Soon the fairy tale affects, but no sooner is done

Unfortunately, new methodological materials appear on the site not at such a speed with which many visitors would like. It is not surprising, because the creation of a quality lesson requires quite a long time. But what to do? Here you have a topic or a separate task that you have not found on my resource .... And it is necessary to figure out today!

Therefore, as the project develops, it is necessary to create bank of ready-made solutions According to various sections of the highest mathematics. And this page should like you exactly because the bank perfectly free! Right now you have the opportunity to download file archives for free of charge on various tower topics.

Job source?

All tasks are fulfilled personally to me, which guarantees high quality solutions.

A typical archive contains, as a rule, 200-300 tasks with ready-made solutions, and I tried to collect the most diverse materials, including rarely found tasks and examples of increased complexity. Salvanka consists of test work, individual tasks performed at one time by me to order. In addition, we will delight students-glasses - the archives include typical calculations from the Column of Kuznetsov, the IDA of the Collection of Ryabushko, as well as the theory of probabilities from the column of Wonderland. For reasons that are mentioned in the review Useful mathematical sites, I distribute them completely free. Yes, of course, the calculation is not very much, but some students are big lucky!

Only, Comrades, let's not complaint and offended. Yes, the quality is high, all examples and tasks are tested by teachers, but in solutions there may be typos, incorrect things and even errors. The tasks are represented by "as is". It does not make sense To inform me about the found shoals, because, firstly, they are technically difficult to correct, and secondly, it is simply no time (one repacking and the recalculation of the archive is worth). Exception is made PDF files that are located directly on the server, please email me if you find serious oversight in them.

Perhaps some will have misunderstanding, and even an error will arise. But almost all visitors to the site have a nonzero level of mathematical training, so sample solutions will bring much more benefit than harm; Ideally, if you are doing well in one topic or another and want to find additional examples.

Each collection of tasks is accompanied by brief comments on the contents of the archive. Moreover, the bank from time to time is updated with new materials.

In short, go to us on the light!

Ready tasks with solutions on the topic
Linear algebra and analytical geometry

The archive contains the order of three hundred tasks according to linear algebra and analytical geometry, including several calculations of Kuznetsov and several Ids Ryabushko. Almost all standard objectives of algebra are serviced: solving systems of equations, calculation of determinants, research systems for units, tasks for determining the grade matrix, matrix equations, tasks for eigenvalues \u200b\u200b/ eigenvectors. Analytical geometry is represented by both tasks on the plane and in three-dimensional space.

Examples of solution limits

The archive contains a couple of hundreds of split limits, including the limits of sequences. Examples of solving limits with remarkable equivalences are considered. The collection contains 3 cells of the Kuzntz and 3 options of the IDA Ryabushko. Say, what options, I will not - a pleasant game of the lottery and entertainment! If you have read the existing lessons on the topic, then you will not understand much of the selection limits will not be much difficult

Differentiation of the functions of one variable

The archive is presented mainly by typical calculations from the Kuznetsov Collection (10 options), there are 3 options from Ryabushko. Examples will allow to significantly increase their differentiation technique, since derivatives from the Kuznetsov collection are sufficiently heavy. Moreover, some derivatives have to find in several stages! In addition to derivatives, there are typical tasks: finding derivatives of arbitrary, "enon" order, examples using the Lagrange formula; Tasks for building tangential and normal, and some tasks to find a derivative derivative to determine the derivative.

Studies of functions

Perhaps the most time-consuming and painstaking selection. Reshebnik contains 69 fully studied functions of one variable, including function-polynomials, fractional rational functions, functions with exhibitors, logarithms, and other, rare samples. It is enough likely that you will find your example or a very similar function. The piggyback acts as the application theme and graphics theme and is intended for self-test / workout.

Ready solutions of uncertain integrals

Basically, uncertain integrals, but there are few and certain integrals. The collection includes more than two hundred integrals, including very complex. A variety of examples are considered that did not fit into my lessons! The archive includes 6 typical calculations of Kuznetsov and 2 Ids Ryabushko. Kuznetsova calculations contain tasks to find the volume of bodies, arc lengths and surface area, and, not only in the Cartesian, but also in the polar coordinate system, as well as for parametrically specified functions.

Tasks for numerical and functional series

Another weighty brick. Of course, in stock examples of the study of numerical rows for convergence, and there are rows of creative, requiring experience and non-standard approach. My pride - there was no such row, which I would not have been able to hack. The tasks of finding the sum of the series are considered, various tasks for approximate calculations using a row. Functional series are presented with a common task to find the region of convergence (again with creative cases). There is a popular task to decompose a private solution of the Du in a row. There are a dozen examples of solutions of Fourier series.
And even the disclosure of uncertainties within the limits by decomposition in a row. The archive contains 13 Kuznetsov typics and a pair of Ryabushko variants. Bon Appetit!

