(FSI-K-MAT)

In the course we will repeat the curriculum of secondary schools to the extent necessary for passing the entrance exam in mathematics at FME BUT in Brno. The course will end with a final test, which corresponds to the entrance tests at FME BUT in Brno. If the final test is successfully passed, the entrance exam will be waived in accordance with the FSI Admission Guidelines.

In case of unsuccessful completion of the final test, the applicant for study at FSI will be able to take the entrance exam in due time.

To successfully pass the final test, it is necessary to obtain at least 50 % of points.

1. Calculation with polynomials, the binomial theorem, simplifying algebraic expressions, powers, roots, rationalizing fractions.


2. Linear equations and inequalities of one variable, equivalent manipulations. A system of two linear equations of two variables. Solving a linear equation or inequality with absolute values. 


3. Quadratic equations and inequalities of one variable; the relationships between the roots and coefficients of a quadratic equation; factoring a quadratic trinomial. Graphical solution of a quadratic equation. Equations and inequalities with the variable in the denominator; simple irrational equations.


4. Deduction problems – direct and inverse proportion, the rule of three, percentages. 


5. Functions of one real variable: the domain, the range, and the graph of the function. Linear function, quadratic function, linear rational function, function with an absolute value – graphs.


6. Exponential and logarithmic functions - graphs. Exponential and logarithmic equations. Trigonometric functions, angles in degrees and radians, formulas, graphs. Trigonometric equations and inequalities.


7. Sequences - arithmetic and geometric.


8. Plane geometry – focused on the triangle. Solution of a right triangle and a general triangle. Pythagorean and Thales’ theorems, Euclidean theorems, the law of sines and cosines. A disc and a circle, circumferential and central angles. 


9. Calculation of the circumference, area, surface, and volume of basic figures in a plane and in a 3D space.


10. Plane analytical geometry (distance between two points; vectors; a straight line in a plane; conic sections).


11. Complex numbers (basic operations, the algebraic and trigonometric forms, De Moivre’s theorem, solution of quadratic equations).


12. Combinatorics (variations, combinations, permutations, Pascal’s triangle, the factorial, a binomial coefficient).


13. Final test.