What to do if the USE result is actually incorrect? Typical mistakes of students on the Unified State Examination in the Russian language Error in the Unified State Examination results
The better a student knows a subject, the more difficult it is for him to get 100 points on the exam
On May 27, the Unified State Exam (USE) will begin with the Russian language test in Russian schools. High scores obtained on tests give the graduate a chance to enter a university. But, as practicing teachers say, analyzing collections on preparation for the Unified State Exam, it is very difficult for a student who really knows the subject to earn the highest grade. The problems contain many inaccurate formulations and even errors, which can only be “overcome” by mechanically memorizing the answer, which is stored in the checking computer as supposedly the only correct one!
Employees of the Institute named after. Goethe (Germany) was randomly checked Unified State Exam assignments for Russian schoolchildren German language, identifying syntactic, lexical, grammatical errors and non-existent expressions. Representatives of Rosobrnadzor, who supervise the state exam, responded that the tests are compiled by competent specialists from Federal Institute pedagogical measurements (FIPI), and they are checked by the Unified State Examination Commission under the Ministry of Education. So the comments of “native speakers” are subjective.
This case is not the only one. Errors in state exam materials can be found by yourself. school teachers. This is an incorrect formulation of the tasks, and incorrect conditions, and sometimes there may be several correct answers - just guess which one was noted as the only one by the test compilers.
The Deputy Chairman of the State Duma Committee on Education speaks about this Oleg Smolin:
I was shown a test in the Russian language, where it was reported that ancient people sailed on “ships”, and not on “vessels”.
Disadvantages test tasks Unified State Examination in biology leads to an unfair assessment of students’ knowledge, says associate professor Boris Sadykov . - For this reason, it is actually impossible to write test tasks worth 100 points. Unless you know the ready-made answers, known only to the compilers. There are errors related to distortion of terms: separate layer of plant leaves instead separative, sympathetic nervous system, which, as follows from the answers, somatic, etc.
Or here's an example when it is impossible to choose one answer:
Which of the following phenomena does not characterize a biological process:
1) ecological diversity; 2) caring for offspring; 3) wide distribution area; 4) high number of individuals in the population.
All these answers are correct and precisely characterize the “biological process”! It’s another matter if the authors meant the term “progress” - then, indeed, answer No. 2.
Sometimes it's just the answer is incorrect:The production of hybrids based on the combination of cells from different organisms is carried out... “Microbiology” was chosen instead of “Cell Engineering”;
Competition is the relationship between... The compilers called "predator and prey", although there must be "species with similar needs";
Substances that perform a construction function. The answer is “ nucleic acids and water”, in fact “lipids, polysaccharides and proteins”.
Example assignment In Russian:
What word consists of a prefix, a root, one suffix and an ending?
 |
Or a literature question:
Rodion Raskolnikov is a) small man, b) an extra person, c) a special person, d) a new person?
There are several options.
I’ve been collecting Unified State Exam tests with errors since 2002,” says the chemistry teacher. Galina Alexandrova. - Many tasks have no solution at all due to the fact that the compilers know the subject “on paper”. This is far from harmless. Faced with this, strong students experience great difficulties and pass the exam worse than “average” students. As a result, a talented student, having missed 5 - 7 points due to an incorrect question, will not enter a prestigious university, and his place will be taken by someone who did not study chemistry, but trained himself to take tests, memorizing the answers given by the authors.
For example, this task from the Unified State Exam tests in chemistry:
Place 46 g of sodium in 156 g of water and determine the mass fraction of sodium hydroxide in the resulting solution.
In fact, there will be an explosion of such force that there will be neither solution nor mass fraction, nor the one who should count it. Another example:
In one stage, butane can be obtained from:
1) butanol-1
2) butanoic acid
3) butene-1
4) butanol-2
There is not one correct answer here (No. 3), as the authors claim, but three! Butane can be obtained in one stage from alcohols: butanol-1, butanol-2, reducing them with hydrogen iodide. This reaction went down in the history of chemistry.
And here is from the new collection for 2013:
Option 6, task A 4: As a substance with a covalent non-polar bond ozone is given. But the ozone molecule is polar. Its dipole moment is 0.53 D.
And there are a lot of such mistakes. I feel very sorry for the capable guys who love science and are interested in the experimental part. It will be the most difficult for them to choose the correct answer in Unified State Exam tests.
Slide 1. Typical mistakes of students on the Unified State Exam in Russian
Slide 2. I. What is your GOAL?
Do you want to enroll in a university based on the results of the Unified State Exam, and in a budget department? In most universities, the “budget” competition starts at a level above 80 test scores. Without preparation, it is almost impossible to achieve such results on the Unified State Exam in the Russian language.
Slide 3. THINK, this truth is as old as time: NO ONE can EVER teach you ANYTHING against your will!
Slide 4. If you have a strong desire and motivation, then you can ALWAYS learn ANYTHING.
You will never learn to swim by standing on the shore! And you can’t escape the obvious fact: without training in taking tests in preparation for the Unified State Exam in the Russian language, you can only dream of an excellent result. Until I'm blue in the face.
