Mathematics Part I-1

Mathematics Part I-2

Mathematics Part I-3

Maxim threw twice dice, whose faces are numbered from 1 to 6. and built a rectangle with sides equal to the dropped numbers. What is the probability that the area of ​​this rectangle will be more 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 the 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), at each of which the tangent drawn to the graph of the function coincides or is parallel to the abscissa axis

Mathematics Part I-8

Mathematics Part II-9

Mathematics Part II-10

Devices with a total resistance of R1 = 90 Ohm are connected to the power outlet. 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) = (R1 * R2) / (R1 + R2) (Ohm), and for the normal functioning of the electrical network, 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. Points K, L, M are located on 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 SKLMD pyramid to the volume of the SABCD pyramid.

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 divide the trapezoid into four overlapping triangles DAB, ABC, BCD, CDA. Each triangle contains 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 a 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 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 of the 10th month, the debt was 200 thousand rubles;
- by the 15th day of the 11th month, the debt must be repaid in full.
Find p if 1021 thousand rubles were paid to the bank in total.

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

Examination paper comprises two parts including 19 tasks. Part 1 contains 8 tasks basic level difficulty with a short answer. Part 2 contains 4 tasks increased level difficulty with a short answer and 7 tasks high level difficulties 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.

The average 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 (a 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 exams in USE form one of which is math. In accordance with the Concept for the Development of Mathematical Education in Russian Federation The 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 decimals, be able to convert one unit of measurement to another.

Example 1. An expense meter was installed in the apartment where Peter lives cold water(counter). 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 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 when different ways assigning a function and describing the behavior and properties of the function according to its schedule. It is also necessary to be able to find the greatest or smallest value and build graphs of the learned 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.