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Preparation for the Unified State Exam in specialized mathematics with Nina Novoselova, 11th grade - free course from Foxford, training 64 lessons, Date: December 7, 2023.
Miscellaneous / / December 09, 2023
The course is suitable for preparing for the specialized Unified State Examination in mathematics at any level. Problems of practical content will be analyzed: simple word problems, reading graphs, probability theory, problems of applied content and word problems. A variety of problems in planimetry and stereometry will also be considered. The algebra portion will provide a comprehensive look at simplifications of expressions and equations (linear quadratic, fractional rational, exponential, and logarithmic). Much attention will also be paid to problems on derivatives and integrals. As a result, all knowledge will be systematized and will allow you to solve any task on the Unified State Exam.
Cooking from scratch
The course is suitable for students with any level of knowledge: both beginners and those who have already begun to prepare
With expert support
Manual checking of homework and samples by an Unified State Exam expert who will evaluate the work just like in the exam
Unique modular program
The course covers all the necessary topics, the knowledge of which will be tested on the Unified State Exam. Module by module, you will go through all the necessary material, learn how to solve typical tasks and test your knowledge on trial versions.
In 64 lessons we will cover all topics from the specialized Unified State Examination in mathematics
We structure the training in such a way that without any hassle and at a calm pace we give you only the necessary theory and all the practice of solving problems for successfully passing the Unified State Exam.
Schemes, tables and algorithms for solving problems
During the course, we will do everything to make solving the tasks of the profile Unified State Examination in mathematics as simple and understandable as possible. Cheat sheets on module topics, selections of typical tasks, emphasis on the design of complex part tasks - for your success on the Unified State Exam.
We manually check samples and homework
We do not leave the written part assignments for self-testing - this is done by OGE experts.
We check “for real”, like in an exam, and as a result you receive detailed feedback. All this is for the sake of speed of preparation and your results.
A personal curator will answer questions within two hours, 24/7
Curators understand the program and subject matter, so they can easily answer your questions about the course and homework - at any time
They know well how difficult it can be to prepare and understand your worries.
The most important task of a tutor is to help you cope with stress and fear before exams
The lesson lasts 2 academic hours. Classes are held online twice a week.
Graduated from NSU. Her students have an average score of 80. Passed math with 98 points
Module 1.Rational equations and inequalities. Text problems and problems with economic content
We will develop skills in solving rational equations and inequalities, and apply these skills to solving various word problems. Let's learn to solve economic problems about deposits and loans. Let's master the method of solving equations and inequalities with modules
- Conversion of rational expressions. Solving rational equations.
- Solving rational inequalities.
- Solving equations and inequalities with modulus
- Solving word problems with short answers (percentages, mixtures and alloys, progressions)
- Solving word problems with short answers (movement problems, work problems)
- Economic tasks No. 15: deposit transactions, loan repayment in equal payments
- Economic tasks No. 15: deposit transactions, loans with a uniform reduction of the principal debt
- Economic tasks No. 15: credit schemes with different conditions
Module 2. Irrational equations and inequalities. Trigonometry
Let's learn how to solve and correctly formulate solutions to irrational equations and inequalities. Let's practice calculations and transformations of trigonometric expressions and equations, learn how to correctly select roots belonging to a given interval.
- Transformation of irrational expressions, techniques for solving irrational equations of the profile level
- Irrational inequalities (part 1)
- Irrational inequalities (part 2)
- Practice solving irrational equations and inequalities in the Unified State Examination
- Transformation of trigonometric expressions in Unified State Examination problems
- Solving trigonometric equations
- Trigonometric equations with a limited range of acceptable values. Sampling Equation Roots
- Solving mixed trigonometric equations
Module 3. Planimetry
Let us repeat the most important theorems and properties of planimetry for solving Unified State Exam problems. We will solve the most complex planimetry problems from the test part of the Unified State Exam and concentrate on solving problems of an increased level of complexity. Let's discuss the design features of the solution and evaluation criteria
- Review of theorems and properties of planimetry that are important for solving Unified State Exam problems
- Solving triangles in problem No. 16 of the Unified State Exam
- Solving problems using the theorems of Menelaus and Cheva
- Solving problems using the properties of quadrilaterals. Special methods for solving problems in planimetry.
