**Algebra#
- Basic operations
- Operations with real numbers and algebraic expressions (addition, subtraction, multiplication, division)
- Algebraic constants (square differences, perfect square formula, etc.)
- Factoring and Factoring Techniques
- Equations and Inequalities
- Primary equations and inequalities
- Quadratic equations (root formulas, factorization, collocation methods)
- Solving higher equations
- Absolute value equations and inequalities
- Exponential and logarithmic equations
- Fractional equations and irrational equations
- Functions and Images
- Linear functions and their images
- Quadratic functions (open directions, vertices, axis of symmetry, zeros, etc.)
- Inverse proportional functions
- Exponential and logarithmic functions
- Segmented functions
- Composite and Inverse Functions
- Sequences and series
- Equal difference series (general formula, sum of first n terms)
- Isoperimetric series (general formula, sum of first n terms)
- Recurrence formula for series
- Summation formulas (split term elimination, misplaced subtraction)
**Geometry#
- **Plane Geometry
- Triangles (side-angle relationships, triangle inequalities, triangle similarity, congruence)
- Quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoidal properties)
- Circles (tangent properties, chord length, central angle, circumferential angle)
- Measurement of angles (angle bisector, median, altitude line)
- Analytic Geometry*
- Plane Cartesian Coordinate System
- Slope, intercept, equation of a straight line
- Relationship between the positions of two straight lines (parallel, perpendicular)
- Equation of a circle and its geometric properties
- Parabolas, ellipses, hyperbolas (conic sections)
**Trigonometry (Trigonometry)
- Trigonometric ratios
- Definition of Sine, Cosine, Tangent
- Induced formulas (180°±α, 360°±α, etc.)
- Images and properties of trigonometric functions
- Trigonometric constant transformations
- Multiplication and half-angle formulas
- Sum and difference into product, product into sum and difference formulas
- Solving triangles
- Cosine theorem, sine theorem
- Calculating the area of an oblique triangle
- **Trigonometric equations
- Solving trigonometric equations in general form
**Vectors#
- **Basic concepts of vectors
- Definition, modulus, and direction of vectors
- Linear operations on vectors (addition, subtraction, number multiplication)
- Vector operations **Vector dot product and its geometric significance
- Vector dot product and its geometric meaning
- Clipped angle formulas and applications
Probability & Statistics Probability & Statistics*
- **Data Analysis
- Frequency and Frequency
- Statistical Graphs (Bar Charts, Pie Charts, Box Plots)
- Mean, Median, Plural, Variance, Standard Deviation
- Fundamentals of Probability
- Definition and basic properties of probability
- Addition theorem, multiplication theorem
- Independent events and conditional probability
- Binomial and Poisson distributions (part of the competition)
Fundamentals of Calculus (Pre-Calculus & Calculus)
- Limits & Continuity Limits & Continuity **Limits & Continuity
- Calculating the Limits of Functions
- Infinitesimals and infinities
- Continuity of Functions
- **Derivatives and Differentials
- Definition and geometric significance of the derivative
- Basic rules of derivation (power functions, exponential functions, logarithmic functions, etc.)
- Product and quotient rules, chain rule
- Applications of the derivative (tangent equations, monotonicity, extreme values)
- Curvature, points of inflection, concavity
- Integral
- Indefinite integrals (basic integral formula, commutative method, partial integrals)
- Definite integrals (Newton-Leibniz formula)
- Area calculations
- Velocity, acceleration, and positional relationships
- **Division and congruence **
- Prime factorization
- Greatest common factor, least common multiple
- Congruence theorem, Fermat’s Little Theorem
- Integral point problems
- Peake’s theorem
- Extended Euclidean algorithm
- Chinese remainder theorem (advanced)
- **Combinatorial Mathematics **
- Ranking, Combination
- Binomial Theorem
- recurrence relations
- Fundamentals of graph theory
- Euler diagrams, Hamiltonian diagrams
- Shortest path problems
- Connectivity of graphs