Slide 5. II. Typical mistakes when filling out answer forms for the Unified State Exam
Slides 6-10. Processing of Unified State Exam answer forms is carried out on computers. The forms are scanned, the inscriptions and marks on them are recognized, converted into a “digital” format and automatically checked. This technology allows you to process a huge number of forms in a limited time, but requires test participants to follow some simple rules. We will illustrate all errors with real images from the answer forms, which clearly show what is written on the answer form and what is recognized by the computer. Some people don't believe this happens. So let's begin:
| Description of the error | Slide number with an image illustrating the error | What should you do to avoid this error? |
| 1. The form is filled out with a blue pen or pencil. Nothing is visible in the image that got into the computer. | 1 | Unified State Exam forms must be filled out with a BLACK GEL PEN. The pen should leave a clear (not greasy) mark without glare. Bring 2 good black gel pens to the exam. |
| 2. The form is not filled in according to the pattern of writing characters. | 2 | At the top of the answer form it is indicated how letters, numbers and other valid characters must be written so that they are successfully recognized. |
| 3. People have problems with the alphabet. | 3 | If you don't know how to write some letters, look at the top of your answer sheet. |
| There you will find all the letters of the Russian alphabet and numbers. An amazing situation, but it happens often. | 4 | 4. Unsuccessful attempt to undo the wrong label. As an answer to task A6, the computer will simultaneously receive answer options 1 and 2 |
| Any mark (a cross, a line, even a dot) in the boxes for answers to part A is recognized as an answer, so painting over it will not cancel the incorrectly chosen answer option. To replace an erroneous answer in part A, there is a special area in the form. The number of the test task is written in the field of two windows, and next to it (in the squares) you should indicate the correct (corrected) answer to the task. | 5. Spelling errors in answers. |
Learn not only terms, but also their correct spelling. It’s a shame to write “DIMITRIYDONTSOY” instead of “DMITRYDONSKAYA”. It would be a shame to miss a point for an “almost correct answer.”
This concludes our story about the mistakes of test participants. The article discussed only typical mistakes that are repeated in every exam. There are also individual ones (they abbreviate words, confuse fields, cannot find the number and series in their document, write first and patronymic names with errors, etc.) that cannot be systematized. But most mistakes can be avoided if:
During testing, be attentive and collected, focus on completing the test.
It is recommended that before the real exam, you try to go through a similar testing procedure in the Unified State Exam mode in order to identify and evaluate the negative factors that you may encounter during one of the most important exams in your life.
Slide 11. Prepared by RCIO of the Ulyanovsk region. ege.karelia.ru Slide 12. Doing task (A1) on phonetics
, the graduate must show an understanding of the essence of Russian verbal stress and its features. As is known, Russian accent
not only unfixed, as, for example, in the Tatar or French languages, but also free - that is, capable of “dragging” from one syllable to another in different forms of one word or in words of the same root (cf. stol - but stolA, nachal - nachalA) .
Problems that use vocabulary with common spelling errors in youth speech (catalogue, beginning, calling, prettier, cakes) are solved worse.
Therefore, more attention should be paid to studying the basic norms of pronunciation and stress of modern Russian literary language. And the basis of this approach is constant attention to the sound of speech, systematic work with spelling dictionaries.
Slide 13. To cope with vocabulary tasks , you need to have a fairly large vocabulary of words, be able to use words correctly, taking into account their lexical meaning.
The greatest difficulties arose when determining the lexical meaning of a polysemantic word that has only one meaning in the context.
Errors related to use of paronyms, are found quite often in speech. Their reasons are explained by the polysemy of affixes in the Russian language and the different combinability of words. This is confirmed by the results of the examination test. So, for example, paronyms are very often mixed present and provide : Education will present enormous opportunities (instead of: provide).
They allow a lot grammatical errors consisting of incorrect formation and use of various grammatical forms of words, for example:
1) violations in the use of forms of nouns (incorrect formation of plural forms of nouns, for example, delicious cakes (from colloquial speech, norm: cakes; incorrect version of the gender form, for example: pies with jam (norm: ... with jam); new shoes (norm: shoe); incorrect formation of case forms: at the airport (norm : ...at the airport), with new shoes (norm: new shoes); a pair of boots (norm: a pair of boots);
2) errors in the formation of degrees of comparison: louder (norm: louder); younger (the comparative form of this adjective is redundant);
3) incorrect formation of pronominal forms: around them (norm: around them); their books (norm: their books);
4) errors in the declension of numerals: in two thousand and one (norm: in two thousand and one); less than seventy-five rubles (norm: less than seventy-five rubles);
5) incorrect formation of verb forms (errors in the formation of personal forms of verbs: run a hundred meters (norm: runs); burns a fire (norm: kindles); incorrect formation of aspectual forms of verbs: let's try (norm: let's try); incorrect formation of reflexive forms of the verb : dress warmer (norm: dress warmer); errors in the formation of gerunds: after reading a story (norm: after reading a story);
6) Violation of the norms of unquestioned management:
Many were surprised by the simplicity and naturalness of Chekhov's plays. Correct: Many were surprised at the simplicity and naturalness of Chekhov's plays.
7) Homogeneous members sentences govern the various case forms of the noun: Grandmother loved and was proud of her only grandson. It is necessary to use various additions: Grandmother loved her only grandson and was proud of him.
8) Incorrect construction of sentences with participial phrases:
A) impersonal offer cannot have an adverbial turn: Having opened the magazine, there was a lot of new information in it. Correct: When I opened the magazine and began to read it, it contained a lot of new information.
b) different characters perform a main action, expressed by a predicate, and an additional action, expressed by a gerund: Having opened the latest newspaper, my attention was drawn to one interview. That's right: when I opened the latest newspaper, one interview caught my attention.
9) It is unacceptable to combine simple and compound forms of comparative and superlative adjectives: more beautiful, worse. That's right: more beautiful, most beautiful, worst.
10) When specifying a date after an ordinal number, the noun is placed in the genitive case, and not in the dative case: the correct form is: by the first of January, by the eighth of March.
11) Collective numerals are not used with nouns denoting female persons, naming adult animals, having both number forms. Observing grammatical standards, you need to say: five students in the class, three beautiful houses.
