Mathematics - 3

Mathematics - 3

Objective: Advanced study of algebra and calculus, development of mathematical thinking, and preparation for higher-level mathematics and applied problem-solving.

What They Learn:

Algebra:

Advanced study of polynomials, including factorization.

Working with rational and irrational expressions.

Solving higher-degree equations and systems of equations.

Understanding properties of polynomial roots, Vieta’s theorem.

Basics of matrices and determinants: introduction to linear algebra.

Calculus:

Basics of function analysis, including monotonicity and extrema.

Limits and continuity of functions: introduction to limit theory.

Differentiation: derivative and its physical and geometric interpretation.

Integration: indefinite and definite integrals, applications to areas and volumes.

Logarithms and Exponents:

Study of properties of logarithmic and exponential functions.

Solving logarithmic and exponential equations and inequalities.

Applying logarithms to growth and decay problems, compound interest.

Application of Knowledge:

Solving applied problems using algebraic and calculus methods.

Mathematical modeling of real-world processes.

Preparing for math competitions, exams, and advanced mathematics courses.