Early exam math profile March. Taking the Unified State Exam early: disadvantages

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Early Unified State Exam in Mathematics. What was on it?

And, as often happens after the end of the exam, an intense exchange of opinions began on the Internet. This is what monitoring of websites and social networks shows.

Organization of the Unified State Exam. According to many, the overall impression of the exam is positive - the atmosphere is usually calm, the observers are friendly. The most annoying thing was two things: a close check before entering the classroom, when some were even asked to take off their shoes or roll up their trousers, and video cameras monitoring the progress of the exam.

As for the tasks, they were mostly typical. The most difficult numbers for most turned out to be numbers 16 and 18. There were some surprises. So, for example, the problem on parameters (No. 18) for many people represented a system of three inequalities, without the usual y. The condition of problem 17 also looked somewhat unexpected, where instead of banks, deposits and loans, which were on the Unified State Exam in 2016, it was required to calculate the profit from the sale of shares of a pension fund. It is also noted that many options, despite the regions, had very similar tasks.

The conditions of real problems that were on the Unified State Exam can be seen. We believe that getting to know them will benefit those school graduates who will be taking specialized level mathematics in June.

Don’t miss the opportunity to practice on those tasks that were on the Unified State Exam earlier. As an analysis of the conditions of the tasks of the early stage of the Unified State Exam showed, many problems were either already on the exams (for example, No. 17 was in 2015) or fully corresponded to one of the prototypes (problems No. 4,6,8,15).

Determine which atoms of the elements indicated in the series contain one unpaired electron in the ground state.
Write down the numbers of the selected elements in the answer field.
Answer:

Answer: 23
Explanation:
Let's write down the electronic formula for each of the indicated chemical elements and depict the electron-graphic formula of the last electronic level:
1) S: 1s 2 2s 2 2p 6 3s 2 3p 4

2) Na: 1s 2 2s 2 2p 6 3s 1

3) Al: 1s 2 2s 2 2p 6 3s 2 3p 1

4) Si: 1s 2 2s 2 2p 6 3s 2 3p 2

5) Mg: 1s 2 2s 2 2p 6 3s 2

From the chemical elements indicated in the series, select three metal elements. Arrange the selected elements in order of increasing reducing properties.

Write down the numbers of the selected elements in the required sequence in the answer field.

Answer: 352
Explanation:
In the main subgroups of the periodic table, metals are located under the boron-astatine diagonal, as well as in secondary subgroups. Thus, the metals from this list include Na, Al and Mg.
The metallic and, therefore, reducing properties of the elements increase when moving to the left along the period and down the subgroup.
Thus, the metallic properties of the metals listed above increase in the order Al, Mg, Na

From among the elements indicated in the series, select two elements that, when combined with oxygen, exhibit an oxidation state of +4.

Write down the numbers of the selected elements in the answer field.

Answer: 14
Explanation:
The main oxidation states of elements from the presented list in complex substances:
Sulfur – “-2”, “+4” and “+6”
Sodium Na – “+1” (single)
Aluminum Al – “+3” (single)
Silicon Si – “-4”, “+4”
Magnesium Mg – “+2” (single)

From the proposed list of substances, select two substances in which an ionic chemical bond is present.

Answer: 12

Explanation:

In the vast majority of cases, the presence of an ionic type of bond in a compound can be determined by the fact that its structural units simultaneously include atoms of a typical metal and atoms of a non-metal.

Based on this criterion, the ionic type of bond occurs in the compounds KCl and KNO 3.

In addition to the above characteristic, the presence of an ionic bond in a compound can be said if its structural unit contains an ammonium cation (NH 4 + ) or its organic analogues - alkylammonium cations RNH 3 + , dialkylamonium R 2NH2+ , trialkylammonium R 3NH+ and tetraalkylammonium R 4N+ , where R is some hydrocarbon radical. For example, the ionic type of bond occurs in the compound (CH 3 ) 4 NCl between the cation (CH 3 ) 4 + and chloride ion Cl − .

