Ukraine Mathematics (11th Grade)

This information is based on the textbook "Algebra and the beginnings of analysis" (Merzlyak et al., 2019), which is recommended by the Ministry of Education and Science of Ukraine. It appears to be representative of the curriculum for students following a mathematics-focused path after 8th grade.

The textbook opens with a quote by scientist Kravchuk: "My love is Ukraine and mathematics."

Textbook Structure:

The textbook is divided into five sections:

• Section 1: Exponential and Logarithm Functions: This section covers the function f(x) = a^x, including discussions of irrational powers, increasing/decreasing functions, continuity, the Cauchy functional equation, and applications to bacterial growth modeling. The section also includes enrichment material on Kravchuk and problems from the first Kyiv Mathematical Olympiad for schoolchildren (1935).
• Section 2: Integrals and their Application: This section covers integrals and their applications. Enrichment material discusses Newton, Leibniz, and Cavalieri.
• Section 3: Elements of Probability Theory: This section covers probability theory, including geometric approaches to problem-solving.
• Section 4: Complex Numbers: This section covers complex numbers, roots of unity, de Moivre's theorem, trigonometric relationships, and geometric applications.
• Section 5: Polynomials: This section covers finding complex roots of polynomials (e.g., quadratics), multiplicity of roots, Viete's formulae in the cubic case, and Cardano's approach to solving cubics. Enrichment material discusses the "lady with the dog" proof of the fundamental theorem of algebra.

Exercises:

The textbook includes numerous exercises with a variety of problems designed to reinforce concepts and explore connections between different mathematical topics. Some problems are marked as suggested homework tasks, often following similar problems intended for classroom practice. More challenging problems are also included.

Other Resources:

Other potentially relevant resources include materials available on the Global Learning House platform:

• Ukraine - Algebra 11th grade:
• Ukraine - Mathematics 11th grade: