Preparation for the Unified State Exam in mathematics at basic and specialized levels

The Unified State Examination in mathematics (profile) is optional. This exam is necessary for those who plan to further study this discipline, enter the Faculty of Economics, Mathematics, or continue their studies at technical universities. The profile level, unlike the basic level, requires in-depth knowledge. The exam focuses on skills practical application skills acquired over the years of study, but knowledge of theory for the Unified State Examination in mathematics is no less important.

What do you need to know?

As when passing the Unified State Exam at a basic level, knowledge obtained from school courses algebra and geometry, ability to work with various inequalities and equations, fluency in terminology and knowledge of solution algorithms various tasks. To successfully complete tasks of increased complexity, knowledge in the following areas is required:

• planimetry;
• inequalities;
• interest;
• progression;
• stereometry;
• equations;
• parametric systems, equations, inequalities;
• financial mathematics.

It is impossible to do without theory in the preparation process: without knowing the rules, axioms and theorems, it is impossible to solve those presented in exam papers tasks. At the same time, it would be a mistake to study theory at the expense of practice. Simply memorizing the rules will not help in the exam - it is important to develop and improve the ability to apply acquired knowledge when solving problems.

How to prepare for the exam?

It is better to start preparing for the exam at the beginning academic year. In this case, you can calmly, without haste, go through all the sections, and then repeat them, refreshing your knowledge immediately before testing.

The classic method of preparation - simply reading a textbook in a row, memorizing the rules by heart - is ineffective. To remember information, you need to understand it. You can, for example, try, after reading the rule, retell it in your own words or explain it to yourself. This approach allows you to remember what you read for a long time.

Individual formulas and axioms will have to be memorized. To facilitate the memorization process, you should make sure that the necessary data is in sight at all times - on the wall near the bed, in the bathroom, on the refrigerator, above desk. If tables with formulas are always in front of your eyes, they will gradually be remembered without much effort.

Those who are preparing for the Unified State Exam not alone, but in the company of other graduates, can be advised to explain the theory to each other. This method disciplines and helps to better understand the material.

When executing practical tasks It is necessary to analyze the most common errors. If they are associated not with inattention, but with ignorance of certain rules, it is important to carefully study such topics. The whole theory is structured, and the search the necessary rules will take a minimum of time.

Theory is important, but practice is indispensable. During the exam, the ability to apply the acquired knowledge is tested. It is necessary to practice, practicing the same algorithms over and over again, repeating the same topics, until completing tasks ceases to cause difficulties. Without practical application, knowledge is useless and easily forgotten.

We wish you success in studying the theory and applying the acquired knowledge in the exam!

This article presents an analysis of tasks 9-12 of part 2 of the Unified State Exam in mathematics profile level from a tutor in mathematics and physics. The tutor's video lesson with an analysis of the proposed tasks contains detailed and understandable comments on each of them. If you have just started preparing for the Unified State Exam in mathematics, this article may be very useful for you.

9. Find the meaning of the expression

Using the properties of logarithms, which you can familiarize yourself with in detail in the video tutorial above, we transform the expression:

10. A spring pendulum oscillates with a period T= 16 s. Suspended weight m= 0.8 kg. The speed of movement of the load changes over time in accordance with the formula . At the same time m/s. The defining formula for kinetic energy (in joules) is: , where m taken in kilograms, - in meters per second. What is the kinetic energy of the load in joules 10 s after the start? oscillatory motion?

The speed of movement of the load 10 s after the start of the oscillatory motion will be equal to:

Then the kinetic energy at this moment in time will be equal to:

J.

Let x- the price of one candy, and y- price of chocolate. Then 6 lollipops cost 6 x, and 2% of the cost of a chocolate bar is equal to 0.02 y. Since it is known that 6 lollipops cost 2% less than a chocolate bar, the first equation holds: 6 x + 0,02y = y, from which we obtain that x = 0,98/6 y = 98/600 y = 49/300 y. In turn, 9 lollipops cost 9 x, that is 9·49/300 y = 49/300 y = 1,47 y. The task comes down to determining by what percentage 1.47 y more than y. If y is 100%, then 1.47 y is 1.47·100% = 147%. That is 1.47 y more than y by 47%.

12. Find the minimum point of the function.

1) DL is given by the inequality: title="Rendered by QuickLaTeX.com" height="23" width="106" style="vertical-align: -5px;"> (так выражение, стоящее под знаком логарифма, должно быть больше нуля), откуда получаем, что .!}

2) We are looking for the derivative of the function. For a detailed description of how the derivative of this function is calculated, see the video above. The derivative of the function is equal to:

3) Looking for values x, for which the derivative is equal to 0 or does not exist. It does not exist for , since in this case the denominator goes to zero. The derivative is set to zero when.

