Presentation in physics on the topic "movement of a body in a circle." Presentation "Movement of a body in a circle" Uniform movement of a point in a circle
Alexandrova Zinaida Vasilievna, teacher of physics and computer science
Educational institution: MBOU secondary school No. 5, Pechenga, Murmansk region
Item: physics
Class : Grade 9
Lesson topic : Movement of a body in a circle with a constant modulo speed
The purpose of the lesson:
give an idea of curvilinear motion, introduce the concepts of frequency, period, angular velocity, centripetal acceleration and centripetal force.
Lesson objectives:
Educational:
Repeat the types of mechanical motion, introduce new concepts: circular motion, centripetal acceleration, period, frequency;
To reveal in practice the connection of the period, frequency and centripetal acceleration with the radius of circulation;
Use educational laboratory equipment to solve practical problems.
Educational :
Develop the ability to apply theoretical knowledge to solve specific problems;
Develop a culture of logical thinking;
Develop interest in the subject; cognitive activity in setting up and conducting an experiment.
Educational :
To form a worldview in the process of studying physics and to argue their conclusions, to cultivate independence, accuracy;
To cultivate a communicative and informational culture of students
Lesson equipment:
computer, projector, screen, presentation for the lessonMovement of a body in a circle, printout of cards with tasks;
tennis ball, badminton shuttlecock, toy car, ball on a string, tripod;
sets for the experiment: stopwatch, tripod with a clutch and a foot, a ball on a thread, a ruler.
Form of organization of training: frontal, individual, group.
Lesson type: study and primary consolidation of knowledge.
Educational and methodological support: Physics. Grade 9 Textbook. Peryshkin A.V., Gutnik E.M. 14th ed., ster. - M.: Bustard, 2012
Lesson Implementation Time : 45 minutes
1. Editor in which the multimedia resource is made:MSPowerPoint
2. Type of multimedia resource: a visual presentation of educational material using triggers, embedded video and an interactive test.
Lesson plan
Organizing time. Motivation for learning activities.
Updating of basic knowledge.
Learning new material.
Conversation on questions;
Problem solving;
Implementation of research practical work.
Summing up the lesson.
During the classes
Lesson stages
Temporary implementation
Organizing time. Motivation for learning activities.
slide 1. ( Checking readiness for the lesson, announcing the topic and objectives of the lesson.)
Teacher. Today in the lesson you will learn what acceleration is when a body moves uniformly in a circle and how to determine it.
2 minutes
Updating of basic knowledge.
Slide 2.
Fphysical dictation:
Change in body position in space over time.(Movement)
A physical quantity measured in meters.(Move)
Physical vector quantity characterizing the speed of movement.(Speed)
The basic unit of length in physics.(Meter)
A physical quantity whose units are year, day, hour.(Time)
A physical vector quantity that can be measured using an accelerometer instrument.(Acceleration)
Trajectory length. (Path)
Acceleration units(m/s 2 ).
(Conducting a dictation with subsequent verification, self-assessment of work by students)
5 minutes
Learning new material.
Slide 3.
Teacher. We quite often observe such a movement of a body in which its trajectory is a circle. Moving along the circle, for example, the point of the wheel rim during its rotation, the points of the rotating parts of machine tools, the end of the clock hand.
Experience demonstrations 1. The fall of a tennis ball, the flight of a badminton shuttlecock, the movement of a toy car, the vibrations of a ball on a thread fixed in a tripod. What do these movements have in common and how do they differ in appearance?(Student answers)
Teacher. Rectilinear motion is a motion whose trajectory is a straight line, curvilinear is a curve. Give examples of rectilinear and curvilinear motion that you have encountered in your life.(Student answers)
The motion of a body in a circle isa special case of curvilinear motion.
Any curve can be represented as a sum of arcs of circlesdifferent (or the same) radius.
Curvilinear motion is a motion that occurs along arcs of circles.
Let us introduce some characteristics of curvilinear motion.
slide 4. (watch video " speed.avi" link on slide)
Curvilinear motion with a constant modulo speed. Movement with acceleration, tk. speed changes direction.
slide 5 . (watch video “Dependence of centripetal acceleration on radius and speed. avi » from the link on the slide)
slide 6. The direction of the velocity and acceleration vectors.
