Preparation for the Unified State Exam in specialized mathematics in a group. Express course. — free course from Foxford, training 8 sections, Date: December 2, 2023.

Part 1. Rational equations and inequalities. Text problems and problems with economic content
Let's develop skills in solving rational equations and inequalities. Let's learn to solve problems on motion, work, mixtures and alloys, economic problems. Let's master the method of solving equations and inequalities with modules
- Solving word problems with short answers (percentages, mixtures and alloys, progressions)
- Solving word problems with short answers (movement problems, work problems)
- Economic tasks No. 16: deposit transactions, loan repayment in equal payments
- Economic tasks No. 16: deposit transactions, loans with a uniform reduction of the principal debt

- Economic tasks No. 16: credit schemes with different conditions
- Calculations and transformations of rational expressions. Solving rational equations
- Solving rational inequalities
- Solving equations and inequalities with modulus

Part 2. Transformation of irrational expressions, solution of irrational equations and inequalities. Trigonometry
Let's learn how to transform irrational expressions without errors, solve irrational equations and inequalities. Let's practice calculating trigonometric expressions and solving trigonometric equations.
- Conversion of irrational expressions. Solving irrational equations of basic complexity level
- Irrational equations of increased complexity
- Irrational inequalities (part 1)
- Irrational inequalities (part 2)
- Transformation of trigonometric expressions in Unified State Examination problems
- The simplest trigonometric equations. Sampling Equation Roots
- Advanced trigonometric equations (part 1)
- Advanced trigonometric equations (part 2)

Part 3. Planimetry
Let us repeat the most important theorems and properties of planimetry for solving Unified State Exam problems. We will solve all the typical planimetry problems from the test part and get acquainted with the basic ideas for solving problems of an increased level of complexity.
- Planimetry in the test part of the Unified State Exam: triangles and their properties (task No. 1 of the Unified State Exam)
- Planimetry in the test part of the Unified State Exam: quadrilaterals, elements of a circle, the relative position of polygons and circles (task No. 1 of the Unified State Exam)
- Solving problems of increased complexity using the properties of triangles (task No. 17 of the Unified State Exam)
- Solving problems of increased complexity using the properties of quadrilaterals (task No. 17 of the Unified State Exam)
- The relative position of the triangle and the circle
- The relative position of quadrilaterals and circles
- The relative position of two circles
- Vectors on a plane. Repetition

Part 4. Exponential and logarithmic equations and inequalities
Let us repeat the properties of powers and logarithms. We will master solution techniques and learn how to solve simple and the most complex exponential and logarithmic equations and inequalities without errors.
- Conversion of power expressions. Solving exponential equations of basic complexity level
- Converting logarithmic expressions. Solving basic level logarithmic equations
- Solving exponential and logarithmic equations of increased complexity
- 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
- Practice solving exponential and logarithmic inequalities from task No. 15 of the Unified State Exam

Part 5. Study of functions in Unified State Examination tasks. Tasks with applied content
Let's analyze the most complex problems with applied content into calculations using formulas. Let's learn how to solve Unified State Exam problems from the test part on the analysis of functions and their graphs. Let's learn to solve economic problems of optimal choice.
- Problems with applied content (task No. 9 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. Antiderivative (task No. 8 of the Unified State Examination). Part 1
- Study of a function using derivatives. Antiderivative (task No. 8 of the Unified State Examination). Part 2
- Economic problems: application of the derivative to solving optimal choice problems
- Economic problems: solving optimal choice problems (without derivatives).
- Practice solving economic problems

Part 6. Stereometry
Let us repeat the theorems and properties of stereometry that are most important for solving Unified State Exam problems. We will solve all the typical stereometry problems from the test part and get acquainted with the basic ideas for solving problems of an increased level of complexity.
- Stereometry in the test part of the Unified State Exam: polyhedra
- Stereometry in the test part of the Unified State Exam: bodies of rotation, relative position of thetas
- 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
- Practice solving problems No. 14 Unified State Examination
- Lesson - repetition

Part 7. Probability theory. Tasks with a parameter
Let's learn to solve even the most complex problems in probability theory. Let's get acquainted with various methods for solving problems with parameters: algebraic, functional, functional-graphical. Let's discuss how to get at least 1 point in a problem with a parameter.
- 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
- Practice solving problems in probability theory
- Linear equations and systems of linear equations with a parameter
- Quadratic equations with parameter
- Second order equations and systems of equations with a parameter
- Systems of equations with a parameter
- Equations with parameter and modulus

Part 8. Plot problems on the properties of numbers (task No. 19 of the Unified State Examination). Repetition
We will learn useful ideas for solving problems No. 19 of the Unified State Exam, learn to apply the properties of numbers, progressions, basic properties and laws of combinatorics. Let's learn how to correctly justify the answers in task No. 18 of the Unified State Exam.
- Numbers and their properties. Features of task No. 19 in the Unified State Exam
- Numbers and their properties: GCD and LCM, decimal notation of numbers
- Sequences and their properties in problems No. 19 of the Unified State Exam
- Average quantities and their properties in problems No. 19 of the Unified State Examination
- Solving plot problems of assignment No. 18 of the Unified State Examination
- Repetition: solving problems of the test part of the Unified State Exam
- Repetition: solving problems of the second part of the Unified State Exam
- Repetition: solving problems of the second part of the Unified State Exam