Establish a correspondence between the formula of a substance and the class/group to which this substance belongs: for each position indicated by a letter, select the corresponding position indicated by a number.

Answer: 241

Explanation:

N 2 O 3 is a non-metal oxide. All non-metal oxides except N 2 O, NO, SiO and CO are acidic.

Al 2 O 3 is a metal oxide in the oxidation state +3. Metal oxides in the oxidation state +3, +4, as well as BeO, ZnO, SnO and PbO, are amphoteric.

HClO 4 is a typical representative of acids, because upon dissociation in an aqueous solution, only H + cations are formed from cations:

HClO 4 = H + + ClO 4 -

From the proposed list of substances, select two substances, with each of which zinc interacts.

1) nitric acid (solution)

2) iron(II) hydroxide

3) magnesium sulfate (solution)

4) sodium hydroxide (solution)

5) aluminum chloride (solution)

Write down the numbers of the selected substances in the answer field.

Answer: 14

Explanation:

1) Nitric acid is a strong oxidizing agent and reacts with all metals except platinum and gold.

2) Iron hydroxide (ll) is an insoluble base. Metals do not react at all with insoluble hydroxides, and only three metals react with soluble (alkalis) - Be, Zn, Al.

3) Magnesium sulfate is a salt of a more active metal than zinc, and therefore the reaction does not proceed.

4) Sodium hydroxide - alkali (soluble metal hydroxide). Only Be, Zn, Al work with metal alkalis.

5) AlCl 3 – a salt of a metal more active than zinc, i.e. reaction is impossible.

From the proposed list of substances, select two oxides that react with water.

Write down the numbers of the selected substances in the answer field.

Answer: 14

Explanation:

Of the oxides, only oxides of alkali and alkaline earth metals, as well as all acidic oxides except SiO 2, react with water.

Thus, answer options 1 and 4 are suitable:

BaO + H 2 O = Ba(OH) 2

SO 3 + H 2 O = H 2 SO 4

1) hydrogen bromide

3) sodium nitrate

4) sulfur oxide(IV)

5) aluminum chloride

Write down the selected numbers in the table under the corresponding letters.

Answer: 52

Explanation:

The only salts among these substances are sodium nitrate and aluminum chloride. All nitrates, like sodium salts, are soluble, and therefore sodium nitrate cannot form a precipitate in principle with any of the reagents. Therefore, salt X can only be aluminum chloride.

A common mistake among those taking the Unified State Exam in chemistry is not understanding that in an aqueous solution ammonia forms a weak base - ammonium hydroxide due to the reaction:

NH 3 + H 2 O<=>NH4OH

In this regard, an aqueous solution of ammonia gives a precipitate when mixed with solutions of metal salts that form insoluble hydroxides:

3NH 3 + 3H 2 O + AlCl 3 = Al(OH) 3 + 3NH 4 Cl

In a given transformation scheme

Cu X > CuCl 2 Y > CuI

substances X and Y are:

Answer: 35

Explanation:

Copper is a metal located in the activity series to the right of hydrogen, i.e. does not react with acids (except for H 2 SO 4 (conc.) and HNO 3). Thus, the formation of copper (ll) chloride is possible in our case only by reaction with chlorine:

Cu + Cl 2 = CuCl 2

Iodide ions (I -) cannot coexist in the same solution with divalent copper ions, because are oxidized by them:

Cu 2+ + 3I - = CuI + I 2

Establish a correspondence between the reaction equation and the oxidizing substance in this reaction: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 1433
Explanation:
An oxidizing agent in a reaction is a substance that contains an element that lowers its oxidation state

Establish a correspondence between the formula of a substance and the reagents with each of which this substance can interact: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 1215

Explanation:

A) Cu(NO 3) 2 + NaOH and Cu(NO 3) 2 + Ba(OH) 2 – similar interactions. A salt reacts with a metal hydroxide if the starting substances are soluble, and the products contain a precipitate, gas or slightly dissociating substance. For both the first and second reactions, both requirements are met:

Cu(NO 3) 2 + 2NaOH = 2NaNO 3 + Cu(OH) 2 ↓

Cu(NO 3) 2 + Ba(OH) 2 = Na(NO 3) 2 + Cu(OH) 2 ↓

Cu(NO 3) 2 + Mg - a salt reacts with a metal if the free metal is more active than what is included in the salt. Magnesium in the activity series is located to the left of copper, which indicates its greater activity, therefore, the reaction proceeds:

Cu(NO 3) 2 + Mg = Mg(NO 3) 2 + Cu

B) Al(OH) 3 – metal hydroxide in the oxidation state +3. Metal hydroxides in the oxidation state +3, +4, as well as the hydroxides Be(OH) 2 and Zn(OH) 2 as exceptions, are classified as amphoteric.

By definition, amphoteric hydroxides are those that react with alkalis and almost all soluble acids. For this reason, we can immediately conclude that answer option 2 is appropriate:

Al(OH) 3 + 3HCl = AlCl 3 + 3H 2 O

Al(OH) 3 + LiOH (solution) = Li or Al(OH) 3 + LiOH(sol.) =to=> LiAlO 2 + 2H 2 O

2Al(OH) 3 + 3H 2 SO 4 = Al 2 (SO 4) 3 + 6H 2 O

C) ZnCl 2 + NaOH and ZnCl 2 + Ba(OH) 2 – interaction of the “salt + metal hydroxide” type. The explanation is given in paragraph A.

ZnCl 2 + 2NaOH = Zn(OH) 2 + 2NaCl

ZnCl 2 + Ba(OH) 2 = Zn(OH) 2 + BaCl 2

It should be noted that with an excess of NaOH and Ba(OH) 2:

ZnCl 2 + 4NaOH = Na 2 + 2NaCl

ZnCl 2 + 2Ba(OH) 2 = Ba + BaCl 2

D) Br 2, O 2 are strong oxidizing agents. The only metals that do not react are silver, platinum, and gold:

Cu + Br 2 t° > CuBr 2

2Cu + O2 t° >2CuO

HNO 3 is an acid with strong oxidizing properties, because oxidizes not with hydrogen cations, but with an acid-forming element - nitrogen N +5. Reacts with all metals except platinum and gold:

4HNO 3(conc.) + Cu = Cu(NO 3)2 + 2NO 2 + 2H 2 O

8HNO 3(dil.) + 3Cu = 3Cu(NO 3) 2 + 2NO + 4H 2 O

Establish a correspondence between the general formula of a homologous series and the name of a substance belonging to this series: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 231

Explanation:

From the proposed list of substances, select two substances that are isomers of cyclopentane.

1) 2-methylbutane

2) 1,2-dimethylcyclopropane

3) penten-2

4) hexene-2

5) cyclopentene

Write down the numbers of the selected substances in the answer field.

Answer: 23
Explanation:
Cyclopentane has the molecular formula C5H10. Let's write the structural and molecular formulas of the substances listed in the condition

From the proposed list of substances, select two substances, each of which reacts with a solution of potassium permanganate.

1) methylbenzene

2) cyclohexane

3) methylpropane

Write down the numbers of the selected substances in the answer field.

Answer: 15

Explanation:

Of the hydrocarbons that react with an aqueous solution of potassium permanganate are those that contain C=C or C≡C bonds in their structural formula, as well as homologs of benzene (except benzene itself).
Methylbenzene and styrene are suitable in this way.

From the proposed list of substances, select two substances with which phenol interacts.

1) hydrochloric acid

2) sodium hydroxide

4) nitric acid

5) sodium sulfate

Write down the numbers of the selected substances in the answer field.

