Tasks for the OGE. Reading graphs of real dependencies

Dear friends! For you, the next three tasks for reading graphs and charts. If interested, see the tasks about. The type of tasks in this category is one of the simplest. Consider the tasks:

26868. The figure shows the change in air temperature over the course of three days. The date and time of the day are indicated horizontally, the temperature value in degrees Celsius is indicated vertically. Determine from the figure the highest air temperature on January 22. Give your answer in degrees Celsius.


Immediately note that the highest temperature must be determined in the interval from 00:00 on January 22 to 00:00 on January 23.


The highest temperature will be -10 degrees Celsius (lies in the time interval from 12:00 to 18:00 hours).

Answer: -10

26869. The figure shows the change in air temperature over the course of three days. The date and time of the day are indicated horizontally, the temperature value in degrees Celsius is indicated vertically. Determine from the figure the lowest air temperature on April 27. Give your answer in degrees Celsius.


The lowest temperature must be determined in the interval from 00:00 on April 27 to 00:00 on April 28:


The graph shows that the lowest temperature will be -7 0 С (it lies in the time interval from 00:00 to 6:00 hours).

Answer: -7

26870. The figure shows the change in air temperature over the course of three days. The date and time of the day are indicated horizontally, the temperature value in degrees Celsius is indicated vertically. Determine the difference between the highest and lowest air temperatures on July 15 from the figure. Give your answer in degrees Celsius.


Please note that the temperature difference must be determined for the date July 15:


The minimum temperature will be 8C 0, the maximum 21C 0.

The difference is 13.

Answer: 13

That's all! Good luck to you!

Sincerely, Alexander Krutitskikh.

Parent meetings are more and more reminiscent of the prayers of sectarians: everyone listens attentively to the class teacher, then they give him the money and disperse thoughtfully at dusk ...

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Reading graphs of real dependencies


  1. Find the difference between the highest temperature and the lowest. Give your answer in degrees Celsius.
  2. According to the figure of problem 1, find the difference between the highest temperature and the lowest.
  3. The figure shows how the air temperature changed during one day. The horizontal shows the time of day, the vertical shows the temperature in degrees Celsius.
    Find the highest temperature value. Give your answer in degrees Celsius.
  4. According to the picture of task 3, determine how many hours the temperature exceeded 2 o C.
  5. According to the picture of task 3, determine how many hours in the first half of the day the temperature did not exceed 2 o C.
  6. When an aircraft is in level flight, the lift acting on the wings depends only on the speed. The figure shows this dependence for some aircraft.
    On the abscissa axis, speed is plotted (in km / h), on the ordinate axis - force (in tons of force). Determine from the figure at what speed (in km / h) the lifting force reaches 1 ton of force.
  7. At some point, the lifting force was equal to one ton of force. Determine from the figure of problem 6 by how many kilometers per hour the speed must be increased so that the lifting force increases to 4 tons of forces.
  8. 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 torque in N m is plotted on the ordinate axis. What number of revolutions per minute must the engine make in order for the torque to be at least 20 N m?
  9. According to the graph of problem 8, determine by how much Nm the torque increased if the engine speed increased from 1000 to 2500?
  10. The graphs show how during the televised debate between candidates A and B, viewers voted for each of them.
    How many thousands of TV viewers voted in the first 50 minutes of the debate?
  11. The diagram shows the number of SMS sent by listeners for each hour of the four-hour broadcast of the program by request on the radio.
    Determine how many more messages were sent in the first two hours of the program compared to the last two hours of this program.

  12. Andrey and Ivan competed in a 50-meter pool at a distance of 100 m. The graphs of their swims are shown in the figure.
    The horizontal axis shows time, and the vertical axis shows the swimmer's distance from the start. Who won the competition? In response, write down how many seconds he overtook the opponent.

1. Calculate the value of the expression Write down the answer as a decimal fraction. Solution: 2. The figure shows how the air temperature changed during one day. The horizontal shows the time of day, the vertical shows the temperature in degrees Celsius. Find the highest temperature value. Give your answer in degrees Celsius. Answer: 0.23125 Answer: Initially, the T-shirt cost 320 rubles. On sale, its price decreased by 15%. How much did the T-shirt cost after the discount? Solution: Answer: The number a is marked on the coordinate line. Choose the correct one from the following inequalities: Solution: Answer: 4


5. Write the largest of the following numbers: Solution: Answer: 3 The largest of the numbers is the largest root number 6. The projector fully illuminates a 70 cm high screen A located 170 cm away from the projector. What is the closest distance (in centimeters) from the projector that the 210 cm high screen B must be placed to be fully illuminated if the projector settings remain unchanged?. KST ~ MSR: Solution: Answer: Solve the equation Solution: Answer: In triangle ABC, the external angle at vertex B is 66 0, AB = BC. Find angle A of triangle ABC. Give your answer in degrees. A B C 66 0 Solution: In isosceles ABC: A \u003d C, By the property of the external angle of the triangle: A + C \u003d 66 0 A \u003d 33 0 Answer: 33 C M K R T x


