A higher percentage of female applicants will be admitted to the engineering schools at Princeton and Columbia than to the colleges of arts & sciences.
BUT .. applying to engineering might be a bad choice for you for a couple reasons.
The first is the one you’ve cited … a math score that is below par for the top engineering colleges. However, if you retake the SAT and do somewhat better, or if you have a good score on the Math 2 Subject Test, then you can revisit this issue.
I would also recommend taking Subject Tests (or AP Tests) in physics and/or chemistry, if you are aiming for a highly selective engineering college. Princeton actually requires one subject test in physics or chem for its engineering candidates. Columbia says candidates can choose from among bio, physics, and chemistry. Although you would meet that requirement with just the bio Subject Test, I think you might disadvantage yourself if you haven’t taken chemistry and/or physics, too, because many of your “competitor” applicants will have earned high scores in those areas.
The other reason why you shouldn’t apply to engineering schools is that you aren’t committed to engineering. Although you would have some space in the engineering curriculum for liberal arts electives, engineering programs don’t allow a lot wiggle room to explore new fields.
But what if you think you might want engineering but can’t tell until you try it? Here’s some good advice from the FAQ section of the Princeton engineering Web pages:
I’m an A.B. student but I might be interested in engineering. How do I keep my options open?
Take Physics 103-104 or 105-106 (unless you have AP credit based on scores of 5 on both parts of the Physics C exam) and Math 103 or higher (depending on your preparation) in freshman year. The other two courses can advance you toward the A.B. degree, so maybe a language course and a humanities or writing course. If you really want to take the full B.S.E. program, you could also take chemistry, but we can usually work that in later unless you want to do CBE. If you’re interested in Computer Science, take CS 126 sometime in freshman year. Come see Dean Bogucki as soon as possible.
While I know that it is daunting to see how many outstanding high school seniors are turned away from Ivy and other “elite” colleges each year, and I realize that it is tempting to do whatever you believe will help you to beat the odds, I don’t think that engineering sounds like the right route for you … at least not at present. If your math score goes up, if you do well on physics and/or chem tests, and if you have a chance (maybe over the summer?) to explore engineering and to decide that it’s really the path you want, then maybe my advice will change. But for now, I recommend steering clear of engineering schools but considering some of those prerequisite courses as a freshman so that you can leave the option open.