I recently received my SAT scores (the 2400-scale SAT, not the new 1600 point one) and was both disappointed and relieved. I achieved a high score in reading, a somewhat decent score in writing, and a relatively poor score in math.
While practicing for the SATs, I neglected the math sections, thinking they would be easy. Nevertheless, on the test, I answered four questions wrongly, and my mistakes costed me 110 points!
Given that I would like to major in engineering, having a high SAT math score is crucial. Since I would prefer not to complete the new SATs, I was wondering if achieving a higher score in SAT math II compensate for my lower SAT math score? Also, do colleges tend to overlook SAT math scores if SAT math II scores are higher?
While a high Math II score can certainly help you in the admissions process, it will not fully compensate for a lower-than-average SAT I Math score. Your SAT I scores (or ACT scores, as the case may be) are the most important standardized test scores that colleges will consider in judging your academic abilities.
My first piece of advice is to check where your score falls compared to the average Math SAT score ranges for the colleges where you plan on applying (just Google "[school name] SAT Scores PrepScholar" to find our database page with this information). Since you said you lost 110 points, I assume your score is a 690, which is by no means a bad score in the eyes of most schools. You should only consider retaking the test if you find that your score is below the 50th percentile at the schools that interest you.
In that situation, you can either taking a break from testing until senior fall so you have more time to prepare for the new version of the SAT, or consider taking the ACT this spring instead. Try taking an ACT practice test to see how well you do. You might find that the ACT math section is easier for you.
If you got a 690 without any review and are applying to top-tier engineering schools, it's probably worth it to spend a bit of additional time studying, retake either the SAT or ACT, and get a perfect or close to perfect score on the Math section.