The main general education
Russian language
Demo version of the OGE-2020 in Russian
Demo version of the OGE-2020 in Russian from the official website of the FIPI.Download the demo version of the OGE 2020 along with the codifier and specification:
What's new?There are no changes in the structure and content of the CMM.
Follow the information about our webinars and broadcasts on the YouTube channel, very soon we will discuss the preparation for the OGE in the Russian language.
The reference book is intended to prepare students for the OGE in the Russian language. The manual contains detailed theoretical material on all topics tested by the exam, as well as training tasks in the form of an OGE. Answers are provided at the end of the handbook. The publication will be useful for teachers of the Russian language, as it makes it possible to effectively organize studying proccess and preparation for the exam. The reference book contains detailed theoretical material on all topics checked by the OGE in the Russian language. After each section, different-level tasks are given in the form of an OGE. Students don't have to search additional information online and buy other manuals. In this guide, they will find everything they need to prepare for the exam independently and effectively.
Analysis of the tasks of the demo version of control measuring materials for the 2020 main state exam in
RUSSIAN LANGUAGE
The examination paper consists of three parts, including 15 tasks. For execution examination work the Russian language is 3 hours 55 minutes (235 minutes).
Part 1 includes one task and is a small written work based on the text heard (concise presentation).
Part 2 consists of 13 tasks (2-14). Part 2 assignments are performed on the basis of the text read.
Part 3 task is performed based on the same text that you read while working on the tasks of part 2.
Starting part 3 of the work, choose one of the three proposed tasks (15.1, 15.2 or 15.3) and give a written detailed, reasoned answer.
The examination paper in the Russian language consists of two parts, containing 27 tasks. Part I contains 26 tasks, part II contains 1 task.
Part 2
Assignment 3
Punctuation Analysis
Arrange punctuation marks. Indicate the numbers that must be followed by commas.
Many outstanding scientists worked in Alexandria (1) among (2) whom the geographer and mathematician Eratosthenes (3) managed to calculate the diameter of the Earth with high accuracy at that time (4) mathematician Euclid (5) who wrote 13 volumes of "Principles" of geometry (6) astronomer Aristarchus of Samos (7), almost two thousand years before Copernicus, established (8) that the Earth is a ball (9) revolving around the Sun.
Assignment 4
Syntactic analysis.
Replace management-based purpose of life with a synonym for reconciliation. Write the resulting phrase.
The choice of the union will be determined by the semantic relations between the parts of a complex sentence:
Assignment 5
Spelling analysis.
Indicate the answer options that correctly explain the spelling of the highlighted word. Write down the numbers of these answers.
1) RATES - at the end of the prefix, before the letter denoting a voiceless consonant sound, the letter C is written.
2) SUMMED UP (results) - in short form the name of the adjective is written as much H as in the full form of this adjective.
Specification
control measuring materials for
in 2018 of the main state exam
mathematics
1. Appointment of KIM OGE - to assess the level of general education in mathematics of graduates of IX classes of general educational organizations for the purpose of 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
The content of the exam work of the OGE is determined on the basis of the Federal component state standard basic general education in mathematics (order of the Ministry of Education of Russia dated 05.03.2004 No. 1089 "On the approval of the federal component of state educational standards for 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 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 tasks high level.
Basic general education
UMK line A.G. Merzlyak. Algebra (7-9) (basic)
Mathematics
Demo version of the OGE-2020 in mathematics
Demovariant, codifier and specification of the OGE 2020 in mathematics from the official website of FIPI.Download the demo version of the OGE 2020 along with the codifier and specification from the link below:
Major changes in the new demo
The CMM includes a new block of practice-oriented tasks 1-5.
OGE schedule in mathematics in 2020
At the moment it is known that the Ministry of Education and Rosobrnadzor have published projects for public discussion oGE schedule... Estimated dates of examinations in mathematics of the main wave: June 9, reserve days June 24, 25, 30.
Soon we will talk about the upcoming USE on and on the air our YouTube channel.