(working with slide materials and analysis of drawings, rational use of animation effects embedded in drawing elements, Fig 1.)
Fig.1.
Slide 7.
When a body moves uniformly along a circle, the acceleration vector is always perpendicular to the velocity vector, which is directed tangentially to the circle.
A body moves in a circle, provided that that the linear velocity vector is perpendicular to the centripetal acceleration vector.
slide 8. (working with illustrations and slide materials)
centripetal acceleration - the acceleration with which the body moves in a circle with a constant modulo speed is always directed along the radius of the circle to the center.
a c =
slide 9.
When moving in a circle, the body will return to its original point after a certain period of time. Circular motion is periodic.
Period of circulation - this is a period of timeT , during which the body (point) makes one revolution around the circumference.
Period unit -second
Speed is the number of complete revolutions per unit of time.
[ ] = with -1 = Hz
Frequency unit
Student message 1. A period is a quantity that is often found in nature, science and technology. The earth rotates around its axis, the average period of this rotation is 24 hours; a complete revolution of the Earth around the Sun takes about 365.26 days; the helicopter propeller has an average rotation period from 0.15 to 0.3 s; the period of blood circulation in a person is approximately 21 - 22 s.
Student message 2. The frequency is measured with special instruments - tachometers.
The rotational speed of technical devices: the gas turbine rotor rotates at a frequency of 200 to 300 1/s; A bullet fired from a Kalashnikov assault rifle rotates at a frequency of 3000 1/s.
slide 10. Relationship between period and frequency:
If in time t the body has made N complete revolutions, then the period of revolution is equal to:
Period and frequency are reciprocal quantities: frequency is inversely proportional to period, and period is inversely proportional to frequency
Slide 11. The speed of rotation of the body is characterized by the angular velocity.
Angular velocity(cyclic frequency) -
number of revolutions per unit of time, expressed in radians.
Angular velocity - the angle of rotation by which a point rotates in timet.
Angular velocity is measured in rad/s.
slide 12. (watch video "Path and displacement in curvilinear motion.avi" link on slide)
slide 13 . Kinematics of circular motion.
Teacher. With uniform motion in a circle, the modulus of its velocity does not change. But speed is a vector quantity, and it is characterized not only by a numerical value, but also by a direction. With uniform motion in a circle, the direction of the velocity vector changes all the time. Therefore, such uniform motion is accelerated.
Line speed: ;
Linear and angular speeds are related by the relation:
Centripetal acceleration: ;
Angular speed: ;
slide 14. (working with illustrations on the slide)
The direction of the velocity vector.Linear (instantaneous velocity) is always directed tangentially to the trajectory drawn to its point where the considered physical body is currently located.
The velocity vector is directed tangentially to the described circle.
The uniform motion of a body in a circle is a motion with acceleration. With a uniform motion of the body around the circle, the quantities υ and ω remain unchanged. In this case, when moving, only the direction of the vector changes.
slide 15. Centripetal force.
The force that holds a rotating body on a circle and is directed towards the center of rotation is called the centripetal force.
To obtain a formula for calculating the magnitude of the centripetal force, one must use Newton's second law, which is applicable to any curvilinear motion.
Substituting into the formula value of centripetal accelerationa c = , we get the formula for the centripetal force:
F=
From the first formula it can be seen that at the same speed, the smaller the radius of the circle, the greater the centripetal force. So, at the turns of the road on a moving body (train, car, bicycle), the greater the force should act towards the center of curvature, the steeper the turn, i.e., the smaller the radius of curvature.
The centripetal force depends on the linear speed: with increasing speed, it increases. It is well known to all skaters, skiers and cyclists: the faster you move, the harder it is to make a turn. Drivers know very well how dangerous it is to turn a car sharply at high speed.
slide 16.
Summary table of physical quantities characterizing curvilinear motion(analysis of dependencies between quantities and formulas)
Slides 17, 18, 19. Examples of circular motion.
Roundabouts on the roads. The movement of satellites around the earth.
slide 20. Attractions, carousels.