12). In formal communication situations, the suffix -well- is lost in some forms of past tense verbs: correct form: dissolved, withered, wet.
Low Unified State Exam results morphemics and word formation can be explained by a formal approach to analyzing a word by composition, ignorance of the morphological features of some parts of speech and forms (participles, gerunds), identification of the concepts “zero ending” - “absence of ending”, “word-forming affixes” - “form-forming affixes”.
Word formation in Unified State Exam tests is a task of increased difficulty, the solution of which requires finding a word in the text formed in one way or another, or, conversely, determining and writing down the method of formation of the proposed word. Failure to complete this task is explained by ignorance of the essence of the basic methods of word formation in the Russian language, especially prefix-suffix and suffixless.
Slide 14. 1 task
insensitively
heard
lit
weak-willed
2. Determine the method of word formation: idleness, fun, pilgrimage.
case(s) -> without-del -[th]-( f) - prefix-suffix method;
cheerful -> fun -[th]-(f) - suffixal method;
god(s) pray->god- O-mol -[th]- e - addition of stems with suffixation.
3. In each row, find superfluous word. Explain your answer.
1) Collar, problem book, night light.
2) Undress, open, disassemble.
3) To be wise, to rage, to honor.
4) Parrot, be modest, be lazy.
1. In the word night light, suffixes are highlighted -n- And -hic-(night -> night-n-oh -> night-n-ik). In other words - suffix -Nick-.
2. The verb to dress up has two prefixes: once- And O-(cf. put on, undress). In other words - one derivative prefix times.
3. The suffix in the word honor is highlighted -Vova-(honor -> honor). In other words - suffix -stvova-.
The verb to be modest has a suffix -icha-(modest -> modest). In other words - suffix -nothing-. For example: lazy > lazy-nothing.
4. Write out from the sentence words formed in the prefix-suffix way.
At a quarter to nine he got out of the dungeon onto the square, at five minutes he crossed the alley and, going around the cars parked near the entrance, entered the door, next to which hung under the glass a black table “GINEGA” (Yu. Trifonov).
Answer: dungeon, alley
5. Write out from the sentence words formed in a suffixless way (using a zero suffix).
All varieties morphological method word formations are studied quite thoroughly in secondary school. Let's just focus on affixless (suffixless,) way . This is the formation of new words without adding a suffix: wide - breadth, deep - depth, water - watering, exit - exit.
Not all scientists recognize the existence of an affix-free method of word formation. Thus, Vladimir Vladimirovich Lopatin and Elena Andreevna Zemskaya believe that in words like expanse, distance, run, turn the zero derivational suffix should be highlighted. It was proposed to call this method of word formation zero suffixation .
It [the bridge] lies with its belly on the ground, at the entrance to the city - like a whale washed ashore, or like a sailboat run aground, puzzling visitors with its outright postmodern non-functionality. (D. Rubina).
Answer: entry, stranded
6. Write out a word from the sentence in which the morphemes are not arranged linearly, but overlap each other:
There was a clear pattern in her actions: as soon as he kicked the elastic and warm partition that separated him from chaos. and from there came an echo - a soft pressure, accompanied by thick cooing sounds, from which the whole world shook slightly. (V. Pelevin)
Answer: kick
7. Write out a word with a multiple word-formation structure from the sentence:
There was always some kind of discord between him and his mother. Tell me why you can never do anything for others? After all, this is ignoble, Leo! This is very low. (Yu. Trifonov)
Answer: ignoble
Difficult cases of morphological analysis
Different variants exam paper 2010 included tasks to identify various parts of speech and their categorical features (for example, various categories of pronouns - possessive, indefinite, attributive; adjectives in the superlative degree, as well as adjectives in the complex form of the superlative degree; conjunctions - coordinating and subordinating; derivative prepositions; particles).
The task requires writing down either parts of speech (for example, particles, conjunctions, prepositions), or individual forms or categories, superlative adjectives; derivative preposition; short passive participle; indefinite, possessive, attributive pronoun. Difficulties for examinees are usually caused by identifying pronouns of various categories, as well as auxiliary parts of speech: conjunctions, particles, prepositions. In general, the reasons for erroneous answers in the task AT 2 consist in superficial mastery of the theoretical part of the Russian language course; When performing morphological analysis, students are not always able to comprehensively take into account the various features that determine whether a word belongs to a particular part of speech: the meaning of the word as a part of speech, morphological features and the syntactic function of the word in a sentence.
Functional homonyms are etymologically related words that have the same sound, but belong to different parts of speech, differ in their general grammatical meaning, morphological and syntactic features.
Lexical homonyms belong to the same part of speech and have the same general grammatical meaning.
Any number is divisible by one. One student. Numeral
I'm going out one(lonely) I'm on the road. Adjective
Remained alone(only, only) memories. Particle
Father came, and with him more one(somebody). Indefinite pronoun
- I see only one way to solve this problem.
- I admit, I’m glad that you are of the same opinion as me (N. Gogol).
- I remember one incident that happened to me several years ago (M. Prishvin).
- Some forests stood like a wall around, and only the huge rain danced in the grass (I. Brodsky).
- Numeral
- Adjective
- Pronoun
- Particle
The word is used in all sentences one, which functions as different parts of speech.
In the first example one- numeral: denotes a specific quantity, which can be indicated by a number.
In the second sentence - an adjective: denotes a feature of an object, is a synonym for the adjective same.
In the third sentence one- pronoun: indicates an indefinite attribute of an object, synonymous with an indefinite pronoun some.
In the fourth sentence one- particle: serves as a means of logical highlighting of the word it precedes; synonymous replacement with particles is possible only.
