I was half unschooled, half homeschooled for 9th and 10th grade
I finished high school with a degree but I never actually completed high school. I think I had the credits of a sophomore. As a freshman admit I got into the most competitive public school in the world. I was very methodical in my approach and I think I know a couple of things.
Domination3000, your grades are poor, but that won't stop you. AP History is good, an A in it is good, but you need to score high on the test. You said you could do upward algebra 1 in your head. Excellent. I suspect you might have good test taking skills.
Here's what you need to do:
Testing: enroll in a Princeton review SAT prep course. Practice your ass off. I studied 35-40 hours a week for the SAT 1 reasoning test for 2 months following my course, and about the same for the SAT II subject test but for 1 month (I took them a month apart). For the SAT II subject tests, take History and either Literature or Spanish. Buy the princton review literature book, and the both the Princeton Review and the Kaplan history books..
This is a matter of practice
Here's how you study. After school everyday you take half of an SAT test. Use a timer, be strict. Do the practice essay when you do the practice test and use the template provided by the princeton review book. Your intro should read similarly (There are five sentences in the intro, they are applicable to any topic. There are two supporting examples. They do not need to be true, they need to be logical. etc) score yourself brutally.
On Saturday and Sunday do a full test each day.
After you finish each test, immediately score it. Scoring your test and reading why you got your answers wrong is one of the most important parts.
Doing this rose my score from an attrociously low 1580 on my first practice exam to a dramatically improved (but still disappointing for me) score of 2110. I got an 11 on the essay.
When doing the subject tests:
For history: read the princton review book first. It gives you the perspective and the narrative. The Kaplan book gives you the data. Read this book constantly. There's a family photo of me at thanksgiving. I am holding the Kaplan book. I got an 800 on that test.
For literature. The princeton review literature book will teach you everything you need. It's a brutal book. The author is an idiot and gets some of her own questions wrong. When you do the practice tests, if you are like me or my little brother, you will score about 100-200 points lower than when you actually take the test. Something about the book really improves your game. I knew none of the literature I was tested on, and this book saved my butt.
Personal Statement:
The personal statement/essay is huge. Don't kid yourself, this is the most important part of your application. This becomes increasingly true when a school's reputation is secure and they are looking to take risks on potentially extraordinary candidates. In your personal statement you are asked and expected to present your best side. Don't be humble. Don't be obnoxious, of course, but say it all.
You need to identify what makes you unique and what challenges you have overcome. The key word here is "overcome". You were homeschooled and behind. You will catch up working extra hard. This shows your potential. You need to sell yourself as a leader, which means someone who will take initiative and succeed regardless of not only where you go to college, but whether or not you even do.
You want to write about how you are a learned, self-educating person (you could include a reference about reading lots of books, respected newspapers, etc) who will
contribute. What are you going to give. Who are you and what do you have to give?
Before you write your essay you need to write a self-brag sheet. Write everything possibly cool about yourself. I wrote a huge one that I referenced for my essay.
Once you write your essay, edit it and re-edit it over and over until you think it's rock solid and true for you. Be smart about every word.
Pick words that engender positive feelings. Express gratitude. Even when talking about negative things think about the connotations of your language and how people emotionally react to those words. This is especially important because you will have your essay skimmed.
Your essay will be read and decided upon in under a minute. Maybe in 15 seconds. But it's the most important thing in your application. That and your scores. Grades matter but they matter the least.
Because having an A+ in 8th grade math or AP US History does not compensate for getting a C- in AB Calculus.
Getting a C- in Calc looks better to a top school than capping out with an A+ in Algebra II. That said it's very important to try for all A's. An A is expected. A "B" is forgivable but dings you, a C is outright harmful. However my little brother got into every school I did and more and had some C's.