Publications in preparation for Gia OGE. Useful aids for preparing for the OGE in English

UDC 373:512
BBK 22.14ya721
M52
Merzlyak, A.G.
M52
Mathematics: A new complete reference book for preparing for the OGE / A.G. Merzlyak, V.B. Polonsky,
M.S. Yakir. - Moscow: AST, 2017. - 447, strength New complete reference book for preparing for the OGE)
ISBN
The reference book contains the Mathematics course material to the extent tested at the state final certification.
The structure of the book corresponds to the modern one, on the basis of which control measuring materials (CMMs) are formed.
main state exam (OGE).
The reference book consists of two chapters. First chapter of Arithmetic. Algebra corresponds to the content of the mathematics and algebra courses for grades 7–9 of the basic school, the second chapter of Geometry corresponds to the content of the geometry course for grades 7–9.
In addition to theoretical material, the reference book presents a significant number of analyzed examples illustrating the basic methods and techniques for solving problems. Answers for self-testing are provided for all tasks at the end of the manual.
Working with the manual will allow you to review all the main topics of the mathematics course for grades 5–9 and successfully prepare for passing the OGE.
The directory is addressed to graduates of 9th grade.
UDC 373:512
BBK I 5 17 096816 New complete reference book for preparing for the OGE)
ISBN
978 5 17 096817 The most popular reference book for preparing for the OGE)
© Merzlyak A.G., Polonsky V.B.,
Yakir MS LLC Publishing House AST"

TABLE OF CONTENTS
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER ARITHMETIC. ALGEBRA 1. Natural numbers. . . . . . . . . . . . . . . . . . . . 17 1.1. Decimal notation of natural numbers. . . . 17 1.2. Arithmetic operations on natural numbers.
Degree with a natural indicator. . . . . 18 1.3. Divisibility of natural numbers. . . . . . . . . . 20 1.4. Signs of divisibility. . . . . . . . . . . . . . . . . . . 21 1.5. Prime and composite numbers. . . . . . . . . . . . . 22 1.6. Greatest common divisor.
Least common multiple. . . . . . . . . . . . . 24 1.7. Division with remainder. . . . . . . . . . . . . . . . . . . . Examples of tasks No. 1. . . . . . . . . . . . . . . . . . . . . 27
§ 2. Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.1. Ordinary fraction. The main property of a fraction. Comparing fractions. . . . . . . . . . . . . . . 31 2.2. Arithmetic operations with ordinary fractions. . . . . . . . . . . . . . 34 2.3. Decimal.
Comparing decimals. . . . . . . . . . . 35 2.4. Arithmetic operations with decimals. . . . . . . . . . . . . . . . 37 2.5. Finding a part from a whole and a whole from its part. . . . . . . . . . . . . . . . . . . 39

TABLE OF CONTENTS. Representation of an ordinary fraction as a decimal. Infinite periodic decimals. . . . . . . . . . . . . . . . . . . . . 40 2.7. Rounding numbers. . . . . . . . . . . . . . . . . . . . . Examples of tasks
No. 2. . . . . . . . . . . . . . . . . . . . . 43 2.8. Interest. . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.9. Finding percentages of a quantity and a quantity from its percentages. . . . . . . . . . . 48 2.10. Attitude. Percentage. . . . . 49 2.11. Proportions. . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.12. Direct and inverse proportional relationships. . . . . . . . . . . . . . . . . . . . . . . . Examples of tasks No. 3. . . . . . . . . . . . . . . . . . . . . 53
§ 3. Rational numbers. . . . . . . . . . . . . . . . . . 57 3.1. Whole numbers. Rational numbers. . . . . . . 57 3.2. Coordinate line. . . . . . . . . . . . . . . . . 58 3.3. Number module.
Comparison of rational numbers. . . . . . . . . 59 3.4. Arithmetic operations with rational numbers. . . . . . . . . . . . . Examples of tasks No. 4. . . . . . . . . . . . . . . . . . . . . 62
§ 4. Whole expressions. . . . . . . . . . . . . . . . . . . . . 66 4.1. Literal expression
(expression with variables).
Algebraic expressions. . . . . . . . . . . . 66 4.2. Properties of a degree with a natural exponent. . . . . . . . . . . . . 67 4.3. Monomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.4. Polynomial. Polynomial degree.
Root of a polynomial with one variable. . . 70 4.5. Addition, subtraction and multiplication of polynomials. . . . . . . . . . . . . . . . . . . . . . . . . 72

