Mathematics Part I-1

Mathematics Part I-2

Mathematics Part I-3

Maxim threw a dice twice, the sides of which are numbered from 1 to 6, and built a rectangle with sides equal to the numbers drawn. 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 on the graph of f(x), at each of which the tangent drawn to the graph of the function coincides with or is parallel to the x-axis

Mathematics Part I-8

Mathematics Part II-9

Mathematics Part II-10

Devices with a total resistance of R1 = 90 Ohms are connected to the power outlet. In parallel with them, an electric heater is supposed to be connected to the outlet. Determine the lowest 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 For 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 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 the 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. The diagonals AC and BD divide the trapezoid into four overlapping triangles DAB, ABC, BCD, CDA. Circles w1, w2, w3, w4 are inscribed in each triangle, respectively, the centers of which are located at 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 out 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 of each month it is necessary to pay part of the debt in one payment;
- on the 15th day of each month from the 1st to the 10th month, the debt should 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 bank was paid a total of 1021 thousand rubles.

The Unified State Examination in mathematics is one of the main tests for school graduates before receiving a certificate and entering a higher education institution. This type of knowledge control is used to assess knowledge in disciplines acquired during schooling. Single State exam takes place in the form of testing, the preparation of tasks for the final test is carried out by Rosobrnadzor and other authorized bodies in the field of education. The passing grade in mathematics depends on the individual requirements of the university to which one is applying.graduate. Successfully passing the exam with a high grade is an important factor for success in admission.

Profile-level mathematics is required for admission to technical and economic universities. The basis of the exam tasks is the basic level, with more complex problems and examples added to it. Short and detailed answers are expected:

• The first tasks do not require in-depth knowledge - this is a test of basic level knowledge;
• The next 5 are more difficult, requiring an average to high level of mastery of the subject. These tasks are checked using a computer because the answer is short.

If a student chooses this level, this implies his desire to continue studying the exact sciences at a higher educational institution. The choice in favor of a specialized exam also indicates that the student’s level of knowledge is quite high, in other words, fundamental preparation is not needed.
The preparation process includes repetition of the main sections, solving problems of increased complexity that require a non-standard, creative approach.

Methods of preparation

• Basic training is carried out at school, where the student masters the basics, sometimes the teacher conducts additional electives for graduates. The main recommendation is to carefully and thoroughly master all topics, especially in graduate school.
• Independent work: this requires special self-discipline, will and self-control. You need to carefully read . The problem is in the direction - only a specialist can competently guide the future applicant to those topics that need attention.
• Tutoring: a professional specialist will help you solve complex tasks effectively and quickly.
• Courses and online learning: a modern and proven method that saves time and money. An important advantage: you can take tests online, quickly get answers, and practice on different tasks.

Don’t flatter yourself, of course I won’t solve the Unified State Exam for you, I won’t go to the exam for you, I won’t bring you the magic elixir of “Omniscience” or “Answers to the Unified State Exam in Mathematics.” No, all this will not happen. But I can solve problems for you from open bank assignments (hereinafter referred to as OBZ) - that is, to guide you along the path of what you are likely to see in the exam. Everything depends on you. In this section of my website you can always see video tutorials, analyzes of problems from the obz, recommendations for solving various problems, and useful literature for self-study.

Will I solve the basic level Unified State Exam for you and will I solve the profile level Unified State Exam for you?

Everything is quite simple here - our exam is divided into two levels. For the basic one, you ultimately receive a grade and a certificate. That is, for the majority, this is where the “problems” with mathematics end. If you are going to go into the technical field, or play it safe “to pass the mathematics profile just in case,” then Welcome to problems of increased and high complexity, covering all areas of mathematics from grades 5 to 11, plus related sciences and real-life examples.

At the same time, separation of materials always occurs. You can see the “profile” or “base” mark, so you won’t get confused in a large amount of information.

Is this section for students?

In many ways, yes. But it can also be useful for young colleagues to read materials or watch video lessons. It will always be interesting to receive comments, reviews, criticism on all proposed materials. This will allow you to more accurately and rationally distribute efforts in working on this project.

How to navigate the Unified State Exam section

I will solve the Unified State Exam - it is planned as a large section. For easy access For tasks, use the site search. You can navigate in the “Categories” section, which is located in the right column of the site, and select the required task category there. Plus, at the bottom of this page you can see current materials that have been added recently. This will allow you to always stay up to date with updated materials.

In this section, we are preparing for the Unified State Examination in mathematics as a basic, specialized level - we provide analysis of problems, tests, a description of the exam and useful recommendations. Using our resource, you will at least understand how to solve problems and be able to successfully pass the Unified State Exam in mathematics in 2019. Begin!

The Unified State Examination in mathematics is a mandatory exam for any student in the 11th grade, so the information presented in this section is relevant for everyone. The mathematics exam is divided into two types - basic and specialized. In this section I provide an analysis of each type of task with a detailed explanation for two options. Unified State Exam assignments strictly thematic, so for each issue you can give precise recommendations and provide the theory necessary specifically for solving this type of task. Below you will find links to assignments, by clicking on which you can study the theory and analyze examples. Examples are constantly replenished and updated.

Structure of the basic level of the Unified State Examination in mathematics

The examination paper in basic level mathematics consists of one piece , including 20 short-answer tasks. All tasks are aimed at testing the development of basic skills and practical skills in applying mathematical knowledge in everyday situations.

The answer to each of tasks 1–20 is integer, trailing decimal , or sequence of numbers .

A task with a short answer is considered completed if the correct answer is written down in answer form No. 1 in the form provided for in the instructions for completing the task.