Summer school and annual courses for the 2025 Unified State Exam with an MSU mathematician: https://3.shkolkovo.online/math-msu My Telegram channel: https://t.me/mathmsu Materials for the SIROP intensive course are here: https://mnlp.cc/mini?domain=mathmsu&i... If you are in 10th grade, then this is where you should go: https://t.me/+yeAlGTQAn5E0ZmZi Everything about the MSU DWI is here: https://t.me/+hNmZJa59rY9hMjli VK group: https://vk.com/hitman_math Tik-Tok: / hitman_math My Instagram: / andreypavlikov_math Time codes: 00:00 Greeting and connection check 00:35 Syrup mini 01:05 Lesson plan 01:45 Telegram channel 02:15 Getting to know the teacher 03:01 Intensive course schedule 04:56 The meaning of a problem with a parameter 07:05 Formulations of problems with a parameter on the Unified State Exam 08:06 Methods for solving problems with a parameter 08:45 Analytical method 11:07 Graphical method 13:52 Parameter plane 17:55 Functional method 20:03 Answers to questions 20:38 What graphs need to be drawn 21:44 Linear function and straight line 23:33 Answers to questions 24:37 Vertex and direction of branches of a parabola 25:49 Isolation of a perfect square 28:28 Answers to questions 29:34 Inverse proportionality and hyperbola 34:17 Answers to questions 38:02 Module 39:00 Vertex and direction of branches of the graph of the modulus function 41:14 Answers to questions 42:34 Equation of a circle, center and radius 43:29 Why the intensive course is called Mini Syrup 44:25 Equation of a circle and the Pythagorean theorem 46:17 Problem 1 - the system of equations has exactly two different solutions 48:35 Problem 1 - gross error in solving 49:15 Problem 1 - identifying the full square, center and radius of the circle 50:41 Problem 1 - determining the ODP 51:37 Problem 1 - transforming the first equation of the system 53:20 Problem 1 - graphic representation 58:57 Answers to questions on Problem 1 1:01:53 Problem 1 - working with the ODP 1:07:49 Answers to questions on Problem 1 1:17:49 Problem 2 - the system of equations has exactly two different solutions 1:18:44 Problem 2 - determining the ODP 1:19:45 Problem 2 - working with the first equation of the system 1:22:50 Problem 2 - graphic representation 1:25:30 Answers to questions on Problem 2 1:27:01 Problem 2 - intersection points of a hyperbola and a line 1:29:10 Problem 2 - depicting lines 1:34:11 Problem 2 - analyzing graphs 1:39:12 Problem 3 - finding lines 1:40:26 Problem 3 - point of tangency 1:45:06 Answers to questions on Problem 3 2:00:05 Problem 4 - the system of equations has exactly two different solutions 2:03:33 Problem 4 - introducing a substitution, the center and radius of a circle 2:04:55 Problem 4 - graphic representation 2:06:14 Problem 4 - inverse substitution 2:07:11 Problem 4 - depicting lines 2:09:50 Answers to questions on Problem 4 2:11:57 Problem 4 - finding straight lines 2:19:09 Problem 4 - looking for a tangent 2:24:30 Answers to questions on Problem 4 2:38:36 Problem 5 - the system of equations has a unique solution 2:40:38 Setting up the solution time for the Unified State Exam 2:44:51 Problem 5 - transforming the second equation of the system 2:45:34 Intensive course schedule 2:46:35 Problem 5 - working with the first equation of the system 2:49:17 Problem 5 - center and radius of a circle 2:51:07 Problem 5 - location of all centers of all circles 2:54:38 Problem 5 - graphic image 2:57:46 Problem 5 - distance from a point to a straight line, radius of a circle 3:04:56 Answers to questions on Problem 5 3:07:27 Breaking Bad 3:08:26 Answers to questions and summing up the lesson #USE2024 #profileUSE #mathematics USE 2024 USE in Mathematics Profile USE Parameter Problem with parameter Equation with parameter Analytical method Graphical method Geometric method