The demo version is intended to enable the exam participant and the general public to get an idea of \u200b\u200bthe structure of the future examination work, the number and form of tasks, as well as their level of complexity. This information provides an opportunity to develop a strategy for preparing for the mathematics exam.
Demonstration version of the OGE 2018 in mathematics, grade 9
| Demo OGE 2018 mathematics | Assignments + answers and assessment criteria |
| Specification | download |
| codifier | |
| Requirements codifier | kodifikator |
| Mathematics reference | download |
Changes in CMM 2018 compared to 2017
Compared to the structure of 2017, the module "Real Mathematics" is excluded from the work. The tasks of this module are divided into modules "Algebra" and "Geometry".
Characteristics of the structure and content of KIM OGE 2018 in mathematics
The work consists of two modules: "Algebra" and "Geometry". Each module has two parts corresponding to the basic and advanced checks. When checking basic mathematical competence, students must demonstrate proficiency in basic algorithms, knowledge and understanding of key elements of the content ( mathematical concepts, their properties, methods of solving problems, etc.), the ability to use mathematical notation, apply knowledge to solving mathematical problems, not reduced to the direct application of the algorithm, as well as to apply mathematical knowledge in the simplest practical situations.
Parts 2 of the modules "Algebra" and "Geometry" are aimed at checking the proficiency of the material at an advanced level. Their purpose is to differentiate well-performing schoolchildren by levels of training, to identify the most prepared part of graduates, which makes up the potential contingent of specialized classes. These parts contain tasks of an increased level of difficulty from various sections of the mathematics course. All tasks require a record of decisions and answers. Tasks are arranged in increasing difficulty - from relatively simple to complex, involving fluency material and a good level of mathematical culture.
The "Algebra" module contains 17 tasks: in part 1 - 14 tasks; in part 2 - 3 tasks.
Module "Geometry" contains 9 tasks: in part 1 - 6 tasks; in part 2 - 3 tasks. There are 26 tasks in total, of which 20 tasks basic level, 4 advanced tasks and 2 high-level tasks.
Duration of the OGE 2018 in mathematics - 235 minutes.
Requirements codifier to the level of preparation of students for the main state exam in mathematics is one of the documents that determine the structure and content of control tests measuring materials - KIM. The codifier is a systematized list of requirements for the level of training of graduates and checked content elements, in which a certain code corresponds to each object.
Content element codifier for the main state exam in mathematics is one of the documents that determine the structure and content of control measuring materials - CMM. The codifier is a systematized list of requirements for the level of training of graduates and checked content elements, in which a certain code corresponds to each object.
Specification
control measuring materials for carrying out
in 2018 of the main state exam
in Russian
1. Purpose of CMM for OGE - to assess the level of general education in the Russian language of graduates of the 9th grade of general educational organizations for the purpose of state final certification graduates. The exam results can be used when admitting students to profile classes high school.
The OGE is carried out in accordance with the Federal Law Russian Federation dated December 29, 2012 No. 273-FZ "On Education in the Russian Federation".
2. Documents defining the content of CMM
3. Approaches to the selection of content, development of the structure of CMM
Conceptual approaches to the formation of KIM for the OGE in the Russian language were determined by the specifics of the subject in accordance with the normative document specified in clause 2.
Outlined in the Federal component of the state standard of the main general education and the competence-based approach implemented in the materials of the unified state examination was reflected in the content of the examination work of the OGE... The work tests the linguistic competence of students (knowledge of language and speech; the ability to apply linguistic knowledge in working with linguistic material, as well as identification, classification, analytical teaching and language skills). The degree of formation of the language competence is indicated by the skills and abilities of students associated with the observance of language norms (lexical, grammatical, stylistic, spelling, punctuation). Communicative competence is tested in the work at the level of learners' proficiency in productive and receptive speech skills.
The fulfillment of the totality of the tasks presented in the work by the examinees makes it possible to assess the compliance of the level of their training achieved by the end of their studies in the basic school with the state requirements for the level of training in the Russian language, which ensures the possibility of successful continuation of their studies in the senior school.
The examination work for the OGE is built taking into account variability: the examinees are given the right to choose one of three essay options.
The assessment system for individual assignments and examination work as a whole was created taking into account the requirements of the theory and practice of pedagogical measurements and domestic traditions of teaching the Russian language.
4. Characteristics of the structure and content of CMM
Each CMM variant consists of three parts and includes 15 tasks that differ in form and level of difficulty.
Part 1 - summary (task 1).
Part 2 (tasks 2-14) - tasks with a short answer.
In the examination paper, the following types of tasks with a short answer are proposed:
- open-ended tasks to write a self-formulated short answer;
- assignments to choose and record one correct answer from the proposed list of answers.
Part 3 (alternative task 15) is an open-ended task with a detailed answer (essay), which tests the ability to create your own statement based on the text read.
Russian language | OGE 2018
The solution of the OGE online test in Russian introduces students to the tasks of the 2018 OGE demo version and helps to master the necessary skills for solving CMM tasks. Teachers can use online testing for free in the classroom to practice exercises and control knowledge.
