Ukraine 9th Grade Curriculum - Mathematics

This information is based on the curriculum document from the Ministry of Education and Science of Ukraine.

Algebra (70 hours, 2 hours/week, 18 hours reserve)

• Inequalities (14 hours): Numerical inequalities, properties of numerical inequalities, inequalities with variables, linear inequalities with one variable, double inequalities, union and intersection of numerical intervals, systems of linear inequalities.
• Quadratic Function (20 hours): Definition and properties of quadratic functions, transformations of quadratic function graphs (f(x) -> f(x)+a, f(x) -> f(x+a), f(x) -> kf(x), f(x) -> -f(x)), graphing quadratic functions, solving quadratic inequalities, solving systems of equations involving quadratic equations.
• Numerical Sequences (10 hours): Numerical sequences, arithmetic and geometric progressions, properties of arithmetic and geometric progressions, formulas for the nth term and sum of the first n terms of arithmetic and geometric progressions.
• Fundamentals of Combinatorics, Probability Theory, and Statistics (8 hours): Basic rules of combinatorics, frequency and probability of random events, basic statistical concepts, methods of data presentation and processing.

Geometry (70 hours, 2 hours/week, 24 hours reserve)

• Coordinates on the Plane (8 hours): Sine, cosine, and tangent of angles from 0 to 180 degrees, equation of a figure, representing lines and circles on the coordinate plane, distance between two points, coordinates of the midpoint of a segment, equation of a circle and a straight line.
• Vectors on a Plane (12 hours): Vectors, vector magnitude and direction, equality of vectors, vector coordinates, addition and subtraction of vectors, multiplication of a vector by a number, collinear vectors, scalar product of vectors.
• Solving Triangles (10 hours): Cosine and sine theorems, formulas for finding the area of a triangle (Heron's formula, using two sides and the included angle).
• Regular Polygons, Circumference, and Circle Area (10 hours): Regular polygons, types and properties of regular polygons, arc length, circumference, circle area, regular polygons inscribed in and circumscribed around a circle.
• Geometric Transformations (6 hours): Transformations (motion) and their properties, symmetry with respect to a point and a line, rotation, parallel translation, congruence of shapes.