Graduates of the 9th grade are offered a new manual for preparing for the main state exam in mathematics. The collection includes assignments for all sections and topics tested on the main state exam: "Numbers and Calculations", "Practice-Oriented Problems", "Equations and Inequalities", "Algebraic Expressions", "Geometry", "Sequences, Functions and Graphs ". Tasks of different difficulty levels are presented. At the end of the book, answers are given that will help in monitoring and assessing knowledge, skills and abilities. The materials of the manual can be used for systematic repetition of the studied material and training in performing tasks of various types in preparation for the OGE. They will help the teacher organize the preparation for the main state exam, and the students - independently test their knowledge and readiness to take the exam.
The examination paper (OGE) consists of two modules: "Algebra" and "Geometry", included in two parts: the basic level (part 1), advanced and high level (part 2). 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. 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. 3 hours 55 minutes (235 minutes) are allocated for the examination work in mathematics.
Part 1
Exercise 1
Find the meaning of the expression
Decision
Answer:0,32.
Decision
Since the time is 5.62 s., The girl's standard for grade “4” has not been met, however, this time does not exceed 5.9 s. - the standard for the assessment "3". Therefore, its mark is "3".
Answer:3.
Decision
The first number is greater than 11, therefore it cannot be the number A. Note that point A is located on the second half of the segment, which means that it is certainly greater than 5 (for reasons of the scale of the coordinate line). So this is not number 3) and not number 4). Note that the number satisfies the inequality:
Answer:2.
Assignment 4
Find the meaning of the expression
Decision
By the property of the arithmetic square root 
(at a ≥ 0, b ≥ 0), we have:
Answer:165.
Decision
To answer this question, it is enough to determine the division price along the horizontal and vertical axes. Along the horizontal axis, one notch is 0.5 km, and along the vertical axis, 20 mm. r.s. Therefore, the pressure is 620 mm. r.s. is reached at an altitude of 1.5 km.
Answer:1,5.
Assignment 6
Solve the equation x 2 + x – 12 = 0.
If your equation has more than one root, write down the largest root in your answer.
Decision
We use the formula for the roots of the quadratic equation
From where x 1 = –4, x 2 = 3.
Answer:3.
Assignment 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?
Decision
A student's ticket will cost 0.5 198 \u003d 99 rubles. This means that travel for 4 adults and 12 schoolchildren will cost
4 198 + 12 99 \u003d 792 + 1188 \u003d 1980.
Answer:1980.
Decision
Statements 1) and 2) can be considered correct, since the areas corresponding to proteins and carbohydrates occupy approximately 36% and 24% of the total part of the pie chart. At the same time, it can be seen from the diagram that fats occupy less than 16% of the entire diagram, and therefore statement 3) is incorrect, as well as statement 4) is incorrect, since fats, proteins and carbohydrates make up most of the diagram in their totality.
Answer:12 or 21.
Assignment 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.
Decision
The probability of an event in the classical definition is the ratio of the number of favorable outcomes to the total number of possible outcomes:
In this case, the number of all possible outcomes is 4 + 8 + 3 \u003d 15. The number of favorable outcomes is 3. Therefore,
Answer:0,2.
Establish a correspondence between the graphs of functions and the formulas that define them.
Decision
The first graph obviously corresponds to a parabola, general equation which has the form:
y = ax 2 + bx + c.
Therefore, this is formula 1). The second graph corresponds to a hyperbola, the general equation of which is:
Therefore, this is formula 3). The third graph remains, which is a direct proportionality graph:
y = kx.
This is formula 2).
Answer: 132.
Assignment 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.
Decision
The problem deals with an arithmetic progression with the first term a 1 \u003d 6 and difference d \u003d 4. Formula of the common term
a n = a 1 + d · ( n - 1) \u003d 6 + 414 \u003d 62.
Answer: 62.
Decision
Instead of immediately substituting numbers into this expression, we first simplify it by writing it as a rational fraction:
Answer: 1,25.
Task 13
To convert the temperature value from Celsius to Fahrenheit, use the formula t F = 1,8t C + 32, where t C - temperature in degrees Celsius, t F - temperature in degrees Fahrenheit. How many degrees Fahrenheit is –25 degrees Celsius?
Decision
Substitute the value -25 into the formula
t F \u003d 1.8 · (–25) + 32 \u003d –13
Answer: –13.
Indicate the solution to the system of inequalities
Decision
Solving this system of inequalities, we get:
Therefore, the solution to the system of inequalities is the segment [–4; –2.6], which corresponds to Figure 2).
Answer: 2.
