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Exercise 1
In the store, all furniture is sold disassembled. The buyer can order the assembly of furniture at home, the cost of which is \ (20 \% \) of the cost of the purchased furniture. The wardrobe costs 4,100 rubles. How much will it cost to buy this cabinet together with the assembly?
Let's find the cost of the assembly: \ (4100 \ cdot 20: 100 = 820 \) rubles. Therefore, the buyer will pay \ (4100 + 820 = 4920 \) rubles for the cabinet and assembly.
Answer: 4920
Assignment 2
The diagram shows the average monthly air temperature in Minsk for each month of 2003. The horizontal indicates the months, the vertical indicates the temperature in degrees Celsius. Determine from the diagram in which month the average monthly temperature first exceeded \ (14 ^ \ circ C \). In your reply, write down the number of the month. (For example, answer 1 means January.)
Assignment 3
A triangle is depicted on checkered paper with a square \ (1 \ times1 \). Find the radius of the circle circumscribed about it.
By the theorem of sines, the ratio of the side length to the sine of the opposite angle is equal to two radii of the circumscribed circle: \ [\ dfrac a (\ sin \ alpha) = 2R \] Take the angle \ (\ alpha \) angle \ (A \), then \ ( a = BC \). Note that \ (\ alpha = 45 ^ \ circ \), since \ (\ triangle B "AC" \) is rectangular and isosceles. Hence, \ (\ sin \ alpha = \ dfrac (\ sqrt2) 2 \).
Find from rectangular \ (\ triangle BHC \) by the Pythagorean theorem \ (BC \): \ Therefore, \
Answer: 5
Assignment 4
There are three sellers in the store. Each of them is busy serving a customer with a probability of 0.7, regardless of other sellers. Find the probability that at a random moment in time all three salespeople are busy.
The event “all three sellers are simultaneously busy” is equal to the event “the first seller is busy AND the second seller is busy AND the third seller is busy”. Since each seller is busy with a probability of 0.7 independently of the others, the probability of this event is equal to the product of the probabilities of the events “the first seller is busy”, “the second seller is busy” and “the third seller is busy”: \
Answer: 0.343
Assignment 5
Find the root of the equation \ [\ log _ (\ frac14) (9-5x) = - 3 \]
ODZ this equation: \ (9-5x> 0 \). Let's solve at ODZ: \ [\ log _ (\ frac14) (9-5x) = - 3 \ quad \ Rightarrow \ quad 9-5x = \ left (\ dfrac14 \ right) ^ (- 3) \ quad \ Leftrightarrow \ quad 9-5x = 64 \ quad \ Leftrightarrow \ quad x = -11. \] This answer is appropriate for ODU.
Answer: -11
Assignment 6
In an isosceles triangle \ (ABC \) with base \ (AB \), the side is \ (16 \ sqrt7 \), \ (\ sin \ angle BAC = 0.75 \). Find the length of the height \ (AH \).
Consider the picture:
Draw \ (CK \ perp AB \). Since the triangle \ (ABC \) is isosceles, then \ (\ angle BAC = \ angle ABC \), therefore, \ (\ sin \ angle ABC = 0.75 = \ frac34 \).
Then from \ (\ triangle CKB \): \ [\ dfrac34 = \ dfrac (CK) (CB) \ quad \ Rightarrow \ quad CK = 12 \ sqrt7. \] Then by the Pythagorean theorem from \ (\ triangle CKB \): \
Therefore, since \ (CK \) is also a median, that is, \ (AK = KB \), we have: \ (AB = 2KB = 56 \).
Then from \ (\ triangle AHB \): \ [\ dfrac34 = \ dfrac (AH) (AB) \ quad \ Rightarrow \ quad AH = 42. \]
Answer: 42
Assignment 7
The figure shows the graph of the function \ (y = f "(x) \) - the derivative of the function \ (f (x) \). Find the abscissa of the point at which the tangent to the graph of the function \ (y = f (x) \) is parallel to the straight line \ (y = 10-7x \) or the same.
It is necessary to find \ (x_0 \), in which a tangent is drawn to \ (f (x) \), and this tangent is parallel or coincides with \ (y = 10-7x \).
Let the tangent equation be: \ (y = kx + b \). Since it is parallel or the same as \ (y = 10-7x \), their slopes are equal, that is, \ (k = -7 \).
Slope of the tangent to \ (f (x) \) equal to the value\ (f "(x) \) at the point of tangency \ (x_0 \), that is, \ (k = -7 = f" (x_0) \).
Since the derivative is just given on the graph, it is necessary to find a point with an abscissa \ (x_0 \), for which the value of the ordinate \ (y_0 = f "(x_0) \) is \ (- 7 \). on the chart there is only one point with ordinate -7 - this is the point \ ((- 2; -7). \)
Answer: -2
Assignment 8
Two cylinders are given. The volume of the first cylinder is \ (8 \). The height of the second cylinder is 4 times less, and the radius of the base is 3 times greater than that of the first. Find the volume of the second cylinder.
The volume of a cylinder with a height \ (h \) and a base radius \ (R \) is calculated by the formula \ Therefore, for the first cylinder we have the equality: \ For the second cylinder, the height is \ (\ frac14h \), and the base radius is \ (3R \ ). Therefore, its volume: \
Answer: 18
Assignment 9
Find the meaning of the expression \ [\ dfrac (\ sqrt (5,6) \ cdot \ sqrt (1,4)) (\ sqrt (0,16)) \]
Let's put everything under one root: \ [\ sqrt (\ dfrac (5.6 \ cdot 1.4) (0.16)) = \ sqrt (\ dfrac (56 \ cdot 14) (16)) = \ sqrt (\ dfrac (14 \ cdot 14 ) (4)) = \ dfrac (14) 2 = 7. \]
Answer: 7
Assignment 10
The car, the mass of which is \ (m = 2000 \) kg, begins to move with an acceleration that remains unchanged for \ (t \) seconds, and travels a path \ (S = 1000 \) meters during this time. The value of the force (in newtons) applied at this time to the car (engine thrust) is \ (F = \ dfrac (2mS) (t ^ 2) \).
Determine the time after the start of the movement of the car, for which it will pass specified path if it is known that the force \ (F \) applied to the car is \ (1600 H \). Express your answer in seconds.
Let's substitute the values into the formula: \ since \ (t> 0 \) is time.
Answer: 50
Assignment 11
On two parallel railroad tracks in one direction are passenger and freight trains, the speeds of which are respectively 90 km / h and 30 km / h. The length of the freight train is 900 meters. Find the length of a passenger train if the time it took it to pass a freight train is 1 minute 3 seconds. Give your answer in meters.
The phrase “a passenger train passed the freight train” means that at the beginning of the observation, the passenger's nose was opposite the goods’s tail, and at the end, the passenger’s tail was opposite the freight train’s nose:
Let's fix two points: the nose of the passenger and the tail of the commodity. Then, at the beginning of the observation, the distance between them was equal to 0 m, and at the end of the observation, the distance between them was equal to the length of the freight train plus the length of the passenger train.
Note that the nose of the passenger train moves away from the tail of the freight train by \ (90-30 = 60 \) km per hour. Therefore, the removal rate is \
Let \ (l \) m be the length of a passenger train. 1 minute 3 seconds is equal to 63 seconds, therefore: \
Answer: 150
Assignment 12
Find the minimum point of the function \ (y = x ^ 3-4x ^ 2-3x-13. \)
Find the derivative: \ Find the zeros of the derivative: \ Let us find the signs of the derivative on the intervals:
The minimum point is the point at which the derivative changes its sign from minus to plus, therefore, \ (x_ (min) = 3 \).
