yes, there are many different types of engineering course to choose. But when you say you're not good in math...you actually have to at least know the stuff they teach in high school.
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Of course not. Certainly, you won't be bad at physics or engineering BECAUSE OF your math skills. You NEED math for physics, and both math and physics for engineering, so somebody who is not good at math is more likely to have trouble with physics or engineering.
Possibly. You also have to be good at and enjoy engineering concepts which do involve math.
Not really. Science Engineering deals basically with Math subjects. Therefore, if you're good in Math, you'll do good in Science Engineering.
Nope, understanding math is the basis of understanding engineering
Math will help, not hinder, you in this. You actually need a LOT of math, especially for physics and engineering.