About Dmitry Gushchina. Preparation for the Unified State Exam in mathematics (profile level): assignments, solutions and explanations Dmitry Gushchin Unified State Exam profile

Sergey, many people in education, and not only in education, do not even imagine that our world has many more dimensions than we study in school. If a person is compared to physical object, which has sensors only in three dimensions, then this means that a person is simply far from perfect. I already wrote at the teachers’ council that the current level of knowledge acquired will be a strong constraint on the development of human society. Even the author of quaternions went to his discovery for an extremely long time, and the result from today’s ideas is surprising why he chose this particular path, because there was another path that was more universal and faster. Something similar happens in education, we take the longest path to the goal, teaching outdated ideas, thereby setting up fences for ourselves in the future, so that we can then overcome them. Today you can teach mathematics in school so that it makes it possible to perform various transformations that will allow you to get any other triangle from one triangle (I’m even afraid to write more revolutionary things), and then immediately move on to polygons. And then move on to multidimensional space. Those constants that we use to describe known physical fields are determined by parameters that are determined at higher levels (another level of spatial measurement).

It's not clear why school mathematics divided into 3 branches: geometry, algebra and computer science. After all, they are so closely related, moreover, by dividing mathematics into 3 areas of knowledge, we lose the existing connection between theory and practical human activity. The result we get is the following: we provide knowledge, a significant part of which does not find application in the real activities of people. Such abstractionism kills the desire to learn the real direction of knowledge, its meaning and application in practice. The school curriculum is very far from complete in terms of the practical use of knowledge. The expression has long been known: theory without practice is dead. Are there really people in the leadership of the ministry who do not understand the importance of the practical orientation of knowledge?

“Officials don’t need to explain anything.”
But it is officials who determine the development strategy of the country and education in particular.

The task of the school is not to give knowledge, but to lead schoolchildren to perceive new knowledge through efforts on their part. The school traditionally offers chewed food and offers only one thing - to swallow what is offered. But no one pays attention to the fact that no a large number of connections that would arise if the student himself came to new knowledge. But the teacher’s task is completely different - to lead the student to master new knowledge. Efforts on the part of the learner lead to an increase in the depth of knowledge; a person, gaining speed when mastering new knowledge, by inertia, often goes further than is determined by the program. Today we are in dire need of new educational paradigms. Why do some people remember what they studied for many decades, while others are unable to reproduce what they studied a month ago? The reason is banal: the first knowledge was obtained, and the second was given it, but without movement, weak ties were destroyed, which led to their loss. In pedagogy, it’s time to study machine learning methods, artificial intelligence, writing programming languages, then methods will become available for comparing the structures of the organization of thinking, learning and memorization of humans and machines. At the same time, eyes are opened to the peculiarities of perception and mastery of new knowledge, clear criteria appear for choosing optimal development paths educational activities based on in-depth comparative analysis.

Essentially, the program is a set of digitized collections that can be useful in the process of preparing for testing. In this case, the Android version of your mobile device must be at least 4.0.

Main advantages

With this convenient application, you can prepare for the upcoming Unified State Exam at any convenient time. For any of the subjects, 15 training options of the new format are provided. By the way, the application includes both the usual tests and training in realistic mode.

The developers are constantly updating tasks, so you will always have access to up-to-date information. A thematic list of all available tests is also provided.

Installation and use

The program has a clear and simple interface. In the main menu you will find all the important elements that will be lined up in a column. Among them you can find exam mode, task options, settings and theory.

There are several options available for each item. If we talk about the subjects themselves, the collection includes physics, mathematics, chemistry, computer science and other disciplines. By the way, 2 levels of mathematics are offered (profile, basic).

When you use the tests for the first time, you will need to first download them to your device. Moreover, you will have to search for tests on Google Play yourself, since links to download them are not provided in the program.

Assessment


two parts, including 19 tasks. Part 1 Part 2

3 hours 55 minutes(235 minutes).

Answers

But you can make a compass Calculators on the exam not used.

passport), pass and capillary or! Allowed to take with myself water(in a transparent bottle) and I'm going


The examination paper consists of two parts, including 19 tasks. Part 1 contains 8 tasks of a basic difficulty level with a short answer. Part 2 contains 4 tasks higher level difficulties with short answer and 7 tasks high level Difficulty with a detailed answer.

For execution exam paper in mathematics is assigned 3 hours 55 minutes(235 minutes).

Answers for tasks 1–12 are written down as an integer or finite decimal . Write the numbers in the answer fields in the text of the work, and then transfer them to answer form No. 1, issued during the exam!

When performing work, you can use the ones issued along with the work. Only a ruler is allowed, but it's possible make a compass with your own hands. Do not use instruments with reference materials printed on them. Calculators on the exam not used.

You must have an identification document with you during the exam ( passport), pass and capillary or gel pen with black ink! Allowed to take with myself water(in a transparent bottle) and I'm going(fruit, chocolate, buns, sandwiches), but they may ask you to leave them in the corridor.

The Unified State Examination in mathematics is the main discipline that is taken by all graduates. The examination test is divided into two levels - basic and profile. The second is required only for those who plan to make mathematics the main subject of study in a higher education institution. Everyone else passes the basic level. The purpose of this test is to check the level of skills and knowledge of graduate students for compliance with norms and standards. The division into specialized and basic levels was first used in 2017 so that students who do not need advanced mathematics to enter a university do not waste time preparing for complex tasks.