Answer: 3
Assignment 13
a) Solve the equation \ [\ dfrac1 (\ sin ^ 2x) - \ dfrac3 (\ cos \ left (\ dfrac (11 \ pi) 2 + x \ right)) = - 2 \]
b) Indicate the roots of this equation that belong to the segment \ (\ left [-2 \ pi; - \ dfrac (\ pi) 2 \ right]. \)
a) According to the reduction formula \ (\ cos \ left (\ dfrac (11 \ pi) 2 + x \ right) = \ sin x \), therefore, the equation will take the form: \ [\ dfrac1 (\ sin ^ 2x) - \ dfrac3 (\ sin x) + 2 = 0 \]
Let's make the replacement \ (t = \ dfrac1 (\ sin x) \), then \ Therefore, \ (\ sin x = 1 \), which is equivalent to \ (x = \ dfrac (\ pi) 2 + 2 \ pi m, m \ in \ mathbb (Z) \);
\ (\ sin x = \ dfrac12 \), which is equivalent to \ (x = \ dfrac (\ pi) 6 + 2 \ pi k \) and \ (x = \ dfrac (5 \ pi) 6 + 2 \ pi n \ ), \ (k, n \ in \ mathbb (Z) \).
b) Let's select the roots.
\ (- 2 \ pi \ leqslant \ dfrac (\ pi) 6 + 2 \ pi k \ leqslant - \ dfrac (\ pi) 2 \ quad \ Rightarrow \ quad - \ dfrac (13) (12) \ leqslant k \ leqslant - \ dfrac13 \)... Since \ (k \) is an integer, then \ (k = -1 \), therefore, \ (x = - \ dfrac (11 \ pi) 6 \).
\ (- 2 \ pi \ leqslant \ dfrac (5 \ pi) 6 + 2 \ pi n \ leqslant - \ dfrac (\ pi) 2 \ quad \ Rightarrow \ quad - \ dfrac (17) (12) \ leqslant n \ leqslant - \ dfrac23 \)... Since \ (n \) is an integer, then \ (n = -1 \), therefore, \ (x = - \ dfrac (7 \ pi) 6 \).
\ (- 2 \ pi \ leqslant \ dfrac (\ pi) 2 + 2 \ pi m \ leqslant - \ dfrac (\ pi) 2 \ quad \ Rightarrow \ quad - \ dfrac54 \ leqslant m \ leqslant - \ dfrac12 \)... Since \ (m \) is an integer, \ (m = -1 \), therefore \ (x = - \ dfrac (3 \ pi) 2. \)
Answer:
a) \ (\ dfrac (\ pi) 6 + 2 \ pi k; \ dfrac (5 \ pi) 6 + 2 \ pi n; \ dfrac (\ pi) 2 + 2 \ pi m; \ k, n, m \ in \ mathbb (Z) \)
b) \ (- \ dfrac (11 \ pi) 6; - \ dfrac (3 \ pi) 2; - \ dfrac (7 \ pi) 6 \)
Assignment 14
At the base of the pyramid \ (SABCD \) lies the rectangle \ (ABCD \) with side \ (AB = 5 \) and diagonal \ (BD = 9 \). All side edges of the pyramid are \ (5 \). The point \ (E \) is marked on the diagonal \ (BD \) of the base \ (ABCD \), and the point \ (F \) is marked on the edge \ (AS \) so that \ (SF = BE = 4 \).
a) Prove that the plane \ (CEF \) is parallel to the edge \ (SB \).
b) The plane \ (CEF \) intersects the edge \ (SD \) at the point \ (Q \). Find the distance from the point \ (Q \) to the plane \ (ABC \).
a) Extend \ (CE \) to the intersection with \ (AB \) at the point \ (K \). We obtain the segment \ (FK \) along which the plane \ (CEF \) intersects the face \ (SAB \). Consider the base of the pyramid:
\ (DE = 9-4 = 5 = DC \), therefore \ (\ triangle DEC \) is isosceles. Then \ (\ angle DCE = \ angle DEC = \ angle BEK = \ angle BKE \) therefore \ (\ triangle BEK \) is also isosceles and \ (BE = BK = 4 \). Then \ (AK = 5-4 = 1 \).
Note that the side faces \ (ASB \) and \ (CSD \) are equilateral triangles with side \ (5 \). So in \ (\ triangle AFK \) \ (AF = AK = 1 \) and \ (\ angle FAK = 60 ^ \ circ \), hence it is also equilateral, that is \ (FK \ parallel SB \) ( \ (\ angle AKF = \ angle ABS = 60 ^ \ circ \) as corresponding for the secant \ (AB \)). Thus, in the plane \ (CEF \) there is a line \ (FK \) parallel to \ (SB \). Therefore, according to the feature, the plane \ (CEF \) is parallel to \ (SB \).
b) Since the plane \ (CEF \ parallel SB \), it will intersect the plane \ (BSD \) along the straight line \ (EQ \) parallel to \ (SB \) (otherwise \ (EQ \) will intersect \ ( SB \), therefore, the plane \ (CEF \) will intersect \ (SB \)). Consider \ (\ triangle BSD \): 
Note that since all the side edges of the pyramid are equal, the height \ (SO \) will fall to the point of intersection of the base diagonals (all triangles \ (SAO \), \ (SBO \), \ (SCO \) and \ (SDO \) will be equal as rectangular along the leg and hypotenuse, therefore, \ (AO = BO = CO = DO \), therefore, \ (O \) is the point of intersection of the diagonals).
Let's draw \ (QH \ parallel SO \). Since \ (SO \) is perpendicular to the plane \ (ABC \), then \ (QH \ perp (ABC) \). Thus, you need to find \ (QH \).
Since \ (EQ \ parallel SB \), then by Thales's theorem: \ [\ dfrac54 = \ dfrac (DE) (EB) = \ dfrac (DQ) (QS) \ quad \ Rightarrow \ quad \ dfrac (DQ) (DS) = \ dfrac59 \] Because \ (\ triangle DQH \ sim \ triangle DSO \)(in two corners), then \ [\ dfrac (DQ) (DS) = \ dfrac (QH) (SO) \ quad \ Rightarrow \ quad QH = \ dfrac59SO \] Thus, you need to find \ (SO \).
From rectangular \ (\ triangle SOB \): \
Hence, \
Answer:
b) \ (\ dfrac (5 \ sqrt (19)) (18) \)
Task 15
Solve inequality \ [\ dfrac (\ log_3 (9x) \ cdot \ log_4 (64x)) (5x ^ 2- | x |) \ leqslant 0 \]
Let's find the ODZ of the logarithms: \ [\ begin (cases) 9x> 0 \\ 64x> 0 \ end (cases) \ quad \ Leftrightarrow \ quad x> 0 \] Note that on this ODZ \ (| x | = x \). Then the inequality on the ODZ according to the method of rationalization is equivalent to: \ [\ dfrac ((3-1) (9x-1) (4-1) (64x-1)) (x (5x-1)) \ leqslant 0 \ quad \ Leftrightarrow \ quad \ dfrac ((9x-1 ) (64x-1)) (x (5x-1)) \ leqslant 0 \] Let's solve this inequality by the method of intervals:
Therefore, the solution will be \ (x \ in \ left (0; \ dfrac1 (64) \ right] \ cup \ left [\ dfrac19; \ dfrac15 \ right) \).
