Passed the Unified State Exam 2017. Our graduates have entered universities, and for today’s tenth-graders, next year will be a year of preparation for graduating from school and passing final exams. Therefore, many of them have already begun to prepare for the 2018 unified exam. The proposed analysis of Unified State Examination tasks in mathematics (profile level) will help to systematize information, remember and consolidate acquired knowledge at school.
Let me remind you that for several years now the mathematics exam has been divided into basic and specialized levels. Will there be changes next year? There will be, but they will not concern mathematics. There will be changes in the number of mandatory exams for graduates, but in any case, mathematics and the Russian language will remain mandatory. There are no plans for any changes in the content of the mathematics exam itself.
We will analyze the Unified State Exam tasks that are offered during the exam by the developers of the Unified State Exam in mathematics for the profile level I.V. Yashchenko, P.V. Semenov and others. Many tasks are published on the “Solve the Unified State Exam” website and on the FIPI website.
I would like to note that in order to better understand the material, I recommend that you complete the homework that will be attached to this article. This will be a small set of problems with answers for independent solution and self-test.
So, let's begin. Task No. 1 in mathematics requires the ability to solve simple text problems, which are divided into:
- calculation problems;
- problems involving rounding with excess;
- rounding problems;
Let's start with calculation problems. The proposed calculation problems are conventionally divided into several types, so our lessons with you will be divided into parts.
- Computing problems. Part 1
- Computing problems. Part 3
Computing problems. Part 1
Problem 1 . A kilogram of carrots costs 40 rubles. Oleg bought 2 kilograms of carrots. How many rubles in change should he receive from 100 rubles?
The simplest task in life. Always introduce yourself. You are buying carrots. You have 100 rubles and you bought 2 kg of carrots.
Since a kilogram of carrots costs 40 rubles, then for 2 kg you have to pay 80 rubles. That is . This means that Oleg will receive rubles in change.
Answer: 20 rubles.
Problem 2. In summer, a kilogram of strawberries costs 80 rubles. Mom bought 1 kg 200 g of strawberries. How many rubles will she receive in change from 500 rubles?
Similar task. The only difference is that you need to convert grams to kilograms.
Let me remind you that 1 kg = 1000 g. Then 1 kg 200 g = 1.2 kg. How can this be done differently? You can first convert 1 kg 200 g into grams, i.e. 1 kg 200 g = 1200 g, after that 1200: 1000 = 1.2 (kg).
Now we have 1.2 kg, and 1 kg costs 80 rubles, which means we need to multiply. That is, mom will pay 96 rubles for her purchase. And change from 500 rubles will be 500 – 96 = 404 (rubles).
Task 3. In the apartment where Alexey lives, a cold water flow meter (meter) is installed. On September 1, the meter showed a consumption of 103 cubic meters. m of water, and on October 1 - 114 cubic meters. m. What amount should Alexey pay for cold water in September, if the price is 1 cubic meter? m of cold water is 19 rubles. 20 kopecks? Give your answer in rubles.
To solve this problem, you need to remember that the months September and October follow each other (for those who don’t remember, look at the calendar).
Further, do not be afraid of the words “cub.m.” It's just a unit of measurement. Recording “cub.m.” and “m 3” are the same thing. In this problem, there is no need to convert cubic meters to any other unit of measurement. The only thing is that when performing actions, we remember that we perform actions with the same values: rubles with rubles, cubic meters with cubic meters.
This means that for the full month of September, 114 – 103 = 11 (cubic meters) of cold water was spent. There is also no need to focus on “cold water”; this is not important for the task.
2) It is known that 1 cubic m. costs 19 rubles 20 kopecks. Here we need to convert kopecks into rubles, since in the answer we are asked about rubles.
1 ruble – 100 kopecks
x rubles – 20 kopecks
You can use your knowledge of proportion (in the correct proportion, the product of the extreme terms is equal to the product of the middle terms). We also remember that in proportion we sign units of the same name below each other.
We find x from the equation: , x=0.2.
