Dear friends! There are also a number of simple tasks with graphs and charts for you. Tasks about the daily amount of precipitation and the average monthly temperature. All tips and points that you need to pay attention to are given in the course of the solution. Consider examples:

26871 (27523). In the figure, bold dots show the daily amount of precipitation that fell in Kazan from February 3 to February 15, 1909. The dates of the month are indicated horizontally, and the amount of precipitation on the corresponding day, in millimeters, is indicated vertically. For clarity, bold dots in the figure are connected by a line. Determine from the figure, on what date did 5 millimeters of precipitation fall for the first time? How many days did it not rain during this period?

We carefully look, starting from the first day, the amount of precipitation. For the first time, 5 mm of precipitation fell on the 11th.

*Please note that the indicated amount of precipitation may fall twice or more. The question can be posed, for example, as follows: determine from the figure what date the second (third) time 5 millimeters of precipitation fell.

The figure shows that precipitation did not fall on the fifth, eighth, ninth and twelfth of February. Just 4 days.

Answer: 11 and 4

26876 (25528). The figure shows the daily amount of precipitation that fell in Tomsk from 8 to 24 January 2005. The dates of the month are indicated horizontally, and the amount of precipitation on the corresponding day, in millimeters, is indicated vertically. For clarity, bold dots in the figure are connected by a line. Determine from the figure what the greatest amount of precipitation fell in the period from January 13 to 20. Answer (give in millimeters). Determine from the figure how many days more than 2 millimeters of precipitation fell.

Here is an important point - immediately visually limit the chart to the 13th and from the 20th, you can close these sections of the chart with a piece of paper.

It can be seen that during the specified period, the largest amount of precipitation was 3 mm (it was on the 14th).

Answer: 3

We list the days on which more than 2 mm of precipitation fell (we look carefully from the very first day of the specified period), these are: January 8, 12 and 14.

Only 3 days.

Answer: 3

26878. The figure shows the average daily air temperature in Brest every day from July 6 to 19, 1981. Dates of the month are indicated horizontally, temperatures in degrees Celsius are indicated vertically. For clarity, bold dots are connected by a line. Determine from the figure the difference between the highest and lowest average daily temperatures for the specified period. Give your answer in degrees Celsius.

The highest temperature for the specified period was 26 degrees Celsius (on the 19th), and the lowest was 16 degrees (on the 16th).

The temperature difference is 26 -16 \u003d 10 degrees.

Answer: 10

27510. The figure shows the average monthly air temperature in Sochi for each month in 1920. Months are indicated horizontally, temperatures are indicated vertically in degrees Celsius. For clarity, bold dots are connected by a line. Determine from the figure the lowest average monthly temperature in the period from May to December 1920. Give your answer in degrees Celsius.

*Immediately note that the price of division of the vertical scale is 2 degrees, this is important.

May is the fifth month, December is the twelfth. We single out this period for analysis (from the 5th to the 12th months) and determine the lowest average monthly temperature. It can be seen that it was in November (this is the 11th month) and amounted to 6 degrees.

Answer: 6

263597. The figure shows the average daily air temperature in Brest every day from 6 to 19 July 1981. Dates of the month are indicated horizontally, temperatures in degrees Celsius are indicated vertically. For clarity, bold dots are connected by a line. Determine from the figure what the temperature was on July 15. Give your answer in degrees Celsius.

Answer: 19

263598. The figure shows the average daily air temperature in Brest every day from 6 to 19 July 1981. Dates of the month are indicated horizontally, temperatures in degrees Celsius are indicated vertically. For clarity, bold dots are connected by a line. Determine from the figure how many days during the specified period the temperature was exactly 21 0 FROM.

During the specified period, the temperature was exactly 21 degrees Celsius:

10th, 11th, 12th and 14th.

Just 4 days.

Answer: 4

27527. The figure shows the daily amount of precipitation that fell in Murmansk from 7 to 22 November 1995. The dates of the month are indicated horizontally, and the amount of precipitation on the corresponding day, in millimeters, is indicated vertically. For clarity, bold dots in the figure are connected by a line. Determine from the figure how many days from this period less than 3 millimeters of precipitation fell.

We list the days on which less than 3 mm of precipitation fell (we look carefully from the very first day of the specified period), these are:

7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22.

Just 14 days. Answer: 3

That's all. Good luck to you!

Sincerely, Alexander Krutitskikh.

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3 UDC: LBC 22.1y72 Y11 Module course "I will pass the OGE!" created by a team of authors from among the members of the Federal Commission for the Development of Control Measurement Materials and experts from the OGE. It includes Toolkit“Method of preparation. Keys and answers” ​​and the manual “Workshop and diagnostics”. Tutorial is designed to prepare students in grades 8-9 for the state final certification. The manual activates the work of students in the following areas: replenishment, updating and systematization of knowledge on all content elements tested at the OGE; exercise in practical application knowledge when performing standard examination tasks. The manual is addressed to teachers, schoolchildren and their parents to check / self-check the achievement of requirements educational standard to the level of training of graduates. Educational edition I will pass the OGE! Modular course Mathematics Practicum and diagnostics Textbook for educational organizations Head of the publishing project, editor-in-chief O. G. Kotlyar Head of the editorial office of mathematics and computer science T. A. Burmistrova Deputy head of the editorial office of mathematics and computer science T. Yu. Akimova Project coordinator M. A. Efremova Editor N. N. Sorokina Design A. G. Bushin Computer graphics I. V. Gubina, A. G. Vyunikovskaya, O. Yu. Tupikina Computer layout and technical editing E. M. Zavalei Proofreaders I. A. Grigalashvili, N. A. Erokhina, O. N. Leonova, I. V. Chernova Tax benefit All-Russian classifier products OK Ed. persons. Series ID from Signed for printing Format / 16. Offset paper. Headset SchoolBookCSanPin. Offset printing. Uch.-ed. l. 26.34. Circulation copies. Order. Joint-stock company"Publishing house" Enlightenment ", Moscow, 3rd proezd of Maryina grove, 41. Printed in JSC "First Exemplary Printing House", branch "ULYANOVSK PRINTING HOUSE", Ulyanovsk, st. Goncharova, 14. ISBN Enlightenment Publishing House, 2017 Artistic design. Prosveshchenie Publishing House, 2017 All rights reserved

