Using the data presented. Problem solving
1
The table shows the standards for jumping from a place for students in grade 11.
What mark will get the girl who jumped 177 cm?
1) mark “5”
2) mark “4”
3) mark “3”
4) the norm is not fulfilled
2
The table shows the distances from the Sun to the four planets of the Solar system. Which of these planets is farther than the others from the sun?
1) Venus
2) Mars
3) Saturn
4) Jupiter
3
The table shows the fines established on the territory of Russia from September 1, 2013 for exceeding the maximum allowed speed recorded using automatic fixation.
What penalty should a car owner pay, whose fixed speed was 95 km / h on a road section with a maximum allowed speed of 60 km / h?
1) 500 p.
2) 1000 p.
3) 2000 p.
4) 5000 p.
4
Scientist Ivanov leaves Moscow for a conference at St. Petersburg University. The conference starts at 10:00. The table shows the schedule of night trains Moscow-St. Petersburg.
The journey from the station to the university takes an hour and a half. Indicate the number of the latest train (at the time of departure) of the train that suits the scientist.
1) 026A
2) 002A
3) 038A
4) 016A
5
Chicken eggs, depending on their weight, are divided into five categories: highest, selected, first, second, third. Using the data presented in the table, determine to which category an egg weighing 73.4 g belongs.
1) higher
2) selective
3) second
4) the third
6
During the game, the jury gave the following ratings to the teams for participating in competitions:
For each team, points for all competitions are added up; the winning team is the team that scored the most points. What is the total score of the team that finished last?
7
The table shows information about the largest cities in Russia (according to data for 2014). The area of \u200b\u200bwhich of these cities is the third largest? In response, indicate the population of this city (in people per sq. M.)
| City | Population (thousand people) | Area (sq. Km) | Density (people per sq. Km) |
|---|---|---|---|
| Yekaterinburg | 1412 | 491 | 2866 |
| Kazan | 1191 | 425 | 1560 |
| Moscow | 12108 | 2511 | 4823 |
| Nizhny Novgorod | 1273 | 410 | 3100 |
| Novosibirsk | 1548 | 506 | 3961 |
| Omsk | 1166 | 573 | 1968 |
| Rostov-on-Don | 1110 | 349 | 3167 |
| Samara | 1172 | 541 | 2164 |
| St. Petersburg | 5132 | 1439 | 3566 |
| Chelyabinsk | 1169 | 500 | 2254 |
8
The table shows the income and expenses of the company for 5 months.
Using the table, put in line with each of the indicated time periods the characteristic of income and expenses.
In the response, indicate the values \u200b\u200bin the order: ABVG
9
Vasya decided to visit the amusement park. Information about tickets for attractions is presented in the table. Some tickets allow you to visit two attractions at once.
Using the table, select tickets so that Vasya visits all four attractions: Ferris wheel, fear room, laughter room, circuit, and the total ticket price does not exceed 1000 r. In the response, indicate in ascending order any one set of ticket numbers without spaces, commas or other additional characters.
The new price for the washing machine is 0.95 from the previous one. How much has the price of a washing machine decreased? Pears and apple trees grow in the garden. Pears make up 2/5 of all trees. How many percent of all trees are apple trees? Relate fractions that express fractions of a certain value, and the corresponding percentages. 1) 50% 2) 80% 3) 75% 4) 8%
During the seasonal sale, a jacket worth 3200 rubles. discounted by 20%. Find a new jacket price. Goods on sale were discounted by 20%, while it began to cost 680 p. How much did the goods cost before the sale? In January, the price of the goods was x rubles. In February, it decreased by 20%. What is the new price of the item?