Student message 3. In the Middle Ages, jousting tournaments were called carousels (the word then had a masculine gender). Later, in the 18th century, to prepare for tournaments, instead of fighting with real opponents, they began to use a rotating platform, the prototype of a modern entertainment carousel, which then appeared at city fairs.
In Russia, the first carousel was built on June 16, 1766 in front of the Winter Palace. The carousel consisted of four quadrilles: Slavic, Roman, Indian, Turkish. The second time the carousel was built in the same place, in the same year on July 11th. A detailed description of these carousels is given in the newspaper St. Petersburg Vedomosti of 1766.
Carousel, common in courtyards in Soviet times. The carousel can be driven both by an engine (usually electric), and by the forces of the spinners themselves, who, before sitting on the carousel, spin it. Such carousels, which need to be spun by the riders themselves, are often installed on children's playgrounds.
In addition to attractions, carousels are often referred to as other mechanisms that have similar behavior - for example, in automated lines for bottling drinks, packaging bulk materials or printing products.
In a figurative sense, a carousel is a series of rapidly changing objects or events.
18 min
Consolidation of new material. Application of knowledge and skills in a new situation.
Teacher. Today in this lesson we got acquainted with the description of curvilinear motion, with new concepts and new physical quantities.
Conversation on:
What is a period? What is frequency? How are these quantities related? In what units are they measured? How can they be identified?
What is angular velocity? In what units is it measured? How can it be calculated?
What is called angular velocity? What is the unit of angular velocity?
How are the angular and linear velocities of a body's motion related?
What is the direction of centripetal acceleration? What formula is used to calculate it?
Slide 21.
Exercise 1. Fill in the table by solving problems according to the initial data (Fig. 2), then we will check the answers. (Students work independently with the table, it is necessary to prepare a printout of the table for each student in advance)
Fig.2
slide 22. Task 2.(orally)
Pay attention to the animation effects of the picture. Compare the characteristics of the uniform motion of the blue and red balls. (Working with the illustration on the slide).
slide 23. Task 3.(orally)
The wheels of the presented modes of transport make an equal number of revolutions in the same time. Compare their centripetal accelerations.(Working with slide materials)
(Work in a group, conducting an experiment, there is a printout of instructions for conducting an experiment on each table)
Equipment: a stopwatch, a ruler, a ball attached to a thread, a tripod with a clutch and a foot.
Target: researchdependence of period, frequency and acceleration on the radius of rotation.
Work plan
Measuretime t is 10 full revolutions of rotational motion and radius R of rotation of a ball fixed on a thread in a tripod.
Calculateperiod T and frequency, speed of rotation, centripetal acceleration Write the results in the form of a problem.
Changeradius of rotation (length of the thread), repeat the experiment 1 more time, trying to maintain the same speed,putting in the effort.
Make a conclusionabout the dependence of the period, frequency and acceleration on the radius of rotation (the smaller the radius of rotation, the shorter the period of revolution and the greater the value of frequency).
Slides 24-29.
Frontal work with an interactive test.
It is necessary to choose one answer out of three possible, if the correct answer was chosen, then it remains on the slide, and the green indicator starts flashing, incorrect answers disappear.
The body moves in a circle with a constant modulo speed. How will its centripetal acceleration change when the radius of the circle decreases by 3 times?
In the centrifuge of the washing machine, the laundry during the spin cycle moves in a circle with a constant modulo speed in the horizontal plane. What is the direction of its acceleration vector?
The skater moves at a speed of 10 m/s in a circle with a radius of 20 m. Determine his centripetal acceleration.
Where is the acceleration of the body directed when it moves along a circle with a constant speed in absolute value?
A material point moves along a circle with a constant modulo speed. How will the modulus of its centripetal acceleration change if the speed of the point is tripled?
A car wheel makes 20 revolutions in 10 seconds. Determine the period of rotation of the wheel?
slide 30. Problem solving(independent work if there is time in the lesson)
Option 1.
With what period must a carousel with a radius of 6.4 m rotate in order for the centripetal acceleration of a person on the carousel to be 10 m / s 2 ?
