Ukraine 10th Grade Curriculum - Mathematics

This information is based on the curriculum provided by the Ministry of Education and Science of Ukraine.

10th Grade Mathematics

Algebra and Beginning of Analysis (54 hours total):

• Semester 1: 16 hours (1 hour/week)
• Semester 2: 38 hours (2 hours/week)
• Reserve: 7 hours
• Topic 1: Functions, Their Features and Graphics (15 hours)
• Defining functions, including numerical functions and their properties.
• Domain and range of functions.
• Even and odd functions.
• Nth degree roots and their properties.
• Rational exponents and their properties.
• Power functions, properties, and graphs.
• Modeling real-world processes using power functions.
• Topic 2: Trigonometric Functions (18 hours)
• Radian and degree angle measures.
• Trigonometric functions (sine, cosine, tangent) and their relationships.
• Periodicity of functions.
• Properties and graphs of trigonometric functions.
• Summation formulas and their applications.
• Basic trigonometric equations.
• Topic 3: Derivative and its Application (14 hours)
• Geometric and physical meaning of derivatives.
• Calculating rates of change.
• Differentiation rules and table of derivatives.
• Monotonicity and extrema of functions.
• Applications of derivatives in problem-solving.

Geometry (51 hours total):

• Semester 1: 32 hours (2 hours/week)
• Semester 2: 19 hours (1 hour/week)
• Reserve: 7 hours
• Topic 1: Parallelism of Lines and Planes in Space (17 hours)
• Basic concepts and axioms of stereometry.
• Mutual placement of lines in space.
• Parallel lines and planes, and their properties.
• Representing figures in stereometry.
• Topic 2: Perpendicularity of Lines and Planes in Space (17 hours)
• Perpendicular lines and planes.
• Theorem on three perpendiculars.
• Dihedral angles.
• Measuring distances and angles in space.
• Topic 3: Coordinates and Vectors (10 hours)
• Rectangular coordinates in space.
• Midpoint and distance formulas.
• Vectors in space and vector operations.
• Calculating vector length, angle between vectors, and distance between points.
• Symmetry with respect to origin and coordinate planes.

11th Grade Mathematics (Included for context and curriculum continuity)

Algebra and Beginning of Analysis (54 hours total):

• Semester 1: 16 hours (1 hour/week)
• Semester 2: 38 hours (2 hours/week)
• Reserve: 18 hours
• Topic 1: Exponential and Logarithmic Functions (16 hours)
• Topic 2: Integral and its Application (10 hours)
• Topic 3: Elements of Combinatorics, Probability Theory and Mathematical Statistics (10 hours)

Geometry (51 hours total):

• Semester 1: 32 hours (2 hours/week)
• Semester 2: 19 hours (1 hour/week)
• Reserve: 14 hours
• Topic 1: Polyhedra (14 hours)
• Topic 2: Solids of Revolution (12 hours)
• Topic 3: Volumes and Areas of Surfaces of Geometric Bodies (11 hours)