Several varieties of sweets were brought to the store. Using the table, find how many percent of all sweets are “Fun” sweets? Variety of sweets “Kid” “Fun” “Lemon” Amounts in kg
In the garden, 3 teams of schoolchildren picked apples. Using the table, find how many percent of all apples were collected by students of the 2nd brigade? Team number 123 Amount in kg
Eugene collects stamps on three topics: "Animals", "Plants", "Monuments of Architecture". Using the data in the table below, find how many percent of the entire collection are stamps on the topic "Animals"? Theme “Plants” “Animals” “Monuments of architecture” Number of stamps
The table shows the distribution of the number of inhabitants of the village "Star" depending on their gender and age. Determine how many percent of all residents of the village are men under 30? Age and gender of residents Women under 30 years old Men under 30 years old Women over 30 years old Men over 30 years old Number of inhabitants
In stores A and B, prices in January were the same. The change in prices over the next four months is shown in the table. Compare the prices in these stores in May: which of them has lower prices and by what percentage? february march by 50% 2.5 times the mind. 2 times Vuv. 2 times the mind. 2.5 times SW. 40% mind. 20%
The table shows the cost of painting ceilings. Using the data presented in the table, determine what the cost of work will be if the ceiling area is 90 m2, the color of the ceiling is green and there is a seasonal discount of 10%. ” Ceiling color Price in rubles per 1sq.m (depending on the area of \u200b\u200bthe room) up to 10sq.mot11 to 30from 31 to 60 over 60 White color
Standings RM -15
1. Payment for electricity consumption is carried out on a two-tariff meter. The tariff depends on the time of day. The total payment amount consists of the amounts for each of the two tariffs. The receipt for payment contains the following table.Calculate the total payment amount for the electricity consumption indicated in the table.
2. During sudden braking, the distance traveled by the vehicle to a complete stop (braking distance) depends on the speed at which the vehicle was moving. The figure shows a graph of this relationship. The horizontal axis represents speed (in km / h), and the vertical axis represents the stopping distance (in meters). Determine from the schedule what the braking distance of a car that moves at a speed of 70 km / h will be. Give the answer in meters.
3.
The graph shows the dependence of atmospheric pressure (in millimeters of mercury) on altitude (in kilometers). At what altitude (in km) does a balloon fly if the barometer located in the basket of the balloon shows a pressure of 540 millimeters of mercury?
4.
The graph shows the dependence of engine torque on the number of revolutions per minute. The number of revolutions per minute is plotted on the abscissa axis, and the torque in N · m is plotted on the ordinate axis. How much N · m increased torque if the engine speed increased from 1000 to 1500 revolutions per minute?
5.
The table shows the results of two semifinal races at a distance of 60 m. In the final race there are 6 participants. From each semifinal, two athletes go to the finals, having shown the first and second results. To them are added two more athletes who have shown the best time among all the other participants in the semifinals.
Record in response the numbers of athletes who did not make it to the finals.
6. The diagram shows some of the largest countries in terms of area. How much is approximately the area of \u200b\u200bthe United States more than the area of \u200b\u200bSudan? (Round off the answer to the nearest integer.)
7. The company offers a choice of two different tariffs for paying for telephone calls: tariff A and tariff B. For each tariff, the dependence of the cost of the conversation on its duration is shown graphically. How long will 550 rubles last if tariff B is used?
8.
The figure shows a graph of dependence
amplitudes of forced vibrations from the frequency of vibrations. The amplitude (in m) is plotted along the vertical axis, and the oscillation frequency (in Hz) along the horizontal axis. From the figure, determine the oscillation frequency if the amplitude was 3 m.
9. The table shows the cost of painting ceilings.
Ceiling colorPrice in rubles per 1 m 2 (depending on the area of \u200b\u200bthe room)
up to 10 m 2
from 11 to 30 m 2
from 31 to 60 m 2
over 60 m 2
white
105
color
120
100
Using the data presented in the table, determine what the cost of work will be if the ceiling area is 40 m 2 , the ceiling is colored and there is a seasonal discount of 10%. Indicate the answer in rubles.
10. The graph shows how many people registered from December 25, 2012 to February 13, 2013 as participants in the conference. The horizontal indicates the number of months, and the vertical indicates the number of people. How many times has the number of registrants increased from January 4 to February 3?
12.
When the flashlight is in operation, the battery gradually discharges, and the voltage in the electric circuit of the flashlight drops. The figure shows the dependence of the voltage in the circuit on the operating time of the flashlight. On the horizontal axis, the flashlight operating time in hours is marked, on the vertical axis - voltage in volts. Determine from the figure how many volts the voltage drops in 15 hours of operation of the flashlight.
14. The diagram shows some of the largest countries in terms of population.
The population of which state is about 6 times less than the population of China? In response, write the population of this state in million people.
15. During a chemical reaction, the amount of the starting material (reagent) that has not yet entered into a reaction gradually decreases over time. In the figure this dependence is represented by a graph. The time in minutes elapsed since the start of the reaction is plotted on the abscissa axis, and the mass of the remaining reactant that has not yet reacted (in grams) on the ordinate axis. Determine from the schedule how many grams of reactant reacted in three minutes?