This means 20 kopecks = 0.2 rubles. But we still have 19 rubles. Then 19 rubles 20 kopecks = 19 + 0.2 = 19.2 (rubles).
3) Then 11 cubic meters (from point 2) will be paid
1 cubic meter – 19.2 rubles
11 cubic meters – x rub
Find x from the proportion, x = 211.2 (rub)
Comment. Although you can do it differently (just a little longer). You can first convert rubles into kopecks.
1 rub = 100 kopecks. So 19 rubles = (kopecks). Then 19 rubles 20 kopecks = 1900 + 20 = 1920 (kopecks).
1 cubic meter – 1920 kopecks
11 cu. m. – x kop.
X = 21,120 (kopecks)
But you can’t stop there, since the answer requires you to indicate rubles. You need 21,120: 100 =211.2 (rub)
Answer: 211.2
Let's summarize the analysis of task 1 (part 1)
So, we have analyzed some Unified State Examination tasks in mathematics (profile level), which are found in task No. 1, and now you can solve the simplest calculation problems. You probably noticed yourself that there is nothing complicated. And to consolidate your knowledge, I recommend that you definitely complete the tasks to solve on your own. You cannot use a calculator. Practice performing actions in a column. It is important.
If you have any questions, write them in the comments. I will definitely answer and help you figure it out. The main thing is not to lose heart and not to panic.
P.S. You will find tasks for independent solution and answers to them on my Telegram channel @egematem(via search) or by link
There are 25 tasks in the Unified State Examination in History. They are divided into two parts - 1 part of tasks with a short answer (1-19) and 2 part of tasks with a detailed answer (20-25). The answer to the first part of the task is a group of numbers, a word or a phrase. The answer to the tasks of the second part is the text (or several sentences) written by you. Remember that an appeal can only be filed against points awarded for tasks in the second part because The first part is checked by the computer.
We would like to draw your attention to the fact that at the Hodograph training center you can sign up for. We offer individual and group lessons for 3-4 people and provide discounts on training. Our students score on average 30 points more!
Historical periods in the Unified State Exam 2018
Tasks in the Unified State Examination in history 2018 are divided depending on the competence being tested, as well as the historical period. The last three stand out:
- Antiquity and the Middle Ages (from the 7th to the end of the 17th century)
- New history (from the end of the 17th to the beginning of the 20th century)
- Recent history (from the beginning of the twentieth to the beginning of the twenty-first century) - about 40% of the tasks belong to this section.
Tasks 1-6 of the Unified State Examination in History 2018
Now let's take a closer look at the tasks of the first part.
Task No. 1 in the Unified State Examination in History 2018- This is a task to establish the correct chronological order of events. The answer to task 1 is a sequence of three numbers, where the first is the earliest, from your point of view, event, and the third is the latest. Please note that in Task 1 one of the events presented Always relates to the course of world history, so be sure to download a table of the dates of world history found in the Unified State Exam and try to learn them. Task No. 1 is worth 1 point.
Task No. 2 in the Unified State Examination in history 2018- This is a task to establish correspondence between events and dates. The left column shows four events in Russian history, the right column shows six dates, two of which are redundant. The answer to task 2 will be a sequence of four numbers. Correctly completed task No. 2 is scored 2 points. Moreover, if you make one mistake, you can get 1 point. Since task No. 2 tests your knowledge of the main dates of Russian history, try to find or download such a list and gradually learn it.
Task No. 3 in the Unified State Examination in History 2018– a task on knowledge of historical concepts and terms. The task presents six terms, four of which relate to one historical period, and two to others. You need to find terms that fall out of the general list and write down the answer in the form of two numbers. Task No. 3 is worth 2 points. A task completed with one error is scored 1 point.
Task No. 4 in the Unified State Examination in History 2018- this task is also about knowledge of historical terms, but unlike the third, it requires an answer in the form of a word or phrase. Task No. 4 is worth 1 point.
Task No. 5 in the Unified State Examination in History 2018– a task to establish correspondence, as a rule, between processes, phenomena or events and the facts associated with them. The task contains four processes and six facts, two of which are redundant. The answer to task No. 5 is a sequence of four numbers. A task completed correctly is scored 2 points, with one error – 1 point.
