Options for tasks for oge. Oge practice test in mathematics

The OGE in Mathematics is a mandatory exam for all 9th grade graduates who enter the 10th grade or leave school with the aim of enrolling in other educational institutions.To pass the exam for a student who carefully and thoroughly completed all the tasks in the classroom, specific preparation efforts do not have to be made.Moreover, if you need a minimum passing score - three.

All tasks are presented in 3 directions: algebra, geometry, real mathematics. The most important feature is the restriction on completing tasks in blocks: if you solve 2 or less tasks from the geometry part, the score will be "2", the total score does not matter.
The structure does not change: the student is asked to complete 5 tasks of the geometry block, 8 in algebra, 7 in real mathematics. This is the first part of the test - each correct answer is worth 1 point.
Second part: tasks are supposed to be solved increased complexity, the maximum score for each is 2.

How to effectively prepare for the OGE in mathematics?

The main thing is to set the goal correctly: the goal is the desired score.
It is required to effectively study the theory, go through the program of previous classes, get acquainted with for the exam.
It is very important to "fill your hand" - I mean regular practice in solving problems in mathematics different levels difficulties. It is easy to learn how to solve tasks of one type according to the model - when you bring the process to automatism, no exam will cause difficulties.
Online testing will help you immerse yourself in the atmosphere of the final test - it's just solving problems, but also training to do it for a while. If there are systematic errors, you can contact your tutor or school teacher with them.
If planned self-preparation, it is worth starting it in advance, give yourself time.
Learn to plan and save time.

The main principle of preparation is an integrated approach: it is worth studying all topics evenly, if a gap is found, more time is devoted to this topic. For high-quality preparation for mathematics, there is little dry theory, the basis of success on the exam is skillful practice.

Geometry: Requires more thorough preparation, as it is much less time devoted to it in school than to algebra. To cope with problems, study the rules, laws, algorithms for solving.
Algebra: some tasks require simple adherence to algorithms, more complex tasks - for building complex graphs of functions and word problems.

To ensure your success in the exam, do not pass up every opportunity to exercise: attend school electives, online courses remotely, engage in self-education, carefully study the topics in the classroom.
"I will solve the OGE in mathematics" is a simple and affordable way gain experience for solving tasks of varying complexity for a while. Regular preparation will allow you to correctly plan your time for the exam, not to get nervous and get a high result.

Evaluation

The work consists of two modules: "Algebra and geometry". A total of 26 tasks in work... Module "Algebra" "Geometry"

3 hours 55 minutes(235 minutes).

as one digit

, squarecompass Calculators on exam not used.

passport), pass and capillary or! Allow to take with myself water(in a transparent bottle) and food

The work consists of two modules: "Algebra and geometry". A total of 26 tasks in work... Module "Algebra" contains seventeen tasks: in part 1 - fourteen tasks; in part 2 - three tasks. Module "Geometry" contains nine tasks: in part 1 - six tasks; in part 2 - three tasks.

For execution examination work in mathematics 3 hours 55 minutes(235 minutes).

Write down the answers to tasks 2, 3, 14 in the answer form number 1 as one digit, which corresponds to the number of the correct answer.

For the rest of the tasks of part 1 the answer is a number or a sequence of digits... Write the answer in the answer field in the text of the work, and then transfer it to the answer form №1. If the response received common fraction, convert it to decimal.

When performing the work, you can use the basic formulas of the mathematics course, issued along with the work. It is allowed to use a ruler, square, other templates for building geometric shapes (compass). Do not use tools with reference materials printed on them. Calculators on exam not used.

During the exam, you must have an identity document ( passport), pass and capillary or gel pen with black ink! Allow to take with myself water(in a transparent bottle) and food(fruits, chocolate, rolls, sandwiches), but may be asked to be left in the hallway.

OGE practice test in MATH

Grade 9

Work instructions

Total time work - 235 minutes (3 hours 55 minutes)

Characteristics of the work. In total, there are 26 tasks in the work, of which 20 tasks basic level(part 1), 4 tasks increased level(part 2) and 2 tasks high level complexity (part 2). The work consists of three modules: "Algebra", "Geometry", "Real Mathematics".

Module "Algebra" contains 11 tasks: in part 1 - 8 tasks; in part 2 - 3 tasks. Module "Geometry" contains 8 tasks: in part 1 - 5 tasks; in part 2 - 3 tasks. The "Real Mathematics" module contains 7 tasks: all tasks are in part 1.

Tips and instructions for performing the work. First, complete the tasks of part 1. We recommend starting with the module, the tasks of which cause you less difficulty, then move on to other modules. To save time, skip a task that you cannot complete right away and move on to the next. If you have time left, you can return to the missed tasks.

