Pre-Calculus Know-It-ALL

Book Preface

This book is intended to complement standard pre-calculus texts at the high-school, trade-school, and college undergraduate levels. It can also serve as a self-teaching or home-schooling supplement. Prerequisites include beginning and intermediate algebra, geometry, and trigonometry. Pre-Calculus Know-It-ALL forms an ideal “bridge” between Algebra Know-It-ALL and Calculus Know-It-ALL.

This course is split into two major sections. Part 1 (Chapters 1 through 10) deals with coordinate systems and vectors. Part 2 (Chapters 11 through 20) is devoted to analytic geometry. Chapters 1 through 9 and 11 through 19 end with practice exercises. They’re “open-book” quizzes. You may (and should) refer to the text as you work out your answers. Detailed solutions appear in Appendices A and B. In many cases, these solutions don’t represent the only way a problem can be figured out. Feel free to try alternatives!

Chapters 10 and 20 contain question-and-answer sets that finish up Parts 1 and 2, respectively. These chapters aren’t tests. They’re designed to help you review the material, and to strengthen your grasp of the concepts.

A multiple-choice Final Exam concludes the course. It’s a “closed-book” test. Don’t look back at the chapters, or use any other external references, while taking it. You’ll find these questions more general (and easier) than the practice exercises at the ends of the chapters. The exam is meant to gauge your overall understanding of the concepts, not to measure how fast you can perform calculations or how well you can memorize formulas. The correct answers are listed in Appendix C.

I’ve tried to introduce “mathematicalese” as the book proceeds. That way, you’ll get used to the jargon as you work your way through the examples and problems. If you complete one chapter a week, you’ll get through this course in a school year with time to spare, but don’t hurry. Proceed at your own pace.

Stan Gibilisco