Well it depends on which calculus class you are longing for. If you want AB Calculus then you are not required to take pre-calculus; however you must finish all of state's required math courses. Which is probably Algebra, geometry, algebra 2/trig.
If you want BC calculus, you need Pre calc and all of the required math classes. BC calculus is a lot more difficult and it will require a lot more time after school. If you are not willing to spend as much time as required , dont dare to take it
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You must have a strong basis in Algebra, Algebra II, Geometry and Trigonometry. Usually high schools offer a pre-Calculus course which is somewhat of a conglomeration of the aforementioned courses. Then you would move into differential calculus, integral calculus, vector (multi-variable) calculus, and finally differential equations, which is considered to be at the top of the hierarchy of the calculus courses. So take Algebra, Algebra II, Geometry and Trigonometry to get your strong foundation before begining the calculus sequence.
Pre-calculus covers the basics you will need for calculus, including exponents, algebraic formulas and solving equations. Calculus is where mathematics and physics intersect - you can calculate the speed and velocity from a nonlinear function describing the distance traveled at a given time.
Calculus is much harder than statistics, and don't really have anything in common other than algebraic process. Calculus is the study of rates, while statistics is probability.
Yes, most premed students do take 3 semesters of calculus in college.
It depends on your degree. If it is required by your degree, often an opportunity is provided to take it at the college. Math college classes proceed at a faster pace, so don't procrastinate if you are interested in math oriented degree.