The exam program, as in previous years, is composed of materials from basic mathematical disciplines. The tickets will include mathematical, geometric and algebraic problems.

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

Features of exam 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.
• Practice solving tasks separately.
• It is important to show non-standard thinking.

Exam structure

Unified State Exam Tasks in 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 - short and detailed answers... Consists of 11 tasks, 4 of which require a short answer, and 7 - expanded with the reasoning of the actions performed.

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

Important! Therefore, when preparing for the exam, always reinforce the theory in mathematics by solving practical problems.

How the points will be distributed

The tasks of the first part of the KIMs in mathematics are close to the tests of the USE at the basic level, so it is impossible to get a high score on them.

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

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

Exam duration and rules of conduct for the exam

To complete the examination work -2020 student assigned 3 hours 55 minutes(235 minutes).

During this time, the student should not:

• behave noisy;
• use gadgets and other technical means;
• write off;
• trying to help others, or asking for help for yourself.

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

For the state exam in mathematics allowed to bring only a ruler with you, the rest of the materials will be given to you immediately before the exam. issued locally.

Effective preparation is the solution to online math tests 2020. Choose and get the maximum score!

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

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 (complete record of the decision with 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) 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 spent water:

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.

USE 2017 Trial version

Profile level
Conditions of tasks with

The examination paper consists of two parts, which include 19 tasks. 3 hours 55 minutes are allotted for the performance of the examination work in mathematics. Answers to tasks 1–12 are written as an integer or a final decimal fraction. When completing tasks 13-19, you need to write down the complete solution.

Part 1

Answer to tasks 1-12 is an integer or final decimal fraction. The answer should be written in answer form No. 1 to the right of the number of the corresponding task,starting from the first cell. Write each digit, minus sign and decimal point ina separate cell in accordance with the samples provided in the form. You do not need to write the measurement units.

1 ... At a gas station, one liter of gasoline costs 33 rubles. 20 kopecks The driver filled the tank with 10 liters of gasoline and bought a bottle of water for 41 rubles. How many rubles in change will he receive from 1000 rubles?

2 ... The figure shows a graph of precipitation in Kaliningrad from 4 to 10 February 1974. Days are plotted on the abscissa, and precipitation in mm is plotted on the ordinate. Determine from the figure how many days from this period fell from 2 to 8 mm of precipitation.

3 ... Two circles are depicted on checkered paper. The area of ​​the inner circle is 2. Find the area of ​​the shaded shape.

4 ... The probability that student Petya will correctly solve more than 8 problems on the history test is 0.76. The probability that Petya will correctly solve more than 7 problems is 0.88. Find the probability that Petya will correctly solve exactly 8 problems.

5 ... Solve the equation. If your equation has more than one root, indicate the smaller one in your answer.

6 ... A circle inscribed in an isosceles triangle divides at the point of tangency one of the lateral sides into two segments, the lengths of which are 10 and 1, counting from the apex opposite to the base. Find the perimeter of the triangle.

7 ... The figure shows the graph of the derivative of the function , defined on the interval (–8; 9). Find the number of minimum points of the function , belonging to the segment [–4; eight].

8 ... Find the area of ​​the lateral surface of a regular triangular prism inscribed in a cylinder whose base radius is equal to, and the height is equal to.

9 ... Find the meaning of the expression

10 ... Distance from an observer at a height h m above the ground, expressed in kilometers, to the horizon line visible to them is calculated by the formula, where R = 6400 km is the radius of the Earth. A person standing on the beach sees the horizon 4.8 kilometers away. A staircase leads to the beach, each step of which is 10 cm high. What is the smallest number of steps a person needs to climb so that he can see the horizon at a distance of at least 6.4 kilometers?

11 ... Two people go for a walk from the same house to the edge of the forest, which is 1.1 km from the house. One goes at a speed of 2.5 km / h, and the other - at a speed of 3 km / h. Having reached the edge, the second one returns back at the same speed. At what distance from the point of departure will they meet? Give your answer in kilometers.

12 ... Find the minimum point of the function that belongs to the interval.

To record solutions and answers to tasks 13-19 use answer sheet # 2.Write down the number of the assignment to be performed first, followed by the complete informed decision andanswer.