Take the test "OGE 2018 Russian language Training option number 1" online
Russian language | OGE 2018
Take the test "OGE 2018 Russian language Training option number 2" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. Training option The OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 3" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 4" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 5" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 6" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 7" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 8" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 9" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "OGE 2018 Russian language Training option number 10" online
Russian language | OGE 2018
The solution of the OGE online test in Russian in 2018 acquaints students with the tasks of the present OGE and helps them master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in the Russian language was compiled in accordance with the 2018 demo version.
Take the test "Demonstration version of control measuring materials of the main state exam of 2018 in MATH" online
Mathematics | OGE 2018
The solution to the OGE online test in mathematics introduces students to the tasks of the 2018 OGE demo version and helps to master the necessary skills for solving CMM tasks. Teachers can use online testing for free in class to train and supervise students.
Take the test "OGE 2018 Mathematics Training option number 1" online
Mathematics | OGE 2018
Take the test "OGE 2018 Mathematics Training option number 2" online
Mathematics | OGE 2018
The solution of the OGE online test in mathematics in 2018 acquaints students with the tasks of the present OGE and helps to master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in mathematics corresponds to the demo version of 2018.
Take the test "OGE 2018 Mathematics Training option number 3" online
Mathematics | OGE 2018
The solution of the OGE online test in mathematics in 2018 acquaints students with the tasks of the present OGE and helps to master the necessary skills for solving KIM tasks. Teachers can use online testing for free in class to train and supervise students. The training version of the OGE in mathematics corresponds to the demo version of 2018.
Specification
control measuring materials for carrying out
in 2018 of the main state exam
mathematics
1. Appointment of KIM OGE - to assess the level of general education in mathematics of the 9th grade graduates of general educational organizations for the purpose of the state final certification of graduates. The results of the exam can be used when enrolling students in specialized secondary school classes.
The OGE is conducted in accordance with the Federal Law of the Russian Federation dated December 29, 2012 No. 273-FZ "On Education in the Russian Federation".
2. Documents defining the content of CMM
The content of the exam work of the OGE is determined on the basis of the Federal component of the state standard of basic general education in mathematics (order of the Ministry of Education of Russia dated 05.03.2004 No. 1089 "On approval of the federal component of state educational standards of primary, general, basic general and secondary (complete) general education").
In addition, the examination paper reflects the conceptual provisions of the Federal State educational standard basic general education (order of the Ministry of Education and Science of Russia dated December 17, 2010 No. 1897 "On approval of the federal state educational standard of basic general education"). CMMs are developed taking into account the provision that the result of mastering the main educational program basic general education should be the mathematical competence of graduates, i.e. they must: master the knowledge and activities specific to mathematics; learn how to transform knowledge and its application in educational and extracurricular situations; to form the qualities inherent in mathematical thinking, as well as to master mathematical terminology, key concepts, methods and techniques.
3. Approaches to the selection of content, development of the structure of CMM
The structure of the KIM OGE meets the goal of building a system of differentiated teaching of mathematics in modern school... Differentiation of teaching is aimed at solving two problems: the formation of basic mathematical training in all students, which constitutes the functional basis of general education, and the simultaneous creation of conditions conducive to the receipt by a part of students of training of an increased level, sufficient for active use mathematics during further learning, first of all, when studying it in secondary school at a specialized level.
In order to ensure the effectiveness of verification of development basic concepts course of mathematics, the ability to apply mathematical knowledge and solve practice-oriented problems, as well as taking into account the presence in the practice of the basic school of both separate teaching of subjects of the mathematical cycle, and teaching an integrated course of mathematics in the examination work, two modules are distinguished: "Algebra" and "Geometry" ...
4. Communication examination model OGE with KIM USE
The substantive unity of the state final certification for the course of basic and secondary schools is ensured by common approaches to the development of codifiers for content elements and requirements for the level of training of graduates in mathematics. Both codifiers are based on the "Mathematics" section of the Federal component of the state standard for general education.
5. Characteristics of the structure and content of CMM
The work consists of two modules: "Algebra" and "Geometry". Each module has two parts corresponding to the basic and advanced checks.
When checking basic mathematical competence, students must demonstrate proficiency in basic algorithms, knowledge and understanding of key elements of content (mathematical concepts, their properties, methods of solving problems, etc.), the ability to use mathematical notation, apply knowledge to solving mathematical problems that are not limited to direct application algorithm, as well as apply mathematical knowledge in the simplest practical situations.
Parts 2 of the modules "Algebra" and "Geometry" are aimed at checking the proficiency of the material at an advanced level. Their purpose is to differentiate well-performing schoolchildren by levels of training, to identify the most prepared part of graduates, which makes up the potential contingent of specialized classes. These parts contain tasks of an increased level of difficulty from various sections of the mathematics course. All tasks require a record of decisions and answers. Tasks are arranged in increasing difficulty - from relatively simple to complex, assuming fluency in the material and a good level of mathematical culture.