Transition to status words:
- adverbs: Thickly and smelly the samovar smokes (I. Bunin) - > It was warm and familiar in the tavern, smelly and noisy (M. Gorky);
- short adjectives: His face was young and freshly - >On the street freshly;
- nouns: You need to choose the appropriate one time- > Time drive.
Slides 24-25.
Differences between homonymous parts of speech
Slide 26. Part “C” is a task with a detailed answer. Executed from the source text and checked by experts. When performing part “C” assignments on the Unified State Examination in Russian:
It is not necessary to create a literary masterpiece, nor is it necessary to conduct a detailed linguistic analysis of the source text;
75 words or less is ZERO points;
More than 250 words will ruin the expert’s mood, but he won’t be in debt.
The key to success when completing part “C” of the Unified State Examination in the Russian language is compliance with all formal criteria that guide experts when assigning grades.
Slide 27. Success awaits you at the Unified State Exam!
Literature
- Methods of preparation for the Unified State Exam in the Russian language: lesson planning, lesson organization, exercise system. M., Pedagogical University"First of September". 2009.
- Methodological letter on conducting the state final exam in the Russian language in 2010-2011 academic year. - MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION. federal Service for supervision in the field of education and science (Rosobrnadzor) .
Errors in Unified State Exam tests in biology
Posted on 18.09.2012 by Boris Sadykov
This article is addressed to those of you who are preparing for passing the Unified State Exam in biology, not content printed publications test items from previous years, or Open bank FIPI tasks on and, and checks the level of his preparation using electronic tests on various sites on the Internet.
So this is what I, a biology tutor, would like to warn you against.
Yes, it seems very convenient to be tested using such electronic tests. He pointed at the appropriate “circle” and quickly received information about his level of preparedness. Everything would be fine if these tasks themselves were compiled without errors. And the talk here is no longer about some incorrect, incorrectly composed tasks (which, unfortunately, is found both in the official publications of FIPI and in real tests of different years), but more about “mechanical” errors, not verified tasks by the compilers of these sites .
These electronic tests reach the point of absurdity. The test question is good. The answers themselves are chosen correctly. But when answering such a test, in the end, having answered it correctly, your result will be assessed as incorrect due to the dishonesty of the administrators of such sites. Often the same errors appear in the tests of these sites for quick self-testing of students' knowledge.
Why create new tests? It's easier to just copy them from another resource. And this is how a mistake made by someone once becomes replicated in many places on the Internet.
In this article I will give just a few examples of such “woe” tasks that I came across unchanged on different resources several times.
Semantic errors not related to typos in the text
The most common mistake of this kind is assignments on the theory of evolution. For example, in tasks B, when choosing three correct points out of six proposed, there is such a question.
Factors of evolution include1) crossing over; 2) mutation process; 3) modification variability; 4) isolation; 5) variety of species; 6) natural selection.
The correct answers, according to the compilers, are 2,4,6 . In fact, here we can only highlight two the answers are clearly incorrect - these are 3) modification variability (as a generally non-heritable form of variability) and 5) variety of species (which is a consequence of an active evolutionary process, and not one of the factors of evolution themselves).
Selecting an item as the correct answer 6) It is completely inconsistent with the general logic of choosing answers from the proposed ones. Since, most often the term « natural selection « in textbooks it is considered (and quite rightly, as was the case) not as one of the factors of evolution, but as a driving force of evolution or as a guiding factor of evolution (that is, it is worth above all factors of evolution).
Why do I write “does not agree with the general logic of choosing answers from the proposed ones”, since choosing the correct answer is an item 2) mutation process and at the same time do not consider the point true 1) crossing over(both of these phenomena are equally related to the elementary factors of evolution , being ), is not possible.
By the way, this obviously erroneously composed test “wanders” from the real Demonstration materials of the KIM Unified State Exam 2010.
It is absolutely no good when there are errors in tests regarding the basic principles of life - genetics, the knowledge of which is not easy for everyone. Such mistakes can completely throw some students off track. For example, in tasks A there is such a question.
The gene that causes diabetes is recessive to the gene for the normal condition. Healthy parents gave birth to a child with diabetes. What is the probability of having a healthy child in this family? 1) 15%;2) 25%; 3) 50%; 4) 75%.
Designating the allelic gene A-high normal insulin production (since according to the conditions of the task it is known that this is a dominant trait), a gene allelic to it A- low presence of diabetes (since this is a recessive trait), we have the genotype of a diabetic organism ahh.
How can two healthy parents give birth to a diabetic? Only if they are both heterozygotes, that is, in addition to the allele A- each of them definitely has a lot and A-small. So, we have the genotypes of the parents Ahh.
5. Which Mendelian law explains the divergence of chromosomes to the poles of the cell randomly in anaphase I of mitosis. But there is no anaphase I of mitosis. Meant in anaphase I of meiosis (this is Mendel’s third law of characteristics, which is based on random distribution homologous chromosomes in the dividing cell nucleus in anaphase I of meiosis).
Errors associated with an incorrectly named term in assignment answers
The bat's ability to catch insects using the ultrasound they produce is the result 1) driving actions their strength evolution; 2) manifestations of the laws of heredity; 3) manifestations of modification variability; 4) the action of anthropogenic factors.
The authors of the test have the correct answer 1) . But there is no such definition as driving no strength s evolution at all. There is one driving and I strength A- which is incorrect to call one of the factors of evolution (see above).
Errors related to incorrect response
Which of the paths of biological progress is associated with the emergence of the sexual process in evolution? 1) idioadaptation; 2) mutation; 3) degeneration; 4) aromorphosis.
It is clear that the emergence of the sexual process in the evolution of living systems on Earth is one of the largest 4) that occurred during the transition from a unicellular to a multicellular life form. And this very test, with the supposedly correct answer 3) degeneration, is “walking” on the pages of the Internet.