All necessary calculations, transformations, etc. do it in draft. If the task contains a drawing, then on it directly in the text of the work, you can perform the constructions you need. We recommend that you carefully read the condition and check the received answer.

When completing the tasks of part 1, first indicate on the sheets with the tasks of the training work, and then transfer it to the answer form No. 1.

Write down the solutions to the tasks of part 2 and the answers to them on the answer form №2. Tasks can be completed in any order, starting with any module. You do not need to rewrite the text of the task, you just need to indicate its number. Please note that the entries in the draft will not be taken into account when evaluating the work.

When performing work, you can use reference materials.

How the work is evaluated. The points received by you for correctly completed tasks are summed up. To successfully pass the training test, you must score at least 8 points in total: of which at least 3 points in the Algebra module, at least 2 points in the Geometry module and at least 2 points in the module 2 points in the module "Real Mathematics". For each correctly completed task of Part 1, 1 point is awarded. In each module of part 2, the tasks are arranged according to the increasing difficulty and are estimated at 2 points.

We wish you success!

Part 1

Answers to tasks 2, 3, 8, 14 are written in the form of one digit, which corresponds to the number of the correct answer. Write this figure in the answer field in the text of the work. Then transfer the answer to answer form No. 1 to the right of the number of the corresponding task, starting from the first cell.

For the rest of the tasks of part 1, the answer is a number or a sequence of numbers that must be written in the answer field in the text of the work. Then transfer the answer to the answer form №1. If the answer is an ordinary fraction, convert it to decimal.

Write each number, minus sign and comma in a separate box in accordance with the samples provided in the form. Units do not need to be specified. If the answer to the equation (task 4) is several numbers, write them down in ascending order in answer form No. 1, separating them with a semicolon, for example: -3; 10.

If the answer contains a table, then transfer the sequence of numbers you wrote down without spaces and the use of other symbols into answer form No. 1.

In tasks 13 and 18, enter the numbers of the selected answers in any order without spaces and using other symbols.

Module "Algebra"

№1.

Find the value of the expression 0.7 (- 10)3 - 20.

Answer: ____________________

№2.

Point A is marked on the coordinate line.

It is known to match one of the four numbers below. Which of the numbers does point A correspond to?

1) 2) 3) 0,6 4) 4

Answer: ____________________

№3.

Which of the following numbers is the value of the expression · ?

1) 2) 3) 4)

Answer: ____________________

№4.

Find the roots of the equation x2 - 3x - 18 = 0

If there are several roots, write them separated by semicolons in ascending order.

Answer: ____________________

№5.

The figure shows graphs of functions of the form y =kx +b... Establish a correspondence between the signs of the coefficients and the graphs of the functions.

GRAPHIC FACTORS

BUT)k>0, b>0

B)k>0, b<0

IN)k<0, b>0

Answer:

№6.

The first three members of the numerical sequence are written down: 20; 17; 14. What number is in the 6th place in this sequence?

Answer: ____________________

№7.

Simplify the expression · and find its value ata = 19, b= 8.2. Write down the found value in the answer.

Answer: ____________________

№8.

Indicate the solution to the inequality 9x - 4 (x - 7)< - 3.

1)(5; + ∞) 2)(- 6,2; +∞) 3)(- ∞; - 6,2) 4) (- ∞; 5)

Answer: ____________________

Module "Geometry"

№9.

The height of an isosceles trapezoid drawn from vertex C divides the base AD into segments of length 1 and 5. Find the length of the base BC.

Answer: ____________________

№10.

Triangle ABC is inscribed in a circle centered at point O. Find the degree measure of the angle C of triangle ABC if the angle AOB is 63 °.

Answer: ____________________

№11.

In triangle ABC the midpoints M and N of sides BC and AC are marked, respectively. The area of triangle CNM is 2. Find the area of quadrilateral ABMN.

Answer: ____________________

№12.

On checkered paper with a cell size 1x1, three points are marked: A, B and C. Find the distance from point A to the middle of the segment BC.

Answer: ____________________

№13.

Which of the following statements is true?

1. All angles of the rhombus are equal.

2. The inscribed angle, based on the diameter of the circle, is straight.

3. If the two sides and the angle of one triangle are respectively equal to two

sides and angle of another triangle, then such triangles are equal.

Answer: ____________________

Module "Real Mathematics"

№14.

The table shows the standards for cross-country skiing for 1 km for grade 10

	boys				girls
Mark	"3"	"four"	"five"	"3"		"four"	"five"
Time (in minutes and seconds)	5:00	5:30	4:40	7:10		6:30	6:00

What mark will a girl get when she skied 1 km in 6 minutes 15 seconds?

