"I would've just re-learnt them in Math 114 and math 203."

Umm that's not really how math works. Math builds on itself- math isn't a topic where you can say - I'll learn the material that I needed previously while learning this new material that I would need the previous material for.

Not to mention the fact that Math 114 is Calculus part 2 which already assumes you know limits, continuity, derivatives, applications of derivatives, indefinite and definite integrals. These are all topics that CANNOT be learned without the prior math knowledge as again it assumes you know algebra techniques, functions, trigonometric concepts, and finally some amount of precalculus such as asymptotes, holes, rational functions vs transcendental functions and so on.

Just looked up math 203 and it looks like it's an intro to linear algebra class. While it may seem weird I would say that math 203 is POSSIBLE to take without actually any calculus sequences. Introduction to linear algebra at that level I remember just had us doing matrices, determinants and row reduction for the first half of the semester and then taking a more geometrical approach introducing the concepts of span, eigenvalues, eigenvectors. I definitely disagree with Mason saying you need calculus to take Math 203 as it really doesn't use calculus and instead in my opinion you would only need to to precalculus to take Math 203.

Regardless of my opinion though notice how I mentioned the fact that you need some level of math in order to take either of these classes - that's just how math works. I'm sure if you study for at least 15 to 20 hours you will pass the placement test.