The "Algebra" module contains 17 tasks: in part 1 - 14 tasks; in part 2 - 3 tasks.
Module "Geometry" contains 9 tasks: in part 1 - 6 tasks; in part 2 - 3 tasks.
In total, there are 26 tasks in the work, of which 20 tasks of the basic level, 4 tasks of an advanced level and 2 tasks of a high level.
Module "Algebra"
1 ... Find the meaning of the expression
2.
The table shows the standards for running 30 meters for students in grade 9. 
What mark will the girl get when she ran this distance in 5.62 seconds?
1) mark "5" 2) mark "4"
3) mark "3" 4) standard not met
3
... A point is marked on the coordinate line A... It is known to match one of the four numbers below. 
Which of the numbers corresponds to the dot AND?
1) 2) 3) 4)
4 ... Find the meaning of the expression
5
... The graph shows the relationship between atmospheric pressure and altitude. The horizontal axis shows the height above sea level in kilometers, the vertical axis - the pressure in millimeters of mercury. Determine from the graph at what height atmosphere pressure equal to 620 millimeters of mercury. Give your answer in kilometers. 
6. Solve the equation. If your equation has more than one root, write down the largest root in your answer.
7. The fare on the electric train is 198 rubles. Students receive a 50% discount. How much will the fare for 4 adults and 12 schoolchildren cost?
8.
The diagram shows the content nutrients in dried porcini mushrooms. 
Which of the following statements are correct?
1) 1000 grams of mushrooms contains about 360 g of fat.
2) 1000 grams of mushrooms contains about 240 grams of carbohydrates.
3) 1000 grams of mushrooms contains approximately 140 grams of protein.
4) 1000 grams of mushrooms contains approximately 500 g of fat, protein and carbohydrates.
In response, write down the numbers of the selected statements without spaces, commas or other additional characters.
9. On the plate are pies that look the same: 4 with meat, 8 with cabbage and 3 with apples. Petya chooses one pie at random. Find the probability that the pie will end up with apples.
10.
Establish a correspondence between the graphs of functions and the formulas that define them. 
11. In the sequence of numbers, the first number is 6, and each next is greater than the previous by 4. Find the fifteenth number.
12. Find the value of the expression at.
13. To convert the temperature from Celsius to Fahrenheit, use the formula, where - temperature in degrees Celsius, - temperature in degrees Fahrenheit. How many degrees Fahrenheit is -25 degrees Celsius?
14.
Indicate the solution to the system of inequalities 
15.
The sloping roof is installed on three vertical supports, the bases of which are located on one straight line. The middle support stands in the middle between the small and large supports (see fig.). The height of the small support is 1.7 m, the height of the middle support is 2.1 m. Find the height of the large support. Give your answer in meters. 
16
... In an isosceles triangle ABCwith the foundation ACouter apex angle Cis equal to 123 °. Find the angle YOU... Give your answer in degrees. 
17
... Find the chord length of a circle with a radius of 13 cm, if the distance from the center of the circle to the chord is 5 cm. Give your answer in cm. 
18.
Find the area of \u200b\u200bthe trapezoid shown in the figure. 
19
... Find the tangent of the acute angle shown in the figure. 
20
... Which of the following statements are correct?
1) Through a point not lying on a given line, you can draw a line parallel to this line.
2) A triangle with sides 1, 2, 4 exists.
3) Any parallelogram has two equal angles.
In response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.
Module "Algebra"
21
... Solve the equation 
22 ... The fisherman at 5 o'clock in the morning on a motor boat set off from the pier against the stream of the river, after a while he dropped anchor, fished for 2 hours and returned back at 10 o'clock in the morning of the same day. How far from the dock he sailed if the river speed is 2 km / h, and own speed boats 6 km / h?
23
... Plot a function graph 
and determine at what values
the line has exactly one point in common with the graph.
Module "Geometry"
24 ... In a right triangle ABCright angle Clegs are known: AC= 6, BC\u003d 8. Find the median CKthis triangle.
25 ... In a parallelogram ABCDdot E- middle of the side AB... It is known that EC \u003d ED... Prove that the given parallelogram is a rectangle.
26 ... Base ACisosceles triangle ABCequals 12. A circle of radius 8 centered outside this triangle touches the extensions of the lateral sides of the triangle and touches the base AC... Find the radius of a circle inscribed in a triangle ABC.
Answers
| 1 | 0,32 |
| 2 | 3 |
| 3 | 2 |
| 4 | 165 |
| 5 | 1,5 |
| 6 | 3 |
| 7 | 1980 |
| 8 | 12;21 |
| 9 | 0,2 |
| 10 | 132 |
| 11 | 62 |
| 12 | 1,25 |
| 13 | -13 |
| 14 | 2 |
| 15 | 2,5 |
| 16 | 57 |
| 17 | 24 |
| 18 | 168 |
| 19 | 2 |
| 20 | 13;31 |
| 21 | -5;1 |
| 22 | 8 kilometers |
| 23 | -6,25; -4; 6 |
| 24 | 5 |
| 25 | |
| 26 | 4,5 |