We now come to Problem Book In High School Mathematics edited by A. I. Prilepko.

The present problem book is meant for high-school students
who intend to enter technical colleges. I t contains more than
two thousand problems and examples covering all divisions
of high-school mathematics.

The main aim of the book is to help students to revise their
school knowledge of mathematics and develop a technique
in solving a variety of problems.

The book consists of nine chapters divided into sections,
each of which deals with a certain theme. The problems on
a definite theme are arranged in the order of increasing
difficulty, which makes it possible for a student to gradually
acquire the necessary techniques and experience in problem
solving. Thus, the problems are classified as far as possible.
Most of the problems were given at the entrance examinations
in various colleges to the USSR in recent years. All the
problems are supplied with answers, and some of them with
solutions or instructions. The words “Solution” and “Hint”
are replaced by the signs A and. respectively. The list of
designations makes the use of the book more convenient.
All the contributors to the book have a long experience
as lecturers at preparatory courses of colleges, as teachers
at high schools specializing in physics and mathematics and
as examiners in mathematics.

This book was translated from the Russian by I. A. Aleksanova. The
book was published by first Mir Publishers in 1985.

All credits to the original uploader.

DJVU | 4 MB | Pages: 280 | Cover

You can get the book here
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Table of Contents

Chapter 1. Rational Equations, Inequalities and Functions in One Variable

1.1. Linear Equations and Inequalities in One Variable. A Linear Function
1.2. Quadratic Equations and Inequalities. A Quadratic Function
1.3. Inverse Proportionality
1.4. Equations and Inequalities of Higher Degrees. A Rational Function
1.5. Linear Systems of Equations and Inequalities
1.6. Systems of Equations and Inequalities in Several Higher-Degree Variables
Chapter 2. Transcendental Functions, Equations and Inequalities

2.1. Irrational Equations and Inequalities
2.2. Systems of Irrational Equations and Inequalities
2.3. An Exponential and a Logarithmic Function, Exponential and
Logarithmic Equations, Systems of Equations, and Inequalities
2.4. Transformation of Trigonometric Expressions
2.5. Trigonometric Functions
2.6. Inverse Trigonometric Functions
2.7. Trigonometric Equations and Systems of Equations
2.8. Trigonometric Inequalities

Chapter 3. Problems on Deriving Equations and Inequalities

3.1. Problems on Motion
3.2. Problems on Percentages, Mixtures, Numbers and Work
3.3. Problems on Deriving Inequalities and Systems of
Inequalities. Problems on the Extremum

Chapter 4. The Antiderivative and the Integral

4.1. The Antiderivative. The NewtonLeibniz Formula
4.2. Calculating the Areas of Plane Figures

Chapter 5. Progressions and Number Sequences

5.1. Progressions
5.2. Number Sequences

Chapter 6. Elements of Vector Algebra

6.1. Linear Operations on Vectors
6.2. The Scalar Product of Vectors

Chapter 7. Plane Geometry

7.1. Problems on Proving Propositions
7.2. Construction Problems
7.3. Problems on Calculation

Chapter 8. Solid Geometry

8.1. A Straight Line, a Plane. Polyhedra. Solids of Revolution
8.2. Problems on Combinations of Polyhedra and Solids of Revolution
8.3. Volumes of Solids of Revolution

Chapter 9. Miscellaneous Problems

9.1. Problems in Algebra
9.2. Limit of a Function. Continuity
9.3. The Derivative of a Function
9.4. Integral Calculus. Miscellaneous Problems