9. Reduce the fraction. Solution: Answer: 4y 10. The diagram shows the distribution of land in the Volga Federal District by category. Determine from the diagram the limits of the share of agricultural land. 25% Solution: Draw two perpendicular diameters. The circle is divided into 4 equal sectors, each of which accounts for 25% The sector of agricultural land lies within 50-75% Answer: A die (dice) was thrown once. What is the probability that the number rolled is not less than 3? Solution: Dice roll, points roll: All possible outcomes - 6 Favorable outcomes (number of points, not less than 3) - 4 (that's 3, 4, 5, 6) Answer: 2 / 3


12. Establish a correspondence between the function graphs and the formulas that define them. Solution: You can use the following method: 1) A) parabola, it corresponds to the formula 4) 2) B) hyperbola, it corresponds to the formula 2) 3) C) direct proportionality, it can correspond to two formulas 1) or 3) Let's choose a graph point, for example: (1;2), it satisfies the formula 3) Answer: Geometric (a n) is given by the formula a n = 3. 2 n. Which of the following numbers is not a member of this progression? 1) 24 2) 72 3) 192 4) 384 instead of n, substitute the numbers 1,2,3,4, ... and 1 = 3. 2=6 and 2=3. 4=12 and 3=3. 8=24, etc. 2) Make equations for the variable n, if the root is a natural number, then n is a member of the progression. Answer: 2 Solution:


14. The height CH is drawn in the triangle ABC. It is known that AB = 3CH, CH = 3. Find the area of ​​the triangle. Solution: AB = 9, S=0, = 13.5 Answer: 13.5 15. Indicate the numbers of correct statements. 1) Through any two different points of the plane, at most one straight line can be drawn. 2) Through any two different points of the plane, at least one straight line can be drawn. 3) If the angle is equal to 54 0, then the vertical angle with it is equal) Any two different lines pass through one common point. 5) A straight line can be drawn through any three different points of the plane. 1) that's right, more than one line cannot be drawn. 2) true, less than one cannot be carried out 3) incorrect, because vertical angles are equal 4) False, because two lines can be parallel and have no common points. 5) False, because A straight line does not always pass through three points. Answer: 12 AB C N


16. In what coordinate quarter is the point of intersection of the lines -8x - 4y \u003d -1 and 4x + 8y \u003d 8? 1) in the 1st quarter 2) in the 2nd quarter 3) in the 3rd quarter 4) in the 4th quarter 25 y \u003d -0.5x way: X0 2 quarter 17. From the formula for the circumference C \u003d 2 r, express the radius r. Answer: 2 Solution: Answer: r = C / Solve the inequality. 0.5-6 Answer: (-; -6) ; (0.5;+)2r=C, r=C/2


19. Solve the equation x 3 - 5x 2 -4x + 20 = 0. Let's factorize the left side using the grouping method: Answer: -2; 2; 5 The domain of the equation: x R 20. In the figure, BE = CD, AE = AD. Prove that BD = CE. Given: BE = CD, AE = AD Prove: BD = CE Proof: 1) Since. BE = CD, AE = AD, then BE + AE = CD + AD, AB = AC 2) DAB = EAC (on two sides and the angle between them): AD = AE (by condition) AB = AC (by 1) action ) A - common Hence, BD = CE (as the corresponding sides of equal triangles) etc.


S (km) V (km/h)t (h) Against the current 60x - 2 Downstream 60x The motorboat traveled upstream 60 km and returned to the point of departure, having spent 45 minutes less on the way back. Find the speed of the boat in still water if the speed of the current is 2 km/h. Give your answer in km/h. Knowing that the boat spent 45 minutes on the way back = 45 / 60 h = 3 / 4, we make the equation: ODZ: (x-2) (x + 2) 0 Answer: 18 km / h 22. Build a graph of the function and determine , for which values ​​of m the line y = m has exactly one common point with the graph. The line y \u003d m is parallel to the Ox axis. It is obvious that one point of intersection of this graph with the line will be At m 9 / 4 Answer: 1; 2 9/49/4 Answer: m 9 / 4 or (-; 0) U (2.25; +)


23. The bisectors of angles A and B at the lateral side AB of the trapezoid ABCD intersect at point F. The bisectors of angles C and D at the lateral side CD intersect at point G. Find FG, if the median line of the trapezoid is 21, the sides are 13 and 15. A B C D G N Solution : 1) AMB = MBC (as lying across AD BC and secant BM) Then ABM is isosceles and AB = AM AF is the bisector, median, i.e. BF=FM 2) Similarly, we get that CG = GN 3) FG is the middle line of the trapezoid MNBC, which means FG BC AD Let's draw a straight line through the segment FG until it intersects C with the sides of the trapezoid ABCD. According to Thales, if KF AM b BF \u003d FM, then BK \u003d AK, Similarly, CP \u003d DP So, KR \u003d 21 is the middle line of the trapezoid ABCD KF - cf. AVM line, KF = 13: 2 = 6.5 GP - cf. CDN line, PG = 15: 2 = 7.5 FG = KP - KF - PG = 21 - 6.5 - 7.5 = 7 Answer: 7 F M K P