A Review of Algebra
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A Review of Algebra - Romeyn Henry Rivenburg
Romeyn Henry Rivenburg
A Review of Algebra
Published by Good Press, 2019
goodpress@okpublishing.info
EAN 4057664651365
Table of Contents
PREFACE
OUTLINE OF ELEMENTARY AND INTERMEDIATE ALGEBRA
A REVIEW OF ALGEBRA
ORDER OF OPERATIONS, EVALUATION, PARENTHESES
SPECIAL RULES OF MULTIPLICATION AND DIVISION
CASES IN FACTORING
FACTORING
HIGHEST COMMON FACTOR AND LOWEST COMMON MULTIPLE
FRACTIONS
COMPLEX FRACTIONS AND FRACTIONAL EQUATIONS
FRACTIONAL EQUATIONS
SIMULTANEOUS EQUATIONS
SIMULTANEOUS EQUATIONS AND INVOLUTION
SQUARE ROOT
THEORY OF EXPONENTS
RADICALS
MISCELLANEOUS EXAMPLES, ALGEBRA TO QUADRATICS
QUADRATIC EQUATIONS
THE THEORY OF QUADRATIC EQUATIONS
OUTLINE OF SIMULTANEOUS QUADRATICS
SIMULTANEOUS QUADRATICS
RATIO AND PROPORTION
ARITHMETICAL PROGRESSION
GEOMETRICAL PROGRESSION
THE BINOMIAL THEOREM
MISCELLANEOUS EXAMPLES, QUADRATICS AND BEYOND
PROBLEMS
COLLEGE ENTRANCE EXAMINATIONS
UNIVERSITY OF CALIFORNIA
ELEMENTARY ALGEBRA
COLORADO SCHOOL OF MINES
ELEMENTARY ALGEBRA
COLUMBIA UNIVERSITY
ELEMENTARY ALGEBRA COMPLETE
CORNELL UNIVERSITY
ELEMENTARY ALGEBRA
CORNELL UNIVERSITY
INTERMEDIATE ALGEBRA
HARVARD UNIVERSITY
ELEMENTARY ALGEBRA
HARVARD UNIVERSITY
ELEMENTARY ALGEBRA
HARVARD UNIVERSITY
ELEMENTARY ALGEBRA
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ALGEBRA A
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ALGEBRA B
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ALGEBRA A
MOUNT HOLYOKE COLLEGE
ELEMENTARY ALGEBRA
UNIVERSITY OF PENNSYLVANIA
ELEMENTARY ALGEBRA
PRINCETON UNIVERSITY
ALGEBRA A
ALGEBRA B
ALGEBRA TO QUADRATICS
SMITH COLLEGE
ELEMENTARY ALGEBRA
SMITH COLLEGE
ELEMENTARY ALGEBRA
VASSAR COLLEGE
ELEMENTARY AND INTERMEDIATE ALGEBRA
VASSAR COLLEGE
ELEMENTARY AND INTERMEDIATE ALGEBRA
YALE UNIVERSITY
ALGEBRA A
YALE UNIVERSITY
ALGEBRA B
PREFACE
Table of Contents
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