Mathematics Courses for CT and CE Preparation (11th Grade)

Goals and Objectives:

• Expanding and deepening 10th-grade students' knowledge of mathematics through studying topics from the school curriculum for grades 5–10 at an advanced level
• Developing logical thinking
• Fostering students' ability to solve a problem using multiple methods and identifying the simplest and most original (flexibility of thinking)
• Enhancing creative abilities in applying acquired knowledge to solve standard and non-standard mathematical problems
• Intellectual development and the formation of personal qualities necessary for full-fledged life in modern society, characteristic of mathematical activity: clarity and precision of thought, critical thinking, intuition, logical reasoning, spatial representations, and the ability to overcome difficulties
• Developing students' capacity for dynamic reflection of various mathematical objects in necessary combinations and relationships (spatial imagination)
• Cultivating the ability to see the final solution of a problem based on intuition, feeling, or sudden insight (mathematical intuition)

When selecting and building the content of the study programme, the following didactic principles were used as a basis:

• Scientific validity, according to which the material presented in the curriculum must align with modern scientific concepts, and during the learning process, students should become familiar with certain methods and techniques of scientific research (observation, description, experiment, etc.), with the teacher building on students' personal experience to elevate their understanding to a higher level
• Continuity and Perspective, according to which the education is built using students' previous knowledge and skills, taking into account future development (preparing them for perceiving more complex material), as well as ensuring the interconnectedness of each component of the pedagogical system in content, organizational, and activity aspects
• Practical orientation, which aims to prepare students for applying their acquired knowledge and skills in real life
• Creative learning, which involves engaging students in independent creative activities and developing personal creative qualities
• Psychological comfort, which requires considering students' interests, needs, aptitudes, and abilities, creating a comfortable environment for each learner

As a result of studying the discipline, students should:

Know the definitions of mathematical concepts, theorems, formulas, and algorithms

They should be able to:

• Perform calculations for practical needs: addition, subtraction, multiplication, and division of real numbers
• Find the value of a number raised to a natural or integer power
• Perform operations with numbers written in standard form
• Determine the order of operations with numbers in standard form
• Evaluate expressions and find their values
• Find the value of expressions with variables given specific variable values
• Compare the values of expressions
• Represent an infinite decimal periodic fraction as a common fraction
• Round numbers and calculation results to a specified accuracy
• Use notation for numerical intervals when solving problems
• Control calculations by assessing the plausibility of results, estimating, re-computing, or solving inverse problems
• Find the domain of an expression with a variable
• Perform identical transformations of rational, irrational, exponential, logarithmic, and trigonometric expressions
• Solve linear, quadratic, and basic rational equations reducible to them
• Solve irrational equations and equations reducible to them
• Solve systems of equations with one variable of the first and second degree, and equations/systems reducible to them
• Solve systems of equations with two variables (systems of linear equations and systems where one equation is linear and the other quadratic)
• Solve inequalities and systems of inequalities of the first and second degree with one variable, and inequalities/systems reducible to them
• Solve basic trigonometric equations and equations reducible to them
• Solve exponential and logarithmic equations and equations reducible to them
• Solve rational, exponential, and logarithmic inequalities and inequalities reducible to them
• Solve equations and inequalities containing a variable under the modulus
• Understand the graphical interpretation of solutions to equations, systems of equations, and inequalities
• Solve word problems using equations, inequalities, and their systems
• Plot graphs of elementary functions
• Use the properties of functions to solve problems
• Apply geometric representations to solve and analyze equations, inequalities, and systems
• Use the properties of plane figures and fundamental concepts of plane geometry
• Apply the properties of solid figures and basic relationships in solid geometry
• Use various methods to solve geometric problems
• Solve proof-based and computational problems
• Solve problems involving combinations of prisms and pyramids, and of prisms and pyramids with solids of revolution
• Calculate geometric quantities
• Find the distance from a point to a plane, the distance between parallel lines, the distance between a line and a parallel plane, and the distance between parallel planes
• Find the angle between lines, the angle between a line and a plane, and the angle between planes
• Solve basic construction problems using a compass and straightedge
• Draw geometric figures
• Construct cross-sections of three-dimensional geometric figures using a plane

Be proficient in completing test items used in centralized mathematics testing

Service period: From September 20 to May 10, 2024

Duration: 30 weeks (once a week, 4 academic hours per session)

Total hours: In-class work – 120 hours, methodological work – 240 hours

Minimum group size: 11 participants

Target audience (age): Children and youth

Location: 22 Ozhesko Street

Cost: 580 BYN

Service provided by:

Viktor Mikhailovich Petsievich, PhD in Physics and Mathematics, Associate Professor

Yuri Prokofyevich Zolotukhin, PhD in Physics and Mathematics, Associate Professor

Irina Vladimirovna Trifonova, PhD in Physics and Mathematics, Associate Professor

Contact information:

Faculty of Mathematics and Computer Science

Department of Mathematical Analysis, Differential Equations, and Algebra

Grodno, 22 Ozhesko Street

+375 (152) 39 64 79