Secondary general education

Line UMK G.K. Muravin. Algebra and principles of mathematical analysis (10-11) (in-depth)

UMK Merzlyak line. Algebra and beginnings of analysis (10-11) (U)

Mathematics

Preparation for the Unified State Exam in mathematics ( profile level): tasks, solutions and explanations

Examination paper profile level lasts 3 hours 55 minutes (235 minutes).

Minimum threshold- 27 points.

The examination paper consists of two parts, which differ in content, complexity and number of tasks.

The defining feature of each part of the work is the form of the tasks:

• part 1 contains 8 tasks (tasks 1-8) with a short answer in the form of a whole number or a final decimal fraction;
• part 2 contains 4 tasks (tasks 9-12) with a short answer in the form of an integer or a final decimal fraction and 7 tasks (tasks 13–19) with a detailed answer (a complete record of the solution with justification for the actions taken).

Panova Svetlana Anatolevna, mathematics teacher of the highest category of school, work experience 20 years:

“In order to receive a school certificate, a graduate must pass two mandatory exams in the form of the Unified State Examination, one of which is mathematics. In accordance with the Concept of development of mathematics education in Russian Federation The Unified State Examination in mathematics is divided into two levels: basic and specialized. Today we will look at profile-level options.”

Task No. 1- tests the Unified State Examination participants’ ability to apply the skills acquired in the course of grades 5 - 9 in elementary mathematics, in practical activities. The participant must have computational skills, be able to work with rational numbers, be able to round decimals, be able to convert one unit of measurement to another.

Example 1. A cold water flow meter (meter) was installed in the apartment where Peter lives. On May 1, the meter showed a consumption of 172 cubic meters. m of water, and on the first of June - 177 cubic meters. m. What amount should Peter pay for cold water in May, if the price is 1 cubic meter? m of cold water is 34 rubles 17 kopecks? Give your answer in rubles.

Solution:

1) Find the amount of water spent per month:

177 - 172 = 5 (cubic m)

2) Let’s find how much money they will pay for wasted water:

34.17 5 = 170.85 (rub)

Answer: 170,85.

Task No. 2- is one of the simplest exam tasks. The majority of graduates successfully cope with it, which indicates knowledge of the definition of the concept of function. Type of task No. 2 according to the requirements codifier is a task on the use of acquired knowledge and skills in practical activities and Everyday life. Task No. 2 consists of describing, using functions, various real relationships between quantities and interpreting their graphs. Task No. 2 tests the ability to extract information presented in tables, diagrams, and graphs. Graduates need to be able to determine the value of a function from the value of its argument when in various ways specifying a function and describing the behavior and properties of the function based on its graph. You also need to be able to find the largest or smallest value from a function graph and build graphs of the studied functions. Errors made are random in reading the conditions of the problem, reading the diagram.

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Example 2. The figure shows the change in the exchange value of one share of a mining company in the first half of April 2017. On April 7, the businessman purchased 1,000 shares of this company. On April 10, he sold three-quarters of the shares he purchased, and on April 13, he sold all the remaining shares. How much did the businessman lose as a result of these operations?

Solution:

2) 1000 · 3/4 = 750 (shares) - constitute 3/4 of all shares purchased.

6) 247500 + 77500 = 325000 (rub) - the businessman received 1000 shares after selling.

7) 340,000 – 325,000 = 15,000 (rub) - the businessman lost as a result of all operations.

• Absolute winner All-Russian competition"Teacher of the Year in Russia - 2007."
• Honorary Worker of Education of the Russian Federation
• Two-time Winner of the competition for the best teachers of the Russian Federation of the Ministry of Education and Science of the Russian Federation
• Member of the Federal Commission for the Development of Testing and Measuring Materials for the Unified State Examination in Mathematics (2009-2010), expert of the Federal Subject Commission of the Unified State Examination in Mathematics (2011-2012, 2013-2014), Deputy Chairman of the Regional Subject Commission of the State Academy of Mathematics in Mathematics 2012-2014 ).

Olga Sergeevna Pyankova, school mathematics teacher, Elekmonar Dear Dmitry Dmitrievich and the team of the “DAEGE” project!
Thank you for creating such a wonderful online resource to help teachers. Now I have the opportunity to conduct lessons, consultations, and additional classes using detailed video lessons. Your lessons are structured competently, thought out to the smallest detail. And the “presence” of Dmitry Dmitrievich in the lesson gives me confidence, makes my lessons more interesting and meaningful. Using tests, notes, and videos, I noticed that the time for preparing for mathematics lessons and consultations was significantly reduced. After all, there is no need to prepare assignments for tests and independent work, compose tests. Just take a ready-made summary for each lesson, homework based on the Unified State Examination task base with a verification system, test papers and use it!!!
Your work is invaluable!!! Thanks again!

Lepikhina Olga Viktorovna, mathematics teacher, Izhevsk I went to the "DAEGE" course, watched several videos, took several tests and a test.

