The exam program, as in previous years, is made up of materials from the main mathematical disciplines. The tickets will include mathematical, geometric, and algebraic problems.

There are no changes in KIM USE 2020 in mathematics at the profile level.

Features of USE assignments in mathematics-2020

• When preparing for the exam in mathematics (profile), pay attention to the basic requirements of the examination program. It is designed to test the knowledge of an in-depth program: vector and mathematical models, functions and logarithms, algebraic equations and inequalities.
• Separately, practice solving tasks for.
• It is important to show non-standard thinking.

Exam Structure

Tasks USE profile mathematics divided into two blocks.

1. Part - short answers, includes 8 tasks that test basic mathematical training and the ability to apply knowledge of mathematics in everyday life.
2. Part - brief and detailed answers. It consists of 11 tasks, 4 of which require a short answer, and 7 - a detailed one with an argumentation of the actions performed.

• Increased complexity- tasks 9-17 of the second part of KIM.
• High level difficulties- tasks 18-19 –. This part of the exam tasks checks not only the level of mathematical knowledge, but also the presence or absence of a creative approach to solving dry "number" tasks, as well as the effectiveness of the ability to use knowledge and skills as a professional tool.

Important! Therefore, in preparation for USE theory in mathematics, always support the solution of practical problems.

How will points be distributed?

The tasks of the first part of KIMs in mathematics are close to USE tests baseline, so high score it's impossible to get them.

The points for each task in mathematics at the profile level were distributed as follows:

• for correct answers to tasks No. 1-12 - 1 point each;
• No. 13-15 - 2 each;
• No. 16-17 - 3 each;
• No. 18-19 - 4 each.

The duration of the exam and the rules of conduct for the exam

To complete the exam -2020 the student is assigned 3 hours 55 minutes(235 minutes).

During this time, the student should not:

• be noisy;
• use gadgets and other technical means;
• write off;
• try to help others, or ask for help for yourself.

For such actions, the examiner can be expelled from the audience.

On State exam mathematics allowed to bring only a ruler with you, the rest of the materials will be given to you immediately before the exam. issued on the spot.

Effective preparation is the solution online tests Math 2020. Choose and get the highest score!

Mathematics Part I-1

Mathematics Part I-2

Mathematics Part I-3

Maxim twice threw a dice, the faces of which are numbered from 1 to 6. and built a rectangle with sides equal to the numbers that fell out. What is the probability that the area of ​​this rectangle will be greater than 15? Round your answer to the nearest hundredth.

Mathematics Part I-4

Mathematics Part I-5

Mathematics Part I-6

Mathematics Part I-7

The figure shows a graph of the derivative of the function f(x) defined on the interval [–5; 6]. Find the number of points of the graph f (x), in each of which the tangent drawn to the graph of the function coincides or is parallel to the x-axis

Mathematics Part I-8

Mathematics Part II-9

Mathematics Part II-10

Devices are connected to the power outlet, the total resistance of which is R1 \u003d 90 Ohm. In parallel with them, an electric heater is supposed to be connected to the outlet. Determine the smallest possible resistance of this electric heater if it is known that when two conductors with resistances R1 Ohm and R2 Ohm are connected in parallel, their total resistance is given by the formula R_(total) \u003d (R1 * R2) / (R1 + R2) (Ohm), and for For the normal functioning of the mains, the total resistance in it must be at least 9 ohms. Express your answer in ohms.

Mathematics Part II-11

Mathematics Part II-12

Mathematics Part II-13

Mathematics Part II-14

The base of the pyramid SABCD is the parallelogram ABCD. The points K, L, M are located on the edges SA, SB, SC, respectively, and at the same time

SK/SA = 1/2; SL/SB = 2/5; SM/SC = 2/3

A) Prove that lines KM and LD intersect.

B) Find the ratio of the volume of the pyramid SKLMD to the volume of the pyramid SABCD.

Mathematics Part II-15

Mathematics Part II-16

In an isosceles trapezoid ABCD AD BC, AD = 21, AB = 10, BC = 9. Diagonals AC and BD break the trapezoid into four overlapping triangles DAB, ABC, BCD, CDA. Each triangle is inscribed with circles w1, w2, w3, w4, respectively, whose centers are located at the points O1, O2, O3, O4.

A) Prove that the quadrilateral O1O2O3O4 is a rectangle.

