You will need to buy the book then send a email to the author. He will send you the solution manual. The email address of the author is listed in the introduction page of the book. I ordered the book from
http://universal-publishers.com/book.php?method=ISBN&book=1599428229
Years ago my high school math teacher showed us how to find the center of a given circle using only a compass, nothing else. I can't remember how. I need to do it now. Does anyone have the answer?
Your description of the topics you've covered suggests that you have studied mostly algebra II. You are still missing matrices, complex numbers, sequences and series, and conics to complete algebra II.
As to whether you could go all the way to calculus without precalculus, a qualified answer...
If you order Aboughantous' book from the publisher, because of your status as selflearner you will qualify for a free copy of the solution manual. It contains detailed solutions of all the problems in the book.
good luck