Answer: 24

Explanation:

Phenol has weak acidic properties, more pronounced than alcohols. For this reason, phenols, unlike alcohols, react with alkalis:

C 6 H 5 OH + NaOH = C 6 H 5 ONa + H 2 O

Phenol contains in its molecule a hydroxyl group directly attached to the benzene ring. The hydroxy group is an orienting agent of the first kind, that is, it facilitates substitution reactions in the ortho and para positions:

From the proposed list of substances, select two substances that undergo hydrolysis.

1) glucose

2) sucrose

3) fructose

5) starch

Write down the numbers of the selected substances in the answer field.

Answer: 25

Explanation:

All of the substances listed are carbohydrates. Of carbohydrates, monosaccharides do not undergo hydrolysis. Glucose, fructose and ribose are monosaccharides, sucrose is a disaccharide, and starch is a polysaccharide. Therefore, sucrose and starch from the above list are subject to hydrolysis.

The following scheme of substance transformations is specified:

1,2-dibromoethane → X → bromoethane → Y → ethyl formate

Determine which of the indicated substances are substances X and Y.

2) ethanal

4) chloroethane

5) acetylene

Write down the numbers of the selected substances under the corresponding letters in the table.

Answer: 31

Explanation:

Establish a correspondence between the name of the starting substance and the product, which is mainly formed when this substance reacts with bromine: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 2134

Explanation:

Substitution at the secondary carbon atom occurs to a greater extent than at the primary one. Thus, the main product of propane bromination is 2-bromopropane, not 1-bromopropane:

Cyclohexane is a cycloalkane with a ring size of more than 4 carbon atoms. Cycloalkanes with a ring size of more than 4 carbon atoms, when interacting with halogens, enter into a substitution reaction with preservation of the cycle:

Cyclopropane and cyclobutane - cycloalkanes with a minimum ring size preferentially undergo addition reactions accompanied by ring rupture:

The replacement of hydrogen atoms at the tertiary carbon atom occurs to a greater extent than at the secondary and primary ones. Thus, the bromination of isobutane proceeds mainly as follows:

Establish a correspondence between the reaction scheme and the organic substance that is the product of this reaction: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 6134

Explanation:

Heating aldehydes with freshly precipitated copper hydroxide leads to the oxidation of the aldehyde group to a carboxyl group:

Aldehydes and ketones are reduced by hydrogen in the presence of nickel, platinum or palladium to alcohols:

Primary and secondary alcohols are oxidized by hot CuO to aldehydes and ketones, respectively:

When concentrated sulfuric acid reacts with ethanol upon heating, two different products may form. When heated to a temperature below 140 °C, intermolecular dehydration occurs predominantly with the formation of diethyl ether, and when heated above 140 °C, intramolecular dehydration occurs, resulting in the formation of ethylene:

From the proposed list of substances, select two substances whose thermal decomposition reaction is redox.

1) aluminum nitrate

2) potassium bicarbonate

3) aluminum hydroxide

4) ammonium carbonate

5) ammonium nitrate

Write down the numbers of the selected substances in the answer field.

Answer: 15

Explanation:

Redox reactions are those reactions in which one or more chemical elements change their oxidation state.

The decomposition reactions of absolutely all nitrates are redox reactions. Metal nitrates from Mg to Cu inclusive decompose to metal oxide, nitrogen dioxide and molecular oxygen:

All metal bicarbonates decompose even with slight heating (60 o C) to metal carbonate, carbon dioxide and water. In this case, no change in oxidation states occurs:

Insoluble oxides decompose when heated. The reaction is not redox because Not a single chemical element changes its oxidation state as a result:

Ammonium carbonate decomposes when heated into carbon dioxide, water and ammonia. The reaction is not redox:

Ammonium nitrate decomposes into nitric oxide (I) and water. The reaction relates to OVR:

From the proposed list, select two external influences that lead to an increase in the rate of reaction of nitrogen with hydrogen.

