Ukraine 10th Grade Curriculum - Mathematics (Standard Level)

This curriculum outlines the expected learning outcomes and content of study for 10th-grade mathematics in Ukraine at the standard level. It covers Algebra and the Beginning of Analysis, and Geometry. The curriculum is structured into topics with allocated hours, expected learning outcomes, and specific content details.

Mathematics (Algebra and the Beginning of Analysis)

• Topic 1: Functions, Their Features and Graphics (15 hours)
• Learning Outcomes: Students will be able to define functions in various ways, determine their range, identify basic properties from charts and graphs, calculate and compare expressions with rational exponents and roots, recognize and graph power functions, and model real-world processes using these functions.
• Content: Numerical functions and their properties, ways of defining functions (paired, odd functions), roots of the nth degree, power with rational exponents, power functions, properties and graphs.
• Topic 2: Trigonometric Functions (18 hours)
• Learning Outcomes: Students will be able to convert between radian and degree angle measures, establish correspondence between real numbers and points on a unit circle, recognize and graph trigonometric functions, illustrate their properties using graphs, convert trigonometric expressions, apply functions to real-world processes, and solve basic trigonometric equations.
• Content: Sine, cosine, tangent, angle, radial measurement of angles, trigonometric functions of a numerical argument, basic relationships between trigonometric functions, summation formulas, periodicity of functions, properties and graphs of trigonometric functions, simplest trigonometric equations.
• Topic 3: Derivative and its Application (14 hours)
• Learning Outcomes: Students will understand the concept of a derivative and its application to real-world processes, find the rate of change of magnitude at a point, differentiate functions using tables and rules, use derivatives to find intervals of monotonicity and extrema, plot functions, find maximum and minimum values, and solve applied problems involving these concepts.
• Content: Derivative of a function (geometric and physical meaning), rules of differentiation, sign of the constancy of the function, sufficient conditions for growth and decline of the function, extremes of the function, application of the derivative to the study of functions and construction of their graphs, largest and smallest values of the function in the interval.

Geometry

• Topic 1: Parallelism of Lines and Planes in Space (17 hours)
• Learning Outcomes: Students will be able to identify basic concepts of stereometry, differentiate between defined and undefined concepts, axioms, and theorems, formulate and apply axioms of stereometry, classify mutual placement of lines and planes, establish parallelism, determine if lines are incidental, depict figures in space, and apply parallelism concepts to real-world objects.
• Content: Basic concepts, axioms of stereometry and their consequences, mutual placement of lines in space, parallel design and its properties, images of figures in stereometry, parallel line and plane, parallel planes.
• Topic 2: Perpendicularity of Lines and Planes in Space (17 hours)
• Learning Outcomes: Students will be able to establish and justify perpendicularity of lines and planes, define angles between lines and planes, formulate the theorem on three perpendiculars, apply relationships between lines and planes to real-world objects, and solve problems involving distances and angles in space.
• Content: Perpendicularity of lines, perpendicularity of a line and a plane, the theorem on three perpendiculars, perpendicularity of planes, dihedral angle, measurement of distances and angles in space.
• Topic 3: Coordinates and Vectors (10 hours)
• Learning Outcomes: Students will be able to draw analogies between vectors and coordinates in planes and space, understand the vector-coordinate method, perform vector operations, use vectors to model geometric and physical quantities, find distances between points, coordinates of midpoints, and coordinates of symmetrical points, and use coordinates to measure distances and angles.
• Content: Rectangular coordinates in space, coordinates of the middle of the segment, distance between two points, vectors in space, operations on vectors, formulas for calculating vector length, angle between vectors, distance between points, symmetry with respect to the origin and coordinate planes.