Intersecting this answer with ODZ \ (x> 0 \), we get the final answer: \\ cup \ left [\ dfrac19; \ dfrac15 \ right) \]
Answer:
\ (\ left (0; \ dfrac1 (64) \ right] \ cup \ left [\ dfrac19; \ dfrac15 \ right) \)
Task 16
Line passing through the midpoint \ (M \) of the hypotenuse \ (AB \) right triangle\ (ABC \), is perpendicular to \ (CM \) and intersects the leg \ (AC \) at the point \ (K \). Moreover, \ (AK: KC = 1: 2 \).
a) Prove that \ (\ angle BAC = 30 ^ \ circ \).
b) Let the lines \ (MK \) and \ (BC \) intersect at the point \ (P \), and the lines \ (AP \) and \ (BK \) - at the point \ (Q \). Find \ (KQ \) if \ (BC = 2 \ sqrt3 \).
a) Let \ (AK = x, \ KC = 2x \). Let's draw \ (BL \ parallel MK \). Then by Thales' theorem \ [\ dfrac (BM) (MA) = \ dfrac11 = \ dfrac (LK) (KA) \ quad \ Rightarrow \ quad LK = KA = x \ quad \ Rightarrow \ quad CL = x. \]
Then also by Thales' theorem: \ [\ dfrac (CL) (LK) = \ dfrac11 = \ dfrac (CO) (OM) \ quad \ Rightarrow \ quad CO = OM. \] Therefore, \ (BO \) is the median and height ( \ (MK \ perp CM, \ BO \ parallel MK \ quad \ Rightarrow \ quad BO \ perp CM \)), therefore \ (\ triangle CBM \) is isosceles and \ (CB = BM \). Therefore, \ (CB = \ frac12BA \). Since the leg, equal to half of the hypotenuse, lies opposite the angle at \ (30 ^ \ circ \), then \ (\ angle BAC = 30 ^ \ circ \).
b) Consider \ (\ triangle PMC \): \ (\ angle PMC = 90 ^ \ circ \). Since \ (BM = BC \), then \ (BM = BC = BP \), that is, \ (B \) is the middle of \ (CP \) ( \ (\ angle BCM = \ angle BMC = 60 ^ \ circ \), hence, \ (\ angle CPM = 30 ^ \ circ = \ angle PMB \) therefore \ (BP = BM \)).
Let's draw \ (BS \ parallel AP \). Then \ (BS \) is the midline of the \ (APC \) triangle. Hence, \ (CS = SA \).
From rectangular \ (\ triangle ABC \): \ [\ mathrm (tg) \, 30 ^ \ circ = \ dfrac (BC) (AC) \ quad \ Rightarrow \ quad AC = BC \ cdot \ sqrt3 = 6. \] Therefore, \ (CS = SA = 3 \), and since \ (CK: KA = 2: 1 \), then \ (KA = 2 \) and \ (SK = 1 \).
notice, that \ (\ triangle BKS \ sim \ triangle QKA \) in two angles (\ (\ angle BKS = \ angle QKA \) as vertical, \ (\ angle BSK = \ angle QAK \) as criss-cross at \ (AQ \ parallel BS \) and \ (SA \) secant). Hence, \ [\ dfrac (SK) (AK) = \ dfrac12 = \ dfrac (BK) (KQ) \ quad \ Rightarrow \ quad KQ = 2BK. \] Find \ (BK \).
By the Pythagorean theorem from \ (\ triangle BKC \): \
Hence, \
Answer:
b) \ (4 \ sqrt7 \)
Task 17
:has only one solution.
We make the change \ (t = 5 ^ x, t> 0 \) and transfer all terms to one part: \
We got a quadratic equation, the roots of which, according to Vieta's theorem, are \ (t_1 = a + 6 \) and \ (t_2 = 5 + 3 | a | \). For the original equation to have one root, it is sufficient that the resulting equation with \ (t \) also has one (positive!) Root.
Note right away that \ (t_2 \) will be positive for all \ (a \). Thus, we get two cases:
1) \ (t_1 = t_2 \): \ & a = - \ dfrac14 \ end (aligned) \ end (gathered) \ right. \]
A) Suppose that the equality \ [\ dfrac (a + c) (b + d) = \ dfrac7 (23) \] Then \ (a + c = 7k \), \ (b + d = 23k \), where \ (k \) - natural number... Since \ (a, c \) are two-digit numbers, then smallest value\ (a + c \ geqslant 10 + 11 = 21 \), therefore \ (7k \ geqslant 21 \ quad \ Rightarrow \ quad k \ geqslant 3 \).
Take \ (k = 3 \). Then \ (a + c = 21 \), \ (b + d = 69 \). Therefore, we can take, for example, \ (a = 10 \), \ (c = 11 \), \ (b = 16 \), \ (d = 53 \).
The answer is yes.
b) Suppose that maybe \
Let's rewrite this equality in a different form: \
Let us prove that \
From this it will follow that the assumption is false and such equality is impossible. Consider the first inequality. \
Since all numbers are two-digit, then \ (11b \ geqslant 11 \ cdot 10 = 110 \)... Therefore, \ (d<11b\)
, а значит и левая дробь всегда строго больше правой.
The second inequality is proved similarly.
Therefore, the answer is no.
c) Since all numbers are natural, then from \ (a> 4b \) we can conclude that \ (a \ geqslant 4b + 1 \). Similar to \ (c \ geqslant 7d + 1 \). Let's substitute: \ [\ dfrac (a + c) (b + d) \ geqslant \ dfrac (4b + 1 + 7d + 1) (b + d) = 4 + \ dfrac (3d + 2) (b + d) \] Thus, the expression will take the smallest value at the smallest value of the expression \ (\ dfrac (3d + 2) (b + d) \). Since the fraction is smaller, the larger its denominator (with a fixed numerator), we maximize the denominator (that is, we maximize \ (b \)).
Since \ (a \) is two-digit, the maximum value for \ (a \) is 99, therefore \ (4b + 1 \ leqslant 99 \), hence \ (b \ leqslant 24 \). Thus, we get: \ [\ dfrac (a + c) (b + d) \ geqslant 4+ \ dfrac (3d + 2) (24 + d) = 4 + \ dfrac (3 (d + 24) + 2-72) (d + 24) = 4 + 3- \ dfrac (70) (d + 24) \]
Now, in order for the expression obtained on the right to be as small as possible, you need to make as much \ (\ dfrac (70) (d + 24) \) as possible, that is, make \ (d \) as small as possible.
The smallest value for \ (d \) is \ (10 \). Hence: \ [\ dfrac (a + c) (b + d) \ geqslant4 + 3- \ dfrac (70) (10 + 24) = 4 \ frac (16) (17) \] Thus, if the smallest value \ (4 \ frac (16) (17) \) is attained, then \ (b = 24 \), \ (d = 10 \), \ (a = 4 \ cdot 24 + 1 = 97 \), \ (c = 7 \ cdot 10 + 1 = 71 \).
Answer:
c) \ (4 \ frac (16) (17) \)
The Federal Service for Supervision in Education and Science has summed up the preliminary results of the Unified State Exam in Mathematics profile level, which took place on June 2.The average score of the participants increased by almost 1 point compared to last year and amounted to 47.1 points. The number of participants who failed to overcome the minimum threshold of 27 points decreased by 1%. Total in the exam for profile mathematics attended by about 391 thousand participants.