TABLE OF CONTENTS. Squared sum and squared difference.
Formula for difference of squares. . . . . . . . . . . . 73 4.7. Formulas for sum of cubes and difference of cubes. . . . . . . . . . . . . . . . . . . . . . 75 4.8. Factoring polynomials. . . Examples of tasks No. 5. . . . . . . . . . . . . . . . . . . . . 77
§ 5. Fractional expressions. . . . . . . . . . . . . . . . . . . 82 5.1. Algebraic (rational) fractions. . . 82 5.2. Identity. Identical transformations of expressions. . . . . . . . . . . . . 83 5.3. The main property of a rational fraction. Reducing fractions. . . . . . . . . . . . . . . . . . . . 83 5.4. Operations with algebraic fractions. . . . . Examples of tasks No. 6. . . . . . . . . . . . . . . . . . . . . 88 5.5. A degree with zero integer negative exponents. . . . . . . . . . . 94 5.6. Standard type of number. . . . . . . . . . . . . . . . Examples of tasks No. 7. . . . . . . . . . . . . . . . . . . . . 96
§ 6. Root of a number. . . . . . . . . . . . . . . . . . . . . . . 99 6.1. Square root. Arithmetic square root. . . . . . . . . . . . . . . . . . . . 99 6.2. Properties of the arithmetic square root. . . . . . . . . . . . . . . . . . . . 100 6.3. Identical transformations of expressions containing square roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.4. Third root. . . . . . . . . . . . . . . . 104 6.5. Writing a root using a fractional exponent. . . . . . . . . . . . . . . . . 104 6.6. The concept of an irrational number. Decimal approximations of irrational numbers. . . . . . . . . . . . . . . . . 105

TABLE OF CONTENTS. The concept of multitude. Numerical sets. The set of real numbers. . . . . . . Examples of tasks No. 8. . . . . . . . . . . . . . . . . . . . . 109
§ 7. Equations with one variable. . . . . . . . . . 114 7.1. General information about equations with one variable. . . . . . . . . . . . . . . . . . . 114 7.2. Linear equation with one variable. . 117 7.3. Quadratic equation. . . . . . . . . . . . . . . . . 118 7.4. Vieta's theorem. . . . . . . . . . . . . . . . . . . . . . . . 121 7.5. Square trinomial. Factoring a quadratic trinomial. . . . Examples of tasks No. 9. . . . . . . . . . . . . . . . . . . . . 124 7.6. Rational equations. . . . . . . . . . . . . . . 128 7.7. Variable replacement method. . . . . . . . . . . . . . Examples of tasks No. 10. . . . . . . . . . . . . . . . . . . . 131
§ 8. Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 8.1. The concept of function. The domain of definition and the range of values ​​of a function. . . . . . . . . . . . 134 8.2. Methods for specifying a function. . . . . . . . . . . . . . 135 8.3. Function graph. . . . . . . . . . . . . . . . . . . . . . 137 8.4. Function zeros. Intervals of sign constancy. Increasing and decreasing function. The largest and smallest values ​​of a function. . . . . . . . 139 8.5. Reading function graphs,
reflecting real processes. . . . . . . 142 8.6. Linear function and its properties.
Direct proportionality. . . . . . . . . . . . 144 8.7. Inverse proportional relationship.
Function y= , where k 0, and its properties. . . Examples of tasks No. 11. . . . . . . . . . . . . . . . . . . . 149
k
x

TABLE OF CONTENTS. Quadratic function and its properties. . . . . 164 8.9. Function and its properties. . . . . . . . . 169 8.10. Graph of a function
. . . . . . . . . . . . . 170 8.11. Function y = | x| and its properties. . . . . . . . . . 170 8.12. Solving equations graphically. . . . . . . . . . . . . . . . . Examples of tasks No. 12. . . . . . . . . . . . . . . . . . . . 173
§ 9. Equations with two variables. . . . . . . . 184 9.1. Solving an equation with two variables.
Equation graph. . . . . . . . . . . . . . . . . . . . . 184 9.2. Systems of equations with two variables. Solving systems of equations by graphical method. . . . . . . . . . . . . . . . . . 186 9.3. Methods for solving systems of two equations with two variables. . . . . . . . . . . . . . . . . . Examples of tasks No. 13. . . . . . . . . . . . . . . . . . . . 194
§ 10. Word problems. . . . . . . . . . . . . . . . . . . . 199 10.1. Solving word problems using equations. . . . . . . . . . . . . . . . Examples of tasks No. 14. . . . . . . . . . . . . . . . . . . . 202 10.2. Solving word problems using systems of equations. . . . . . . . . . . Examples of tasks No. 15. . . . . . . . . . . . . . . . . . . . 209 10.3. Solving word problems using an arithmetic method. . . . . . . . . . . . . Examples of tasks No. 16. . . . . . . . . . . . . . . . . . . . 213
§ 11. Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . 216 11.1. Numerical inequalities and their properties. . . . . 216 11.2. Evaluating the values ​​of numerical expressions using the properties of numerical inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . 218
y
x
y
x
3