How many ATP molecules are formed in the third oxygen step of oxidative phosphorus n rationing Not only is there a typo in the question: “phosphorus” n ation" instead of "phosphorination l ation, the answer in the test is 34 ATP molecules instead of correct answer .
The nucleus of a fertilized egg contains 16 chromosomes. How many chromosomes are there in the nucleus of liver cells? Instead of the correct answer 16 chromosomes (the life of this organism from a fertilized egg is a zygote. And since the zygote had 16 chromosomes in its nucleus, then any diploid somatic cells of this future organism will also have 16 chromosomes in its nucleus) the answer is indicated 8 chromosomes (8 chromosomes will only have the nuclei of the haploid sex cells of this organism - its gametes).
What signs are characteristic only of animals? How the correct answer in the test is chosen "heterotrophic mode of nutrition" . But it is clear that this applies to the entire kingdom of fungi and most bacteria.
The production of hybrids based on the combination of cells of different organisms is carried out by . Selected answer "microbiology" instead of cell engineering.
Phenotypic splitting in dihybrid crosses . The correct answer is “3:1” instead of 9:3:3:1.
Which of the following plants has an achene? The answer given is “in corn” (which has a caryopsis as its fruit) instead of the correct answer at the sunflower.
What is the difference between natural selection and artificial . "Artificial Selection"- the guiding factor of evolution, instead of natural selection.
Competition is the relationship between : as correct answer selected "predator and prey" instead of species with similar needs.
The elementary material for evolution is : selected in test "phenotype modifications" instead of gene mutation.
Non-membrane component of the cell. The answer chosen was “nucleus” (which is not only not a “non-membrane” component, but even a double-membrane one) instead of ribosome.
A plant cell is different from an animal cell. Listed as correct answer "presence of cellular inclusions» "presence of cellulose shell"(there may be inclusions in animal cells, but there is no cellulose shell).
Indicate the substances that perform a construction function. Which is the correct answer? "nucleic acids and water" instead of lipids, polysaccharides and proteins.
How many sperm are involved in fertilization in flowering plants? . The correct answer is “1 sperm” instead of 2 sperm (that’s why fertilization in flowering plants is called “double”, since in addition to the diploid cells of the seed embryo, triploid endosperm cells are formed).
What is the role of lichens in nature. Which is the correct answer? "main source of oxygen" instead of soil formation and destruction of rocks.
What is a group of plants that includes related species called? Specified environmental term“population” instead of the taxonomy term genus.
During the process of respiration, the mass of plants “does not change” instead of decreases.
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I. Unified State Exam (USE) | errors in Unified State Exam tests in biologyBiology tutor via Skypebiology tutorUnified State Exam tests in biologybiology tests |
The most common errors in the Unified State Examination in mathematics are related to fractions and negative numbers - such results are noted year after year by specialists from the federal group of developers of the Unified State Examination in mathematics. That is, the “weak point” turned out to be the topics that students study in grades 5-7. The “top” also includes: inattentive work with probability, incorrect reading of graphs, ignorance of basic planimetric statements, inability to work with stereometry formulas.
Examiners note that students do not understand the conditions of the task, make simple arithmetic errors and do not know how to test themselves - all this, of course, has a very negative impact on the result. It also turned out that schoolchildren know geometry worse than algebra. According to the observations of examiners, more than half of the students do not know how to prove, and even a correctly solved example without a proof is not counted. In order to successfully pass the exam in mathematics, it is important to go through the entire program, and not just “what will be useful in the exam”, to improve your culture of calculations, that is, to minimize the use of calculators, develop the ability to read graphs, correctly use terminology and learn formulas.
The more students know, the less stress and more confidence in themselves and their abilities. A very important axiom: The more you know, the less you are afraid; the less you are afraid, the more you believe in victory; the more you believe in victory, that means you will win. The task of teachers and parents is to make students believe in this.
1) Practice-oriented tasks at the basic level
For tasks at the basic level of the first part (1, 2, 4), testing the ability to use
use acquired knowledge and skills in practical activities
And Everyday life, build and explore the simplest mathematical models
whether the level of absorption has been achieved (over 50%). Practice-oriented tasks
are not unexpected for the participants; they solved tasks of this type when
passing the main state exam in the module "Real Mathematics".
The ability to solve tasks in this module was mandatory (at least 2) for
passing the certification milestone in most regions of the Russian Federation
deration, therefore students solved such tasks in mathematics lessons
no school. Tasks of this type were also included in the educational material when studying
learning mathematics in high school
2) Let's consider the main approaches to a new type of solution Unified State Exam problems in mathematics - problems with "economic content».
Solving problems using the formula.
We know that if the number A is increased by p%, it becomes A(1+). If the number A is decreased by p%, it becomes A(1-.)
Product price A rub. was increased by 25%. By what percentage should it now be reduced to get the original price of the product?
Solution: The price of the product after the increase became A(1+). Let’s say we need to reduce by p%, then the price of the product after the reduction will become A(1+)(1-) and we will get the initial price of the product: A(1+)(1-) = A. Where do we get the answer: 20%
2. The bank accepted a certain amount at a certain percentage. A year later, a quarter of the accumulated amount was withdrawn from the account. But the bank increased the annual interest rate by 40%. By the end of the next year, the accumulated amount was 1.44 times the initial contribution. What is the new APR percentage?
Solution: Let's deposit rubles in bank A at p% per annum. After a year, the amount in the account will be equal to A(1+) rubles. By removing a quarter of this amount, we get A(1+). Now a new percentage A(1+)(1+) is added to this amount, which has become 1.44A. Having decided given equation, we get the answer p=20%, then the new percentage is 60%.
