Learning Mathematics using Khan Academy

My experience with Khan Academy is that it has decent coverage of K-12 mathematics, and increasingly spotty coverage the more advanced you get. In answer to the question, I would say that mastering the Khan Academy materials would put you ready to take a GED (high school equivalency exam) or SAT (college entrance exam). You would also have hit-and-miss knowledge of calculus and additional advanced topics. It's no substitute for taking the courses at an accredited college or university.

For example, I've taught flip (upside-down) calculus classes where the students view lectures from online sources that I've aggregated. Khan Academy videos alone would not enable anyone to pass the course; some topics get decent coverage while others are completely omitted.

I've used Khan Academy here and there while earning my degree in mathematics to reinforce my understanding of topics that were covered hastily during lecture etc. I enjoy it because I can focus specifically on those topics that I want to focus on.

However, Khan Academy is better used, in my opinion, as an ancillary resource. I think subscribing to a structured course, such as those offered through MIT's open courseware program, might be a better idea. If nothing else, those structured courses are likely to more thoroughly cover each subject, which helps you avoid holes in your understanding of each subject.

As I have begun to teach myself advanced topics in my spare time, I've found that working my way through books while supplementing with online materials works best. Perhaps that is just me? I think having lots of exercises really helps reinforce my understanding of ideas. For example, I can absolutely understand the definition of continuity offered in analysis. However, reading the definition and the proof and understanding both is much different than sitting down and working my way through a dozen delta-epsilon proofs. This coursework is often missing when using online material, hence my reasons for guiding my studies with textbooks.

If your concerns are more broad - something along the lines of "what topics should I study if I want to give myself the rough equivalent of an undergrad degree in mathematics" - then your best bet is to pick out a few course catalogs from some top programs and systematically study each subject in whatever way works best for you.

Khan Academy tends to oversimplify some topics, so that they can be easily understood by newcomers. Although this is totally understandable, when you study at a university you want to emphasize more in some things..

That being said, the only way (imo) to gain the most from Khan Academy is by following your class lectures and keep watching the parts, you have difficulty in undestanding during class. This way you can benefit from the simplicity of the lessons, and as Bib mentioned in a comment above, it will sometimes give you a different perspective on a difficult math theory for example.