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Simmons Precalculus Mathematics in a Nutshell - Geometry, Algebra, Trigonometry - Preface","","A concise preface explains the book’s purpose: consolidating essential precalculus skills into three nearly independent chapters—geometry, algebra, and trigonometry—to help high school students build the background needed for further study. It emphasizes reducing repetitive, unnecessary material while maintaining brevity and clarity, and notes that each chapter includes many exercises with answers and selected fully worked solutions. 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\nBooK 5  \nPREFACE  \nFor a variety of reasons,many bright peoplefind it difficult to learn in high school the mathe-matics they need to know in order to continueeffectively with their education.My purpose inthis little book is to try to help by pulling togetherthe essentials of the subject into three convenientsmall packages:geometry,algebra,and trigonom-etry.Most college mathematics teachers wouldbe overjoyed (and astounded)if their studentscame to them from high school in full commandof this much background material,but most highschool graduates today do not even come close.  \nThe three chapters that make up this bookwere written atdifferent times with different aims.They are almost completely independent,andeach can be mastered without reference to theother two.Chapter 3 contains several repetitionsof earlier material which I have left in place sothat students who wish to study only trigonometrycan easily do so.Each chapter has many exer-cises,and answers are provided along with anumber of fully worked-out solutions.  \nPrecalculus mathematics is not an infiniteshapeless mass that no one can hope to master.In order to demonstrate this,I have eliminatedmost of the repetitious and unnecessary materialoften included in precalculus mathematics text-books.I have also tried to achieve the utmostbrevity that will still permit students who arewilling to work at it to understand the material.If I overstep the bounds here and there,and pro-vide explanations that are too concentrated forclarity,I welcome suggestions from teachers andstudents for improvements that can be included infuture editions.  \nCopyright C1987 by Janson Publications,Inc.  \nThis edition published by Barnes&Noble,Inc.by arrangement with Everyday Learning Corporation  \nAll rights reserved.No part of this book may be used or reproduced in anymanner whatsoever without the written permission of the Publisher.  \n1997 Barnes &Noble Books  \nEven though few students enjoy studying math-ematics,many find it necessary to do so.If thisbook can occasionally ease the pain and smooththe learning process for these students,it willhave done its job.  \nISBN 0-76070-660-3  \nPrinted and bound in the United States of America  \n01 M 9876  \nRRDH  \nCONTENTS  \nCHAPTER 1.GEOMETRY  \nIntroduction………………………………………………………………………………2  \n1. Triangles…………………………………………………………………4  \n2. Circles…………………………………………………………………………………7  \n3. Cylinders……………………………………………………………………9  \n4. Cones………………………………………………………………………………10  \n5. Spheres…………………………………………………………………13  \nAppendix A. The main formulas of  \ngeometry……………………………………………15  \nAppendix B. A number of exercises, some easy  \nand some hard…………………………………………15  \nAppendix C. The answers to the exercises,  \nwith full solutions for a  \nselected few……………………………………………24  \nAppendix D. Triangular pyramids with equal  \nheights and bases……………………………27  \nAppendix E. Ceva's theorem………………………………27  \nAppendix F. Brahmagupta's formula………………30  \nCHAPTER 2. ALGEBRA  \nIntroduction……………………………………………………………………………………33  \n1. Basics………………………………………………………………………………………34  \n1.1 The real line…………………………………………………………34  \n1.2 Notation and the simplest rules of  \nprocedure………………………………………………………36  \n1.3 Integral exponents ………………………………………39  \n1.4 Roots and radicals……………………………………………40  \n1.5 Fractional exponents………………………………………42  \n1.6 Polynomials ………………………………………………43  \n1.7 Factoring…………………………………………………………45  \n1.8 Linear and quadratic equations………………461.9 Inequalities and absolute values………………49  \n2. Functions and Graphs…………………………………………51  \n2.1 The concept of a function ………………………512.2 Coordinates in a plane………………………………53  \n2.3 Straight lines…………………………………………………………55  \n2.4 Circles…………………………………………………………………………57  \n2.5 Parabolas……………………………………………………………………58  \n2.6 More about functions and their graphs.60  \n3. Special Topics………………………………………………………63  \n3.1 Logarithms……………………………","cbCaidln1Zb62OCT","https://ap.wps.com/l/cbCaidln1Zb62OCT","pdf",16667388,63,"English","# CHAPTER 1. GEOMETRY\n## Introduction\n## Triangles\n## Circles\n## Cylinders\n## Cones\n## Spheres\n## Appendix A. The main formulas of geometry\n## Appendix B. A number of exercises, some easy and some hard\n## Appendix C. The answers to the exercises, with full solutions for a selected few\n## Appendix D. Triangular pyramids with equal heights and bases\n## Appendix E. Ceva's theorem\n## Appendix F. Brahmagupta's formula\n# CHAPTER 2. ALGEBRA\n## Introduction\n## Basics\n## Functions and Graphs\n## Special Topics\n## Answers\n# CHAPTER 3. TRIGONOMETRY\n## Introduction\n## Misconceptions and necessary facts\n## Radian measure and trigonometric functions\n## Special angles, graphs, identities, inverses\n## Law of cosines and law of sines\n## Appendix A-E","[{\"question\":\"What is the main goal of the book described in the preface?\",\"answer\":\"To gather the essential background of geometry, algebra, and trigonometry into three compact, study-friendly packages for learners who lack preparation after high school.\"},{\"question\":\"How are the three chapters organized for study?\",\"answer\":\"The chapters are written at different times with different aims and are almost completely independent, so each can be mastered without relying on the others.\"},{\"question\":\"What learning aids does each chapter include?\",\"answer\":\"Each chapter provides many exercises, with answers included and a number of fully worked-out solutions.\"}]","George F. Simmons Precalculus Mathematics in a Nutshell - Geometry, Algebra, Trigonometry - Preface | PDF",159]