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1 Training work in MATHEMATICS grade 9 September 27, 2017 Option MA90103 Completed by: Full name class Instructions for completing the work The work consists of two modules: “Algebra” and “Geometry”. There are 26 tasks in total. The Algebra module contains seventeen tasks: in part 1 there are fourteen tasks; Part 2 contains three tasks. The Geometry module contains nine tasks: part 1 has six tasks; Part 2 contains three tasks. For execution exam paper in mathematics, 3 hours 55 minutes (235 minutes) are allotted. Write down the answers to tasks 2, 3, 14 as one number, which corresponds to the number of the correct answer. For the remaining tasks in Part 1, the answer is a number or sequence of numbers. If the answer is received common fraction, convert it to decimal. Write down the solutions to the tasks in Part 2 and the answers to them on a separate sheet of paper. Tasks can be completed in any order, starting from any module. There is no need to rewrite the text of the assignment, you just need to indicate its number. First complete the tasks of part 1. We advise you to start with those tasks that cause you the least difficulties, then move on to other tasks. To save time, skip a task that you cannot complete immediately and move on to the next one. If you have time left, you can return to missed tasks. When performing Part 1, perform all necessary calculations and transformations in a draft. Entries in the draft are not taken into account when grading work. If the task contains a drawing, then you can use it directly in the text of the work to carry out the constructions you need. We recommend that you carefully read the conditions and check the response received. When performing work, you can use reference materials, issued along with the option. The points you receive for completed tasks are summed up. Try to complete as many tasks as possible and gain greatest number points. We wish you success! StatGrad uch. on
2 Mathematics. 9th grade. Option MA Part 1 The answers to tasks 1 20 are a digit, a number or a sequence of numbers Module “Algebra” Find the value of the expression 3 3.9 9.6. Scientist Kulikov leaves Moscow for a conference at St. Petersburg University. The conference starts at 10:00. The table shows the schedule of night trains Moscow-St. Petersburg. Train number Departure from Moscow Arrival in St. Petersburg 026A 22: :32 002A 23:55 07:55 038A 22: :A 00: :12 The journey from the station to the university takes half an hour. Indicate the number of the latest (by departure time) train that suits scientist Kulikov. 1) 026A 2) 002A 3) 038A 4) 016A Answer: Which of these intervals does the number 4 9 belong to? 1) 0.1; 0.2 2) 0.2; 0.3 3) 0.3; 0.4 4) 0.4; 0.5 Answer: StatGrad academic. on
3 Mathematics. 9th grade. Option MA Find the value of the expression The graph shows the dependence of atmospheric pressure on altitude above sea level. On horizontal axis The height above sea level is marked in kilometers, and the vertical pressure is marked in millimeters of mercury. Determine from the graph at what height atmospheric pressure equal to 420 millimeters of mercury. Give your answer in kilometers Solve the equation x x If the equation has more than one root, write down the smaller root in your answer. StatGrad uch. on
4 Mathematics. 9th grade. Option MA The cost of travel on an electric train is 140 rubles. Schoolchildren receive a 50% discount. How many rubles will it cost for 5 adults and 3 schoolchildren? 8 9 The diagram shows the seven largest countries in the world by area (million km 2). 2 Area, million km,1 Russia 10.0 9.6 9.5 8.5 7.7 Canada China USA Which of the following statements are they correct? Brazil Australia 1) The USA is one of the seven largest countries in the world by area. 2) The area of India is 4 million km 2. 3) The area of Australia more area territory of China. 4) The area of Russia is more than twice the area of Brazil. In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters. There are 50 tickets in the exam, Seryozha did not learn 11 of them. Find the probability that he will come across the learned ticket. 3.3 India StatGrad uch. on
5 Mathematics. 9th grade. Option MA The figures show graphs of functions of the form y kx b. Establish a correspondence between the signs of the coefficients k and b and the graphs of the functions. COEFFICIENTS A) k 0, b 0 B) k 0, b 0 C) k 0, b 0 GRAPHICS 1) y 2) 0 x In the table, indicate the corresponding number under each letter. Answer: A B C Is the sequence a given by the sequence formula greater than 6? Find the value of the expression n y 0 a n 2 2 x 3) y 0 x 34. How many members of this n 1 6a 36a 49c 7c 36a with a 77, c 69. 7c 42ac 6a In the company " Clean water» the cost (in rubles) of a well made of reinforced concrete rings is calculated using the formula C n, where n is the number of rings installed in the well. Using this formula, calculate the cost of a well of 14 rings. Give your answer in rubles. StatGrad uch. on
6 Mathematics. 9th grade. Option MA Indicate the solution to the system of inequalities 27 3x 0, 6 3x 6. 1) 4 3)) Answer: 9 4) Module “Geometry” The projector completely illuminates screen A with a height of 80 cm, located at a distance of 120 cm from the projector. Find the smallest distance from the projector that screen B, 330 cm high, must be placed so that it is fully illuminated, if the projector settings remain unchanged. Give your answer in centimeters. IN triangle ABC angle C is 90, BC 8, AB 10. Find cos B. The side of the square is 34. Find the radius of the circle inscribed in this square. 9 A A B B C StatGrad uch. on
7 Mathematics. 9th grade. Option MA Find acute angle parallelogram ABCD if the bisector of angle A forms an angle equal to 8 with side BC. Give your answer in degrees. A B D C On checkered paper a figure is depicted with a cell size of 1 1. Find its area. Which of the following statements are true? 1) There is a rectangle whose diagonals are mutually perpendicular. 2) If one of the angles in a rhombus is 90 degrees, then this rhombus is a square. 3) B obtuse triangle all angles are obtuse. In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters. StatGrad uch. on