TABLE OF CONTENTS. General information about inequalities with one variable. . . . . . . . . . . . . . . . . . . 220 11.4. Numerical intervals. . . . . . . . . . . . . . . . 222 11.5. Linear inequalities with one variable.
Systems of linear inequalities. . . . . . . . . 223 11.6. Quadratic inequalities. . . . . . . . . . . . . . Examples of tasks No. 17. . . . . . . . . . . . . . . . . . . . 228
§ 12. Number sequences. . . . . . . . . 234 12.1. The concept of sequence. . . . . . . . . . . 234 12.2. Methods for setting a sequence. . . . 235 12.3. Arithmetic progression. . . . . . . . . . . 238 12.4. Sum n the first terms of an arithmetic progression. . . . . . . . . . . . . 239 12.5. Geometric progression.
Compound interest formula. . . . . . . . . . 240 12.6. Sum n the first terms of a geometric progression. . . . . . . . . . . . . 244 12.7. The sum of an infinite geometric progression whose denominator is less than one. . . . . . . . . . . . . . . . . . . . . Examples of tasks No. 18. . . . . . . . . . . . . . . . . . . . 245
§ Elements of combinatorics, probability theory, descriptive statistics. . 249 13.1. Combinatorial problems.
Enumeration of options. . . . . . . . . . . . . . . . . . . 249 13.2. Combinatorial sum and product rules. . . . . . . . . . . . . . . . . . . . . . 251 13.3. Presentation of data in the form of tables, charts, graphs. . . . . . . . . . . . . . . . . . 253 13.4. Statistics.
Statistical characteristics. . . . . . . . 255 13.5. Frequency and probability of a random event. . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

TABLE OF CONTENTS. Reliable and impossible events.
Equally possible events. Classic definition of probability. . . . . . . . . . . . . . 259 13.7. The idea of ​​geometric probability. . . . . . . . . . . . . . . . . . . . . . . . . Examples of tasks No. 19. . . . . . . . . . . . . . . . . . . . CHAPTER II
GEOMETRY
§ The simplest geometric figures
and their properties. . . . . . . . . . . . . . . . . . . . . . . . 273 14.1. Straight line, ray, segment.
Measuring segments. . . . . . . . . . . . . . . . . . 273 14.2. Corner. Measuring angles. . . . . . . . . . . . . . . . 275 14.3. Adjacent and vertical angles. . . . . . . . . 277 14.4. Perpendicular lines. The angle between intersecting lines. Perpendicular and oblique.
Distance from a point to a line. . . . . . . . . Examples of tasks No. 20. . . . . . . . . . . . . . . . . . . . 279
§ 15. Parallel lines. . . . . . . . . . . . . . . . 282 15.1. Signs of parallel lines. . . . . . 282 15.2. Properties of parallel lines. . . . . . . . Examples of tasks No. 21. . . . . . . . . . . . . . . . . . . . 285
§ 16. Triangle. . . . . . . . . . . . . . . . . . . . . . . . . 287 16.1. Elements of a triangle.
Equal triangles. . . . . . . . . . . . . . . . . 287 16.2. Types of triangles. . . . . . . . . . . . . . . . . . 290 16.3. Signs of equality of triangles. . . . . 291

