If you want to go the engineering route it all begins in high school by taking 4 if not 5 years worth of math to be able to handle the rigor. I had 5 years in math including calculus to go along with AP classes in the humanities. In my school district only honors students were permitted to take the courses from a lineage that starts from the gifted programs in elementary school.
It is possible to get an engineering degree starting from not having the traditional prep background for it but its fairly rare.
A lot depends on the how rigorous the high school program is.
I work with the Civil Engineering and the Civil Engineering Technology and Construction Engineering Technology programs at FDU.
So I can only,speak to that.
Most of our freshman come in with 4 years of math.
(Algebra 1 and 2,geometry and trig/pre-calculus)
We get a limited number of students who also have had high school calculus.
If they only have 3 years of math,they have to take Pre calculus.
We find,regardless of the high school,a large % of freshman need some remedial classes in math.
Our freshman classes aren't that large.
We tend to get a lot of sophomore transfers.
Most of those kids found out they didn't like the large "name" universities.
Again,we find a number of those students have issues with Calc.III and Differential Equations.
A lot end up retaking Calc.II
The quality of high school AP programs varies a lot.
We've found that kids who were in programs that required taking the AP exam have a much higher level of competency then those who didn't have to.
At FDU we strive to prepare our graduates to take (and pass) the P.E. Exam.
Our exam questions are modeled after the Exam.
In fact,all seniors are required to take,but not pass,the FE exam.