Part 1

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This book includes extensive mathematical expressions and equations, which can not always be easily represented in plain text. The reader is encouraged to download the HTML version of the text, which represents the math more clearly.

For the plain text version, the following conventions are used:

Mixed fractions are represented by a dash with no spaces, while subtraction is represented by a dash with spaces on either side. For example: 1-1/2 is "one and one half." 1 - 1/2 is "one minus one half."

The "sideways-8" symbol for infinity is represented as [infinity].

Square, cube, and other roots are shown by raising a quantity to the appropriate fractional power. For example: ^(1/2) is "the square root of 4." ^(1/n) is "the nth root of x."

Extra parentheses have been added as needed to clarify the correct order of operations.]

A REVIEW OF ALGEBRA

BY ROMEYN HENRY RIVENBURG, A.M.

HEAD OF THE DEPARTMENT OF MATHEMATICS THE PEDDIE INSTITUTE, HIGHTSTOWN, N.J.

AMERICAN BOOK COMPANY NEW YORK CINCINNATI CHICAGO

COPYRIGHT, 1914, BY ROMEYN H. RIVENBURG.

COPYRIGHT, 1914, IN GREAT BRITAIN.

A REVIEW OF ALGEBRA.

E. P. 6

PREFACE

In most high schools the course in Elementary Algebra is finished by the end of the second year. By the senior year, most students have forgotten many of the principles, and a thorough review is necessary in order to prepare college candidates for the entrance examinations and for effective work in the freshman year in college. Recognizing this need, many schools are devoting at least two periods a week for part of the senior year to a review of algebra.

For such a review the regular textbook is inadequate. From an embarrassment of riches the teacher finds it laborious to select the proper examples, while the student wastes time in searching for scattered assignments. The object of this book is to conserve the time and effort of both teacher and student, by providing a thorough and effective review that can readily be completed, if need be, in two periods a week for a half year.

Each student is expected to use his regular textbook in algebra for reference, as he would use a dictionary,--to recall a definition, a rule, or a process that he has forgotten. He should be encouraged to think his way out wherever possible, however, and to refer to the textbook only when forced to do so as a last resort.

The definitions given in the General Outline should be reviewed as occasion arises for their use. The whole Outline can be profitably employed for rapid class reviews, by covering the part of the Outline that indicates the answer, the method, the example, or the formula, as the case may be.

The whole scheme of the book is ordinarily to have a page of problems represent a day's work. This, of course, does not apply to the Outlines or the few pages of theory, which can be covered more rapidly. By this plan, making only a part of the omissions indicated in the next paragraph, the essentials of the algebra can be readily covered, if need be, in from thirty to thirty-two lessons, thus leaving time for tests, even if only eighteen weeks, of two periods each, are allotted to the course.

If a brief course is desired, the Miscellaneous Examples (pp. 31 to 35, 50 to 52), many of the problems at the end of the book, and the College Entrance Examinations may be omitted without marring the continuity or the comprehensiveness of the review.

ROMEYN H. RIVENBURG.

CONTENTS

PAGES

OUTLINE OF ELEMENTARY AND INTERMEDIATE ALGEBRA 7-13

ORDER OF OPERATIONS, EVALUATION, PARENTHESES 14

SPECIAL RULES OF MULTIPLICATION AND DIVISION 15