Practise

In the 2026/2027, the midterm test will be written in the week since 30th November 2026.

  1. Functions – definitions and basic properties, definition of composite functions (superposition), definition of elementary functions. Examples of domains of elementary functions, composition of functions and their domains of definition.
  2. Calculation of the rank of a matrix, determination of linear dependence or independence of vectors using the rank of a matrix.
  3. Solving systems of linear equations. Gauss and Jordan methods, use of the theorem on the number of solutions of a system of linear equations, particular and general solutions (vector notation), homogeneous systems. Linear combinations of vectors.
  4. Operations with matrices – calculation of the product of matrices, calculation of the inverse matrix, solution of matrix equations. Solution of systems of linear equations using the inverse matrix.
  5. Calculation of 2nd and 3rd order determinants, use of theorems for calculating higher order determinants, determinant of a regular matrix, Cramer’s rule. Characteristic (eigen) numbers of a matrix.
  6. Limit of a sequence (limit of a polynomial, limit of a quotient of polynomials, limit containing qn), limits with parameters. Solving inequalities using Bolzano’s theorem. Limit of a function (limit at non-eigenpoints, indefinite type a/0, limits at extreme points of the domain of definition).
  7. Innovation week (without scheduled lessons).
  8. Calculation of limits of composite functions. Mechanical differentiation of elementary functions!
  9. Extremes of a continuous function on a closed interval. Using the theorem on the meaning of the first derivative for the course of a function: determining the intervals in which the function is increasing, decreasing and local extremes. Using the theorem on the meaning of the second derivative for the course of a function: determining the intervals in which the function is convex, concave and inflection points. L’Hospital’s rule – calculating limits of functions (0/0, ∞/∞).
  10. Domains of definition of functions of two variables. Partial derivatives of the 1st and 2nd order. Local extremes of functions of two variables.
  11. Midterm test. Local bound extrema of functions of two variables (substitution method), bound extrema of functions of two variables (Jacobian).
  12. Indefinite integral – basic rules, per partes method, f’/f formula.
  13. Substitution method. Definite integral. Improper integral.