Supplemental math textbook for high school students, with innovative features:

- shortcuts in solving linear equations and inequalities
- innovative techniques in solving by number line
- innovative approaches in solving by graphing, using graphing calculators

This book is a review and study guide to the basic skills needed to understand basic math and pre-algebra concepts. It focuses on fractions, simple equations and geometry formulas.

It will help parents of students who need extra help in their math homework. It will help the adult who may need to refresh their math skills to reenter the educational arena. It will act as a review book for those who may have to take a math placement test for their employment.

This book condenses the vast amount of subject matter, presents it in step-by-step format to better understand the way to work problems. It eliminates the many pages that a traditional textbook would use and capsulizes on the important concepts to maximize its usefulness.

This book was written for high school students and teachers who love exploring beyond standard math curricula for a deeper understanding of the principles and applications of mathematics. It is also for anyone who loves the pursuit of a problem solution, including both professional and amateur mathematicians. The vehicle that transports us through this exploration is the study and solution of classical and advanced math problems.

As a high school math student, an engineer, a businessman and, ultimately, a high school math teacher, I collected and created math problems and solutions that can be used for advanced study. Some of the problems may be very familiar to you; some may not. A few may be quite easy to do; others will take more time. Included are classical proofs and their extensions that are often omitted in today's curricula.

Beyond the pure enjoyment of this exploration, we also attempt to find a "deeper understanding" of the math. We address four larger aspects of "understanding," namely: convention, evidence, perspective and connection. A portion of these aspects is addressed in the solutions, themselves. The rest is in comments, which come after the solutions. The comments range widely, including: additional points regarding the math itself, historical factoids, linguistics, suggestions for teachers, some personal experiences regarding the material, etc. Readers who only skim the problems and solutions might still find the applications and comments quite interesting.

It is hoped that this book will assist teachers and students alike in exploring the subject of mathematics in a new way, whether using material that is thousands of years old, or recently developed. Each problem can be used as a single assignment, done in a few minutes, or a term project that could require intuition, technique, research and/or fortitude (to plow through it). The material can be adapted for use in the standard classroom, subject to students' ability and the constrictions of uniform curricula. It is, perhaps, more applicable to classrooms with the freedom to experiment with project learning and with longer assignment periods. School math clubs or math teams might find this text a handy reference to hone skills, learn new techniques and satisfy the quest for more exciting material beyond the routine.

Although the primary focus here is the application of math principles to math problems, these studies are extended to interdisciplinary examples in the sciences, engineering, finance, social studies, etc. The subject material itself is organized into groups. There are twenty-two geometry/trigonometry problems, many of which are "classic proofs." Though some have been forgotten or ignored at large, they are offered here with some new ideas and approaches. There are ten algebra problems, all of which are extensions of a standard curriculum, and offer fresh insights when studied as a group. Statistics, the newest subject to be added to the high school curriculum, has three problems. And calculus, which is not always studied in high schools, has five problems.

Originally formulated for the home-schooled student, this five hundred page text and study guide provides extremely detailed explanations in simple English with numerous example problems accompanied by narrative explanations for each topic presented. Reader friendly and logically organized, this volume serves as an all-inclusive high-school algebra text for the college bound student or as an excellent study guide to accompany any serious algebra or trigonometry course. Hundreds of practice problems complete with solutions are included in the text, covering every aspect of a high school or introductory level college algebra course. Also, it is perfect as summer reading for the student who wishes to get ahead or for adults participating in continuing education courses.

Topics presented include: Review of Fundamental Concepts, Systems of Linear Equations, The Matrix (Determinants, The Augmented Matrix, CrammerÕs Rule, Row-echelon Form), Linear Functions, Graphs of Linear Functions, Absolute Value Functions, Systems and Inequalities, Linear Programming, The Polynomial (Factoring, Binomial Theorem, Rational Factor Theorem), Polynomial Equations and Imaginary Numbers, Polynomial Functions, Rational Expressions, Inverse Functions, The Conic Sections (Parabola, Circle, Ellipse, Hyperbola), Exponents and Logarithms, Logarithmic Equations, The Natural Logarithm, Exponential Functions and Applications, Triangle Trigonometry (Law of Sines, Law of Cosines, Law of Tangents), Radian Measure, Inverse Trigonometric Functions, Graphing Trigonometric Functions, Trigonometric Identities, Sequences and Series, Summation Notation, and much more.