Hi, my name is Evgeniy, and I have been preparing for the Unified State Exam and Basic State Exam in mathematics for 13 years. In this video, we will analyze the Unified State Exam 2025 version for 100 points. The variant is made up of problems that have already been asked on the Unified State Exam and from FIPI, so the variants are of the level of difficulty of the real Unified State Exam ???? LINKS: Download the variant: https://vk.com/wall-40691695_99107 VK group: https://vk.com/shkolapifagora Video courses: https://vk.com/market-40691695 How I passed the Unified State Exam: https://vk.com/wall-40691695_66680 Reviews: https://vk.com/wall-40691695_98328 Insta: / shkola_pifagora ???? TIMECODES: Start – 00:00 Problem 1 – 05:03 In triangle ABC, sides AC and BC are equal, angle C is 72°, angle CBD is external. Find angle CBD. Give the answer in degrees. Problem 2 – 06:55 Vectors a ⃗ (41;0) and b ⃗ (1;-1) are given. Find the length of the vector a ⃗-20b ⃗. Problem 3 – 10:47 Find the volume of the polyhedron shown in the figure (all dihedral angles are right). Problem 4 – 12:18 There are only 20 tickets in a collection of mathematics tickets, 16 of which contain a question on logarithms. Find the probability that a student will get a question on logarithms on a ticket randomly selected during the exam. Problem 5 – 13:00 In a city, 48% of the adult population are men. Pensioners make up 12.6% of the adult population, with the proportion of pensioners among women equal to 15%. A man living in this city is randomly selected for a sociological survey. Find the probability of the event "the selected man is a pensioner". Problem 6 – 18:18 Find the root of the equation 7^(-6-x)=343. Problem 7 – 19:17 Find the value of the expression 21(sin^2 66°-cos^2 66°)/cos⁡〖132°〗 . Problem 8 – 21:30 The figure shows the graph of the function y=f(x). Eight points are marked on the abscissa axis: x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8. At how many of these points is the derivative of the function f(x) negative? Problem 9 – 22:49 To wind the cable at a factory, a winch is used that winds the cable onto a reel with uniform acceleration. The angle through which the spool rotates changes with time according to the law φ=ωt+(βt^2)/2, where t is the time in minutes that has passed since the winch started working, ω=50 deg/min is the initial angular velocity of the spool rotation, and β=4 deg/〖min〗^2 is the angular acceleration with which the cable is wound. Determine the time that has passed since the winch started working if it is known that during this time the winding angle φ has reached 2500°. Give your answer in minutes. Problem 10 – 25:33 A motorcyclist and a cyclist left simultaneously from point A to point B, the distance between which is 60 km. It is known that in an hour the motorcyclist travels 50 km more than the cyclist. Determine the speed of the cyclist if it is known that he arrived at point B 5 hours later than the motorcyclist. Give your answer in km/h. Problem 11 – 35:03 The figure shows the graph of a function of the form f(x)=kx+b. Find the value of f(7). Problem 12 – 36:50 Find the smallest value of the function y=18x^2-x^3+19 on the interval [-7;10]. Problem 13 – 41:54 a) Solve the equation cos⁡(3π/2+2x)=cos⁡x. b) Indicate the roots of this equation that belong to the interval [5π/2;4π]. Analysis of errors 13 – 56:30 Problem 15 – 01:03:54 Solve the inequality (log_4⁡x+2)^2/(log_4^2 x-9)≥0. Analysis of errors 15 – 01:11:43 Problem 16 – 01:17:57 In July 2020, it is planned to take out a loan from a bank in the amount of 419,375 rubles. The conditions for its repayment are as follows: - every January, the debt increases by 20% compared to the end of the previous year; - from February to June of each year, part of the debt must be repaid in one payment. How many rubles will be paid to the bank if it is known that the loan will be fully repaid in four equal payments (that is, over four years)? Analysis of errors 16 – 01:37:46 Problem 18 – 01:40:40 Find all values ​​of the parameter a, for each of which the equation (x ^ 2 + 4x - a) / (15x ^ 2 - 8ax + a ^ 2 ) = 0 has exactly two different solutions. Problem 19 – 02:06:56 There are 16 coins of 2 rubles and 29 coins of 5 rubles. a) Is it possible to collect the sum of 175 rubles with these coins? b) Is it possible to collect the sum of 176 rubles with these coins? c) What is the smallest number of coins, each worth 1 ruble, that must be added to be able to collect any whole sum from 1 ruble to 180 rubles inclusive? Problem 17 – 02:31:39 A circle with center at point O touches the sides of the angle with vertex N at points A and B. Segment BC is the diameter of this circle. a) Prove that ∠ANB=2∠ABC. b) Find the distance from point N to line AB if it is known that AC=14 and AB=36. Problem 14 – 02:46:40 In a regular triangular pyramid SABC, the side of the base AB is equal to 6, and the lateral edge SA is equal to 4. Points M and N are the midpoints of the edges SA a