To receive a certificate and submit documents to a university, you must satisfactorily complete basic level tasks. Preparation Includes Repetition school curriculum in algebra and geometry. Basic-level Unified State Examination tasks are available to schoolchildren with different levels knowledge. The basic level can be passed by students who were simply attentive in class.
The main recommendations for preparation are:

  • It is worth starting systematic preparation in advance so that you do not have to be nervous, mastering all the tasks 1-2 months before the exam. Period required for quality training, depends on the initial level of knowledge.
  • If you are not confident that you will complete the tasks on your own, seek help from a tutor - he will help you systematize your knowledge.
  • Practice solving problems, examples, assignments, according to the program.
  • Solve problems in online mode– “I will solve the Unified State Exam” will help with regular training and preparation for the exam. With a tutor, you will be able to analyze mistakes and analyze tasks that cause particular difficulties.
To successfully pass the test, you need to review the following topics: equations and inequalities, coordinate systems, geometric figures, identity transformations, functions and vectors.
During the preparation process, decide as much as possible more tasks of varying difficulty, gradually move on to completing tasks for a while. Get to know
.
Preparation methods
  • Studying a subject at school;
  • Self-education - solving problems by example;
  • Lessons with a tutor;
  • Training courses;
  • Online preparation.
The last option is to save time and money, an opportunity to test your strengths and outline a range of problematic tasks.

There are 20 tasks (the number may change every year), to which you must give short answers. This is enough for a student who plans to enter higher education. educational establishments for humanitarian specialties.
The subject is given 3 hours to complete the tasks. Before starting work, you must carefully read the instructions and act in accordance with their provisions. The exam notebook is accompanied by reference materials that are necessary to pass examination test. For successful completion of all tasks, 5 points are given, the minimum threshold score is 3.

About the exam

dateUnified State Exam
Early period
March 20 (Fri)geography, literature
March 23 (Mon)Russian language
March 27 (Fri)mathematics B, P
March 30 (Wed)foreign languages(except for the “Speaking” section), biology, physics
April 1 (Wed)
April 3 (Fri)social studies, computer science and ICT
April 6 (Mon)history, chemistry
April 8 (Wed)reserve: geography, chemistry, computer science and ICT, foreign languages ​​(section “Speaking”), history
April 10 (Fri)reserve: foreign languages ​​(except for the “Speaking” section), literature, physics, social studies, biology
April 13 (Mon)reserve: Russian language, mathematics B, P
Main stage
May 25 (Mon)geography, literature, computer science and ICT
May 28 (Thu)Russian language
June 1 (Mon)mathematics B, P
June 4 (Thu)history, physics
June 8 (Mon)social studies, chemistry
June 11 (Thu)foreign languages ​​(except for the “Speaking” section), biology
June 15 (Mon)foreign languages ​​(section “Speaking”)
June 16 (Tue)foreign languages ​​(section “Speaking”)
June 18 (Tue)reserve: history, physics
June 19 (Fri)reserve: geography, literature, computer science and ICT, foreign languages ​​(section “Speaking”)
June 20 (Sat)reserve: foreign language (except for the “Speaking” section), biology
June 22 (Mon)reserve: Russian language
June 23 (Tue)reserve: social studies, chemistry
June 24 (Wed)reserve: history, physics
June 25 (Thu)reserve: mathematics B, P
June 29 (Mon)reserve: for all academic subjects

Total number of main participants period of the Unified State Exam in mathematics at the profile level in 2018 - more than 391 thousand people. The average test score in 2018 increased by more than 2 test points compared to 2017. The number of exam participants who scored 61 points or more increased over the year from 120.6 thousand to 125.6 thousand. At the same time, the greatest increase was shown by completing tasks with a short answer; tasks with a complete solution were generally completed somewhat worse than in 2017 .

As in previous years, the minimum primary score required to pass the exam was 6 (27 test scores). In 2018 minimum score 7.48% of exam participants failed, in 2017 - 14.35%, this figure has almost doubled. The upward trend in results relates to Unified State Exam results both for the country as a whole and for most regions.

More detailed analytical and methodological Unified State Exam materials 2018 available at .

EXAMINATION PLAN FOR THE USE IN MATHEMATICS 2019

Designation of the level of difficulty of the task: B - basic, P - advanced, V - high.

Content elements and activities tested

Task difficulty level

Maximum score for completing the task

Estimated task completion time (min.)
a basic level of/ profile level

Exercise 1.
Task 2. Be able to use acquired knowledge and skills in practical activities and in everyday life
Task 3.
Task 4.
Task 5.
Task 6. Be able to perform actions with geometric shapes, coordinates and vectors
Task 7.
Task 8. Be able to perform actions with geometric shapes, coordinates and vectors
Task 9. Be able to perform calculations and transformations
Task 10.
Task 11. Be able to build and explore simple mathematical models
Task 12. Be able to perform actions with functions
Task 13 (C1). Be able to solve equations and inequalities
Task 14 (C2). Be able to perform actions with geometric shapes, coordinates and vectors
Task 15 (C3). Be able to solve equations and inequalities
Task 16 (C4). Be able to perform actions with geometric shapes, coordinates and vectors
Task 17 (C5). Be able to use acquired knowledge and skills in practical activities and everyday life
Task 18 (C6). Be able to solve equations and inequalities
Task 19 (C7). Be able to build and explore simple mathematical models

Correspondence between minimum primary scores and minimum test scores 2019. Order on amendments to Appendix No. 1 to the order of the Federal Service for Supervision in Education and Science. .

OFFICIAL SCALE 2019

THRESHOLD SCORE
The order of Rosobrnadzor established minimal amount points confirming that exam participants have mastered the basic general education programs of secondary (complete) general education in accordance with the requirements of the federal government educational standard secondary (complete) general education.
MATH THRESHOLD: 6 primary points(27 test points).

EXAMINATION FORMS
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