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Algebra

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Algebra

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$1. Numbers and Calculations 1.1 Operations with common fractions 1.2 Operations with decimal fractions 1.3 Powers with natural exponents 1.4 Square roots 1.5 Divisibility rules, GCD and LCM 1.6 Proportions and percentages 1.7 Powers with integer exponents, scientific notation 2. Algebraic Expressions 2.1 Formulas for shortened multiplication 2.2 Transformation of integer and fractional-rational expressions 2.3 Polynomials and operations with them 2.4 Factorization 3. Equations and Inequalities 3.1 Linear equations 3.2 Quadratic equations (discriminant, Vieta's theorem) 3.3 Fractional-rational equations 3.4 Systems of two linear equations 3.5 Linear inequalities and systems of inequalities 3.6 Quadratic inequalities (parabola method) 4. Functions and Graphs 4.1 Concept of a function, domain 4.2 Linear function (y = kx + b) 4.3 Quadratic function (parabola) 4.4 Inverse proportionality (y = k/x) 4.5 Reading graphs of real dependencies 4.6 Constructing graphs with absolute value (advanced level) 5. Word Problems 5.1 Motion problems 5.2 Work and productivity problems 5.3 Mixture, alloy, percentage problems 5.4 Part and ratio problems 5.5 Progression problems (arithmetic and geometric) 6. Geometry: Basic Concepts 6.1 Angles: vertical, adjacent, with parallel lines 6.2 Triangle: types, sum of angles, inequality 6.3 Isosceles and equilateral triangles 6.4 Criteria for congruence and similarity of triangles 6.5 Right-angled triangle, Pythagorean theorem 6.6 Sine, cosine, tangent of an acute angle 7. Geometry: Areas and Circles 7.1 Areas: triangle, parallelogram, trapezoid 7.2 Area of a circle and circumference 7.3 Inscribed and circumscribed circles 7.4 Tangent and secant 7.5 Central and inscribed angles 8. Statistics and Probability Theory 8.1 Arithmetic mean, median, range 8.2 Classical definition of probability 8.3 Problems with coin tosses and dice 9. Applied Mathematics (Problems 1–5 OGE) 9.1 Terrain map, scale, distances 9.2 Tariffs, discounts, choosing the cheapest option 9.3 Greenhouses, tires, stoves: calculation using formulas 9.4 Geometry on graph paper 9.5 Analysis of tables and diagrams$