TABLE OF CONTENTS. Properties of an isosceles triangle. . . 292 16.5. Signs of an isosceles triangle. . . 293 16.6. Sum of angles of a triangle. Property of an exterior angle of a triangle. . . . . . . . . . . 295 16.7. Triangle inequality.
The relationship between the sizes of the sides and angles of a triangle. . . . . . . . . . . . . . . . . 297 16.8. Signs of equality of right triangles. Properties of a right triangle. . . . . . . . . . . . . . . . . . . . . . . . 298 16.9. Tower of Thales. Theorem on proportional segments. . . . . . . . . . 301 Middle line of the triangle. . . . . . . . . . 302 Similar triangles. . . . . . . . . . . . . . 303 Signs of similarity of triangles. . . . . . Examples of tasks No. 22. . . . . . . . . . . . . . . . . . . . 308 16.13. Metric ratios in a right triangle. . . . . . . . 314 16.14. Pythagorean theorem. . . . . . . . . . . . . . . . . . 314 16.15. Sine, cosine, tangent and cotangent of an acute angle of a right triangle. . . . . . . . . . . . . . . . . . . . . . . 315 Sine, cosine, tangent and cotangent of an angle from 0 to 180. . . . . . . . . . . . . . . . . . . . 318 Cosine theorem. . . . . . . . . . . . . . . . . . 321 Theorem of sines. . . . . . . . . . . . . . . . . . . . Examples of tasks No. 23. . . . . . . . . . . . . . . . . . . . 323
§ 17. Circle and circle. . . . . . . . . . . . . . . . . . . 328 17.1. The concept of the geometric location of points.
Examples of HMT. . . . . . . . . . . . . . . . . . . . . . . 328 17.2. Circle and circle, their elements. . . . . . . 329 17.3. Properties of circle elements. . . . . . . . 331 17.4. Tangent and secant to a circle. . . 332

TABLE OF CONTENTS. The relative position of two circles. . . . . . . . . . . . . . . . . . . . . . . . 334 17.6. A circle circumscribed around a triangle. . . . . . . . . . . . . . . . . . . . . . . . 335 17.7. A circle inscribed in a triangle. . . 337 17.8. Central and inscribed angles.
Degree measure of an arc of a circle. . . . . . . 339 17.9. Circumference. . . . . . . . . . . . . . . . . . . Examples of tasks No. 24. . . . . . . . . . . . . . . . . . . . 342
§ 18. Polygon. . . . . . . . . . . . . . . . . . . . . . 349 18.1. Quadrangle and its elements. . . . . . . 349 18.2. Parallelogram and its properties. . . . . . . . . 351 18.3. Signs of a parallelogram. . . . . . . . . . . . 353 18.4. Rectangle, rhombus, square. . . . . . . . . Examples of tasks No. 25. . . . . . . . . . . . . . . . . . . . 356 18.5. Trapezoid. Midline of trapezoid. . . . . 361 18.6. Quadrangle,
inscribed in a circle. . . . . . . . . . . . . . 364 18.7. Quadrangle,
circumscribed about a circle. . . . . . . . . . 365 18.8. Sum of angles of a convex polygon. . . 365 18.9. Regular polygons. . . . . . . . . . . Examples of tasks No. 26. . . . . . . . . . . . . . . . . . . . 368
§ 19. Area and volume. . . . . . . . . . . . . . . . . . . . . 374 19.1. The concept of polygon area.
Area of ​​a rectangle. . . . . . . . . . . . . 374 19.2. Area of ​​a parallelogram and trapezoid. . . 376 19.3. Formulas for finding the area of ​​a triangle. . . . . . . . . . . . . . . . . . . . . . . . 377 19.4. Area of ​​a circle. Sector area. . . . . . . 379 19.5. Formulas for the volumes of a rectangular parallelepiped, cube and sphere. . . . . . . . . . Examples of tasks No. 27. . . . . . . . . . . . . . . . . . . . 381

CONTENTS 20. Cartesian coordinates on a plane. . . 388 20.1. Coordinate plane. . . . . . . . . . . . . . 388 20.2. Formula for the distance between two points. Coordinates of the midpoint of the segment. . 390 20.3. Figure equation.
Equation of a circle. . . . . . . . . . . . . . . . 391 20.4. General equation of a straight line. Equation of a straight line with an angular coefficient. . . . . . 393 20.5. Graphic interpretation of inequalities with two variables. . . . . . . . . . . . . . . . Examples of tasks
№ 28 . . . . . . . . . . . . . . . . . . . . 396
§ 21. Vectors on the plane. . . . . . . . . . . . . . . . . 399 21.1. Vector concept. Vector module. Collinear vectors.
Equal vectors. . . . . . . . . . . . . . . . . . . . . . 399 21.2. Vector coordinates. . . . . . . . . . . . . . . . . . 402 21.3. Addition and subtraction of vectors. . . . . . . . 404 21.4. Multiplying a vector by a number. . . . . . . . . . . 407 21.5. Decomposition of a vector into two non-collinear vectors. . . . . . . . . . . . . 408 21.6. Dot product of vectors. . . . . . . Examples of tasks
№ 29 . . . . . . . . . . . . . . . . . . . . 412
§ 22. Geometric transformations. . . . . . . . 416 22.1. Movement of the figure.
Parallel transfer. . . . . . . . . . . . . . . . 416 22.2. Axial symmetry. . . . . . . . . . . . . . . . . . . . 418 22.3. Central symmetry. . . . . . . . . . . . . . . 420 22.4. Turn. . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 22.5. Homothety. Similarity of figures. . . . . . . . . . . . . Examples of tasks No. 30. . . . . . . . . . . . . . . . . . . . Answers to sample assignments. . . . . . . . . . . . . . . . 434

