Ege dmitry gushchin is basic. Preparation for the exam in mathematics (profile level): tasks, solutions and explanations

  • The absolute winner of the All-Russian competition "Teacher of the Year of 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 Control and Measuring Materials for the Unified State Exam 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 Examination of Mathematics 2012-2014 ).

    Olga Sergeevna Pyankova, school mathematics teacher, Elekmonar Dear Dmitry Dmitrievich and the team of the DAEGE project!
    Thank you for making such a great electronic resource for teacher assistance. Now I have the opportunity to conduct lessons, consultations, additional classes using detailed video lessons. Your lessons are built 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, videos, I noticed that the time for preparing for math lessons and consultations was significantly reduced. After all, there is no need to prepare tasks for control and independent work, to draw up tests. Just take a ready-made synopsis for each lesson, homework based on the USE assignments with a verification system, test papers and use it !!!
    Your work is invaluable !!! Thanks again!

    Olga Lepikhina, mathematics teacher, Izhevsk I went to the "DAEGE" course, watched several videos, completed several tests and a test. Very useful and necessary materials, video tutorials with detailed explanations and, most importantly, tests with an online verification mode. Students love this because the result can be seen immediately and the errors can be deciphered. It is very useful that before each test there is an analysis of the tasks and you can watch the video as many times as the student needs - in your own mode. You have a wonderful team that tries to make the teacher's work easier and helps the teacher in working with all categories of students.

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    Maisuradze Victoria Vladimirovna, teacher of mathematics, Mezhdurechensk Thank you very much Dmitry Dmitrievich for everything he does. His website will solve the USE and this resource is a lifesaver when working.
    With the current workload, there is absolutely not enough time to do something else besides checking notebooks. Only such resources are saved. Thanks.

    Egorova Victoria Valerievna, teacher of mathematics, Elabuga There are no words to express gratitude. Very, very wonderful material, I would even call it an educational and methodological complex. All material is strictly systematized and presented for almost all exam tasks. There is repetition, and the necessary theoretical material, and test assignments, and even tests for a block of lessons. I really want to find a place for all this in my lessons.

    Nasibullina Zulfiya Salavatovna, teacher of mathematics, Maloyaz Having looked at the Daege website, I made sure that it is possible to solve tests online here together with the students. I offered my students your site, course names. I think that we will actively work with the site. Prior to that, we actively used the site I SOLVE the Unified State Exam, I Solve the OGE. We took tests from there and also solved it 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 Caro, student Thank you for such an interesting project. It helps a lot!
    Especially in the last days before the exam :) An excellent system for excellent results.

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

    Olga V. Kultysheva, teacher of mathematics, Saratov Hello! I have been using your site for several years, both in preparation for the Unified State Exam in grades 10-11, and when studying topics in grades, starting from 5. Seeing that it is possible to enroll in the "DAEGE" course, I decided to try it. I got acquainted with the course. I really liked it. It would be nice to have this course always at hand. Thank you!

    Busova I.I., mathematics teacher, Novosibirsk Good afternoon, colleagues!
    A wonderful and useful resource !!!
    The lessons are carefully worked out, everything is competent, clear, consistent, detailed and clear. The educational material is strictly systematized. The course is a huge help for both students and teachers. Thank you very much!!!

As in previous years, the division of exams into basic and specialized levels remains. But unlike the previous three years, it will not be possible to take both exams in one session, you will have to decide on the choice of the level in advance. The results of the USE at the basic level are recognized by educational organizations of secondary general education and educational organizations of secondary vocational education as the results of state final certification, i.e. allow you to get a full-fledged document on secondary education. The tasks of the basic variant are very simple, however basic variant intended for attestation of graduates who do not plan to continue their education in professions that have special requirements for the level of mathematical training, i.e. graduates who have passed this type of exam will not be able to enter universities in which the study programs include certain exact sciences. And there are quite a few such universities, to put it mildly.
In my opinion, graduates of the intermediate level of academic performance are faced with a difficult task - to take a risk and try to pass the exam of the profile level of difficulty or stay at the basic one, but limit themselves in the future to the choice of a profession only in the purely humanitarian sphere. Good for those who have already decided on their talents and inclinations. What should the rest of us do?

I believe that in the coming year, the competition for science and technology specialties will continue to grow. Therefore, I recommend that, starting from the basic level, make sure that you can handle this option if necessary. And then, during the school year, build up your abilities. In this case, you will limit yourself in choosing a future profession only by your own inclinations, and not by the fear of difficult exams.

The basic level option contains 20 tasks, designed for 3 hours of work and designed to test the ability to apply the knowledge gained in practice, develop logical thinking, and the ability to work with information. As in the previous year, the basic level examination paper will contain a References section.

I suggest that you familiarize yourself with the Demo version in an interactive form , to
1) check your capabilities and decide on the training regime: what level you will prepare for during the academic year;
2) start preparing now and continue it at any time convenient for you.
To do this, first solve the task yourself, check the answer, then see a possible solution.

The answer to each task is a final decimal fraction, integer, or sequence of numbers. If the answer is a sequence of numbers, then enter this sequence in the answer field without spaces, commas or other additional characters. You do not need to write the measurement units. Also, do not put spaces at the beginning and end of the line.

Demo version with solutions.
Maths. Grade 11. Unified State Exam 2020. Basic level.

ExerciseComments and links for preparation
1aFind the value of the expression (6.7 - 3.2) · 2.4.When working with fractions, remember these simple rules:
1) Fractions lead to a common denominator when adding and subtracting.
2) To multiply 2 regular ordinary fractions, it is enough to multiply the numerator by the numerator, and the denominator by the denominator.
3) Divide by fraction is the same as multiply by inverted.

