We all have different kinds of intelligences. I'm the opposite of you in that I am great at writing assignments but I suck at math. Try taking a "types of intelligences" quiz online or something.
If you are good at math but not at writing papers throughout your entire education, does that make you unintelligent?
It is also important not to confuse education with intelligence. Some very well educated people show limited intelligence. It is rare, but perfectly possible to be highly intelligent and completely illiterate.
Intelligence is itself difficult to define, but it is usually defined in terms of educability, ability to solve problems, memory and creativity (but opinions vary and those are not everyone's definitives).
Not at all.
There are two specific types of "reasoning" ability---concrete vs abstract.
They are measured on one axis but the graph is not a typical one.
If you are 5% concrete, then you are 95% abstract. If you are 95% concrete, then you are 5% abstract.
Engineers tend to be "concrete" thinkers; lawyers tend to be "abstract" thinkers.
Engineers are good at math a physics; lawyers are great with written output.
Some are good at both---50% and 50%.
It's just like being born either male or female---both human, both different, both essential.