Ready solutions of differential equations

Good Sophhelen Diffures. The tasks applied various methods for solving differential equations of the first order, including those that I have not considered in the lessons. There are diffuses of increased complexity - a second order and higher order, examples using the method of variation of arbitrary constants. Differential equations are attached. The archive contains 8 typical calculations of Kuznetsov and 2 variants of Ryabushko. In addition, I spare a collection of exam tickets, in them, in addition to differential equations, there are tasks for rows and multiple integrals.

Examples of solutions of multiple and curvilinear integrals

Double integral, changing the order bypass bypass, calculating the area with a double integral. Triple integral, calculation of body volume with a triple integral. Examples of solutions not only in Cartesian, but also in polar, cylindrical coordinate systems. Basic applications of multiple integrals: finding the center of gravity of a flat plate, center of body mass and other tasks. Curvilinear integrals on the curve, along the contour. The campaign to find the work of force along the contour and using the Green formula.

Do you believe that it is difficult?!

Examples of solving problems on field theory

Among other things, the collection includes the most popular tasks with the solutions of the following types: finding the derivative in the direction and gradient, calculating the flow of the vector field through part of the plane, calculating the flow of the vector field through the closed surface according to the Ostrogradsky-Gauss formula, calculate the circulation of the vector field along the contour. The archive has several calculations from the Column of Kuznetsov.

Examples of solutions of tasks on combinatorics and probability theory

In the following PDFs, you can familiarize yourself with additional tasks to the lessons combinatorics and probability theories. At the same time, I did not have a goal to collect hundreds of examples, on the contrary - I tried to filter out obvious duplicates. In addition, most of the tasks files are ordered in order of increasing complexity:

Objectives with economic content

Many know how difficult it is to "rock" after the long winter holidays, and once after the holidays, I found a great way to return to the working rhythm - to create collections of finished tasks with a pronounced economic content, which are mothballed in my collection and which do not benefit anyone. These are some tasks of economic and mathematical modeling, these are the tasks of financial mathematics (interest, rent, etc.)And finally, these are tasks relating to the economy. So let's replant the gloomy January weather with the following useful materials:

Tasks of financial mathematics

In fact, it is actually said too loudly - in the next file, you will find pressing and practically useful tasks of interest and the calculation of payments on deposits / loans.
I rested a few solutions found and made them as clear as possible! Moreover, in the course of the case, and something itself was shaked \u003d)

And, of course, the calculator to the tasks! Yes, at least in order to instantly find the interest of interest from any number:

The task of intersectoral balance (model Leontiev)

One of the most famous economic and mathematical models describing many sectors of the economy, some of the products of which are mutually spent as a result of production, and the other part is the final product. There were difficulties with matrices of direct / complete costs, painstakingly find the return matrix and matrix multiplication with fractional numbers? The following program will instantly hold the calculations that simply roll on to perform on the usual microcalculator:

This program is created in MS Excel and is available to active library users.. Or for moderate points.

Demo version You can see. Calculations were carried out for the most common educational case - three industries; Moreover, the solution can be printed and pass!

And that is especially nice, before you an example of practical use algebra Matrix..

Typical objectives for economic indices

The next modest PDF, of course, does not cover all the variety of economic indices, but I disassembled thoroughly and systematized, perhaps, all the varieties of the most popular task on price indices / physical sales / trade + similar task on cost indexes and total costs. Even the child will figure out:

... and if it also takes this program, I will never allow mistakes!

Objectives of economic statistics

As in the previous file, all the highest mathematics here is limited to the simplest arithmetic actions \u003d) ... and it would be funny if it were so sad (the economy is not my profile subject, but, nevertheless, your submissive servant had to extract Several dozen tasks on the socio-economic and production statistics, which were "an imminible" to test work on mathematical statistics. In this regard, I do not guarantee the supercope, although, on the other hand, there is no hauting too:

And finally, the joy of students-glasses open two more distributions:

Typical calculations on the theory of probabilities from the collection of Wonderland for free!

The first 22 tasks are solved, where a little more, where less. The first option for the demonstration is located directly on the site: other options (2, 5, 7, 8, 9, 10, 11, 12, 15, 20, 21, 24, 11, 12, 12, 20, 21, 24, 25) due to their light weight I moved from the file to the newly created library Site. Also, the archive can be useful in that in the collections of wonderful difficult tasks on probability theory, and perhaps you will find what they were looking for.

Ids from the task of Ryabushko - free !!

