Pre-Calculus Textbook

Taken from the intro: One challenge I had throughout my first semester at Thomas Jefferson High School for Science and Technology ("TJ") was difficulty adjusting, especially with math. I was used to half-listening to my teacher's lectures, cramming for 30 minutes the night before tests, and then doing well on them. After a very short time at TJ, however, I quickly realized the results I was accustomed to would not be the case if I continued with my same approach and level of effort. Although I tried to study more effectively and efficiently, including doing all the review sheets I was given, I performed below my standards on basically every test. I attribute this to three main things: bad study habits, a lack of useful resource materials to help support success in rigorous math courses, and not taking summer-school classes before my freshmen year to prepare me better for what was to come. The purpose of this book is to solve two of these issues. First, I have "attempted" to provide a deeper analysis of topics covered in Pre-Calculus, designing this book to be almost entirely proofbased. As a result, most equations we derive will have a complete, annotated proof preceding them. I have also included what I think are relatively difficult problems, hopefully providing "TJ-level" test questions that driven, yet usually nervous, students so fervently desire. Although there are no guarantees, I believe that if one does all the examples and problems and truly understands them then they will be in good shape for the relevant test. Emphasis on the 'truly understand' part. Now, the other issue I hope to address: I feel there has been some deficiency and inherent unfairness in the TJ system for some time; for the most part, only students who are willing to sacrifice large portions of their summers and come from families financially well off enough to pay for summer school can learn and get ahead. The rest of the students aren't "left behind" but, based on my observation and experience, are certainly at a disadvantage compared to their peers. This has always bothered me and I'd like to do a small part to address this situation constructively and level the playing field.