8 Mathematics. 9th grade. Option MA Part 2 When completing tasks, use a separate sheet of paper. First, indicate the task number, and then write down its solution and answer. Write clearly and legibly. Algebra module Solve the system of equations 2 x + y = , 9x y = 2. Two runners started simultaneously in the same direction from the same place circular track running several laps. One hour later, when one of them had 4 km left before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 6 km/h less than the speed of the second. Graph the function x 3 at x< 3, y = 1,5 x + 4,5 при 3 x 4, 1,5 x 7,5 при x >4. Determine for what values of m the straight line y = m has exactly two common points with the graph. Module "Geometry" Bisectors of angles A and B with lateral side AB of trapezoid ABCD intersect at point F. Find AB if AF =16, BF =12. Through the intersection point O of the diagonals of the parallelogram ABCD, a straight line is drawn intersecting the sides BC and AD at points L and N, respectively. Prove that the segments CL and AN are equal. In triangle ABC, the bisector BE and the median AD are perpendicular and have the same length equal to 36. Find the sides of triangle ABC. StatGrad uch. on
Training work in MATHEMATICS 9th grade September 27, 2017 Option MA90103 Completed by: Full name class Instructions for completing the work The work consists of two modules: “Algebra” and “Geometry”. Total in progress
Training work in MATHEMATICS grade 9 September 27, 2017 Option MA90104 Completed by: Full name class Instructions for completing the work The work consists of two modules: “Algebra” and “Geometry”. Total in progress
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Mathematics. 9th grade. Option MA9070 m0006 District City (settlement) School Class Last name First name Patronymic Training work in the GIA format in MATHEMATICS May 6, 04 9th grade Option MA9070 StatGrad
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1. The T-shirt cost 650 rubles. After the price increase, it began to cost 780 rubles. By what percentage was the price of the T-shirt increased?
Let's take the original price of the T-shirt as 100%. The price of the T-shirt was increased by RUB. Let's find what percentage of the price of a T-shirt is 130 rubles. from original price:
%
2. The diagram shows the distribution of aluminum smelting in 10 countries (in thousands of tons) for 2009. Among the countries represented, Bahrain occupied first place in aluminum smelting, tenth place - New Zealand. Where did Iceland rank?
It is easy to see from the graph that the bar indicating aluminum smelting in Iceland is the third highest.
3. A triangle is depicted on checkered paper with a 1x1 square size. Find the length of its height lowered to the side.
A perpendicular from a point to a line containing the side has a length of 5 cells.
4. There are two payment machines in the store. Each of them can be faulty with probability 0.05, regardless of the other machine. Find the probability that at least one machine is working.
The following events are possible
1)Both machines are working: AI
2) The first machine is working, but the second is not: IN
3) The second machine is working, but the first is not: NI
4) Both machines are faulty: NN.
We are satisfied with the first three events; the combination of these events is the opposite event of the fourth.
The serviceability of one machine does not depend on the serviceability of the second; these events are independent.
The probability that one machine is faulty is equal to
The probability that both machines are faulty is equal to the product of the probabilities:
The probability of the opposite event is
Answer: 0.9975
5. Find the root of the equation .
Examination:
6. Central angle 27˚ more than an acute inscribed angle subtended by the same arc of a circle. Find the inscribed angle. Give your answer in degrees.
The central angle is twice the inscribed angle. Let the inscribed angle be equal to , then the central angle is equal to .
We get the equation:
7. The figure shows the graph of the function And tangent to it at the abscissa point . Find the value of the derivative of the function at point .
The derivative of the function at the point of tangency is equal to the tangent of the tangent. To find the tangent of the angle of inclination of a straight line, using the points highlighted in the figure, we define a right triangle:
The vertical leg is 3, the horizontal leg is 6, 
The tangent is inclined to the right, the angle between the tangent and the positive direction of the OX axis is acute, therefore,
8. The cylinder and cone have general basis and height. The volume of the cylinder is 36. Find the volume of the cone.
The volume of the cone is
The volume of the cylinder is
Base area, - height.
If a cylinder and a cone have the same base and height, then the volume of the cone is three times less than the volume of the cylinder.
The volume of the cone is
9. Find the meaning of the expression
When multiplying powers with the same basis We add up the indicators and subtract when dividing.
10. The distance from an observer located at a low altitude of kilometers above the earth to the horizon line he observes is calculated by the formula , where R = 6400 km is the radius of the Earth. From what height is the horizon visible at a distance of 48 kilometers? Express your answer in kilometers.
By condition
Let's substitute these values into the formula:
Let's square both sides.
Answer: 0.18
11. Two teams, consisting of workers of the same qualifications, simultaneously began to fulfill two identical orders. The first brigade had 18 workers, and the second - 22 workers. 9 days after the start of work, 3 workers from the second team moved to the first brigade. As a result, both orders were completed simultaneously. Find how many days it took to complete the orders.
Let the productivity of each worker be equal.
In the first 9 days, the workers of the first team completed a volume of work.
In the first 9 days, the workers of the second brigade completed a volume of work.
After this, in the first brigade it became 
workers, and in the second - workers.
Let both teams complete the rest of the work in days. Both teams completed the same amount of work:
Let's divide both sides of the equation by:
Taking into account the first 9 days we get
12. Find highest value functions on the segment.
Let's find the derivative:
Let's equate the derivative to zero:
This equation has no solutions, therefore, the derivative does not vanish and does not change sign. Since , therefore, and the function decreases for all real values. Therefore, it takes the greatest value at the left end of the segment, that is, at
