Textbook recommendations for self-studying high school math? I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a complex issue for me, as other students at my competitive high school have tutors and the like. Please recommend textbooks that have detailed explanations and progressive practice problems, for self-study for each area such as:
Algebra
Geometry
Trigonometry and Analytic Algebra
Pre-calculus
BC Calculus
Other people have skipped grades of math due to help from tutors and parents. Can I cover all of geometry and trigonometry in 8 months without going insane and be able to skip a grade?
 A: If you master pre-algebra, then you can figure out almost any other branch of mathematics using the appropriate study material. Geometric formulas will be second nature to you. Trigonometry and Calculus are not required to graduate from every high school. If you are strong in Algebra, then your college placements scores will exempt you from college preparatory courses. 
College preparatory courses are great if you want to master the fundamentals. I suggest you take all the college preparatory courses in your field if you are going to specialize. For Mathematics, you should take discrete mathematics.
Because of the way the brain works, you will gain better dominion of subject matter by studying for a few hours everyday rather than cramming. Yet, you seem to have found out how some high school experiences are less adequate than independent studies.
You might want to go for the General Education Development test, then transfer to a college or university. A community college offers more advantages for students. You can get an associates in arts degree and transfer to a university from there to get a four-year college degree and postgraduate degrees. (You will need to pass college algebra and another college level mathematics course to get your associate in arts degree.)
Have you ever skimmed or read from a GED preparation workbook? You should go a college library and take it out. It's similar to the SAT workbooks. These books will give you detailed explanations. Yet, what do you mean by progressive practice problems? The word progressive can have many meanings; do you mean updated versions? That's up to the student to send in suggestions and report errors to the publishing company.
Remember, it's what you learn that counts. Most things we believe to be requisites are psychological exaggerations. Remember, being a student is a profession.
A: You probably won't find one book that covers everything, but in all honesty if you're a good math student you could probably skip through trigonometry with ease. I'd recommend Algebra Demystified and Trigonometry Demystified. They have a good amount of practice questions, and go through the motivations of the topics involved (especially in trigonometry). You could also find more than enough around the internet, say through Khan Academy which has plenty of videos and more importantly a decent practice section.
While I'm not sure what the curriculum is where you are, in my high school we did:
Grade 9: Cartesian coordinates and linear equations
Grade 10: Quadratic Equations (factoring, expanding, completing the square and the quadratic formula) and basic trigonometry (working with definitions of $\sin$, $\cos$ and $\tan$).
Grade 11: Functions, factoring higher-degree polynomials, proving trigonometric identities, shifting/stretching functions, graphs of trig functions.
Grade 12: More functions, inverses, exponentials and logarithms, inverse trig functions, secant,cosecant and cotangent functions, how to divide polynomials the long way and with synthetic division, the remainder theorem and rational root theorem.
I don't think that's quite everything, but it's more than enough. Stroll through google books (you can see quite a bit of the books on there, including whole sections and practice problems) and the internet at large if you want more. Also see this wonderful list of legitimately free textbooks and/or course notes.
A: I have created some autocorrected online exercises in Mathematics that you could use as supplemental material.
I have also started an online index to the fourth edition of James Stewart’s Calculus textbook, as a subset of “Mike’s Ready Reference”. My online index is much more detailed than that of the textbook itself.
A: The books Stewart's pre-calculus, mathematical Ideas and Stewart's calculus contain all of the material that is assumed to be needed to enter college and more. I used all of those during elementary and high school.
However I also recommend that you go to practice contest type questions because they are good for learning some problem solving and they can be very fun.
A: Have a go at the book Mathematical omnibus. Thirty lectures on classic mathematics by Dmitry Fuchs and Sergei Tabachnikov. This book will engage your mind and point you to very interesting mathematics.
Another good book to try out is this one: Vladimir Arnold: Problems for children from 5 to 15. 
A: Algebra: 
1. Algebra for Beginners.
2. Elementary Algebra.
3. Higher Algebra.
All three by by Hall and Knight.
A: You can check out the following books for "detailed explanations and progressive practice problems":
Schaum's Outline of Review of Elementary Mathematics
Schaum's Outline of Elementary Algebra
Schaum's Outline of Intermediate Algebra
Schaum's Outline of Geometry
Schaum's Outline of Trigonometry
Schaum's Outline of Precalculus
Do note that these books from the Schaum's Outline Series are not intended to replace traditional textbooks on the subject matter, but are meant as supplements.  Personally, I have obtained the best-possible benefits from these books by reading some other introductory textbooks on the subject matter,  supplementing my readings with further material from the Schaum's Outline Series books, and then trying to solve the practice problems afterwards.