Option No. 4379352 (offset RM-15)
p / proom
A type
Your Answer
Correct answer
311511
Not decided
606,1
322042
Not decided
311686
Not decided
2,5
322173
Not decided
311504
Not decided
315197
Not decided
314788
Not decided
220
311377
Not decided
337762
Not decided
3240
316376
Not decided
311401
Not decided
0,6
315200
Not decided
215
206196
Not decided
Exam RM - 18
1.
The store sells t-shirts in five sizes: XS, S, M, L and XL. January sales data are presented in a pie chart.
Which statement regarding the T-shirts sold in January is incorrect if a total of 150 such T-shirts were sold in January?
1) The least sold were XS t-shirts.
2) More than half of T-shirts sold are T-shirts of sizes M or L.
3) Less than half of all T-shirts sold are T-shirts in sizes S or M.
4) Less than 40 pieces were sold in XL size t-shirts.
2. Pupils of grades 5–8 go to the mathematical circles of the city. The distribution of participants in mathematical circles is presented in a pie chart.
What statement about the members of the circles is true if all of them are visited by 354 students?
1) fifth graders do not go to circles
2) eighth graders walk more than seventh graders
3) more than half of the participants in the circles are not in seventh grade
4) sixth graders less than 88 people
3. Which of the following pie charts shows the distribution of ocean areas in the World Ocean, if the Pacific Ocean occupies about 48% of the entire World Ocean, the Atlantic - 26%, the Indian - 21% and the Arctic - 5%?
4.
2
) countries of the world.
Which of the following statements is true?
1) Sudan is one of the seven largest countries in terms of area of \u200b\u200bthe world.
2) The area of \u200b\u200bthe United States is 10 million km 2 .
3) The area of \u200b\u200bAustralia is greater than the area of \u200b\u200bCanada.
4) The area of \u200b\u200bRussia is approximately twice that of Brazil.
In the response write down the number of the selected statement.
5.
The house has one-room, two-room, three-room and four-room apartments. Data on the number of apartments is presented in a pie chart.
What statement about the apartments in this house is true if there are 120 apartments in the house?
1) There are more one-room apartments than two-room apartments.
2) The smallest three-room apartments.
3) One-room apartments no more than 25% of the total number of apartments in the house.
4) Two-room apartments less than 40.
6. The chart shows the age composition of the population of Japan. Determine from the diagram which age category is the smallest.
1) 0−14 years 2) 15−50 years 3) 51−64 years 4) 65 years or more
7. Which of the following pie charts shows the distribution of grades in the math test in the 8th grade of the school, if out of all grades in the class of quintuples, about 35%, quartet - about 25%, and triples - about 23%?
10.
Students in grades 5–8 attend the math group. Data on the number of schoolchildren attending the circle is presented in a pie chart. What statement regarding the members of the circle is true if all 60 students attend it?
1) More than a third of eighth-graders.
2) Fifth graders are less than seventh graders.
3) Seventh graders more than 7 people.
4) Sixth graders more than 50% of all students.
11.
The diagram shows the distribution of the number of users of a certain social network by countries of the world. In total, this social network has 9 million users.
Which of the following statements is false?
1) There are more users from Russia than users from Belarus.
2) There are less than one third of the total number of users from Ukraine.
3) There are more users from Belarus than users from Denmark.
4) There are less than 4 million users from Russia.
13.
The diagram shows the nutrient content of cream breadcrumbs. Use the chart to determine the extent to which your carbohydrate content is.
* - water, vitamins and minerals are among other things.
1) 45-55% 2) 55-65% 3) 65-75% 4) 75-80%
15. The diagram shows the seven largest territories by area (in million km 2 ) countries of the world. Which of the following statements is false?
1) Canada occupies the second place in the world in terms of area.
2) The territory of Australia is 7.7 million km 2 .
3) The area of \u200b\u200bChina is greater than the area of \u200b\u200bCanada.
4) US area is 1 million km more than Brazil 2 .
Option No. 4380205 (Credit RM - 18)
p / proom
A type
Your Answer
Correct answer
325314
Not decided
311906
Not decided
325886
Not decided
315179
Not decided
325320
Not decided
340899
Not decided
311950
Not decided
325324
Not decided
315170
Test RM-19
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. A IN and with the teamFROM A .
12. does not flow ?
13.
14.
15.
Offset RM - 19
1. There are 25 tickets on the exam; Sergey did not learn 3 of them. Find the likelihood that he will come across a learned ticket.
