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1 Hawthorne Mathematics- General

Algebra & Trigonometry (Rea's Problem Solvers)

by

Algebra & Trigonometry (Rea's Problem Solvers) Cover

 

Synopses & Reviews

Publisher Comments:

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.

Here in this highly useful reference is the finest overview of algebra and trigonometry currently available, with hundreds of algebra and trigonometry problems that cover everything from algebraic laws and absolute values to quadratic equations and analytic geometry. Each problem is clearly solved with step-by-step detailed solutions.

DETAILS

- The PROBLEM SOLVERS are unique - the ultimate in study guides.

- They are ideal for helping students cope with the toughest subjects.

- They greatly simplify study and learning tasks.

- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.

- They cover material ranging from the elementary to the advanced in each subject.

- They work exceptionally well with any text in its field.

- PROBLEM SOLVERS are available in popular subjects.

- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.

- Most are over 1000 pages.

- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.

- Educators consider the PROBLEM SOLVERS the most effective and valuable study aids; students describe them as "fantastic" - the best books on the market.

TABLE OF CONTENTS

Introduction

Chapter 1: Fundamental Algebraic Laws and Operations

Chapter 2: Least Common Multiple / Greatest Common Divisor

Chapter 3: Sets and Subsets

Chapter 4: Absolute Values

Chapter 5: Operations with Fractions

Chapter 6: Base, Exponent, Power

Chapter 7: Roots and Radicals

Simplification and Evaluation of Roots

Rationalizing the Denominator

Operations with Radicals

Chapter 8: Algebraic Addition, Subtraction, Multiplication, Division

Chapter 9: Functions and Relations

Chapter 10: Solving Linear Equations

Unknown in Numerator

Unknown in Numerator and/or Denominator

Unknown Under Radical Sign

Chapter 11: Properties of Straight Lines

Slopes, Intercepts, and Points of Given Lines

Finding Equations of Lines

Graphing Techniques

Chapter 12: Linear Inequalities

Solving Inequalities and Graphing

Inequalities with Two Variables

Inequalities Combined with Absolute Values

Chapter 13: Systems of Linear Equations and Inequalities

Solving Equations in Two Variables and Graphing

Solving Equations in Three Variables

Solving Systems of Inequalities and Graphing

Chapter 14: Determinants and Matrices

Determinants of the Second Order

Determinants and Matrices of Third and Higher Order

Applications

Chapter 15: Factoring Expressions and Functions

Nonfractional

Fractional

Chapter 16: Solving Quadratic Equations by Factoring

Equations without Radicals

Equations with Radicals

Solving by Completing the Square

Chapter 17: Solutions by Quadratic Formula

Coefficients with Integers, Fractions, Radicals, and Variables

Imaginary Roots

Interrelationships of Roots: Sums; Products

Determining the Character of Roots

Chapter 18: Solving Quadratic Inequalities

Chapter 19: Graphing Quadratic Equations / Conics and Inequalities

Parabolas

Circles, Ellipses, and Hyberbolas

Inequalities

Chapter 20: Systems of Quadratic Equations

Quadratic/Linear Combinations

Quadratic/Quadratic (Conic) Combinations

Multivariable Combinations

Chapter 21: Equations and Inequalities of Degree Greater than Two

Degree 3

Degree 4

Chapter 22: Progressions and Sequences

Arithmetic

Geometric

Harmonic

Chapter 23: Mathematical Induction

Chapter 24: Factorial Notation

Chapter 25: Binomial Theorem / Expansion

Chapter 26: Logarithms and Exponentials

Expressions

Interpolations

Functions and Equations

Chapter 27: Trigonometry

Angles and Trigonometric Functions

Trigonometric Interpolations

Trigonometric Identities

Solving Triangles

Chapter 28: Inverse Trigonometric Functions

Chapter 29: Trigonometric Equations

Finding Solutions to Equations

Proving Trigonometric Identities

Chapter 30: Polar Coordinates

Chapter 31: Vectors and Complex Numbers

Vectors

Rectangular and Polar/Trigonometric Forms of Complex Numbers

Operations with Complex Numbers

Chapter 32: Analytic Geometry

Points of Line Segments

Distances Between Points and in Geometrical Configurations

Circles, Arcs, and Sectors

Space-Related Problems

Chapter 33: Permutations

Chapter 34: Combinations

Chapter 35: Probability

Chapter 36: Series

Chapter 37: Decimal / Factional Conversions / Scientific Notation

Chapter 38: Areas and Perimeters

Chapter 39: Angles of Elevation, Depression and Azimuth

Chapter 40: Motion

Chapter 41: Mixtures / Fluid Flow

Chapter 42: Numbers, Digits, Coins, and Consecutive Integers

Chapter 43: Age and Work

Chapter 44: Ratio, Proportions, and Variations

Ratios and Proportions

Direct Variation

Inverse Variation

Joint and Combined Direct-Inverse Variation

Chapter 45: Costs

Chapter 46: Interest and Investments

Chapter 47: Problems in Space

Index