The video course “Get an A” includes all the topics necessary for successful passing the Unified State Exam in mathematics for 60-65 points. Completely all tasks 1-13 of the Profile Unified State Exam in mathematics. Also suitable for passing the Basic Unified State Examination in mathematics. If you want to pass the Unified State Exam with 90-100 points, you need to solve part 1 in 30 minutes and without mistakes!

Preparation course for the Unified State Exam for grades 10-11, as well as for teachers. Everything you need to solve Part 1 of the Unified State Exam in mathematics (the first 12 problems) and Problem 13 (trigonometry). And this is more than 70 points on the Unified State Exam, and neither a 100-point student nor a humanities student can do without them.

All the necessary theory. Quick ways solutions, pitfalls and secrets of the Unified State Exam. All current tasks of part 1 from the FIPI Task Bank have been analyzed. The course fully complies with the requirements of the Unified State Exam 2018.

The course contains 5 large topics, 2.5 hours each. Each topic is given from scratch, simply and clearly.

Hundreds of Unified State Exam tasks. Word problems and probability theory. Simple and easy to remember algorithms for solving problems. Geometry. Theory, reference material, analysis of all types of Unified State Examination tasks. Stereometry. Tricky solutions, useful cheat sheets, development spatial imagination. Trigonometry from scratch to problem 13. Understanding instead of cramming. Clear explanations of complex concepts. Algebra. Roots, powers and logarithms, function and derivative. Basis for solution complex tasks 2 parts of the Unified State Exam.

To successfully solve specialized Unified State Exam options in mathematics it is worth abandoning such an algorithm. When preparing for an exam, you need to focus not on passing it as an end in itself, but on increasing the student’s level of knowledge. To do this, you need to study theory, practice skills, solving various options for the profile Unified State Examination in mathematics in non-standard ways with detailed answers, and monitor the dynamics of learning. And the Shkolkovo educational project will help you with all this.

Why should you choose our resource?

We do not offer you typical examples of profile problems of the Unified State Exam in mathematics, which wander on the Internet from one site to another. Our experts have independently developed a database of tasks, which consists of interesting and unique exercises and is updated daily. All USE problems in mathematics at the profile level contain answers and detailed solutions. They allow us to identify strengths and weaknesses in preparing a student and teaching him to think freely and outside the box.

In order to complete tasks and view solutions to USE tasks in mathematics at a profile level, select an exercise in the “Catalogue”. This is quite easy to do because it has a clear structure that includes topics and subtopics. All tasks are arranged in ascending order from simple to more complex and contain answers to the profile Unified State Exam in mathematics with solutions.

In addition, the student is given the opportunity to independently create variants of problems. Using the "Constructor" he can choose Unified State Exam assignments in mathematics of a profile level on any topic that interests him and view their solutions. This will allow you to practice skills in a specific section, for example, geometry or algebra.

Also, the student can analyze the tasks of the profile Unified State Examination in mathematics in “ Personal account student." In this section, the student will be able to monitor his own dynamics and communicate with the teacher.

All this will help you effectively prepare for the specialized Unified State Exam in mathematics and easily find solutions to even the most complex problems.

Practice shows that problems on finding the area of ​​a triangle appear in the Unified State Exam every year. That is why, if students want to get decent scores on the assessment test, they should definitely review this topic and understand the material again.

How to prepare for the exam?

The Shkolkovo educational project will help you learn to solve problems on finding the area of ​​a triangle, similar to those found in the Unified State Examination. Here you will find all the necessary material to prepare for passing the certification test.

To ensure that exercises on the topic “Area of ​​a triangle in Unified State Exam problems” do not cause difficulties for graduates, we recommend that you first refresh your memory of basic trigonometric concepts and rules. To do this, just go to the “Theoretical Information” section. It presents basic definitions and formulas that will help in finding the correct answer.

To consolidate the learned material and practice solving problems, we suggest doing exercises that were selected by experts educational project"Shkolkovo". Each task on the site has a correct answer and a detailed description of how to solve it. Students can practice with both simple and more complex problems.

Schoolchildren can “upgrade” their skills in performing such exercises online both in Moscow and in any other city in Russia. If necessary, the completed assignment can be saved in the “Favorites” section in order to return to it later and discuss the progress of the solution with the teacher.