1. Fundamentals of set theory: sets and their definition, relationships between sets, set operations. Number systems: natural, integer, rational, irrational, and real numbers (motivation for extending the set of natural numbers and an overview of construction principles); operations on these numbers, absolute value. Prime numbers, divisibility, factorization, greatest common divisor, least common multiple (Euclid's algorithm). 2. Number systems: types of number systems, expression of the natural number in the number system, abbreviated and extended notation. Number notation conversions between systems with different bases (grouping, successive division algorithm), numerical operations in systems with different bases. 3. Algebraic expressions and their modifications: powers with a rational exponent and operations with them. Polynomials (definition and operations with polynomials), algebraic formulas. Logarithms (definition and operations with logarithms). Modifications of algebraic expressions. 4. Elementary functions: linear, linear-fractional, quadratic, power, exponential, logarithmic, and trigonometric functions. An overview of the definitions of elementary functions, their graphs, and their properties. Transformations of function graphs; absolute value functions. 5. Polynomial and rational functions, power functions with rational exponents, parametric systems of functions, cyclometric functions. Transformations of function graphs, absolute value functions 6. Equations and inequalities: definition of concepts (equation, equality, domain of an equation, domain of a variable, equivalent adjustments), solution of individual types of equations and inequalities, numerical and graphical solutions, equations and inequalities with absolute value (linear, quadratic, equations and inequalities with parameters). 7. Irrational equations; more complex exponential, logarithmic, and trigonometric equations and inequalities, including those involving absolute value, and systems of such equations and inequalities. 8. Systems of Equations and Inequalities: definition of terms, systems of linear equations with two and three unknowns, matrix representation and discussion of solvability, systems of linear inequalities. Selected systems of equations (logarithmic, exponential, irrational). 9. Analytic Geometry in the Plane: equations of lines, positional and metric properties of figures in the plane, conic sections, and the relative positions of conic sections and lines. 10. Planimetry - construction problems: sets of points with given properties, tangents to a circle, construction of plane figures (circles, triangles, quadrilaterals, etc.), central and inscribed angles, constructions based on algebraic expressions. 11. Measurement in Geometry: the triangle inequality, angles, similarity, the Pythagorean and Euclidean theorems, central and inscribed angles, perimeter, area of plane figures, volume of solids. 12. Complex Numbers: the field of complex numbers, the Gaussian plane, the algebraic and geometric forms of a complex number, operations with complex numbers, absolute value, Moivre's theorem and its applications, solving quadratic equations in the field of complex numbers, binomial equations. 13. Combinatorics and Probability: Definition of basic concepts in combinatorics and probability (combinatorial rules of sum and product, variations, permutations, combinations, random experiment, random event, complementary event), the classical definition of probability. 14. Fundamentals of Statistics: statistical data set, classification of data sets, frequency, graphical representation, characteristics of a statistical data set, arithmetic, weighted, harmonic, and geometric means, median, mode, range, and deviations from mean values.
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