You can have a high IQ and fairly low scores. My brother had a 138 IQ, and a 1900-ish on the SAT. His ACT was pretty bad too, below 27. Given, he attends a good school (UNC Chapel Hill) and is doing pretty well. If you speak with him, it is very obvious that he is very intelligent.
His low scores should also be coupled with his work ethic. Throughout high school he hated to do anything academic, never studied for anything, and thought that he should put his time into more productive aspects of life. He would volunteer at so many different places, and his ECs are at the level of a student who you would think would attend an Ivy League like institution. He didn’t do them to build up his resume, he did them because he was motivated by the thought of being productive.
A high IQ can get you to the 1900-2000 mark of the SAT, but I do believe it takes hard work and practice from there if you want to achieve a 2200+.