"Level difficulties of the exam in mathematics of the profile level in 2017 did not change. The preliminary exam results show that the participants performed better on the assignments this year. You can also state a more conscious choice of the USE level in mathematics by graduates: fewer participants signed up for both exams at once, the profile USE was chosen mainly by graduates who need mathematics to enter a university, "said the head of Rosobrnadzor Sergei Kravtsov.
Thanks to the introduction of the technology for scanning the answer sheets of the USE participants at the examination points, the processing of the results was promptly completed. Participants of the USE in mathematics of the profile level will be able to find out their result two days earlier than the deadline. This can be done through Personal Area on the USE portal - http: //check.site/.
On June 28, in the main period of the USE in 2017, there is a reserve deadline for passing the USE in mathematics. Graduates of previous years who want to improve their results will be able to take the exam on this day. Also, the USE in mathematics will be able to retake the graduates of the current year who have received a positive USE result in the Russian language, but do not have a satisfactory USE result in mathematics, neither a basic nor a specialized level. For retake, such graduates can choose any level of the USE in mathematics - profile or basic.
The video course "Get an A" includes all the topics necessary to successfully pass the exam in mathematics at 60-65 points. Completely all tasks 1-13 Profile exam mathematics. Also suitable for passing the Basic exam in mathematics. If you want to pass the exam for 90-100 points, you need to solve part 1 in 30 minutes and without mistakes!
Preparation course for the exam for grades 10-11, as well as for teachers. Everything you need to solve part 1 of the exam in mathematics (first 12 problems) and problem 13 (trigonometry). And this is more than 70 points on the exam, and neither a hundred-point student nor a humanities student can do without them.
All the theory you need. Quick solutions, traps and secrets of the exam. Disassembled all the relevant tasks of part 1 from the Bank of tasks of the FIPI. The course fully meets the requirements of the exam-2018.
The course contains 5 large topics, 2.5 hours each. Each topic is given from scratch, simple and straightforward.
Hundreds of exam assignments. Word problems and probability theory. Simple and easy to remember algorithms for solving problems. Geometry. Theory, reference material, analysis of all types of USE assignments. Stereometry. Tricky solutions, helpful cheat sheets, developing spatial imagination. Trigonometry from scratch to problem 13. Understanding instead of cramming. Visual explanation of complex concepts. Algebra. Roots, degrees and logarithms, function and derivative. The basis for solving complex problems of the 2nd part of the exam.
Instructions
to do the work
The examination paper consists of two parts containing 25 tasks. Part 1 contains 24 tasks, part 2 contains one task.
For execution examination work in the Russian language 3.5 hours (210 minutes) are allotted.
Answers to tasks 1-24 are a digit (number) or a word (several words), a sequence of numbers (numbers). Write the answer in the answer field in the text of the work, and then transfer it to the ones below samples in the answer form number 1.
Assignment 25 of part 2 is an essay based on the text read. This task is performed on answer sheet number 2.
All USE forms are filled in with bright black ink. The use of gel, capillary or fountain pen.
When completing assignments, you can use the draft. Draft entries do not count towards grading work.
The points you received for the completed tasks are summed up. Try to complete as many tasks as possible and gain the largest number points.
We wish you success!
OPTION 1
Part 1
Read the text and complete assignments 1-3.
| (1) It was believed that the famous Greek mathematician Pythagoras invented musical notation. (2) ... the musical notation we know originated on the territory of modern Syria a thousand years before Pythagoras developed a system of musical notation, which includes seven musical signs. (3) These findings are based on an examination of the records found in ancient city Ugarit in northwestern Syria in the 50s of the last century. (4) Then archaeologists managed to find recorded musical symbols dating back to the middle of the second millennium BC. (5) In the course of the completed study, experts confirmed that the Ugaritic find is the first recording of a piece of music in the history of mankind. (6) Scientists explain the absence of other information about the history of music and singing in Syria by the influence of catastrophes, earthquakes and wars, which for a long time did not make it possible to obtain the necessary evidence. |
1. Indicate two sentences in which correctly conveyed HOME information contained in the text. Write down the numbers of these sentences.
1) Catastrophes, earthquakes and wars for a long time did not make it possible to obtain the necessary evidence about the existence of musical literacy in the middle of the second millennium BC.
2) In the 50s of the last century, in the ancient city of Ugarit in northwestern Syria, archaeologists managed to find the first recorded musical symbols in history, and this refuted the information that Pythagoras invented musical notation.
3) The Ugaritic find is the first record of a piece of music in the history of mankind.
4) Before the discovery in the 50s of the last century on the territory of Syria of recordings of musical symbols dating back to the middle of the second millennium BC, it was believed that the musical notation was invented by Pythagoras.
5) Not so long ago, Syrian scholars came out with the assertion that the musical notation we know originated in the territory of modern Syria a thousand years before Pythagoras developed a system of musical notation, which includes seven musical signs.
Answer:___________________
2 ... Which of the following words (combinations of words) should be in place of the gap in the second (2) sentence text? Write down this word (combination of words).
Even Only After All, However, And
Answer _______________________________
3 ... Read the snippet vocabulary entry, which gives the meanings of the word LETTER. Determine the meaning in which this word is used in the second (2) sentence of the text. Write down the number corresponding to this value in the given fragment of the dictionary entry.
LETTER, -a, cf.
1) Written text sent to message something to someone. Write a letter to your relatives.
2) Ability to write. Learn to read and write.
3) A system of graphic signs to convey information. Verbal and syllabic writing.
4) The manner of artistic depiction. Old letter icon.
Answer _________________________________________________________
4. One of the words below contains a mistake in the stress setting: WRONG the letter denoting the stressed vowel sound is highlighted. Write this word down.
The garbage chute understood and will strengthen the inadequately bent
Answer __________________________________
5. In one of the sentences below WRONG used the highlighted word. Fix lexical error by selecting a paronym for the highlighted word. Write down the chosen word.
The novel shows the life of both the capital and the LOCAL nobility. It is difficult for a person with POOR fantasy to write creative work.
V Past years classmates often gathered in the old park. The location of the camp was FAVORABLE in that there was a lake on the right and a dirt road on the left.
Grandchildren can PAY for grandfather's hospitality with help at the apiary.
______
6. In one of the words highlighted below, a mistake was made in the formation of the word form. Correct the mistake and spell the word correctly.
ripe APRICOTS WILL Kindle fire over THREE HUNDRED THOUSANDS
CONTRAINING PREDICTION A MORE HONEST decision
7 ... Establish a correspondence between grammatical errors and sentences in which they are allowed: for each position of the first column, select the corresponding position from the second column.
| Grammatical errors | Offers |
| A) violation in the construction of a sentence with participle B) error in construction complex sentence B) violation in the construction of a sentence with an inconsistent application D) violation of the connection between the subject and the predicate E) violation of the temporal correlation of verb forms | 1) Our memory tends to reduce all color shades to several colors, which for some reason we made the main ones for ourselves. 2) Forgotten memories can be returned by activating the cells responsible for accessing stored information in the brain. 3) M. Gorky included two legends in the story "The Old Woman Izergil". 4) In office centers, you rarely meet a person without disturbing disturbances. 5) In May 1820, Pushkin and the family of General Raevsky went to the Caucasian Mineral Waters and spent the night in Taganrog at the house of the mayor Papkov. 6) These animals are called creepers because they have special stinging capsules with which they hunt crustaceans and roundworms. 7) Women, in comparison with men, are very little genetically changeable, and this is precisely why their high adaptability is connected. 8) In addition to lack of sleep, chronic stress and depression, other disorders can lead to memory loss. 9) Every year at the end of summer, a star fall falls on the Earth, despite this that in fact we do not see stars at all. |
Write down the selected numbers in the table under the corresponding letters.
