In this post, we will see the book Solving Problems In Algebra and Trigonometry – V. Litvinenko, A. Mordkovich. In an earlier post, we had seen the companion volume to this book Solving Problems in Geometry. The companion volume also has been updated with a fresh scan and new links have been added.
About the book:
This study aid is intended for students of physical and mathematical faculties of pedagogical institutes.
The book contains about 2000 examples, problems, and exercises of which 1700 problems are for solving independently. Along with rather simple problems, there are also problems whose solution requires serious and sometimes inventive work. In the course of preparing the manuscript for print we tried to distribute the space among the basic types of “school” problems in algebra and trigonometry. Solving these problems will help the student to acquire professional skill necessary for a teacher who must know how to solve mathematical problems of the high-school level.
This book is not only a collection of problems, it is rather a study aid for practical work, as can be seen in the structure of the text book. Each section contains necessary theoretical material and an ample number of worked examples (the total number of which amounts to about 300), which are very useful for the student pri marily from the methodological point of view.
The book was translated from the Russian by Leonid Levant and was first published by Mir in 1987.
PDF | Bookmarked | Cover
PART 1. ALGEBRA 7
Chapter 1. IDENTICAL TRANSFORMATIONS 7
Sec. 1. Factorization of Polynomials 7
Sec. 2. Identical Transformations of Rational Functions 11
Sec. 3. Identical Transformations of Irrational Functions 20
Sec. 4. Identical Transformations of Exponential and Logarithmic Functions 29
Sec. 5. Proving Inequalities 33
Sec. 6. Comparing Numerical Expressions 41
Chapter 2. SOLVING EQUATIONS AND INEQUALITIES 45
PART II. TRIGONOMETRY 202
Chapter 3. IDENTICAL TRANSFORMATIONS 202
Sec. 21. Identical Transformations of Trigonometric Functions 202
Sec. 22. Transforming Functions Containing Inverse Trigonometric Functions 218
Sec. 23. Proving Inequalities 224
Chapter 4. SOLVING EQUATIONS AND INEQUALITIES 234
Sec. 24. Equations 234
Sec. 25. Systems of Equations 254
Sec. 26. Inequalities 265
Sec. 27. Parametric Equations and Inequalities 276