2. Kolya chooses a three-digit number. Find the probability that it is divisible by 5.
3. Masha’s TV has broken and shows only one random channel. Masha turns on the TV. At this time, comedy films are shown on three of the twenty channels. Find the likelihood that Masha will fall on a channel where the comedy does not go.
4. On a plate are 12 pies: 5 with meat, 4 with cabbage and 3 with cherries. Natasha randomly chooses one pie. Find the likelihood that he will be with a cherry.
5. In every tenth can of coffee, according to the terms of the promotion, there is a prize. Prizes are randomly assigned to banks. Varya buys a can of coffee in the hope of winning a prize. Find the likelihood that Varia will not find a prize in her bank.
6. On average, out of 50 working flashlights, two are faulty. Find the probability of buying a working flashlight.Round the result to the nearest hundredth.
7. On average, out of every 80 batteries sold, 76 are charged. Find the likelihood that the purchased battery is not charged.
8. For the exam, tickets with numbers from 1 to 50 were prepared. What is the probability that a randomly taken ticket has a unique number?
9. The bag contains tokens with numbers from 5 to 54 inclusive. What is the likelihood that a randomly extracted token from a bag contains a two-digit number?
10. The box contains 14 tea bags with black tea and 6 tea bags with green tea. Pavel randomly takes out one bag. What is the likelihood that this is a green tea bag?
11. Before the start of a football match, the referee throws a coin to determine which team will be the first to own the ball. TeamA must play two matches - with the teamIN and with the teamFROM . Find the likelihood that in both matches the team will own the first ballA .
12. Out of 1600 packets of milk, an average of 80 are leaking. What is the likelihood that a randomly selected packet of milkdoes not flow ?
13. Determine the probability that an odd number of points will drop out when you roll a dice.
14. Determine the likelihood that when you roll the die, the number of points dropped is no more than 3.
15. The stationery store sells 100 pens, of which 37 are red, 8 are green, 17 are purple, there are still blue and black, they are equally divided. Find the chance that Alice will randomly pull out a red or black pen.
MCOU "Novokayakentsky secondary school"
from. Novokayakent
Kayakent district, Republic of Dagestan
(for students in grades 9)
MCOU "Novokayakentskaya secondary school"
Umalatova Ravganiyat Biybulatovna
v. Novokayakent
2017 year
Explanatory note
This material is OGE. Task 30. "The ability to work with the statistical data presented in the table" is recommended for students in grade 9. The material includes questions with working with statistical data presented in the table, with answers to questions given in the tasks. This material can be used to prepare for the OGE. The work includes 10 questions.
Tasks: test the knowledge and ability of students to work with the static data presented in the table, with the answer to the questions given in the tasks.
Student Activities : Students writing tests.
Teacher activities : providing each student with a test text sheet. An explanation of the progress of the work. Verification of work. Analysis of the responses.
Equipment : handout with tests.
OGE. Task 30. “Ability to work with statistical data presented in the table”
1. Using the table “Respiratory surface of gills in fish” and knowledge of the biology course, answer the following questions.
Respiratory surface of gills in fish
What class are the fish species listed in the table?
What are gill petals in gills for?
What explains the fact that the flounder has a smaller surface area of \u200b\u200bthe gills than the perch, although the mass of the flounder is larger?
2. Using the table “Connection between the growth of the Earth’s population and the extinction of animal species”, answer the following questions
The relationship between the growing population of the Earth and the extinction of animal species.
World population growth from 1650 to 1950,billion people
The number of extinct animal species over 50 years (1650 to 1950)
Year
Number of population
Mammals
Birds
1650
0,4
1700
0,5
1750
0,7
1800
1850
1,25
1900
1,7
1950
2,5
1) In what years was the population growth the fastest?
2) What can be said about the comparative rates of extinction of birds and mammals?
3) What reasons may be associated with an increase in the number of exterminated animal species by 1950?
3. Using the table "Results of the experiment on the survival of butterflies of different colors", answer the following questions.
The results of an experiment on the survival of butterflies of different colors.
Unpolluted(rural)
Released
469
473
Caught by scientists
120
Eaten by birds
335
Polluted
(city)
Released
137
447
Caught by scientists
Eaten by birds
How many gray butterflies did the scientist release in rural areas, and how many in urban?
What kind of butterflies did birds eat more in the countryside?