3.The farmer received a loan from a bank at a certain percentage per annum. A year later, in order to repay the loan, the farmer returned to the bank 3/4 of the total amount that he owed the bank by that time, and a year later, in order to fully repay the loan, he deposited into the bank an amount that was 21% greater than the amount of the loan received. What is the annual interest rate on a loan from this bank?
Solution: Let’s say a farmer received A rubles at p% per annum. In a year the debt will be A(1+) rub. Because the farmer repaid the debt, then A(1+) remains. After the 2nd year, the debt increased by p% and became A(1+)A(1+)= A(1+)2. Now, in order to pay off the debt, the farmer contributed an amount 21% larger, i.e. A(1+) and repaid the loan, i.e. A(1+)2 - A(1+)=0. Solving this equation, we get p=120%.
II. Some problems are better solved in general view, without substituting the original data, as you can get confused in the calculations.
4. The amount of 3,900 thousand rubles was placed in the bank at 50% per annum. At the end of each of the first four years of storage, after calculating interest, the depositor additionally contributed the same fixed amount to the account. By the end of the fifth year, after accrual of interest, it turned out that the size of the deposit had increased compared to the original by 725%. What amount did the investor add to the deposit annually?
Solution: let the initial deposit amount to A rubles and the investor annually added x rubles. By the beginning of the 2nd year, the amount of the contribution was A (1+) = 1.5A rubles;
By the beginning of the 3rd year, the amount of the contribution was (1.5A + x) 1.5 + x rubles;
By the beginning of the 4th year, the amount of the contribution was ((1.5A + x) 1.5 + x) 1.5 + x rubles;
By the beginning of the 5th year, the amount of the contribution was (((1.5A +x)1.5+x)1.5+x)1.5+x rubles;
By the end of the 5th year The amount of the contribution was ((((1.5A +x)1.5+x)1.5+x)1.5+x)1.5 rubles. According to the conditions of the problem, the size of the contribution increased compared to the original by 725%, i.e. it became A(1+).
Opening the brackets, we get the following expression:
()5A+()4x+()3x+()2x+()x=A=A
From here, substituting instead of A = 3900 thousand, we get x = 210000.
3. Application of the property of powers
5. During the time the deposit was kept in the bank, interest was accrued monthly, first in the amount of , then , then and, finally, per month. It is known that under the influence of each new interest rate, the deposit
was kept for an integer number of months, and upon expiration of the storage period, the initial deposit amount increased by . Determine the deposit retention period.
Solution: Let the initial deposit amount be A rubles, then after a month this amount will become A(1+) rubles. If the bet is not changed, then the amount will increase again by 5% and become A(1+)2, etc. Let the first bet last k, second - m, third - n, last - t months.
Then the sum increased by A(1+)k(1+)m(1+)n(1+)t times. And after the expiration of the storage period, the initial amount became A (1+)
А(1+)к(1+)m(1+)n(1+)t=Applying the properties of powers, we get 2 -3.3-1.50.72
equate the indicators with the same bases and solve the system:
Where k=m=1. n=3, t=2. Then the deposit period is 1+1+3+2=7 months.
4. Solving problems using mathematical analysis
6. In January 2000, the rate on deposits at Bank Vozrozhdenie was x% per annum, while in January 2001 it was y% per annum, and it is known that x+y=30%. In January 2000, a depositor opened an account with Vozrozhdenie Bank, depositing a certain amount into it. In January 2001, a year later, the investor withdrew a fifth of this amount from the account. Specify the value x at which the amount in the depositor's account in January 2002 will become the maximum possible.
Solution: Let a depositor open a bank account in January 2000 in the amount of A ruble. Then in a year, at x% per annum, the account will have the amount A (1 +) rubles.
Next, the depositor withdraws a fifth of the original amount from the account. That is, the amount appears in the account. The bank's interest rate changes and is now y%, i.e. (30s)%. Then after another year the investor will have a We are interested in the value of x at which the value of f(x) = will be maximum. Let's explore this function methods of mathematical analysis.
f/ (x)=0 at
or Maximum value the function f(x) will take at the point x0 (vertex of the parabola), that is, at the point =25.
Answer: 25%.
5. Comparison tasks.
7. At the end of August 2001, the administration of the Primorsky Territory had a certain amount of money, which was supposed to be used to replenish the region’s oil reserves. Hoping for a change in market conditions, the regional leadership, postponing the purchase of oil, deposited this amount in the bank on September 1, 2001. It is further known that the amount of deposit in the bank increased on the first day of each month by 26% in relation to the amount on the first day of the previous month, and the price of a barrel of crude oil decreased by 10% monthly. By what percentage more (from the initial volume of purchases) was the regional leadership able to replenish the region’s oil reserves by withdrawing on November 1, 2001 the entire amount received from the bank along with interest and directing it to the purchase of oil?
| The regional leadership put A rubles at 26% per month | the price of a barrel of crude oil decreases by 10% monthly |
|
| the amount will be A(1+) rub | The invested amount will decrease and become A(1-)rub |
|
| A(1+) 2 rub. | will become A(1-)2 rub |
Then the amount will increase by =1.96, i.e. by 96%
Answer: 96%.
Problems with economic content are practical problems. And their solution, undoubtedly, contributes to a better assimilation of the content of the mathematics course high school, allows for the transfer of acquired knowledge and skills into economics, which in turn activates interest in applied problems and the study of mathematics in general. Such tasks make it possible to more fully realize the applied orientation in training and contribute to a better assimilation of the educational material and developing problem solving skills of this type.
