It varies by state as to whether there are standardized tests required. Our state didn't (still doesn't, far as I know) require testing, but required students to either be under an umbrella school (like the private school served for our son for early on) or to come in to meet with teachers I think it was twice a year for a portfolio review. The teachers we had for our reviews were incredibly supportive of our son and our homeschooling him. The meeting place was a huge internal room with no windows, and one time, there was a power outage and we were all in pitch blackness. Our son was 8 at the time and had brought it a Lego Mindstorms creation of his and he felt around on the table for his remote control for it and had the lights on it turned on in no time and was using that light to escort people out. One of the teachers asked for our son's autograph and said, "You'll be on the cover of magazines in no time!"
He never applied for a GED. At age 8, he took the SAT to see if he could qualify for a CTY engineering summer course that could also give Johns Hopkins college credit (for an extra price), and his scores not only qualified him for that course and all the other CTY courses, but had the state U close to us interested in him. They asked to meet with him as soon as they saw his scores, and handed him an application when he met with them, which he filled out and mailed as soon as he got back home, and within a week, his admission was in our mailbox. This was not at all what I expected when we approved of his taking the SAT so young, nor anything I was particularly comfortable with happening (and we did hold him off till he turned 9, at least), but he had been asking to attend college math and engineering courses since he was 6, and had we to do things over again, I actually think we'd have been better off letting him start college at 6, bizarre that I know that sounds.
We never had the issue with our son not being interested in learning an important skill. Instead, we had the issue of his wanting to learn skills before we were feeling it was worth his learning them. For example, he wanted to learn calculus when he was 7. I typically bought him whatever books he wanted, but this was one where I drew the line. But then he became the top fundraiser in the state for a Multiple Sclerosis read-a-thon (his third year in a row doing so) and one of the prizes was a $50 Borders gift certificate and he used that to buy himself a calculus book. When he took calculus at the university at age 9 (as that is the level the college placement test put him at, must to we parents' shock), he was one of the top students in his class of over 160 students, and he had never even taken anything past algebra I formally before taking that calculus class. But his lack of having had geometry/algebraII/trig/precalc prior to college did not cause him problems in math down the road; he earned one of his bachelor's degree in math at age 13, and took a mix of five college upper level and graduate level courses one semester in modern algebra and number theory, math analysis II, and three other math subjects plus an upper level CS while doing a paid internship off campus and still got a 4.0 that semester (he also did fine in graduate-level math courses at MIT and Harvard). And math is probably the area where most think a linear progression is key, but for some, it actually doesn't appear to be.
He never applied for a GED. At age 8, he took the SAT to see if he could qualify for a CTY engineering summer course that could also give Johns Hopkins college credit (for an extra price), and his scores not only qualified him for that course and all the other CTY courses, but had the state U close to us interested in him. They asked to meet with him as soon as they saw his scores, and handed him an application when he met with them, which he filled out and mailed as soon as he got back home, and within a week, his admission was in our mailbox. This was not at all what I expected when we approved of his taking the SAT so young, nor anything I was particularly comfortable with happening (and we did hold him off till he turned 9, at least), but he had been asking to attend college math and engineering courses since he was 6, and had we to do things over again, I actually think we'd have been better off letting him start college at 6, bizarre that I know that sounds.
We never had the issue with our son not being interested in learning an important skill. Instead, we had the issue of his wanting to learn skills before we were feeling it was worth his learning them. For example, he wanted to learn calculus when he was 7. I typically bought him whatever books he wanted, but this was one where I drew the line. But then he became the top fundraiser in the state for a Multiple Sclerosis read-a-thon (his third year in a row doing so) and one of the prizes was a $50 Borders gift certificate and he used that to buy himself a calculus book. When he took calculus at the university at age 9 (as that is the level the college placement test put him at, must to we parents' shock), he was one of the top students in his class of over 160 students, and he had never even taken anything past algebra I formally before taking that calculus class. But his lack of having had geometry/algebraII/trig/precalc prior to college did not cause him problems in math down the road; he earned one of his bachelor's degree in math at age 13, and took a mix of five college upper level and graduate level courses one semester in modern algebra and number theory, math analysis II, and three other math subjects plus an upper level CS while doing a paid internship off campus and still got a 4.0 that semester (he also did fine in graduate-level math courses at MIT and Harvard). And math is probably the area where most think a linear progression is key, but for some, it actually doesn't appear to be.