8 Determine the word missing the unstressed verifiable vowel of the root. Write this word by inserting the missing letter.
t ... printing
cn ... gray
support ...
to ... mpromiss
pop ... wok
Answer__________________________
9 Identify the row in which the same letter is missing in both words. Write these words by inserting the missing letter.
pr ... boring, pr ... hail
without ... artificial, can you have
pre ... feel, oh .... guess
neither ... fall back nor ... fall
from ... revealed, to ... young
Answer_________________________
10. Write down a word in which a letter is written at the place of the pass O... recruits ... vat
look ... look
command ...
unwind
permeate
Answer _____________________________
11 ... Write down a word in which a letter is written at the place of the pass E.
pumping out ... nnaya (oil)
dreaming ... tsya (figure)
stele ... tsya (fog)
cleared… .was (path)
real (tea)
Answer_________________________________
12. Define a sentence in which NOT with a word is written LITTLE. Expand the parentheses and write out this word.
In Russia in the 30s, people (NOT) finished eating.
His eyes were cloudy, (NOT) EXPRESSING joy at the meeting.
This locality(NOT) INCLUDED in the list of most visited by tourists.
Deryugin chose a profession that is (NOT) EASY.
There are many typos, (NOT) NOTED by the author of the manuscript.
Answer____________________________________
13. Define a sentence in which both highlighted words are spelled LITTLE. Expand the brackets and write out these two words.
(FROM) ANYWHERE a rider appeared, who was in a hurry (AND) so drove the horse that it fizzled out.
LIKE (SAME), like us, this group of tourists visited (IN) NEAR Proval in Pyatigorsk.
THAT (WOULD) please the groom's parents, the girl was friendly, (FOR) WHAT she behaved naturally.
Avdonin THAT (SAME) leaned on mathematics, BECAUSE (THAT) was going to participate in subject Olympiad.
(AT) THE CONCLUSION of the ballet the music sounded (ON) LIKE an adagio.
14. Indicate all the numbers in the place of which is written NN.
In the courtyard of the house there was a dump (1) sawn (2) logs in the courtyard, weaving (3) chairs, a kitchen (4) table, more beautiful (5) silver (6) paint, prepared (7) still old owners.
15. Arrange punctuation marks. Please indicate two sentences in which you need to put ONE comma. Write down numbers these proposals.
1) The hunter and breadwinner at that time was fourteen years old and he did not have the strength to carry such a cart for a long time.
2) The rails did not withstand the test for deflection and fracture and, according to Antipov's assumptions, should have burst in the cold.
3) Although the steamer had indeed already rolled away from the pier, it was still not on a straight course, but was just turning around.
4) Calls rattled every minute and numbers flew out in a long glass box on the wall.
5) In mid-August, the Smokovnikovs, together with Dasha, moved to St. Petersburg to their large apartment on Panteleimonovskaya.
Answer__________________________________________
16.
Old women (1) carrying in front of them (2) in both hands, tin bowls of porridge (3) carefully left the kitchen and sat down to dine at a common table (4) trying not to look (5) at the slogans hung in the dining room (6) (7) composed personally by Alexander Yakovlevich (8) and artistically performed by Alexandra Yakovlevna.
Answer______________________________________
17. Arrange punctuation marks. List all numbers that must be followed by commas in sentences.
Lively sympathy hello (1)
From an unattainable height (2)
Oh (3) do not embarrass (4) I pray (5) the poet!
Don't tempt his dreams!
All my life (6) lost in a crowd of people,
Sometimes (7) is available to their passions,
Poet (8) I know (9) superstitious
But he rarely serves the authorities.
(F. Tyutchev)
Answer________________________________________
18 .Place punctuation marks. List all numbers that must be followed by commas in the sentence.
He told his son (1) what a camera obscura is (2) that a dark box with a small hole (3) and a plate (4) covered with a light-sensitive substance (5) is enough (6) to take a picture (7) to stop a moment of life.
Answer________________________________________
19. Arrange punctuation marks. List all numbers that must be followed by commas in the sentence.
During the night, a lot of new snow poured (1) the trees dressed in white (2) and the air was unusually light (3) transparent and gentle (4) so (5) that (6) when Anna Akimovna looked out the window (7) then she, first of all, I wanted to breathe deeply, deeply.
Answer____________________________________________
(1) Our ideas about the ideal of beauty are embodied in external human beauty. (2) Outward beauty is not only the anthropological perfection of all the elements of the body, not only health. (3) This is inner spirituality - a rich world of thoughts and feelings, moral dignity, respect for people and for oneself ... (4) The higher the moral development and general level spiritual culture of a person, the more vividly reflected the inner spiritual world in external features. (5) This illumination of the soul, in the words of Hegel, is more and more manifested, understood and felt by modern man. (6) Inner beauty is reflected in the outward appearance.
(7) The unity of inner and outer beauty is an aesthetic expression of a person's moral dignity. (8) There is nothing wrong with the fact that a person strives to be beautiful, wants to look beautiful. (9) But, it seems to me, one must have a moral right to this desire. (10) The morality of this striving is determined by the extent to which this beauty expresses the creative, active essence of man.
(11) The beauty of a person is most vividly manifested when he is engaged in his favorite activity, which, by its nature, emphasizes in him something good inherent in his personality. (12) At the same time, his outer appearance is illuminated by inner inspiration. (13) It is no coincidence that Miron embodied the beauty of the disco ball at the moment when the tension of internal spiritual forces is combined with the tension of physical forces, in this combination - the apotheosis of beauty ...
(14) External beauty has its own internal, moral sources. (15) Favorite art makes a person beautiful, transforms facial features - makes them subtle and expressive.
(16) Beauty is also created by anxiety, care - what is usually called "the pangs of creativity." (17) As grief leaves indelible wrinkles on the face, so creative cares are the most subtle, most skillful sculptor who makes the face beautiful. (18) Conversely, the inner emptiness gives the external features an expression of dull indifference.
(19) If the internal spiritual wealth creates human beauty, then inactivity, and even more immoral activity, this beauty is ruined.
(20) Immoral activity disfigures. (21) The habit of lying, hypocrisy, and gossip creates a wandering gaze: a person avoids looking into the eyes of other people; it is difficult to see a thought in his eyes, he hides it. (22) Envy, selfishness, suspicion, fear that "I will not be appreciated" - all these feelings gradually coarse the features of the face, give it gloom, unsociability. (23) Being yourself, cherishing your dignity is the living blood of genuine human beauty.
24) The ideal of human beauty is at the same time the ideal of morality.
(25) The unity of physical, moral, aesthetic perfection is precisely the harmony about which so much is said. (V. A. Sukhomlinsky *)
* Vasily Alexandrovich Sukhomlinsky (1918-1970) - Corresponding Member of the USSR Academy of Pedagogical Sciences, Candidate of Pedagogical Sciences, Honored School Teacher of the Ukrainian SSR, Hero of Socialist Labor.
20. Which of the statements correspond to the content of the text? Enter the answer numbers.
1) A person who is improving spiritually does not attach importance to appearance.
2) A person who has experienced anxiety becomes kinder, which means more beautiful.
3) External beauty is a manifestation of the inner spiritual strength of a person.
4) A person is beautiful in moments of creativity.
5) A person who is afraid of being underestimated and is jealous of others has a sullen expression on his face.