WHAT THIS BOOK IS FOR

Students have generally found algebra and trigonometry difficult subjects to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of algebra and trigonometry continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of algebra and trigonometry terms also contribute to the difficulties of mastering the subject.

In a study of algebra and trigonometry, REA found the following basic reasons underlying the inherent difficulties of both math subjects:

No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error.

Current textbooks normally explain a given principle in a few pages written by a mathematics professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained.

The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations.

Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do.

Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved.

Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing algebra and trigonometry processes.

Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications.

In doing the exercises by themselves, students find that they are required to devote considerable more time to algebra and trigonometry than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem.

When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations.

This book is intended to aid students in algebra and trigonometry overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books.

The staff of REA considers algebra and trigonometry subjects that are best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields.

In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom.

When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.

Synopsis:

REAs Algebra and Trigonometry Problem Solver

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. They're perfect for undergraduate and graduate studies.

This highly useful reference is the finest overview of algebra and trigonometry currently available, with hundreds of algebra and trigonometry problems that cover everything from algebraic laws and absolute values to quadratic equations and analytic geometry. Each problem is clearly solved with step-by-step detailed solutions.

Synopsis:

REAs Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Algebra & Trigonometry Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Algebra & Trigonometry problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. The Algebra & Trigonometry Problem Solver is the perfect resource for any class, any exam, and any problem!

About the Author

Jerry Shipman, Ph.D., is chair and professor of mathematics at Alabama A&M University, Normal, Alabama. Founded in 1959, Research & Education Association is dedicated to producing the finest and most effective digital and print materials in educational publishing, including some of Americas most popular test preps and study aids. REAs wide-ranging catalog is a leading resource for teachers, students, and professionals.

Product Details

ISBN:
9780878915088
Other:
Ogden, James
Author:
Research & Education Association
Author:
Ogden, James R.
Author:
Algebra Study Guides
Author:
Research &. Education Association
Author:
Rea
Author:
Shipman, Jerry R.
Publisher:
Research & Education Association
Location:
Piscataway, N.J. :
Subject:
General
Subject:
Mathematics
Subject:
Algebra
Subject:
Problems, exercises, etc.
Subject:
Algebra - General
Subject:
Trigonometry
Subject:
Algebra -- Problems, exercises, etc.
Subject:
Trigonometry -- Problems, exercises, etc.
Subject:
Mathematics - Algebra
Subject:
Problem solver
Copyright:
Edition Number:
Rev. printing 1994
Edition Description:
Trade Paper
Series:
Problem Solvers Solution Guides
Publication Date:
19781231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
1040
Dimensions:
10 x 6.69 in 3 lb
Age Level:
from 16

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Related Subjects


Reference » Student Guides
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » General
Textbooks » General

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Product details 1040 pages Research & Education Association - English 9780878915088 Reviews:
"Synopsis" by , REAs Algebra and Trigonometry Problem Solver

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. They're perfect for undergraduate and graduate studies.

This highly useful reference is the finest overview of algebra and trigonometry currently available, with hundreds of algebra and trigonometry problems that cover everything from algebraic laws and absolute values to quadratic equations and analytic geometry. Each problem is clearly solved with step-by-step detailed solutions.

"Synopsis" by ,
REAs Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Algebra & Trigonometry Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Algebra & Trigonometry problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. The Algebra & Trigonometry Problem Solver is the perfect resource for any class, any exam, and any problem!
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