In the circus arena, a horse gallops at such a speed that it runs 2 circles in 1 minute. The radius of the arena is 6.5 m. Determine the period and frequency of rotation, speed and centripetal acceleration.
Option 2.
Carousel rotation frequency 0.05 s -1 . A person spinning on a carousel is at a distance of 4 m from the axis of rotation. Determine the centripetal acceleration of the person, the period of revolution and the angular velocity of the carousel.
The rim point of a bicycle wheel makes one revolution in 2 s. The wheel radius is 35 cm. What is the centripetal acceleration of the wheel rim point?
18 min
Summing up the lesson.
Grading. Reflection.
Slide 31 .
D/z: p. 18-19, Exercise 18 (2.4).
http:// www. stmary. ws/ high school/ physics/ home/ laboratory/ labGraphic. gif
slide 2
In mechanics, examples teach as much as rules. I. Newton
slide 3
Riddles of terrible nature hang everywhere in the air.N. Zabolotsky (from the poem "The Mad Wolf")
slide 4
A4. The body moves in a circle in a clockwise direction. Which of the vectors shown coincides in direction with the velocity vector of the body at point A? eleven; 2) 2; 3) 3; 4) 4.
slide 5
slide 6
The motion of a body in a circle with a constant modulo speed. Lesson topic:
Slide 7
Objectives: Repeat the features of curvilinear motion, consider the features of motion in a circle, get acquainted with the concept of centripetal acceleration and centripetal force, period and frequency of rotation, find out the relationship between the quantities.
Slide 8
Slide 9
Slide 10
slide 11
Conclusion page 70
slide 12
With uniform motion along a circle, the module of its speed does not change. But speed is a vector quantity, and it is characterized not only by a numerical value, but also by direction. With uniform motion in a circle, the direction of the velocity vector changes all the time. Therefore, such uniform motion is accelerated.
slide 13
Slide 14
Slide 15
When a body moves uniformly along a circle, the acceleration vector is always perpendicular to the velocity vector, which is directed tangentially to the circle.
slide 16
Conclusion page 72
Slide 17
Slide 18
The rotation period is the time of one revolution around the circumference. Rotation frequency - the number of revolutions per unit of time.
Slide 19
Kinematics of circular motion
Velocity modulus does not change Velocity modulus changes Linear velocity Angular velocity Acceleration
Slide 20
Answer: 1 1 2
slide 21
d / z § 19 Ex. 18 (1,2) And then a brilliance from on high burst into my mind, Carrying the accomplishment of all his efforts. A. Dante
slide 22
Option 1 Option 2 The body moves uniformly in a circle in a clockwise direction counterclockwise How is the acceleration vector directed during such a movement? a) 1; b) 2; at 3 ; d) 4. 2. The car moves with a constant modulo speed along the trajectory of the figure. At which of the indicated points of the trajectory is the centripetal acceleration the minimum maximum? 3. How many times will the centripetal acceleration change if the speed of a material point is increased and decreased by 3 times? a) will increase by 9 times; b) decrease by 9 times; c) will increase by 3 times; d) will decrease by 3 times.
slide 23
Option 1 4. The movement of a material point is called curvilinear if a) the trajectory of the movement is a circle; b) its trajectory is a curved line; c) its trajectory is a straight line. 5. A body of mass 1 kg moves at a constant speed of 2 m/s in a circle with a radius of 1 m. Determine the centrifugal force acting on the body. Option 2 4. The movement of a body is called curvilinear if a) all its points move along curved lines; b) some of its points move along curved lines; c) at least one of its points moves along a curved line. 5. A body of mass 2 kg moves at a constant speed of 2 m/s in a circle with a radius of 1 m. Determine the centrifugal force acting on the body.
slide 24
Literature Textbooks "Physics -9" A.V. Peryshkin, M.M. Balashov, N.M. Shakhmaev, Laws of physics B.N. Ivanov Unified State Exam assignments Lesson developments in physics V.A. Volkov Multimedia textbook of a new type (physics, basic school 7-9 cells, part 2)
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Slides captions:
Movement in a circle Physics teacher Fedorov Alexander Mikhailovich MOU Kyukyay secondary school Suntarsky ulus Republic of Sakha
In the life around us, we meet with movement in a circle quite often. This is how the clock hands and the gears of their mechanisms move; this is how cars move on convex bridges and on rounded sections of roads; artificial earth satellites move in circular orbits.