Solid appendage to all archives + tasks that have not yet been offered on this page, in particular, examples with functions of several variables. Closed, of course, not all 4 volumes, but for some sections a good half of the options will be thrown, or even more! The proceeded individual tasks can be used both "directly intended" and as an additional self-preparation / training. Long-awaited reshebnik Task Ryabushko Held a separate web page.

And a number of works of various universities of the country:

4) tests MEI. (Moscow Economic Institute).

At the moment, while everything, look from time to time - I will come up with something else!

Secondary education

Line Ukk G. K. Moravina. Algebra and the beginning of mathematical analysis (10-11) (coal.)

Merzlyak Line. Algebra and start analysis (10-11) (y)

Mathematics

Preparation for the exam in mathematics (profile level): tasks, solutions and explanations

The examination work of the profile level lasts 3 hours 55 minutes (235 minutes).

Minimum threshold - 27 points.

The examination work consists of two parts that 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 brief response in the form of an integer or final decimal fraction;
• part 2 contains 4 tasks (tasks 9-12) with a brief response as an integer or final decimal fraction and 7 tasks (Tasks 13-19) with a detailed answer (full record of the solution with the justification of the actions performed).

Panova Svetlana Anatolyevna, teacher of mathematics of the highest category of school, work experience 20 years:

"In order to get a school certificate, a graduate must pass two mandatory exam in the form of the exam, one of which mathematics. In accordance with the concept of the development of mathematical education in the Russian Federation, the EGE in mathematics is divided into two levels: basic and profile. Today we will look at the options for the profile level. "

Task number 1. - checks from the participants of the exam skills to apply the skills obtained in the course of 5 - 9 classes on elementary mathematics in practical activity. The participant must own computing skills, be able to work with rational numbers, be able to round down decimal fractions, be able to translate some units of measurement to others.

Example 1. In the apartment where Peter lives, installed the consumption of consumption of cold water (counter). On May 1, the counter showed the flow rate of 172 cubic meters. m of water, and on the first of June - 177 cubic meters. What the amount should pay Peter for cold water for May if the price is 1 cube. C cold water is 34 rubles 17 kopecks? Give the answer in rubles.

Decision:

1) We find the amount of water spent per month:

177 - 172 \u003d 5 (cubic meters)

2) We will find how much money will be paid for the spent water:

34.17 · 5 \u003d 170.85 (rub)

Answer: 170,85.

Task number 2.- There is one of the simplest tasks of the exam. It successfully copes the majority of graduates, which indicates the ownership of the concept of function. Type of task number 2 by request codifier is a task to use acquired knowledge and skills in practical activity and everyday life. Task number 2 consists of a description using the functions of various actual dependencies between the values \u200b\u200band the interpretation of their graphs. Task number 2 checks the ability to extract information presented in tables in charts, charts. Graduates need to be able to determine the value of the function by the value of the argument at various methods of setting the function and describe the behavior and properties of the function according to its graphics. It is also necessary to be able to find the most or smallest value on the schedule and build graphs of learned functions. Allowed errors are random in reading the terms of the task, reading the chart.

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Example 2. The figure shows a change in the stock exchange value of one promotion of the mining company in the first half of April 2017. On April 7, a businessman acquired 1000 shares of this company. On April 10, he sold three quarters of purchased shares, and on April 13 sold all the remaining. How many businessman lost as a result of these operations?

Decision:

2) 1000 · 3/4 \u003d 750 (shares) - are 3/4 of all purchased shares.

6) 247500 + 77500 \u003d 325000 (rub) - the businessman received after the sale of 1000 shares.

7) 340000 - 325000 \u003d 15000 (rub) - Lost businessman as a result of all operations.

In this section, we are preparing for the exam in mathematics as a basic, profile level - we have preparing tasks, tests, exam description and useful recommendations. Using our resource, you will understand the minimum in solving problems and will be able to successfully pass the exam in mathematics in 2019. Begin!

The exam in mathematics is the mandatory exam for any student in grade 11, so the information presented in this section is relevant for all. The exam in mathematics is divided into two types - the basic and profile. In this section, I analyze each type of tasks with a detailed explanation for two options. The tasks of the ege are strictly thematic, so for each number you can give accurate recommendations and bring the theory necessary to solve this type of task. Below you will find links to tasks by clicking on which you can learn the theory and disassemble examples. Examples are constantly updated and updated.

The structure of the basic level of the exam in mathematics

Examination on mathematics of the baseline consists of one piece including 20 tasks with a brief answer. All tasks are aimed at checking the development of basic skills and practical skills to apply mathematical knowledge in everyday situations.

The answer to each of the tasks 1-20 is integer, finite decimal fraction , or sequence of numbers .

The task with a short response is considered to be executed if the correct answer is recorded in the answer form No. 1 in the form provided by the instructions for performing the task.