Answer_______________________________________
21. Which of the following statements are true? Enter the answer numbers.
1) Sentences 3, 4 supplement and clarify the thought expressed in sentence 2.
2) Sentences 16-18 provide reasoning.
3) Sentences 20, 21 include a description.
4) Sentences 20-22 contain a narrative.
5) Proposition 25 contains a general conclusion from the author's reasoning.
Answer________________________________________
22. Write out the antonyms (antonymic pair) from sentences 7-10.
Answer_________________________________________
23. Among sentences 14-18, find the one (s) that (s) is connected to the previous one using the same root word. Write the number (s) of this offer (s).
Answer_______________________________________
24 ... Read the fragment of the review based on the text that you analyzed in tasks 20-23.
This fragment examines the linguistic features of the text.
Some of the terms used in the review are missing. Insert the numbers corresponding to the number of the term from the list in the places of the gaps (A, B, C, D). Write down the corresponding number in the table under each letter.
“The famous teacher V.A. Sukhomlinsky, speaking about the true beauty of a person, uses (A) __________ (spirituality, illumination, apotheosis, etc.), which gives the text a sublime sound and expresses his own position vividly and figuratively, applying this expressive means like (B) _______ (glow of the soul, moral origins, living blood of beauty). The technique (B) _________ (sentences 10, 11 and 20-22) helps the author to structure the text. Of the syntactic means of expressiveness, it is worth noting (D) _____ (sentences 5, 21) ".
List of terms:
2) question-answer unity
4) metaphor
5) colloquial vocabulary
6) book vocabulary
7) antithesis
8) gradation
9) rhetorical question
Part 2
25. Write an essay based on the text you read. Formulate one of the problems posed by the author of the text. Comment on the formulated problem. Include in the commentary two illustrative examples from the text you read that you think are important to understanding the problem in the original text (avoid overquoting). State the position of the author (narrator). Write whether you agree or disagree with the point of view of the author of the read text. Explain why. Argue your opinion, relying primarily on the reader's experience, as well as on knowledge and life observations (the first two arguments are taken into account).
The length of the essay is at least 150 words.
A work written without reference to the text read (not according to this text) is not evaluated. If the essay is a retelling or completely rewritten of the original text without any comments, then such a work is estimated at 0 points.
Write an essay carefully, legible handwriting.
TRIAL USE 2017 Option 1
| Job No. | Job No. | ||
| to, moreover, to |
|||
| folded | 1347 any other sequence of these numbers |
||
| will ignite | |||
| 12347 any other sequence of these numbers |
|||
| arrogant | 345 any other sequence of these numbers |
||
| Unartificial conceive an unartificial | 125 any other sequence of these numbers |
||
| command | internal external external internal |
||
| spreads | |||
| malnourished | |||
| Part 2 |
|
| Text information |
|
| Approximate circle problems | |
| 1. The problem of the true beauty of a person. | 1. The true beauty of a person is determined by the harmony of the physical, moral, aesthetic. |
| 2. The problem of the connection between the external beauty of a person and his inner world. | 2. External beauty is a manifestation of the inner spiritual strength of a person. |
Preparation for the OGE in mathematics and for the exam in other subjects:
Tell me, would you like to spend the next 5 years so that you will remember them forever, so that they will be the happiest in your life?
Would you like to be proud of yourself for the rest of your life?
And perhaps the most immodest question. Would you like to earn much more than the rest and to be happier?
Ru. I have two higher education, several years of work in top international companies (PwC and E&Y), his own consulting company ...
But I started by saying that I could not enter the university.
For various reasons, but the most main reason- I DIDN'T BELIEVE THAT I NEED IT. And I didn’t prepare.
And so, after I failed, the fun began.
It was a shame ...
Because I had to answer the questions many, many times: “How ?! You didn’t apply ?! Why?! You're smart! ” You can't argue ... You can't say: "No, I'm a fool ..."
Then I had to go to the GPTU. Now it is called by the pretty word "College". And then this abbreviation was deciphered in a different way: "Lord, Help the Dumb One to Settle Up."
In general ... it became completely unbearable. Because some of my friends did and somehow immediately became out of reach.
They went to college, hung out in dorms, had fun, and I went to the factory and nailed the slats to the wooden panels on the conveyor and this was called training.
I took a panel, put slats on it, 12 shots with a pneumatic pistol and ... the next panel. And so 8 hours ... And so all my life ...
And then there was the army - not the most pleasant place on earth. To be honest, it was real hell and just thrown away 2 years of life, so heavy that I could not imagine.
A year of “study” at the GPTU (and, in fact, stupid, mechanical work at the plant) and two years of even more stupid and senseless service in the army were very convincing.
The value of education was clearly explained to me in a simple, intelligible form. I realized one thing: ..
I don’t want to live like that!
I don't want to go to a factory, do mechanical work, earn little money.
And after the army, I gathered my strength and entered with great difficulty ... but not to the institute, but to the preparatory department, where they trained me for another year to enter the university.
It is unrealistic to go directly to a university after a three-year break in studies.
And only after the preparatory department, I was able to somehow “crawl” on the budget to the institute. Far from the best, but still ...
There were two institutes, 6 years of the most beautiful fun!
After my second institute, I found a job and began to receive immediately more, than my parents. AND the work was very interesting(much more interesting than nailing the slats).
I went on business trips all over the country: I visited Nakhodka, Sakhalin, Baikal, beyond the Arctic Circle, took professional exams in the USA, went to training courses in Germany and Hungary. I communicated with different very interesting people, on different languages... I made friends all over the world.
But ... do you want to be honest?
It was incredibly difficult to get out of the hole into which I drove myself. I had to simultaneously earn my living, study, sleep very little, catch up all the time ...
Few can stand it.
Why am I telling all this? Not to brag. There is nothing to brag about.
I can not understand…
Why am I so stupidly missed ... the best four years of my life ?!
And I challenge you to ask yourself a couple of questions right now ...
Perhaps ... you should be smarter than me? Perhaps you should strain a little and go to the university of your dreams this year? Perhaps it is easier to enroll right after school? Think about it. If the answer is yes, read on ...
On urgent preparation for the exam in mathematics
But first, one thought, which, I know, gnaws at many, many schoolchildren like you. There she is:
I have no ability for mathematics. I will not be able to pass the exam.
Let me tell you what about this. This is complete nonsense!
There are no people incapable of mathematics. There are people who are not capable of teaching it.
It may sound harsh, but it is. There are so many “teachers” who are unable to teach.
The teacher's task is not to demonstrate his knowledge (he must have it by definition), but to descend to the level of the student and climb with him at his pace up the steps of knowledge, explaining complex concepts on his fingers.
Maybe you just no luck with the teacher ...
Look at the reviews for our textbook "For Dummies" on the site. Pay attention to how many schoolchildren for the first time dealt with the complex sections of mathematics thanks to the textbook and wrote to us about it!
Why is that?
Because we have created a textbook that explains complex mathematical concepts in simple human terms. Because with the help of it you can deal with any topic in mathematics on your own.
For these students (and their parents and even grandparents!), Our textbook has become an excellent electronic teacher!
One more question that worries you very much:
How difficult is the exam in mathematics ?!
Take a look yourself. Before you is a graph of those who passed the exam in various subjects for 100 points for 2018.
The graph shows that there are only 0.03% of such lucky people from the number of those who passed and that mathematics like English is the most difficult exams.