In the answer, indicate the number of the correct option.

1) Unsatisfactory

2) "4"

3) "3"

4) "5"

Answer: ____________________

№15.

On ri-sun-ke, po-ka-za-but, how from-me-nya-las tem-pe-ra-tu-ra voz-du-ha for about-ty-the same day. By go-ri-zon-ta-li indicate-for-but-but-but-time, by ver-ti-ka-li - the meaning of the tem-pe-ra-tu-ry in the gra-du-sakh Tsel-sia. Nay-di-te the most important-the-temp-pe-ra-tu-ry for this day. Give the answer in gra-du-sakh Purpose-sia.

Answer: ____________________

№16.

A set of pens, which cost 80 rubles, is on sale with a 25% discount. When buying 4 such sets, the buyer gave the cashier 500 rubles. How much change should he get?

Answer: ____________________

№17.

What is the angle (in degrees) of the minute and hour hands of the clock at 5 o'clock?

Answer: ____________________

№18.

The diagram shows the number of SMS sent by listeners for each hour of the four-hour broadcast of the program at the request of the radio. Determine how many more messages were sent in the first two hours of the program compared to the last two hours of this program.

Answer: ____________________

№19.

The average height of a resident of the city in which Nikita lives is 169 cm. Nikita's height is 183 cm. Which of the following statements is correct?

1. There will certainly be a resident with a height of less than 170 cm.

2. All residents of the city, except for Nikita, are less than 169 cm tall.

3. All residents of the city are below Nikita.

4. There will certainly be a resident of the city with a height of 158 cm.

Answer: ____________________

№20.

The area of a quadrilateral can be calculated by the formulaS= where d1 and d2 - the length of the diagonals of the quadrilateral, - the angle between the diagonals. Using this formula, find the length of the diagonald2 , if ad1 = 9, sinα=, aS = 56,25.

Answer: ____________________

Part 2

Use a separate sheet for assignments 21-26. First, indicate the number of the task, and then its solution and answer. Write clearly and legibly.

№21.

Simplify

№22 .

Two people simultaneously go from the same place along the same road for a walk to the edge of the forest, located 4 km from the place of departure. One goes at a speed of 2.7 km / h, and the other - at a speed of 4.5 km / h. Having reached the edge, the second one returns back at the same speed. At what distance from the point of departure will they meet?

№23.

At what value of p does the line y = 2x + p have with the parabola y = x2 - 2x exactly one common point? Find the coordinates of this point. Construct a given parabola and a straight line in the same coordinate system for the found value of p.

№24.

Find the value of the angle COE, if OE is the bisector of the angle AOC, ODIs the bisector of the COB angle.

№25.

The bisectors of angles C and D of trapezoid ABCD meet at point P lying on side AB. Prove that point P is equidistant from lines BC, CD and AD.

№26.

A quadrilateral ABCD with sides AB = 25 and CD = 16 is inscribed in a circle. Diagonals AC and BD meet at point K, and∠ AKB = 60 °. Find the radius of the circle around this quadrilateral.

Answers

Part 1

	Option 1
	− 720


	3; 6
	132

	9,5


	31,5





	260
	150




	3 km
	(2; 0)

Evaluation

The work consists of two modules: "Algebra and geometry". A total of 26 tasks in work... Module "Algebra" "Geometry"

3 hours 55 minutes(235 minutes).

as one digit

, squarecompass Calculators on exam not used.

passport), pass and capillary or! Allow to take with myself water(in a transparent bottle) and food

For the performance of the examination work in mathematics, 3 hours 55 minutes(235 minutes).

Write down the answers to tasks 2, 3, 14 in the answer form number 1 as one digit, which corresponds to the number of the correct answer.

For the rest of the tasks of part 1 the answer is a number or a sequence of digits... Write the answer in the answer field in the text of the work, and then transfer it to the answer form №1. If an ordinary fraction is received in the answer, convert it to decimal.

When performing the work, you can use the basic formulas of the mathematics course, issued along with the work. It is allowed to use a ruler, square, other templates for constructing geometric shapes ( compass). Do not use tools with reference materials printed on them. Calculators on exam not used.

