Since I fall into the second group I think I have a good idea of how long and hard the math track in engineering can be. With that said, don’t worry about it. If I had seen what was done in diff eq’s that first year I was taking algebra I may very well have just given up on the spot. But, these subjects build on one another. You just have to study and practice and before you know it you’ll have a cap in one hand and a sheep skin in the other.
As for being an EMT, maybe you can do that while you go to school. It’s always good to have a fall back plan.
The math is not that bad. The hardest math class I had in college was Linear Algebra. Which is the class after Diff.Eq. That class was matrix math and those concepts were a little harder to grasp. I don't think it helped that I could barely understand the professor either though. Mechanical Engineering pays more than a paramedic and there are a lot of job opprotunities out there. Being a paramedic isn't a bad job either though, but you put yourself at risk for more liabilities that will cost you your job though. You screw up once, it's hard to get another job in that field.
Unless you are a trust fund baby, don't you have any plans for the future? What about supporting a family? Can you make a career as a Paramedic? Will you be able to get on with a fire department? Yes it is the easy way out since there is not much math and no college required but it might not be the job you envision it to be.
I hate to break it to you, but ME has nothing to do with cars. You will not take one course that talks about cars.
The closest thing to cars is Thermodynamics, a course teaching you the science of heat transfer. It is a math intensive class with lots of formulas, but if you excel in that class, you should roughly understand how heat transfer converts to mechanical energy in engines.
Do not let that worry you. Do your best to pass the exam. You will find that you hardly ever need to use it in practise. There are other branches of engineering besides cars.
I like cars and wanted to major in Mechanical engineering because I loved cars and wanted to be an engineer that deals with cars. I got second thoughts when I saw Calculus, Differential equations, and other higher level math. I love math a lot but I have seen samples of higher maths and got nervous about math altogether. Should I go with mechanical engineering or go with my backup plan to be a paramedic ( I like this too)? Note: I don't care about the salary of each occupation.