Very useful and necessary materials, video tutorials with detailed explanations and most importantly tests with online testing mode. Students like this because they can see the results right away and catch mistakes.
It is very useful that before each test there is a review of the tasks and you can watch the video as many times as the student needs - in your own way.
You have a wonderful team that is trying to make the teacher’s work easier and helps the teacher work with all categories of students.
Ksenia Vladimirovna, mathematics teacher, Izhevsk
At a quick glance it is very impressive, in terms of volume and quality.

This is a serious help for rural children, as well as for those who are unlucky with a teacher... very good idea: to be able to buy the activity you are interested in, and not everything
And I'm also pleased with the price...

Thank you! Maisuradze Victoria Vladimirovna, mathematics teacher, Mezhdurechensk Thank you very much to Dmitry Dmitrievich for everything he does. His website I will solve the Unified State Exam and this resource is a lifesaver when working. With the current workload, there is absolutely no time to do anything other than check notebooks. Only such resources save. Thank you. Egorova Victoria Valerievna, mathematics teacher, Elabuga There are no words to express my gratitude. Very, very wonderful material, I would even call it educational and methodological complex, and even tests for a block of lessons. I really want to find a place for all this in my lessons.

Nasibullina Zulfiya Salavatovna, mathematics teacher, Maloyaz Having looked through the Daege website, I made sure that here you can solve tests online together with students. I suggested your website and course names to my students. I think that we will actively work with the site. Before this, we actively used the site I will SOLVE the Unified State Exam, I will Solve the OGE. We took tests from there and also solved them online. Thanks to the creators of the site for helping teachers and students, because not everyone has the opportunity to go to courses or study with a tutor.

Anna Karo, student Thanks for this interesting project. Great help!
Especially in last days before the Unified State Exam :) Excellent system for excellent results.

Surina Zoya Petrovna, mathematics teacher, Moscow Dear Colleagues! Thank you for the interesting and informative material.
I consider the preparation course for the Unified State Exam in mathematics accessible, brief, rational and useful.
I hope that solving more complex problems will be understandable and exciting for graduates.

Kultysheva Olga Valerievna, mathematics teacher, Saratov Hello! I have been using your site for several years now, both when preparing for the Unified State Exam in grades 10-11, and when studying topics in grades starting from 5. When I saw that I could sign up for the “DAEGE” course, I decided to try it. I got acquainted with the course. I liked it very much. It would be nice to have this course always at hand. Thank you!

Busova I. I., mathematics teacher, Novosibirsk Good afternoon colleagues!
Wonderful and useful resource!!!
The lessons are carefully worked out, everything is competent, clear, consistent, detailed and clear. Educational material strictly systematized. The course is a huge help for both students and teachers. Thanks a lot!!!

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 a physical object that 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 is happening in education, we are going the most the long way towards the goal, by teaching outdated ideas, we thereby set 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 is not clear why school mathematics is 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 give 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 the perception of 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 the methods of machine learning, artificial intelligence, and 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.

Don’t flatter yourself, of course I won’t solve the Unified State Exam for you, I won’t go to the exam for you, I won’t bring you magic elixir“Omniscience” or “Answers to the Unified State Exam in Mathematics.” No, all this will not happen. But I can solve problems for you from open bank assignments (hereinafter referred to as OBZ) - that is, to guide you along the path of what you are likely to see in the exam. Everything depends on you. In this section of my website you can always see video tutorials, analyzes of problems from the Obz, recommendations for solving various problems, and useful literature for self-study.

Will I solve the basic level Unified State Exam for you and will I solve the profile level Unified State Exam for you?

Everything is quite simple here - our exam is divided into two levels. For the basic one, you ultimately receive a grade and a certificate. That is, for the majority, this is where the “problems” with mathematics end. If you are going to go into the technical field, or play it safe “to pass the mathematics profile just in case,” then Welcome to problems of increased and high complexity, covering all areas of mathematics from grades 5 to 11, plus related sciences and real-life examples.

At the same time, separation of materials always occurs. You can see the “profile” or “base” mark, so you won’t get confused in a large amount of information.

Is this section for students?

In many ways, yes. But it can also be useful for young colleagues to read materials or watch video lessons. It will always be interesting to receive comments, reviews, criticism on all proposed materials. This will allow you to more accurately and rationally distribute efforts in working on this project.

How to navigate the Unified State Exam section

I will solve the Unified State Exam - it is planned as a large section. For easy access to tasks, use the site search. You can navigate in the “Categories” section, which is located in the right column of the site, and select the required task category there. Plus, at the bottom of this page you can see current materials that have been added recently. This will allow you to always stay up to date with material updates.

About the exam

The total number of participants in the main period of the Unified State Examination in mathematics at the specialized level in 2018 is 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 points). In 2018, 7.48% of exam participants did not achieve the minimum score, in 2017 - 14.35%, this figure 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 teaching materials The 2018 Unified State Examination is 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.

Correspondence between minimum primary scores and minimum test scores for 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 (full) 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
You can download the forms in high quality at