1) decrease in temperature

2) increase in pressure in the system

5) use of an inhibitor

Write down the numbers of the selected external influences in the answer field.

Answer: 24

Explanation:

1) temperature decrease:

The rate of any reaction decreases as the temperature decreases

2) increase in pressure in the system:

Increasing pressure increases the rate of any reaction in which at least one gaseous substance takes part.

3) decrease in hydrogen concentration

Decreasing the concentration always reduces the reaction rate

4) increase in nitrogen concentration

Increasing the concentration of reagents always increases the reaction rate

5) use of an inhibitor

Inhibitors are substances that slow down the rate of a reaction.

Establish a correspondence between the formula of a substance and the products of electrolysis of an aqueous solution of this substance on inert electrodes: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 5251

Explanation:

A) NaBr → Na + + Br -

Na+ cations and water molecules compete with each other for the cathode.

2H 2 O + 2e — → H 2 + 2OH —

2Cl - -2e → Cl 2

B) Mg(NO 3) 2 → Mg 2+ + 2NO 3 —

Mg 2+ cations and water molecules compete with each other for the cathode.

Alkali metal cations, as well as magnesium and aluminum, are not able to be reduced in an aqueous solution due to their high activity. For this reason, water molecules are reduced instead according to the equation:

2H 2 O + 2e — → H 2 + 2OH —

NO3 anions and water molecules compete with each other for the anode.

2H 2 O - 4e - → O 2 + 4H +

So answer 2 (hydrogen and oxygen) is appropriate.

B) AlCl 3 → Al 3+ + 3Cl -

Alkali metal cations, as well as magnesium and aluminum, are not able to be reduced in an aqueous solution due to their high activity. For this reason, water molecules are reduced instead according to the equation:

2H 2 O + 2e — → H 2 + 2OH —

Cl anions and water molecules compete with each other for the anode.

Anions consisting of one chemical element (except F -) win competition with water molecules for oxidation at the anode:

2Cl - -2e → Cl 2

Therefore, answer option 5 (hydrogen and halogen) is appropriate.

D) CuSO 4 → Cu 2+ + SO 4 2-

Metal cations to the right of hydrogen in the activity series are easily reduced under aqueous solution conditions:

Cu 2+ + 2e → Cu 0

Acidic residues containing an acid-forming element in the highest oxidation state lose competition to water molecules for oxidation at the anode:

2H 2 O - 4e - → O 2 + 4H +

Thus, answer option 1 (oxygen and metal) is appropriate.

Establish a correspondence between the name of the salt and the medium of the aqueous solution of this salt: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 3312

Explanation:

A) iron(III) sulfate - Fe 2 (SO 4) 3

formed by a weak “base” Fe(OH) 3 and a strong acid H 2 SO 4. Conclusion - the environment is acidic

B) chromium(III) chloride - CrCl 3

formed by the weak “base” Cr(OH) 3 and the strong acid HCl. Conclusion - the environment is acidic

B) sodium sulfate - Na 2 SO 4

Formed by the strong base NaOH and the strong acid H 2 SO 4. Conclusion - the environment is neutral

D) sodium sulfide - Na 2 S

Formed by the strong base NaOH and the weak acid H2S. Conclusion - the environment is alkaline.

Establish a correspondence between the method of influencing the equilibrium system

CO (g) + Cl 2 (g) COCl 2 (g) + Q

and the direction of the shift in chemical equilibrium as a result of this effect: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 3113

Explanation:

The equilibrium shift under external influence on the system occurs in such a way as to minimize the effect of this external influence (Le Chatelier's principle).

A) An increase in the concentration of CO causes the equilibrium to shift toward the forward reaction because it results in a decrease in the amount of CO.

B) An increase in temperature will shift the equilibrium towards an endothermic reaction. Since the forward reaction is exothermic (+Q), the equilibrium will shift towards the reverse reaction.