4 Foreword Study guide “I will pass the OGE! Modular course. Maths. Practicum and Diagnostics” was prepared with the scientific and methodological support of the Federal Institute of Pedagogical Measurements (FIPI) and is intended to prepare students in grades 7–9 to successfully pass the OGE in mathematics. The manual consists of three modules: "Real Mathematics", "Algebra", "Geometry", corresponding to the modular structure of the OGE in mathematics. The tasks of each module are divided into double lessons on various topics and, along with the main block of tasks, contain tasks for repetition on other topics. Clean problem solving is not required. Checking tasks with a short answer is made only by the answer. Solutions to tasks with a detailed answer are recorded in a separate notebook. Most of the tasks of the manual are similar to real ones OGE assignments in mathematics and adapted to their format. The answer to such problems is an integer, the final decimal or a set of numbers that establishes a correspondence between the data in the problem statement and statements. The answer entry in the decision form can only contain numbers, a comma, a minus sign. Each character is written in a separate cell. No other characters, including units of measure, are recorded. Checking answers to tasks with a short answer of a real exam is carried out by a computer after scanning the answer sheet and comparing the scan results with the correct answers. Therefore, the numbers in the answer sheet should be written legibly (so that, for example, 1 and 7 or 8 and B are recognized correctly). If there are additional characters, the answer is recognized as incorrect. If the result of solving problem 1 was common fraction, for example, then before writing the answer to the form, it must be converted to decimal, i.e., write 0.125 in the answer, using a separate cell to write each character (in this case exactly 6 cells). An answer recorded in a different form will be recognized as incorrect. Systematic lessons on the manual (even in the case of significant gaps in knowledge at the beginning of working with it) provide an opportunity to form stable skills for solving the main types of tasks necessary for application in real life. life situations and successful passing of the OGE in mathematics in order to continue education at the senior level high school or in college. Such skills will allow you to successfully overcome the minimum threshold for the OGE in mathematics. Of course, the manual also includes material, the assimilation of which guarantees not only overcoming the minimum threshold, but also getting a higher grade for the OGE. Each lesson is aimed at a specific result and contains a sufficient number of tasks for high-quality preparation. The manual is intended both for use in the educational process in combination with any basic educational kit, and for extracurricular activities in preparation for the OGE.

5 4 MODULE "REAL MATHEMATICS" READING AND ANALYSIS OF DATA PRESENTED IN THE FORM OF TABLES Training work 1 1. The table shows the standards for jumping from a place for students of grade 11. Boys Girls Mark "5" "4" "3" "5" "4" "3" Distance (in cm) What mark will the girl get if she jumps 167 cm? 1) Mark "5" 2) Mark "4" 3) Mark "3" 4) The standard is not met 2. The table shows the distances from the Sun to four planets solar system. Which of these planets is closest to the Sun? Planet Venus Mars Saturn Jupiter Distance (in km) 1,) Venus 2) Mars 3) Saturn 4) Jupiter using automatic fixation. Exceeding the speed limit (in km/h) or more Amount of the fine (in r.) What fine must the owner of a car whose recorded speed was 90 km/h on a road section with a maximum speed limit of 40 km/h pay? 1) 500 rubles 2) 1000 rubles 3) 2000 r. 4) 5000 rubles

6 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 Saint Petersburg. 5 Train number Departure from Moscow Arrival in St. Petersburg 026А 22:41 06:32 002А 23:55 07:55 038А 22:42 06:40 016А 00:43 09:12 The journey from the station to the university takes an hour and a half. Specify the number of the latest (in terms of departure time) train that suits the scientist. 1) 026A 2) 002A 3) 038A 4) 016A 5. Chicken eggs, depending on their mass, are divided into five categories: the highest, selective, first, second, third. Using the data presented in the table, determine which category an egg weighing 82.2 g belongs to. Category Highest Weight of one egg (g) 75.0 and more Selected 65.0 74.9 First 55.0 64.9 Second 45, 0 54.9 Third less than 45.0 1) Highest 2) Choice 3) Second 4) Third 6. During the game, the jury gave the following marks to the teams for participating in the competitions: Team Points for the first competition Points for the second competition Points for the third competition A B C D For each team, the scores for all competitions are summed up, the winning team is the one with the most points in total. By how many points did team B beat the fourth-place team?

7 6 7. The table provides information about largest cities Russia (as of 2014). Which city has the sixth largest population? In your answer, indicate the population density of this city (in people per sq. km). City Population (thousand people) Area (sq. km) Density (persons per sq. km) Yekaterinburg Kazan Moscow Nizhny Novgorod Novosibirsk Omsk Rostov-on-Don Samara St. Petersburg Chelyabinsk The table shows the income and expenses of the company for 5 months . Month Income (thousand rubles) Expense (thousand rubles) July August September October November Using the table, match each of the indicated time periods with a characteristic of income and expenses. Period A) August B) September C) October D) November Characteristic 1) this month's expenditure is greater than the previous month's expenditure 2) the largest difference between income and expenditure 3) the largest income from August to November 4) income this month less than income in the previous In the table, under each letter, indicate the corresponding number. A B C D

8 9. Vasya decided to visit an amusement park. Information about tickets for attractions is presented in the table. Some tickets allow you to visit two attractions at once. 7 Ticket number Attractions Cost (rubles) 1 Fun room Panic room, fun room Autodrome, fun room Ferris wheel Ferris wheel, autodrome Autodrom 100 Using the table, select tickets so that Vasya visits all four attractions: Ferris wheel, fear room, room laughter, a circuit, and the total cost of tickets did not exceed 850 rubles. In your answer, indicate in ascending order any one set of ticket numbers without spaces, commas and other additional characters. 10. To process a summer cottage, a summer resident needs to purchase a shovel, chopper, pitchfork and rake. The store sells sets of tools, some sets consist of only one tool. Prices are shown in the table. Set Number Tools Cost (R. per item) 1 Pitchfork Chopper, Pitchfork Chopper Rake, Shovel Shovel Rake, Pitchfork 440 Using the table, assemble a complete set of necessary tools so that the total cost is the lowest. In the answer for the assembled kit, indicate in ascending order the numbers of the kits without spaces, commas and other additional characters.

