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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 decimal fractions, be able to convert one unit of measure 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.

USE 2017 Trial version

Profile level
Task conditions with

The 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 segment [–4; 8].

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

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 of difficulty- tasks 18-19 –. This part 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, 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 basic level, That's why 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!

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 of a basic level of complexity with a short answer. Part 2 contains 4 tasks advanced level difficulties with a short answer and 7 tasks high level Difficulties with extended answers.

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.

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 at 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.