It means that you have to seriously prepare for them. But don't worry if you are reading these lines, you will know how to pass this unfortunate USE in mathematics!
Why can our exam preparation program in mathematics and our textbook “For Dummies” help you prepare in the remaining time?
It's all about the interaction of the five parts of the site 100gia.ru and the site
See what these parts are:
The school does not prepare for the Unified State Exam for admission to a top university on a budget!
It is not clear what needs to be repeated, what tasks to pay attention to when preparing!
Where I live there are no good teachers and I can't find a tutor!
Which of these problems apply to you?
Preparatory program for the exam in mathematics
Our exam preparation program in mathematics is your electronic tutor. Its algorithms were developed by the best tutors in Moscow. You don't have to look for other materials, you don't have to think about anything - just go from module to module and solve problems. As in the game. If you can't, go through the answers and solutions.
At school, I had a weak math teacher. I do not understand anything.
I fell ill and fell behind. I could no longer catch up.
Math is a very difficult subject, accessible only to geeks!
I have no ability for mathematics!
Did we mention that this is nonsense?
Textbook "For Dummies" to prepare for the exam in mathematics
You have 100% ability in mathematics. Read the reviews for our tutorial. A lot of people figured out complex topics on their own. We have written this tutorial to be clear so that anyone can understand any topic. In simple human language about complex things.
I understood the solution correctly, but did not notice the trap and solved the problem incorrectly!
The tasks were so unfamiliar! We were not given such at school!
The theory is clear, but the practice is not enough!
I solved difficult problems correctly. I know a lot and tried very hard, but I was mistaken on some nonsense!
Sound familiar, right? Be sure that all the tasks will seem unfamiliar to you on the exam.
Trainers by type and topic
Therefore, it makes no sense to solve typical tasks all the time. You need to look for and solve original problems in order to learn how to think and are not afraid if the task seems incomprehensible at first.
Our problems (especially complex ones) are thought up by our mathematicians Elena Evgenievna Bashtova and Aleksey Sergeevich Shevchuk. The tasks are original, that is, unfamiliar. Just what you need. Solving them, you will learn to think and prepare for the exam in mathematics in the best way!
If you only knew how often we hear this phrase ?! Why it happens?! Because you did not adapt to stress, solving problems for a while, you are not used to controlling time.
Trial exam in mathematics
This part will let you get used to stress, learn to control time and find out your real level.
You can take a trial exam in mathematics unlimited. Each time the program selects a new variant of problems from a database of 6000 problems.
The result of the trial exam, the answers to each problem and solutions you get it right away!
- I cannot force myself to study. I need someone who will help and motivate me!
- I'm not sure if I have enough time. Before the exam there is… nothing, nothing!
- I need help. I do not like to study alone.
It's that simple!
Parent's office
In the parent's office, you can see all the statistics of your progress. It is impossible to deceive him. Only correctly solved problems are displayed.
Together with your parents, you will be able to accurately estimate how much time you need to study per day in order to have time to complete the entire Program before the exam.
Our authors: who are they?
What exactly will you get by purchasing our exam preparation program in mathematics and access to the textbook "For Dummies"
Preparatory program for the exam in mathematics
- 25 modules in geometry;
- 25 algebra modules;
- An entrance test that determines the level of the student and the training program adapted to his level;
- Just go as in the game, from module to module;
- Parent's office (to help the student).
A great option for those who want to study on their own.
Why super? because the most budgetary (but very high quality!).
Because it was prepared by the best tutors in Moscow as an electronic substitute for a tutor.
If you complete the Program to the end, increase your result by an average of 40%(according to a survey of students).
Simulators for solving problems by topics and types:
- 6000 tasks in the database for each topic and each type;
- All problems with solutions and answers.
An excellent option for those who do not need a program, but need to get their hands on tasks on a specific topic or type.
to don't make stupid mistakes in simple tasks
to learn how to write down the answer correctly
to achieve stability results
to step on all the rake and learn solve problems with traps(of which there will be many in the exam)
so that they are not afraid to solve unknown problems (our tasks are unique, you cannot download them on the Internet)
The best way to prepare with a simulator?
You read the topic in our textbook “For Dummies”, solve all the problems on the topic, and then solve all the problems on the same topic in the simulator.
Trial exam - unlimited.
- At any time, you can sit down and write a trial exam, for a while. And immediately get the result and analysis of tasks.
- Our trial exam is as close as possible to the real one.
You will know exactly what you are capable of.
And most importantly, you can feel exam stress(the test is for a while) and get used to it.
Parent's office.
You can help the student by complicating or, on the contrary, simplifying his program.
You can estimate whether you have time to prepare for the exam or not, because all student statistics are visible.
Textbook (written in human language)
Any complex math topic can be understood simply by reading a chapter from a textbook.
Don't believe me?
Look at the students' reviews on any page of the textbook.
Where I live there is no good math teacher. I found your training course and studied on my own for about 5 months. Plus I read your textbook and solved problems from it. Passed 78 points. That's a lot for me! This is just a miracle! I recommend you to everyone!
Galya Ferzhikova
I was looking for inexpensive math courses for my son so that I could figure it out and help him. Happiness to have stumbled upon your course by accident. Sometimes we studied together, sometimes separately, and now he is in his first year! I wish you and your project good luck!
Alexander Viktorovich Lovtsov
I took the exam 2 years ago, when your course was free (thanks for that!). I've never been friends with mathematics, but your textbook helped a lot! I realized that I could master any topic. The preparation program was difficult at first because I lied on your entrance test and got the program. increased complexity... She's really hard. Then I passed the entrance test again and everything went fine. The ability to understand the material itself was very useful at the institute. I am still reading the tutorial :)
Galina K.- Student
Who is our textbook and training program for?
It is for the very smart, for the independent.
For those who do not have much money to hire tutors.
For those for whom it is important to achieve everything on their own and then, at the institute, when there will be no dad, no mother, or tutors nearby, they will not get confused and get out of any situation.
Of course, we love the idea of studying with a tutor. But what about those who don't have much money to hire?
What to do for those who lives in a small village where there are no good tutors?
It seems to us that everyone should have a chance!
What do we dislike about other exam preparation programs in mathematics and textbooks?
We don't like HOW most math textbooks are written.
It seems that they were written by people who, right from birth, knew everything and were able to, and no one taught them addition, subtraction, multiplication, division, did not patiently explain tricky tasks step by step. On fingers. In understandable language.
No. They immediately knew how to “differentiate and integrate”, immediately understood the mathematical language as their native language.
Of course this was not the case. If they know mathematics well, then someone was messing with them, then they had a good teacher.
What is a good teacher?
This is not the one who knows everything and constantly demonstrates this, but the one who descends to the level of the student and together with him climbs the steps of knowledge, step by step, helping him so that he does not stumble.
In order for you to master something new, you need to first explain it on your fingers, then help you to practice it, and only then you can use this new skill yourself very quickly.
Otherwise it doesn't work.
So we tried to do this in our tutorial.
What does our textbook and training program NOT do?
This is not just a theory. It's a focus on problem solving. Because on the exam in mathematics, you will not be asked theory, but problem solving. If you need an ordinary textbook on theory, this is not our place.
They won't learn for you. If you are not in the mood to prepare, do not buy anything from us. We cannot help you.
Who is NOT suitable for our textbook and training program?
They will not suit you if you:
- unable to convince himself of the need to learn;
- unable to sit down regularly, open the computer and study.
Or if you don't have someone to spur and motivate you.