Mathematics Part II-17

On April 15, it is planned to take a loan in the amount of 900 thousand rubles from the bank for 11 months.
The conditions for its return are as follows:
- On the 1st day of each month, the debt increases by p% compared to the end of the previous month;
- from the 2nd to the 14th day of each month, it is necessary to pay a part of the debt in one payment;
- on the 15th day of each from the 1st to the 10th month, the debt must be the same amount less than the debt on the 15th day of the previous month;
- on the 15th day of the 10th month, the debt amounted to 200 thousand rubles;
- By the 15th day of the 11th month, the debt must be repaid in full.
Find p if the total amount paid to the bank was 1021 thousand rubles.

The USE in mathematics is the main discipline that all graduates take. 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 higher education. A basic level of surrender all the rest. 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 core and basic levels was first used in 2017 so that students who do not need advanced mathematics for admission to a university do not waste time preparing for difficult assignments.

To get a certificate and apply to a university, you need to satisfactorily complete the tasks of the basic level. Preparation includes repetition school curriculum in algebra and geometry. Tasks in the USE of the basic level are available to schoolchildren with different levels knowledge. The basic level can be passed by students who were just attentive in the classroom.
The main recommendations for preparation are:

• Systematic preparation should be started in advance so that you do not have to be nervous, mastering all the tasks 1-2 months before the exam. The period required for high-quality training depends on the initial level of knowledge.
• If you are not sure that you will master the tasks on your own, ask a tutor for help - he will help you systematize your knowledge.
• Practice solving problems, examples, tasks, according to the program.
• Solve tasks online - "I will solve the exam" will help with regular training and preparation for the exam. With a tutor, you will be able to analyze mistakes, analyze tasks that cause particular difficulties.

• Studying the subject at school;
• Self-education - solving problems by example;
• Lessons with a tutor;
• Training in courses;
• Online preparation.

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

Average general education

UMK line G. K. Muravina. Algebra and beginnings mathematical analysis(10-11) (deep)

Line UMK Merzlyak. Algebra and the Beginnings of Analysis (10-11) (U)

Mathematics

Preparation for the 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 tasks:

• 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 (full record of the decision with the rationale for the actions performed).

Panova Svetlana Anatolievna, mathematic teacher the highest category schools, 20 years of work experience:

"In order to receive school certificate, the graduate must pass two mandatory exams in USE form, one of which is mathematics. In accordance with the Development Concept mathematics education V Russian Federation The USE in mathematics is divided into two levels: basic and specialized. Today we will consider options for the profile level.

Task number 1- checks with USE participants the ability to apply the skills acquired in the course of 5-9 classes in elementary mathematics in practical activities. The participant must have computer 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 An expense meter was installed in the apartment where Petr lives cold water(counter). On the first of May, the meter showed an 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 for May, if the price of 1 cu. 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 (cu m)

2) Find how much money will be paid for the spent water:

34.17 5 = 170.85 (rub)

Answer: 170,85.

Task number 2- is one of the simplest tasks of the exam. The majority of graduates successfully cope with it, which indicates the possession of the definition of the concept of function. Task type No. 2 according to the requirements codifier is a task for using 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 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 with various ways of specifying the function and describe the behavior and properties of the function according to its graph. It is also necessary to be able to find the largest or smallest value from the function graph and build graphs of the studied functions. The mistakes made are of a random nature 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 purchased shares, and on April 13 he sold all the remaining ones. 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 after the sale of 1000 shares.

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 for successful delivery tests before admission. In 2017, they often turn to the Internet to find a solution. There are many solutions, the truly worthwhile ones are worth looking for for a very long time. Fortunately, there are well-known and proven systems. One of them is Reshu USE Dmitry Gushchin.

The training system of Dmitry Gushchin called "I will solve the exam" implies a comprehensive preparation for the upcoming exam. Dmitry Gushchin created and 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 items. I solve the Unified State Examination based on the uniform presentation of information, which consistently, topic by topic, fits into the student's brain.

USE-2017 in mathematics, basic level

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

Tasks are available on the basic and profile levels. Mathematics is a prime example of such tasks. The main (basic) level covers the school-wide body of knowledge. It requires the knowledge that each student receives in 11 years. The profile level is designed for graduates of specialized schools with an emphasis on a particular subject.

An interesting feature of the system is its similarity with the real exam. In the event of a final control task submitted in the USE format. The student can also find out his final score after passing the test. This helps to 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 you need to learn.

The most popular subjects in "I will solve the exam" are provided along with others. The Russian language of Dmitry Gushchin includes the rules of grammar, punctuation and syntax, as well as vocabulary. Chemistry contains examples of solving specific problems, special formulas. The chemistry section also includes various compounds and concepts about chemicals. The biology section covers the vital activity of all kingdoms of living organisms. It contains an important theory that will ultimately help you succeed in 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 no longer feel like studying. Your own result always makes you do more.

The system also has criteria for evaluating works. They will make the preparation for the exam planned and thoughtful. A future 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.