Algebra helps you solve real-world problems that you will face when you are on your own.
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Being able to use algebra is essential to studying physics. Being good with algebra can make studying physics easier than it would be if you were not good with algebra. However, being good with algebra will not ensure that you will find studying physics to be easy.
There is no way to know. Some aspects of calculus depend on a good understanding of algebra, others don't. It all depends on which aspects of algebra you were good at and also whether or not you retain that edge.
Oh, please... How would being good at something make you bad at something else? That just doesn't make sense. Specifically in the case of calculus, you NEED math and algebra, so:If you have trouble with algebra, you will also have trouble with calculus, andIf you are good at algebra, your chances at calculus are much better.
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No. Chances are it will be the other way around: if you are bad at math, you stand a good chance of failing calculus or linear algebra. You will perform best at calculus and algebra if you have a strong math background.