Set notation, interval notation, some knowledge about logical statements and mathematical proof. Knowledge on sequences, functions, trignometry, exponential and logrithimic are assets as when you get deeper into Calculus you do have formal definitions for them.
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Algebra and calculus
I need calculus because I am not in a job where they put pictures on the cash register.
In order to solve problems using Calculus, you have to know Calculus.
You need to know calculus, as well as other advanced math topics, if you are going to work in engineering, physics or astronomy, chemistry, (sometimes) biology and generally any science. Otherwise, for many other areas, you really don't need calculus - although knowing the basics is interesting, for general culture.
Discuss with your tutor(s). They will know whether you will able to do it or not. Also, you will may to consider what courses you will need for whatever you wish to do after your senior year.