Textbook recommendations for self-studying high school math?

Question

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?

Answer 1

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.

Answer 2

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.