13 ... a) Solve the equation. b) Determine which of its roots belong to the segment.

14 ... In a parallelepiped ABCDA 1 B 1 C 1 D 1 point M mid-rib C 1 D 1, and point K divides an edge AA 1 in relation AK: KA = 1: 3. Through points K and M the plane α is drawn parallel to the straight line BD and the intersecting diagonal A 1 C at the point O.
a) Prove that the plane α divides the diagonal A 1 C in a relationship A 1 O: OC = 3:5.
b) Find the angle between the plane α and the plane ( ABC) if it is known that ABCDA 1 B 1 C 1 D 1- cubic meter

15 ... Solve inequality .

16 ... Parallelogram ABCD and the circle are located so that the side AB touches the circle CD is a chord and the sides D A and BC intersect the circle at points P and Q respectively.
a) Prove that near the quadrangle ABQP you can describe a circle.
b) Find the length of the segment DQ if it is known that AP= a, BC= b, BQ= c.

17 ... Vasya took out a bank loan in the amount of 270,200 rubles. The loan repayment scheme is as follows: at the end of each year, the bank increases the remaining amount of the debt by 10%, and then Vasya transfers his next payment to the bank. It is known that Vasya repaid the loan in three years, and each of his next payments was exactly three times more than the previous one. How much did Vasya pay for the first time? Give your answer in rubles.

18 ... Find all such values ​​of the parameter, for each of which the equation has solutions on the interval ..

Series “Unified State Exam. FIPI - school "prepared by the developers of control measuring materials (CMM) of the unified state examination. The collection contains:
36 standard examination options, drawn up in accordance with the draft demo version of the KIM USE in mathematics of the profile level in 2017;
instructions for performing examination work;
answers to all tasks;
solutions and assessment criteria for tasks 13-19.
Completing tasks of typical examination options provides students with the opportunity to independently prepare for the state final certification, as well as objectively assess the level of their training.
Teachers can use standard examination options to organize monitoring of the results of mastering by schoolchildren of educational programs of secondary general education and intensive preparation of students for the Unified State Exam.

Examples.
30 athletes compete in the diving championship, among them 3 divers from Holland and 9 divers from Colombia. The order of performances is determined by drawing lots. Find the probability that the Dutch jumper will be eighth.

By mixing 25% and 95% acid solutions and adding 20 kg of pure water, a 40% acid solution was obtained. If, instead of 20 kg of water, 20 kg of a 30% solution of the same acid were added, then a 50% acid solution would be obtained. How many kilograms of the 25% solution were used to make the mixture?

20 athletes compete in the diving championship, among them 7 divers from Holland and 10 divers from Colombia. The order of performances is determined by drawing lots. Find the probability that the Dutch jumper will be eighth.

Content
Introduction
A student's individual achievement map
Work instructions
Standardized answer forms for the Unified State Exam
Option 1
Option 2
Option 3
Option 4
Option 5
Option 6
Option 7
Option 8
Option 9
Option 10
Option 11
Option 12
Option 13
Option 14
Option 15
Option 16
Option 17
Option 18
Option 19
Option 20
Option 21
Option 22
Option 23
Option 24
Option 25
Option 26
Option 27
Option 28
Option 29
Option 30
Option 31
Option 32
Option 33
Option 34
Option 35
Option 36
Answers
Solutions and assessment criteria for assignments 13-19.

Free download an e-book in a convenient format, watch and read:
Download the book Unified State Exam, Mathematics, Profile level, Typical exam options, 36 options, Yashchenko I.V., 2017 - fileskachat.com, fast and free download.

• I will pass the exam, Mathematics, Self-study course, Technology for solving tasks, Profile level, Part 3, Geometry, Yashchenko I.V., Shestakov S.A., 2018
• I will pass the exam, Mathematics, Self-study course, Technology for solving tasks, Profile level, Part 2, Algebra and the beginning of mathematical analysis, Yashchenko I.V., Shestakov S.A., 2018
• I will pass the exam, Mathematics, Self-study course, Technology for solving problems, Basic level, Part 3, Geometry, Yashchenko I.V., Shestakov S.A., 2018
• I will pass the exam, Mathematics, Profile level, Part 3, Geometry, Yashchenko I.V., Shestakov S.A., 2018

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