9 8 Home (test) work 1 1. The table shows the standards for jumping from a place for students in grade 11. Boys Girls Mark "5" "4" "3" "5" "4" "3" Distance (in cm) What mark will the girl get if she jumps 177 cm? 1) Mark "5" 2) Mark "4" 3) Mark "3" 4) The standard is not met 2. The table shows the distances from the Sun to the four planets of the solar system. Which of these planets is farthest from the Sun? Planet Venus Mars Saturn Jupiter Distance (in km) 1,) Venus 2) Mars 3) Saturn 4) Jupiter using automatic fixation. Exceeding the speed limit (in km/h) or more Amount of the fine (in rivers) What fine must the owner of a car whose recorded speed was 95 km/h on a road section with a maximum speed limit of 60 km/h pay? 1) 500 rubles 2) 1000 rubles 3) 2000 r. 4) 5000 rubles 4. Scientist Petrov leaves Moscow for a conference at St. Petersburg University. The conference starts at 9:00. The table shows the schedule of night trains Moscow Saint Petersburg.

10 Train number Departure from Moscow Arrival in St. Petersburg 026А 22:41 06:А 23:55 07:55 038А 22:42 06:40 016А 00:43 09:12 The journey from the station to the university takes an hour and a half. Specify the number of the latest (in terms of departure time) train that suits the scientist. 1) 026A 2) 002A 3) 038A 4) 016A 5. Chicken eggs, depending on their mass, are divided into five categories: the highest, selective, first, second, third. Using the data presented in the table, determine which category an egg weighing 73.4 g belongs to. Category Highest Weight of one egg (g) 75.0 and more Selected 65.0 74.9 First 55.0 64.9 Second 45, 0 54.9 Third less than 45.0 1) Highest 2) Choice 3) Second 4) Third 6. During the game, the jury gave the following marks to the teams for participating in the competitions: Team Points for the first competition Points for the second competition Points for the third competition A B C D For each team, the scores for all competitions are summed up, the winning team is the one with the most points in total. How many points does the last place team have?

11 10 7. The table contains information about the largest cities in Russia (as of 2014). Which of the following cities has the third largest area? Enter the population of this city in your answer. City Population (thousand people) Area (sq. km) Density (persons per sq. km) Yekaterinburg Kazan Moscow Nizhny Novgorod Novosibirsk Omsk Rostov-on-Don Samara St. Petersburg Chelyabinsk The table shows the income and expenses of the company for 5 months . Month Income (thousand rubles) Expense (thousand rubles) March April May June July Using the table, match each of the indicated time periods with a characteristic of income and expenses. Period A) April B) May C) June D) July Characteristics 1) expenditure this month exceeded income 2) the smallest expenditure in the period from April to July 3) income this month is greater than in the previous 4) expenditure this month is greater than in the previous In the table, under each letter, indicate the corresponding number. A B C D

12 9. Venya decided to visit an amusement park. Information about tickets for attractions is presented in the table. Some tickets allow you to visit two attractions at once. 11 Ticket number Attractions Cost (rubles) 1 Ferris wheel, autodrome Panic room, fun room Fun room Autodrome, fun room Ferris wheel Autodrome 150 Using the table, select tickets so that Venya visits all four attractions: Ferris wheel, fear room, room laughter, a circuit, and the total cost of tickets did not exceed 1000 rubles. In your answer, indicate in ascending order any one set of ticket numbers without spaces, commas and other additional characters. 10. To process a summer cottage, a summer resident needs to purchase a shovel, chopper, pitchfork and rake. The store sells sets of tools, some sets consist of only one tool. Prices are shown in the table. Set number Tools Cost (r. per piece) 1 Rake Pitchfork, rake Shovel Chopper, rake Pitchfork, shovel Chopper 200 Using the table, assemble a complete set of necessary tools so that the total cost is the lowest. In the answer for the assembled kit, indicate in ascending order the numbers of the kits without spaces, commas and other additional characters.

13 12 Tasks for repetition 1. Find the average arithmetic numbers 6 and Find the arithmetic mean of the numbers 8, 7 and Find the arithmetic mean of the numbers 5, 4, 29, 40. Practice 2 1. To serve an international seminar, it is necessary to assemble a group of translators. Using the table, collect at least one group in which interpreters together speak all four languages: English, German, Spanish and French, and the total cost of their services does not exceed p. in a day. In your answer, indicate in ascending order any one set of translator numbers without spaces, commas and other additional characters. Interpreter's number Languages ​​Cost of services (rubles per day) 1 French, English German English, German French French, Spanish Spanish The table contains information about pizzas in the online store. Pizza number Ingredients / name Type Cost (R.) 1 “4 cheeses” Vegetarian Tomatoes, sweet peppers Vegetarian “Bolognese” Meat Chicken fillet, pineapple, cheese Meat Olives, mushrooms, tomatoes Vegetarian Chicken fillet, mushrooms, tomatoes Meat 580 Vitaly needs to buy three different pizzas so that among them there is at least one with mushrooms, at least one is vegetarian and at least one is meat. What pizzas should Vitaliy choose if he expects to spend on everything

14 more than 1250 rubles? In your answer, indicate in ascending order any one set of pizza numbers without spaces, commas and other additional characters. For a group of foreign guests, you need to buy 12 guides. The price of the guide and the terms of delivery of the entire purchase are shown in the table. Online store Guidebook price (rubles per item) Shipping costs (rubles) Additional conditions A No B C How much will the cheapest purchase option with delivery cost? Delivery is free if the order amount exceeds 3700 rubles. Delivery is free if the order amount exceeds 3500 rubles. 4. The ISP offers three tariff plans. Tariff plan Subscription fee Traffic fee "0" No 0.9 rub. for 1 MB "200" "900" 208 rubles. for 200 Mb of traffic per month 736 rubles. for 900 Mb of traffic per month 0.6 p. for 1 Mb over 200 Mb 0.5 p. for 1 Mb over 900 Mb The user assumes that his traffic will be 550 Mb per month and chooses the cheapest tariff plan. How many rubles will a user have to pay per month if his traffic is really 550 MB? 5. To transport 42 tons of cargo for 120 km, you can use the services of one of three carrier companies. The cost of transportation and the carrying capacity of vehicles of each carrier are indicated in the table. Carrier Cost of transportation by one car (r. per 10 km) Carrying capacity of one car (t) A B 400 5.5 C How many rubles will you have to pay for the cheapest transportation?