Task No. 6 in the Unified State Examination in History 2018– this is also a task to establish correspondence, but here the work will be carried out with the historical text. You will be offered two fragments of texts and six characteristics for them. For each of the fragments you need to select two correct characteristics (two of the six characteristics, just like in tasks 2 and 5, are extra). The answer to task No. 5 is a sequence of four numbers, if all are correct – 2 points. A task completed with one error is scored 1 point.
Tasks 7-12 of the Unified State Examination in History 2018
Task No. 7 in the Unified State Examination in History 2018– a multiple choice task in which you need to choose three (out of six proposed) correct characteristics of a period, phenomenon, politics, war, etc. The answer is a sequence of three numbers and this task is worth 2 points.
Task No. 8 in the Unified State Examination in History 2018 entirely dedicated to the Great Patriotic War of 1941-1945. This task, as a rule, tests knowledge of dates (with an accuracy of up to a month), geographical objects, special terms (names of operations, conferences), as well as personalities (war heroes, front commanders, etc.). The correct answer is worth 2 points. A task completed with one error is scored 1 point.
Task No. 9 in the Unified State Examination in History 2018 its structure resembles tasks 2 and 5. Only here knowledge of historical figures is tested. The scoring system is the same as in tasks 2 and 5.
Task No. 10 in the Unified State Examination in History 2018– this is a task to analyze a text source dedicated to the events of the early 20th – early 21st centuries. The answer to task 10 is the name of the figure, the name of the policy, period, historical term, etc. Evaluated as 1 point.
Task No. 11 in the Unified State Examination in History 2018 is a table in which you need to enter the missing elements from the list below. As a rule, you need to correlate the date (century, period) with the events of Russian history and world history. Correctly completed task 11 is scored 3 points, with one error - 2 points, with two - 1 point.
Task No. 12 in the Unified State Examination in History 2018 also contains a fragment of historical text, which contains six statements, three of which are true. To solve task 12, carefully read the text several times, because sometimes it directly contains hints. A task completed correctly is scored 2 points, with one error - 1 point.
Tasks for working with historical maps and images in the Unified State Exam
Tasks 13, 14 and 15 in the Unified State Examination in History 2018 are performed using a historical map or diagram. During the preparation process, try to pay special attention to working with the map; to do this, download atlases on the history of Russia from the Internet or a selection of maps and diagrams specifically for the Unified State Exam in history. These tasks, as a rule, ask for the name of the figure associated with events on the map, a geographical name (city, fortress, river, etc.) and, sometimes, a time period. Tasks 13-15 are each worth 1 point.
Task No. 16 in the Unified State Examination in History 2018 is also associated with a historical map and involves choosing from a list of judgments related to the events to which the map is dedicated. As in other multiple choice tasks, you need to write down the answer in the form of three consecutive numbers. A task completed correctly - 2 points, with one error - 1 point.
Task No. 17 in the Unified State Examination in History 2018 tests knowledge of Russian culture. Here you need to correlate the cultural monument with its author/characteristics/time of origin, etc. To successfully complete this task, you need to master a huge layer of information about the culture of Russia; to do this, download or buy special textbooks on culture for the Unified State Exam. This will help you not to get confused in the variety of cultural monuments. A task completed correctly - 2 points, with one error - 1 point.
Tasks No. 18-19 in the Unified State Examination in History 2018– working with a picture, stamp, photograph or other image. Often tasks 18 and 19 are related to Russian culture. To successfully complete them, carefully examine each image, paying special attention to the inscriptions on the pictures, if any. Often they can answer the question asked. Each task is worth 1 point.
Tasks with detailed answers in the Unified State Exam 2018
Part 2, tasks 20-25
Now let's move on to the tasks of part 2 i.e. parts with a detailed answer. Here are some useful tips that we hope will help you score maximum points for these tasks.
