Oge typical variant 1 yashchenko.

OGE 2017. Mathematics. Three modules. 30 variants of typical test tasks. Ed. Yashchenko I.V.

M.: 2017. - 168 p.

The manual contains 30 variants of standard control measuring materials of the Main State Exam. The purpose of the manual is to develop the practical skills of students in preparing for the exam in mathematics (in a new form) in the 9th grade. The collection contains answers to all tasks of the options. The manual is addressed to teachers and methodologists who use standard test tasks to prepare students for the 2016 Main State Exam, it can also be used by students for self-study and self-control.

Format: pdf

The size: 4.9 MB

Watch, download:drive.google

CONTENT
Theoretical course 6
I. Numbers and Expressions 6
1. Expressions, transformations of expressions 6
2. Degree with a natural indicator, its properties 8
3. Monomials, polynomials 9
4. Rational fractions and their properties 11
5. Square roots 14
6. Degree with an integer exponent and its properties 17
7. Root of the n-th degree, a degree with a rational exponent and their properties 18
II. Equations and inequalities 20
1. Equations with one variable 20
2. Systems of linear equations 21
3. Quadratic equations 23
4. Inequalities in one variable and their systems 26
III. Functions 29
1. Functions, their properties. Linear function and inverse proportionality 29
2. Quadratic function 31
3. Power function 32
IV. Progressions and word problems 34
1. Arithmetic progression 34
2. Geometric progression 36
3. Solving word problems 38
V. Elements of combinatorics, statistics and probability theory 41
Elements of combinatorics 41
Elements of Probability Theory 42
Tasks for independent solution 44
I. Numbers and Expressions 44
1. Expressions, expression transformations 44
2. Degree with a natural indicator, its properties 46
3. Monomials, polynomials 47
4. Rational fractions and their properties 48
5. Square Roots 51
6. Degree with an integer exponent and its properties 53
7. The root of the w-th degree, a degree with a rational exponent and their properties 54
II. Equations and inequalities 56
1. Equation with one variable 56
2. Systems of linear equations 57
3. Quadratic equations 59
4. Inequalities in one variable and their systems 61
III. Functions 62
IV. Progressions and word problems 73
IV. Elements of combinatorics, statistics and probability theory 79
Answers to problems 81
Variants of typical test tasks 84
Option 1 84
Part 1 84
Part 2 90
Option 2 92
Part 1 92
Part 2 97
Option 3 99
Part 1 99
Part 2 104
Option 4 105
Part 1 105
Part 2 software
Option 5 111
Part 1 111
Part 2 116
Option 6 117
Part 1 117
Part 2 122
Option 7 124
Part 1 124
Part 2 130
Option 131
Part 1 131
Part 2 137
Option 9 138
Part 1 138
Part 2 143
Option 10 144
Part 1 144
Part 2 149
Answers to variants of standard test tasks 151
Solution 5 153
Part 1 153
Part 2 157

OGE 2017. Mathematics. Three modules. 30 variants of typical test tasks. Ed. Yashchenko I.V.

M.: 2017. - 168 p.

Format: pdf

The size: 4.9 MB

Watch, download:drive.google

The manual contains 30 options for typical control measuring materials for the 2017 Basic State Exam.
The purpose of the manual is to develop the practical skills of students in preparing for the exam in mathematics (in a new form) in the 9th grade.
The collection contains answers to all tasks of the options.
The manual is addressed to teachers and methodologists who use standard test tasks to prepare students for the 2017 Main State Exam, it can also be used by students for self-study and self-control.

Examples.
Which of the following statements is correct?
1) The area of a parallelogram is equal to half the product of its diagonals.
2) The sum of the angles of a right triangle is 90 degrees.
3) The bisectors of a triangle intersect at a point that is the center of a circle inscribed in the triangle.

At the beginning of the year, the number of subscribers of the Vostok telephone company was 800 thousand people, and at the end of the year there were 880 thousand people. By what percent did the number of subscribers of this company increase during the year?

The taxi company currently has 15 free cars: 4 black, 3 yellow and 8 green. On a call, one of the cars left, which happened to be closest to the customer. Find the probability that a yellow taxi will arrive.

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Download the book OGE 2017, Mathematics, grade 9, 3 modules, 30 options, Vysotsky I.R., Yashchenko I.V. - fileskachat.com, fast and free download.

The following tutorials and books.

Model 1 in Mathematics Yashchenko

Work instructions
The work consists of three modules: "Algebra", "Geometry", "Real Mathematics". There are 26 tasks in total. The module "Algebra" contains 11 tasks: in part 1 - eight tasks; in part 2 - three tasks. The module "Geometry" contains eight tasks: in part 1 - five tasks; in part 2 - three tasks. The "Real Mathematics" module contains seven tasks: all tasks of this module are in part 1.
3 hours 55 minutes (235 minutes) are allotted to complete the examination paper in mathematics.
Answers to tasks 2, 3, 8, 14 write down in the answer form No. 1 in the form of one number, which corresponds to the number of the correct answer.
For the rest of the tasks in 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 No. 1. If an ordinary fraction is received in the answer, turn it into a decimal.
Write the solutions to the tasks of part 2 and the answers to them on the answer sheet No. 2. The tasks can be completed in any order, starting from any module. The text of the task does not need to be rewritten, it is only necessary to indicate its number.
First complete the tasks of part 1. We advise you to start with the module whose tasks cause you less difficulty, then move on to other modules. To save time, skip the task that you can't complete right away and move on to the next one. If you have time left, you can return to the missed tasks.
All necessary calculations, transformations, etc. do it in draft. Draft entries do not count towards the assessment of the work. If the task contains a drawing, then you can perform the constructions you need directly on it in the text of the work. We recommend that you carefully read the condition and check the received answer.
As you work, you can use reference materials.
Points received for correctly completed tasks are summed up. To successfully pass the final certification, 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 Real Mathematics module. For each correctly completed task of part 1, 1 point is given. In each module of part 2 tasks are estimated at 2 points.
We wish you success!

