When I was an undergraduate, my professors sometimes liked to put that extra question on the test to "separate the As from the Bs". Sometimes it was a thinking question. That's great for me because I like to think (even though it can be hard to do in a short amount of time on a test). You had to go a little bit beyond what they taught you in class to answer the question.
Occasionally, they might make a mistake. You might get a question that requires you to think a little, but it doesn't depend on the material as much as it should. Those questions saved me on some engineering tests. I'm not as good at solving analog circuit problems as I am at just thinking a little.
I'm also better at doing the math than some of the engineering problems. That's why when the special question is just a math question, I often outperform the other engineers. Professors love to put a short linearity question on their tests. I also love these questions because if you understood linear algebra, they're free points.
And so that brings me to the point of all this: learn math. If nothing else, study linear algebra. You will get higher grades on your engineering tests. You will be able to answer the challenge questions.
But more importantly, having a solid understanding of basic higher level math will make you a more valuable engineer or scientist (depending on what you're doing). Specifically, learn linear algebra, numerical analysis, probability, and statistics. You don't need to know really advanced linear algebra theorems or really advanced probability techniques. You just need a solid understanding of the basics. All of the advanced research papers you read (if you read them) will assume an understanding of these things. All of your advanced classes will be easier if you understand basic math.
When sophomore year rolls around, and all your professors are going over matrix multiplication and complex arithmetic for the twenty-third time, you can gloat privately. You know what the other students are in for when the professor zips through basic linear algebra concepts at ninety miles per hour later on during the course. But you're not worried. You took linear algebra last semester. On the test, you're going to solve the challenge problem in 30 seconds. They're going to sweat for ten minutes. Better start studying.