3) In the specialized Unified State Examination of 2017, the model of task 15 (previously task C1) did not undergo any changes. changes compared to last year. Traditionally, this was a task consisting of two points: solve a trigonometric equation and select the roots of the equation from the specified interval.
Problem 15 of the Unified State Exam (profile level) in 2015 assumed students’ ability to solve equations. Namely:
Knowledge of basic trigonometric formulas (basic trigonometric identity);
Knowledge of the method of replacing a variable when solving an equation;
Ability to solve quadratic equations;
Computational skills working with numbers irrational expressions;
Ability to solve simple trigonometric equations using general and particular formulas;
Knowledge of the range of values of trigonometric functions;
Knowledge of at least one of the methods for selecting roots of a trigonometric equation from a specified interval: using unit circle, solving a double inequality, brute force, using a graph of a function.
Here is one example of problem 15:
a) Solve the equation: .
b) Indicate the roots of this equation that belong to the segment.
The task was assessed Unified State Exam experts:
2 points for a well-founded solution to both points;
1 point for a well-founded solution to one of the points of the problem or if incorrect answers are received due to a computational error, but there is a correct sequence of all steps in solving both points;
0 points in all other cases.
The figure clearly shows the results of completing task 15 of the exam Unified State Examination work(profile level) by students of the Altai Territory in 2015 in primary scores.
Results of task 15 in primary points
There are a number of typical mistakes made by exam participants when performing this task.
1. One of the most common mistakes when solving problem 15 in 2015 was inaccuracies and misconceptions in the formulas of the roots of the simplest trigonometric equations: using the root formula for the simplest trigonometric equation for sine - to an equation for cosine and, conversely, incorrect periodicity of roots, typos and other errors in writing the root. These errors led to the fact that the solutions to the equation were indicated incorrectly, and as a result, the first point of the task was not completed.
For example, when solving the simplest trigonometric equation for sine, students cited:
a) wrong decision 
, , mistakenly using the formula for the roots of the simplest trigonometric equation with respect to cosine;
b) wrong decision 
, instead of the right decision 
, .
2. An equally rare mistake when solving problem 15 in 2015 was the incorrect calculation of the value of the inverse trigonometric function: either incorrect values of arc functions, or incorrect transformation of arc functions of a negative argument. These errors also led to the fact that the roots of the equation were indicated incorrectly, and as a result, the first point of the task was not completed.
For example, when solving the simplest trigonometric equation, students made a typical mistake: they considered equal and not.
In addition, students often believed that 
instead of the correct one. Possibly transferring the function's parity property to the function.
3. Quite a lot of errors were associated with ignorance of the set of values of the trigonometric functions sine and cosine. Students wrote down the formula for the roots of trigonometric equations or without taking into account the condition under which these equations generally have solutions.
For example, in students’ works quite often non-existent values of inverse trigonometric functions were encountered in the formula for the roots of a trigonometric equation: (without noticing that ) etc.
4. Typical errors when solving Problem 15 include the loss of roots when moving from solving the simplest trigonometric equation in general form to a particular form.
For example, writing down the correct solution 
equations, while simplifying the expression on the right side of the equation, students made a mistake: for example, writing 
. The last formula sets completely different values from the first formula. As a result, the answer to point a) contains an incorrect solution.
5. Violation of the logic of inferences, lack of logical connectives, consideration of one particular case of a true equality instead of solving the problem
For example, from an equation of the form “the sum is equal to zero,” students quite often moved on to a system of equations in which each term was equated to zero. At the same time, making the erroneous conclusion “the sum is equal to zero if and only if each term is equal to zero.” Among the works of 2015, this type of error gained popularity. The students mixed global solution equations for the study of one particular case. Moreover, reflections were most often carried out without the logical connectives “and” or “or”.
6. Inaccuracies and errors when solving a trigonometric equation or selecting the roots of an equation from a specified interval
7. An error that was uncharacteristic in past years for a task of this type is the inability to work with irrational numerical expressions. In this regard, for many students the solution quadratic equation with irrational coefficients was difficult (most often the solution was not completed).
For example, having obtained (after replacing the trigonometric function by t) the quadratic equation 
, many students had difficulty even calculating the discriminant (due to the irrationality of the coefficients). Some students, having nevertheless calculated the discriminant and obtained , did not carry out the transformation. This made the roots of the equation unwieldy 
and basically brought the decision to a dead end.
8. As before, as in previous years, students lose points in paragraph b) of the solution to problem 15 due to the lack of justification for selecting roots from the interval. 1 point for the solution to point b) is awarded provided that there are “traces” of root selection, which often did not occur in the works of the 2015 exam participants.
It should be noted that compared to 2014, when solving problem 15, the situation with a reasonable selection of roots of their interval has improved. Students actively used various ways root selection:
a) direct substitution of the resulting roots into the equation and existing restrictions;
b) enumerating the values of an integer parameter and calculating the roots.
2. Algebraic method:
a) solving an inequality with respect to an unknown integer parameter and calculating the roots;
b) study of an equation with two integer parameters.
3. Geometric method:
a) depiction of roots on a trigonometric circle with subsequent selection and taking into account existing limitations;
b) depiction of roots on a number line with subsequent selection and taking into account existing restrictions.
4. Functional-graphic method:
choosing roots using a graph of the simplest trigonometric function.
In general, students successfully selected roots belonging to the gap.
Thus, based on the analysis of typical errors in solutions to the problem of 15 participants in the Unified State Examination in Mathematics in 2015, among the reasons for their occurrence we can highlight: ignorance of the basic formulas for the roots of the simplest trigonometric equations, tabular values of trigonometric functions; lack of knowledge of the concept of multiple values of a trigonometric function, insufficiently developed computational skills and abilities identity transformations.