INTRODUCTION
The main state exam (OGE) in mathematics includes topics covered in grades 5–6 mathematics, algebra and geometry courses. The basis of preparation for the OGE is the organization of systematic repetition of material studied in grades 5–9. There are a number of ways to accomplish this task. For example, you can use school textbooks.
The disadvantages of this approach are obvious, firstly,
you need to have at hand all school textbooks on mathematics at the corresponding stages of its study;
secondly, searching for the necessary material can lead to a considerable loss of time. It is much more convenient to use a manual that briefly outlines the basic facts of definition, theorems, formulas, properties of mathematical objects, etc. This is the kind of book you can hold in your hands. It is a reference guide for preparing for
OGE in mathematics.
This manual contains not only theoretical material necessary for solving options
OGE, but also a significant number of analyzed examples illustrating the basic methods and techniques for solving problems.
This reference book also fulfills its traditional role - it allows you to quickly find the necessary information: what properties does a degree with an integer exponent have, what is the sum of the first terms of a geometric progression, how to find a fraction of a number, what formula can be used to calculate the area of ​​a trapezoid, etc.

14
INTRODUCTION
The reference book consists of two chapters. First chapter
"Arithmetic. Algebra corresponds to the content of mathematics courses for grades 5–6 and algebra for grades 7–9 of the basic school, the second chapter Geometry corresponds to the content of the geometry course for grades 7–9. Each of the chapters is divided into paragraphs. Their content corresponds to the codifier, on the basis of which tasks for the OGE in mathematics are formed.
It is clear that to successfully write the OGE you need to be able to solve problems. Therefore, the reference book includes extensive didactic material.
Each paragraph contains one or two (depending on the volume of material) test work in the Examples of tasks section. This title of the section is due to the fact that most of the problems presented in it are similar or close in content and form to the tasks offered in different years at the OGE in mathematics.
Most test work consists of two parts. The tasks in the second part are more difficult. Therefore, we advise you to start solving them after
how the tasks of the first part will be completed.
Some tasks in the first part are problems whose solution consists in choosing one correct answer from four proposed ones. For such problems, in the Answers section for example tasks, the number of the correct answer is indicated.
We wish you success in passing the main state exam in mathematics

CHAPTER I
ARITHMETIC.
ALGEBRA

The results of the mandatory state exam not only influence the grade in the certificate, but also help schoolchildren decide on the choice of direction for further education. According to the government decree of 2017 and current information from the FIPI website, students this year will have to take tests in four subjects - two compulsory and two optional. It is not at all uncommon for a topic that was once missed due to illness to come up when taking an important exam. Special OGE textbooks help you avoid annoying obstacles to getting a high score.

What to choose to prepare for the OGE

On the website of the online store “Virtual Book” you can easily find the necessary literature on all subjects:

Practice tests and collections with a variety of oral topics in the English language;

Books with variants of tasks and answers in the Russian language Tsybulko;

Typical tasks in biology that help determine the level of your preparation;

Manuals with tasks of varying complexity in social studies;

OGE 2018 textbooks in mathematics and other subjects.

A huge advantage of special literature for preparing for the state exam is the availability of expert advice and recommendations on how to prepare work. This helps you not to get confused during testing and save time on actually doing the work. Model exam options can be used by students for independent work and by teachers for classroom teaching.

Where is the best place to buy textbooks?

Considering the significant amount of necessary educational literature, the choice of where to buy it is very important. Compared to regular stores, “Virtual Book” provides a pleasant opportunity to save 20-25% of the total cost for the family budget. From us you can buy all the textbooks necessary for the 9th grade OGE, atlases with maps, stationery and other goods necessary for the exam. A well-thought-out search system facilitates the choice, and fast delivery ensures that you receive the desired book in the shortest possible time. If the OGE is due only next year, buy the necessary literature now and take advantage of the extra time for quality preparation.

