Textbook in PDF format This book is intended for all those who wish to enter technical colleges, and its aim is to help students revise the material they studied at school and consolidate their skills in solving the problems and questions they will encounter during the entrance examinations to technical colleges. We hope that the book will also be useful to high-school teachers, who will thereby become acquainted with the requirements of the entrance examinations of technical colleges. All the theoretical questions are followed by brief answers, and the problems are given with detailed solutions and hints. However, we advise the reader to only turn to the answers and solutions after a long and fruitless consideration of the problem. In this book, we use the terminology usually accepted in textbooks. In selecting the questions, we drew upon our long experience of teaching at technical colleges and at schools and have included sample examination papers that contain almost all the questions and problems usually encountered in the entrance examinations. Preface Notation Elements of Arithmetic and Algebra Sets Integers Fractions Per Cent Ratios and Proportions Rational Numbers Approximate Values of Quantities Expressions with Variables Monomials and Polynomials Abridged Multiplication Identities Polynomial Factorization Fractional Expressions Roots A Power with a Rational Exponent Elementary Functions Equations Quadratic Equations Simultaneous Equations Inequalities Sequences Common Logarithms Elements of Geometry Fundamental Concepts of Geometry Congruence of Figures and Their Displacement Perpendicular and Parallel Straight Lines Triangles Quadrilaterals Vectors Similarity and Homothety of Geometric Figures Circles Inscribed and Circumscribed Triangles Trigonometric Functions Areas of Polygons Metric Relations in a Triangle Regular Polygons The Length of a Circumference and the Area of a Circle Elementary Constructions on a Plane Sample Examination Papers Questions and Problems for an Oral Examination Arithmetic and Algebra Geometry More Difficult Problems Answers, Hints and Solutions Answers to Sample Examination Papers Answers to Questions and Problems for Oral Examinations Answers to More Difficult Problems