These could be your parents (In this case, open the parent's office for them so that they can see all your statistics and, if you are lagging behind, help you)
These could be your friends. You can negotiate with a friend and open each other's parent's office, compete with each other.
Thanks for the trial exam!
I was very worried that my daughter would not be able to cope with the excitement and she would not have enough time for a real exam. And here's your training program! We actually studied with a tutor, but on your website you only took a trial exam. Many many times.
The tasks are different all the time, but my daughter coped with them and this gave confidence. Passed the exam at 91!
Andrey Gusev
I have been using your sites since the 8th grade. Basically a tutorial and training on topics. They don't understand at school that your textbook is better!
If something is not clear, I first look at the tutorial and usually this is enough. But if not, I solve problems in the simulator on the same topic until I feel that I understand everything.
OGE passed without problems. Now I will prepare for the exam.
Irina Samoilova
Questions and answers:
What's on the site e site?
The site contains our famous textbook "For Dummies", written in human language, allowing you to understand the topic yourself. The explanation is carried out “on the fingers”, it is very clear. If you look at the reviews under each topic, you can see how many students figured out complex topics on one's own.
What's on the 100gia.ru website?
The website 100gia.ru contains:
- The preparation program for the exam in mathematics and the exam in mathematics, as well as preparation programs for grades 8 and 10 (for those who would like to prepare for exams in advance);
- Simulators for solving problems by topic and by type. For those who do not need a full-fledged training program, but who need to get their hands on solving problems of a specific type or on a specific topic. The database contains more than 6000 problems with solutions and answers.
- Trial exam in mathematics and trial OGE in mathematics. For those who need to understand their real level, determine weak sides, feel the stress associated with the lack of time and get used to it.
For how long is access to the textbook (website) given?
We give lifetime access to the tutorial located on the site site. It is limited only by the lifetime of the site.
For how long do you give access to the site 100gia.ru?
We give lifetime access to all services located on the 100gia.ru website. It is limited only by the lifetime of the site.
Do you only prepare for the exam in mathematics?
Yes, we only prepare for the exam and exam in mathematics.
How many options are available for the trial exam in mathematics and the trial exam in mathematics?
You can take the trial exam and trial exam an unlimited number of times. The program generates a new list of tasks each time.
When are the results of the trial exam in mathematics and the trial OGE in mathematics available, if I submit them on your website?
Results are available instantly. You can also see the correct answers and solutions to problems and understand where you made a mistake and what topics you need to pull up. Further, these topics can be trained on simulators by topic or by type.
For what level of student training is your training program located on the 100gia.ru website suitable?
Our preparation program is suitable for any student's skill level. Before starting the training, the student takes an entrance test and the system determines its level. Based on this level, the system develops a training program suitable for a particular student. Then the student studies according to his own program, according to the principle “from simple to complex”, step by step, module by module, going through the entire program.
Where did you get the tasks from?
We wrote all 6000 problems in the database ourselves. Simple problems are similar to simple problems from other sources because it is difficult to come up with something original. Difficult tasks, however, are unique. Our mathematicians worked on them. You can't google them on the internet. Therefore, solving these problems will teach you how to think and prepare you for the stress of the exam. It's no secret that all the tasks on the exam seem unfamiliar. So, there won't be such a problem for you.
My child cheats. How can you help with this?
To be honest, it is difficult to help in this situation. To get a high score on the exam, you need to learn to think, not cheat. It takes time and work on your child's part. All that can be advised is to try to explain to the child the importance of the exam. It is most important. If you succeed, you can try to progress through the training program as far as possible in the remaining time. You can open a parent's account, see all his progress and help him, praise, encourage ...
What's the best way to learn from our sites?
Option 1. You read the topic in our textbook “For Dummies”, solve all the problems on the topic, and then solve all the problems on the same topic in the simulator of the Preparatory Program for the Unified State Examination in Mathematics.
Option 2. You follow the Program of Preparation for the Unified State Exam in Mathematics and, if the topic is not clear, read the materials of the textbook “For Dummies” on this topic.
And now the story that I promised is that you must not give up under any circumstances.
1991 year. My friend is 24 years old. He is a 3rd year student. He just had a child, prices were released in the country, and if he starts working by profession after graduation, the money he will earn will not be enough for food ... The wife and child live in a hostel in another city. That is, he and his family have nowhere to live either.
I do not know who told him, but he is in this situation for some reason began to learn English. In those days it was not as easy as it is now, there were no good textbooks, courses, the teachers themselves could not always speak English well. But he took whatever textbooks he could find and studied them from cover to cover.
When he announced to everyone that he would go to the International University they laughed at him openly. The university was supervised by Russian President Yeltsin and Moscow Mayor Popov. The university gave a hotel room for two for nonresidents. Nobody believed that it was possible to enter there "from the street."
Next, what did my friend do ... He understood that objectively he has no chance to enter because of english. He also knew that the exam would be an English essay on a free topic. And he thought that the topic might be: "Why do you want to study at the International University?"
Again, what were the chances of him getting it right? Very small...
A friend of mine hired a tutor, wrote an essay on this topic with him, and memorized it to the comma. He wanted to write a few more essays on other topics, but he no longer had the money for a tutor.
And then he took and for some reason corrected one sentence in this essay - made it more difficult grammatically, the same as in one grammar textbook ...
Exam
English was the last exam. And - a miracle! Indeed, the essay had such a theme and my friend diligently rewrote everything to the comma got 23 points out of 25 possible!
Did it help him?
Despite all the efforts he was 12th on the list with 10 budget places. It seemed like it was possible to surrender. He did the best he could. But this guy was not like that.
He went to dispute the work for English language, because this is the only thing that could be disputed (mathematics and Russian could not be disputed). Although even if he was given 25 points out of 25, he would still not be enough to get into the top ten lucky ones. But he went ...
He asked why he was given 23 points and not 25? The teacher replied that the essay was excellent, but he had one stylistic mistake and pointed out the MOST sentence that my friend corrected!
Can you imagine what a shame! He ruined everything with his own hands! End?
Yeah .. shchaz!
A friend finds right there at the department the same grammar textbook, opens it to a page with an example of that very complex grammatical structure and shows the teacher: “This is not a mistake, but a stylistic device”.
The teacher looks and penetrates: “Oh, so this is what you mean! This is interesting ... Okay. I will give you 25 points ... and on my own I will add 2 more points for deep knowledge of English language!"
Bingo! 27 points out of 25 possible! Just unbelieveble!
The guy entered ?!
It was not so. He became 11th in the list for 10 budget places ...
And then he had a dilemma. It was possible to transfer to another faculty, where he would have had enough points, but this faculty, as he thought then, was not so interesting and he decided not to twitch, hoping that someone would leave the race in front of him ...
If you do not give up and do everything to be lucky, you will be lucky to the end!
And so it happened. Two girlfriends in front of him transferred to the same lighter faculty. They wanted to study together, and one of them did not pass ...
And he became the 10th ...
The International University changed everything in his life. He has built an excellent career and everything is great with him now.
Conclusion od?
NEVER GIVE UP, MY FRIEND!
NEVER GIVE UP MY FRIEND!
You have ... 3 months left.
Or already 2 or even 1 ... day! - no matter!
Do not give up!
Take our textbook and learn as much as you can before the exam. Learn to solve problems in our simulator. Or take the Learning Program and complete it as much as you can.
Try your best. Do not give up!
One day left?
Learn ONE topic and learn to solve problems on it.
Perhaps this topic will give you the same 27 points out of 25, which will solve EVERYTHING.
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