If your calculations contain decimal fractions, pay close attention to the position of the decimal point.

Attention, © mathematichka... Direct copying of materials on other sites is prohibited.

Evaluation


two parts including 19 tasks. Part 1 Part 2

3 hours 55 minutes(235 minutes).

Answers

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

passport), pass and capillary or! Allow to take with myself water(in a transparent bottle) and food


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

The examination work in mathematics is assigned 3 hours 55 minutes(235 minutes).

Answers to tasks 1-12 are written as an integer or final decimal... Write the numbers in the answer fields in the text of the work, and then transfer them to the answer form number 1, issued on the exam!

When performing work, you can use those issued along with the work. Use only a ruler but you can make a compass do it yourself. Do not use tools with reference materials printed on them. Calculators on exam not used.

During the exam, you must have an identity document ( passport), pass and capillary or gel pen with black ink! Allow to take with myself water(in a transparent bottle) and food(fruits, chocolate, rolls, sandwiches), but may be asked to be left in the hallway.

Secondary general education

UMK line G.K. Muravin. Algebra and the beginnings of mathematical analysis (10-11) (in-depth)

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

Maths

Preparation for the exam in mathematics (profile level): tasks, solutions and explanations

We analyze tasks and solve examples with a teacher

The examination work at the 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 assignments:

  • part 1 contains 8 tasks (tasks 1-8) with a short answer in the form of an integer 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 the justification of the actions performed).

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

“In order to receive a school certificate, a graduate must pass two compulsory examinations in the form of the Unified State Exam, one of which is mathematics. In accordance with the Concept for the Development of Mathematical Education in the Russian Federation, the Unified State Exam in Mathematics is divided into two levels: basic and specialized. Today we will consider options for the profile level. "

Task number 1- tests the USE participants' ability to apply the skills acquired in the course of 5-9 grades in elementary mathematics in practical activities. The participant must have computational skills, be able to work with rational numbers, be able to round decimal fractions, be able to convert one unit of measurement to another.

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

Solution:

1) Let's find the amount of water spent per month:

177 - 172 = 5 (cubic meters)

2) Let's find how much money will be paid for the water spent:

34.17 5 = 170.85 (rub)

Answer: 170,85.


Task number 2-is one of the simplest exam tasks. Most graduates successfully cope with it, which testifies to the possession of the definition of the concept of function. Type of task number 2 according to the requirements codifier is a task for using the acquired knowledge and skills in practical activities and everyday life. Task number 2 consists of the description using functions of various real relationships between quantities and the interpretation of their graphs. Task number 2 tests the ability to extract information presented in tables, diagrams, graphs. Graduates need to be able to determine the value of a function by the value of the argument in various ways of defining a function and describe the behavior and properties of a function according to its schedule. It is also necessary to be able to find the largest or smallest value on the graph of the function and plot the graphs of the studied functions. The mistakes made are random in reading the problem statement, reading the diagram.

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


Solution:

2) 1000 3/4 = 750 (shares) - make up 3/4 of all purchased shares.

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

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

Many applicants are concerned about how to independently acquire the knowledge necessary to successfully pass the pre-admission tests. In 2017, they often turn to the internet to find a solution. There are many solutions, for the truly worthwhile it is worth looking for a very long time. Fortunately, there are well-known and proven systems out there. One of them - I will solve the exam by Dmitry Gushchin.

The educational system of Dmitry Gushchin called "I will solve the Unified State Exam" implies a comprehensive preparation for the upcoming exam. Dmitry Gushchin tried to give the necessary knowledge for free so that the future generation could successfully pass the exams. The system is designed for independent study of subjects. I will solve the exam based on the uniform presentation of information, which consistently, topic by topic, fits into the brain of the student.

USE-2017 in mathematics, basic level

Dmitry Gushchin undertakes to help with such exams as the OGE and the Unified State Examination, using a very common method. It lies in the fact that all new knowledge is submitted and systematized by topic. The student can easily choose what he needs to repeat for the final consolidation of the material.

Assignments are available at basic and specialized levels. Mathematics is a prime example of such tasks. The main (basic) level covers the general school volume of knowledge. It requires the knowledge that each student receives in 11 years. The profile level is designed for graduates of specialized schools with a focus on a particular subject.

An interesting feature of the system is its similarity to a real exam. In the case of the final test assignments are submitted in the USE format. The student can also find out their final score after taking the test. This helps motivate a person to achieve new goals and to learn new material. Realizing your real chances on the exam helps you gather your thoughts and understand what exactly needs to be learned.

The most demanded subjects in the "Reshu Unified State Exam" are provided along with others. Dmitry Gushchin's Russian language includes the rules of grammar, punctuation and syntax, as well as vocabulary. Chemistry contains examples of solving specific problems, special formulas. Also, the chemistry section includes various compounds and concepts of chemicals. The section of biology covers the vital activity of all kingdoms of living organisms. It contains important theory that will ultimately help you pass the exam.

The next feature is that your progress is recorded and you can track your progress. This approach will help you motivate yourself even when you don't feel like learning anymore. Your own result always forces you to do more.

The system also has criteria for evaluating work. They will make your exam preparation planned and thoughtful. The prospective student will always be able to read them and understand what the examiner will pay attention to. This is important in order to pay attention to certain important aspects of the work. In general, the student is fully aware of the importance of his choice and remembers the assessment criteria.