C) A decrease in pressure will shift the equilibrium towards the reaction that results in an increase in the amount of gases. As a result of the reverse reaction, more gases are formed than as a result of the direct reaction. Thus, the equilibrium will shift towards the opposite reaction.

D) An increase in the concentration of chlorine leads to a shift in the equilibrium towards the direct reaction, since as a result it reduces the amount of chlorine.

Establish a correspondence between two substances and a reagent that can be used to distinguish these substances: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 3454

Explanation:

It is possible to distinguish two substances with the help of a third one only if these two substances interact with it differently, and, most importantly, these differences are externally distinguishable.

A) Solutions of FeSO 4 and FeCl 2 can be distinguished using a solution of barium nitrate. In the case of FeSO 4, a white precipitate of barium sulfate forms:

FeSO 4 + BaCl 2 = BaSO 4 ↓ + FeCl 2

In the case of FeCl 2 there are no visible signs of interaction, since the reaction does not occur.

B) Solutions of Na 3 PO 4 and Na 2 SO 4 can be distinguished using a solution of MgCl 2. The Na 2 SO 4 solution does not react, and in the case of Na 3 PO 4 a white precipitate of magnesium phosphate precipitates:

2Na 3 PO 4 + 3MgCl 2 = Mg 3 (PO 4) 2 ↓ + 6NaCl

C) Solutions of KOH and Ca(OH) 2 can be distinguished using a solution of Na 2 CO 3. KOH does not react with Na 2 CO 3, but Ca(OH) 2 gives a white precipitate of calcium carbonate with Na 2 CO 3:

Ca(OH) 2 + Na 2 CO 3 = CaCO 3 ↓ + 2NaOH

D) Solutions of KOH and KCl can be distinguished using a solution of MgCl 2. KCl does not react with MgCl 2, and mixing solutions of KOH and MgCl 2 leads to the formation of a white precipitate of magnesium hydroxide:

MgCl 2 + 2KOH = Mg(OH) 2 ↓ + 2KCl

Establish a correspondence between the substance and its area of ​​application: for each position indicated by a letter, select the corresponding position indicated by a number.

Write down the selected numbers in the table under the corresponding letters.

Answer: 2331
Explanation:
Ammonia - used in the production of nitrogenous fertilizers. In particular, ammonia is a raw material for the production of nitric acid, from which, in turn, fertilizers are obtained - sodium, potassium and ammonium nitrate (NaNO 3, KNO 3, NH 4 NO 3).
Carbon tetrachloride and acetone are used as solvents.
Ethylene is used to produce high molecular weight compounds (polymers), namely polyethylene.

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 of an increased level of complexity with a short answer and 7 tasks of a high level of complexity with a detailed answer.

The exam work in mathematics is allotted 3 hours 55 minutes(235 minutes).

Answers for tasks 1–12 are written down as a whole number or finite decimal fraction. 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 instruments with reference materials printed on them. 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.

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 of an increased level of complexity with a short answer and 7 tasks of a high level of complexity with a detailed answer.

The exam work in mathematics is allotted 3 hours 55 minutes(235 minutes).

Answers for tasks 1–12 are written down as a whole number or finite decimal fraction. 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 instruments with reference materials printed on them. 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 should you pay for cold water in 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. A quadrilateral is depicted on checkered paper with a square size of 1 x 1. 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 of the equation log 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 the 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 the average speed of the car along the entire route. Express your answer in km/h

12. Find the smallest value of the function on the interval [−2π/3;0]

13. a) Solve the equation

b) Indicate the roots of this equation belonging to the segment

14. The section of the rectangular parallelepiped ABCDA 1 B 1 C 1 D 1 by the plane α containing the straight line BD 1 and parallel to the straight 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. In 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 money into a bank account, and at the end of each subsequent year the amount in 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 ​​of r 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 natural numbers are written on the board, 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?

c) What is the greatest value that the sum of the numbers on the board can take 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. }