Assessment
two parts, including 19 tasks. Part 1 Part 2
3 hours 55 minutes(235 minutes).
Answers
But you can make a compass Calculators on the exam not used.
passport), pass and capillary or! Allowed to take with myself water(in a transparent bottle) and I'm going
The examination paper consists of two parts, including 19 tasks. Part 1 contains 8 tasks of a basic difficulty level with a short answer. Part 2 contains 4 tasks higher level difficulties with short answer and 7 tasks high level Difficulty with a detailed answer.
For execution exam paper in mathematics is assigned 3 hours 55 minutes(235 minutes).
Answers for tasks 1–12 are written down as an integer or finite decimal . Write the numbers in the answer fields in the text of the work, and then transfer them to answer form No. 1, issued during the exam!
When performing work, you can use the ones issued along with the work. Only a ruler is allowed, but it's possible make a compass with your own hands. Do not use tools with markings on them. reference materials. Calculators on the exam not used.
You must have an identification document with you during the exam ( passport), pass and capillary or gel pen with black ink! Allowed to take with myself water(in a transparent bottle) and I'm going(fruit, chocolate, buns, sandwiches), but they may ask you to leave them in the corridor.
Early version of the Unified State Exam 2017 in mathematics profile level March 31, 2017
1. The apartment has a cold water meter. Readings March 1 - 270 cubic meters. m., and on April 1 - 320 cubic meters. m. How much do you need to pay for cold water for March, if the cost is 1 cubic meter. m. of water is equal to 14 rubles. 50 kopecks?
2. In the figure, the bold dots show the price of palladium at the close of trading. The dates of the month are indicated horizontally, and the price of palladium in rubles per gram is indicated vertically. For clarity, the bold points in the figure are connected by a line. Determine from the figure the maximum cost of metal in the second half of the month.
3. On checkered paper with a cell size of 1 x 1, a quadrilateral is depicted. Find the radius of the circle that can be inscribed in the given quadrilateral.
4. Before the start of a football match, team captains toss a coin. What is the probability that the Stator team will start all three games?
5. Find the root log equations 7(5x−3)=2log 7 3
6. Find cosA if it is known that AB = 10, CB = √19
7. The figure shows the graph of the function y=f(x) and the tangent to it at the point with the abscissa x 0. Find the value of the derivative of the function y=f(x) at the point x 0 .
8. Given a rectangular parallelepiped ABCDA1B1C1D1. It is known that AA1 = 5, BC = 4 and D1C1 = 3. Find the volume of the polyhedron ADA1B1C1D1.
9. Find the meaning of the expression
10. For the heating element of a certain device, the dependence of temperature (in Kelvin) on operating time was experimentally obtained: T(t)=T0+bt+at 2, where t is time in minutes, T 0 =1400 K, a=−10 K /min 2, b=200 K/min. It is known that if the heater temperature exceeds 1760 K, the device may deteriorate, so it must be turned off. Determine through what longest time After starting work, you need to turn off the device. Express your answer in minutes.
11. The car drove for the first hour at a speed of 60 km/h, then for 2 hours at a speed of 110 km/h, and for the next 2 hours at a speed of 120 km/h. Find average speed car all the way. Express your answer in km/h
12. Find smallest value functions on the interval [−2π/3;0]
13. a) Solve the equation
b) Indicate the roots of this equation belonging to the segment
14. Section rectangular parallelepiped ABCDA 1 B 1 C 1 D 1 the plane α containing the line BD 1 and parallel to the line AC is a rhombus.
a) Prove that the face ABCD is a square.
b) Find the angle between planes α and BCC 1 if AA 1 = 6 and AB = 4.
15. Solve the inequality
16.V triangle ABC points A 1, B 1 and C 1 are the midpoints of sides BC, AC and AB, respectively, AH is the height, angle BAC is 60 o, angle BCA is 45 o.
a) Prove that points A 1, B 1, C 1 and H lie on the same circle.
b) Find A 1 H if BC is equal to
17. The pension fund owns securities that cost t 2 thousand rubles at the end of year t (t=1;2;,…). At the end of any year, the pension fund can sell securities and deposit the money into a bank account, and at the end of each next year the amount on the account will increase by r+1 times. The pension fund wants to sell securities at the end of the year so that at the end of the twenty-fifth year the amount in its account will be the largest. Calculations showed that for this, securities must be sold strictly at the end of the twenty-first year. At what positive values is this possible?
18. Find all values of the parameter a, for each of which the system of inequalities
has at least one solution on the interval
19. Several different ones are written on the board natural numbers, the product of any two of which is greater than 40 and less than 100.
a) Can there be 5 numbers on the board?
b) Can there be 6 numbers on the board?
in which highest value can take the sum of the numbers on the board if there are four of them?
1. 725
2. 315
3. 3
4. 0,125
5. 2,4
6. 0,9
7. -0,5
8. 30
9. 6
10. 2
11. 104
12. -14
13. a) 2; 1/2 b) 1/2
14. arctg(5/3)
15. (−5;−√17]∪[−3;3]∪[√17;5)
16. 1
17. (43/441;41/400)
18. }