- Angles and segments associated with a circle
- The relative position of the triangle and the circle
- The relative position of the quadrilateral and the circle
- The relative position of two circles
Module 4. Exponential and logarithmic equations and inequalities
Let's repeat the properties of powers and logarithms using examples from task No. 4 of the Unified State Examination. Let's learn to solve simple (task No. 1) and the most complex exponential and logarithmic equations and inequalities (tasks No. 12, 14) without errors.
- Solving exponential equations with a constant base
- Solving logarithmic equations with a constant base
- Solving exponential and logarithmic equations with variable base
- Exponential and logarithmic equations of mixed type.
- Solving exponential inequalities with a constant base
- Solving logarithmic inequalities with a constant base
- Solving exponential and logarithmic inequalities of mixed type
- Solving exponential and logarithmic inequalities with variable base
Module 5. Study of functions in Unified State Examination tasks. Tasks with applied content
Let's analyze the most complex problems with applied content. Let us recall the elementary transformations of function graphs and apply them to solving Unified State Examination problems. Let's learn how to solve relevant problems without errors.
- Problems with applied content (task No. 7 of the Unified State Exam)
- Functions: elementary transformations and actions on functions, graphs of functions.
- Study of a function using derivatives: finding extrema and largest (smallest) values of a function on a segment
- Study of a function using derivatives: solving problems No. 6 of the Unified State Examination
- Economic problems: application of the derivative to solving optimal choice problems.
- Economic problems: solving optimal choice problems (without derivatives).
- Combinatorics formulas in problems of probability theory. Probability addition and multiplication theorems.
- Formula for the total probability of an event. Tree of Probabilities. Bernoulli's formula.
Module 6. Stereometry
Let us repeat the theorems and properties of stereometry that are most important for solving Unified State Exam problems. We will solve the most complex problems of stereometry from the test part of the Unified State Exam and concentrate on solving problems of an increased level of complexity.
- Stereometry in the test part of the Unified State Exam.
- Constructing sections of polyhedra, finding the cross-sectional area
- Determination of distances in space
- Determination of angles in space
- Determination of volumes of polyhedra and bodies of rotation
- Method of coordinates in space: reference problems
- Solving problems in stereometry using the coordinate method
- Practice solving Unified State Exam problems in stereometry
Module 7. Problems with a parameter (task No. 17 of the Unified State Exam)
Let's learn how to solve problems with a parameter using various methods: algebraic, functional, functional-graphical (task No. 17). Let's discuss how to get at least 1 point and how to earn a full point in a problem with a parameter.
- Linear equations and inequalities with a parameter, as well as their systems. Algebraic solution methods
- Equations and inequalities of the second degree with parameters. Root Research
- Functional methods for solving problems with a parameter. Method for analyzing the location of the roots of a square trinomial
- Functional methods for solving problems with parameters. Using Function Properties
- Problems with parameters that reduce to quadratic equations and inequalities
- Functional-graphical methods for solving problems with parameters
- Functional-graphical solution of problems with a parameter
- Solving problems with parameters: generalization and repetition.
Module 8. Number theory, combinatorics, plot problems (Unified State Exam problem No. 18)
To solve task No. 18 of the Unified State Exam, we will learn to apply the properties of numbers, progressions, basic properties and the laws of combinatorics. We will discuss the correct rationale for answers and evaluation criteria. Let's apply the studied methods and techniques to solving various plot problems No. 18 of the Unified State Examination.
- Numbers and their properties: divisibility, signs of divisibility, fundamental theorem of arithmetic, division with remainder
- Numbers and their properties: GCD and LCM, decimal notation of numbers
- Practice solving problems on the topic “Numbers and their properties”
- Sequences and their properties in problems No. 18 of the Unified State Exam
- Average values, inequalities and estimates in task No. 18 of the Unified State Exam
- Combinatorics and methods for solving non-standard problems (task No. 18 of the Unified State Examination)
- Various plot tasks in task No. 18 of the Unified State Exam
- Repetition, solution of trial version
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