Gufaizina Alena Petrovna, teacher of Russian language and literature

MBOU "Irakinda Secondary School"

Five best aids for preparing for the State Examination

1) “A set of materials for preparing students” by Drabkina S.V. Subbotin D.I. 2017 (2nd edition)

I used to use the 2014 edition, but a revised edition appeared, which turned out to be very convenient, because they removed the tasks that were removed from the OGE.The analysis of the tasks presented in the manual is very convenient for students to understand. The tasks correspond to real tasks from the State Academy of Sciences. The assignments can also be used as visual examples in lessons. I think the difficulty level of the tasks is basic.

The topics from the school curriculum of the subject are worked out, in my opinion, quite well. Test tasks are given with an algorithm for solving them, so students can independently work on a particular topic on their own.

There are no comments on the answers, however, as in other manuals. But there is a solution algorithm, after reading which you can execute it correctly.

The material presented in the book is systematized by task numbers according to the OGE type, which is also a plus.

These tests assess the degree of preparedness of a State Examination School student objectively.

The manual is very universal for use, suitable for children who have yet to graduate - students in grades 8 and 10.

To the questions: “Can this manual be used by college students? Can university applicants use it when preparing for entrance tests of a creative and professional orientation?” - I think so.

Some material is presented in tabular form, which is very convenient for perception. The students love it. There is an illustration, but this is not so important for ninth graders.

This textbook can be used for self-study, for class work, or for training with a tutor. Using this guide, interested parents can always check how their child is preparing for the exam. Last year, motivated students using this manual scored higher on the exam than previously expected. The cost of the manual is not very expensive, but the benefits of its practical application are great. Theoretical material is presented in a concise and structured form. It contains methodological recommendations for writing a concise presentation and essay, and provides sample essays, which is important for a weak student. Standard training tasks with methodological instructions are given, and answers are provided. All this allows students to prepare well for passing the OGE in the Russian language.

2) Typical test tasks 50 variants of tasks Vasiliev I.P., Gosteva Yu.N., Egoraeva G.T. 2017

The benefit of the manual is that it provides many test options to practice. A detailed analysis of the tasks of the first and thirteenth options is given. During the lesson, students read an analysis of one of the options and find key words. Using these words, children can use their revision notebooks to find information. The material is presented quite clearly. The manual provides a system for assessing examination work. The criteria for assessing presentation and essay are described. Knowing these criteria, students can write their work consciously. After the test, students can check and evaluate the presentation and essay themselves using these criteria. Knowing the requirements for essay and presentation helps to consciously work on this type of work. A tabular version of the criteria for assessing presentation and essay is displayed on the screen in the class for both group work and individual work. The answers are given at the end of the manual. The price and quality of the manual, I think, correspond. Using this textbook, students can prepare independently and monitor their implementation.

3) OGE Workshop on completing standard test tasks. Real tests Egoraeva G.T. 2017

No materials for repetition are provided. Students can only solve tests and check answers on their own. This manual is aimed at developing practical skills of the test part, although at the end there are 12 texts of presentations, but there are no answers to the statements. Answers to the tests are given at the end of the manual. On the plus side, it can be noted that the assessment criteria provide explanations about the work of experts in checking the examination work.

Plenty of space on the sheet on the right or left is left for student responses, although there is a special line for this. To save paper, you need to organize this.

4) Russian language 30 training versions of examination papers to prepare for the main state exam Stepanova L.S. 2015, 2017 - new edition

The manual is interesting because at the very beginning there is a brief methodological commentary on the tasks of part 3. This is a very big plus that the material is clearly described on how to write an essay correctly. The textbook contains six texts for presentation, and answers are given to them. This allows students to monitor themselves. Thirty tests are given, there are answers at the end, but there are no materials for solving the tasks.

5) I begin preparing for the Unified State Exam in fifth grade. The "Workbook Thematic assignments of levels A, B, C for preparation for the State Examination" 9th grade Baronova M.M. is suitable for this. 2010

There are no assignment reviews in this notebook, only material for practicing the acquired knowledge.

The tests in this manual are presented by section, so as I study a particular topic in grades 5-8, I use these tests to reinforce them. By the end of the eighth grade, this workbook has already been worked out, so I offer this manual to those ninth graders who have large gaps in their knowledge. This manual is not entirely suitable for ninth graders.