Decision
The figure shown in the figure is a rectangular trapezoid. The middle support is nothing more than the middle line of a trapezoid, the length of which is calculated by the formula
where a, b - the length of the bases. Let's make the equation:
b = 2,5.
Answer: 2,5.
In an isosceles triangle ABC with the foundation AS the external apex angle C is 123 °. Find the angle YOU... Give your answer in degrees.
Decision
Triangle ABC isosceles, so the angle YOU equal to the angle ICA... But the angle ICA - adjacent with an angle of 123 °. Hence
∠YOU = ∠ICA \u003d 180 ° - 123 ° \u003d 57 °.
Answer: 57 °.
Find the chord length of a circle of radius 13 if the distance from the center of the circle to the chord is 5.
Decision
Consider a triangle AOB (see figure).
He is isosceles ( JSC = OV) and IT in it the height (its length is equal by condition 5). Hence, IT Is the median by the property of an isosceles triangle and AN = HB... Find AN from a right triangle ANO by the Pythagorean theorem:
Hence, AB = 2AN = 24.
Answer: 24.
Find the area of \u200b\u200bthe trapezoid shown in the figure.
Decision
The bottom base of the trapezoid is 21. Let's use the formula for the area of \u200b\u200ba trapezoid
Answer: 168.
Find the tangent of the acute angle shown in the figure.
Decision
Select a right-angled triangle (see figure).
Tangent is the ratio of the opposite leg to the adjacent one, from here we find
Answer: 2.
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.
Decision
The first statement is the parallel line axiom. The second statement is false, since the triangle inequality does not hold for segments with lengths 1, 2, 4 (the sum of the lengths of any two sides is less than the length of the third side)
1 + 2 = 3 > 4.
The third statement is true - in a parallelogram, the opposite angles are equal.
Answer: 13 or 31.
Part 2
Solve the equation x 4 = (4x – 5) 2 .
Decision
Using the formula for the difference of squares, the original equation is reduced to the form:
(x 2 – 4x + 5)(x 2 + 4x – 5) = 0.
The equation x 2 – 4x + 5 \u003d 0 has no roots ( D < 0). Уравнение
x 2 + 4x – 5 = 0
has roots −5 and 1.
Answer: −5; 1.
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 pier did he sail if the river speed is 2 km / h, and own speed boats 6 km / h?
Decision
Let the angler set sail for a distance equal to s... The time during which he sailed this path is equal to hours (because against the current the speed of the boat is 4 km / h). The time that he spent on the way back is equal to hours (since the speed of the boat downstream is 8 km / h). The total time taking into account the parking is 5 hours. Let's compose and solve the equation:
Answer: 8 kilometers.
Decision
The domain of the function under consideration contains all real numbers, except for the numbers –2 and 3.
Let us simplify the form of the analytical dependence by factoring out the numerator of the fraction:
Thus, the graph of this function is the parabola
y = x 2 + x – 6,
with two "punctured" points, the abscissas of which are equal to –2 and 3. Let's construct this graph. Parabola vertex coordinates
(–0,5; –6,25).
Straight y = c has exactly one point in common with the graph, either when it passes through the vertex of the parabola, or when it intersects the parabola at two points, one of which is punctured. The coordinates of the "punctured" points
(−2; −4) and (3; 6). therefore c = –6,25, c \u003d –4 or c = 6.
Answer: c = –6,25; c = –4; c = 6.
In a right triangle ABC right angle FROM legs are known: AS = 6, Sun \u003d 8. Find the median CK of this triangle.
Decision
In a right-angled triangle, the median drawn to the hypotenuse is equal to half of it. therefore
Answer: 5.
In a parallelogram ABCD dot E - middle of the side AB... It is known that EC \u003dED... Prove that the given parallelogram is a rectangle.
Decision
Consider triangles EBC and AED. They are equal on three sides. Indeed, AE= EB, ED= EC (by condition), AD= BC (opposite sides of the parallelogram). Therefore, ∠ A = ∠B, but the sum of adjacent angles in a parallelogram is 180 °, so ∠ A \u003d 90 ° and ABCD - rectangle.
Base AS isosceles triangle ABC equals 12. A circle of radius 8 centered outside this triangle touches the extensions of the lateral sides of the triangle and touches the base AS... Find the radius of a circle inscribed in a triangle ABC.
Decision
Let be O is the center of this circle, and Q - the center of a circle inscribed in a triangle ABC .