Task Conditions

Module "Algebra"

1 . Find the value of an expression

2 . One of the numbers marked on a straight line by a dot. What is this number?
1) 2) 3) 4)

3 . Which of the following numbers is the value of the expression?
1) 2) 3) 4)

4 . Solve the equation. If the equation has more than one root, write down the smaller of the roots in response.

5 . The figures show graphs of functions of the form . Establish a correspondence between the graphs of functions and the signs of the coefficients and .

In the table, under each letter A B C corresponding to the schedule, indicate the corresponding number.

6 . The first few terms of a geometric progression are written out: . Find its fourth member.

7 . Find the value of an expression at .

8 . Specify the solution of the system of inequalities > .
1) no solutions 2) 3) 4)

Module "Geometry"

9 . In a triangle ABC injection C is equal to 90°, , . Find the sine of an angle AT.

10 . The radius of a circle inscribed in a square is . Find the radius of the circle circumscribed about this square.

11 . The side of the square is . Find the area of this square.

12 . An angle is depicted on checkered paper with a cell size of 1x1. Find the tangent of this angle.

13 . Which of the following statements is correct?
1) The area of a parallelogram is equal to half the product of its diagonals.
2) The sum of the angles of a right triangle is 90 degrees.
3) The bisectors of a triangle intersect at a point that is the center of a circle inscribed in the triangle.
In response, write down the number of the selected statement.

Module "Real Mathematics"

14 . Chicken eggs, depending on their mass, are divided into five categories: the highest, the best, the first, the second, the third. Using the data presented in the table, determine which category an egg weighing 35.9 g belongs to. www.site

1) selected 2) first 3) second 4) third

15 . The graph shows the change in air temperature over three days. The date and time are indicated horizontally, the temperature value in degrees Celsius is indicated vertically. Determine from the graph the highest air temperature on December 18. Give your answer in degrees Celsius.

16 . At the beginning of the year, the number of subscribers of the Vostok telephone company was 800 thousand people, and at the end of the year there were 880 thousand people. By what percent did the number of subscribers of this company increase during the year?

17 . The figure shows a wheel with five spokes. How many spokes are in a wheel in which the angle between any adjacent spokes is 24°?

18. The diagram shows the distribution of the number of users of some social network by country. In total, this social network has 9 million users.

Which of these statements wrong?
1) There are more users from Paraguay than users from Brazil.
2) Users from Argentina are less than a third of the total number of users.
3) There are more users from Paraguay than users from Denmark.
4) There are less than 4 million users from Brazil.

In response, write down the numbers of the selected statements without spaces, commas, or other additional characters.

19 . The taxi company currently has 15 free cars: 4 black, 3 yellow and 8 green. On a call, one of the cars left, which happened to be closest to the customer. Find the probability that a yellow cab will arrive.

20 . The area of a quadrilateral can be calculated by the formula , where and are the lengths of the diagonals of the quadrilateral, is the angle between the diagonals. Using this formula, find the length of the diagonal if , , and .

Module "Algebra"

21 . Solve System of Equations .

22 . There are two vessels containing 4 kg and 16 kg of acid solution of various concentrations. If you merge them together, you get a solution containing 57% acid. If we drain equal masses of these solutions, then the resulting solution will contain 60% acid. How many kilograms of acid are contained in the first solution?

23 . Plot the Function and determine for what values the line has exactly one common point with the graph.

Module "Geometry"

24 . A line parallel to side AC of triangle ABC intersects sides AB and BC at points M and N, respectively. Find BN if MN is 15, AC is 25 and NC is 22.

25 . The bases BC and AD of the trapezoid ABCD are 8 and 32 respectively, BD is 16. Prove that triangles CBD and BDA are similar.

26 . In triangle ABC, the bisector BE and the median AD are perpendicular and have the same length equal to 36. Find the sides of triangle ABC.

Answers

1	-1,95
2	2
3	1
4	0
5	312
6	-4725
7	255
8	4
9	0,65
10	8
11	12
12	0,75
13	3
14	4
15	1
16	10
17	15
18	14
19	0,2
20	11
21	(4;2),(4;-2)
22	2,6
23	-5;-4;4
24	24
25
26

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OGE 2017. Mathematics. Three modules. 30 variants of typical test tasks. Ed. Yashchenko I.V.

OGE 2017. Mathematics. Three modules. 30 variants of typical test tasks. Ed. Yashchenko I.V.

Model 1 in Mathematics Yashchenko

Task Conditions

Answers

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