15 14 6. The table shows the results of Olympiads in physics and biology in 10 "A" class. Student number Score in physics Score in biology Commendation certificates are given to schoolchildren who have a total score in two Olympiads of more than 120 or at least one subject scored at least 65 points. In your answer, indicate in ascending order the numbers of students 10 "A" who scored less than 65 points in physics and received commendable letters, without spaces, commas and other additional characters. 7. The client wants to rent a car for a day for a trip of 600 km. In addition to the rental, the client is obliged to pay for fuel for the car for the entire trip. The price of diesel fuel is 25 rubles. per liter, gasoline 35 p. per liter, gas 20 r. per litre. How many rubles will the client pay for rent and fuel if he chooses the cheapest option? Vehicle Fuel Fuel consumption (l per 100 km) Rent (R. for 1 day) A Diesel B Gasoline C Gas Furniture Salon concludes contracts with furniture manufacturers. The contracts indicate what percentage of the proceeds from the sale of furniture goes to the income of the furniture salon. Producer Percentage of revenue received by the salon Notes "Alpha" 6.5 Products priced up to r. "Alpha" 2.5 Products priced over r. Beta 3.5 All Omicron products 5 All products

16 The price list shows prices for four buffets. Determine which buffet is most profitable for the salon to sell. In response, write down how many rubles will go to the salon's income from the sale of this buffet. 15 Manufacturer Product Price (r.) Alpha Buffet Ambrose Alpha Buffet Boleslav Beta Buffet Vyacheslav Omikron Buffet Mir The construction contractor plans to buy 20 tons of facing bricks from one of three suppliers. One brick weighs 5 kg. The price of a brick and the terms of delivery of the entire purchase are shown in the table. Supplier Brick price (r. per unit) Shipping cost (r.) Special conditions A No B C Delivery is free if the order amount exceeds R. Delivery with a 50% discount if the order amount exceeds r. How much will the cheapest purchase option with delivery cost? 10. An independent expert laboratory determines the rating of meat grinders based on a value coefficient equal to 0.01 of the average price P (in rub.), Functionality F, Quality Q and Design D. Rating R is calculated by the formula R = 4(2F + 2Q + D ) 0.01P. The table shows the prices and performance of four models of meat grinders. Meat grinder model Meat grinder price (r. per piece) Functionality Quality Design A B C D Find the meat grinder model with the highest rating from those presented in the table.

17 16 Home (test) work 2 1. Using the table, gather at least one group in which interpreters together speak all four languages: English, German, Spanish and French, and the total cost of their services does not exceed p. in a day. In your answer, indicate in ascending order any one set of translator numbers without spaces, commas and other additional characters. Interpreter's number Languages ​​Cost of services (rubles per day) 1 English Spanish, English German German, Spanish German, French French Artyom needs to buy three different pizzas so that at least one of them is with mushrooms, at least one is vegetarian and at least one meat. What pizzas should Artyom choose if he expects to spend no more than 1000 rubles on everything? In your answer, indicate in ascending order any one set of pizza numbers without spaces, commas and other additional characters. Pizza Number Ingredients Type Price (R.) 1 Ham, Cheese Meat Cheese, Tomatoes Vegetarian Cheese Vegetarian Chicken, Mushrooms, Tomatoes Beef Beef, Salami, Mushrooms Meat Spinach, Mushrooms, Cheese, Olives Vegetarian For a group of foreign guests, you need to buy 13 guidebooks. Internet shop Price of the guide (rubles per item) Delivery cost (rubles) Additional conditions A No B C Delivery is free if the order amount exceeds 4000 rubles. Delivery is free if the order amount exceeds 3000 rubles.

18 How much will the cheapest purchase option with delivery cost? The ISP offers three tariff plans. Tariff plan Subscription fee Traffic fee "0" No 1.5 p. for 1 MB "200" "700" 204 rubles. for 200 Mb of traffic per month 672 rubles. for 700 Mb of traffic per month 1.2 rubles. for 1 Mb over 200 Mb 0.5 p. for 1 Mb over 700 Mb The user assumes that his traffic will be 700 Mb per month and chooses the cheapest tariff plan. How many rubles will a user have to pay per month if his traffic is really 700 MB? 5. To transport 45 tons of cargo for 130 km, you can use the services of one of three carrier companies. Carrier Cost of transportation by one car (r. per 10 km) Carrying capacity of one car (t) A 320 3.5 B C How many rubles will you have to pay for the cheapest transportation? 6. The results of Olympiads in mathematics and social science in the classroom are given. Student number Score in mathematics Score in social studies Commendation certificates are given to schoolchildren who have a total score in two Olympiads of more than 140 or at least 75 points in at least one subject. In your answer, indicate in ascending order the numbers of students in the class who scored less than 75 points in mathematics and received commendable letters, without spaces, commas and other additional characters.

19 18 7. The client wants to rent a car for a day for a trip of 500 km. The table shows the characteristics of three cars and the cost of their rental. Car Fuel Fuel consumption (l per 100 km) Rent (R. per 1 day) A Diesel B Petrol C Gas In addition to the rental, the client is obliged to pay for fuel for the car for the entire trip. The price of diesel fuel is 25 rubles. per liter, gasoline 35 p. per liter, gas 20 r. per litre. How many rubles will the client pay for rent and fuel if he chooses the cheapest option? 8. The furniture salon concludes contracts with furniture manufacturers. The contracts indicate what percentage of the proceeds from the sale of furniture goes to the income of the furniture salon. Percentage of revenue received by the salon Notes "Alpha" 7 Items priced up to r. "Alpha" 2 Products priced over r. Beta 3.5 All Omicron products 6 All products The price list shows prices for four wardrobes. Determine which wardrobe is most profitable for the salon to sell. In response, write down how many rubles will go to the salon's income from the sale of this wardrobe. Manufacturer Firm Manufacturer Product Price (r.) Alpha Wardrobe Anisya Alpha Wardrobe Vlasta Beta Wardrobe Inga Omikron Wardrobe Leocadia The construction contractor plans to buy 10 tons of facing bricks from one of the three suppliers. One brick weighs 5 kg. The price of a brick and the terms of delivery of the entire purchase are shown in the table.

