作者：Romeyn Henry Rivenburg
格式: AZW3, DOCX, EPUB, MOBI, PDF, TXT
A Review of Algebra试读：
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.
OUTLINE OF ELEMENTARY AND INTERMEDIATE ALGEBRA
Important Definitions
Factors; coefficient; exponent; power; base; term; algebraic sum; similar terms; degree; homogeneous expression; linear equation; root of an equation; root of an expression; identity; conditional equation; prime quantity; highest common factor (H. C. F.); lowest common multiple (L. C. M.); involution; evolution; imaginary number; real number; rational; similar radicals; binomial surd; pure quadratic equation; affected quadratic equation; equation in the quadratic form; simultaneous linear equations; simultaneous quadratic equations; discriminant; symmetrical expression; ratio; proportion; fourth proportional; third proportional; mean proportional; arithmetic progression; geometric progression;
Special Rules for Multiplication and Division
1. Square of the sum of two quantities.
2. Square of the difference of two quantities.
3. Product of the sum and difference of two quantities.
4. Product of two binomials having a common term.
5. Product of two binomials whose corresponding terms are similar.
6. Square of a polynomial.
7. Sum of two cubes.
8. Difference of two cubes.
9. Sum or difference of two like powers.
Cases in Factoring
1. Common monomial factor.
2. Trinomial that is a perfect square.
3. The difference of two squares.
(a) Two terms.
(b) Four terms.
(c) Six terms.
(d) Incomplete square.
4. Trinomial of the form
5. Trinomial of the form
6. Sum or difference of● two cubes. See "Special Rules," 7 and 8.● two like powers. See "Special Rules," 9.
7. Common polynomial factor. Grouping.
8. Factor Theorem.
H. C. F. and L. C. M.
H. C. F.
L. C. M.
Fractions
Reduction to lowest terms.
Reduction of a mixed number to an improper fraction.
Reduction of an improper fraction to a mixed number.
Addition and subtraction of fractions.
Multiplication and division of fractions.
Law of signs in division, changing signs of factors, etc.
Complex fractions.
Simultaneous Equations
Solved by● addition or subtraction.● substitution.
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