In my preparation for exams, I use various aids. I take some material from one manual, some from another. Of the five selected, I consider the best textbook “Complex of materials for preparing students” by Drabkina S.V. Subbotin D.I. 2017 (2nd edition).

At the very beginning of the manual, recommendations are given for preparing for the OGE 2017. Everything is explained for students in an accessible form. Section 1 is about writing a concise summary. Section 2 contains material to prepare for the test part. Section 3 prepares students to write an argumentative essay. Approximate versions of the OGE and answers to them are given.All this allows students to prepare well for passing the OGE in the Russian language, not only with a teacher, but also independently. Preparation using this manual gives good results.

Although the books were purchased in 2014, the manuals are slightly modified: the cover and text are changed. I compared it with 2013 myself. I'll give a brief review of each.

I wrote it right after passing the exams in 9th grade, I didn’t correct the text, the article was lost on the disk)

1) Russian preparation for State Examination-2014 (N.A. Senina)

— the manual includes 4 parts.

• 5-109 pages - includes a bunch of useful information, such as text compression techniques and rules, formatted in table form.
• 109-122 pages - definitions copied from Wikipedia.
• 123-147 pages - version downloaded from the FIPI website + debriefing and comments from the author.
• 147-346 pages - as many as 30, which were compiled by Senina (the author of this manual). The first tests of the norms, then the hack began (the text for writing essays increased from 1 to 4 pages + several incorrect answers at the end of the collection).

We were forced to buy this book for school, where we studied on it during consultations and in class.

Separately, you can buy an application for it - a disk with expositions that are soundly voiced.

But buy the book itself. Because if you have a printer at home, printing is clearly not an option and reading from the monitor is also not an option.

The book is ahead of its competitors in terms of quantity and quality.

2) Russian Language for GIA-9 Legion (Yu.N. Gosteva and others...).

Arriving at the store, I saw a beautiful and bright cover promising 30 options + 300 tasks of part C, from the developers of FIPI and all sorts of other goodies... Even a publishing house promising Exam :)

I opened it, flipped through it... everything seemed fine... I bought it.

When I started looking I couldn’t find it. Maybe I'm stupid - perhaps, but after finishing this book I still couldn't find the assignments for Part C! The books say in large letters “Created by FIPI developers.” Yes, there are two of them (Vasiliev and Gostev), only they write from 1 to 10 and from 21 to 30. And besides, they are hacking using the same text and compositions in other versions...

In the second part, the authors honestly admit and write “based on materials from the Internet” :) Next are 10 more options - a workshop on writing stupid essays on a linguistic topic. Even a hedgehog can understand how to write them! And these options include answers to the easiest questions...

By the way, the only book in which, a day before the OGE, I solved about 20 options at once and I want to note that they are much easier and more plausible than those in Senina.

3) Mathematics training Legion (F.F. Lysenko)

The book contains a good theory (33 pages in total) + 30 tests + a collection of problems on various topics + solutions to some problems.

I thought I would decide on an option every three or four days and by the end of the year I would have solved everything...

But in reality there were only 4 :)

4) Mathematics Reshak Legion (F.F. Lysenko)— a very incomprehensible solution to problems from the previous collection (it’s easier to google it).

The reference book, addressed to graduates of the 9th grade of general education organizations, presents the material of the “Social Studies” course in the volume tested at the main state exam.
The structure of the book corresponds to the modern codifier of content elements in the subject, on the basis of which the control measuring materials of the OGE are compiled.
The content of the course is grouped into six module blocks: “Man and Society”, “Sphere of Spiritual Culture”, “Economics”, “Social Sphere”, “Sphere of Politics and Social Management”, “Law”.
Completeness, compactness, clarity and clarity of presentation ensure maximum efficiency in preparing for the exam.
Samples of tasks of different types and all levels of complexity (basic, advanced and high), answers to them and an indication of the approximate time for their completion will help to objectively assess the level of knowledge and skills.