Tasks No. 20, 21, 22 in the Unified State Examination in history 2018(maximum 2 points each) are related to the historical text given at the beginning of Part 2. Don’t be lazy to read the text several times (preferably 3 times). The first time - you form a general impression of the text, try to determine the time when it was written. Then look at 20-22 tasks. The second time - you read, paying special attention (or even highlighting with a pen) historical terms, first and last names of figures, as well as any other elements that seemed important to you in the context of the questions asked. Then, on the third reading, you highlight phrases or phrases that you will then use when answering 21 tasks (it is almost always in the text).
In tasks No. 23 and 24 in the Unified State Examination in History 2018(maximum 3 and 4 points, respectively) write as detailed as possible. Don't be shy about your knowledge! In this case, you should avoid common phrases. Construct each position according to the scheme argument/position + fact confirming this argument.
The Unified State Examination in Russian consists of two parts and 25 tasks.
First part represents 24 tasks. They can be test-type, with a choice of one or more answers, open-ended (fill in the blank yourself).
The answer to the tasks of Part 1 is given by the corresponding entry in the form of a number (number) or a word (several words), a sequence of numbers (numbers) written without spaces, commas and other additional characters.
Part 1 tasks test graduates’ mastery of educational material at both basic and high levels of complexity (tasks 7, 23–24).
Second part - consists of one task - 25. This task involves writing an essay based on the read and analyzed text.
Part 2 task (task 25 - essay) can be completed by the examinee at any level of difficulty (basic, advanced, high).
The work is given 210 minutes - 3.5 hours.
Distribution of tasks by parts of the examination paper
| Parts of the work | Number of tasks | Maximum primary score | Type of tasks |
| 1 part | 24 | 33 | Short answer |
| part 2 | 1 | 24 | Detailed response |
| Total | 25 | 57 |
Unpointing for tasks
Below I will give the “cost” of each task performed.
For the correct completion of each task first part (except for tasks 1, 7, 15 and 24) the examinee receives 1 point. For an incorrect answer or lack thereof, 0 points are given.
For completing tasks 1 and 15, you can score from 0 to 2 points.
The answer that contains all the numbers from the standard and no other numbers is considered correct.
For completing task 7, you can score from 0 to 5 points.
For each correctly indicated digit corresponding to a number from the list, the examinee receives 1 point (5 points: no errors; 4 points: one error was made; 3 points: two errors were made; 2 points: two digits were indicated correctly; 1 point: correctly indicated only one digit; 0 points: completely incorrect answer, i.e. incorrect sequence of numbers or lack thereof.
For completing task 24, you can score from 0 to 4 points. The answer that contains all the numbers from the standard and no other numbers is considered correct.
The maximum number of points that an examinee can receive if he or she completes the task correctly second part , is 24 points.
For correct completion of all tasks of the examination paper, you can receive the maximum 57 primary points .
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. The Unified State Exam tasks are 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.
Lesson developments (lesson notes)
Secondary general education
Attention! The site administration is not responsible for the content of methodological developments, as well as for the compliance of the development with the Federal State Educational Standard.
Learning to perform the “Listening” section
This task is aimed at understanding the main information in the text and tests the following skills: highlighting the main information, consolidating basic information in memory, ignoring unfamiliar words, correlating a detailed text and its main idea. Before listening, we highlight the key words in each of the statements and find differences in statements that are similar in topic. The general theme is “Sports”. Having highlighted the key words, we divide the statements into two groups. The first group consists of statements from people who do not play sports or have a negative attitude towards it. The second group expresses a positive attitude. During the first listening, we pay attention to the key words that come at the beginning or end of the text. We listen a second time and compare. After listening, we check ourselves again and write down the answers on the form.
Before the first listening, you need to review the task, but do not try to correlate, since you can choose correctly only after listening to the text. The proposed statements, as a rule, go in the same sequence as in the audio text, so when listening it is easier for you to complete the task. During the second listening, check your answers and fill in any missing ones. You need to make sure that if you chose the answer “the text does not say,” then this information really is not in the text. Make sure that when choosing the answer “True”, “False”, you rely on the text you listened to, and not on your guesses.
