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 version is made up of problems that have already been asked on the Unified State Exam and from FIPI, so the versions are of the same difficulty level as the real Unified State Exam 👍 LINKS: Download the version: https://vk.com/wall-40691695_101249 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 – 03:41 The area of ​​parallelogram ABCD is 132. Point G is the midpoint of side CD. Find the area of ​​trapezoid ABGD. Problem 2 – 05:28 Vectors a ⃗ and b ⃗ whose coordinates are integers are shown on the coordinate plane. Find the length of the vector a ⃗ + 4b ⃗. Problem 3 – 10:57 A plane parallel to the lateral edge is drawn through the midline of the base of a triangular prism. The lateral surface area of ​​the cut-off triangular prism is 37. Find the lateral surface area of ​​the original prism. Problem 4 – 14:45 A scientific conference is held over 4 days. A total of 80 reports are planned – 12 reports on the first two days, the rest are distributed equally between the third and fourth days. Professor M. is scheduled to give a report at the conference. The order of the reports is determined by drawing lots. What is the probability that Professor M.’s report will be scheduled for the last day of the conference? Problem 5 – 17:34 A symmetrical die was thrown 3 times. It is known that the total number of points rolled is 6. What is the probability of the event "3 points rolled at least once"? Problem 6 – 21:46 Find the root of the equation 6^(1+3x)=36^2x. Problem 7 – 24:33 Find the value of the expression (-6 sin⁡〖374°〗)/sin⁡〖14°〗 . Problem 8 – 26:03 The figure shows the graph of the function y=f(x), defined on the interval (-6;6). Find the number of solutions of the equation f^' (x)=0 on the interval [-4.5;2.5]. Problem 9 – 27:58 The current in the circuit I (in A) is determined by the voltage in the circuit and the resistance of the electrical appliance according to Ohm's law: I=U/R, where U is the voltage (in V), R is the resistance of the electrical appliance (in Ohms). A fuse is included in the electrical network, which melts if the current exceeds 2.5 A. Determine what is the minimum resistance that an electrical appliance connected to a 220 V network can have so that the network continues to work. Give your answer in ohms. Problem 10 – 31:06 The distance between cities A and B is 630 km. The first car left city A for city B, and three hours later a second car left city B to meet it at a speed of 70 km/h. Find the speed of the first car if the cars met at a distance of 350 km from city A. Give your answer in km/h. Problem 11 – 37:17 The figure shows the graph of a function of the form f(x)=a^x. Find the value of f(4). Problem 12 – 39:57 Find the smallest value of the function y=2/3 x√x-6x-5 on the interval [9;36]. Problem 13 – 42:47 a) Solve the equation x-3√(x-1)+1=0. b) Indicate the roots of this equation that belong to the segment [√3;√20]. Problem 15 – 53:31 Solve the inequality 9^x-3^x-3^(1-x)+1/9^(x-1) ≤6. Analysis of errors 15 – 01:12:30 Problem 16 – 01:16:12 In July 2020, it is planned to take out a loan from a bank for a certain amount. The terms of 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, it is necessary to repay part of the debt in one payment. How many rubles are planned to be taken from the bank if it is known that the loan will be fully repaid in four equal payments (that is, over four years) and the bank will be paid 311,040 rubles? Problem 18 – 01:33:33 Find all values ​​of a, for each of which the equation x^2+(a+7)^2=x-7-a+x+a+7 has a unique root. Problem 19 – 01:57:21 n units in a row are written on the board. Between some of them, “+” signs are placed and the resulting sum is calculated. For example, if 10 units were written, then the sum 136 can be obtained: 1+1+111+11+11+1=136 a) Is it possible to obtain the sum 141 if n=60? b) Is it possible to obtain the sum 141 if n=80? c) For how many values ​​of n can the sum 141 be obtained? Problem 17 – 02:10:56 In trapezoid ABCD angle BAD is right. A circle constructed on the larger base AD as a diameter intersects the smaller base BC at points C and M. a) Prove that ∠BAM=∠CAD. b) The diagonals of trapezoid ABCD intersect at point O. Find the area of ​​triangle AOB if AB=√10 and BC=2BM. Problem 14 – 02:34:44 On edge AA_1 of rectangular parallelepiped ABCDA_1 B_1 C_1 D_1 point E is taken such that A_1 E:EA=6:1, on edge BB_1 point F such that B_1 F:FB=3:4, and point T is the midpoint of edge B_1 C_1. It is known that AB=4√2, AD=30, AA_1=35. a) Prove that the plane EFT passes through the vertex D_1. b) Find the cross-sectional area of ​​the parallelepiped by the plane EFT. #OptionsUSEprofilePythagorasSchool