What hypothesis did the scientist try to verify by observing bird catching of butterflies?
4. Using the table “Composition of inhaled and exhaled air”, answer the following questions.
Composition of inhaled and exhaled air
What gas that is part of the air is not involved in breathing?
What gas concentration changes as much as possible during breathing?
Why is the percentage of oxygen in exhaled air reduced?
5. Using the table “The chemical composition of sea water in blood serum”, answer the following questions.
The chemical composition of seawater in blood serum.
What percentage of chemical elements is higher in seawater than in blood serum?
What metal element prevails in seawater and blood serum?
How is blood serum different from plasma?
6. Using the table “Relative content of basic chemical elements”, answer the following questions.
The relative content of basic chemical elements
Which of the objects listed in the table (groups of objects) have a similar chemical composition?
What substance reaches the maximum value in living organisms?
Which protein molecule contains iron ions?
7. Using the table “Dependence of the oxygen capacity of mammalian blood on altitude”, as well as using knowledge from a biology course, answer the following questions.
Dependence of the oxygen capacity of mammalian blood on altitude.
1) For which of the listed mammals do habitats extend to an altitude of 3.6 km?
2) What is the relationship between the height at which the animal lives and the hemoglobin content (in g%)?
3) What is the function of red blood cells in mammals?
8. Using the table “The influence of the main factors on human health and life”, as well as using knowledge from a biology course, answer the following questions.
“The influence of the main factors on human health and life”
How much does heredity affect human health and life?Which of the following diseases is most associated with a person’s lifestyle?
What should students do at school to reduce the health effects of this risk factor?
9. Using the table "Fish Reproduction", as well as using knowledge from a biology course, answer the following questions.
"Reproduction of fish"
What type of fish has the largest average diameter of eggs?What kind of fish are caught in immature age?
Why, with high fecundity, the abundance of most non-commercial species remains relatively constant?
10. Using the table “Comparative composition of blood plasma, primary and secondary urine of the human body”, as well as using knowledge from a biology course, answer the following questions.
Comparative composition of blood plasma, primary and secondary urine of the human body.
1) What substance concentration remains practically unchanged by the conversion of blood plasma into secondary urine?
2) What substance and why is it absent in the composition of secondary urine compared to primary?
Sources of information:
1. Biology. General patterns. 9 cl. S.G. Mamontov, V. B. Zakharov, N.I. Sonin. -M.: Bustard, 2002.288 s.
2. OGE 2017. Biology: thematic training tasks: Grade 9 /
G.I. Lerner.- Moscow: Eksmo, 2016 .- 272 p.
3. OGE. Biology: Typical Exam Options: About -32 Options / Ed. V.S. Rokhlova.-M.: Publishing House "National Education", 2016.- 288с.
4. OGE. Biology: Typical Exam Options: About -30 Options / Ed. V.S. Rokhlova.-M.: Publishing House "National Education", 2017.- 400p.
§ 1 Task No. 1
In this lesson, we will look at solutions to basic-level text problems from math final exam tests conducted in different years.
A sporting goods store buys balls at a wholesale price of 320 rubles per ball and sells it at a 20% mark-up. How much change will a coach of a children's sports club receive from 5,000 rubles if he has acquired 9 goals?
DECISION. We will solve this problem in an arithmetic way, applying the method of solving text problems with interest. We determine the proportion of the new price of the ball from the old. The concept of the word “margin” implies an increase in the price, which means 100% + 20%. We get 120% or a fraction expressed in decimal 1.2. To answer the main question of the problem, it is necessary to subtract the cost of buying balls from 5,000 rubles. Determine the amount of money spent on the purchase. To do this, find the price of the ball with an extra charge of 20% and multiply the result by 9. We have 320 · 1.2 · 9 \u003d 3456 rubles that the coach paid for the balls. Now we will answer the main question of the task: the coach of the children's sports club with 5,000 rubles will receive the change from 5000 to 3456 \u003d 1544 rubles. Answer: 1544 rubles.
§ 2 Task No. 2
At the time of the taxi call, the company “Taxi-Express” had 10 free cars: 3 black, 4 white, 2 yellow and one green. On call, one of the cars left, accidentally finding itself closest to the place of order. Find the likelihood that a white taxi will be ordered.
DECISION. We solve the problem in an arithmetic way, applying the method of solving text problems for probability. To answer the main question of the problem, according to the definition of probability, it is necessary to divide the number of favorable outcomes by the number of all possible outcomes.
