its VERY VERY VERY hard math its VERY VERY VERY hard math
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Generally pre-calculus is taken after trigonometry, unless the trigonometry course was supplemented by a pre-calculus course, in which case the next course would be calculus.
Pre-calculus is hard because it is very algebra intensive but forces you to also incorporate your geometry and trigonometry to solve complex problems. Not only this, but precalculus is designed to expose you to a few of the oddities in advanced mathmatics (holes, end behavior etc). Calculus is then even more difficult because it differs so greatly from pre-calculus. rather than definite answers and standard functions, you now move into "theoretical math," where many problems either have very complex answers or no answer at all, and very often, you are required to prove that your answers are logical using mathematical therums. however without your strong base from pre-calculus, trying to learn these new concepts would be almost completely impossible. My advice you anyone struggling in either calculus or pre-calculus would be to keep at it. study hard and practice as much as possible. Good luck!
Definitely AP Algebra (1)^2.
No, you can't. Although similar in concepts, Pre-Calculus is more advanced than Algebra 2. Algebra 2 is taken between Algebra 1 and Geometry or after Geometry and before Pre-Calculus. The reason that you can't take both at the same time is because of the curriculum. Pre-Calculus does not spend nearly as much time on linear topics (linear equations, linear programming, etc.) as Algebra 2 does. Pre-Calculus also almost always is 2 courses in one: Pre-Calculus and Trigonometry. Algebra 2 has very little, if any, trig. Topics that they have in common are quadratics equations/functions, polynomial equations/functions, rational functions, exponential & logarithmic functions (sometimes these are not covered in Algebra 2), possibly conic sections in Algebra 2, definitely in Pre-Calculus, factoring, and probability/sequences/series/statistics. In addition to trigonometry, pre-calculus also covers polar and parametric topics (these will NEVER NEVER NEVER be seen in Algebra 2) and an introduction to limits. So, you must take Algebra 2 before pre-calculus. If you want to take 2 math courses in 1 year, try algebra 1 and geometry (not very common), algebra 2 and geometry (somewhat common), and some schools allow honors students with a solid A in Algebra 2 (assuming you took Algebra 2 before Geometry, this differs between schools) allow you to take geometry and pre-calculus in the same year. The study of proofs is not a major topic in pre-calculus, and proofs make up a majority of geometry.
At my high school, pre-cal mainly consists of trigonometry and advanced algebra and geometry. As the name suggests, it is very important for the preparation of entering a calculus course. In Calculus, using some, but not all, knowledge learned in pre-cal, you start to do things like solving derivatives and anti-derivatives. These help to solve instantaneous rate of change (or slope) of a curve, and the area under the curve, respectively, and much more advanced calculations. I think it is quite fun, though pretty hard sometimes. But then again I am a nerd.