(FSI-K-MAT)

The aim of the course is to prepare applicants for studies at the Faculty of Mechanical Engineering at Brno University of Technology for successfully completing their first semester.

A solid foundation in mathematics is essential for all technical subjects, including physics, statics, mechanics, strength of materials, elasticity, and more.

High school mathematics knowledge is assumed. The course builds upon elementary principles, which are always reviewed at the beginning of each lesson. The aim is to standardize the participants' level of knowledge.

The course emphasizes solidifying fundamental knowledge, demonstrating the interconnections between concepts and formulas, and providing thorough practice.

The course is designed for high school students preparing for studies at a university with a technical focus. The content covers high school material, making it suitable for use as preparation for final exams as well.

The course concludes with a test that is equivalent in difficulty to the mathematics entrance exam for the Faculty of Mechanical Engineering at Brno University of Technology.

Course Content:

1. Polynomial Operations: Binomial theorem, simplifying algebraic expressions, powers, roots, and rationalizing fractions.
2. Linear Equations and Inequalities: Single-variable linear equations and inequalities, equivalent transformations. Systems of two linear equations with two unknowns. Solving linear equations or inequalities involving absolute values.
3. Quadratic Equations and Inequalities: Single-variable quadratic equations and inequalities, relationships between roots and coefficients, factorization of quadratic trinomials, graphical solutions of quadratic equations. Equations and inequalities with variables in the denominator, basic irrational equations.
4. Applied Problems: Direct and inverse proportionality, rule of three, percentages.
5. Functions of a Single Real Variable: Domain, range, and graph of a function. Linear functions, quadratic functions, rational functions, and functions with absolute values – including graphs.
6. Exponential and Logarithmic Functions: Graphs of exponential and logarithmic functions, solving exponential and logarithmic equations.
7. Trigonometric Functions: Degree and radian measure, formulas, graphs, and solving trigonometric equations and inequalities.
8. Sequences: Arithmetic and geometric sequences.
9. Plane Geometry: Focus on triangles, solving right and general triangles. Pythagorean theorem, Thales' theorem, Euclidean theorems, sine and cosine rules. Circle and circular arc, inscribed and central angles.
10. Geometric Calculations: Perimeter, area, surface area, and volume of basic shapes in the plane and space.
11. Analytic Geometry in the Plane: Distance between two points, vectors, lines in the plane, and conic sections.
12. Complex Numbers: Basic operations, algebraic and trigonometric forms, De Moivre’s theorem, solving quadratic equations.
13. Combinatorics: Variations, combinations, permutations, Pascal’s triangle, factorials, and binomial coefficients.
14. Final Test.

The course spans 26 hours over 13 weeks, with 2 hours per week.

Attendance is not monitored, and participants can attend in person, watch a live online stream, or view recorded lessons, which are made available on the e-learning platform afterwards.

In the 13th week, participants take a final test, which is conducted exclusively in person. The test is equivalent in difficulty to the entrance exam for the Faculty of Mechanical Engineering at Brno University of Technology.

To pass the final mathematics test, participants must score at least 50%. Successfully passing this test (or the physics test in the K-FYZ Preparatory Physics Course) allows participants to request an exemption from the mathematics and physics entrance exams for the Faculty of Mechanical Engineering at Brno University of Technology.