The instantaneous velocity of a body moving in a circle is directed tangentially to it at that point. This is easy to observe.
We will study the movement of a point along a circle with a constant modulo speed. It is called uniform circular motion. The speed of a point moving in a circle is often called linear speed. If a point moves along a circle uniformly and in time t passes a path L equal to the length of the arc AB, then the linear velocity (its modulus) is equal to V = L / t A B
Uniform motion in a circle is motion with acceleration, although the modulus of speed does not change. But the direction is constantly changing. Therefore, in this case, the acceleration a should characterize the change in speed in the direction. О v a The acceleration vector a with uniform motion of a point along a circle is directed along the radius to the center of the circle, therefore it is called centripetal. The acceleration module is determined by the formula: a \u003d v 2 /R, Where v is the module of the speed of the point, R is the radius of the circle.
PERIOD OF REVOLUTION The movement of a body in a circle is often characterized not by the speed of movement v, but by the time interval during which the body makes one complete revolution. This value is called the period of revolution. Designate it with the letter T. In calculations, T is expressed in seconds. During the time t, equal to the period T, the body travels a path equal to the circumference: L = 2 R. Therefore, v = L/T=2 R/T. Substituting this expression into the formula for acceleration, we get another expression for it: a= v 2 /R = 4 2 R/T 2 .
Frequency of circulation The movement of a body along a circle can be characterized by another quantity - the number of revolutions along the circle per unit time. It is called the frequency of circulation and is denoted by the Greek letter (nu). The frequency of revolution and the period are related as follows: = 1/T The unit of frequency is 1/s or Hz. Using the concept of frequency, we obtain formulas for speed and acceleration: v = 2R/T = 2R; a \u003d 4 2 R / T 2 \u003d 4 2 2 R.
So, we have studied the movement in a circle: Uniform movement in a circle is movement with acceleration a = v 2 /R. The period of revolution is the period of time during which the body makes one complete revolution. Designate it with the letter T. The frequency of circulation is the number of revolutions in a circle per unit time. It is denoted by the Greek letter (nu). Frequency of revolution and period are related by the following relation: = 1/T Formulas for velocity and acceleration: v = 2R/T = 2R; a \u003d 4 2 R / T 2 \u003d 4 2 2 R.
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Lesson for solving problems on the topic "Dynamics of motion in a circle." In the process of solving problems in groups, mutual learning of students takes place ....
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Slides captions:
Movement in a circle (closed track) Savchenko Elena Mikhailovna, mathematics teacher of the highest qualification category. Municipal educational institution gymnasium No. 1, Polyarnye Zori, Murmansk region State (final) certification Training modules for distance self-training XIV All-Russian competition of methodological developments "One Hundred Friends"
If two cyclists simultaneously start moving in a circle in one direction with speeds v 1 and v 2, respectively (v 1 > v 2, respectively), then the 1st cyclist approaches 2 with speed v 1 - v 2. At the moment when the 1st cyclist catches up with the 2nd for the first time, he covers the distance by one lap more. Continue Show At the moment when the 1st cyclist catches up with the 2nd for the second time, he covers the distance for two laps and more, and so on.