Since the point ABOUT equidistant from the sides of the corner ∠СВА, insofar as it lies on its bisector. At the same time, on the bisector of the angle ∠СВА point lies Q and at the same time, due to the properties of an isosceles triangle, this bisector is both the median and the height of the triangle ABC... It is easy to deduce from these considerations that the circles under consideration touch at one point M, touch point M circles divides AC in half and OQ perpendicular AC.
Let's spend rays AQ and AO... It's not hard to understand that AQ and AO are the bisectors of adjacent angles, and therefore the angle OAQ straight. From a right triangle OAQ we get:
AM 2 = MQ · MO.
Hence,
On the official website of FIPI, documents are presented that determine the structure and content of control measuring materials of the main state exam in mathematics in 2020. Demo version presented so far as a project. Compared to last exam academic year there are significant changes, consider studying the option carefully. Here is a draft of the Demonstration version of the OGE 2020 in mathematics with comments in a form convenient for training and preparation.
Unlike last year, the examination work does not explicitly highlight the modules "Algebra" and "Geometry", however, the condition for successful passing of the exam - among at least two correctly solved problems in geometry - remains in force.
Added a block of practical tasks. These tasks are solved based not only on knowledge of mathematics, but also on the basis of reasonable practical considerations.
All tasks, as before, are divided into two parts. Part 1 contains 20 tasks with a short answer, part 2 contains 6 tasks with a detailed answer.
In the tasks of the first part, only the answers are checked, which need to be transferred to a special form. All necessary calculations, transformations are performed in the draft. Notes in the draft, as well as in the text of control measurement materials are not taken into account when evaluating the work. Part two requires recording the complete solution to the problem. Tasks can be completed in any order. There is no need to rewrite the task condition, you just need to specify the task number.
Also, do not forget that the content of the basic exam for the 11th grade overlaps significantly with the OGE for the ninth grade, because in the first 9 years of studying mathematics you learned more than you can do in the remaining two years. Use all links and comments, to find the necessary material to prepare for the exam.
Attention:
the simulator is arranged as follows.
1) Blue field - the field of the problem condition. The white area next to the word "Answer" is, in fact, a button that you click on to reveal the correct answer. If you have not solved the demo version yet, then before pressing the button, try to get the answer yourself and compare it with the known correct one.
2) Orange field - comment field, links to other pages of the site or to the USE tasks.
The buttons are triggered after the page is fully loaded.
Part 1
Read the text carefully and complete tasks 1-5.
The plan shows a household at the address: s. Avdeevo, 3rd Poperechny lane, 13 (the side of each cell on the plan is 2 m). The plot has a rectangular shape. Exit and entry are made through a single gate.
At the entrance to the site to the right of the gate there is a bathhouse, and to the left is a garage, marked on the plan with number 7. The area occupied by the garage is 32 sq. M. m.
The residential building is located in the depths of the territory. In addition to a garage, a residential building and a bathhouse, the plot has a barn (utility room) located next to the garage, and a greenhouse built on the territory of the vegetable garden (the vegetable garden is marked with number 2). There are apple plantings in front of the residential building.
All paths within the plot are 1 m wide and are paved with 1m × 1m paving slabs. Between the sauna and the garage there is a 64 sq. m, paved with the same tiles.
The household is supplied with electricity. There is a main gas supply.
You can see it on a separate page of the site.
1. For the objects indicated in the table, determine what numbers they are indicated on the plan. Fill out the table, transfer the sequence of four numbers to the answer form.
Answer: ______.
2. Paving slabs are sold in packs of 4. How many packs of tiles did it take to lay out all the paths and area in front of the garage?
Answer: ______.
3. Find the area occupied by a residential building. Give your answer in square meters.
Answer: ______.
4. Find the distance from the residential building to the garage (the distance between the two nearest points in a straight line) in meters.
Answer: ______.
5. The landlord plans to arrange winter heating in the residential building. He is considering two options: electric or gas heating. Prices for equipment and the cost of its installation, data on the consumption of gas, electricity and their cost are given in the table.
Having considered both options, the owner decided to install gas equipment. After how many hours of continuous heating operation, the savings from using gas instead of electricity compensate for the difference in the cost of installing gas and electric heating?
Answer: ______.
6. Find the meaning of the expression
1 _ 4 + 0,07.