20 Supplier Brick price (r. per unit) Delivery cost (r.) Special conditions A No B C Delivery is free if the order amount exceeds R. Delivery with a 50% discount if the order amount exceeds r. 19 How much will the cheapest purchase option with delivery cost? 10. An automobile magazine determines the rating of cars based on safety S, comfort C, functionality F, quality Q and design 3S+ 2C+ 2F + 2Q+ D on D. Rating R is calculated by the formula R =. Table 50 shows the performance of three car models. Car model Comfort Safety Functionality Quality Design A B C Find the highest rating of the car model in the table. Tasks for repetition 1. Find the value of the expression Find the value of the expression Find the value of the expression 43,

21 20 READING AND ANALYZING DATA PRESENT IN THE FORM OF GRAPHS Training work 3 1. 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 August 7. Give your answer in degrees Celsius. 2. The graph shows the dependence of atmospheric pressure on altitude above sea level. On the horizontal axis is the height above sea level in kilometers, on the vertical axis is the pressure in millimeters of mercury. Determine from the graph at what height the atmospheric pressure is 400 mmHg. Give your answer in kilometers. 3. When the flashlight is on, the battery is gradually discharged and the voltage in the electric circuit of the flashlight drops. The graph shows the dependence of the voltage in the circuit on the operating time of the flashlight. The horizontal axis shows the flashlight operating time in hours, the vertical axis shows the voltage in volts. Determine from the graph how many hours of flashlight operation the voltage will drop from 1.4 to 1.2 V.

22 4. The figure shows the speed of an athlete during cardio training. The minutes that have passed since the beginning of the training are indicated horizontally, the speed of the athlete in km / h is indicated vertically. What was the speed of the athlete 2 minutes after the start of training? Give your answer in km/h. In the figure, the bold dots show the average monthly air temperature in Sochi for each month in 1920. Months are indicated horizontally, temperatures are indicated vertically in degrees Celsius. For clarity, bold dots are connected by a line. Determine from the figure the highest average monthly temperature in the period from May to December 1920. Give your answer in degrees Celsius. 6. The graph shows the change in temperature during the warming up of a passenger car engine. The horizontal axis shows the time in minutes since the engine was started, the vertical axis shows the engine temperature in degrees Celsius. Determine from the graph how many degrees Celsius the engine will heat up from 1 to 3 minutes from the start. 7. The figure shows the power consumption of electricity in the city N during the day. Hours of the day are indicated horizontally, power in megawatts is indicated vertically. What is the difference between the highest and lowest power consumption from 2 am to 2 pm? Give your answer in megawatts.

23 22 8. In the figure, bold dots show the number of dangerous hydrometeorological phenomena in the Russian Federation from 1996 to 2011. The year is indicated horizontally, the number of phenomena is indicated vertically. How many years for the specified period annual number hazardous phenomena did not exceed 240? 9. The graph shown in the figure shows the change in the exchange value of the shares of an oil producing company in the first two weeks of May. The price of one share in rubles is plotted along the vertical axis, and the date of May is shown along the horizontal axis. In the first week of May, the businessman bought 20 shares and then sold them in the second week. What is the maximum profit he could make? Give your answer in rubles. 10. The graph shown in the figure shows the change in the exchange value of the shares of a mining company in the first half of September. The value of one share in rubles is plotted along the vertical axis, and the number of September is shown along the horizontal axis. On September 7, the businessman bought a block of shares, and on September 13 he sold it. As a result of these operations, the businessman's profit amounted to 3600 rubles. How many shares were in the package?

24 Home (test) work 3 1. 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. Decide on a schedule lowest temperature air 8 August. Give your answer in degrees Celsius. The graph shows the dependence of atmospheric pressure on altitude above sea level. On the horizontal axis is the height above sea level in kilometers, on the vertical axis is the pressure in millimeters of mercury. Determine from the graph at what height the atmospheric pressure is 300 mmHg. Give your answer in kilometers. 3. When the flashlight is on, the battery is gradually discharged and the voltage in the electric circuit of the flashlight drops. The graph shows the dependence of the voltage in the circuit on the operating time of the flashlight. The horizontal axis shows the flashlight operating time in hours, the vertical axis shows the voltage in volts. Determine from the graph how many hours of flashlight operation the voltage will drop from 1.2 to 0.8 V.

25 24 4. The figure shows the speed of an athlete during cardio training. The minutes that have passed since the beginning of the training are indicated horizontally, the speed of the athlete in km / h is indicated vertically. In how many minutes after the start of training did the athlete's speed reach 10 km/h for the first time? 5. In the figure, bold dots show the average daily air temperature in Brest every day from July 6 to July 19, 1981. The dates of the month are indicated horizontally, the temperature in degrees Celsius is indicated vertically. For clarity, bold dots are connected by a line. Determine from the figure the difference between the highest and lowest average daily temperatures for the specified period. Give your answer in degrees Celsius. 6. The graph shows the change in temperature during the warming up of a passenger car engine. The horizontal axis shows the time in minutes since the engine was started, the vertical axis shows the engine temperature in degrees Celsius. Determine from the graph how many degrees Celsius the engine will cool down from 7 to 10 minutes from the start. 7. The figure shows the power consumption of electricity in the city N during the day. Hours of the day are indicated horizontally, power in megawatts is indicated vertically. What is the difference between the highest and lowest power consumption between 10 am and 10 pm? Give your answer in megawatts.

26 8. In the figure, bold dots show the number of dangerous hydrometeorological phenomena in the Russian Federation from 1996 to 2011. The year is indicated horizontally, the number of phenomena is indicated vertically. For how many years during the indicated period did the annual number of dangerous phenomena not exceed 320? The graph shows the change in the stock price of the company's shares on one of the days from 9:00 (beginning of trading) to 15:00 (end of trading). The price of one share in rubles is plotted along the vertical axis, and the time of day is plotted along the horizontal axis. The businessman bought 3,000 shares before noon and then sold them before the close of trading that day. What is the maximum profit he could make? Give your answer in rubles. 10. The graph shows the change in the exchange value of the company's shares in the first half of September. The value of one share in rubles is plotted along the vertical axis, and the number of September is shown along the horizontal axis. On September 3, the businessman bought a block of shares, and on September 10 he sold it. As a result of these operations, the businessman's loss amounted to r. How many shares were in the package? Tasks for repetition 5 1. Find the value of the expression, Find the value of the expression,. 3. Find the value of the expression, + 3.

27 26 Practice 4 1. The graph shows the engine torque versus RPM. On the horizontal axis the number of revolutions per minute is indicated, on the vertical axis the torque is in N m. Assign each interval of the number of revolutions per minute to the torque characteristic. Interval A) rpm B) rpm C) rpm D) rpm In the table, under each letter, indicate the corresponding number. Characteristic 1) with an increase in the number of revolutions, the torque drops, but remains more than 60 Nm over the entire interval 2) with an increase in the number of revolutions, the torque drops and does not exceed 80 Nm over the entire interval 3) with an increase in the number of revolutions, the torque does not change 4) with an increase in the number of revolutions, the torque increases. The horizontal axis shows the time in minutes since the engine was started, the vertical axis shows the engine temperature in degrees Celsius. Assign a temperature characteristic to each time interval. Interval A) 0 1 min B) 2 3 min C) 5 6 min D) 7 9 min from 40 to 50 C In the table, under each letter, indicate the corresponding number. A B C D 3. The graph shows the dependence of the pulse rate of a gymnast on time during and after his performance in floor exercises. On the horizontal axis is the time (in minutes) that has elapsed since the start of the gymnast's performance, on the vertical axis is the pulse rate (in beats per minute).