Let event A - by order, a white taxi arrive. Then the number of favorable outcomes m is 4, since by the condition of the problem there were 4 free white taxis. The number of all possible outcomes of n is 10, since, according to the condition of the problem, 10 companies were free at the time of the call. Substituting the selected numerical data of the problem into the formula for calculating the probability, we have:
We answered the main question of the problem: the probability of arrival by calling a white taxi is 0.4. Answer: 0.4
§ 3 Task No. 3
The table shows the cost of painting ceilings.
Using the data presented in the table, determine what the cost of the work will be if the ceiling area is 33 m2, the color of the ceiling is beige and a seasonal discount of 15% applies. Indicate the answer in rubles.
DECISION. We will solve this problem in an arithmetic way, applying the method of solving text problems by percent. According to the task data, there are 4 groups of conditions for painting the ceiling depending on the area of \u200b\u200bwork performed and the ceiling area of \u200b\u200b33 m2. The table shows that for solving the problem, a data group is suitable for an area from 31 m2 to 60 m2, where painting 1 m2 with ceiling white paint costs 70 rubles, and color - 90 rubles. Since the estimated color of the ceiling is beige, to solve the problem, you should stop at a rate of 90 rubles per 1 square meter of ceiling. The concept of the word "discount" implies a reduction in price, which means that you need 100% - 15%. We get 85% or 0.85 in fractional terms. To answer the main question of the problem, it is necessary to multiply the work price of 90 rubles by a fraction of 0.85 and multiply the result by the area of \u200b\u200bthe painted ceiling 33 m2. 90 · 0.85 · 33 \u003d 2524.5 We get 2524 and a half rubles the cost of work on painting ceilings. Answer: 2524.5 rubles.
§ 4 Task No. 4
There are two solutions. The first contains 10% salt, the second - 30% salt. From these two solutions, a third solution was obtained, weighing 200 kg, containing 25% salt. How many kilograms is the mass of the first solution less than the mass of the second?
DECISION. We solve this problem in a schematic way. We write down the percentages of the mixed first and second salt solutions in a column under each other in increasing order of 10% and 30%. In the center of the second column, next we write the percentage of the new third solution of 25%. In the third column, from top to bottom, write the difference in the number of the last row of 30 and 25, and then the difference - 25 and the number of the first row of 10. Thus, in the third column, the results of the module of the difference in the numbers of the first column and 25, i.e. 5% and 15%, are written from top to bottom. Divide these numbers by their largest common divisor - by 5, and write the results in the fourth column according to their lines from top to bottom. The result is a column with numbers 1 and 3. These numbers determine the proportion of the first and second salt solutions of the corresponding concentration in the third solution. Thus, we have that the third solution accounts for 4 parts. According to the conditions of the problem, the third solution has a mass of 200 kg. The main question of the problem: how many kilograms is the mass of the first solution less than the mass of the second? To answer it, we find the difference of the parts of the second and first solutions in the third solution. We have 3 - 1 equals 2 m. It turned out that the difference of the parts of the solutions is 2 times less than their sum, since 4 divided by 2 is equal to 2. Therefore, the mass difference of the second and first solutions is 2 times less than the mass of the third solution, that is, 200 kg divided by 2 or 100 kg. We answered the main question of the problem: the mass of the first solution is less than the mass of the second solution by 100 kg.
Answer: per 100kg.
Thus, in this lesson, we solved basic-level text problems from tests of final math exams conducted in different years.
List of used literature:
- A.G. Mordkovich, P.V. Semenov. Algebra. Grade 9. In 2 parts. Part 1. The textbook. (GEF) 16th edition, amended. - M.: Mnemosyne, 2013.
- A.G. Mordkovich, P.V. Semenov. Algebra. Grade 9. In 2 parts. Part 1. The book of problems. 16th edition, revised. - M.: Mnemosyne, 2013.
- A.G. Mordkovich, P.V. Semenov. Algebra. Grade 9. Methodical manual for the teacher. M .: Mnemosyne, 2013.
- A.G. Mordkovich, N.P. Nikolaev. Algebra. Grade 9. In 2 parts. Part 1 - a textbook. (GEF) Textbook for classes with in-depth study of mathematics. - M.: Mnemosyne, 2014.
- A.G. Mordkovich. Teaching Algebra. Methodical manual for the teacher. 8-9 grade. - M.: Mnemosyne, 2014.
Used Images:
