Precalculus - A Unique Approach

The title “Pre-calculus - A Unique Approach” immediately suggests the ques- tion; “What exactly is unique about this book?” Before I answer this question, I need to describe most pre-calculus textbooks. They typically run to more than one thousand pages. The contents include irrelevant visuals, examples and solutions for every type of problem the student will be asked to solve, SAT practice, multiple practice exams and topics the student is supposed to know before taking pre-calculus and topics that are beyond the scope of the course. In addition, the practice exercises usually contain as many as 100 problems, many more then will ever be assigned by a teacher. This book is designed for the high school student. The amount of material in each teaching unit is limited to what is reasonable to cover in a single 50 - 60 minute class. Most exercise sets contains exactly 15 problems, about the number most student can complete within an hour. Approximately 10 are dedicated to the material in the lesson. The remainder are problems re- lated to lessons that are taught earlier in the course. This approach solves a retention problem with which we are all familiar. Too often students are pre- sented material which they don’t revisit for a year or more. How often do you ask your students to apply the quadratic formula only to realize they forgot the details. Or ask your students to apply the definition of a trigonometric function to discover that they confuse the definitions of sine and cosine. We include problems on these topics and all the others throughout the book. The student never finishes learning a topic. The size of the book is also unique. The book contains fewer than 500 pages, less than half the size of most pre-calculus books. All the topics in other pre- calculus books are covered and the contents meet the pre-calculus standards in all 50 states. However, we omit the extraneous, irrelevant material, the exercise sets with 100 problems most of which are never solved, the SAT practice and a study of limits, which properly belongs in calculus. Furthermore, we encourage students to think more deeply about the topics covered. We offer a few questions that go beyond those modeled in the lesson. We also offer a challenge problem with most exercise sets. These problems are optional and will probably only be of interest to the more inquisitive student. They are problems this author came across over his career or problems taken from mathematics contests.