28 Using the graph, match each time interval with the characteristic of the gymnast's pulse at this interval. 27 A) 0 1 min B) 1 2 min C) 2 3 min D) 3 4 min Interval Characteristic 1) pulse rate fell 2) the greatest increase in pulse rate 3) pulse rate first fell and then increased 4) pulse rate did not exceed 90 bpm In the table, under each letter, indicate the corresponding number. A B C D 4. The graph shows the dependence of the speed of a car on time. On the vertical axis is the speed of the car in km / h, on the horizontal axis is the time in seconds elapsed since the start of the car. Assign to each time interval the characteristics of the movement of the car on this interval. Interval A) 0 30 s B) c C) c D) c Characteristic 1) the speed of the car reached its maximum for the entire time the car was moving 2) the speed of the car did not decrease and did not exceed 40 km/h 3) the car stopped for 15 s 4) the speed of the car did not increase throughout the entire interval In the table, under each letter, indicate the corresponding number. A B C D 5. The graph shows the dependence of the bathyscaphe sinking speed on time. The vertical axis shows the speed in m/s, the horizontal axis shows the time in seconds since the start of the dive. Using the graph, match each time interval with the submersion characteristic of the bathyscaphe at this interval.

29 28 Interval Characteristic A) 0 60 c B) c C) c D) c exactly 15 s In the table, under each letter, indicate the corresponding number. A B C D 6. The dots in the figure show the number of boys and girls born for each calendar month of 2013 in the city maternity hospital. Months are indicated horizontally, the number of born boys and girls (separately) is indicated vertically. For clarity, the points are connected by lines. Using the figure, match each of the indicated time periods with a characteristic of the birth rate in this period. Period A) January March B) April June C) July September D) October December Characteristics 1) the difference between the number of born boys and the number of girls born in one of the months of this period reaches the highest value for the year 2) the birth rate of girls increased 3) the birth rate of girls decreased 4) the birth rate of boys exceeded the birth rate of girls In the table, under each letter, indicate the corresponding number. A B C D 7. Dots in the figure show the atmospheric pressure in the city N for three days from April 4 to April 6, 2013. During the day, the pressure is measured 4 times: at night (00:00), in the morning (06:00), in the afternoon (12:00) and in the evening (18:00). The time of day and date are indicated horizontally, the pressure is indicated vertically in millimeters of mercury. For clarity, the points are connected by a line.

30 Using the figure, match each of the indicated time periods with the pressure characteristic in city N during this period April April 5 April 6 ) C) April 5 night (from 00:00 to 06:00) D) April 6 day (from 12:00 to 18:00) Characteristic 1) after reaching a three-day maximum, the pressure began to fall 2) the smallest pressure drop 3) the smallest pressure increase 756 mmHg Art. In the table, under each letter, indicate the corresponding number. A B C D 8. In the figure, dots show the volume of monthly sales of refrigerators in a household appliance store. Months are indicated horizontally, the number of refrigerators sold is indicated vertically. For clarity, the points are connected by a line. Using the figure, match each of the indicated time periods with the characteristics of refrigerator sales. Period A) January March B) April June C) July September D) October December In the table, under each letter, indicate the corresponding number. Characteristic 1) monthly sales decreased by more than 200 refrigerators for the entire period 2) the same number of refrigerators were sold in the first and second months of the period 3) the slowest decrease in monthly sales 4) monthly sales increased by 200 refrigerators in one month A B C 9. In the figure, the dots show the average daily air temperature in Moscow in January 2011. The day of the month is indicated horizontally, and the temperature in degrees Celsius is indicated vertically. For clarity, the points are connected by a line.

31 30 Assign a temperature characteristic to each time period. Period A) 1 January 7 B) 8 January 14 C) January D) January Characteristic 1) the temperature reached a monthly maximum 2) in the second half of the week the temperature did not change 3) the temperature reached a monthly minimum 4) at the end of the week an increase in temperature was observed In the table under Write the corresponding number for each letter. A B C D 10. The figure shows the annual volume of open-pit coal mining in Russia from 2001 to 2010. The year is indicated horizontally, the volume of coal production in million tons is shown vertically. For clarity, the points are connected by a line. Using the figure, match each of the indicated time periods with the characteristics of coal production. Period Characteristic A) years. 1) during the period, production volumes first grew, and then began to fall B) gg. B) yrs. D) years 2) the annual production volume in each year was more than 175, but less than 200 million tons 3) the period contains the year in which the volume of coal production was minimal 4) the volume of production in this period grew every year In the table, under each letter, indicate the corresponding number. A B C D

32 Home (test) work The graph shows the dependence of the engine torque on the number of revolutions per minute. On the horizontal axis the number of revolutions per minute is indicated, on the vertical axis the torque is in N m. Assign each interval of the number of revolutions per minute to the torque characteristic. Interval A) rpm B) rpm C) rpm D) rpm In the table, under each letter, indicate the corresponding number. Characteristic 1) when the number of revolutions increases, the torque decreases 2) when the number of revolutions increases, the fastest increase in torque 3) the torque does not exceed 20 Nm over the entire interval 4) the torque does not change over the entire interval A B C D 2. On the graph shows the dependence of temperature on time in the process of warming up the engine of a car. The horizontal axis shows the time in minutes since the engine was started, the vertical axis shows the engine temperature in degrees Celsius. Assign a temperature characteristic to each time interval. Interval A) 0 1 min B) 3 4 min C) 5 6 min D) 7 9 min Characteristic 1) the temperature rose, and its increase was less than 10 C 2) the temperature rose and reached 60 C in this interval 3) the fastest growth temperature 4) the temperature fell In the table, under each letter, indicate the corresponding number. A B C D 3. The graph shows the dependence of the pulse rate of a gymnast on time during and after his performance in floor exercises. On the horizontal axis is the time (in minutes) that has elapsed since the start of the gymnast's performance, on the vertical axis is the pulse rate (in beats per minute).

