USE 2017 Trial version

Profile level
Task conditions with

Examination paper consists of two parts, including 19 tasks. 3 hours and 55 minutes are allotted for the completion of the examination paper 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

The answer to tasks 1-12 is an integer or a final decimal. The answer should be written in the answer sheet No. 1 to the right of the number of the corresponding task,starting with the first cell. Write each digit, minus sign, and decimal point ina separate cell in accordance with the samples given in the form. Units of measurement are not required.

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

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

3 . There are two circles on the checkered paper. The area of ​​the inner circle is 2. Find the area of ​​the shaded figure.

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

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

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

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

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

9 . Find the value of an expression

10 . Distance from an observer at a height h m above the ground, expressed in kilometers, to the horizon line he sees is calculated by the formula, where R= 6400 km is the radius of the Earth. A person standing on the beach sees the horizon at a distance of 4.8 kilometers. A staircase leads to the beach, each step of which has a height of 10 cm. What is the least number of steps that 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 from the same house for a walk to the edge of the forest, located 1.1 km from the house. One is walking at a speed of 2.5 km/h and the other one is walking at a speed of 3 km/h. Having reached the edge, the second one returns at the same speed. At what distance from the starting point 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 the answer sheet number 2.First write down the number of the task being performed, and then the full reasoned 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 dot M mid-rib C 1 D 1 and dot K divides an edge AA 1 against AK:KA= 1:3. through dots K And M a plane α is drawn parallel to a straight line BD and 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- cube.

15 . Solve the inequality .

16 . Parallelogram ABCD and the circle are arranged 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 quadrilateral ABQP 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 a loan from a bank 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 subsequent payments was exactly three times 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 ..

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 the exam not used.

passport), pass and capillary or! Allowed 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 basic level Difficulty with short answers. Part 2 contains 4 tasks advanced level difficulty with a short answer and 7 tasks of a high level of complexity with a detailed answer.

To complete the examination work in mathematics is given 3 hours 55 minutes(235 minutes).

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

When doing work, you can use the ones issued with the work. You can only use a ruler, but you can make a compass with your own hands. It is forbidden to use tools with reference materials. Calculators on the exam not used.

You must have an identity document with you for the exam. passport), pass and capillary or gel pen with black ink! Allowed to take with myself water(in a transparent bottle) and food(fruit, chocolate, buns, sandwiches), but may be asked to leave in the hallway.

Secondary 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

The profile-level examination paper 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.

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

Examples.
30 athletes compete at the diving championship, among them 3 divers from Holland and 9 divers from Colombia. The order of performances is determined by a draw. Find the probability that the jumper from Holland will be the 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 a 25% solution were used to make the mixture?

20 athletes compete at the diving championship, including 7 divers from Holland and 10 divers from Colombia. The order of performances is determined by a draw. Find the probability that the jumper from Holland will be the eighth.

Content
Introduction
Map of individual achievements of the student
Work instructions
Standard USE answer forms
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
Decisions and criteria for assessing tasks 13-19.

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

• I will pass the Unified State Exam, Mathematics, Self-study course, Problem solving technology, Profile level, Part 3, Geometry, Yashchenko I.V., Shestakov S.A., 2018
• I will pass the Unified State Examination, Mathematics, Self-study course, Problem solving technology, Profile level, Part 2, Algebra and the beginning of mathematical analysis, Yashchenko I.V., Shestakov S.A., 2018
• I will pass the Unified State Examination, Mathematics, Self-study course, Problem solving technology, 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

The following tutorials and books.

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

USE assignments 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!