To prevent these errors, in a narrow sense, it is necessary, when studying the “Trigonometry” section in primary and high school, to ensure that students have absolute knowledge of all the basic theoretical information in this section, since this serves as the basis for a successful transformation trigonometric expression, solutions to trigonometric equations and inequalities present in CMMs profile Unified State Examination mathematics.
In a broad sense, it is necessary to ensure a tendency to improve the quality of Unified State Examination results using a set of measures, primarily of an organizational, methodological and methodological nature, to identify potential errors in solving problems 15 profile level future participants in the 2016 exam and the implementation of appropriate corrective measures.
For students with different levels preparation, fundamentally different strategies for preparing for a specialized exam must be built; differentiation of training is necessary, development of a strategy for training and preparation for the final exam, taking into account the level the graduate already has educational training. First of all, the teacher needs to get acquainted with the structure and content of CIMs, compare them with the content of the program material and the textbook from which schoolchildren study. It is also advisable to organize individual repetition, taking into account the gaps in the knowledge and skills of a particular student, and with the help diagnostic work systematically record the progress of a high school student towards achieving the level of planned requirements.
At new form To diagnose the quality of education, a teacher needs to continuously improve his professional academic level. If earlier (before the Unified State Exam) a teacher believed that preparing graduates for entering a university is not his task and the task of the school, that the teacher is not responsible for entering or not entering a university, now every teacher (both primary and high school) is interested in obtaining high USE results, since they can be used to judge his professional and academic level. In this sense, problem 15 ( higher level complexity) of the profile Unified State Examination in mathematics is promising due to its accessibility to students with average and good level preparation on the subject.
4) Problems with physical content
The problems are more about physics than mathematics, but the necessary formulas and quantities are given in the conditions. Most problems come down to solving a linear or quadratic equation, or a linear or quadratic inequality.
Therefore, it is necessary to be able to solve such equations and inequalities, and determine the answer (there are problems in which you need to choose one of two solutions, there are other nuances, we will consider them).
There are problems that boil down to solving exponential, logarithmic, trigonometric equations and inequalities. In any case, the answer must be obtained as an integer or a final decimal fraction.
What you need to pay attention to:
1. EIf the question said “to determine highest value", "define smallest value", then the problem in most cases is solved by constructing an inequality.
2. Correctly determine the sign when composing an inequality. For example:bat least 21 is written asb≥21.
3. If the question in the problem says “how much,” then an equation is drawn up.
4. Don’t forget about units of measurement, if necessary (convert meters from centimeters, vice versa, etc.)
5. Don’t lose sight of what units of measurement you need to write the answer in (for example, having solved the problem, you got 0.5 hours, the condition says to write the answer in minutes, it turns out 30 minutes; if you write 0.5, this is an error and a lost point , although the problem is solved, right).
5) Tasks on %
8) http://fdp.tsu.tula.ru/useful/TrainingMathematicEGE
Question: I had one very unpleasant situation. We need your professional help. The fact is that the admissions committee of St. Petersburg State University came to Novokuznetsk. On 07/02/2013 I submitted the documents, the original certificate, and in the application I indicated the scores that are listed on the regional website of the Education Department. Unified State Examination result English language at that time I had 98 points. There was no certificate in hand, as the city Department of Education said that the certificates were delayed. Today, 10.07. 2013, I came to my school and picked up a certificate, discovering that in the certificate the Unified State Examination result in English was underestimated by one point and amounted to 97 points. The school administration advised me to contact the city Department of Education. The city Department of Education printed out an “Extract from the decision of the meeting of the state examination commission”, where it was indicated that 06.27. In 2013, my work was rechecked, and, due to the overestimation of the grade in violation of the criteria, the commission lowered my Unified State Examination result in English by one point. In the database I still have 98 points, although it is already July 10th. The certificate itself arrived at the school on 07/08/2013. That is, I, not knowing the change in my result in English, now entered the wrong score. Will I now be included in the list of persons not allowed to participate in the competition? After all, it’s not my fault that the certificate and extract arrived only on 07/08/2013. It turns out that I signed the application for providing incorrect information, but it was correct until today. And, if possible, indicate the addresses or telephone numbers of specialists with whom this issue can be resolved.
Answer: By general rule The Unified State Exam results you indicated in your application when submitting documents to the relevant faculty of St. Petersburg State University are subject to verification in accordance with the data located in the Federal Database of Certificates on the Results of the Unified State Exam (FBS). In accordance with the provisions of clause 2.30. Rules for admission to St. Petersburg State University to the main educational programs higher vocational education(undergraduate programs, specialist training programs, master's programs) in 2013 (hereinafter referred to as the Rules for Admission to St. Petersburg State University) St. Petersburg State University has the right to verify any documents provided by applicants, including educational documents, certificates of results of the Unified State Exam, documents issued by healthcare institutions , medical and social examination institutions, military units etc., including by sending requests to the relevant state (municipal) bodies and organizations.
At the same time, according to clause 2.31. Rules for admission to St. Petersburg State University: applicants who have submitted deliberately false documents to the Admissions Committee bear responsibility under the legislation of the Russian Federation.
In connection with the above standards, you need to send an application addressed to the secretary admissions committee to the email address of the committee for accepting documents of the faculty of St. Petersburg State University you have chosen and inform about the change in the amount of points you scored on the Unified State Exam in English due to the fact that your results were rechecked after you submitted your documents for admission. You can find the specified address on the St. Petersburg State University website in the section Location of committees for accepting documents or by clicking on the following link. Due to insufficient information regarding which faculty you are going to enroll in, we cannot provide you with the number and email address of the relevant admissions committee.