33 32 Using the graph, match each time interval with the characteristic of the gymnast's pulse at this interval. Interval A) 2 3 min B) 3 4 min C) 4 5 min D) 5 7 min and then increased 4) the pulse rate increased over the entire interval In the table, under each letter, indicate the corresponding number. A B C D 4. The graph shows the dependence of the speed of a car on time. On the vertical axis is the speed of the car in km / h, on the horizontal axis is the time in seconds elapsed since the start of the car. Assign to each time interval the characteristics of the movement of the car on this interval. Interval A) c B) c C) c D) c Characteristic 1) the car did not increase speed throughout the entire interval and drove at a constant speed for some time 2) the car’s speed was constantly decreasing 3) the car stopped for 15 s 4) the car’s speed reached its maximum for the entire time of movement In the table, under each letter, indicate the corresponding number. A B C D 5. The graph shows the dependence of the bathyscaphe sinking speed on time. The vertical axis shows the speed in m/s, the horizontal axis shows the time in seconds since the start of the dive.

34 Using the graph, match each time interval with the submersion characteristic of the bathyscaphe at this interval. 33 Interval A) 0 60 s B) c C) c D) c Characteristic 1) the submersible did not move for 30 s 2) the sinking speed was constantly increasing 3) the sinking speed was not less than 0.3 m/s over the entire interval 4) the speed immersion is not more than 0.1 m/s for the entire interval In the table, under each letter, indicate the corresponding number. A B C D 6. In the figure, the dots show the number of born boys and girls for each calendar month of 2013 in the city's birth house. Months are indicated horizontally, the number of born boys and girls (separately) is indicated vertically. For clarity, the points are connected by lines. Using the figure, match each of the indicated time periods with a characteristic of the birth rate in this period. Period A) January March B) April June C) July September D) October December Characteristics 1) the birth rate of boys fell the fastest 2) in each month of the period the number of girls and boys born differed by no more than 5 3) more boys were born in each month than girls 4) the birth rate of girls was minimal In the table, under each letter, indicate the corresponding number. A B C D

35 34 7. Dots in the figure show the water consumption of the city CHPP during the day. Hours of the day are indicated horizontally, water consumption per day is indicated vertically. past hour in cubic meters. Match each of the specified time periods with the characteristics of water consumption of a given CHP plant during this period. Period Characteristic A) night (from 00:00 to 06:00) 1) water consumption fell during the entire period B) morning (from 06:00 to 12:00) 2) water consumption during the entire period was less than 20 cubic meters per hour C) day (from 12 to 18 hours) 3) water consumption more than tripled during the entire period D) evening (from 18 to 24 hours) 4) water consumption first increased and then fell In the table, under each letter, indicate the corresponding number. A B C D 8. In the figure, dots show the volume of monthly sales of heaters in a household appliance store. Months are indicated horizontally, the number of heaters sold is indicated vertically. For clarity, the points are connected by a line. Using the figure, match each of the indicated time periods with the characteristics of sales of heaters. Period A) winter B) spring C) summer D) autumn Characteristics 1) monthly sales volume was less than 40 units during the whole period 2) monthly sales volume peaked 3) sales volume fell by more than 60 units during the period 4) monthly volume sales grew, but was less than 120 pieces In the table, under each letter, indicate the corresponding number. A B C D

36 9. Dots in the figure show the average daily air temperature in Chelyabinsk in April 2012. The horizontal indicates the day of the month, the vertical temperature in degrees Celsius. Match each of the indicated time periods with a characteristic of temperature change. 35 Period A) April 1 7 B) April 8 14 C) April D) April Characteristic 1) in the second half of the week the temperature decreased 2) 4 days a week the temperature took the same value 3) the temperature reached a monthly maximum 4) the temperature did not decreased during the week In the table, under each letter, indicate the corresponding number. A B C D 10. The figure shows the change in the value of the company's shares in the period from September 1 to September 12, 2012. The horizontal indicates the day of the month, the vertical is the cost of one share in rubles. Using the figure, match each of the indicated time intervals with a characteristic of a change in the value of a share. Period A) B) C) D) Characteristic 1) the share price did not fall below 300 rubles. 2) the share price reached a two-week high 3) the share price grew daily 4) the share price did not exceed 300 rubles. In the table, under each letter, indicate the corresponding number. A B C D Tasks for repetition 1. Find the value of the expression 088,. 22, 2. Find the value of the expression: Find the value of the expression,.

37 36 READING AND ANALYZING DATA PRESENTED IN THE FORM OF DIAGRAM Workout 5 1. The diagram shows the nutrient content of breadcrumbs. Determine from the diagram, the content of which substances prevails. 1) Proteins 2) Fats 3) Carbohydrates 4) Other Write down the number of the answer you chose. 2. The chart shows the age composition of the Chinese population. Determine from the diagram which of the age categories is the smallest. 1) 0 14 years 2) years 3) years 4) 65 years and older Write down the number of the answer you chose. 3. The diagram shows the distribution of land in the Volga Federal District by category. Determine from the diagram which categories of land occupy more than 25% of the area of ​​the district. 1) Forest fund lands 2) Agricultural lands 3) Reserve lands 4) Other lands Write in ascending order the numbers of the selected answer options without spaces, commas and other additional characters.

38 4. The charts show the nutrient content of cocoa, chocolate, cheese and condensed milk. Determine from the diagrams which product has the highest fat content. 1) Cocoa 2) Chocolate 3) Cheese 4) Condensed milk Write down the number of the chosen answer The diagrams show the distribution of land by category of the Ural, Volga, Southern and Siberian federal districts. Determine from the diagrams in which districts the share of forest fund lands exceeds 50%. 1) Ural Federal District 2) Volga Federal District 3) Southern Federal District 4) Siberian Federal District Write in ascending order the numbers of the selected answer options without spaces, commas and other additional characters.

