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
• Cases in Factoring 16, 17
• Factoring 18
• Highest Common Factor and Lowest Common Multiple 19
• Fractions 20
• Complex Fractions and Fractional Equations 21, 22
• Simultaneous Equations and Involution 23, 24
• Square Root 25
• Theory of Exponents 26-28
• Radicals 29, 30
• Miscellaneous Examples, Algebra to Quadratics 31-35
• Quadratic Equations 36, 37
• The Theory of Quadratic Equations 38-41
• Outline of Simultaneous Quadratics 42, 43
• Simultaneous Quadratics 44
• Ratio and Proportion 45, 46
• Arithmetical Progression public@vhost@g@gutenberg@html@files@38536@[email protected]#Page_47" class="pginternal"