The state final certification of 2019 in algebra (mathematics) for graduates of the 9th grade of educational institutions is carried out in order to assess the level of general education of graduates in this discipline. The main verifiable requirements for the mathematical preparation of students:

Be able to perform calculations and transformations.
Use the basic units of length, mass, time, speed, area, volume; express larger units through smaller ones and vice versa.
Describe various real relationships between quantities using functions; interpret graphs of real dependencies.
Be able to solve equations, inequalities and their systems.
Solve simple practical computational problems.
Analyze real numerical data presented in tables, diagrams, graphs.
Solve practical problems requiring a systematic enumeration of options using the apparatus of probability and statistics.
Be able to build and read function graphs.
Carry out practical calculations using formulas, draw up simple formulas expressing the relationship between quantities.
Describe real situations in the language of geometry, investigate the constructed models using geometric concepts and theorems, solve practical problems associated with finding geometric quantities.
Be able to perform actions with geometric shapes, coordinates and vectors.
Conduct evidence-based reasoning when solving problems, evaluate the logical correctness of reasoning, recognize erroneous conclusions.
Be able to build and explore the simplest mathematical models.

In this section, you will find online tests that will help you prepare for passing the OGE (GIA) in algebra (mathematics). We wish you every success!

The standard test of the OGE (GIA-9) of the 2019 format consists of two modules: "Algebra" and "Geometry". Each module consists of two parts, corresponding to the basic and advanced level checks. Parts 2 of the modules "Algebra" and "Geometry" are aimed at checking proficiency in the material at an advanced level, they contain complex tasks that do not lend themselves to test assessment, since the examiner gives a grade based on complex criteria and analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among them, according to the current structure of the exam, answer options are offered only in a few problems. However, for the convenience of passing the tests, the site administration offers several answer options for each of the tasks. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMM), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face on the exam.

The standard test of the OGE (GIA-9) of the 2018 format consists of two modules: "Algebra" and "Geometry". Each module consists of two parts, corresponding to the basic and advanced level checks. Parts 2 of the modules "Algebra" and "Geometry" are aimed at checking proficiency in the material at an advanced level, they contain complex tasks that do not lend themselves to test assessment, since the examiner gives a grade based on complex criteria and analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among them, according to the current structure of the exam, answer options are offered only in a few problems. However, for the convenience of passing the tests, the site administration offers several answer options for each of the tasks. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMM), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face on the exam.

The standard OGE test (GIA-9) of the 2017 format contains two parts. In the first part there are 3 modules: Algebra (8 problems), Geometry (5 problems), Real mathematics (7 problems). In the second part there are 2 modules: Algebra (3 tasks) and Geometry (3 tasks). The second part contains complex tasks and does not lend itself to test evaluation. The assessor assigns a grade based on complex criteria and analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among the 20 problems, according to the current structure of the exam, answer options are offered in only a few problems. However, for the convenience of passing the tests, the site administration decided to offer answer options for each of the problems. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMMs), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face at the end of the school year.

The standard test of the OGE (GIA-9) of the 2016 format contains two parts. In the first part there are 3 modules: Algebra (8 problems), Geometry (5 problems), Real mathematics (7 problems). In the second part there are 2 modules: Algebra (3 tasks) and Geometry (3 tasks). The second part contains complex tasks and does not lend itself to test evaluation. The assessor assigns a grade based on a complex criterion and an analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among the 20 problems, according to the current structure of the exam, answer options are offered in only a few problems. However, for the convenience of passing the tests, the site administration decided to offer answer options for each of the problems. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMMs), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face at the end of the school year.

The standard test of the OGE (GIA-9) of the 2015 format contains two parts. In the first part there are 3 modules: Algebra (8 problems), Geometry (5 problems), Real mathematics (7 problems). In the second part there are 2 modules: Algebra (3 tasks) and Geometry (3 tasks). The second part contains complex tasks and does not lend itself to test evaluation. The assessor assigns a grade based on complex criteria and analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among the 20 problems, according to the current structure of the exam, answer options are offered in only a few problems. However, for the convenience of passing the tests, the site administration decided to offer answer options for each of the problems. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMMs), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face at the end of the school year.

The standard GIA test of the 2014 format contains two parts. In the first part there are 3 modules: Algebra (8 problems), Geometry (5 problems), Real mathematics (7 problems). In the second part there are 2 modules: Algebra (3 tasks) and Geometry (3 tasks). The second part contains complex tasks and does not lend itself to test evaluation. The assessor assigns a grade based on a complex criterion and analysis of the adequacy of the student's justifications. Therefore, in this test, only the first part (first 20 problems) is presented. Among the 20 problems, according to the current structure of the exam, answer options are offered in only four problems. However, for the convenience of passing the tests, the site administration decided to offer answer options for each of the problems. Naturally, for problems in which the answer options are not provided by the compilers of real control and measuring materials (CMMs), we decided to significantly increase the number of these answer options in order to bring our test as close as possible to what you will have to face at the end of the school year.

When performing tasks A1-A14, select only one correct option.

When performing tasks A1-A16, select only one correct option.