1 2 1. From one point of the circular track, the length of which is 15 km, two cars started simultaneously in the same direction. The speed of the first car is 60 km/h, the speed of the second is 80 km/h. How many minutes will pass from the moment of the start before the first car is exactly 1 lap ahead of the second? 1 red 2 green 60 80 v, km/h 15 km less (1 lap) Equation: Answer: 45 x we get in hours. Don't forget to convert to minutes. t , h x x S, km 60x 80x Show
2 1 2. From one point of the circular track, the length of which is 10 km, two cars started simultaneously in the same direction. The speed of the first car is 90 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h. 1 car 2 cars 90 x v, km/h per 10 km more (1 lap) Answer: 75 t , h 2 3 2 3 S, km 2 3 90 2 3 x Equation: Show
3. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points of a circular track, the length of which is 14 km. In how many minutes will the motorcyclists catch up for the first time if the speed of one of them is 21 km/h more than the speed of the other? 1 red 2 blue x x + 21 v, km/h 7 km less (half circle) Equation: Answer: 20 t we get in hours. Don't forget to convert to minutes. t , h t t S, km t x t(x +21) How many laps each motorcyclist has driven is not important to us. It is important that blue has traveled half a circle more to the meeting point, i.e. at 7 km. Another way is in the comments. Show
start finish 2 1 2 1 1 2 2 1 1 2 Let the full circle be 1 part. 4. Ski competitions are held on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later he is exactly one lap ahead of the second. How many minutes does the second skier complete one lap? Show
4. Ski competitions are held on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later he is exactly one lap ahead of the second. How many minutes does the second skier complete one lap? 1 lap more Answer: 10 1 skier 2 skier v, lap/min t , min 60 60 S, km x x+2 1 1 t , min 1 skier 2 skier S, part v, part/min 1 x+2 1 x 1 x + 2 1 x 60 x 60 x + 2 First, let's express the speed of each skier. Let the 1st skier complete a full circle in x minutes. The second one is 2 minutes longer, i.e. x+2. 60 x 60 x + 2 - = 1 This condition will help to enter x ...
5. From one point of the circular track, the length of which is 14 km, two cars started simultaneously in the same direction. The speed of the first car is 80 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h. 1 yellow 2 blue S, km 80 x v, km / h t , h 2 3 2 3 2 3 80 2 3 x 14 km more (1 circle) Equation: You could first find the speed in pursuit: 80 - x Then the equation will be look like this: v S t Answer: 59 You can press the button several times. How many laps each car drove is not important to us. It is important that the yellow car drove 1 more lap, i.e. at 14 km. Show 1 2
6. A cyclist left point A of the circular track, and after 30 minutes a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the track is 30 km. Give your answer in km/h. 1 motorcycle. 2 bike. S, km x y v, km/h t , h 1 6 2 3 2 3 y 1 equation: 1 6 x = Show 1 meeting. The cyclist was up to 1 meeting 40 minutes (2/3 h), the motorcyclist 10 min (1/6 h). And the distance during this time they traveled equal.
6. A cyclist left point A of the circular track, and after 30 minutes a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the track is 30 km. Give your answer in km/h. 1 motorcycle. 2 bike. S, km x y v, km/h t , h 1 2 1 2 1 2 y 30 km more (1 lap) Equation 2: Answer 80 1 2 x Desired value - x Show (2) 2nd meeting. The cyclist and the motorcyclist were on their way to the 2nd meeting in 30 min (1/2 h). And the distance during this time the motorcyclist traveled 1 lap more.
7. Clock with hands shows 8 hours 00 minutes. After how many minutes will the minute hand align with the hour hand for the fourth time? minute hour x S, lap v, lap/h t , h 1 1 12 x 1x 1 12 x over laps 2 3 3 1x – = 1 12 x 2 3 3 Answer: 240 min 2 3 1 3 For the first time the minute hand you have to go a circle more to catch up with the minute hand. 2nd time - 1 more lap more. 3rd time - 1 more round. 4th time - 1 more lap more. Total 2 3 laps over 2 3 3
6 12 1 2 9 11 10 8 7 4 5 3 Show (4) The first time the minute hand needs to go one more lap to catch up with the minute hand. 2nd time - 1 more lap more. 3rd time - 1 more round. 4th time - 1 more lap more. Total 2 3 laps more than 2 3 3 Check Another way is in the comments.
USE 2010. Mathematics. Task B12. Edited by A. L. Semenov and I. V. Yashchenko http://www.2x2abc.com/forum/users/2010/B12.pdf An open bank of assignments in mathematics. USE 2011 http://mathege.ru/or/ege/Main.html Drawings by the author http://le-savchen.ucoz.ru/index/0-67 Skier http://officeimg.vo.msecnd.net/en -us/images/MH900282779.gif Materials published on the author's website "Website of the teacher of mathematics" Section "Preparation for the Unified State Examination". Task B12. http://le-savchen.ucoz.ru/publ/17