Examples.
What is common to both humans and animals?
1) transformation of the world
2) accumulation of knowledge
3) need for rest
4) desire for beauty

Pavel studies in the second grade of a comprehensive school. In his free time, he likes to play board games. Compare the two forms of activity mentioned in the task conditions - learning and playing. Select and write down the serial numbers of the similarity traits in the first column of the table, and the serial numbers of the differences in the second column.
1) promotes personal development
2) imitates real actions
3) equips with system knowledge and skills
4) helps to understand the world around us

Content
Preface 6
BLOCK MODULE 1. PERSON AND SOCIETY
Topic 1.1. Society as a form of human life 12
Topic 1.2. Interaction between society and nature 14
Topic 1.3. Main spheres of public life, their relationship 16
Topic 1.4. Biological and social in man 17
Topic 1.5. Personality. Peculiarities of adolescence 19
Topic 1.6. Human activity, its main forms (work, play, learning) 23
Topic 1.7. A person and his immediate environment. Interpersonal relationships. Communication 30
Topic 1.8. Interpersonal conflicts, their constructive resolution 40
BLOCK MODULE 2. SPHERE OF SPIRITUAL CULTURE
Topic 2.1. The sphere of spiritual culture and its features 43
Topic 2.2. Science in the life of modern society 44
Topic 2.3. Education and its importance in the information society. Opportunities for obtaining general and vocational education in the Russian Federation 48
Topic 2.4. Religion, religious organizations and associations, their role in the life of modern society. Freedom of conscience 52
Topic 2.5. Morale 58
Topic 2.6. Humanism. Patriotism, citizenship 61
BLOCK MODULE 3. ECONOMY
Topic 3.1. Economics, its role in the life of society 65
Topic 3.2. Goods and services, resources and needs, limited resources 68
Topic 3.3. Economic systems and property 72
Topic 3.4. Production, labor productivity. Division of labor and specialization 78
Topic 3.5. Exchange, trade 83
Topic 3.6. Market and market mechanism 85
Topic 3.7. Entrepreneurship. Small business and farming 92
Topic 3.8. Money 103
Topic 3.9. Wages and labor incentives 107
Topic 3.10. Income inequality and economic safety net measures 111
Topic 3.11. Taxes paid by citizens 115
Topic 3.12. Economic goals and functions of the state 119
BLOCK MODULE 4. SOCIAL SPHERE
Topic 4.1. Social structure of society 122
Topic 4.2. Family as a small group. Relations between generations 124
Topic 4.3. Diversity of social roles in adolescence 127
Topic 4.4. Social values ​​and norms 130
Topic 4.5. Deviant behavior. The danger of drug addiction and alcoholism for individuals and society. Social significance of a healthy lifestyle 134
Topic 4.6. Social conflict and ways to resolve it. 138
Topic 4.7. Interethnic relations 142
BLOCK MODULE 5. THE SPHERE OF POLITICS AND SOCIAL MANAGEMENT
Topic 5.1. Power. The role of politics in the life of society 146
Topic 5.2. Concept and characteristics of the state 148
Topic 5.3. Separation of powers 151
Topic 5.4. Forms of State 153
Topic 5.5. Political regime. Democracy 157
Topic 5.6. Local government 162
Topic 5.7. Citizen participation in political life 167
Topic 5.8. Elections, referendum 169
Topic 5.9. Political parties and movements, their role in public life 173
Topic 5.10. Civil society and the rule of law 178
BLOCK MODULE 6. LAW
Topic 6.1. Law, its role in the life of society and the state 187
Topic 6.2. Rule of law. Regulatory legal act 188
Topic 6.3. The concept of legal relations 192
Topic 6.4. Signs and types of offenses. Concept and types of legal liability 195
Topic 6.5. Constitution of the Russian Federation. Fundamentals of the constitutional system of the Russian Federation 200
Topic 6.6. Federal structure of Russia 206
Topic 6.7. State authorities of the Russian Federation 209
Topic 6.8. Law enforcement agencies. Judicial system. Relationships between government bodies and citizens 219
Topic 6.9. The concept of rights, freedoms and responsibilities. Rights and freedoms of man and citizen in Russia, their guarantees. Constitutional duties of citizens 223
Topic 6.10. Children's rights and their protection. Features of the legal status of minors 227
Topic 6.11. Mechanism for the implementation and protection of human and civil rights and freedoms 230
Topic 6.12. International legal protection of victims of armed conflicts 233
Topic 6.13. Civil relations. Property rights. Consumer rights 236
Topic 6.14. Family legal relations. Rights and responsibilities of parents and children 245
Topic 6.15. The right to work and labor relations. Employment of minors 254
Topic 6.16. Administrative legal relations, offenses and punishments 259
Topic 6.17. Basic concepts and institutions of criminal law. Criminal liability of minors 263
Training version of the examination paper in social studies 271
Replies 282
Literature 285.

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