39 38 6. Which of the following pie charts shows the distribution of marks for test in mathematics in grade 8, if fives in the class are about 35% of all grades, fours are about 23%, threes are about 25% and twos are about 17%? Write down the number of the chosen answer. 7. The diagram shows the distribution of the number of users of some social network by countries of the world. In total, this social network has 12 million users. Which of the following statements are incorrect? 1) There are more users from Argentina than users from Poland. 2) There are about three times more users from Argentina than users from Paraguay. 3) More than half of users from Argentina and Belarus together total number users. 4) There are less than 9 million users from Brazil. In your answer, write down the numbers of the selected statements in ascending order without spaces, commas, or other additional characters. 8. In the city of educational institutions there are schools, colleges, colleges and institutes. The data is presented in a pie chart. Which of the statements regarding the number of educational institutions of different types is incorrect if there are 120 educational institutions in the city? 1) There are more than half of the educational institutions of the school in the city. 2) In the city of schools, colleges and schools less than 5 of all educational institutions. 6 3) In the city, about an eighth of all educational institutions are institutes. 4) There are more than 60 schools in the city. In your answer, write down the numbers of the selected statements in ascending order.

Training work Reading and analysis of data presented in the form of tables Answers to tasks are a word, a phrase, a number or a sequence of words, numbers. Write your answer without spaces or commas

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23 task prototypes 2 Demo task: The table shows the standards for running 30 meters for 9th grade students. Boys Girls Marker “5” “4” “3” “5” “4” “3” Time, seconds 4.6 4.9 5.3 5.0 5.5

RM 14-15 option 6 1. The table shows the distances from the Sun to the four planets of the solar system. Which of these planets is closest to the Sun? Planet Jupiter Mars Saturn Neptune Distance (in km) 7.781 2.280

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1. Problem B2 matematem.ru ~ 1 ~ a. (26863) The graph shows the dependence of the engine torque on the number of revolutions per minute. The number of revolutions per minute is plotted on the abscissa axis, and the number of revolutions per minute is plotted on the ordinate axis.

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Task 2 Determining the value according to the graph 1. The graph shows the dependence of the torque of an automobile engine on the number of revolutions per minute. The number of revolutions per minute is plotted on the x-axis.

Option number 1

To renovate an apartment, 63 rolls of wallpaper are required. How many packs of wallpaper glue do you need to buy if one pack of glue is designed for 6 rolls?

200 live in city N  000 inhabitants. Among them, 15% are children and teenagers. Among45% of adult residents do not work (pensioners, students, housewives, etc.). How many adult residents work?

In the figure, bold dots show the daily amount of precipitation that fell in Tomsk from January 8 to January 24, 2005. The dates of the month are indicated horizontally, and the amount of precipitation on the corresponding day, in millimeters, is indicated vertically. For clarity, bold dots in the figure are connected by a line. Determine from the figure what the greatest amount of precipitation fell in the period from January 13 to 20. Give your answer in millimeters.

Ceramic tiles of the same brand are available in three different sizes. Tiles are packed in packs. Using the data in the table, determine in which case the price of one square meter tiles will be the smallest.

Tile size
(cm cm)

Quantity
tiles in a pack

Pack price

20 20

604 r.

20 30

595 r. 20 k.

30 30

594 r.

In response, write down the found lowest price per square meter in rubles.

The area of ​​a rectangle is 18. Find its larger side if it is 3 more than the smaller side.

Cowboy John hits a fly on the wall with a probability of 0.9 if he shoots with a shot revolver. If John fires an unshot revolver, he hits a fly with a probability of 0.2. There are 10 revolvers on the table, of which only 4 are shot. Cowboy John sees a fly on the wall, randomly grabs the first revolver he comes across and shoots at the fly. Find the probability that John misses.

Find the root of the equation .

Find the radius of a circle circumscribed about a rectangle whose two sides are 3 and 4.

The figure shows a graph of the function , defined on the interval (−5; 5). Determine the number of integer points at which the derivative of the function negative.

B10

Find the volume of a polyhedron whose vertices are points , , , regular triangular prism , whose base area is 2 and whose side edge is 3.

B11

Find the value of an expression .

B12

For normal incidence of light with a wavelength nm to a diffraction grating with a period nm, a series of diffraction maxima are observed. At the same time, the angle (counted from the perpendicular to the grating), under which the maximum is observed, and the number of the maximum related by the ratio . What is the minimum angle (in degrees) is it possible to observe a second maximum on a grating with a period not exceeding 1600 nm?

B13

Find volume part of the cone shown in the figure. Please indicate in your answer .

B14

From paragraphA to paragraphB , the distance between which is 75 km, a motorist and a cyclist left at the same time. It is known that in an hour a motorist travels 40 km more than a cyclist. Determine the speed of the cyclist if it is known that he has arrived at the pointB 6 hours later than the motorist. Give your answer in km/h.

B15

Find highest value functions on the segment .

a) Solve the equation

b) Find all the roots of this equation that belong to the segment

In the right quadrangular prism base sides are equal , and the side edges are equal . on edge marked point so Find the angle between planes and

Solve the system of inequalities

Trapezium area equals 810. The diagonals intersect at the point Segments connecting the middle grounds with peaks and intersect with the diagonals of the trapezoid at points and Find the area of ​​a triangle if one of the bases of a trapezoid is twice the other.

At what values ​​of the parametersa andb system has infinitely many solutions?

More than 42 but less than 56 whole numbers are written on the board. The arithmetic mean of these numbers is 4, the arithmetic mean of all the positive ones is 14, and the arithmetic mean of all the negative ones is .

Quest Source: Decision 2649.-15. OGE 2017 Mathematics, I.V. Yashchenko. 36 options.

Task 14. Student Tsvetkova leaves Naro-Fominsk for Moscow to study at the university. Classes start at 9:00. The table shows the schedule of morning electric trains from Nara station to Kievsky railway station in Moscow.

Departure from st. Nara	Arrival at the Kyiv railway station

The journey from the station to the university takes 45 minutes. Enter the departure time from Nara Station of the latest (in terms of departure time) electric train that suits the student.

1) 05:55; 2) 06:29; 3) 06:37; 4) 07:02

Solution.

To be in time before 9:00 a student needs to add 45 minutes by the time the train arrives at the Kyiv railway station and this time must be less than 9:00. Since we need to specify the latest time that is suitable, we will start considering the arrival time from the end of the table:

08:06 + 0:45 = 8:51 - suitable.

This arrival time corresponds to the departure time from Nara station 07:02 and answer option number 4.

Answer: 4.

Task 15. In the figure, bold dots show the daily amount of precipitation that fell in Petrozavodsk from January 6 to January 18, 2005. The dates of the month are indicated horizontally, and the amount of precipitation on the corresponding day, in millimeters, is indicated vertically. For clarity, bold dots in the figure are connected by a line. Determine from the figure on what day of the given period in Petrozavodsk the greatest amount of precipitation fell.