We study the statements and try to understand what information we need to solve the problem. We listen to the interview in its entirety to become familiar with its general content, and make notes about what we hear. Let's listen a second time. We check whether there is a violation of logic in the selected answers, whether they contradict each other. After this, we transfer the answers to the form.
Learning to complete the “Reading” section
The task of matching the text and headings is aimed at understanding the main content. First read all the headings, guess what content of the text should correspond to each of them. Read parts of the text carefully, choosing a title for it.
The highlighted keywords show that the headings can be divided into three groups. In the first group, the information is neutral. The second group includes positive information about sleep. The third is negative. As a rule, the main idea of the text is reflected in key phrases that appear at the beginning or end of the text.
In the next task you need to fill in the blanks with the given fragments. The task is aimed at understanding the structural and semantic connections of the text, since the fragments must correspond both in structure and in meaning. Analyze what part of the sentence each fragment is, think about what precedes it and what comes after it. Pay attention to the words before and after the gap. When substituting, check whether this fragment fits into the sentence as a whole.
You need to make sure that all the fragments you insert are logically connected grammatically and in meaning, and that the extra fragment does not fit into any of the gaps.
In the next task, based on the text you read, you must choose one of four answer options. Here a complete and detailed understanding of the text is tested. You need to familiarize yourself with the general content of the text, then move on to the answer options. After reading each question, you need to make sure whether the required answer is in the text. When referring to the text to check your answer, read only the portion that is necessary for you to understand.
Completing the “Grammar and Vocabulary” sections
Look through the entire text, get the general content. Determine what time the story is told. The structure of the sentence immediately shows which part of the sentence and in what grammatical form is needed to fill in the gap. When checking this task, you need to check whether the form is formed from the reference word given on the right and whether the formed form plays the necessary role in the sentence, the spelling correctness of the word.
The next task checks whether you can use words in a coherent text, taking into account their meaning, compatibility, and grammatical design. To complete this task, you need to look at the entire text as a whole, grasp its general content, plot, logic, and sequence of events. Carefully read the first fragment of text with the first test pass. Think for yourself which word might be in the blank, then check the word options that are given. The correct answer will be easier to find by discarding the wrong answers. When filling in the blank, you need to enter only the missing LE, and not the one that repeats the meaning of the sentence. After filling in the blank, read the text again.
Completing the “Writing” section
When completing this section, the required volume must be observed. You need to logically organize the text, dividing it into paragraphs. It is necessary that the text contains important information, your thoughts and feelings, opinions. Using evaluative vocabulary and a variety of grammatical structures will improve your work. On the draft, you can sketch out an outline of your statement or key words.
Writing a letter involves analyzing and planning a response to the letter, making a list of words and expressions, writing the letter and revising it. Questions must be relevant to the topic specified in the assignment.
The second task in the section is aimed at expressing your opinion on a problem with elements of reasoning. The introduction should begin with a general introduction to the topic. Each paragraph should contain a complete thought. It is necessary to use linking words and conjunctions.
In the introduction, paraphrase the problem, express your opinion, present an alternative opinion. In conclusion, draw a conclusion. Divide text into paragraphs using logical connections. Correctly use lexical, grammatical, spelling, punctuation and stylistic means.
Performing the “Speaking” section
Let's look at what pauses are included in the text by punctuation. Pauses can be noted. We read the text in a whisper, then out loud, paying attention to the unity and fluency of speech.
In this task, you need to request information by asking five direct questions, based on the proposed points of the plan.
The purpose of the task is to describe one of the three photographs, based on the plan given in the task. You need to tell when and where the photo was taken, what it depicts, what is happening, why you keep this photo in the album. When choosing a photo, analyze whether you have enough vocabulary to describe the photo you like.
The task is aimed at comparing two photographs, identifying common and different features.
When preparing, think over key phrases that correspond to the points of the plan, construct a statement in accordance with this plan. Briefly describe the pictures, highlighting similarities and differences. Give a detailed argument in the last paragraph. Avoid redundant information that is not included in the plan.