Answer: ______.
7.
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) 181 ___ 16 2) √37__ 3) 0,6 4) 4
Answer: ______.
8.
Find the meaning of the expression √45 __
√605 ___
.
Answer: ______.
9.
Solve the equation x 2 + x − 12 = 0
.
If your equation has more than one root, write down the largest root in your answer.
Answer: ______.
10. 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.
Answer: ______.
11.
Establish a correspondence between the graphs of functions and the formulas that define them. 
1) y = x 2 2) y = x _ 2 3) y = 2 _ x
In the table below each letter, indicate the corresponding number.
| AND | B | IN |
12. In the sequence of numbers, the first number is 6, and each next is greater than the previous by 4. Find the fifteenth number.
Answer: ______.
13. Find the meaning of the expression
9b + 5a − 9b 2 ______ b
at a = 9, b = 36 .Answer: ______.
14. To convert the temperature value from Celsius to Fahrenheit, use the formula t F = 1,8t C + 32, Where t C - temperature in degrees Celsius, t F - temperature in degrees Fahrenheit. How many degrees Fahrenheit is -25 degrees Celsius?
Answer: ______.
15. Indicate the solution to the system of inequalities
Answer: ______.
16.
In an isosceles triangle ABC with the foundation AC outer apex angle C equals 123º. Find the angle YOU... Give your answer in degrees.
Answer: ______.
17. Find the chord length of a circle of radius 13 if the distance from the center of the circle to the chord is 5.
Answer: ______.
18.
Find the area of \u200b\u200bthe trapezoid shown in the figure.
Answer: ______.
19. Find the tangent of the acute angle shown in the figure.
Answer: ______.
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.
Answer: ______.
Part 2
When completing the tasks in this part, you will need to write down the complete solution to the problem on a separate sheet. And it will be the decision that will be evaluated, the short answer is no longer relevant here. Therefore, the white field after the text of the task is just a button to view the solution recommended by the authors of the option. Do not rush to press it if you have not tried to solve the problem yourself.
The first three tasks of the second part are related to algebra.
21. Solve the equation x 4 = (4x − 5) 2 .
Answer: ______
Decision.
The original equation is reduced to the form: (x 2 − 4x + 5)(x 2 + 4x − 5) = 0.
The equation x 2 − 4x + 5 = 0
has no roots.
The equation x 2 + 4x − 5
has roots −5 and 1.
Answer: −5 ; 1.
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 the boat's own speed is 6 km / h?
Answer: ______.
Decision.
Let the required distance be x km. The speed of the boat when moving against the current is 4 km / h, when moving with the current it is 8 km / h. The time it takes for the boat to sail from the point of departure to the point of destination and back is ( x/4 + x/ 8) hours. It follows from the problem statement that this time is equal to 3 hours. Let's make the equation:
x _ 4 + x _ 8 = 3.
Solving the equation, we get x = 8.
Answer: 8 kilometers.
23. Plot the function
y = x 4 − 13x 2 + 36 _____________ . (x - 3) ( x + 2)
And determine at what values from straight y \u003d c has exactly one point in common with the graph.
Answer: ______.
Decision.
Let us factor out the numerator of the fraction:
x 4 − 13x 2 + 36 = (x 2 − 4)(x 2 − 9) = (x − 2)(x + 2)(x − 3)(x + 3).
When x ≠ −2 and x ≠ 3 function takes the form: y = (x − 2)(x + 3) = x 2 + x − 6
, its graph is a parabola from which points (−2; −4) and (3; 6) are punched out.
Straight y \u003d c has exactly one point in common with the graph, either when it passes through the vertex of the parabola, or when it intersects the parabola at two points, one of which is punctured. The vertex of the parabola has coordinates (−0.5; −6.25). therefore c = −6,25, c \u003d −4 or c = 6.
Answer: c = −6,25 ; c = − 4; c = 6.
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.
the 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.
The examination work in mathematics is assigned 3 hours 55 minutes (235 minutes).
Write down the answers to tasks 2, 3, 14 in the answer form №1 as one digitwhich corresponds to the number of the correct answer.
For the rest of the tasks of part 1 the answer is a number or 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 work, you can use the basic formulas of the mathematics course, issued along with the work. The ruler is allowed, 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 ( the 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 leave in the hallway.