in which you write about things you are interested in?
-- No. You should not be ashamed of yourself. -- No. If you fail science and engineering, that won't be the reason.
Sounds backwards to me.
Not really. Science Engineering deals basically with Math subjects. Therefore, if you're good in Math, you'll do good in Science Engineering.
Yes
In my opinion, it is not TRUE. Engineering courses have more Math subjects than English or Communication subjects. So if you're good in Math, you will be a good engineer someday.
No; it is false.
It always depend on the person if he will pass a subject or not.
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Not necessarily. Math is the language of science, rather than writing. Being a good writer may help, but being strong in the math section is more important. If you understand the math portion, there is no way you can fail
You need good math to do engineering at a professional level.
No
You'll certainly not fail physics BECAUSE you are good at math - you NEED math for physics and engineering.